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PNAS 113(41), E6072-E6079 (2016). 47. Mendoza-Viveros, L. et al. Molecular modulators of the circadian clock: lessons from flies and mice. Cell. Mol. Life Sci. 74, 1035–1059 https://doi.org/10.1007/s00018-016-2378-8 (2017). 48. López-Olmeda, J. F., Tartaglione, E. V., de la Iglesia, H. O. & Sánchez-Vázquez, F. J. Feeding entrainment of food-anticipatory activity and per1 expression in the brain and liver of zebrafish under different lighting and feeding conditions. Chronobiol. Int. 27, 1380–1400 (2010). |
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Targeted Delivery of Chloroquine to Plasmacytoid Dendritic Cells Enhances Inhibition of the
Type I Interferon Response
Marilyn E. Allen1, Amit Golding2, Violeta Rus2, Nicholas B. Karabin3, Sophia Li3, Chamille J.
Lescott3, Sharan Bobbala3, Evan A. Scott3, Gregory L. Szeto4
1Department of Chemical, Biochemical & Environmental Engineering, University of Maryland,
Baltimore County, Baltimore, MD, USA; 2Department of Medicine, Division of Rheumatology &
Clinical Immunology, University of Maryland School of Medicine, Baltimore, MD, USA;
3Department of Biomedical Engineering, Northwestern University, Evanston, IL, USA;
4Department of Experimental Immunology, Allen Institute for Immunology, Seattle, WA, USA. Corresponding author:
Gregory Szeto
615 Westlake Avenue North
Room 565
Seattle, WA 98109
[email protected]
+1 (206) 516-6426
Conflict of interest statement
MEA, AG, NBK, EAS, and GLS are inventors on the pending U.S. Provisional Patent Application
No. 62/730,157 filed in the United States Patent Office by the University of Maryland, Baltimore
County. The patent describes the use of self-assembled nanocarriers for cancer and
autoimmunity drug delivery. The remaining authors certify that the research was conducted with
no affiliations, financial support, or non-financial interests that may be determined as a potential
conflict of interest. 1
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Abstract
Systemic lupus erythematosus (SLE) causes damaging inflammation in multiple organs via the
accumulation of immune complexes. These complexes activate plasmacytoid DCs (pDCs) via
TLR7 and TLR9, contributing to disease pathogenesis by driving secretion of inflammatory type
I IFNs. Antimalarial drugs, such as chloroquine (CQ), are TLR antagonists used to alleviate
inflammation in SLE. However, they require ~3 months of continuous use before achieving
therapeutic efficacy and can accumulate in the retinal pigment epithelium with chronic use
resulting in retinopathy. We hypothesized that poly(ethylene glycol)-b-poly(propylene sulfide)
(PEG-b-PPS) filamentous nanocarriers, filomicelles (FMs) could improve drug activity and
reduce toxicity by directly delivering CQ to pDCs via passive, morphology-based targeting. Healthy human PBMCs were treated with soluble CQ or CQ-loaded FMs, stimulated with TLR
agonists or SLE patient sera, and type I IFN secretion was quantified via multi-subtype IFN-α
ELISA and MX1 gene expression using real-time RT-qPCR. Our results showed that 50 µg
CQ/mg FM decreased MX1 expression and IFN-α production after TLR activation with either
synthetic nucleic acid agonists or immune complex rich sera from SLE patients. |
Cellular uptake
and biodistribution studies showed that FMs preferentially accumulate in human pDCs in vitro
and in tissues frequently damaged in SLE patients (i.e., liver and kidneys) while sparing the eye
in vivo. These results showed that nanocarrier morphology enables drug delivery, and CQ-FMs
may be equally effective and more targeted than soluble CQ at inhibiting SLE-relevant
pathways. 2
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Introduction
Systemic lupus erythematosus (SLE) is an immune complex-mediated autoimmune disease
characterized by dysregulation of the innate and adaptive immune system resulting in loss of
self-tolerance. From 2000 to 2015, SLE was among the leading causes of death among young
women aged 15-24 in the United States (1). Women represent 90% of patients, leading to a
strong female bias in disease demographics (2, 3). Clinical manifestations are heterogeneous
with varying disease severities, organ involvement, and cellular abnormalities (4, 5). The clinical
course is unpredictable, with frequent flares, which contributes to both delayed diagnosis (an
estimated six years after initial presentation) (6) and difficulties in treatment. Circulating immune
complexes, consisting of autoantibodies and endogenous antigen, are deposited in tissues
leading to inflammation and end-stage organ damage. Lupus nephritis is one of the leading
causes of morbidity and mortality in SLE, developing in up to 50% of patients (4). Plasmacytoid
dendritic cells (pDCs) are activated by immune complexes sensed via toll-like receptors (TLR)-7
and -9, leading to production of interferon (IFN)-α, a major driver in SLE pathogenesis (7, 8). Pro-inflammatory IFN-α is upregulated in 50-75% of adult SLE patients (9) and can promote
suppression of regulatory T cells (10), B cell differentiation to plasma cells, and the production
of autoantibodies from those plasma cells (11), resulting in a positive feedback loop driving
autoimmunity. Attenuating this pro-inflammatory type I IFN response is key to treating SLE. Emerging therapeutic strategies targeting type I IFN include anifrolumab, a monoclonal
antibody blocking type I IFN receptor subunit 1 (12); IFN-α kinoid, an inactivated IFN-α coupled
to a carrier protein (13); and pDC inhibition via cell surface receptor blood DC antigen 2 (BDCA-
2/CD303) (14). None have been approved for SLE patients, and broad type I IFN blockade may
blunt antiviral immunity, resulting in an increased risk of infection and infection-related
complications (15, 16). Antimalarial drugs, such as chloroquine (CQ; brand name, Aralen) and
hydroxychloroquine (HCQ; brand name, Plaquenil), have been used for the treatment of SLE
since the 1950s (17). They are the cheapest and most frequently prescribed first line, non-
3
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steroid disease-modifying antirheumatic drug (18). Antimalarial drugs act by binding to nucleic
acids of immune complexes to mask key binding epitopes, preventing TLR7 and TLR9
activation and subsequent type I IFN responses (19-21). Antimalarial drugs are safe during
pregnancy (22, 23), improve survival (24), reduce disease activity (17), and are well-tolerated
with adjunctive immunomodulatory treatment (25). However, significant challenges during
treatment include prolonged (> 3 months) use required before achieving therapeutic efficacy
(26), poor patient compliance (27), and risk of retinopathy with chronic use (28, 29). We sought
to enhance the potency of antimalarial drugs and address key challenges using targeted
delivery. In this work, we used filamentous nanocarriers composed of an oxidation-responsive
block copolymer, (poly(ethylene glycol)-b-poly(propylene sulfide) (PEG-b-PPS) to target CQ to
pDCs and directly inhibit type I IFN activation by TLR-driven signaling. Self-assembled PEG-b-
PPS nanocarriers are non-immunogenic and non-inflammatory, exhibiting neither anti-PEG
antibodies nor complement activation in mice and non-human primates (30, 31). The
hydrophobic PPS block facilitates retention and controlled release of hydrophobic drugs such as
CQ (32). Oxidation converts the hydrophobic PPS block to hydrophilic poly(sulfoxides) or
poly(sulfones), leading to nanocarrier disassembly and release of drug payload (30). The
hydrophilic PEG fraction controls the morphology of the self-assembled structures (32). Previous studies have identified morphology as a passive mechanism for altering cellular
targeting and biodistribution. In particular, PEG-b-PPS filamentous worm-like micelles, or
filomicelles (FMs), preferentially accumulated in splenic pDCs after subcutaneous injection (33). Passive, morphology-based targeting via FMs avoids the use of cell-specific ligands and
improves blood circulation times (34). Furthermore, scalable self-assembly and loading of FMs
can be successfully achieved (35, 36). We hypothesized that targeted delivery of the
antimalarial drug, CQ, to pDCs via nanocarriers will enhance inhibition of type I IFN, reduce
drug toxicity by focusing delivery to specific cells and tissues, and increase efficacy per dose
4
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(Figure 1). Our work found that CQ-loaded FMs were equivalent or more effective than soluble
CQ or CQ-loaded spherical PLGA nanocarriers in decreasing MX1 gene expression and IFN-α
production by purified TLR7 and TLR9 agonists, and SLE patient sera. Combined with their
preferential accumulation in pDCs and tissues of increased inflammation in SLE patients (e.g.,
kidneys and liver) and minimal accumulation in the eyes, CQ-loaded FMs may be a novel, more
effective, and more targeted formulation for treating SLE. |
5
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Results
Synthesis and characterization of chloroquine-loaded nanocarriers
FMs and control spherical PLGA nanocarriers were synthesized by thin-film hydration and
emulsion/solvent evaporation, respectively. Nanocarrier morphology was verified via small angle
x-ray scattering (SAXS). As expected, SAXS analysis of FMs best fit the scattering profile to a
flexible cylinder model (Figure S1). The aspect ratio was calculated, and drug loading had no
significant effect when comparing unloaded (χ2 = 0.008) versus CQ-loaded (χ2 = 0.0012) FMs
(Figure 2A). Key limitations of SAXS analysis methods are the assumptions of constant shape
and homogeneity in a given sample. Direct visualization by TEM was used to complement
SAXS and reveal potential variations in morphology (37). Representative images showed that
the morphology of unloaded and CQ-loaded FMs were consistent with micron length and ~50
nm cross-sectional diameter (Figure 2B). Dynamic light scattering determined control spherical
PLGA nanocarriers had an average hydrodynamic diameter of 662.5 nm and 0.272
polydispersity index (PDI) for blank nanocarriers compared to 562.6 nm and 0.221 PDI for CQ-
loaded nanocarriers. Surface charge is an important nanocarrier characteristic because it is a
major determinant of serum protein adsorption and cellular internalization by the mononuclear
phagocyte system, which consists mainly of tissue-resident macrophages (38). The zeta
potential of blank and loaded nanocarriers was determined to be negative (Figure 2C). Neutral
or anionic nanocarriers are less likely to adsorb serum proteins, be sequestered by tissue-
resident macrophages, and have short serum half-lives in comparison to cationic nanocarriers
(39, 40). These data confirmed that the physical (morphology, size) and biochemical (charge)
properties of nanocarriers were not affected by drug loading. Next, we characterized the loading and release properties of CQ. Loading capacity and
encapsulation efficiency were determined by dissolving CQ-loaded nanocarriers in DMSO and
quantifying CQ by UV/Vis spectrophotometry. The average loading capacity was 49.96 ± 5.529
μg CQ/mg particle (mean ± standard deviation) for FMs (Figure 2D) and 12.07 ± 2.255 μg
6
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CQ/mg particle for spherical PLGA nanocarriers (Figure 2D). The encapsulation efficiency for
CQ was ~50% for FMs and ~0.6% for spherical PLGA nanocarriers (Figure 2D). For kinetic
release studies, FMs were incubated in vitro for up to 24 h, and a characteristic burst release
was observed followed by a plateau at ~50% release of encapsulated CQ (Figure 2E). |
Overall,
these results demonstrated that CQ efficiently loaded into FMs and enabled controlled release. PEG-b-PPS FMs selectively target pDCs in vitro
Nanocarrier size and shape are known to significantly alter their delivery and biodistribution in
vitro and in vivo (38). We evaluated whether FMs could address two key design needs: 1)
targeting and preferential accumulation in pDCs in vitro and 2) biodistribution favoring major
target organs in SLE while avoiding off-target effects in the eye in vivo. FMs were loaded with
the lipophilic fluorescent dye DiD for tracking and added to cultures of human PBMCs in vitro. Flow cytometry was used to determine cellular targeting and association after 6, 24, and 48 h.
pDCs represent an average of 0.29% of all cells in healthy human PBMCs but accumulated
more FMs than B and T cells after 48 h (Figure 3A). DiD+ cells were quantified, and their
median fluorescent intensity calculated to estimate both the fraction of cells taking up
nanocarriers as well as the amount of nanocarriers internalized per cell. pDCs were consistently
associated with nanocarriers compared to more abundant cells (12.6% DiD+ of T cells) and total
live cells (98.08% of PBMCs) (Figure 3A). The intensity of DiD in pDCs was also highest
among all analyzed cell types (average MFI of 25.73 after 48 h), suggesting FMs accumulated
mainly in pDCs (Figure 3B and representative gating strategy shown in Figure S2). Together,
these results demonstrated the highly targeted accumulation of FMs in pDCs despite their
relatively low abundance. The biodistribution of nanocarriers is strongly influenced by parameters such as size,
morphology, dose, and administration route. Typically, accumulation in blood filtration organs
(e.g., kidney, liver, spleen) is undesirable for drug delivery because nanocarriers are
7
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sequestered by the mononuclear phagocyte system (38, 41). In SLE, these are critical sites of
disease activity for targeting drug delivery. Biodistribution of DiD-loaded FMs was analyzed after
intravenous injection in C57BL/6 mice. FMs accumulated in the kidneys and liver 1-h post-
injection and dye signal was cleared by the body after 24 h with minimal accumulation in the eye
(Figure 4A). The decreased accumulation of FMs in the eye suggests the potential to reduce
antimalarial retinopathy by minimizing off-target drug accumulation, potentially eliminating a
primary toxicity of soluble CQ. Within each organ, we analyzed the percentage of immune cells that were DiD+ to
determine FM uptake (Figure 4B). We observed a significant increase in splenic CD19+ B cells
associated with DiD-loaded FMs after 24 h. CD11c+ dendritic cells and CD11b+ myeloid cells
also showed increased DiD signal between 1- and 24-h post-injection in the liver and spleen,
consistent with their passive endocytic function. |
This may also be partially driven by the high
aspect ratio and minimal curvature regions of FMs (normalized curvature, Ω ≥ 45°), which can
induce faster internalization by phagocytosis compared to spherical nanocarriers (Ω ≤ 45°) (42). The increased cellular signal from 1 h to 24 h may be the result of cells in the mononuclear
phagocyte system facilitating the clearance of FMs from circulation and at those organ sites. These results demonstrated favorable drug delivery properties at the tissue and cellular level to
address key disadvantages of a soluble free drug, including avoiding the eye and targeting
drugs into immunopathogenic cell types and tissue sites of disease activity. Chloroquine-Loaded Nanocarriers Decrease Interferon-Stimulated Genes in Human
PBMCs
A major goal for targeted delivery and controlled release is to potentiate drug activity. We
compared the efficacy of CQ-loaded nanocarriers to soluble CQ in two in vitro culture systems:
human PBMCs stimulated with 1) TLR agonists or 2) sera from SLE patients with active
disease. We generated a dose-response curve to determine which concentrations of CQ
8
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inhibited TLR7 and TLR9 activation in healthy human PBMCs. Previous studies show that 100
µM CQ maximally decreases pro-inflammatory cytokine secretion, including TNF-α, IL-6, and IL-
1β (43, 44), and particularly, IFN-α in human PBMCs after in vitro TLR stimulation (45). We
quantified the expression of MX1, an interferon-stimulated gene that is upregulated in SLE
patients compared to healthy controls (46). Healthy human PBMCs were stimulated with either
ssRNA40/LyoVec (TLR7/8 agonist) or CpG ODN 2216 Class-A (TLR9 agonist) and left
untreated or pretreated with soluble drug or drug-loaded nanocarriers at 1.95, 3.91, or 7.81 μM
CQ (Figure 5). CQ-loaded FMs resulted in >90% decrease in MX1 gene expression in human
PBMCs after TLR7/8 (Figure 5A) and TLR9 (Figure 5B) activation. Using the dose-response curve data, we subsequently tested CQ-loaded nanocarriers at
3.91 μM CQ because this dose yielded robust inhibition of MX1 (93.20-97.57%) at
approximately 25-fold lower dose than previous studies with soluble drug (43-45) and less
variability in response after both TLR7/8 and TL9 activation. Soluble CQ and CQ-loaded
nanocarriers had comparable efficacy suppressing TLR7/8-mediated MX1 gene expression in
PBMCs (Figure 6A). In contrast, CQ-loaded FMs were significantly more suppressive of TLR9-
mediated MX1 expression in PBMCs, approximately 2.6-fold more inhibitory than soluble drug
(Figure 6B). Nanocarriers alone, only soluble CQ, or blank nanocarriers cultured with soluble
CQ did not stimulate MX1 gene expression in healthy human PBMCs (Figure S3). pDCs are well-known as the primary producers of type I IFN among immune cells in
PBMCs, but they are notoriously low in abundance. |
We tested the contribution of pDCs to TLR-
driven type I IFN by isolating purified human CD123+ pDCs, stimulating them with TLR
agonists, and treating them with either soluble CQ or CQ-loaded nanocarriers (Figure 6C and
6D). Purified pDCs showed no significant MX1 upregulation after activation by TLR7/8 agonist
ssRNA40/LyoVec (Figure 6C). This suggested the responding PBMC cell type to TLR7/8
stimulation was not pDCs in our experiments. Unlike TLR7/8 stimulation, TLR9 stimulation of
pDCs resulted in robust MX1 upregulation, which could be strongly inhibited by both soluble CQ
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and CQ-loaded FMs. TLR9 stimulation with CpG-A ODN 2216 robustly stimulated type I IFN in
purified pDCs, upregulating MX1 expression ~300X over unstimulated controls after 6 h (Figure
6D). Soluble CQ and CQ-loaded FMs significantly decreased MX1 (95% and 85% inhibition,
respectively). Overall, these results demonstrated that soluble CQ and CQ-loaded nanocarriers
can efficiently suppress TLR7/8 and TLR9-stimulated type I IFN responses in PBMCs, and that
pDCs were a primary target in TLR9 stimulation while a different PBMC cell type drove TLR7/8
responses. Chloroquine Loaded Nanocarriers Reduce Type I IFN Induced by SLE Sera
Purified TLR agonists are strong stimulators of PBMCs but differ substantially from physiologic
agonists. Circulating immune complexes in SLE are unique structures composed of
autoantibodies and endogenous antigens, such as anti-dsDNA antibodies and self-DNA, and
these are hypothesized to be a major driver of endosomal TLR activation and type I IFN
pathogenesis in SLE. Anti-dsDNA autoantibodies are found in approximately 80% of patients
with lupus nephritis (47), and are associated with TLR9 activation (48), and high IFN-α activity
(49). SLE serum has been previously shown to stimulate pDCs and produce IFN-α (50). CQ
also has been shown to decrease IFN-α production after pDC activation by SLE serum (19). We
used SLE patient sera as a more physiologic stimulator of PBMCs and proof-of-principle for
clinical utility. Healthy PBMCs were isolated and co-cultured with 30% v/v SLE sera for 24 h in
vitro. We used a ~75% lower dose of soluble CQ than reported in literature to inhibit SLE serum
(19). Soluble CQ did not significantly decrease type I IFN response stimulated by SLE sera
(Figure 7A). In contrast, pretreatment with equivalent dose of CQ-loaded FMs significantly
decreased MX1 expression induced by SLE sera by approximately 75% compared to no
inhibition by either soluble drug or CQ-loaded spherical PLGA nanocarriers (Figure 7A). We
also analyzed secretion of IFN-α with a multi-subtype ELISA that quantifies all 12 known IFN-α
family proteins in humans (51). As expected, based on MX1 expression, IFN-α production was
10
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significantly decreased by CQ-loaded nanocarriers, while soluble CQ had no effect (Figure 7B). Both FMs and spherical PLGA nanocarriers significantly inhibited IFN-α secretion, suggesting
MX1 is induced by more than IFN-α in our experimental system. These data showed that CQ-
loaded nanocarriers significantly decreased IFN-α production compared to soluble CQ in
response to immune complexes from SLE patient sera. This suggests that CQ-loaded FMs may
have utility as a novel drug formulation for treating SLE. 11
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Discussion
The past decade has seen the first new drug approvals for SLE by the U.S. FDA in over 50
years. In 2011, the monoclonal antibody belimumab blocking B lymphocyte stimulator was
approved for SLE and approved for lupus nephritis in 2020. In 2021, voclosporin, a calcineurin
inhibitor, in combination with background immunosuppressive therapy, was approved for adult
patients with active lupus nephritis. Voclosporin was the second FDA-approved therapy for
lupus nephritis and the first oral treatment specifically for that manifestation (52). Despite FDA
approvals of belimumab and voclosporin, these therapies were studied in combination with a
background of immunosuppressive agents and corticosteroids to achieve efficacy, and drug
delivery and toxicity remain persistent limitations for these and other SLE treatments. Nanocarriers can enhance drug delivery while mitigating adverse side effects by
reducing accumulation in off-target cells and tissues. We demonstrated that targeting pDCs
using antimalarial-loaded FMs could enhance suppression of TLR activation and subsequent
type I IFN responses (Figure 1). To our knowledge, this is the first use of passive, morphology-
based nanocarrier targeting of pDCs to enhance TLR inhibition, and extends prior work
demonstrating accumulation in pDCs (33). TLR inhibition has great potential as a therapeutic
strategy since gene polymorphisms of TLRs lead to disease susceptibility (53), TLR ligands
contained in NETs or resulting from apoptotic cell death exacerbate disease (54, 55), and TLR
inhibitors (i.e., antimalarial drugs) alleviate disease (56). Our approach targets SLE in disease-
relevant sites and cells to inhibit key inflammatory pathways. Our results showed that FMs accumulate in pDCs (Figure 3), professional IFN-α
producing cells that represent <1% of cells in the blood but produce 1,000X more IFN-α than
any other immune cell (57). Concentrating drug delivery to pDCs may potentiate TLR
antagonists, such as CQ, by increasing drug accumulation in the endosomal space to block TLR
signaling more efficiently and downstream type I IFN responses. |
Additionally, passive targeting,
which leverages physicochemical nanocarrier properties (Figure 2) and disease biology,
12
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presents an opportunity for FMs to accumulate at tissue sites of SLE-driven inflammatory
damage like the kidneys (Figure 4). Targeting SLE-relevant organs (e.g., kidneys and liver) can
concentrate drug delivery to tissues where both immune complexes and pDCs are found during
active disease, while limiting off-target effects. pDCs are important in lupus nephritis because
they express high levels of IL-18R which allows the relocation of dendritic cells within the
glomeruli by IL-18 stimulation. These dendritic cells then activate resident T cells, resulting in
promotion of renal damage (58, 59). FMs also escape accumulation in the eye (Figure 4) due to
the size and morphology of the nanocarriers and their impermeability of the blood-retinal barrier
(60, 61). This may reduce the risk of antimalarial-mediated retinopathy with chronic use of CQ
(29) and long-term toxicity associated with the current CQ formulation. We hypothesize that the
filamentous morphology (Figure 2) and phagocytosis of FMs facilitates internalization by pDCs
(34, 42, 62), and thus, its unique morphology advances nanocarrier drug delivery. Future
studies should evaluate the molecular mechanisms and kinetics of FM uptake into endosomes
and degradation by pH-mediated oxidation. We used synthetic oligonucleotide agonists ssRNA40 and CpG-A ODN 2216 to trigger
TLR7/8 and TLR9, respectively, because human pDCs selectively express endosomal TLR7
and TLR9 to sense pathogenic and endogenous nucleic acids (63). Although ssRNA40 is
known to produce high levels of IFN-α in pDCs (64) and induce MX1 gene expression in PBMCs
(65), CQ-loaded FMs were not significantly different from soluble drug or spherical PLGA control
(Figure 6A and 6C). Since isolated pDCs did not show an MX1 response to ssRNA40, we
hypothesize that monocytes and other myeloid cells may be additional mediators of IFN-α
production after TLR7/8 activation by ssRNA40 (66). However, both soluble CQ and CQ-loaded
FMs did suppress TLR9-mediated MX1 in both PBMCs and isolated pDCs at the same CQ
concentration (Figure 6B and 6D). This represents a major advantage in that the total body
exposure and off-target tissue accumulation of CQ is diminished with the delivery of antimalarial
drug in nanocarriers. 13
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Many emerging drug delivery strategies have been tested preclinically against SLE. Previous studies have used mycophenolic acid (67, 68), cyclosporine A (69), azathioprine (70),
and the prodrug of dexamethasone (71) in drug delivery platforms to target SLE relevant
pathways, ameliorate glomerulonephritis in lupus-prone mice, and decrease proinflammatory
cytokines. |
Our work builds upon existing studies by using a novel drug delivery approach to
target pDCs without needing a targeting moiety for delivery of an FDA-approved drug, CQ, for
SLE treatment. We chose antimalarial drugs because they are the mainstay first line, long-term
SLE treatment regardless of renal involvement or disease severity (25). By loading CQ in FMs,
we decreased the in vitro concentration of CQ required to inhibit MX1, which is upregulated in
SLE patients (72) (Figure 5). We showed that CQ-loaded FMs decreased MX1 gene expression
equivalent to soluble CQ in human PBMCs stimulated with purified TLR agonists (Figure 6A
and 6B). In human PBMCs stimulated with anti-dsDNA positive SLE sera, soluble CQ did not
inhibit MX1 gene expression (Figure 7A) or IFN-α secretion (Figure 7B). We propose that SLE
sera is less sensitive to CQ inhibition than synthetic oligonucleotide TLR agonists, as shown in
previous studies (19), and concentration of CQ in the endosomal space may be more important
for treatment in this scenario. Compared to previous studies, we used 75% less CQ loaded in
FMs and showed a significant decrease in MX1 gene expression (Figure 7A) and IFN-α
production (Figure 7B), demonstrating the dose-sparing and dose-enhancement of CQ in FMs
versus soluble CQ. Future studies evaluating the dosing strategies of CQ loaded nanocarriers in lupus-
prone mouse models can better define the frequency of treatment as well as determine
bioavailability of different routes of administration. A preclinical model with a strong type I IFN
signature and clinical manifestations similar to SLE patients, such as the pristane-induced
model (73, 74), will be important in demonstrating the efficacy of this treatment option in vivo. Our approach has therapeutic implications because CQ-loaded FMs may provide a more
targeted inhibition of immune-complex-mediated inflammation in SLE, potentially sparing steroid
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or immunosuppressive treatment. This would result in both lower steroid toxicity as well as lower
risk of infection, a serious threat to SLE patient health (15, 16). To enhance the therapeutic potential of CQ drug delivery, future work should include
investigating other nanocarrier morphologies that can target other IFN-producing cell types such
as myeloid cells. The PEG-b-PPS platform is ideal for these studies because by changing the
hydrophilic weight fractions of the polymer, they can be self-assembled easily to form diverse
morphologies such as spherical (i.e., micelles and polymersomes) (32) and cubic (i.e.,
bicontinuous cubic nanospheres) (75) nanostructures with distinct cellular biodistribution profiles
(76). Overall, this study illustrates the therapeutic potential of drug delivery of CQ for targeting
SLE-relevant pathways, immune cells, and organ sites. |
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Methods
Materials
Chloroquine, 95% purity was purchased from Ark Pharm (Arlington Heights, IL, USA). Acid-
terminated, 50:50 lactide/glycolide molar ratio, molecular weight (MW) 7,000-17,000 poly(D, L-
lactide-co-glycolide) (PLGA); MW 25,000, 88% hydrolyzed polyvinyl alcohol (PVA);
poly(ethylene glycol) methyl ether MW 2000; and organic solvents were purchased from Sigma
Aldrich (St. Louis, MO, USA). Propylene sulfide was acquired from TCI Chemicals. Micro Float-
A-Lyzer Dialysis Device, biotech grade cellulose ester, 8-10 kDa molecular weight cut off
(MWCO) was purchased from Repligen (Waltham, MA, USA). TLR agonists (ssRNA40/LyoVec
and CpG-A ODN 2216) were purchased from Invivogen (San Diego, CA, USA). Antibodies and Dyes
The Zombie Aqua™ Fixable Viability dye and all primary antibodies used for flow cytometry
analysis were obtained from BioLegend (San Diego, CA, USA) (Table 1). Nanocarrier Synthesis
Block copolymer PEG-b-PPS was synthesized as previously described (77). FMs were loaded
with the hydrophobic antimalarial drug, CQ, via thin-film hydration. Briefly, 5-10 mg of PEG45-b-
PPS44 polymer was co-dissolved with equal mass CQ in 200 µL chloroform in a 5 mL sterile,
clear, LPS-free glass vial. The solvent was evaporated at room temperature (RT) for 3-5 h,
resulting in a thin film. The thin film was rehydrated at a total polymer concentration of 5-15
mg/mL with 1X phosphate-buffered saline (PBS) at pH 7.4 under gentle agitation overnight. CQ
loaded nanocarriers were purified from free CQ by 10K MWCO polyethersulfone membrane
spin columns (VWR; Radnor, PA, USA) at 10,000 xg for 1-2 minutes and equilibrated with PBS
solution. 16
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Spherical PLGA nanocarriers were fabricated by oil-in-water emulsion/solvent
evaporation technique (78). Briefly, 5-10 mg PLGA and equal mass CQ was dissolved in 500 µL
chloroform. The organic phase was emulsified in 2 mL of 0.5% PVA in 1X PBS solution using a
probe sonicator at 50% amplification for 2 minutes on ice. The emulsion was added dropwise to
10 mL of 5% PVA in 1X PBS solution at RT. The continuous phase was homogenized at 6,800
x rpm with the T 25 digital ULTRA-TURRAX® (IKA; Wilmington, NC, USA) and left to stir
overnight at 600 x rpm at RT until the organic solvent was evaporated and nanocarriers were
hardened. CQ-loaded spherical PLGA nanocarriers were purified from free drug by
centrifugation for 5 minutes at 14,000 x g and washed three times with diH2O. Nanocarrier Characterization
Small-angle X-ray scattering (SAXS) was performed at the University of Maryland, College Park
X-Ray Crystallographic Center using the Xenocs Xeuss SAXS/WAXS/GISAXS small-angle
system with 8 keV (wavelength = 1.5 A) collimated X-rays. |
Samples were measured at 2.5 m
from the CCD detector and analyzed within the 0.004-0.2 A-1 q-range calibrated by diffraction
patterns of silver behenate. SAXS analysis was performed using IgorPro (WaveMetrics, Inc.;
Portland, OR, USA) for 2D to 1D reduction and normalization of acquired sample scattering
from buffer scattering. Model fitting was completed using SASVIEW 4.X based on the flexible
cylinder model with the following parameters: 2 µm cylinder length, 150 nm persistence length,
and 8 nm PPS core radius (79). The FEI Morgagni 268 100 kV Transmission electron
microscope (TEM) equipped with a Gatan Orius CCD camera was used to compare morphology
and appearance of blank and CQ-loaded nanocarriers. For TEM processing, 12 mg/mL blank or
loaded nanocarriers were added to FCF200-Cu-TB coated grids and stained with 2% uranyl
acetate. The grids were immediately processed after negative staining. Size, size distribution,
and zeta potential were measured at 1 mg/mL of nanocarriers in 1X PBS solution (pH 7.4) using
the Malvern Zetasizer Nano ZS. Loading capacity, total loaded drug per mass of nanocarrier,
17
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and encapsulation efficiency, percentage of initial drug mass successfully entrapped in the
nanocarriers, were measured by dissolving a known mass of loaded nanocarriers in dimethyl
sulfoxide (DMSO) followed by UV/Vis spectrophotometry analysis using the Mettler Toledo UV5
Nano. Drug loading per mass of nanocarriers was determined by developing a standard curve
of CQ dissolved in DMSO using the characteristic wavelength corresponding to maximum
absorption of CQ at approximately 343 nm. Drug release kinetics were determined by placing
drug-loaded nanocarriers into microdialysis devices in 1X PBS with 1% bovine serum albumin
(BSA) at 37 °C (physiological temperature) and 5% CO2. Samples were analyzed by UV/Vis
spectrophotometry, as above, after 0, 2, 4, 6, and 24 h.
Nanocarrier Cellular Uptake and In Vivo Biodistribution
FMs were loaded with the lipophilic fluorescent tracer, Vybrant® DiD cell-labeling solution
(Thermo Fisher; Waltham, MA, USA), via thin-film hydration method. In a 5 mL sterile, clear,
LPS-free glass vial, 2.5 µL Vybrant® DiD cell-labeling solution and 5-10 mg of PEG-b-PPS was
co-dissolved in 150 µL dichloromethane. The solvent was evaporated at RT for 3-5 h and then
resuspended at a total polymer concentration of 5-15 mg/mL with 1X PBS at pH 7.4 under
gentle agitation overnight. Dye-loaded nanocarriers were purified from free dye by dialysis or
10K MWCO polyethersulfone membrane spin columns (VWR; Radnor, PA, USA) at 10,000 xg
for 1-2 minutes and equilibrated with PBS solution. Lipophilic dye loaded nanocarriers at 200
µg/mL were incubated at 37°C, 5% CO2 in 1 million fresh human peripheral blood mononuclear
cells (PBMCs) from healthy donors (New York Blood Center; New York, NY) for up to 48 h in
RPMI 1640 medium with GlutaMAX plus 10% fetal bovine serum (FBS), 1% sodium pyruvate,
1% nonessential amino acids (NEAA), 1% penicillin-streptomycin solution (pen-strep), and 20
ng/mL recombinant human IL-3 (BioLegend; San Diego, CA, USA) to determine cellular
distribution. |
PBMCs were stained with a viability dye and fluorescent antibodies to distinguish
18
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cellular subsets including CD19+ B cells (clone HIB19; Brilliant Violet 421TM), CD3+ T cells
(clone OKT3; APC/Cy7), and CD123+ pDCs (clone 6H6; PE). Female C57BL/6 mice, 6-8 weeks old, (Jackson Laboratory; Bar Harbor, ME USA) were
injected intravenously by retro-orbital sinus with 150 μL free DiD (50 μg/mL in 1X PBS solution)
or DiD loaded FMs (7.5 μg of loaded DiD in each sample in 150 μL PBS). At 1- and 24-h post-
injection, the eyes, kidneys, liver, and spleen were collected, mechanically dissociated, and
digested with 0.1% collagenase, type 4 in Hanks’ Balanced Salt Solution (Worthington;
Lakewood, NJ, USA) followed by red blood cell lysis with ammonium-chloride-potassium lysing
buffer (Lonza; Basel, Switzerland). Cells were filtered through a 70 μm nylon, DNase/RNase
free, non-pyrogenic cell strainer (VWR; Radnor, PA, USA) and washed with 1X PBS. Single cell
suspensions of each tissue at 250,000 cells per 200 μL in 1X DPBS were read on a BioTek
Cytation 5 plate reader at the absorbance maximum of DiD (i.e., 644 nm). The total mass of DiD
per tissue was quantified by interpolation of sample measurements onto a standard curve of
known concentrations of DiD in 1X DPBS using the characteristic maximum absorbance. Cell
suspensions were stained for viability and phenotypic, anti-mouse cell surface markers, CD11b
(clone: M1/70, FITC), CD11c (clone: N418, PE), CD3 (clone: 17A3, Brilliant Violet 605TM), and
CD19 (clone: 6D5, PerCP/Cy5.5). Stained cells were then run on a flow cytometer and analyzed
for uptake of DiD loaded nanocarriers. In Vitro Activity of Nanocarriers in Human Cells
Fresh, healthy human PBMCs were isolated from buffy coats obtained from the New York Blood
Center via density gradient medium (Ficoll-Paque). Flow cytometry was used to establish
viability and cell distribution of each human PBMC donor using the following fluorophore-
conjugated anti-human antibodies: CD4+ T cells (clone RPA-T4; PerCP-Cy5.5), CD19+ B cells
(clone HIB19; Brilliant Violet 421TM), CD123+ pDCs (clone 6H6; PE), and CD1c+ mDCs (clone
L161; APC/Cy7). One million PBMCs in 250 μL total volume of RPMI 1640 with GlutaMAX
19
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medium plus 10% FBS, 1% sodium pyruvate, 1% NEAA, and 1% pen-strep were treated with
soluble CQ, empty nanocarriers, or CQ-loaded nanocarriers for 1 h and then stimulated with
purified TLR agonists: 5 μg/mL ssRNA40/LyoVec (TLR7/8 agonist) (64), or 5 μM CpG-A
ODN2216 (TLR9 agonist) (80), or 30% v/v sera from an SLE patient with moderately active
disease and positive anti-dsDNA titers for 4, 6, and 24 h, respectively. |
Recognition of ssRNA40
is species-dependent where human cells have a bias towards TLR8 and mouse cells bias
towards TLR7 (66). Chloroquine was tested at 1.95, 3.91, or 7.81 μM. To prevent degradation
and enhance cellular uptake of the TLR7/8 agonist, RNA was co-delivered using LyoVec as a
transfection agent. Following incubation at 37 °C, 5% CO2, cells were spun down at 500 xg for 1
minute at RT. Total RNA was isolated from PBMCs using the Quick-RNA Miniprep Plus Kit
(ZymoResearch; Irvine, CA, USA), amplified, and analyzed by real-time reverse transcription-
quantitative PCR (RT-qPCR). Cell-free supernatants were collected and stored at -80°C until
testing for IFN-α production using the Human IFN Alpha All Subtype ELISA Kit (PBL Science;
Piscataway, NJ, USA). Nanocarrier efficacy was determined by analyzing the downstream IFN-
stimulated gene MX1 by RT-qPCR. Expression levels were normalized to β-actin control. Purified pDCs were isolated via the EasySep™ Human Plasmacytoid DC Enrichment Kit
(STEMCELL Technologies; Vancouver, Canada). Soluble or CQ-loaded nanocarriers at 3.91
μM total drug were cultured with 100,000 pDCs in RPMI 1640 with GlutaMAX plus 10% FBS,
1% sodium pyruvate, 1% NEAA, 1% pen-strep, and 20 ng/mL recombinant human IL-3. Cells
and cell-free supernatants were isolated from stimulated pDC cultures and tested by real-time
RT-qPCR and human IFN-α all subtype ELISA, respectively. Flow Cytometry
Either Human TruStain FcXTM or TruStain FcXTM PLUS (BioLegend; San Diego, CA, USA) was
used to block nonspecific binding of human or mouse Fc receptors, respectively, prior to
immunostaining. For human cells, 5 μL of Human TruStain FcXTM was added per million cells in
20
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100 μL staining volume of PBS plus 1% BSA. Cells were incubated for 5 minutes at RT. For
mouse cells, 0.25 µg of TruStain FcXTM PLUS was added per million cells in a volume of 100 µL
PBS plus 1% BSA for 5 minutes at RT. After blocking, cells were stained at 1:100 dilution with
conjugated fluorescent antibodies (Table 1) in PBS plus 1% BSA for 15-20 minutes in the dark
and on ice. Cells were washed with PBS. To discriminate between live and dead cells, Zombie
Aqua™ Fixable Viability dye was diluted 1:1000 in PBS. Diluted Zombie Aqua™ Fixable Viability
dye was added to cells for 15-30 minutes at RT and in the dark. Cells were washed,
resuspended in PBS plus 1% BSA, and immediately analyzed on a flow cytometer. A BD LSR II
with 405, 488, 561, and 640 nm excitation laser lines or Beckman Coulter CyAn ADP consisting
of 405, 488, and 635 nm excitation laser lines was used for flow cytometry analysis of
fluorescently labeled cells. Data were analyzed using FlowJo LLC software v10.7 (BD). The
gating strategies are available in the supplementary figures. |
Real-time RT-qPCR
All real-time RT-qPCR reagents were purchased from ThermoFisher. The TaqMan probes
included: Human MX1, FAM-MGB (assay id: Hs00895608_m1) and Human ACTB VIC-MGB PL
(assay id: Hs01060665_g1). TaqPath 1-Step Multiplex Master Mix (No ROX) was used for all
one-step multiplex real-time RT-qPCRs. Reactions were run on the CFX96 Touch Real-Time
PCR Detection System using the following thermal cycle conditions: UNG incubation (1 cycle,
25°C, 2 minutes), reverse transcription (1 cycle, 53°C, 10 minutes), polymerase activation (1
cycle, 95°C, 2 minutes), and amplification (45 cycles at 95°C for 15 seconds and 60°C for 1
minute). The 2-ΔΔCT (Livak) Method was used for relative gene expression analysis. Statistics
All statistical analyses were performed using GraphPad Prism 9 software (GraphPad Software,
San Diego, CA). A minimum of three independent replicates were conducted for human PBMCs
21
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and nanocarrier characterization experiments. For in vivo biodistribution experiments, 3-4 mice
were used. Paired or unpaired t-tests and ANOVA were used to test for statistical significance. P-values were adjusted for multiple comparisons by Tukey’s, Šídák’s, or Dunnett’s test, and
adjusted p-values <0.05 were considered significant. Study approval
The animal study was reviewed and approved by UMBC Institutional Animal Care and Use
Committee (OLAW Animal Welfare Assurance D16-00462). This study involved human
subjects. Approval for this study was obtained from the University of Maryland School of
Medicine Institutional Review Board (IRB) as well as the Baltimore VA Research Office of
Human Research Protection. There is no identifiable medical information in this manuscript. All
patient identities have been removed. Per our IRB-approved protocol, all participants signed
informed consent. All identifiable information has been removed from the reported data. 22
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Author contributions
MEA and GLS conceptualized the study, designed experiments, analyzed the data, and wrote
the manuscript. AG and VR contributed SLE patient sera and expertise in autoimmunity,
rheumatology, and systemic lupus erythematosus. EAS contributed expertise in nanocarriers
and drug delivery. MEA performed all experiments. EAS, NBK, SL, CJL, and SB synthesized
the PEG-b-PPS polymer. All authors reviewed and edited the manuscript. 23
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this version posted June 9, 2021. |
The copyright holder for this preprint (which
Acknowledgments
We would like to thank Tagide deCarvalho for TEM assistance at the University of Maryland,
Baltimore County Keith R. Porter Imaging Facility and Wonseok Hwang for SAXS assistance at
the University of Maryland, College Park X-ray Crystallographic Center. Flow cytometry was
performed at the University of Maryland Greenebaum Comprehensive Cancer Center Flow
Cytometry Shared Service or the University of Maryland, Baltimore County Keith R. Porter
Imaging Facility. We would like to thank Christine Daniel and Erin Lavik for the use of the
ZetaSizer. This work was partially supported by the Lupus Foundation of America Gina M. Finzi
Memorial Student Summer Fellowship (MEA), a grant from the State of Maryland, TEDCO
Maryland Innovation Initiative (MII) (project #0719-009) (GLS), and the University of Maryland,
Baltimore County Technology Catalyst Fund (GLS). AG wishes to acknowledge his completed
VA CDA-2 award support—VA grant IK2 CX000649-01A1. MEA was supported by an NIH-
NIGMS Initiative for Maximizing Student Development Grant (grant no. R25-GM55036) and the
National Science Foundation LSAMP BD Program (award no. 1500511). This manuscript has
been released as a preprint at bioRxiv. 24
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Karabin NB, et al. Sustained micellar delivery via inducible transitions in nanostructure
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Figure 1. Graphical abstract. (A) Antimalarial drug-loaded polymeric nanocarriers traffic into endosomes where intracellular TLR7 and TLR9 are located. (B) Controlled release of antimalarial drug, such as chloroquine (CQ), inhibits TLR7 and TLR9 activation by masking the binding epitope of nucleic acids contained on immune complexes. (C) TLR inactivation prevents downstream signaling of type I interferon (IFN) and IFN-stimulated genes and production of pro- inflammatory cytokines, such as IFN-α, a major driver of SLE pathogenesis. Created with BioRender.com. 33
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Figure 2. CQ loading did not alter physicochemical properties of nanocarriers. (A) Aspect ratio (width/height) of blank FMs (n = 3) and CQ-loaded FMs (FM-CQ) (n = 3). Length and diameter were measured by SAXS using the flexible cylinder model and the following parameters: 2 µm cylinder length, 150 nm persistence length, and 8 nm PPS core radius. Paired t-test for statistical analysis. (B) Representative images from TEM showed blank (left) and CQ- loaded (right) FMs at 12 mg/mL in 1X PBS. Samples were stained with 2% uranyl acetate. (C) Zeta potential (n = 3) of CQ loaded and blank (left) FMs or (right) PLGA. Data were shown as means with error bars representing standard deviation. Paired t-test was used for statistical analysis. Statistical significance: *p ≤ 0.05. All samples were measured in 1X PBS solution (pH 7.4) at 1 mg/mL. (D) Loading capacity (n = 3) and encapsulation efficiency (n = 3) of CQ-loaded (left) FMs or (right) spherical PLGA nanocarriers. All samples were measured in 1X PBS solution, pH 7.4 at 1 mg/mL. Data show mean and error bars represent standard deviation. (E) CQ drug release profile from FMs. CQ-loaded FMs (n = 3) were placed in 10K MWCO dialysis tubing in 1X PBS buffer plus 1% BSA for 0, 2, 4, 6, and 24 h at 37°C, 5% CO2. |
Each time point shows the average percentage cumulative drug release; error bars represent standard deviation. 34
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A
B
Figure 3. DiD-loaded FMs preferentially accumulated in pDCs in vitro. FMs were loaded with DiD fluorescent tracer dye. Fresh human PBMCs were cultured with 200 µg/mL DiD-loaded FMs for 6, 24 and 48 h in supplemented RPMI 1640 plus GlutaMAX medium with 10% FBS and 20 ng/mL IL-3 at 37°C and 5% CO2 (n = 3 independent donors). (A) Representative histograms and (B) median fluorescent intensity of DiD from (A). Bars represent mean (n = 3) with standard deviation. Statistical analysis: Tukey’s multiple comparison two-way ANOVA and p <0.05 was considered significant: ***p ≤ 0.001. Gating strategies are described in Figure S2. 35
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A
B
Figure 4. Organ- and cellular-level biodistribution of DiD-loaded FMs in C57BL/6 Mice. DiD-loaded FM were synthesized as described and administered by intravenous injection into the retro-orbital sinus. Mice were sacrificed at 1 h or 24 h post-injection and organs were mechanically dissociated and digested by collagenase, type 4. (A) The absorbance at 644 nm of 250,000 single cell suspensions from C57BL/6 mice (n = 3-4) at each organ was calculated against a standard curve of DiD in 1X DPBS. Graphs compare tissue distribution of DiD-loaded FMs or soluble FMs at both 50 µg/mL. Statistical analysis completed by unpaired t tests. Statistical significance: *p ≤ 0.05 and **p ≤ 0.01. (B) Single-cell suspensions were stained and
36
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analyzed by flow cytometry. Immune cells from both eyes were pooled, stained, and analyzed by flow cytometry. Graphs compare cellular uptake of DiD-loaded FMs at different time points. Each cell type was mutually exclusive to other cell markers. Particle uptake was analyzed in the following cells: (I) CD19+ B cells, (II) CD11c+ dendritic cells, (III) CD3+ T cells, and (IV) CD11b+ myeloid cells. Statistical analysis was completed by two-way ANOVA with Šídák’s multiple comparison test. Statistical significance: *p ≤ 0.05, **p ≤ 0.01, and ***p ≤ 0.001. 37
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Figure 5. Dose-response curves of CQ concentration versus percent decrease in MX1 gene expression. Human PBMCs (n = 4 independent donors) were pretreated with CQ or CQ- loaded FM or PLGA nanocarriers for 1 h and then stimulated with (A) ssRNA40/LyoVec (TLR7/8 agonist) for 4 h or (B) CpG-A ODN 2216 (TLR9 agonist) for 6 h. RNA was extracted to quantify MX1 expression using TaqMan real-time RT-qPCR and normalized to β-actin. MX1 expression was normalized to TLR agonist alone. Lines represented the non-linear fit of log(inhibitor) versus normalized response - variable slope model, where CQ was the inhibitor concentration. Data are means ± standard deviation. 38
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Figure 6. Soluble and nanocarrier-delivered CQ decreased MX1 expression in TLR- stimulated human PBMCs and isolated pDCs. Healthy human PBMCs were isolated, treated with 3.91 μM soluble or encapsulated CQ or equal mass blank nanocarriers for 1 h, and then activated for 4 h with (A) 5 μg/mL ssRNA40/LyoVec or for 6 h with (B) 5 μM CpG A 2216. Total RNA was isolated and MX1 expression quantified using TaqMan RT-qPCR normalized to β- actin expression. All samples were normalized to TLR agonists alone. Data are means ± standard deviation for n = 4-8 independent donors. Statistical significance was evaluated by one-way ANOVA with Dunnett’s multiple comparisons test, ***p-adjusted ≤ 0.001 and ****p ≤ 0.0001. PBMCs were processed by magnetic bead negative selection to purify pDCs. Isolated human CD123+ pDCs at 100,000 cells per condition (n = 3 independent donors) were pre- treated with soluble or CQ loaded FMs at 3.91 μM for 1 h and then stimulated with (C) 5 µg/mL ssRNA40/LyoVec or (D) 5 µM CpG-A for 4 or 6 h, respectively. Total RNA was isolated to analyze MX1 expression using TaqMan assays with β-actin control. Statistical analysis: one- way ANOVA with Dunnett’s multiple comparisons test where *p ≤ 0.05. Abbreviation: CL, control. 39
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Figure 7. CQ-loaded nanocarriers suppressed SLE sera-induced type I IFN responses from human PBMCs. Healthy human PBMCs were treated with soluble or CQ-loaded nanocarriers at 3.91 μM or equal mass blank nanocarriers for 1 h, then stimulated with 30% v/v SLE patient sera for 24 h. (A) Total RNA was isolated and MX1 expression quantified using TaqMan RT-qPCR normalized to β-actin expression. (B) Supernatants from cell culture were collected for multi-subtype IFN-α ELISA. All samples were normalized to SLE sera alone. |
Data are means ± standard deviation for n = 3 healthy independent PBMC donors. Statistical significance was evaluated by one-way ANOVA with Tukey's multiple comparisons test, such that, *p ≤ 0.05, **p ≤ 0.01, and ***p ≤ 0.001. Abbreviation: CL, control. 40
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Table 1. Flow Cytometry Antibodies
Antibody
Clone
Catalog Number
Brilliant Violet 421TM anti-
HIB19
302233
human CD19
APC/Cy7 anti-human CD3
OKT3
317341
PE anti-human CD123
6H6
306005
PerCP/Cy5.5 anti-human
RPA-T4
300529
CD4
APC/Cy7 anti-human CD1c
L161
331519
FITC anti-mouse/human
M1/70
101205
CD11b
PE anti-mouse CD11c
N418
117307
Brilliant Violet 605TM anti-
17A3
100237
mouse CD3
PerCP/Cy5.5 anti-mouse
6D5
115533
CD19
41 |
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. Neuronal cholesterol synthesis is essential for repair of chronically demyelinated lesions in mice
Stefan A. Berghoff1#*, Lena Spieth1#, Ting Sun1,2#, Leon Hosang3, Constanze Depp1, Andrew O. Sasmita1, Martina H. Vasileva1, Patricia Scholz4, Yu Zhao2, Dilja Krueger-Burg5, Sven Wichert6, Euan R Brown7, Kyriakos Michael7, Klaus-Armin Nave1, Stefan Bonn2, Francesca Odoardi3, Moritz Rossner6, Till Ischebeck4,8, Julia M. Edgar1,9, and Gesine Saher1*
Astrocyte-derived cholesterol supports brain cells under physiological conditions. However, in demyelinating lesions, astrocytes downregulate cholesterol synthesis and the cholesterol that is essential for remyelination has to originate from other cellular sources. Here, we show that repair following acute versus chronic demyelination involves distinct processes. In particular, we found that in chronic myelin disease, when recycling of lipids is often defective, de novo neuronal cholesterol synthesis is critical for regeneration. By gene expression profiling, genetic loss of function experiments and comprehensive phenotyping, we provide evidence that neurons increase cholesterol synthesis in chronic myelin disease models and MS patients. In mouse models, neuronal cholesterol facilitated remyelination specifically by triggering OPC proliferation. Our data contribute to the understanding of disease progression and have implications for therapeutic strategies in MS patients. Introduction During normal brain development, cholesterol is produced locally by de novo synthesis involving neurons, oligodendrocytes, microglia, and astrocytes (Berghoff et al., 2021; Camargo et al., 2012; Fünfschilling et al., 2012; Saher et al., 2005). Neuronal cholesterol is essential for neurite outgrowth and synapse formation during neurogenesis (Fünfschilling et al., 2012; Mauch et al., 2001) but the highest rates of cholesterol synthesis in the brain are achieved by oligodendrocytes postnatal myelination (Dietschy, 2009). The resulting cholesterol-rich myelin enwraps, shields, and insulates axons to enable rapid conduction of neuronal impulses. Myelin also provides support by mobilizing oligodendroglial lipids (Kassmann et al., 2007; Saab and Nave, 2017). In the adult brain, cholesterol synthesis is attenuated to low steady-state levels (Dietschy and Turley, 2004). during
to
axons,
potentially
Destruction of in demyelinating diseases such as multiple sclerosis (MS) likely impairs neuronal function by disrupting the fine-tuned axon- myelin unit (Stassart et al., 2018). Remyelination is
lipid-rich myelin
considered crucial for limiting axon damage and slowing progressive clinical disability. Statin-mediated inhibition of the cholesterol synthesis pathway impairs remyelination (Miron et al., 2009). |
Previously, we showed that following an acute demyelinating episode, oligodendrocytes import cholesterol for new myelin membrane synthesis from damaged myelin that has been recycled by phagocytic microglia (Berghoff et al., 2021). In contrast, de novo oligodendroglial cholesterol synthesis contributes to remyelination only following chronic demyelination (Berghoff et al., 2021; Voskuhl et al., 2019). Notably, we and others showed that astrocytes reduce expression of cholesterol synthesis genes following demyelination (Berghoff et al., 2021; Itoh et al., 2018). As astrocytes are considered to support neurons by providing cholesterol in ApoE- containing lipoproteins in the healthy brain (Dietschy, 2009), the lack of this support in the diseased brain contributes to the disruption of CNS cholesterol homeostasis. Neuronal activity to OPC proliferation during development and likely also after demyelination (Bacmeister et al., 2020; Gibson et al., 2014; Marisca et al., 2020). However, neuronal responses to myelin degeneration with regard to the contribution of cholesterol metabolism, and
leads
1 Department of Neurogenetics, Max Planck Institute of Experimental Medicine, Göttingen, Germany; 2 Institute for Medical Systems Biology, Center for Molecular Neurobiology Hamburg, Hamburg, Germany; 3 Institute for Neuroimmunology and Multiple Sclerosis Research, University Medical Center Göttingen, Göttingen, Germany; 4 Department of Plant Biochemistry, Albrecht-von-Haller-Institute for Plant Sciences and Göttingen Center for Molecular Biosciences (GZMB), University of Göttingen, Göttingen, Germany; 5 Department of Molecular Neurobiology, Max Planck Institute of Experimental Medicine, Göttingen, Germany; 6 Department of Psychiatry and Psychotherapy, University Hospital, LMU Munich, Munich, Germany; 7 School of Engineering and Physical Sciences, Institute of Biological Chemistry, Biophysics and Bioengineering, James Naysmith Building, Heriot Watt University, Edinburgh, UK; 8 Service Unit for Metabolomics and Lipidomics, Göttingen Center for Molecular Biosciences (GZMB), University of Göttingen, Göttingen, Germany; 9 Axo-glial Group, Institute of Infection, Immunity and Inflammation, College of Medical Veterinary and Life Sciences, University of Glasgow, Glasgow, UK; *Correspondence: [email protected], [email protected]
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. neuronal cholesterol unknown. to
remyelination,
remains
Here, using mice with cell type-specific inactivation of cholesterol synthesis and models of myelin disease, we assess neuronal versus glial cholesterol metabolism. We compare white and grey matter CNS regions and isolated brain cells in the healthy adult brain and during remyelination. We show that active myelin disease is associated with downregulated expression of cholesterol metabolism in neurons. |
Surprisingly, during chronic myelin disease, neurons increase cholesterol synthesis. Similarly, neurons in MS brain upregulate a gene profile related to cholesterol synthesis and metabolism in non-lesion areas. Finally, neuronal to remyelination cholesterol synthesis contributes following experimental demyelination. Our data support the essential role of cholesterol synthesis in neurons for remyelination, a role that is likely relevant for MS disease progression. Results
Loss of Fdft1 in neurons alters white matter cholesterol metabolism In the adult brain, neuronal synthesis as well as horizontal cholesterol transfer from glial cells meets neuronal cholesterol demands. To evaluate neuronal versus glial cholesterol metabolism, we acutely isolated neurons, astrocytes and oligodendrocytes from brain tissue that contained cortex or subcortical white matter of adult mice (Figure1A). The abundance of neuronal mRNA transcripts related to cholesterol metabolism was compared with oligodendrocyte and astrocyte profiles obtained previously (Berghoff et al., 2021). As steady-state showed expected, neurons levels of cholesterol synthesis genes expression (Hmgcr, Fdft1, Cyp51, Dhcr24) compared to oligodendrocytes and astrocytes (Figure 1B, Table S1). to In contrast, several gene cholesterol import (Apobr, Scarb1, Lrp1), storage (Soat1) and brain export (Cyp46a1) were higher in relative abundance. To assess the relevance of cell type-specific cholesterol synthesis, we genetically inactivated squalene synthase (SQS, Fdft1 gene), an essential enzyme of the sterol biosynthesis pathway, in (OLcKO, Plp1-CreERT2), adult oligodendrocytes (OPCcKO, CSPG4::CreERT2), astrocytes OPCs (AcKO, GLAST::CreERT2), or neurons (NcKO, CaMKII-Cre) (Figure 1C, S1A-B) (Berghoff et al., 2021; Fünfschilling et al., 2012; Saher et al., 2005). Comparable to oligodendroglial and astrocyte conditional mutants (Berghoff et al., 2021), loss of cholesterol synthesis in neurons did not affect peripheral serum cholesterol level or body weight
low
transcripts related
(Figure S1C). In an open field test, neuronal, astrocyte or OPC mutants appeared similar to controls (Figure 1D, S1D-E), whereas OLcKO animals showed signs of anxiety, which were enhanced in OPC/OL double these behavioral mutants (Figure S1F). Notably, changes occurred in the absence of overt myelin / oligodendrocyte deficits (Figure S1G), which were also not observed in the other conditional mutants (Berghoff et al., 2021; Fünfschilling et al., 2012). Next, we evaluated the impact of conditional loss of for squalene synthase cholesterol homeostasis by gene transcription profiling of cortex or subcortical white matter (corpus callosum) from the conditional cholesterol synthesis mutants and the cortex, conditional respective controls. inactivation of cholesterol synthesis in neurons or oligodendrocytes resulted in moderate upregulation of cholesterol synthesis genes, possibly to compensate for the loss of cholesterol synthesis in the affected cell type (Figure 1E, Table S2, S3). |
In contrast, in all conditional mutants we observed a moderate but consistent downregulation of expression related to cholesterol metabolism in white matter (Figure 1E-F, S1H). Here, reduced expression of genes associated with horizontal cholesterol transfer such as Abca1, Apoe and Lcat was noted in all conditional mutants, particularly in AcKO animals (Figure 1F). In agreement, sterol profiling revealed only moderate alteration in conditional mutants (Figure S2A). / cholesterol synthesis
In
Surprisingly, comparison of significant transcript changes in conditional mutants revealed a marked downregulation of genes related to the blood-brain barrier (BBB) in corpus callosum samples of OLcKO and NcKO mice. This was accompanied by upregulation of inflammatory mediators with profiles being unique to each mutant (Figure 1E-F). Interestingly, biochemical quantification of BBB permeability revealed that reduced tight junction gene expression was paralleled by increased CNS influx of the small molecular weight BBB tracer NaFl (376 Da) in OLcKO and NcKO brains. Perhaps surprisingly, given the role of astrocytes in BBB formation, this was not the case in AcKO animals (Figure 1F, S1D, SB-C). few
In summary, genetic elimination of cholesterol synthesis in oligodendrocytes, neurons and astrocytes leads to altered transcriptional expression of genes related to cholesterol metabolism in grey and white matter. These data confirm that all cell types contribute to cholesterol homeostasis in the adult brain by cell autonomous cholesterol synthesis. Of note, in cortex but also corpus callosum of neuronal Fdft1 mutants,
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. Fdft1 expression was significantly reduced and the abundance of cholesterol synthesis intermediates was attenuated (Figure 1E, S2A). This suggests axonal localization of cholesterol synthesis transcripts in vivo, contrary to neurons in compartmentalized culture (Vance et al., 2000). Myelin disease leads to increased cholesterol synthesis in neurons Experimental demyelination is associated with axonal pathology (Berghoff et al., 2017b; Nikic et al., 2011), and chronic loss of myelin in multiple sclerosis patients leads to persistent disabilities. Even subtle myelin defects can lead to axonal damage, myelin instability and glial activation, as observed in null mutants of the myelin-specific genes Plp1 (proteolipid protein 1) and Cnp1 (2',3'-cyclic-nucleotide 3'-phosphodiesterase) (Edgar et al., 2009; Edgar et al., 2004; Lappe-Siefke et al., 2003; Trevisiol et al., 2020). To assess neuronal responses to mild alterations in myelin integrity, we combined the well-characterized Plp1 and Cnp1 knockout mice with Thy1-EYFPnuc transgenes to label neuronal nuclei, predominantly of callosal projection neurons (CPN) (Wehr et al., 2006). |
Despite the axonal pathology, CPN loss was not a feature of Plp1 and Cnp1 mutants up to 12 months of age as quantified by EYFPnuc+ cell counting (Figure S2D). We then isolated CPN from cortical layer five by fluorescence- directed laser microdissection at various ages (1, 3, 6 and 12 month) for transcriptional profiling (Figure 2A). Neuronal identity of Thy1-EYFPnuc+ cells isolated from cortical layer five was verified by cell type-specific marker gene expression (Figure S2E). Transcriptional profiling revealed 412 differentially expressed genes in neurons from Cnp1 knockout mice and 104 genes from Plp1 knockout mice compared to Thy1-EYFPnuc controls p-val<0.001, Benjamin-Hochberg correction, at least 1.8-fold changed expression) (Figure S2F). Surprisingly, by gene set enrichment analysis (GSEA) the gene set “cholesterol metabolism” was upregulated in CPNs of both mutants (Figure 2B). This included genes involved in cholesterol synthesis (Hmgcr, Fdft1, Cyp51, Dhcr24) and transport (Ldlr, Apoe) (Figure 2C). (adj. followed by two weeks of cuprizone withdrawal, 12+2 weeks) (Figure 2D). During acute disease (EAE or 6 weeks cuprizone), neurons consistently downregulated gene expression related to cholesterol metabolism (Figure 2E). In contrast, during remyelination following chronic demyelination the cuprizone model, in expression of genes involved in cholesterol synthesis (Hmgcr, Fdft1, Dhcr24) and transport (Vldlr, Apoe) were increased (Figure 2E). To test whether the upregulation of cholesterol synthesis genes was functionally relevant, we determined the abundance of chronic cholesterols demyelination/remyelination paradigm. Cholesterol as well as several precursors of the cholesterol synthesis pathway were increased 4-5 fold in isolated neurons (Figure 2F), suggesting enhanced cholesterol synthesis in neurons during remyelination in this paradigm. by GC/MS
in
the
Increased cholesterol synthesis gene expression in neurons from MS patients We next determined whether increased neuronal expression of cholesterol synthesis genes is relevant in human MS and used single-nuclei gene expression profiles from MS patients and healthy control tissue from and studies GSE124335). We separately merged expression profiles of neurons, oligodendrocytes and astrocytes as annotated in each study (Figure 3A-B, S3A-C). Although the disease history of the MS tissue samples is unknown, we categorized MS samples in two subsets. One comprises the different stages of active MS lesions (termed “lesion”). The other subset (termed “non-lesion”) contains normal-appearing MS tissue that was derived from areas adjacent to active lesions. Neuronal nuclei contributed considerably to each of the MS subsets (3122 lesion, 3547 non-lesion). Next, we performed pairwise comparisons of expression profiles separately, in neurons, oligodendrocytes or astrocytes, focusing on cholesterol metabolism. two
recent
(GSE118257
Considering the possibility that neuronal upregulation of genes related to cholesterol metabolism is a general response to chronic myelin alterations, we analyzed transcriptional profiles of isolated cortical neurons autoimmune following encephalomyelitis (EAE) induction and following acute- phase (6 weeks cuprizone) and chronic-phase remyelination (chronic demyelination for 12 weeks
acute
experimental
As expected, lesion-derived astrocytes showed significantly reduced transcript levels of several genes related to cholesterol synthesis (HMGCR, FDFT1, DHCR7, DHCR24), while this gene set was not differentially regulated in non-lesion-derived astrocytes to astrocytes, both (Figure 3C). |
lesions, oligodendrocytes and neurons in MS increased expression of apolipoproteins including APOE, indicating active participation in local lipid transport in areas of active disease. Moreover, MS oligodendrocytes upregulated genes associated with cholesterol synthesis and metabolism, most markedly
In contrast
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. in lesions. This confirms the relevance of cholesterol availability for oligodendrocytes in myelin disease (Berghoff et al., 2017b; Berghoff et al., 2021; Voskuhl et al., 2019) and potentially reflects ongoing remyelination or attempts to remyelinate. Notably, neurons in MS lesions showed reduced transcript levels of genes associated with cholesterol synthesis including the rate-limiting enzyme of this process, HMGCR (Figure 3C). In contrast, in non-lesion MS tissue, neurons upregulated this gene set, suggesting increased neuronal cholesterol synthesis in normal- appearing MS tissue areas. Neuronal Fdft1 ablation following chronic cuprizone The contrasting expression of neuronal cholesterol synthesis genes in lesion versus non-lesion areas of MS brain and in acute versus chronic-phase remyelination in mouse models prompted us to test the importance of this finding for lesion repair. To explore whether loss of neuronal cholesterol synthesis affects remyelination efficiency, NcKO animals were challenged with acute and chronic demyelination paradigms using EAE and cuprizone. We evaluated disease (Gallyas), oligodendrocyte differentiation (CAII), number of oligodendrocyte linage cells (Olig2) and gliosis (GFAP, Iba1, MAC3). impairs remyelination
expression,
remyelination
I, J). Interestingly, cholesterol administration enhanced OPC proliferation and differentiation in myelinating co- cultures, but only OPC proliferation was impaired by abolishing neuronal activity (Figure 4K, S4H). Together, these findings raise the possibility that elevating neuronal cholesterol synthesis is essential for OPC proliferation and differentiation facilitate remyelination. to
Discussion Complete from demyelinating episodes and prevention of persistent disabilities is the ultimate goal of multiple sclerosis (MS) therapies. In addition to decreasing the rate of demyelinating events and dampening pathological inflammation, the support of remyelination has come into focus in MS drug development (Plemel et al., 2017). Repair following immune-mediated degeneration of oligodendrocytes and destruction of myelin involves the resolution of inflammation, OPC migration, proliferation and differentiation (Reich et al., 2018). Tissue regeneration is achieved by synthesis of lipid- and cholesterol-rich myelin membranes differentiated by oligodendrocytes and oligodendrocytes that survived (Franklin et al., 2020). the immune attack Remyelination contributes the to neuroprotection, restoration of impulse conduction and may facilitate (re)establishing neural circuits (Bacmeister et al., 2020). |
functional recovery
newly
As anticipated, loss of neuronal cholesterol synthesis did not affect acute-phase remyelination in cuprizone treated mice (Figure 4A-B, S4A-C, Video1) or pathology immune mediated myelin degeneration (Figure 4C-E). However, after cuprizone- induced chronic demyelination, we observed reduced oligodendrocyte density and impaired remyelination in both the corpus callosum and cortex of NcKO animals compared to controls (Figure 4F-H, S4A-C). Defective repair of chronically demyelinated lesions in NcKO animals occurred without affecting gliosis, neuronal degeneration (NeuN+ cell number, Fluorojade, TUNEL) or axonal stress (APP+ spheroids) (Figure S4D-F). The degree of sustained hypomyelination in NcKO animals was comparable to mutants with inactivated cholesterol synthesis in OPCs (NcKO 53±5% of controls, OPCcKO 55±3%; Figure 4I). Further, displayed comparable defects in motor performance after chronic cuprizone administration (Figure S4G). However, in contrast to oligodendroglial mutants that showed normal OPC densities, the loss of neuronal cholesterol synthesis caused a reduction of Olig2/PCNA+ proliferating OPCs in the corpus callosum (Figure 4G,
following
both
conditional mutants
Disparate repair processes during acute and chronic myelin disease With respect to lipid metabolism, repair after an acute demyelinating episode differs markedly from repair in chronic myelin disease or after repeated demyelinating events. Tissue remodeling and repair after an acute demyelinating by microglial/macrophage activation and lipid recycling (Berghoff et al., 2021; Cunha et al., 2020; Miron et al., 2013). Correspondingly, acute-phase remyelination is independent of squalene synthase / Fdft1 inactivation in oligodendrocytes, OPCs, astrocytes, or neurons (this study and Berghoff et al., 2021). attack
is
coordinated
In chronic myelin disease, myelin debris is largely cleared from demyelinated lesions. Correspondingly, in chronically demyelinated lesions in cuprizone-treated mice (Berghoff et al., 2017b) and in chronically inactive (Hess et al., 2020) lesions predominantly foamy microglia/macrophages remain. This suggests that lipid recycling by microglia could be inefficient in chronically demyelinated lesions. These lipid trafficking defects in microglia could not only impede remyelination but also
in MS patients
lipid-laden
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. aggravate axonal damage, as observed in TREM2 mutants (Cantoni et al., 2015). As cholesterol is essential for myelin formation (Saher et al., 2005), these findings underscore the necessity of local de novo synthesis. This is supported by the observation of cholesterol synthesis blocks remyelination (Miron et al., 2009). However, astrocytes, which provide cholesterol in the healthy brain, fail as a local cholesterol source in myelin disease as they strongly downregulate its synthesis both in mouse models (Berghoff et al., 2021; Borggrewe et al., 2021; Itoh et al., 2018) and MS lesions (this study). |
We hypothesize that chronic myelin disease depletes neuronal and oligodendroglial cholesterol levels, which triggers cell-autonomous cholesterol synthesis by In agreement, the cholesterol for remyelination originates at from de novo oligodendroglial synthesis (Berghoff et al., 2021; Jurevics et al., 2002; Voskuhl et al., 2019). The that dietary cholesterol supplementation also supports myelin repair (Berghoff et al., 2017b; Saher et al., 2012) suggests that endogenous cholesterol synthesis is insufficient for complete remyelination. In the current study, we provide evidence that neuronal cholesterol synthesis repair of chronically for demyelinated lesions. that
statin-mediated
inhibition
feedback regulation. least partially
finding
is essential
Neuronal remyelination Following chronic demyelination, we found impaired remyelination in both white and grey matter of animals lacking neuronal cholesterol synthesis. This is in agreement with the increased neuronal expression of cholesterol synthesis genes in human non-lesion MS tissue experimental demyelination. In neuronal mutants of cholesterol synthesis, but not in corresponding oligodendroglial mutants, we showed a marked reduction in the density of oligodendrocyte lineage cells. This finding points to an that precedes myelin membrane synthesis, likely in OPC proliferation and oligodendrocyte differentiation. cholesterol
synthesis
during
chronic
following
and
inference with
repair
What is the mechanism by which regeneration of chronically demyelinated white matter tracts such as the corpus callosum benefits from neuronal cholesterol synthesis? Neuronal electrical activity triggers OPC proliferation and oligodendrocyte differentiation during development and after demyelination through unknown signals (Demerens et al., 1996; Marisca et al., 2020; Mitew et al., 2018; Ortiz et al., 2019). The hyperactivity of cortical neurons observed after acute demyelination
(Bacmeister et al., 2020) could offset conduction deficits of demyelinated white matter tracts (Crawford et al., 2009). This could lead to synaptic vesicle release from callosal axons (Almeida et al., 2020; Pfeiffer et al., 2019) and provide the endogenous signal to white matter OPCs to proliferate and initiate repair. We observed that neuronal cholesterol plays a role in this process. In cultured OPCs, short term pharmacological induces OPC inhibition of cholesterol synthesis differentiation (Miron et al., 2007). It is possible that reducing cellular cholesterol levels in OPCs decreases input via the probability of neurotransmitter channels (Korinek et al., 2020). In agreement, we showed that administration of cholesterol facilitates OPC proliferation (this study). However, OPC proliferation was amplified only, when cholesterol was supplied in the context of neuronal activity. It is possible that neurotransmitter release release of neuronal occurs concomitant with to prevent cholesterol. This could be a means (premature) OPC differentiation and to generate sufficient numbers of oligodendrocyte lineage cells to accomplish repair. |
receiving neuronal
In addition, cholesterol-depleted denuded axons as in chronic lesions of NcKO mice are likely more fragile as suggested from increased plasma membrane tether forces of cholesterol synthesis mutant neurons (Fünfschilling et al., 2012). Especially when electrically hyperactive, impaired stability of axonal membranes could increase axon damage and the probability of conduction blocks. Moreover, cholesterol is essential for the biogenesis and exocytosis of synaptic vesicles (Linetti et al., 2010; Thiele et al., 2000). This is that cholesterol the observation compatible with synthesis reduced show spontaneous activity in culture (Fünfschilling et al., 2012). deficient
neurons
Several studies have highlighted the importance of cholesterol availability for developmental OPC proliferation, oligodendrocyte differentiation and myelin membrane synthesis (Mathews and Appel, 2016; Saher et al., 2012; Zhao et al., 2016). The finding that administration of dietary cholesterol during chronic- phase the density of proliferating OPCs (Berghoff et al., 2017b) suggests that the entire oligodendrocyte lineage can benefit from externally administered cholesterol. It is possible that neurons increase cholesterol production not only to fulfill their own cholesterol demands but also to support oligodendrocytes Indeed, cholesterol synthesis in callosal axons would position the lipid optimally to supply proliferating OPCs and
remyelination
increases
to synthesize myelin. bioRxiv preprint
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. for newly remyelination. This suggestion is reinforced by the observation that electrically hyperactive neurons in demyelinated lesions release lipids as ApoE-containing lipoproteins (Ioannou et al., 2019; Xu et al., 2006). Our data show that increased expression of neuronal cholesterol synthesis genes is paralleled by strongly elevated expression of ApoE. Thus, following chronic demyelination, neurons could export cholesterol via ApoE to support myelination by oligodendrocytes in a lipid-poor environment. Although we have not measured neuronal activity in demyelinated conditional mutants, we speculate that Fdft1 mutant neurons produce less activity-dependent pro-repair signals to local OPCs than controls. differentiating
oligodendrocytes
Taken together, our data show that loss of neuronal cholesterol synthesis strongly impairs remyelination with relevance for human MS disease. Our study confirms distinct cell type-specific roles in brain cholesterol biogenesis and import during remyelination and provides an additional explanation for disease progression related to age-associated decline of cholesterol synthesis (Berghoff et al., 2021; Scalfari, 2019; Thelen et al., 2006). Further studies are needed to design that stimulate cholesterol synthesis in affected neuronal populations. |
therapeutic strategies
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. Figure 1. Loss of cholesterol synthesis in oligodendrocytes, astrocytes and neurons (A) Scheme depicting MACS isolation of neurons, astrocytes and oligodendrocytes from the indicated brain region. (B) Gene expression profile of isolated neurons (N), oligodendrocytes (OL) and astrocytes (A) from adult wild type animals (* Berghoff et al., 2021). (C) Scheme depicting isolation of tissue samples from oligodendrocyte (Plp1-CreERT2), astrocyte (GLAST::CreERT2) and neuronal (CaMKII-Cre) cholesterol synthesis deficient (Fdft1fl/fl) animals (left) from boxed brain regions for expression analysis. (D) Open field test of OLcKO (n=14), AcKO (n=9) and NcKO (n=8-11) animals compared to corresponding controls (n=10-15) in the center (two-sided Student’s t- test). (E) Expression profile of genes related to cholesterol metabolism, inflammation, blood-brain barrier and cellular identity in indicated CNS tissues of cell type-specific cholesterol synthesis deficient animals. Heat maps show mean fold expression of biological replicates (n=4-7) normalized to controls (two-sided Student’s t-test). (F) Venn diagram of downregulated genes in corpus callosum of animals in (E). (G) Extravasated Evans Blue (EB) and sodium fluorescein (NaFl) in conditional Fdft1 mutants in oligodendrocytes (OLcKO, n=5), astrocytes (AcKO, n=5) and neurons (NcKO, n=4) compared to corresponding controls (n=4; two-sided Student’s t-test). ***p<0.001, **p<0.01, *p<0.05
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. Figure 2. Expression of genes related to cholesterol metabolism in neurons of genetic and experimental myelin disease models (A) Representative fluorescent micrographs depicting the isolation of EYFPnuc+ callosal projection neurons (CPN) from the primary motor and somatosensory cortex (yellow line) of PLP-KO and CNP-KO mutants (scale 200 µm). Insets show the tissue section before and after laser microdissection, and isolated neurons (scale 20 µm). (B) Selected gene sets in microdissected neurons from PLP-KO and CNP-KO mutants compared to controls (1, 3, 6, 12 months of age). Significantly up-regulated and down-regulated gene sets (P-val<0.05) are indicated in red and blue, respectively. (C) Gene expression profile of genes related to cholesterol metabolism in callosal projection neurons from PLP-KO and CNP- KO mutants at 6 month of age. Heat maps show fold expression of biological replicates (n=3) normalized to controls (Table S5). (D) Time points of analysis related to the course of demyelination/remyelination in the cuprizone model and the clinical score of EAE-induced animals analyzed in (E). |
(E) Gene expression profile of genes related to cholesterol metabolism in isolated neurons following acute (6 weeks) and chronic (12w+2w) cuprizone challenge (left) and following EAE (right). Heat maps show fold expression normalized to controls (Table S6-S7). Each square represents an individual animal (n=3-4). (F) Cholesterol synthesis pathway with major enzymes and sterol intermediates. Mean relative abundance of sterol intermediates in isolated neurons from chronic cuprizone-treated mice (n=4) compared to untreated controls (n=3), measured by GC-MS (two-sided Student’s t-test). bioRxiv preprint
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. Figure 3. Gene expression related to cholesterol metabolism in neurons, oligodendrocytes and astrocytes from patients with MS (A) UMAP (Uniform Manifold Approximation and Projection) of neurons, oligodendrocytes and astrocytes from human MS snRNAseq datasets according to dataset (GSE118257, GSE124335). (B) UMAP projection of neurons, oligodendrocytes and astrocytes from human MS snRNAseq datasets according to patient samples identity (GSE118257, GSE124335). (C) Heat map of mean gene expression related to cholesterol metabolism in cellular subsets comparing control and MS (lesion and non-lesion) samples. Data represent log2fold changes (logFC) and p-value (Wilcoxon Rank Sum test, two sided). bioRxiv preprint
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. Figure 4. Neuronal Fdft1 ablation impairs remyelination following chronic cuprizone (A-B) Repair efficiency and gliosis in the corpus callosum (A) and cortex (B) during acute cuprizone (6 weeks) in NcKO (n=4 animals) compared to controls (n=4, set to 100%) based on histochemical stainings for myelin (Gallyas), oligodendrocytes (CAII), oligodendrocyte lineage cells (Olig2), microgliosis (MAC3) and astrogliosis (GFAP), shown as 95% confidence ellipses with individual data points. (C) Mean clinical EAE score ± SEM of control and NcKO mice (n=11). (D) Flow cytometric quantification of inflammatory cells of EAE animals in (C, n=5). (E) Representative light sheet microcopy with quantification of lumbar spinal cord from NcKO and controls 35d after EAE induction, stained for Iba1+ phagocytes (n=3). (F) Representative micrographs of the corpus callosum of control and NcKO animals following chronic cuprizone challenge (12w+2w) illustrating myelination (Gallyas), oligodendrocytes (CAII), and oligodendrocyte lineage cells (Olig2). (G-H) Repair efficiency and gliosis in the corpus callosum (G) and cortex (H) during chronic cuprizone (12w+2w) in NcKO mice compared to controls (n=4, set to 100%). |
(I) Repair efficiency in the corpus callosum during chronic cuprizone (12w+2w) in OPC cholesterol mutants (OPCcKO, n=7) compared to controls (n=4, set to 100%). (J) Representative micrographs of Olig2/PCNA double labeling in the corpus callosum with quantification of NcKO (n=3) and OPCcKO (n=7) mutants compared to controls (n=4) following chronic remyelination (12w+2w; two-sided Student’s t-test). **p<0.01, *p<0.05, scales 50 µm, 1 mm (E). (K) Mean OPC proliferation (NG2+, BrdU+) and oligodendrocyte differentiation (MBP+) in spinal cord cultures at 17 days in vitro (n=16-31 images from 2-3 cultures) in the presence of cholesterol (10 µg/ml) with or without inhibition of neuronal activity by TTX (1µM). Data show the mean number of NG2+/BrdU+ positive cells normalized to DAPI+ cell density and the mean MBP-positive area with individual values (one-way ANOVA with Sidak’s post-test; Scale 50 µm). bioRxiv preprint
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Animals All animal studies were performed in compliance with the animal policies of the Max Planck Institute of Experimental Medicine, and were approved by the German Federal State of Lower Saxony. Animals were group-housed (3-5 mice) with 12 hour dark/light cycle and had access to food and water ad libitum. Adult male and female C57BL/6N mice (8-10 weeks of age) or cholesterol synthesis mutants (8–10 weeks of age) were taken for all experiments. Male mice were subjected to cuprizone experiments. Female mice were used for non-induced pathology experiments. Animals randomly assigned of same gender were to (3-12 mice). Cholesterol experimental groups synthesis mutants in this study were generated by crossbreeding cell type-specific Cre-driver lines (see Key Resources table) with mice harboring squalene synthase floxed mice (Fdft1flox/flox). Conditional mutants were compared with the respective Cre or homozygous floxed controls, i.e. CaMKII-Cre::Fdft1flox/flox mutants and Fdft1flox/flox controls, Plp1-CreERT2::Fdft1flox/flox mutants controls, Cspg4/NG2CreERT2/+::Fdft1flox/flox and Cspg4/NG2CreERT2/+ controls, GLASTCreERT2/+::Fdft1flox/flox mutants and GLASTCreERT2/+ Cspg4/NG2CreERT2/+::Plp1- controls, CreERT2::Fdft1flox/flox Plp1- and CreERT2::Fdft1flox/flox and Fdft1flox/flox controls. Cnp null and Plp1 null mice were crossbreed to Thy1-EYFPnuc mice to generate CNP mutants (TYNC +/-, Cnp -/-, Plp1 +/y) and PLP mutants (TYNC +/-, Cnp +/+, Plp1 -/y) that were compared with TYNC +/- mice. Fdft1flox/flox
and
mutants
Tamoxifen induced recombination Transgenic mice received tamoxifen either by oral administration, three times every second day at a concentration of 0.4 mg/g body weight dissolved in corn oil:ethanol (1:9) or by intraperitoneal injections on 5 consecutive days at a concentration of 75 μg/g body weight. |
within 15 days after induction or the clinical score rose above 4, animals were excluded from the analysis. The clinical score was: 0 normal; 0.5 loss of tail tip tone; 1 loss of tail tone; 1.5 ataxia, mild walking deficits (slip off the grid); 2 mild hind limb weakness, severe gait ataxia, twist of the tail causes rotation of the whole body; 2.5 moderate hind limb weakness, cannot grip the grid with hind paw, but able to stay on a upright tilted grid; 3 mild paraparesis, falls down from a upright tiled grid; 3.5 paraparesis of hind limbs (legs strongly affected, but move clearly); 4 paralysis of hind limbs, weakness in forelimbs; 4.5 forelimbs paralyzed; 5 moribund/dead. Cuprizone Cuprizone pathology was induced by feeding mice with 0.2% w/w cuprizone (Sigma-Aldrich) in powder chow. Mice received cuprizone for ‘acute remyelination’ (6 weeks) and ‘chronic remyelination’ (12 weeks followed by 2 weeks normal chow) paradigms. Chow was replaced three times a week. Age-matched untreated controls were fed powder chow without cuprizone. Serum Analysis Blood was collected by cardiac puncture, and serum was prepared after 4h clotting by centrifugation. Cholesterol measurements were done with the Architect II system (Abbott Diagnostics). Open field Exploratory activity in a novel environment was tested in an open field chamber (50x50x50 cm) at 20 lux light intensity. Individual female mice at the age of 22 weeks were placed into left bottom corner of the open field chamber. The exploratory behavior of the mouse was recorded for 10 min using an overhead camera system and scored automatically using the Viewer software (Biobserve, St. Augustin, Germany). The overall traveled distance was analyzed as a parameter of general activity. Time, distance and visits in the center area (25x25 cm) was analyzed to measure behavior related to anxiety. Results were normalized to the mean of corresponding control animals and statistically analyzed using one-way ANOVA with Sidak’s post-test. Experimental (EAE) immunizing induced MOG-EAE subcutaneously with 200 mg myelin oligodendrocyte glycoprotein peptide 35–55 (MOG35–55) in complete Freund’s adjuvant (M. tuberculosis at 3.75 mg ml-1) and i.p. injection twice with 500 ng pertussis toxin as described (Berghoff et al., 2017b; Berghoff et al., 2021). Animals were examined daily and scored for clinical signs of the disease. If disease did not start
autoimmune
encephalomyelitis
was
by
Blood-brain barrier permeability Measurements of BBB permeability were done as described (Berghoff et al., 2017a). Tracers were i.v. injected (Evans Blue 50 mg/g body weight, sodium fluorescein 200 mg/g body weight). Animals were flushed with PBS. Brain samples were isolated, weighed, lyophilized at a shelf temperature of –56 °C for 24h under vacuum of 0.2 mBar (Christ LMC-1 BETA 1-16), and extracted with formamide at 57°C for 24h on
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All rights reserved. No reuse allowed without permission. a shaker at 300 rpm. Integrated density of tracer fluorescence was determined in triplicates after 1:3 ethanol dilutions increase sensitivity. Tracer concentration was calculated using a standard curve prepared from tracer spiked brain samples. to
primers (Table S1) were designed to fulfill optimal criteria e.g. length (18-22 bp), melting temperature (52- 58°C), GC content (40-60%), low number of repeats, and amplicon length (<220 bp). All primers were intron- spanning. Flow cytometry Single-cell suspensions from spinal cord were obtained via mechanical dissociation on a cell strainer. Immune cells were separated over a two-phase Percoll-density gradient by centrifugation. Staining of CD4+ T cells, cells CD8+ (macrophages/microglia) was performed using the following antibodies in a 1:200 dilution: anti-CD3e (clone 145-2C11, BioLegend), anti-CD4 (clone GK 1.5, BD), anti-CD8 (clone 53-6.7, BD), anti-CD11b (clone M1/70, BioLegend), 104, BioLegend). The addition of CaliBRITE APC beads (BD) allowed for cell quantification. Flow cytometry was performed using a CytoFLEX S (Beckman Coulter) operated by CytExpert software (Beckman Coulter, v2.4). T
cells
and
CD45/CD11b+
anti-CD45.2
(clone
Magnetic cell isolation (MACS). Glial cells and neurons were isolated according to the adult brain dissociation protocol (Miltenyi biotec) form corpus callosum and/or cortex. Antibody labeling was done according to the Microbead kit protocols (Miltenyi biotec) for oligodendrocytes (O4) or astrocytes (ACSA- 2). Neurons were isolated by negative selection. Purity of cell populations was routinely determined by RT- qPCR on extracted and reverse transcribed RNA. Expression analyses For expression analyses of tissue samples, mice were killed by cervical dislocation. Samples were quickly cooled and region of interest prepared. RNA was extracted using RNeasy Mini kit (Qiagen). cDNA was (Invitrogen). synthesized with Superscript Concentration and quality of RNA was evaluated using a NanoDrop spectrophotometer and RNA Nano (Agilent). RNA from MACS-purified cells was extracted using QIAshredder and RNeasy protocols (Qiagen). cDNA was amplified by Single Primer Isothermal Amplification (Ribo-SPIA® technology) using Ovation PicoSL WTA System V2 (NuGEN) following the manufactures protocol. Quantitative PCRs were done in triplicates using the GoTaq qPCR Master Mix (Promega, A6002) and the LightCycler 480 Instrument (Roche Diagnostics). Expression values were normalized to the mean of housekeeping genes. Quantification was done by applying the ΔΔCt method, normalized to experimental controls (set to 1). All
III
Histochemistry Mice were perfused with 4% formaldehyde (PFA). In case of cuprizone treated animals, brain samples were cut at Bregma 1.58 to account for regional specificity of cuprizone pathology. Tissue was postfixed overnight, embedded in paraffin and cut into 5 µm sections (HMP 110, MICROM). For Gallyas silver impregnation, deparaffinized sections were incubated with a 2:1 mixture of pyridine and acetic anhydride for 30 min at room temperature (RT) to minimize background and increase myelin. |
Tissue was washed with ddH20, following heating in incubation solution (0.1% [w/v] ammonium nitrate, 0.1% [w/v] silver nitrate, 12‰ [w/v] sodium hydroxide pH 7.5) for 1 min (100 W) and further incubation for 10 min at RT. After washing with 0.5% [v/v] acetic acid three times for 5 min, sections were incubated in developer solution for 3-10 min. For reconstitution of the developer, 70 ml of solution B (0.2% [w/v] ammonium nitrate, 0.2% [w/v] silver nitrate, 1% [w/v] wolframosilicic acid) was added to 100 ml of solution A (5% [w/v] sodium carbonate) with constant and gentle shaking and then slowly added to 30ml solution C (0.2% [w/v] ammonium nitrate, 0.2% [w/v] silver nitrate, 1% [w/v] wolframosilicic acid, 0.26% [w/v] PFA). The reaction was stopped and fixed by washing in 1.0% [v/v] acetic acid and 2% [v/v] sodium thiosulfate. Tissue was dehydrated and mounted using Eukitt. For detection of apoptotic cells, a TUNEL assay was done according to the manufacturer (Promega G7130). Fluoro-Jade C staining (Sigma, AG 325) was done according to the manufacturers’ instructions. Immunohistological on deparaffinized sections followed by antigen-retrieval in sodium citrate buffer (0.01 M, pH 6.0). For chromogenic stainings, blocking of endogenous peroxidase activity with 3% hydrogen peroxide was performed followed by 20% goat serum block and incubation with primary antibodies. Detection was carried out with the LSAB2 System-HRP (anti-rabbit/mouse LSAB2 Kit Dako Cat#K0679, dilution 1:100) or the VECTASTAIN Elite ABC HRP Kit (Vector Labs, Anti-Rat IgG Vector Cat#BA-9400, dilution 1:100). HRP substrate 3,30- diaminobenzidine (DAB) was applied by using the DAB Zytomed Kit (Zytomed Systems GmbH). Nuclear labeling was done by hematoxylin stain. For immunofluorescence blocking was performed with serum-free protein block (Dako). stainings were
done
detection,
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. Primary antibodies were diluted in 2% bovine serum albumin (BSA)/PBS and incubated for 48 h followed by incubation with secondary antibodies (Alexa488 donkey anti-mouse Invitrogen Cat #A-21202, dilution 1:1000; Alexa488 donkey anti- rabbit Invitrogen Cat #A-21206,dilution 1:1000; Alexa555 donkey anti-rabbit Invitrogen Cat #A-31572, dilution 1:1000). Stained sections were analyzed on an Axio Imager.Z1 (Zeiss) equipped with an AxioCam MRc3, x0.63 Camera Adaptor and the ZEN 2012 blue edition software using 10x objective (Plan Apochromat x10/0.45 M27) or 20x objective (Plan-Apochromat x20/0.8) and evaluated with Image J software. Quantification of areas (Gallyas, GFAP, MAC3) were done by applying semi-automated ImageJ software macro including thresholding and color deconvolution. Two to four sections per animal were analyzed. fluorophore-coupled
Quantification of sterols lipid gas Sterol abundance was quantified by chromatography coupled to mass spectrometry (GC- MS) in acutely isolated neurons and tissue samples (4- 5 animals grouped for each replicate). |
Samples were lyophilized at a shelf temperature of –56 °C for 24 h under vacuum of 0.2 millibars (Christ LMC-1 BETA 1- 16) and weighed for the calculation of water content and normalization. Metabolites were extracted in a two- phase system of 3:1 methyl-tert-butyl ether:methanol (vol/vol) and water, and pentadecanoic acid was added as an internal standard. The organic phase (10–200 μl) was dried under a stream of nitrogen, dissolved in 10– 15 μl pyridine and derivatized with twice the volume of N-methyl-N-(trimethylsilyl) trifluoroacetamide (MSTFA) to transform the sterols and the standard to their trimethylsilyl (TMS) derivatives. Each sample was analyzed to quantify cholesterol and with a lower split to measure all other sterols. The samples were analyzed on an Agilent 5977N mass-selective detector connected to an Agilent 7890B gas chromatograph equipped with a capillary HP5-MS column (30 m × 0.25 mm; 0.25-μm coating thickness; J&W Scientific, Agilent). Helium was used as a carrier gas (1 ml/min). The inlet temperature was set to 280 °C, and the temperature gradient applied was 180°C for 1 min, 180–320°C at 5 K min–1 and 320°C for 5 min. Electron energy of 70 eV, an ion source temperature of 230 °C and a transfer line temperature of 280°C were used. Spectra were recorded in the range of 70–600 Da/e (ChemStation Software D.01.02.16). Sterols were identified by the use of external standards. twice, with a higher split
Light sheet microscopy PFA immersion fixed spinal cord segments were processed for whole mount immune-labelling and tissue clearing following a modified iDISCO protocol (Berghoff et al., 2021). Briefly, samples were dehydrated in ascending methanol (MeOH)/PBS series followed by overnight bleaching /permeabilization in a mix of 5% H2O2/20% DMSO/MeOH at 4°C. Samples were further washed in MeOH and incubated in 20% DMSO/MeOH at RT for 2h. Then, samples were rehydrated using a descending methanol/PBS series and further washed with in PBS/0.2% TritonX-100 for 2h. The samples were then incubated overnight in 0.2% TritonX-100, 20% DMSO, and 0.3 M glycine in PBS at 37°C and blocked using PBS containing 6% goat serum, 10% DMSO and 0.2% Triton-X100 for 2 days at 37°C. Samples were retrieved, washed twice in PBS containing 0.2% Tween20 and 10µg/ml heparin (PTwH) and incubated with primary antibody solution (Iba1 1:500; PTwH/5%DMSO/3% goat serum) for 7 days at 37°C. After several washes, samples were incubated with secondary antibody solution (1:500 in PTwH/3% goat serum) for 4 days at 37°C. Prior to clearing, the samples were washed in PTwH and embedded in 2% Phytagel (Sigma Aldrich #P8169) in water. The embedded tissue was then dehydrated using an ascending series of Methanol/PBS and incubated overnight incubation in a mixture of 33% dichloromethan (DCM) and 66% MeOH at RT. Samples were further delipidated by incubation in 100% DCM for 40min and transferred to pure ethyl cinnamate (Eci; Sigma Aldrich #112372) as clearing reagent. Tissues became transparent after 15min in Eci and were stored at RT until imaging. |
Light sheet microscopy was performed using a LaVision Ultramicroscope II equipped with 2x objective, corrected dipping cap and zoom body. Spinal cords were mounted onto the sample holder with the dorsal/ventral axis facing down (z imaging axis = dorsoventral axis spinal cord). The holder was placed into the imaging chamber filled with Eci. Images were acquired in 3D multicolour mode with the following specifications: 5µm sheet thickness; 40% sheet width; 2x zoom; 4µm z-step size; one site sheet illumination; 100ms camera exposure time; full field of view. Autofluorescence was recorded using 488nm laser excitation (80% laser power) and a 525/40 emmision filter and red fluorescence was recorded using 561nm laser excitation (30% laser power) and 585/40 emission filters. Images were loaded into Vision4D 3.0 (Arivis) and the image set was cropped to 500 - 2000 pixels corresponding to 2.2 mm of spinal cord length. The volume of the spinal cord was determined by performing an automatic intensity thresholding on the
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. autofluorescence channel. Phagocytes were detected by running a manual intensity thresholding on the 561nm channel and Iba1 cell accumulation with a volume of <1000µm3 was considered lesion positive. Then total lesion volume as well as the lesion volume fraction in respect to the total spinal cord volume were calculated. For 3D rendering, the autofluorescence and Iba1 channel were depicted in green and red pseudocolor, respectively. High-resolution images as well as videos were created using the Arivis 4D viewer. Laser capture microdissection Serial cryostat coronal brain sections at the level of Bregma 1 mm to 0.5 mm were prepared (Leica) for single cell isolation). 700 and 800 EYFP+ neurons for each individual sample were microdissected (Arcturus Veritas microdissection system with fluorescence package) from the motor and somatosensory cortex and captured in HS Transfer Cap (Molecular Devices). Cells were only collected if no adjacent nuclei were detected in close proximity. Successful cutting and collection steps were subsequently validated in bright- field and fluorescent mode on the quality control slot of the device. Microdissected cells were lysed in 100 µl of RNA lysis buffer (Qiagen, Hilden, Germany) and stored at -80°C until further use. All procedures were done under RNase-free conditions. Microarray expression analysis Total RNA of pooled single cells was resuspended with pretested T7-tagged dT21V oligonucleotides. Two- round linear amplification was performed according to optimized protocols for low-input RNA amounts (Small Sample Target Labeling Assay Version II, Affymetrix). Biotin- labeled second-round aRNA was generated with an NTP-mix containing Biotin-11-CTP and Biotin-16-UTP (PerkinElmer, Boston, MA) at 2 mM. |
Biotin-labeled amplified RNA (aRNA) size distribution and quantity was analyzed with the Agilent 2100 Bioanalyser using the RNA 6000 Nano LabChip kit (Agilent Technologies, lower size Boeblingen, Germany). Samples with compressed RNA products were discarded. At least 5 µg of labeled cRNA was fragmented by heating the sample to 95°C for 35 min in a volume of 20 µl containing 40 mM Tris acetate pH 8.1, 100 mM KOAc, and 30 mM MgOAc. Fragmentation was checked by alkaline agarose electrophoresis. Hybridization, washing, staining, and scanning were performed under standard conditions as described by the manufacturer. Mouse430A 2.0 genechips were used that contain over 22,600 probe sets representing transcripts and variants from over 14,000 mouse genes. Microarray raw data
T7-RNA
polymerase-mediated
were exported using Gene chip operating software (Affymetrix). Normalization and higher-level analysis were done in R (for packages see Key Resources table). Normalization was carried out using the Robust Multichip Average (RMA) model implemented in the R package Affy at default settings. The normalized microarray data was quality controlled (box-plot analysis, principal component analysis, and Spearman correlation tree) which led to the exclusion of two microarrays. The remaining data were re-normalized, log filtered based on absolute expression values (100 fold changed signal intensity cutoff). Probe sets with a fold change higher than 1.5 were included in further analysis for single gene analysis. A fold change threshold of 1.3 was applied for level analysis using gene set further pathway enrichment (GSEA; www.broadinstitute.org/gsea/). GSEA was performed with 5214 different gene sets obtained from Molecular Signature Database (MSigDB) at the Broad Institute (MIT). transformed and
analysis
Human single-nuclei transcriptome sequencing datasets Human single-nuclei RNA sequencing profiles were obtained from two available datasets, GSE118257 (Jäkel et al. 2019) and GSE124335 (Schirmer et al. 2019), and re-analyzed by R package Seurat v3.2.3. Both datasets were filtered and embedded according to parameters of original publications. Annotations of neurons, oligodendrocytes, and astrocytes were confirmed using marker gene expression of the different cell types (Figure S3). Subsequently, gene counts from neuron, oligodendrocyte and astrocyte subsets from both datasets were merged by applying Canonical Correlation Analysis (CCA) integration method. Uniform Manifold Approximation and Projection (UMAP) was used to visualize cell merging results. For each cell type, pairwise comparisons (MS lesion versus control and MS non-lesion versus control) of expression of genes related to cholesterol synthesis and metabolism were computed using normalized gene counts by Model-based Analysis of Single-cell Transcriptomics (MAST) R package v.1.12.0. Heatmap visualization was computed using R package pheatmap v.1.0.12 (Pretty Heatmaps). Spinal cord co-cultures Spinal cord co-cultures were established as described (Bijland et al., 2019) from embryonic day 13 mouse embryos. |
Cells were plated initially in 12.5 % horse serum and fed the following day and every second or third day thereafter with serum-free differentiation
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(which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. medium. On day in vitro (DIV) 14 (before myelination commences around DIV 17), cultures were treated with cholesterol (10 µg/ml), cholesterol and tetrodotoxin (TTX) (1µM, Tocris), or 0.1% ethanol (vehicle control) for 3 days. On DIV 17, bromodeoxyuridine (BrdU; 10 µM) was added to the cultures for 2 hours. Cultures were fixed with PFA and washed in PBS. Cells were permeabilized for 10 minutes in 0.5% Triton X in PBS and incubated for 48 hours at 4°C in rabbit anti-NG2 (AB5320, Merck Millipore; 1:500) and rat anti-MBP (MCA409, Biorad, 1:500) in 10 % goat serum, 1 % bovine serum albumin in PBS. Following application of Alexa 596 anti-rabbit IgG and Alexa 488 anti-rat IgG (Invitrogen, 1:1000 for 1 hour), cells were fixed in 50:50 acetic acid and ethanol for 10 minutes and DNA was denatured in 2M HCl for 30 minutes. Then anti-BrdU (MCA2483T, Biorad; 1:500) was added in blocking buffer and incubated overnight. Alexa 647 anti-mouse IgG1 (Invitrogen, 1:1000) was added for ~1 hour at room temperature and coverslips were mounted in Mowiol with DAPI (2.5 µg/ml). 10 predefined locations were selected in the DAPI channel, and images were captured at 10x magnification using a Zeiss Axio Imager M.2 with an AxioCam MRm. Analysis of MBP positive area was performed by automated thresholding (Triangle, Image J). Quantification of the number of NG2 and BrdU double positive cells was done on binarized images and normalized to the DAPI- positive cell density with the particle analyzer plugin (Image J). Whole cell current clamp and microelectrode arrays Whole cell patch clamp recording was performed on DIV 21 cultures using an Axopatch 200B amplifier with a Digidata 1440A digital acquisition system and pClamp 10 software (Molecular Devices). Experiments were performed at 37°C in atmospheric air using an extracellular solution containing (in mM): 144 NaCl, 5.3 KCl, 2.5 CaCl2, 1 MgCl2, 10 HEPES, 10 mM glucose, pH 7.4. The pipette solution contained (in mM): 130 mM K+ gluconate, 4 mM NaCl, 0.5 mM CaCl2, 10 mM HEPES, 0.5 EGTA pH 7.2. Borosilicate glass pipettes were pulled to a resistance of 3-8 MΩ. Liquid junction potentials were measured as 20 mV and traces were offset by this value. For microelectrode arrays, cultures were plated and maintained on commercial MEAs (60MEA200/30iR-Ti-gr; Multi Channel Systems, Reutlingen, Germany) as described previously (Bijland fluorinated ethylene-propylene et al., 2019). A membrane (ALA MEA-MEM-SHEET) sealed the MEA culture dishes. The in differentiation medium. Signals were digitally filtered at
recordings were done
3 Hz high pass filter, 1 kHz low pass filter and amplified up to x20,000. |
A digital notch filter was used to remove 60 Hz noise during recording. For data acquisition and analysis, spikes and potentials were sorted and counted from 3-minute gap-free recordings using the pCLAMP10 software (Molecular Devices Corporation, California, USA). QUANTIFICATION AND STATISTICAL ANALYSIS Number of animals for each experiment is provided in the figure legends. No statistical methods were used to pre-determine sample sizes but our sample sizes are similar to those reported in previous publications (Berghoff et al., 2021). No inclusion or exclusion criteria were used if not otherwise stated. Studies were conducted blinded to investigators and/or formally randomized. Data are expressed as mean ± SEM unless otherwise indicated. For statistical analysis, unpaired two-sided Student’s t-test, one-way ANOVA or two-way ANOVA with Sidak’s or Tukey’s post tests were applied. Normality was tested by using the Kolmogorov-Smirnov test. If the n was below 5, we assumed normal distribution. "Signal-to-Noise ratio" (SNR) statistics were used to rank genes for GSEA of microarray data. Linear model fitting and subsequent testing for differential expression by empirical Bayes in R variance moderation method packaged limma v3.42.2 was applied to the 6-month neuron microarray data. Wilcoxon Rans Sum test was used for analysis of snRNAseq data material. Data analysis was performed using GraphPad Prism Software Version 6 (GraphPad) and the R software. A value of p<0.05 was considered statistically significant. Asterisks depict statistically significant differences (* p<0.05, ** p<0.01, *** p<0.001). implemented
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10130-10139. Author Contributions SAB and GS planned and designed the study. SAB and LS were involved in all experiments. TS, YZ, and SBo performed reanalysis of human snRNAseq datasets. LH and FO did flow cytometry. TI and PS performed lipid mass spectrometry. MHV and AMS performed histology. CD and AOS did light sheet microscopy. DKB was involved in behavior experiments. SW, KAN, and MR analyzed genetic myelin mutants. JME conducted myelinating cell culture experiments. KM and EB conducted electrophysiology experiments on myelinating cell cultures. SAB and GS wrote and edited the manuscript. All authors approved the manuscript. Nat
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Declaration of Interests The authors declare no competing financial interests. Acknowledgments We cordially thank Annette Fahrenholz and Tanja Freerck for technical support. We thank Charles Stiles, John Alberta, Said Ghandour for generous gifts of antibodies. This work was funded by the Deutsche Forschungsgemeinschaft (SA 2014/2-1 to GS), the UK MS Society (Grant 127 to JE); Medical Research Scotland (PhD studentship 791-2014 to EB). LEAD CONTACT AND MATERIAL AVAILABILITY Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Gesine Saher ([email protected]). This study did not generate new unique reagents. |
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CC-BY-NC-ND 4.0 International license . ARTICLE
Enzyme Aggregation and Fragmentation Induced by Catalysis Relevant Species
Received 00th January 20xx, Accepted 00th January 20xx
Kayla Gentile,a Ashlesha Bhide,a Joshua Kauffman,a Subhadip Ghosh,a Subhabrata Maiti,a,b James Adair,c Tae Hee Leea and Ayusman Sen*a
DOI: 10.1039/x0xx00000x
It is usually assumed that enzymes retain their native structure during catalysis. However, the aggregation and
fragmentation of proteins can be difficult to detect and sometimes conclusions are drawn based on the assumption that the
protein is in its native form. We have examined three model enzymes, alkaline phosphatase (AkP), hexokinase (HK) and
glucose oxidase (GOx). We find that these enzymes aggregate or fragment after addition of chemical species directly related
to their catalysis. We used several independent techniques to study this behavior. Specifically, we found that glucose oxidase
and hexokinase fragment in the presence of D-Glucose but not L-glucose, while hexokinase aggregates in the presence of Mg2+ ion and either ATP or ADP at low pH. Alkaline phosphatase aggregates in the presence of Zn2+ ion and inorganic phosphate. The aggregation of hexokinase and alkaline phosphatase does not appear to attenuate their catalytic activity. Our study indicates that specific multimeric structures of native enzymes may not be retained during catalysis and suggests
pathways for different enzymes to associate or separate over the course of substrate turnover. Introduction
Enzyme catalysis is critical to the viability of living systems.1 Enzymes are also employed increasingly in a myriad of technological applications.2–4 Generally, it is assumed that enzymes retain their native structure during catalysis. However, the aggregation and fragmentation of proteins can be difficult to detect and sometimes conclusions are drawn based on the assumption that the protein is in its native form.5 This can be particularly problematical during enzyme purification and immobilization.6 Many enzymes have been shown to exhibit enhanced diffusion while catalyzing the turnover of their substrates.7–16 However, there are hints that experimental artifacts may be vitiating some of the observations.17–19 One suggested possibility is that some enzymes may be fragmenting into their monomeric units during catalysis.8,20 Due to the Stokes-Einstein relationship, size is inversely correlated to diffusion and so smaller sized particles will diffuse faster than larger particles. Thus, it is essential to
a. Department of Chemistry, The Pennsylvania State University, University Park, PA
understand how the size of the enzyme particles change in the course of catalysis. |
In this study, we evaluated three model enzymes, alkaline phosphatase (AkP), hexokinase (HK), and glucose oxidase (GOx). We find that these enzymes either aggregate or fragment following the addition of simple chemicals that are relevant for their catalytic activity. We use several independent techniques to study this behavior: fluorescence resonance energy transfer (FRET) and dynamic light scattering (DLS), along with liquid atomic the aggregation/fragmentation of the enzymes is critical to elucidating their functional properties. force microscopy
(AFM). Understanding
Materials and Methods Fluorescent labeling of AkP, HK, GOx: Alkaline phosphatase (from bovine (from Saccharomyces cerevisiae), glucose oxidase (from Aspergillus niger), and invertase (from baker's yeast (S. cerevisiae) were all purchased from Sigma- Aldrich-Millipore. For experiments with tagged enzymes, each enzyme was divided into two populations and each population was tagged with an amine reactive dye, either Alexa Fluor 488 (AF488; ex/em: 490/525; Thermo Fisher Scientific) or Alexa Fluor 532 (AF532; ex/em: 532/554; Thermo Fisher Scientific). The emission spectra of AF488 and AF532 are shown in Figure S1. intestinal mucosa), hexokinase
16802, USA
b. Current address: Department of Chemical Sciences, IISER Mohali, Manauli
140306, India
c. Department of Materials Science and Engineering, The Pennsylvania State
University, University Park, PA 16802, USA. Electronic Supplementary Information (ESI) available: [details of any supplementary information available should be included here]. See DOI: 10.1039/x0xx00000x
For example, alkaline phosphatase (12.5 µM) was reacted with a six- fold excess of Alexa Fluor 488 and alkaline phosphatase (12.5 µM) was reacted with a two-fold excess of Alexa Fluor 532 in water, along
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with 100 mM sodium bicarbonate, for 1 hour on a rotator. Then the mixtures were allowed to sit in the 4ºC fridge overnight and were allowed to rotate again the next morning for about 2 hours. The enzyme-dye mixtures were purified according to protocol included with the Antibody Conjugate Purification Kit for 0.5-1 mg (Thermo Fisher Scientific). The buffer was replaced with 50 mM HEPES (pH 7; Sigma-Aldrich) for alkaline phosphatase and hexokinase and 50 mM MES (pH 6; Sigma-Aldrich) for glucose oxidase and invertase. The same procedure was followed for all enzymes with varying starting concentrations and enzyme:dye ratios. These are specified in the Supporting Information (SI) in Table S1. Fluorescence Resonance Energy Transfer (FRET) Measurements: FRET measurements were taken on a Fluorolog JobinYvon Horiba spectrofluorometer. |
The slit width was set to 5, the integration time to 0.5 s, the increment to 5 nm and the detector to S1/R1. Spectra were recorded on FluorEssence software and analyzed using OriginPro. Alkaline Phosphatase FRET Measurements. For the FRET experiments, a Micro Hellma® fluorescence cuvette was used. For alkaline phosphatase, an enzyme mixture was made with 0.1 µM AkP-488 and 0.1 µM AkP-532 in 50 mM HEPES (pH 7; Sigma-Aldrich) buffer. For the zinc nitrate and magnesium nitrate titrations, zinc nitrate hexahydrate (Zn(NO3)2; Sigma-Aldrich) or magnesium nitrate hexahydrate (Mg(NO3)2; Sigma-Aldrich) was added so that the final concentration of salt for each experiment was 0, 0.05, 0.1, 0.5, 1, 2.5, 5, 7.5, or 10 mM. Fluorescence was recorded with just the enzyme before salt was added. The fluorescence reading with salt was taken 1 minute after the addition of salt. The Hofmeister salt experiments were conducted in a similar manner. The salts used were ammonium nitrate (NH4NO3; Sigma-Aldrich), sodium nitrate (NaNO3; Alfa Aesar), calcium nitrate tetrahydrate (Ca(NO3)2; Sigma-Aldrich), sodium sulfate anhydrous (Na2SO4; BDH), sodium phosphate dibasic hexahydrate (Na2HPO4; Sigma-Aldrich), sodium chloride (NaCl; Sigma-Aldrich) and sodium thiocyanate (NaSCN; Sigma-Aldrich). The salt was added so that the final concentration was 1 mM and fluorescence readings were taken with just the enzyme and then 1 minute after salt was added. For the alkaline phosphatase reaction experiments, zinc nitrate (Zn(NO3)2; Sigma-Aldrich) or magnesium nitrate hexahydrate hexahydrate (Mg(NO3)2; Sigma-Aldrich), D-Glucose 6-phosphate sodium salt (Sigma-Aldrich), D-(+)-Glucose (Sigma-Aldrich) or sodium phosphate dibasic hexahydrate (Sigma-Aldrich) were added to the experimental solution. All substrates were added so that the final concentration for each substrate was 0.5 mM. Ethylenediamine tetraacetic acid disodium salt (EDTA; IBI Scientific) was added in the last 5 minutes to experiments so that its final concentration was 0.5 mM. For the alkaline phosphatase fragmentation experiments D-(+)- Glucose (D-Glu; Sigma Aldrich, 20 mM) or L-(–)-Glucose (L-Glu; Sigma Aldrich, 20 mM) were used. Hexokinase FRET Measurements. For the experiments, a Micro Hellma® fluorescence cuvette was used. For hexokinase, an enzyme
mixture was made with 0.1 µM HK-488 and 0.1 µM HK-532 in 50 mM HEPES (pH 7; Sigma-Aldrich) buffer. The titration and Hofmeister salt experiments were executed in the same manner as the alkaline phosphatase experiments with the same reagents, but a solution of 0.1 µM HK-488 and 0.1 µM HK-532 was used. In addition, magnesium chloride anhydrous (MgCl2; Alfa Aesar) was used for the titration instead of zinc nitrate or magnesium nitrate. For the hexokinase reaction experiments, magnesium chloride anhydrous (MgCl2; Alfa Aesar) was added to all experiments so that the final concentration was 40 mM. Adenosine 5’-triphosphate disodium salt hydrate (ATP; Sigma-Aldrich), D-(+)-Glucose (Glu; Sigma-Aldrich), D-Glucose 6- phosphate sodium salt (G6P; Sigma-Aldrich), or Adenosine 5’- diphosphate sodium salt (ADP; Sigma-Aldrich) was added so the final concentration for each substrate was 20 mM. |
For the pH experiments described in Figure 7, two solutions of 500 mM ATP and two solutions of 500 mM ADP were made in 50 mM HEPES (pH 7; Sigma-Aldrich). The pH was measured using a Thermo Scientific Orion Star pH meter. For one solution of ATP and one solution of ADP, the pH was adjusted to pH 7 using 3M sodium hydroxide (Alfa Aesar), a summary of the resulting pH values can be found in Table S2. Then approximately 30 µL of the 500 mM ATP or ADP stock solutions were added to the experimental FRET solutions to achieve a final concentration of 20 mM ATP or ADP. Table S3 gives the resulting pH values for the experiment recorded in Figure 7. For the hexokinase fragmentation experiments, D-(+)-Glucose (D-Glu; Sigma-Aldrich, 20 mM) or L-(–)-Glucose (L-Glu; Sigma-Aldrich, 20 mM) were used. Glucose Oxidase FRET Measurements. For the experiments, a Micro Hellma® fluorescence cuvette was used. For glucose oxidase, an enzyme mixture was made with 0.1 µM GOx-488 and 0.1 µM GOx- 532 in a 50 mM MES (pH 6; Sigma-Aldrich) buffer solution. D-(+)- Glucose (D-Glu; Sigma-Aldrich), L-(-)-Glucose (L-Glu; Sigma-Aldrich), D-(+)-Gluconic acid - lactone (Sigma-Aldrich), or hydrogen peroxide, 30% (VWR) were added so that the final concentration for each substrate was 1 mM (Figure 10). For the experiment with invertase (Figure 12), a stock solution was made with 0.1 µM GOx-488 and 0.1 µM GOx-532 in a 50 mM MES (pH 6) buffer solution. Invertase was added so that the final concentration was 0.1 µM. Sucrose (Sigma- Aldrich) was added to the solution so that the final concentration was 1 mM. For determining the concentration of D-Glucose required for fragmentation (Figure S8), D-(+)-Glucose (D-Glu; Sigma-Aldrich) in the required quantity was added to the stock solution of 0.1 µM GOx- 488 and 0.1 µM GOx-532 so that the final concentration was as specified. 𝛿𝛿
Dynamic Light Scattering (DLS) Measurements: The enzymes were analyzed on a NanoBrook Omni instrument. To reduce dust and debris that affect sample measurements, enzymes and buffer were centrifuged twice in 300kDa centrifugal filters at 3000 xg for 20 minutes using a Thermo Scientific Sorvall ST16 Centrifuge. Additionally, all enzyme samples were filtered twice with a 0.2 µm cellulose acetate syringe filter (VWR) immediately before running the experiment. Lastly, all pipette tips, cuvettes (plastic disposable; 4.5
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mL) and syringes were rinsed with DI water prior to experimentation. The following settings were used for the DLS measurements: angle: 90°; correlator layout: proteins; cell type: BI-SCP; set duration: 120 sec; equilibration times: 180s; dust filter: 10-50 nm; liquid: water; baseline normalization: auto (slope analysis); threshold: 2.0 nm-5000 nm. |
Series of 3 or 6 runs were used to obtain data. The same reagents from the FRET experiments were used to conduct the DLS experiments with 3 mL total sample volumes, but at higher concentrations. These are specified in Figures 4, S3 and S7. The DLS low is not sensitive enough to detect the enzymes at the concentrations used for FRET. Atomic Force Microscopy (AFM) Measurements: A Bruker BioScope Resolve AFM and Bruker ScanAsyst-Fluid+ probe was used to obtain control and experimental data. Scan rate was set at 0.501 Hz with 128 samples per line and a drive amplitude of 100 mV. For control experiments, 0.2 µM alkaline phosphatase in HEPES buffer (pH 7; Sigma-Aldrich) was added to a mica surface and visualized. Zn(NO3)2 (0.5 mM; Sigma-Aldrich), Mg(NO3)2 (0.5 mM; Sigma-Aldrich), and Na2HPO4 (0.5 mM; Sigma-Aldrich) were then added to a solution of 0.2 µM alkaline phosphatase and aggregation was characterized. Substrate and buffer solutions were filtered once with a 0.2 µM cellulose acetate syringe filter (VWR) before being added to the mica. tailed P value (calculated using the unpaired t-test) was less than the alpha level (0.05), the results were described as statistically different. Results and Discussion
Enzymes that Exhibit Aggregation
Alkaline Phosphatase aggregates with the addition of Zn2+ and inorganic phosphate. Alkaline phosphatase (AkP) from bovine intestinal mucosa was purchased in a lyophilized powder form from Millipore Sigma. Its structure is shown in Figure 1. It is a the 160 kDa dimeric phosphoesterase decomposition of phosphate containing compounds, including glucose 6-phosphate (G6P) and p-nitrophenyl phosphate (pNPP) (Equations 1-2). that catalyzes
Enzyme Activity Measurements:
Alkaline Phosphatase Activity Measurements. Alkaline phosphatase was tagged according to procedure stated in the fluorescent tagging section. Activity was monitored by measuring absorbance using a Thermo Scientific Evolution 220 UV-Visible Spectrophotometer. For alkaline phosphatase, the reaction illustrated in Equation 2 was used. The reaction product, para-nitro phenol (pNP), is UV active at 405 nm and the activity can be monitored by following the production of pNP over time. An assay mixture, 1 mL in total volume, contained 0.2 µM tagged AkP, 1 mM p-Nitrophenyl phosphate disodium salt hexahydrate (pNPP; Sigma-Aldrich) and either 0, 0.1, 0.5, 1, or 5 mM of Zn(NO3)2 (Sigma-Aldrich) and Mg(NO3)2 (Sigma-Aldrich) in 50 mM HEPES (pH 7; Sigma-Aldrich). Fig 1: AkP Structure. Protein Data Bank (PDB) Structure of alkaline phosphatase (from Escherichia Coli).21
(1)
Hexokinase Activity Measurements. Hexokinase was tagged according to procedure stated in the fluorescent tagging section. Activity was monitored by measuring absorbance using a Thermo Scientific Evolution 220 UV-Visible Spectrophotometer. For hexokinase, the reactions illustrated in Equations 3-4 was used. An assay mixture, 1 mL in total volume, contained 0.2 µM tagged HK, 20 mM D-(+)-Glucose, 20 mM ATP, 2.5 mM ß-Nicotinamide adenine dinucleotide phosphate sodium salt hydrate (NADP+; Sigma-Aldrich), 10 units of Glucose-6-phosphate Dehydrogenase from baker’s yeast (G6PDH; S. cerevisiae; Sigma-Aldrich) and either 0, 20 or 40 mM of MgCl2 in 50 mM HEPES (pH 7). |
Statistical Analysis: The statistical significance of the data sets in Figures 2, 8, S2-S5, and S8 was evaluated using an unpaired t-test. The alpha level chosen for the t-tests was 5% (0.05). When the two-
To begin, we studied the aggregation of this enzyme using fluorescence resonance energy transfer (FRET). FRET is a technique that uses two fluorophores and allows researchers to estimate how close two fluorescently tagged molecules are to each other.22,23 We used two fluorescent dyes in a FRET pair (AlexaFluor 488 nm and Alexa Fluor 532 nm; AF488 and AF532) to tag the enzymes and we report FRET efficiencies as a measure of the proportion of the enzyme population that is within approximately 6 nm of each other (more details can be found in the SI). The higher the FRET efficiency, the higher the proportion of enzymes that are close to each other in the experiment. (2)
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For the FRET experiments, we tagged half of the AkP population (0.1 µM) with AF488 and the other half of the population (0.1 µM) with AF532 (tagging procedures are described in the Materials and Methods). Unless otherwise noted, this is the procedure followed for all enzyme FRET studies described. Literature notes that the catalytic activity of AkP is enhanced by both zinc and magnesium ions.24 Thus, we carried out a FRET assay with increasing concentrations of zinc and magnesium nitrate with the tagged AkP. For reference, the free concentrations of zinc and magnesium ions in the cell are estimated to be about 0.2 – 0.3 mM and 0.5 – 1 mM, respectively.25,26 The results are shown in Figure 2 and that zinc nitrate causes a concentration demonstrate dependent in the enzyme aggregation, while magnesium nitrate has no significant effect. increase
is the cause of the aggregation of AkP. The glucose 6-phosphate reaction produces phosphate over time which is why the FRET signal increases slowly. But, if Pi is added at the start, the FRET efficiency increases immediately. It is important to note that this behavior is only observed when zinc and magnesium are present. Thus, with just alkaline phosphatase and phosphate and no Zn2+ or Mg2+ (green dashes) no aggregation is observed. Additionally, if we add the common zinc chelating agent (ethylenediaminetetraacetic acid, EDTA) to the experiment after 30 minutes, we see an immediate and significant drop in the FRET efficiency back to the baseline. Fig. 2. FRET efficiencies of AkP with Zn2+ and Mg2+. FRET efficiency of 0.2 µM AkP with increasing mM concentrations of Zn(NO3)2 (blue bars) and Mg(NO3)2 (striped bars). |
The buffer used to make all experimental solutions was 50 mM HEPES (pH 7). The error bars represent the standard deviation from two trials. The FRET efficiencies from 1-10 mM Zn(NO3)2 are statistically different from the FRET efficiency with only AkP (P < 0.05; see Materials and Methods). Fig. 3. FRET efficiencies of AkP during catalysis. FRET efficiency for 0.2 µM AkP (blue circles); 0.2 µM AkP, 0.5 mM Zn(NO3)2, 0.5 mM Mg(NO3)2 (orange squares); 0.2 µM AkP, 0.5 mM Zn(NO3)2, 0.5 mM Mg(NO3)2, 0.5 mM G6P (gray diamonds); 0.2 µM AkP, 0.5 mM Zn(NO3)2, 0.5 mM Mg(NO3)2, 0.5 mM D-Glu (yellow triangles); 0.2 µM AkP, 0.5 mM Zn(NO3)2, 0.5 mM Mg(NO3)2, 0.5 mM Na2HPO4 (purple crosses); 0.2 µM AkP, 0.5 mM Na2HPO4 (green dashes). The arrows indicate the addition of 0.5 mM EDTA. The buffer used to make all experimental solutions was 50 mM HEPES (pH 7). The dashed lines are to guide the eye. The error bars represent the standard deviation from two trials. We proceeded to test a variety of ions in the Hofmeister series, a series that dictates whether proteins will salt into solution (dissolve) or salt out of solution (aggregate).27 Surprisingly, other than the Zn2+ ion, these salts do not have a strong effect on enzyme aggregation, regardless of whether they are on the “salting in” or “salting out” side of the series (Figure S2). Next, we introduced the enzyme’s substrate to see if catalysis has an effect on the aggregation (Figure 3). First, we measured the FRET efficiency only with fluorescently tagged alkaline phosphatase (0.2 µM) to act as the baseline. For further experiments, unless otherwise noted, we added minimal zinc and magnesium ions (0.5 mM) to the enzyme solution to ensure enzyme activity. At this concentration, zinc ions will not cause significant aggregation (Figure 2). We examined the effect of adding the substrate glucose 6-phosphate (G6P) as well as the products of the reaction, D-Glucose (D-Glu) and inorganic phosphate (Pi; Na2HPO4). Following the addition of the substrate G6P, the FRET efficiency begins to increase after about 10 minutes and then continues to increase for the remainder of the experiment. Interestingly, an increase in FRET efficiency is observed immediately when Pi is added. However, the addition of the other product in G6P hydrolysis, D-Glu, has no effect. Therefore, we postulate that the inorganic phosphate
The above results suggest that the AkP units are coming close together and aggregating. However, there is a second possibility that can give rise to higher FRET efficiencies. This involves a rapid dynamic equilibrium involving the dissociation and recombination of the enzyme subunits.28,29 If the subunits from the AF488 and AF532 tagged AkP molecules dissociate and in AkP molecules recombine randomly, this will result incorporating subunits tagged with both dyes, resulting in an increase in net FRET efficiency. In order to eliminate this mechanism for the observed increase in FRET efficiency and also to confirm that the fluorescent dyes or tagging procedures did not affect the results, we also examined the behavior without fluorophores by dynamic light scattering (DLS). |
Due to the lower sensitivity of DLS, we had to use higher concentrations of enzyme and substrate. We assessed the count rate and particle diameter versus the concentration of the aggregator or the time that the enzyme was exposed to the aggregator. Count rate is defined as the number of photons per second that the instrument detected and can be used as a measure of aggregation.30 Using these methods, we tested the aggregation with increasing concentrations of zinc and magnesium nitrate. Similar to the FRET results, zinc nitrate caused a concentration dependent increase in size, while magnesium nitrate had no effect (Figure S3). 4 | J. Name., 2012, 00 , 1-3
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When we added either of the two substrates for alkaline (p-nitrophenyl phosphate, pNPP; glucose-6- phosphatase phosphate, G6P), we observe a time dependent aggregation. G6P is a slower substrate than pNPP and Pi will form faster in the latter reaction.31 Although we observe enzyme aggregation with both substrates, the aggregation is immediate for pNPP (Figure 4B) but starts at around 6 minutes for G6P (Figure 4C), when compared to AkP without substrate (Figure 4A), further supporting that Pi is the aggregator. Again, the presence of zinc ions is necessary for the aggregation to occur. Overall, our findings from the DLS experiments are consistent with the FRET results. minutes. The results are shown in Figure S4. Most relevant are the cases with 0.5 mM and 1 mM zinc and magnesium nitrate, which correspond to the FRET and DLS experiments. As can be seen, while there is a small decrease in the activity of AkP, the decrease is not statistically significant, meaning that aggregates formed at these concentrations are still catalytically active. Fig. 5. AFM data of AkP with Zn2+, Mg2+ and Phosphate. AFM (A) 2D image and (B) 3D image of 0.2 µM AkP. AFM (C) 2D image and (D) 3D image of 0.2 µM AkP with 0.5 mM Zn(NO3)2, 0.5 mM Mg(NO3)2 and 0.5 mM Na2HPO4. In the 2D images, white indicates sizes of 15 nm, while in the 3D images, the blue indicates sizes of 15 nm. The buffer used to make all experimental solutions was 50 mM HEPES (pH 7). The substrate solutions were filtered before being dropped on the mica in both experiments. Fig. 4. DLS data for AkP during catalysis. Diameter (blue circles) and count rate (red squares) for (A) 3 µM AkP, 1 mM Zn(NO3)2, 1 mM Mg(NO3)2 and (B) 3 µM AkP, 1 mM Zn(NO3)2, 1 mM Mg(NO3)2, 5 mM pNPP, (C) 3 µM AkP, 1 mM Zn(NO3)2, 1 mM Mg(NO3)2, 5 mM G6P over a period of 12 to 18 minutes. The buffer used to make all experimental solutions was 50 mM HEPES (pH 7). |
In addition to FRET, atomic force microscopy (AFM) was used to characterize enzyme aggregation which allows for direct visualization of the enzyme aggregation in real time. Figure 5 shows both 2D and 3D images of alkaline phosphatase on a mica surface. Before the addition of the salts, the surface has minimal aggregates as most of the enzyme is still in solution (Figure 5A- B). When salts (Zn2+, Mg2+, Pi) are added, aggregates settle to the surface and can be visualized as shown in Figure 5C-D. Taken together, the results from the DLS and AFM experiments suggest the in FRET efficiency stems from the aggregation of the AkP molecules, and not from a dynamic equilibrium involving the dissociation and recombination of monomeric subunits. increase
Hexokinase aggregates with Mg2+ and either ATP or ADP at low pH values. Hexokinase (HK) from Saccharomyces cerevisiae was purchased in a lyophilized powder form from Millipore-Sigma. Its structure is shown in Figure 6. It phosphorylates D-Glucose (D-Glu) to glucose-6-phosphate (G6P) in the presence of magnesium chloride (MgCl2) and adenosine triphosphate (ATP) (Equation 3). It is a dimer with a weight of 110 kDa. Lastly, we measured the activity of alkaline phosphatase using UV-Vis spectroscopy in the presence of pNPP with increasing added concentrations of zinc and magnesium ions. The reaction involving pNPP was used because the product, pNP, is UV active. We let the reaction proceed for 23 minutes to allow for aggregation and calculated the rate during the last three
Fig 6: HK Structure. PDB structure of hexokinase (from Saccharomyces cerevisiae).32
To begin, we examined the possible aggregation of HK in the presence of Mg2+ ion, which is required for activity,33 as well as cations and anions from the Hofmeister series. None of these ions had a discernible effect (Figure S5). Next, we tested the
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FRET efficiency with each of the species involved in HK catalysis, in the presence of the Mg2+ ion (Figure S6). As shown, neither D-Glu nor G6P has a significant effect on the aggregation (indeed, D-Glu causes fragmentation, see next section). However, both ADP and, especially ATP, in the presence of Mg2+, cause HK aggregation and an increase in the FRET efficiency signal (Figure S6). We observed that adding 20 mM ATP or 20 mM ADP to the experimental solution caused a drop in the pH, despite the use literature.34 of HEPES buffer, which has been noted Therefore, we tried two sets of experiments, one set in which we left the pH of the ATP or ADP solution as is and one in which we adjusted the pH of the ATP or ADP stock solutions to pH 7. |
The pH values for the stock solutions used to make the experimental solutions are found in Table S2 of the SI and the pH of the resulting experimental solutions are found in Figure 7 and in Table S3 in the SI. Table S3 contains the pH values for each of the experiments portrayed in Figure 7. The pH does not change dramatically as the experiment progresses, but as shown in Figure 7, lowering the pH significantly increases HK aggregation. The signals with HK; HK, Mg2+; HK, Mg2+, ATP; and HK, Mg2+, ADP all show higher levels of aggregation when the pH is left unadjusted, and the values are close to 4. When the pH is adjusted to 7, the levels of aggregation significantly drop. As with AkP, we used DLS to confirm the results we saw with FRET (Figure S7). Note the pH values were not controlled for these DLS experiments. The results from the DLS again suggests that the increase in FRET efficiency stems from the aggregation of the HK units, and not from the dissociation and recombination of monomeric subunits. It is worth noting that the pH remains at 7 in the FRET, DLS and AFM experiments involving AkP. in
dehydrogenase (G6PDH) and ß-Nictoinamide Adenine Dinucleotide Phosphate (ß-NADP) to measure the activity of hexokinase with D-Glu, MgCl2 and ATP (Equations 3-4). We measured the rate of the reaction after 60 minutes and calculated the rate during the last three minutes. The results are seen in Figure 8. While some Mg2+ ion is required for HK optimal activity, the results for 20 mM and 40 mM Mg2+ appear to suggest that aggregation may result in an increase in the catalytic activity of HK, although the change is not statistically significant. (3)
(4)
Fig. 8. Activity of HK upon catalysis. Activity of 0.2 µM hexokinase between 57- 60 min with 20 mM Glu, 20 mM ATP, 2.5 mM NADP+ and 10 units of G6PDH while increasing the concentration of MgCl2 from 0 to 40 mM. The buffer used to make all experimental solutions was 50 mM HEPES (pH 7). The error bars represent the standard deviation from two trials. The activities are not statistically different from 0 mM Mg2+ (P > 0.05; see Materials and Methods). Fig. 7. FRET efficiencies for HK at different pH values. FRET efficiency of 0.2 µM HK (pH 7.0; blue circles); 0.2 µM HK (pH 4.1; orange squares); 0.2 µM HK, 40 mM MgCl2, 20 mM ATP (pH 6.9; gray diamonds); 0.2 µM HK, 40 mM MgCl2, 20 mM ATP (pH 4.1; yellow triangles); 0.2 µM HK, 40 mM MgCl2, 20 mM ADP (pH 6.9; purple crosses); 0.2 µM HK, 40 mM MgCl2, 20 mM ADP (pH 4.6; green dashes); 0.2 µM HK, 40 mM MgCl2 (pH 4.3; black circles). The buffer used to make all experimental solutions was 50 mM HEPES (pH 7). The dashed lines are to guide the eye. The error bars represent the standard deviation from two trials. Finally, we investigated the effect of aggregation on HK activity. We use a coupled assay with glucose 6-phosphate
Enzymes that Exhibit Fragmentation Glucose Oxidase fragments upon the addition of D-Glucose. Glucose Oxidase (GOx) from Aspergillus niger was purchased from Millipore Sigma. |
Its structure is shown in Figure 9. This enzyme catalyzes the oxidation of D-Glucose (D-Glu) to form gluconic acid and hydrogen peroxide (Equation 5). It is a dimer and has a molecular weight of 160kDa. 6 | J. Name., 2012, 00 , 1-3
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Fig 9: GOx Structure. PDB structure of glucose oxidase (Aspergillus niger).35
Fig 11: Inv Structure. PDB structure of cerevisiae).38
invertase (from Saccharomyces
Since glucose oxidase is not a metalloenzyme36, we did not investigate its aggregation behavior upon the addition of metal ions. Instead, using FRET, we examined the fragmentation of glucose oxidase in the presence of its substrate D-Glucose, the non-substrate enantiomer L-Glucose (L-Glu), the combined products of the reaction, as well as each product individually. (Figure 10). (5)
(6)
Fig. 10. FRET efficiencies for GOx during catalysis. FRET efficiency for 0.2 µM GOx (blue circles); 0.2 µM GOx, 1 mM D-Glu (orange squares), 0.2 µM GOx,1 mM L-Glu (gray diamonds); 0.2 µM GOx, 1 mM gluconic acid (yellow triangles); 0.2 µM GOx, 1 mM gluconic acid and 1 mM hydrogen peroxide (purple crosses); 0.2 µM GOx, 1 mM hydrogen peroxide (green dashes). The buffer used to make all experimental solutions was 50 mM MES (pH 6). The dashed lines are to guide the eye. The error bars represent the standard deviation from three trials. In this experiment, along with glucose oxidase tagged with the two dyes (AF488 and AF532), we added untagged 0.1 µM invertase. We tested the FRET efficiency of this solution by itself and after adding sucrose. We expected a time delay with a gradual onset of glucose oxidase fragmentation since invertase slowly converts sucrose to D-Glucose. The results are shown in Figure 12. We found that the enzyme fragments in the presence of its substrate D-Glucose, but not L-Glucose. Enzymes typically have multimeric structures formed from polypeptide subunits. In principle, they can aggregate or fragment to larger or smaller multimeric structures. Therefore, we postulate that this fragmentation is due to the dissociation of the GOx enzyme into its free subunits.28,37 GOx does not fragment in the presence of the reaction products, gluconic acid and hydrogen peroxide. Furthermore, we investigated what happens if D-Glucose is not present in the reaction mixture initially but is produced gradually over time. To do so, we added another enzyme, invertase, to the solution. Invertase (Inv, also known as sucrase) converts sucrose to glucose and fructose as shown in Equation 6. Invertase from baker’s yeast (S. cerevisiae) was purchased from Millipore Sigma. |
Its structure is shown in Figure 11. Fig. 12. FRET efficiencies for GOx with Inv and Sucrose. FRET efficiency for 0.2 µM tagged GOx, 0.1 µM untagged Inv (blue circles); 0.2 µM GOx, 0.1 µM Inv, 1 mM sucrose (orange squares). The buffer used to make all experimental solutions was 50 mM MES (pH 6). The dashed lines are to guide the eye. The error bars represent the standard deviation from three trials. As shown in Figure 12, we saw that, instead of fragmenting gradually, there was a sudden drop in the FRET efficiency which
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suggests that a minimum concentration of D-Glucose is required for GOx fragmentation. Based on preliminary calculations using the enzyme activity, we estimated that ~0.3 mM D-Glucose was produced in 40 minutes after the addition of invertase and sucrose to the solution of glucose oxidase. These calculations are shown in the SI. We also performed concentration dependent experiments using FRET to obtain the concentration of D-Glucose at which the enzyme starts fragmenting. These results are summarized in Figure S8. They show that fragmentation starts after the addition of ~0.3 mM D-Glucose which is similar to the value obtained in the calculations. Note that the physiological concentration of D- Glucose is well above this concentration. is 4.4-6.6 mM39,40, which
presence of D-Glucose but not L-Glucose, while hexokinase aggregates in the presence Mg2+ ion and either ATP or ADP at low pH. Alkaline phosphatase aggregates in the presence of Zn2+ ion and inorganic phosphate. The aggregation of hexokinase and alkaline phosphatase does not appear to attenuate their catalytic activity. The results are summarized in Figure 14. Hexokinase fragments in the presence of D-Glucose. We assessed the fragmentation behavior of hexokinase with both D- and the non-substrate enantiomer, L-Glucose. We found that D-Glucose by itself or D-Glucose in combination with ATP and MgCl2 causes a fragmentation as opposed to L-Glucose. These results are displayed in Figure 13. Figure 14: Schematic of enzyme aggregation and fragmentation. Glucose oxidase fragments into its subunits in the presence of D-Glu, but not L-Glu. Hexokinase also fragments to its subunits in the presence of D-Glu, but not L-Glu and aggregates in the presence of Mg2+ ion and ATP at low pH. Alkaline phosphatase aggregates in the presence of the Zn2+ ion and inorganic phosphate and does not fragment into its subunits in the presence of D-Glu
Fig. 13. FRET efficiencies of HK with D- and L-Glu. FRET efficiency of 0.2 µM HK (blue circles); 0.2 µM HK, 20 mM D-Glu (orange squares); 0.2 µM HK, 20 mM L-Glu (gray diamonds). |
The buffer used to make all experimental solutions was 50 mM HEPES (pH 7). The error bars represent the standard deviation from two trials. Alkaline Phosphatase does not fragment after the addition of D- Glucose. Based on the results shown above, we wondered whether the fragmentation by D-Glucose was only specific to those enzymes that use D-Glucose as the substrate (namely HK and GOx). Therefore, we examined the behavior of AkP which does not catalyze the transformation of D-Glucose. As is obvious from Figure S9, the addition of either D- or L-Glucose has no effect on the aggregation behavior of AkP. Our study underscores the dynamic nature of protein aggregates. It is clear that, for example, one should not a priori assume that the specific multimeric structure of the native enzyme is maintained during catalysis. Perhaps more interesting is that the work presented suggests pathways for different enzymes to associate or separate in the course of catalysis. Additionally, understanding the causes of enzyme dissociation or aggregation has multiple benefits in the industrial the aggregation and fragmentation of multimeric enzymes must be taken into account in designing enzyme immobilization strategies. The mechanistic underpinnings of the processes are complex, and in this context, we note that a separate study has shown that modest concentrations of ATP can cause fragmentation and solubilization of disordered proteins.42
field.41 For example,
Author Contributions
Conclusion
In this study, we have identified compounds that cause aggregation and fragmentation in several model enzymes. It is particularly noteworthy that these additives are directly involved in catalysis by the respective enzymes. Specifically, we found that glucose oxidase and hexokinase fragment in the
Conceptualization – KG, AB, JA, THL, AS Supervision – JA, THL, AS Funding acquisition – AS Methodology – KG, AB, JK, SM, SG Writing – original draft – KG, AB, AS Writing – review & editing – KG, AB, JK, SG, SM, THL, AS
Conflicts of interest
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There are no conflicts to declare. 21. J. E. Murphy, T. T. Tibbitts and E. R. Kantrowitz, J. Mol. Biol. 1995, 253, 604. Acknowledgements
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We also thank the rest of the Keating lab, especially Charlie Crowe, Saehyun Choi and Jennifer Miller for training us to use the fluorimeter, as well as accommodating us in their lab during the COVID-19 pandemic. We would also like to thank Kelly Collins from Brookhaven Instruments Corporation for her guidance and assistance in using the DLS. Finally, we thank Professor Henry Hess (Columbia) for helpful discussions. We gratefully acknowledge funding of the research by the Air Force Office of Scientific Research FA9550-20-1-0393 (AS). 24. M. Besman and J.E. Coleman, J. Biol. Chem. 1985, 260, 11190. 25. W. Maret, Metallomics. 2015, 7, 202. 26. E. Murphy, Circ. Res. 2000, 86, 245. 27. H.I. Okur, J, Hladílková, K.B. Rembert, Y. Cho, J. Heyda, J. Dzubiella, P.S. Cremer and P. Jungwirth, J. Phys. Chem. B. 2017, 121, 1997. 28. C. Pan, PLoS One 2011, 6, 1. 29. G. Schreiber, Curr. Opin. Struct. Biol. 2002, 12, 41. 30. M.A. Wells, A. Abid, I.M. Kennedy and A.I. Barakat, Nanotoxicology. 2012, 6, 837. 31. R.N. Murdoch, Aust. J. Biol. Sci. 1971, 24, 331. 32. P. R. Kuser, S. Krauchenco, O. A. C. Antunes and I. Polikarpov, J. Biol. Chem. 2000, 275, 20814. Notes and references
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11. T.G. Cha, J. Pan, H. Chen, J. Salgado, X. Li, C. Mao and J.H. Choi, Nat. Nanotechnol. 2014, 9, 39. 12. S. Sengupta, M.M. Spiering, K.K. Dey, W. Duan, D. Patra, P.J. Butler, R.D. Astumian, S.J. Benkovic and A. Sen. ACS Nano. 2014, 8, 2410. 13. C. Riedel, R. Gabizon, C.A.M. Wilson, K. Hamadani, K. Tsekouras, S. Marqusee, S. Pressé and C. Bustamante, Nature. 2015, 517, 227. 14. H. Yu, K. Jo, K.L. Kounovsky, J.J.D. Pablo and D.C. Schwartz, J. Am. Chem. Soc. 2009, 131, 5722. 15. A.Y. Jee, S. Dutta, Y.K. Cho, T. Tlusty and S. Granick. Proc. Natl. Acad. Sci. USA. 2018, 115, 14. 16. M. Xu, J.L. Ross, L. Valdez and A. Sen, Phys. Rev. Lett. 2019, 123, 128101-1. 17. J.P. Günther, G. Majer and P. Fischer, J. Chem. Phys. 2019, 150, 124201-1. 18. Y. Zhang, M.J. Armstrong, N.M. Bassir Kazeruni and H. Hess, Nano Lett. 2018, 18, 8025. 19. J.P. Günther, M. Börsch and P. Fischer, Acc Chem. Res. 2018, 51, 1911. 20. A.Y. Jee, K. Chen, T. Tlusty, J. Zhao, and S. Granick, J. Am. Chem. Soc. 2019, 141, 20062. This journal is © The Royal Society of Chemistry 20xx
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CC-BY 4.0 International license . Framework estimation of stochastic gene activation using transcription average level
Liang Chen1,2,†, Genghong Lin1,2,† and Feng Jiao1,2,∗
1Center for Applied Mathematics, Guangzhou University, Guangzhou, P. R. China. 2School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, P. R. China. Abstract Gene activation is usually a non-Markovian process that has been modeled as various frameworks that consist of multiple rate-limiting steps. Understanding the exact activation framework for a gene of interest is a central problem for single-cell studies. In this paper, we focus on the dynamical data of the average transcription level M (t), which is typically neglected when deciphering gene activation. Firstly, the smooth trend lines of M (t) data present rich, visually dynamic features. Secondly, tractable analysis of M (t) allows the establishment of bijections between M (t) dynamics and system parameter regions. Because of these two clear advantages, we can rule out frameworks that fail to capture M (t) features and we can further test potential competent frameworks by fitting M (t) data. We implemented this procedure to determine an exact activation framework for a large number of mouse fibroblast genes under tumor necrosis factor induction; the cross-talk between the signaling and basal pathways is crucial to trigger the first peak of M (t), while the following damped gentle M (t) oscillation is regulated by the multi-step basal pathway. Moreover, the fitted parameters for the mouse genes tested revealed two distinct regulation scenarios for transcription dynamics. Taken together, we were able to develop an efficient procedure for using traditional M (t) data to estimate the gene activation frameworks and system parameters. This procedure, together with sophisticated single-cell transcription data, may facilitate a more accurate understanding of stochastic gene activation. Author Summary It has been suggested that genes randomly transit between inactive and active states, with mRNA produced only when a gene is active. The gene activation process has been modeled as a framework of multiple rate-limiting steps listed sequentially, parallel, or in combination. The system step numbers and parameters can be predicted
†L.C. and G.L. contributed equally. ∗Corresponding author: F.J. ([email protected]). 1
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by computationally fitting sophisticated single-cell transcription data. However, current algorithms require a prior hypothetical framework of gene activation. We found that the prior estimation of the framework can be achieved using the traditional dynamical data of mRNA average level M (t) which present easily discriminated dynamical features. The theory regarding M (t) profiles allows us to confidently rule out other frameworks and to determine optimal frameworks by fitting M (t) data. We successfully applied this procedure to a large number of mouse fibroblast genes and confirmed that M (t) is capable of providing a reliable estimation of gene activation frameworks and system parameters. 1
Introduction
Gene transcription is a random process in virtually all genomic loci, for which messenger RNA (mRNA) molecules for active genes are produced in a bursting fashion in which an episode of transcriptional activity is interrupted by irregular gene inactivation periods [1–3]. A central problem in the study of stochastic gene transcription has been understanding reg- ulation scenarios that control random gene activation (on) and inactivation (off) in response [4–7]. The tremendous effort expended in this endeavor over to environmental changes the last few decades has generated massive amounts of data at the single-cell level and has produced many important observations [8–10]. Real-time imaging of transcriptional bursting makes it possible to count the durations of each gene on and off period along the entire timeline, which generates duration distribu- tions for both gene on and off periods, respectively. For instances of the Escherichia coli Plac/ara promoter [11] and yeast FLO11 genes [12], their on and off periods are all well fitted by single exponential distributions. These observations support the classical two-state model shown in Fig. 1a, that the gene for turning genes on and off are all controlled by single rate-limiting biochemical steps, with synthesis of mRNA when the gene is on and degradation of the gene all being controlled by single rate-limiting steps [1, 3]. The expo- nentially distributed on period is one of the few universal features of transcription present in both prokaryotic and eukaryotic genes [6, 8, 13]. However, the duration of the off state is highly gene-specific, and is manifested by the observed gamma distribution with a unique peak for mouse fibroblast genes [8] and E. coli tetA promoters [14]. Gamma distribution or more general non-Markovian processes can be mathematically explained by assuming that the gene for activating the on period is directed by a single pathway consisting of multiple sequential rate-limiting steps (e.g., the three-state model in Fig. 1b) [15], the parallel com- petitive rate-limiting pathways (e.g., the cross-talking pathways model in Fig. 1c) [16], or a
2
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CC-BY 4.0 International license . combination of both (e.g., Fig. 1d) [17]. However, these theoretical approaches are unable to determine the best framework to describe the observed non-Markovian gene activation, although they have provided good approximations to the downstream distribution of gene transcription [18, 19]. Figure 1: Different frameworks that direct stochastic gene activation (on). Other processes of gene inactivation (off), mRNA synthesis when the gene is on, and mRNA degradation are all determined by single rate-limiting steps at constant rates. (a) Two-state model. The gene is activated through a single rate-limiting step at a constant rate. (b) Three-state model. Gene activation is regulated by two sequential rate-limiting steps at a constant rate. (c) Cross-talking pathway model. The gene is activated by two different competitive rate-limiting pathways with selection probabilities q1 and q2 of the two pathways satisfying q1 + q2 = 1. (d) Cross-talking three-state model. The gene is activated either by a pathway consisting of two sequential rate-limiting steps, or alternatively, by a single rate-limiting pathway, with constant rates. The snapshot data for the distribution histogram of mRNA copy numbers in an isogenic cell population at different time points carry rich dynamic information on fluctuations in transcription [20]. When combined with mathematical models, the fit of mRNA (or oth- er RNA types) distribution data has served as a powerful tool for revealing the multi-step regulation of the activation of different genes in bacteria, yeast, and human cells [9, 20, 21]. However, the calculation of exact forms of dynamical mRNA distribution requires solving infinite arrays of chemical master equations under the whole parameter region of the models, which is beyond the scope of standard theoretical methods, even for the simplest two-state model (Fig. 1a) [22–24]. Fitting of mRNA distribution data must integrate several com- putational tools to determine the rate-limiting step numbers in the activation framework
3
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CC-BY 4.0 International license . and search for suitable system parameters [9,20]. However, current computation algorithms focus only on a class of prior hypothetical multi-step gene activation; therefore, additional competent frameworks may be ignored. Moreover, some typical dynamical transition pat- terns among the different mRNA distribution modes can be well exhibited by all the models in Fig. 1 [24–26], preventing a direct way to rule out models that do not panoramically match the transition patterns of dynamical mRNA distribution. |
The steady-state measurement of gene transcription under different cellular conditions has generated a large dataset of mRNA distribution and its mean level M , the Fano factor φ (the variance over M ), and noise CV 2 (φ over M ) [1,10]. By virtue of mathematical models, fitting steady-state data has revealed a large spectrum of regulation scenarios that cells utilize in response to environmental changes [3,10]. The steady-state mRNA distributions observed so far are often shown to be decaying, unimodal, or bimodal [1, 3]. However, the models in Fig. 1 can only generate the three distribution modes shown at steady-state [15, 23, 27, 28], suggesting that the limited mRNA distribution modalities are insufficient to map reversely onto the diversified frameworks of gene activation. The steady-state data of noise CV 2, Fano factor φ, and mean level M , when mapped as scattered points onto M -CV 2 and M -φ planes, provide a diagram of trend lines of CV 2 and φ against M under varying environments [2,10]. For a given gene of interest in E. coli, yeast, or mammalian cells, the trend lines fitted by different models have revealed distinct regulation scenarios [29]. However, the scenario that plays a dominant role in gene regulation remains elusive. In contrast to the time-consuming single-cell measurements that require RNA labeling and imaging with high sensitivity and resolution [11, 21], the dynamical mRNA average level M (t) can be relatively easily captured by conventional methods at the cell population level [21,30]. Previous studies have revealed rich temporal profiles of M (t) for different genes and cellular conditions, such as monotonic increases in the E. coli promoter Plac/ara [11], up- and-down behavior in the c-Fos gene in human osteosarcoma [21], multiple peaks in mouse fibroblast genes [30, 31], and even oscillations in yeast stress-induced genes [32]. These observations give rise to the problem of whether such rich dynamical behaviors of M (t) can be mapped back to the diversified frameworks of gene activation. To achieve this goal, the key objective is to establish bijections between the dynamical features of M (t) and the parameter regions for certain mathematical models. This allows us to rule out models that do not capture the exhibited dynamical features of M (t) and to test the simplest of the remaining models on the basis of their fit to M (t) data. In this study, we assumed that gene activation is regulated by a combination of sequential and parallel pathways, as shown in Fig. 1, and we illustrated the way that dynamic mRNA average level data can be utilized to help estimate the gene activation frameworks. 4
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2 Results
2.1 Cross-talking three-state model
To make the paper easier to follow, we focused on analyzing the mRNA average level M (t) data from a large group of mouse fibroblast genes under cytokine tumor necrosis factor (TNF) stimulation conditions [30, 31]. With the exception of the simple monotonic growth of M (t) generated by late response genes, the rich non-monotonic behaviors of M (t) have also been determined, such as up-and-down for the Fos gene, up-down-up for the Cxcl1 gene, and damped oscillation with multiple peaks for the Nfkbia gene. To determine the framework that can best capture the rich transcription dynamics of mouse fibroblast genes, theoretical bijections between the dynamical features of M (t) and three mathematical models were established (Table 1). The two-state model shown in Fig. 1a can only generate monotonic increasing dynamics of M (t) [29], and thus is not suitable for the discussion of non-monotonic dynamical behaviors. The three-state model shown in Fig. 1b is proven to display damped oscillatory dynamics of M (t) under a certain parameter region [33, 34]. However, such oscillation behavior is almost invisible owing to its rapid exponential decay, and only slightly slows down the dynamic increase in M (t) [34]. The frameworks with two or more parallel pathways can capture the up-and-down dynamics of M (t), but fails to generate more complex transcription dynamics [29, 35]. Moreover, the cross-talking pathways model (Fig. 1c) generates up-and-down M (t) only when the stronger pathway is frequently selected to active the gene [29], which is incompatible with the robust up-and-down dynamics of M (t), even if the TNF induction level is extremely low [31]. Taken together, the activation frameworks of a single pathway or parallel pathways alone are insufficient to capture the rich dynamics of M (t) from mouse fibroblast genes (Table 1). By combining the three-state model (Fig. 1b) and cross-talking pathways model (Fig. 1c), it is possible to generate new dynamic M (t) features. The simplest combination is shown in Fig. 1d, which we call the cross-talking three-state model. This model can be viewed as adding a parallel pathway in the three-state model or decomposing a pathway of the
5
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CC-BY 4.0 International license . Mathematical models (a) Two-state model (b) Three-state model
(c) Cross-talking pathways model
(d) Multiple pathways model
M (t) dynamical profiles ⇐⇒ Parameter regions Increase Increase Almost increasea Increase Up-and-down Increase Up-and-down
All parameters α2 ≥ ξ α2 < ξ Λ ≥ min{δ, γ} Λ < min{δ, γ} x1 ≥ min{δ, α1} x1 < min{δ, α1}
Table 1: Bijection theory between M (t) dynamical features and system parameter regions for [29] and (d) multiple the (a) two-state [29], (b) three-state [33, 34], (c) cross-talking pathways pathways models [35]. |
α, ξ, Λ, α1, and x1 are the auxiliary numbers associated with the system parameters, and γ and δ are the gene inactivation rate and mRNA degradation rate, respectively. aThe three-state model generates a damped oscillatory M (t) when α2 < ξ [33, 34]. However, such oscillation decays exponentially and displays visually increasing dynamics
[34]. cross-talking pathways model into two sequential steps, as shown in the following scheme:
gene off 1
κ1 (cid:26) (cid:26)(cid:62) (cid:26) (cid:26) q1q2
gene off 2 (cid:90)
(cid:26)(cid:26)
κ2 (cid:90)(cid:90)(cid:126) (cid:90) (cid:90)
(cid:90)
(cid:26)
λ (cid:45) (cid:27) γ
(cid:90)
(cid:90)(cid:90)
gene on
v
(cid:45)
mRNA. δ (cid:63) ∅
We assumed that the gene is activated by two competitive pathways. These are the weak basal pathway, which is has a selection probability q1 and consists of two sequential rate- limiting steps with strength rates κ1 and κ2, or alternatively the strong rate-limiting signaling pathway, which has a selection probability q2 and strength rate λ, satisfying:
0 < q1, q2 < 1, q1 + q2 = 1, and 0 < κ1, κ2 < λ < ∞. The basal pathway is regulated independently by a spontaneous mechanism to maintain basal transcription levels under normal cellular growth conditions [36, 37]. The assumption of two sequential steps and small strength rates for the basal pathway is in close agreement with the real-time imaging data of the off period of 16 mouse fibroblast genes [8]. Moreover, if κ1 or κ2 is relatively large, then the basal pathway can be mathematically approximated by a single rate-limiting step [33], and the framework (1) reduces to the cross-talking pathways model (Fig. 1c). A stronger signaling pathway is triggered when cells receive external cues,
6
(1)
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CC-BY 4.0 International license . and downstream transcription factors (TFs) are activated by special signal transduction pathways to upregulate gene transcription [31, 38]. For each target gene, its activation is ultimately mediated through the binding of downstream TFs in the basal or signaling pathways at the cognate DNA sites in the gene promoter or enhancer domains [5, 38]. The selection probabilities q1 and q2 may then quantify the concentration and availability of activated TFs in each pathway to competitively form TF/DNA binding configurations, while the inducible activation rate λ of the signaling pathway quantifies the binding accessibility and strength between the corresponding TFs and DNA sites [5, 17, 35, 38]. 2.2 Dynamics of M (t) and the bijection with parameter regions
To establish the bijection between the M (t) profiles and the parameter regions of the model (1), we first need to calculate the exact forms of M (t) in terms of system parameters. |
At time t ≥ 0, let random variable X(t) = X = o11, o12, o2, e, specify the states of gene off 1 for basal pathway, gene off 1 for signaling pathway, gene off 2, and gene on, respectively. Then define:
Pm,X(t) = Prob{the system is residing at state X with m mRNA molecules at time t},
and the mass function:
Pm(t) = Pm,o11(t) + Pm,o12(t) + Pm,o2(t) + Pm,e(t), m = 0, 1, · · ·
that quantifies the probability of m mRNA transcripts at time t in a single cell. Following the standard procedure, we can obtain an infinite array of master equations
with respect to Pm,X(t) [15, 33, 39]:
P (cid:48) m,o11(t) = −(κ1 + mδ)Pm,o11(t) + (m + 1)δPm+1,o11(t) + q1γPm,e(t), P (cid:48) m,o12(t) = −(λ + mδ)Pm,o12(t) + (m + 1)δPm+1,o12(t) + q2γPm,e(t), P (cid:48) m,o2(t) = −(κ2 + mδ)Pm,o2(t) + (m + 1)δPm+1,o2(t) + κ1Pm,o11(t), P (cid:48) m,e(t) = −(γ + v + mδ)Pm,e(t) + (m + 1)δPm+1,e(t) + vPm−1,e(t)
+κ2Pm,o2(t) + λPm,o12(t). Summing up (2)-(5) gives the master equation of Pm(t):
P (cid:48)
m(t) = (m + 1)δPm+1(t) − vPm,e(t) − mδPm(t) + vPm−1,e(t). 7
(2)
(3)
(4)
(5)
(6)
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CC-BY 4.0 International license . We did not focus on solving (2)-(6), which are beyond the scope of current mathematical methods within all parameter regions [22–26]. However, the master equations set a basis for calculating analytical forms for the gene state probabilities Po11, Po12, Po2, Pe, and mean transcript level M (t), defined as:
PX(t) =
∞ (cid:88)
Pm,X(t), X = o11, o12, o2, oe, and M (t) =
∞ (cid:88)
mPm(t). m=0
m=0
Using these definitions and (2)-(6), we derived the equations for the four state probabilities and the mean transcription level:
o11(t) = −κ1Po11(t) + q1γPe(t), P (cid:48) P (cid:48) P (cid:48) o2(t) = κ1Po11(t) − κ2Po2(t), P (cid:48) M (cid:48)(t) = vPe(t) − δM (t). o12(t) = −λPo12(t) + q2γPe(t), e(t) = λPo2(t) + κ2Po2(t) − γPe(t),
Because the system must reside on exactly one gene state at any time, we set an arbitrary initial condition for (7):
Po11(0) + Po12(0) + Po2(0) + Pe(0) = 1 and M (0) ≥ 0. We utilized the Laplace transform method to solve the first-order differential system
(7)-(8) (Materials and Methods). We defined a polynomial function as:
h(x) = [(κ1λ + κ2λ + κ1κ2)Pe(0) + κ1κ2Po11(0) + λ(κ1 + κ2)Po12(0) + κ2(λ + κ1)Po2(0)]x
+Pe(0)x3 + [(κ1 + λ + κ2)Pe(0) + λPo12(0) + κ2Po2(0)]x2 + κ1κ2λ,
and two auxiliary numbers c1 and c2 in terms of the system parameters (Materials and Methods (18)-(19)). It can be verified that zero is a simple eigenvalue of the coefficient matrix for the system of the first four equations in (7). The other non-zero eigenvalues a1, a2, and a3 are calculated in terms of c1, c2, and system parameters (Materials and Methods (15)-(19)). Under the arbitrary initial condition (8), the average mRNA level M (t) is found to be as follows:
(1) If c2
1 < c2, then a1, a2, a3 are real numbers with 0 < a1 < a2 < a3 (Materials and
8
(7)
(8)
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It is made
doi:
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available under a
CC-BY 4.0 International license . Methods (22)), and M (t) takes the form of:
M (t) =
v δ
κ1κ2λ a1a2a3
−
vh(−a1)e−a1t a1(a2 − a1)(a3 − a1)(δ − a1)
+
vh(−a2)e−a2t a2(a2 − a1)(a3 − a2)(δ − a2)
−
vh(−a3)e−a3t a3(a3 − a1)(a3 − a2)(δ − a3)
+
vh(−δ)e−δt δ(δ − a1)(δ − a2)(δ − a3)
+ M (0)e−δt. (2) If c2
1 = c2, then a1, a2, a3 > 0 are real numbers with a1 (cid:54)= a2 = a3 (Materials and
Methods (24)), and M (t) takes the form of:
M (t) =
v δ
κ1κ2λ a1a2 2
(1 − e−a2t) −
vh(−a1)(e−a1t − e−a2t) a1(δ − a1)(a2 − a1)2 +
vh(−a2)te−a2t a2(a2 − a1)(δ − a2)
+
vh(−δ)(e−δt − e−a2t) δ(δ − a1)(δ − a2)2 + M (0)e−δt. (3) If c2
1 > c2, then a1 > 0 is a real number, whereas a2 and a3 are conjugate complexes, then let ar = Re(a2) and ai = Im(a2) (Materials and Methods (26)). Then, M (t) takes the form of:
M (t) =
vh(−a1)e−a1t a1(δ − a1)[(a1 − ar)2 + a2 r + a2 i ] i ) 1 + A2 cos(ait + θ)e−art + M (0)e−δt,
v δ
κ1κ2λ
−
a1(a2 √
+ ¯A
+
vh(−δ)e−δt δ(δ − a1)[(δ − ar)2 + a2 i ]
where the constants ¯A, A, and θ correlate with the parameters and initial conditions (Mate- rials and Methods (28)). We characterized the dynamic profiles of M (t) with almost no expression products at the initial time t [11, 21, 30]. We assumed that transcription starts from the gene off 1 state and counts only the newly produced mRNA molecules. This gives the following initial values:
(Po11(0), Po12(0), Po2(0), Pe(0), M (0)) = (q1, q2, 0, 0, 0). We started with an interesting case, c2 1 > c2. Then, M (t) was expressed in exact form (11), which contains a cosine function, and suggested possible oscillatory dynamics of M (t). However, the coefficient of the cosine function damps exponentially, which dramatically weakened the oscillation visually, as manifested by our numerical examples and observations from the three-state model [34]. The exact form (11) can only be viewed as a steady-state value, adding three exponential functions at most. If the exact form of M (t) with M (0) = 0 has such a structure, then it can be proved that the most complex dynamics of M (t) will
9
(9)
(10)
(11)
(12)
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CC-BY 4.0 International license . only take a unique peak such as up-and-down or up-down-up profiles (Materials and Methods Theorem 1). For the other case of c2
1 ≤ c2, the eigenvalues a1, a2, and a3 are real, and the exact forms (9)-(10) of M (t) do not contain oscillatory functions but contain multiple exponential functions. The case c2 1 = c2 rarely occurs in biology and can be viewed mathematically as a 1 < c2. For c2 limiting case of c2 1 < c2, a rigorous statement of the M (t) profiles is inevitably technical. |
Let x1 and x2 denote the two roots of:
H(x) = vq2λx2 + v(q1κ1κ2 + q2λκ1 + q2λκ2)x + vκ1κ2λ. When both x1 and x2 are complex numbers, there are a total of four parameter correlations, and we showed that M (t), expressed by (9), either increases monotonically for all t > 0, or develops an up-down-up profile. If x1 and x2 are real values, we can classify all 60 correlations among x1, x2, a1, a2, a3, and δ into three categories that correspond to three distinct dynamical behaviors: the increasing, up-and-down, and up-down-up profiles of M (t). We illustrated detailed mathematical results and their proof in Theorem 2 of the Materials In summary, for the cross-talking three-state model (1), even if M (t) is and Methods. expressed in different exact forms (9)-(11) and influenced by various parameter correlations, M (t) can exhibit, but exhibits only three features: increasing, up-and-down, and up-down-up dynamics. 2.3 Fitting dynamical transcription data of mouse fibroblast genes
We demonstrated three dynamical profiles of M (t) generated by model (1). These distinct behaviors are in agreement with the observed dynamic trends of average mRNA levels in mouse fibroblast genes in response to TNF [30, 31]. For instance, Hao and Baltimore [30] divided 180 activated mouse fibroblast genes under TNF induction into three groups, sepa- rately characterized by the short, median, and long half-lives of the transcripts. As shown in Fig. 2, they found that group I genes responded quickly by forming a sharp dynamical peak at average transcription levels, group II genes did not respond quickly but most still formed a gentle transcription peak along the timeline, and group III mRNAs accumulat- ed rather slowly and gradually increased in abundance during the observation window. The transcription data from the 12 representative mouse fibroblast genes shown in Fig. 2 contains four genes displaying the up-down-up trend of transcription dynamics (Edn1, Cxcl1, Ccl2, Icam1), as well as others displaying either dynamical up-and-down or monotonic increasing transcription. Using exact forms (9)-(11) of M (t), the model (1) provides good theoretical
10
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CC-BY 4.0 International license . fits to all 12 datasets (coefficient of determination R2 > 0.9). Figure 2: Fit of transcription data by the cross-talking three-state model (1). Black circles rep- resent the dynamical data of mRNA average levels for 12 mouse fibroblast genes under TNF induction [30]. The genes are divided into groups I, II, and III, which are separately characterized by the short, median, and long half-lives of the transcripts [30]. The red lines are generated using exact forms (9)-(11) of the model (1), which provide a good fit to the data points (R2 > 0.9). |
The fitted system parameters are listed in Table S1 (Supporting Information). When fitting the data shown in Fig. 2, we assigned extremely small values to the activation rates κ1 and κ2 of weak basal pathway, and restricted the mRNA degradation rate δ of each gene within the δ region of the gene group to which they belong [30] (Supporting Information, Table S1). Therefore, the fitted δ values show a significant negative correlation with gene groups I, II, and III because the gene groups themselves are classified by their transcript half-lives (Fig. 3a). Intriguingly, the freely fitted inactivation rate γ and activation rate λ of the signaling pathway also exhibited negative correlation with gene groups (Fig. 3a). This observation suggests that the simultaneous large λ and γ may separately help enhance the height of the peak and suppress the stationary values of M (t) in group I. In contrast, the
11
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CC-BY 4.0 International license . small λ and γ implemented contrary functions that destroy the dynamical peak of M (t) and lift up the stationary mRNA numbers in group III. However, the probability q2 of the signaling pathway does not clearly correlate with the gene groups but varies for different genes (Fig. 3a). Note that the dynamics of M (t) in the three gene groups are mainly discriminated by its first peak. Our observations suggest that, once cells receive external cues, the frequency of the signaling pathway directing gene activation may not play a crucial role in regulating the dynamical peak of transcription level. Figure 3: Regulation of transcription dynamics by system parameters. (a) The fitted parameters for 12 mouse fibroblast genes are listed in units of gene groups (Supporting Information, Table S1). Different gene groups exhibit distinct temporal transcription modes [30]. The values of mRNA degradation rate δ, inactivation rate γ, and activation rate λ of the signaling pathway are all negatively correlated with gene groups I, II, and III. The probability q2 of the signaling pathway does not follow a clear correlation with the gene groups. (b) Based on the fitted parameter set for the Cxcl1 gene, increasing δ, γ, and λ transit transcription dynamics from monotonic to up-down-up mode. An increase in q2 generates switches among multiple transcription dynamical modes, where the non-monotonic modes are displayed within most of the q2 variation region (0, 1). 12
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To further understand the regulation of M (t) profiles, we varied the parameters δ, γ, λ, and q2 under the fitted parameter sets of all 12 genes in Fig. 2. This procedure reveals a uniform regulation mode for each system parameter. As shown in Fig. 3b for Cxcl1 gene, the variation in δ behaves as a bilateral switch to regulate M (t): there is a threshold value such that M (t) increases monotonically while δ stays below the threshold, but switches to a non-monotonic profile once δ exceeds the threshold. Such bilateral regulation of δ has been observed to play an important role in controlling the temporal transcription mode in mouse fibroblasts [30, 31]. In addition, both γ and λ play the same bilateral roles in regulating M (t) dynamics (Fig. 3b), reinforcing previous observation of smaller δ, γ, λ for group III genes that generate increasing M (t) with larger δ, γ, λ for groups I and II genes that exhibit non-monotonic transcription dynamics (Fig. 3a). The regulation scenario of q2 is different because it generates multiple switches among distinct M (t) profiles, when q2 increases from 0 to 1 (Fig. 3b). Exceptions need to be made for cases where q2 approaches 0 or 1, which generates increasing transcription dynamics, because the dynamical peak of M (t) seems to be robust in almost all the variation regions of q2 ∈ (0, 1). Note that q2 is closely related to signal strength. Our observations fit with the ubiquitous transcription dynamical peak of mouse fibroblast genes under TNF induction from the lowest to the highest levels [31]. 2.4 Cross-talking n-state model for oscillatory transcription dy-
namics
Our bijection theory shows that the cross-talking three-state model (1) cannot generate multiple dynamical peaks of M (t). Therefore, the model (1) can be ruled out when M (t) exhibits oscillation [30, 32]. We focused on transcription with constant kinetic rates under stable inductions to avoid complicated M (t) dynamics regulated by time-dependent rates in response to time-varying signals [40]. The bijection theory (Table 1) shows that multi- ple parallel pathways induce at most one dynamical peak, and therefore introducing more parallel pathways in model (1) may not capture oscillatory M (t). We then considered de- composing the basal pathway of model (1) into multiple sequential steps, as shown in Fig. 4a for the cross-talking n-state model. Calculation of M (t) can follow the same procedure for model (1), which relies on solving a system of differential equations for which the coefficient matrix may have multiple pairs of eigenvalues expressed by conjugate complexes (Materials and Methods). According to the classical theory of ordinary differential equations, the exact forms of M (t) may contain multiple periodic cosine functions, and it is therefore plausible to visualize oscillatory dynamics. To test M (t) oscillation induced by the sequential multi-step gene activation, we com-
13
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CC-BY 4.0 International license . Figure 4: Framework for generating oscillatory transcription dynamics. (a) The cross-talking n- state model for which the gene is activated either by the strong signaling pathway with probability q2, or alternatively by the weak basal pathway that consists of n − 1 rate-limiting steps with probability q1 = 1 − q2. (b) When gene activation is directed by a single multi-step pathway (q2 = 0), the increase in the step number prolongs the initial response lag and enhances the damped oscillation of the transcription level M (t). (c) When the gene is activated by the cross-talk between pathways (q2 > 0), the increase in the step number in the basal pathway has almost no impact on the initial quick up-and-down dynamics of M (t), but significantly enhances the following damped oscillatory behavior. (d) The curve of M (t) (red lines) generated by the framework in (a) captures the oscillatory trend of transcription data (black circles) for the mouse fibroblast Nfkbia gene under TNF induction [30]. The parameters in (b) and (c) are the fitted rates of the Cxcl1 gene in Table S1 with κ1 = · · · = κn−1 to maintain a constant Toff . Parameters in (d) are listed in Table S1. pared the M (t) profiles for different step numbers. This procedure requires that all compar- isons are restricted to a constant average duration Toff of the gene off state [15, 34]. For the cross-talk n-state model (Fig. 4a), Toff is given by:
Toff = q1
n−1 (cid:88)
i=1
1 κi
+
q2 λ
, n ≥ 2. To guarantee the unchanged Toff , we set three parameter scaling conditions where activation rates κ1, · · · , κn−1 are separately scaled identically [14, 41], differently [8, 14], and alterna-
14
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available under a
CC-BY 4.0 International license . tively [14]:
(C1) : κ1 = κ2 = · · · = κn−1, with κ1 =
q1(n − 1) Toff − q2/λ
;
(C2) : κ2 = 2κ1, κ3 = 3κ1, · · · κn−1 = (n − 1)κ1, with κ1 = q1
(C3) : κ1 = κ3 = · · · , and κ2 = κ4 = · · · = 3κ1, with κ1 =
1 + 1
2 + · · · + 1 Toff − q2/λ 2q1(n−1) 3(Toff −q2/λ), n is odd, q1(2n−1) 3(Toff −q2/λ), n is even. n−1
;
We initially examined the case of q2 = 0, for which gene activation is directed by a single multi-step pathway [14,15,26]. Under parameter scaling condition (C1), we generated several M (t) curves under different activation step numbers, using numerical simulations from the corresponding system of differential equations (Materials and Methods (43)). As shown in Fig. 4b under the fitted parameters of the Cxcl1 gene in Fig. 2, multi-step gene activation for large step numbers triggers significant damped oscillatory M (t), where the significance of the oscillation is positively correlated with the step number. |
However, the system displays lag times of more than 8 h to reach the first peak of M (t). This slow transcription response contradicts the rapid peak of M (t) within 0.5 ∼ 2 h for mouse fibroblast genes [30, 31]. Moreover, the damped oscillation and response lag of M (t) were robust against the parameter scaling conditions (C2) and (C3) (Supporting Information, Fig. S1). Taken together, the large number of sequential gene activation steps facilitates the oscillatory dynamics of M (t), while a single multi-step pathway was not able to induce quickly-peaked transcription dynamics of mouse fibroblast genes. We then quantified q2 (cid:54)= 0 to introduce the cross-talking regulation of pathways on M (t) dynamics. We generated M (t) curves (Materials and Methods (42)) under the fitted parameters of the Cxcl1 gene in Fig. 2 and conditions (C1)-(C3). As shown in Fig. 4c and Fig. S2 in Supporting Information, the system generates oscillatory M (t) with two major features. Firstly, M (t) displays a quick and sharp first peak within the initial time region, while the height and sharpness of the first peak are nearly independent of the step number and parameter scaling conditions of the basal pathway. Secondly, M (t) displays a damped and gentle second and following peaks that are tightly correlated with the step number and parameter conditions, similarly to the oscillation of M (t) induced by a single multi-step pathway (Fig. 4b). These two features capture multiple dynamical peaks for the transcription of the mouse fibroblast Nfkbia gene [30] (Fig. 4d). Taken together, the cross-talk between signaling and basal pathways plays a dominant role in generating the first quick up-and-down transcription dynamics, while the subsequent gentle and damped transcription oscillation is
15
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available under a
CC-BY 4.0 International license . induced by the multi-step regulation in the weak basal pathway. 2.5 Cross-verification for monotonic transcription dynamics
Our method requires rich M (t) data dynamics to rule out frameworks that cannot sufficiently capture the dynamic features. When M (t) displays simple monotonicity, all frameworks (Fig. 1) may provide good fits to the M (t) data. However, we cannot claim that the two- state model is the best model to explain the data, even if it is the simplest compared to the other frameworks. This is because monotonic M (t) may be generated by the manipulated small degradation rate δ (Fig. 3b) for accurately counting transcript numbers in single-cell measurements [11,14]. One way to avoid the masking effect of small δ on M (t)-rich dynamics is to consider the average level of nascent RNA that is independent of mRNA degradation [4,42]. In contrast, some single-cell data for transcription of mRNA molecules display smooth trend lines along the timeline, such as the noise CV 2(t), Fano factor φ(t), and probability P0(t) of the gene producing zero transcripts. |
These indexes may be used in conjunction with M (t) to cross-verify the gene activation frameworks. The calculation of φ(t) and CV 2(t) are standard, and require solving the second moment µ2(t) of the system of ordinary differential equations derived from the corresponding master equations [33, 39]. We calculated the exact forms of µ2(t) for the cross-talking three-state model (1) (Materials and Methods (48)), and φ(t) = µ2(t)/M (t) − M (t) and CV 2(t) = φ(t)/M (t) were then readily obtained. The probability P0(t) is one of the solutions of master equations. Calculation of P0(t) involves introducing the generating function V (z, t) to transform the master equation into a system of partial differential equations for V (z, t). However, while solving V (z, t) is somewhat difficult, we can still express V (z, t) in closed forms of hypergeometric functions for different models [23, 26]. Consequently, P0(t) can be obtained by P0(t) = V (−1, t). The expressions of φ(t), CV 2(t), and P0(t) are not as neat as that of M (t), which prevents us from establishing theoretical bijections between their dynamical profiles and parameter regions. Nevertheless, the computation of φ(t), CV 2(t), and P0(t) through their expressions or the corresponding differential equations (Materials and Methods) can generate dynamical curves for fitting data [11, 40]. We hypothesized that different gene activation frameworks can generate distinct dynam- ics of φ(t), CV 2(t), and P0(t) under the same monotonic M (t). To verify this, we first fitted a group of increasing M (t) data to all four frameworks in Fig. 1 (see Fig. 5a). Under the fitted parameters we separately generated dynamical curves of φ(t), CV 2(t), and P0(t) corre- sponding to each framework. The curves of noise CV 2(t) clustered within a low-value region, probably because of their large denominator M (t) (Fig. 5b), suggesting that the noise data
16
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CC-BY 4.0 International license . may not help discriminate gene activation frameworks. The curves of the Fano factor φ(t) are clearly separated into two categories: the curves are very high under cross-talking path- ways, but are relatively low under a single pathway (Fig. 5c). This separation reinforces the conclusion that the parallel pathways enhance φ [39], while sequential steps suppress φ [15] under the same mean level M at steady-state. The curves of P0(t) follow the same separa- tion as that of φ(t) (Fig. 5d), which reinforces the observed suppressed P0(t) under multi-step gene activation [26]. Taken together, the dynamics of φ(t) and P0(t) may help discriminate the activation frameworks regulated by cross-talking pathways or a single pathway. Figure 5: Discrimination of gene activation frameworks under monotonic dynamical mRNA average level. |
(a) The increasing transcription mean data (black circles, Mmp13 gene [30]) are fitted by different models. (b) Dynamical curves of transcription noise for each model are clustered with relatively small values most of the time. For (c) transcription Fano factor and (d) probability of genes not producing any transcript, the dynamical curves generated by a single pathway deviate from the curves generated by cross-talking pathways. Parameters: v = 2630 h−1, q2 = 0.5; two-state model, (λ, γ, δ) = (2.21, 4, 0.5) h−1; three-state model, (κ1, κ2, γ, δ) = (5.09, 5.09, 4, 0.55) h−1; cross- talking pathways model, (κ, λ, γ, δ) = (0.07, 1.2, 1.2, 0.15) h−1; cross-talking three-state model, (κ1, κ2, λ, γ, δ) = (0.24, 0.1, 1.2, 1, 0.15) h−1. 3 Conclusion and Discussion
The classical two-state model used in single-cell studies posits that a gene will randomly transition between on (active) and off (inactive) states, with mRNA molecules being pro- duced only when the gene is on (Fig. 1a). Compared to the universal feature of a single rate-limiting step turning gene off [6, 8, 13], the process of turning a gene on is usually non-Markovian, and is influenced by multiple rate-limiting fluctuations [6,7,13]. The frame- work of gene activation has been modeled by listing rate-limiting steps sequentially [8, 14] (Fig. 1b), parallelly [16,35] (Fig. 1c), or in the form of their combinations [17] (Fig. 1d). Re- cent studies have facilitated efficient computation of downstream transcription distribution under non-Markovian gene activation [18, 19]. However, the best method for mapping the
17
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CC-BY 4.0 International license . transcription distribution data back to the exact picture of the activation framework for the gene of interest remains elusive. Distinct gene activation frameworks cannot be discriminated by the steady-state single- cell data on mRNA distribution or its noise, Fano factor, and mean, because the limited steady-state diagrams can be reliably illustrated by different frameworks [15, 23, 27–29]. When the time dimension is included, the distribution histograms of both gene off periods and mRNA copy numbers provide a complete static basis to computationally search the optimal number of rate-limiting steps in gene activation and their kinetic parameters [9, 14, 20]. However, these methods require a prior hypothetical framework of gene activation that cannot be easily deduced from limited gene off distribution modes [15–17] or from similar dynamical transition patterns of mRNA distribution profiles [24–26]. Therefore, an efficient method for determining confident gene activation frameworks is urgently required prior to any attempt to fit single-cell dynamical transcription data. |
In this paper, we demonstrated that the dynamics of transcript average level M (t) can serve as a competent candidate to facilitate the efficient estimation of the gene activation framework and system parameters. Firstly, compared with time-consuming single-cell mea- surements [11,21], the dynamic features of M (t) for a large number of genes can be captured relatively quickly by traditional cell population methods. Secondly, compared to the mul- tiple uneven distribution profiles at discrete time points [9, 20], a single smooth curve of M (t) along the timeline presents easily discriminated dynamic features and provides a more efficient theoretical fit to the data. Thirdly, compared to the lack of a method to calculate dynamical mRNA distribution [22, 23], the exact forms of M (t) are rather neat and can be achieved by the standard theory of ordinary differential equations. By taking advantage of the M (t) expressions and their simple forms (Eqs. (9)-(11)), we were able to establish theoretical bijections between the M (t) dynamics and parameter regions for different gene activation frameworks. Subsequently , frameworks that cannot capture the exhibited M (t) dynamical features can be ruled out, while the optimal forms of the other potential frameworks are further determined by fitting M (t) data. We illustrated this idea by analyzing activation frameworks for a large number of TNF-induced mouse fibroblast genes. These genes display rich transcription dynamics that can be categorized into three main features: increasing, up-and-down, and up-down-up profiles of M (t) [30,31]. Our bijection theories (Table 1 and Materials and Methods Theorems 1-2) show that these three distinct dynamics cannot be achieved by the sequential or parallel rate-limiting steps alone, but can be captured by the simplest form of combined sequential and parallel steps (Fig. 1d). We call this framework the cross-talking three-state model, as depicted in (1), for which the gene is activated either by the weak basal pathway consisting of two sequential
18
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CC-BY 4.0 International license . steps, or alternatively by the strong signaling pathway. The cross-talking three-state model (1) can serve as a reliable model because it provides a good theoretical fit for all the representative datasets on the transcription dynamics of mouse fibroblast genes [30] (Fig. 2). Moreover, analysis of the freely fitted system parameters (Table S1) reveals two regulation scenarios for M (t) dynamics (Fig. 3). For the mRNA degradation rate δ, inactivation rate γ, and activation rate λ of the signaling pathway, M (t) maintains a monotonic increase when δ, γ, and λ remain below their thresholds while switching non-monotonically once δ, γ, and λ exceed the threshold values (Fig. |
3b). This bilateral regulation results in an interesting phenomenon: δ, γ, and λ are simultaneously large for the genes displaying non-monotonic M (t), whereas they are simultaneously small for genes displaying monotonic M (t) (Fig. 3a). In contrast to the gene-specific δ, γ, and λ, the environment influenced the probability q2 that the signaling pathway does not play a crucial role in regulating the first peak of M (t) (Fig. 3). This observation is consistent with the robust transcription dynamical peak of mouse fibroblast genes, regardless of how the TNF induction level varies [31]. We note that a small number of mouse fibroblast genes display damped transcription oscillation, with the first peak forming rapidly within the initial period [30, 31]. We suggest that multiple sequential rate-limiting steps may play a role in triggering oscillatory behavior. Therefore, we developed the cross-talking n-state model by decomposing the basal pathway of model (1) into multiple steps (Fig. 4a). We first ruled out the framework of a single multi-step pathway as it triggers a long lag reaching the first peak of M (t) (Fig. 4b, Fig. S1), which contradicts the observed rapid peak of M (t). However, when we recovered the cross- talk between the signaling pathway and the multi-step basal pathway, the initial lag time disappeared and the first peak of M (t) formed quickly (Fig. 4c, Fig. S2). Intriguingly, the step number and parameter scaling condition in the basal pathway have almost no effect on the first peak of M (t), whereas they significantly influence the other dynamical peaks. Together with the transcription data of the mouse fibroblast genes (Fig. 4d), we found that cross-talking regulation between pathways is crucial to trigger the first rapid, sharp peak of M (t), while the multi-step regulation facilitates the following damped and gentle oscillatory dynamics. Thus, we developed a procedure to estimate frameworks of gene activation using tran- scription level M (t) dynamical data at the cell population level. This procedure readily disqualifies frameworks that do no perform satisfactorily, and determines potential frame- works that provide the best data fit. When more sophisticated single-cell distribution data of the gene off period [8,14] or mRNA copy numbers [9,20,21] are used, our procedure provides a prior estimation of activation frameworks and parameter rates to facilitate more compu-
19
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available under a
CC-BY 4.0 International license . tationally efficient search for optimal step numbers and parameters. This procedure relies on the rich dynamics of M (t). When M (t) behaves monotonically, the other transcription indexes are required to cross-verify the activation frameworks. |
For instance, the dynami- cal Fano factor or the probability of no transcript being produced may help discriminate frameworks regulated by a single pathway or cross-talking pathways (Fig. 5). Future work may utilize additional data for different genes and transcription indexes to test and develop our procedure. In addition, we anticipate the inclusion of nascent RNA data that are not influenced by the mRNA degradation rate and may therefore provide more direct information on gene activation frameworks [4,42]. Finally, a cell cycle description [22,41,43] may be introduced into gene activation frameworks to eliminate estimation errors caused by disregarding cell cycle stochasticity [41]. Materials and Methods
Exact forms of M (t) for cross-talking three-state model (1)
To calculate mRNA average level M (t) for the model (1), we need solve the first four differential equations in system (7) for gene state probabilities Po11, Po12, Po2 and Pe under the arbitrary initial condition (8):
P (cid:48) P (cid:48)
o11(t) = −κ1Po11(t) + q1γPe(t), o2(t) = κ1Po11(t) − κ2Po2(t),
P (cid:48)
o12(t) = −λPo12(t) + q2γPe(t), e(t) = λPo12(t) + κ2Po2(t) − γPe(t),
P (cid:48)
Po11(0) + Po12(0) + Po2(0) + Pe(0) = 1. To solve the above first-order differential system, we denote by
L1j(x) = L(Po1j (t)) =
L2(x) = L(Po2(t)) =
(cid:90) ∞
e−xtPo1j (t)dt,
j = 1, 2,
0 (cid:90) ∞
e−xtPo2(t)dt and Le(x) = L(Pe(t)) =
(cid:90) ∞
e−xtPe(t)dt. 0
0
Then using Laplace transform in the theory of ordinary differential equation to system (13) yields
(cid:40) Po11(0) = (x + κ1)L11(x) − q1γLe(x), Po12(0) = (x + λ)L12(x) − q2γLe(x),
Po2(0) = −κ1L11(x) + (x + κ2)L2(x), Pe(0) = −λL12(x) − κ2L2(x) + (x + γ)Le(x). 20
(13)
(14)
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CC-BY 4.0 International license . The determinant of coefficient matrix for the above system can be directly calculated as
x(x + a1)(x + a2)(x + a3) = x[x3 + (κ1 + λ + κ2 + γ)x2
+ (κ1λ + κ1κ2 + κ2λ + κ1γ + q1λγ + κ2γ)x + κ1λκ2 + q1κ1λγ + q2κ1κ2γ + q1κ2λγ],
where a1, a2 and a3 are non-zero eigenvalues of the coefficient matrix for the system (13). To calculate a1, a2 and a3, we let the above formula equal to 0, and then solve the cubic polynomial equation using Cardano formula. This gives
a1 =
κ1 + κ2 + λ + γ 3
−
(cid:18)
(cid:114) 3
−c1 +
(cid:113)
(cid:114) 1 − c2 + 3 c2
−c1 −
(cid:113)
c2 1 − c2
(cid:19) ,
a2 =
a3 =
κ1 + κ2 + λ + γ 3
κ1 + κ2 + λ + γ 3
−
−
(cid:18) −1 + 2
(cid:18) −1 − 2
√
√
3i
3i
(cid:114) 3
(cid:114) 3
−c1 +
−c1 +
(cid:113)
(cid:113)
c2 1 − c2 −
c2 1 − c2 −
√
1 + 2 √
1 − 2
3i
3i
(cid:114) 3
(cid:114) 3
−c1 −
−c1 −
(cid:113)
(cid:113)
c2 1 − c2
c2 1 − c2
(cid:19)
(cid:19)
where
c1 =
κ1κ2λ + q1κ1λγ + q2κ1κ2γ + q1κ2λγ 2
+
(κ1 + κ2 + λ + γ)3 27
−
(κ1 + κ2 + λ + γ)(κ1λ + κ1κ2 + λκ2 + κ1γ + q1λγ + λγ) 6
(cid:54)= 0,
c2 = −
1 27
(cid:20)
(κ1λ + κ1κ2 + λκ2 + κ1γ + q1λγ + λγ) −
(κ1 + κ2 + λ + γ)2 3
(cid:21)3
(cid:54)= 0. |
Applying Cramer’s rule in the theory of linear algebra on the system (14) readily gives
Le(x) =
h(x) x(x + a1)(x + a2)(x + a3)
, with
h(x) = [(κ1λ + κ2λ + κ1κ2)Pe(0) + λ(κ1 + κ2)Po12(0) + κ2(λ + κ1)Po2(0) + κ1κ2Po11(0)]x
+Pe(0)x3 + [(κ1 + λ + κ2)Pe(0) + λPo12(0) + κ2Po2(0)]x2 + κ1κ2λ. To calculate analytical formula for mRNA average level M (t), we first notice that it satisfies
M
(cid:48)
(t) = −δM (t) + vPe(t). Then applying Laplace transform to M (t) gives
xLM (x) − M (0) = vLe(x) − δLM (x), with LM (x) = L(M (t)) =
(cid:90) ∞
e−xtM (t)dt. 0
21
(15)
, (16)
, (17)
(18)
(19)
(20)
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CC-BY 4.0 International license . The substitution of Le(x) in (20) further leads to
LM (x) =
vLe(x) + M (0) x + δ
=
vh(x) + M (0)x(x + a1)(x + a2)(x + a3) x(x + a1)(x + a2)(x + a3)(x + δ)
. (1) If c2
1 < c2, then a1, a2 and a3 given in (15)-(19) are real numbers satisfying 0 < a1 < a2 < a3. Also, the direct calculation can simplify a1, a2 and a3 to be
a1 =
a3 =
κ1 + κ2 + λ + γ 3 κ1 + κ2 + λ + γ 3
√ − 2 6
√ − 2 6
c2 cos θ0,
a2 =
κ1 + κ2 + λ + γ 3
c2 cos(θ0 + 2π/3), where θ0 =
√ − 2 6
c2 cos(θ0 + 4π/3),
arccos(c1/
3
√
c2)
∈ (0, π/3). We decompose LM (x) given by (21) into the sum of partial fractions as
LM (x) =
α0 x
+
α1 x + a1
+
α2 x + a2
+
α3 x + a3
+
αδ x + δ
,
where the coefficients α0, α1, α2, α3 and αδ satisfy
α0(x + a1)(x + a2)(x + a3)(x + δ) + α1x(x + a2)(x + a3)(x + δ) + α2x(x + a1)(x + a3)(x + δ)
+α3x(x + a1)(x + a2)(x + δ) + aδx(x + a1)(x + a2)(x + a3)
= vh(x) + M (0)x(x + a1)(x + a2)(x + a3). The separate substitution of x = 0, −a1, , −a2, −a3, −δ into above equation yields
α0 =
v δ
κ1κ2λ a1a2a3
, α1 = −
vh(−a1) a1(a2 − a1)(a3 − a1)(δ − a1)
, α2 = −
vh(−a2) a2(a1 − a2)(a3 − a2)(δ − a2)
α3 = −
vh(−a3) a3(a1 − a3)(a2 − a3)(δ − a3)
, and αδ = −
vh(−δ) δ(a1 − δ)(a2 − δ)(a3 − δ)
+ M (0). Then the application of the inverse Laplace transform to LM (x) given in (23) readily leads to
M (t) = α0 + α1e−a1t + α2e−a2t + α3e−a3t + αδe−δt,
which is exactly the expression (9). (2) If c2
1 = c2, then it can be verified that a1, a2 and a3 given by (15)-(19) are positive real
numbers taking the form of
a1 =
κ1 + κ2 + λ + γ 3
√ + 2 3
c1, and a2 = a3 =
κ1 + κ2 + λ + γ 3
√ − 3
c1. We decompose LM (x) given in (21) into the sum of partial fractions as
LM (x) =
¯α0 x
+
¯α1 x + a1
+
¯αδ x + δ
+
¯α2 x + a2
+
¯α3 (x + a2)2 ,
22
(21)
(22)
(23)
,
(24)
(25)
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where the coefficients ¯α0, ¯α1, ¯α2, ¯α3 and ¯αδ satisfy
¯α0(x + a1)(x + a2)2(x + δ) + ¯α1x(x + a2)2(x + δ) + ¯α2x(x + a1)(x + a2)(x + δ) +¯α3x(x + a1)(x + δ) + ¯αδx(x + a1)(x + a2)2 = vh(x) + M (0)x(x + a1)(x + a2)(x + a3). Then the separate substitution of x = 0, −a1, −a2, −δ into this equation yields
¯α0 =
v δ
κ1κ2λ a1a2 2
, ¯α1 = −
vh(−a1)
a1(δ − a1)(a2 − a1)2 , ¯α2 = M (0) − (¯α0 + ¯α1 + ¯αδ),
¯α3 = −
vh(−a2) a2(a1 − a2)(δ − a2)
, and ¯αδ = −
vh(−δ)
δ(a1 − δ)(a2 − δ)2 + M (0). Then the application of the inverse Laplace transform to LM (x) given in (25) readily leads to
M (t) = ¯α0 + ¯α1e−a1t + ¯α2e−a2t + ¯α3te−a2t + ¯αδe−δt,
which verifies the expression (10). (3) If c2
1 > c2, then a1 is a positive real number while a2 and a3 are conjugate complexes. Let
ar = Re(a2) and ai = Im(a2). Then expressions (15)-(19) suggest
a1 =
κ1 + κ2 + λ + γ 3
κ1 + κ2 + λ + γ 3 (cid:114) 3
ar =
√
(cid:18)
3 2
ai = −
−c1 +
−
(cid:18)
(cid:114) 3
−c1 +
(cid:113)
(cid:114) 1 − c2 + 3 c2
−c1 −
(cid:113)
c2 1 − c2
(cid:19) ,
+
1 2
(cid:18)
(cid:114) 3
−c1 +
(cid:113)
(cid:114) 1 − c2 + 3 c2
−c1 −
(cid:113)
c2 1 − c2
(cid:19) ,
(cid:113)
(cid:114) 1 − c2 − 3 c2
−c1 −
(cid:113)
c2 1 − c2
(cid:19) . (26)
We decompose LM (x) of (21) into the sum of partial fractions as
LM (x) =
˜α0 x
+
˜α1 x + a1
+
˜αδ x + δ
+
˜α2x + ˜α3 (x + ar)2 + a2 i
,
(27)
with ˜α0, ˜α1, ˜α2, ˜α3 and ˜αδ satisfying
˜α0(x + a1)(x + δ)[(x + ar)2 + a2 +˜αδx(x + a1)[(x + ar)2 + a2
i ] + ˜α1x(x + δ)[(x + ar)2 + a2
i ] + ( ˜α2x + ˜α3)x(x + a1)(x + δ)
i ] = vh(x) + M (0)x(x + a1)[(x + ar)2 + a2 i ]. Then the separate substitution of x = 0, −a1, −δ into this equation yields
˜α0 =
v δ
κ1κ2λ
a1(a2
r + a2 i )
, ˜α1 =
−vh(−a1) a1(δ − a1)[(a1 − ar)2 + a2 i ]
, and ˜αδ =
−vh(−δ) δ(a1 − δ)[(δ − ar)2 + a2 i ]
+ M (0). 23
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CC-BY 4.0 International license . The other two ˜α2 and ˜α3 are obtained by comparing the coefficients:
˜α2 = M (0) − (˜α0 + ˜α1 + ˜αδ),
˜α3 = vPe(0) + (a1 + 2ar)M (0) − [α0(2ar + a1 + δ) + ˜α1(2ar + δ) + ˜α2(a1 + δ) + ˜αδ(2ar + a1)]. Using above ˜α2 and ˜α3 we further introduce the symbols
¯A = ˜α2, A =
˜α3/˜α2 − ar ai
, and θ = arccos
√
1 1 + A2
. Then the application of inverse Laplace transform to LM (x) given in (27) readily leads to
M (t) = ˜α0 + ˜α1e−a1t + ˜αδe−δt + ¯A[cos(ait) + A sin(ait)]e−art 1 + A2 cos(ait + θ)e−art,
(cid:112)
= ˜α0 + ˜α1e−a1t + ˜αδe−δt + ¯A
which is exactly the expression (11). Dynamical profiles of M (t) for cross-talking three-state model (1)
In this section we utilize exact forms of M (t) to understand its dynamical features. We consider the initial condition (12) for which the gene is silence and there is almost no transcripts at the initial time [11, 21, 30]. |
The following two theorems illustrate the cases of c2 1 < c2, respectively. 1 > c2 and c2
Theorem 1. For arbitrary non-zero real numbers a, b, c and positive real numbers M ∗, α, β, r, if M (t) is expressed as
M (t) = M ∗ + ae−αt + be−βt + ce−rt ≥ 0, 0 < α < β < r, M (0) = 0, and M (cid:48)(0) ≥ 0,
then M (t) displays only one of increasing, up-and-down and up-down-up dynamical profiles. Proof. The derivative of M (t) gives
M (cid:48)(t) = −αae−αt − βbe−βt − rce−rt =⇒ M (cid:48)(t)ert = −[rc + αae(r−α)t + βbe(r−β)t]. We divided the discussion into two cases of a > 0 and a < 0. (I) If a > 0, then limt→∞ M (cid:48)(t) < 0 by noting that the sign of M (cid:48)(t) is dominated by the term
“ − αae−αt” when t → ∞. Taking the derivative of M (cid:48)(t)ert in (29) gives
[M (cid:48)(t)ert](cid:48) = −αa(r − α)e(r−α)tM1(t), with M1(t) = 1 +
βb(r − β) αa(r − α)
e(α−β)t.
24
(28)
(29)
(30)
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CC-BY 4.0 International license . If b ≥ −αa(r − α)/β(r − β), then (30) indicates
M1(t) > 0 =⇒ [M (cid:48)(t)ert](cid:48) < 0 =⇒ M (cid:48)(t)ert decreases,
for t > 0. There are two probabilities of M (cid:48)(0) > 0 and M (cid:48)(0) = 0. limt→∞ M (cid:48)(t) < 0, there exists t1 > 0 such that
If M (cid:48)(0) > 0, then together with
M (cid:48)(t)ert > 0, for t ∈ (0, t1), M (cid:48)(t1)ert1 = 0, and M (cid:48)(t)ert < 0, for t > t1. Therefore, M (t) increases for t ∈ (0, t1) and decreases for t > t1 which presents up-and-down dynamics. If M (cid:48)(0) = 0, then M (cid:48)(t)ert < 0 for t > 0, and thus M (t) decreases with M (t) < 0 all the time. This contradicts to the assumption of M (t) ≥ 0. If b < −αa(r − α)/β(r − β), then (30) suggests that there is t2 > 0 such that
M1(t) < 0, t ∈ (0, t2), M1(t2) = 0, and M1(t) > 0, t > t2, where t2 =
1 α − β
ln
(cid:18) −aα(r − α) bβ(r − β)
Then (30) suggests that [M (cid:48)(t)ert](cid:48) > 0 for t ∈ (0, t2) and [M (cid:48)(t)ert](cid:48) < 0 for t > t2. Therefore, M (cid:48)(t)ert increases in (0, t2) while decreases in (t2, ∞). Since M (cid:48)(0) ≥ 0 and limt→∞ M (cid:48)(t) < 0, there exists t3 such that M (cid:48)(t3)ert3 = 0. Thus M (cid:48)(t)ert > 0 for t ∈ (0, t3) and M (cid:48)(t)ert < 0 for t > t3. This indicates that M (t) increases for t ∈ (0, t3) and decreases for t > t3, which is the up-and-down dynamics. (II) If a < 0, the (29) indicates that limt→∞ M (cid:48)(t) > 0. If b ≤ −αa(r − α)/β(r − β), then (30)
gives
M1(t) > 0 =⇒ [M (cid:48)(t)ert](cid:48) > 0 =⇒ M (cid:48)(t)ert increases,
for t > 0. Since M (cid:48)(0) ≥ 0, we have M (cid:48)(t)ert ≥ 0, t > 0 which suggests that M (t) increases for all the time. On the other hand, if b > −αa(r − α)/β(r − β), then from (30) we find that there exists t4 > 0
such that
M1(t) < 0, t ∈ (0, t4), M1(t4) = 0, and M1(t) > 0, t > t4, where t4 =
1 α − β
ln
(cid:18) −aα(r − α) bβ(r − β)
Together with (30), this further leads to [M (cid:48)(t)ert](cid:48) < 0 for t ∈ (0, t4) and [M (cid:48)(t)ert](cid:48) > 0 for t > t4. |
Therefore, M (cid:48)(t)ert decreases in (0, t4) while increases in (t4, ∞). Since M (cid:48)(0) ≥ 0, there are two possibilities of M (cid:48)(t4)ert4 ≥ 0 and M (cid:48)(t4)ert4 < 0. For M (cid:48)(t4)ert4 ≥ 0, the fact of limt→∞ M (cid:48)(t) > 0 indicates M (cid:48)(t)ert ≥ 0 for all t ≥ 0, and thereby M (t) increases all the time. If it is M (cid:48)(t4)ert4 < 0, then there exist 0 < t5 < t4 < t6 such that M (cid:48)(t5)ert5 = M (cid:48)(t6)ert6 = 0 and
M (cid:48)(t)ert > 0, t ∈ (0, t5), M (cid:48)(t)ert < 0, t ∈ (t5, t6), and M (cid:48)(t)ert > 0, t > t6. 25
(cid:19)
(cid:19)
. . bioRxiv preprint The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
doi:
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available under a
CC-BY 4.0 International license . This indicates that M (t) displays an up-down-up dynamics that M (t) increases for t ∈ (0, t5) ∪ (t6, ∞) and decreases within t ∈ (t5, t6). The proof is completed. Theorem 2. Let Condition c2
1 < c2 hold. Let
H(x) = vh(x) = vq2λx2 + v[q1κ1κ2 + q2λ(κ1 + κ2)]x + vκ1κ2λ,
and x1 and x2 be two roots of H(x). Without loss of generality, assume δ (cid:54)= a1, a2, a3 given by (22). If x1 and x2 are complex valued, then either M (t) increases monotonically for all t > 0, or M (t) develops up-down-up dynamics. If x1 and x2 are real valued and x1 < x2, then we have:
(1) If one of the following occurs: (i) −x2 < {a1, a2, a3, δ} < −x1, (ii) −x2 < {a1, a2, δ} < −x1 < a3, (iii) −x2 < {a1, δ} < −x1 < a2, (iv) −x2 < a1 < a2 < a3 < −x1 < δ, (v) −x2 < a1 < a2 < −x1 < min{a3, δ}, (vi) −x2 < a1 < −x1 < min{a2, δ}, (vii) −x2 < δ < −x1 < a1, then m(t) increases initially until reaching a peak and then goes down (up-and-down). (2) If one of the following occurs: (i) a1 < −x2 < a2 < a3 < −x1 < δ, (ii) a1 < −x2 < a2 < a3 < −x1 < δ, (iii) a1 < −x2 < a2 < −x1 < min{a3, δ}, (iv) a1 < −x2 < {a2, δ} < −x1 < a3, (v) max{a1, δ} < −x2 < a2 < −x1 < a3, (vi) δ < −x2 < a1 < a2 < −x1 < a3, (vii) a1 < −x2 < δ < −x1 < a2, and (viii) δ < −x2 < a1 < −x1 < a2, then M (t) increases monotonically for all t > 0. (3) If one of the following occurs: (i) −x1 < min{a1, δ}, (ii) a1 < −x2 < −x1 < min{a2, δ}, (iii) a2 < −x2 < −x1 < min{a3, δ}, (iv) a3 < −x2 < −x1 < δ, (v) max{a1, δ} < −x2, (vi) max{a2, δ} < −x2 < −x1 < a3, (vii) max{a3, δ} < −x2, (viii) δ < −x2 < −x1 < a1, (ix) a3 < −x2 < δ < −x1, (x) a2 < −x2 < a3 < −x1 < δ,(xi) a2 < −x2 < {a3, δ} < −x1, (xii) {a2, δ} < −x2 < a3 < −x1, (xiii) a1 < −x2 < {a2, a3, δ} < −x1, (xiv) {a1, δ} < −x2 < a2 < a3 < −x1, (xv) δ < −x2 < a1 < a2 < a3 < −x1, then either M (t) increases monotonically for all t > 0, or M (t) develops up-down-up dynamical profile. Proof. The substitution of the initial condition (12) into the differential system (7) gives M (cid:48)(0) = e(0) > 0. Consequently, M (t), M (cid:48)(t), and M (cid:48)(cid:48)(t) are all 0, P (cid:48) positive for t > 0 sufficiently small. |
The initial values (12) simplifies the exact form (9) of M (t) in the form of
e(0) > 0, and in turn, M (cid:48)(cid:48)(0) = vP (cid:48)
M (t) =
v δ
κ1κ2λ a1a2a3
−
β1 a1
e−a1t −
β2 a2
e−a2t −
β3 a3
e−a3t −
βδ δ
e−δt,
where
β1 =
H(−a1) (δ − a1)(a2 − a1)(a3 − a1)
β3 =
H(−a3) (δ − a3)(a1 − a3)(a2 − a3)
,
,
H(−a2) (δ − a2)(a1 − a2)(a3 − a2) H(−δ) (a1 − δ)(a2 − δ)(a3 − δ)
β2 =
βδ =
,
. Thus
M (cid:48)(t) = β1e−a1t + β2e−a2t + β3e−a3t + βδe−δt. 26
(31)
(32)
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available under a
CC-BY 4.0 International license . We first consider the situation of complex valued x1 and x2. There are total 4 parameter cases and we only present the proof for the case δ < a1 < a2 < a3, since the other cases a1 < δ < a2 < a3, a1 < a2 < δ < a3 and a1 < a2 < a3 < δ can be treated similarly. If x1 and x2 are complex valued, then H(x) > 0 for all x. In view of δ < a1 < a2 < a3, we obtain
β1 < 0, β2 > 0, β3 < 0 and βδ > 0. For t > 0 sufficiently large, M (cid:48)(t) is dominated by βδ exp(−δt) in (32) and is therefore positive. It follows from (32) that
(cid:2)ea3tM (cid:48)(t)(cid:3)(cid:48) = e(a3−δ)tg(t), with g(t) = (a3 − δ)βδ + (a3 − a1)β1e(δ−a1)t + (a3 − a2)β2e(δ−a2)t. (34)
It is seen that
g(0) = M (cid:48)(cid:48)(0) > 0 and
lim t→∞
g(t) = (a3 − δ)βδ > 0. We can see from (34) that
M (cid:48)(t) = e−a3tG(t), where G(t) =
(cid:90) t
e(a3−δ)sg(s)ds,
t > 0. 0
It follows from (32) and (36) that
G(0) = 0,
lim t→∞
G(t) = +∞,
and G(cid:48)(t) = e(a3−δ)tg(t). Differentiating g(t) gives
g(cid:48)(t) =
H(−a1) a2 − a1
e(δ−a2)t
(cid:20)
e(a2−a1)t −
H(−a2) H(−a1)
(cid:21)
. If H(−a2) ≤ H(−a1), then g(cid:48)(t) ≥ 0, and so g(t) > 0 for all t > 0. Hence (36) gives M (cid:48)(t) > 0 for all t > 0. If H(−a2) > H(−a1), then g(cid:48)(t) < 0 in (0, t0) for
t0 =
1 a2 − a1
[ln (H(−a2)) − ln (H(−a1))] ,
and becomes positive for t > t0. If g(t0) ≥ 0, then g(t) > 0 for all t > 0 and t (cid:54)= t0. Thus (36) gives again M (cid:48)(t) > 0 for all t > 0. If g(t0) < 0, then (35) implies that g(t) has two zeros t1 > 0 and t2 > 0 with g(t) > 0 in (0, t1) ∪ (t2, +∞), and g(t) < 0 in (t1, t2). It follows from (37) that
G(cid:48)(t) > 0 for t ∈ (0, t1) ∪ (t2, +∞),
and G(cid:48)(t) < 0 for t ∈ (t1, t2). If G(t2) ≥ 0, then G(t) > 0 for all t > 0 and t (cid:54)= t2, and so M (cid:48)(t) > 0 for all t > 0 and t (cid:54)= t2. We recall that G(t) > 0 for t > 0 both sufficiently small and large. Thus, if G(t2) < 0, then (38) implies that G(t) has two zeros t3 > 0 and t4 > 0 with G(t) > 0 in (0, t3) ∪ (t4, +∞), and G(t) < 0
27
(33)
(35)
(36)
(37)
(38)
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It is made
doi:
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available under a
CC-BY 4.0 International license . in (t3, t4). It follows from (36) that M (cid:48)(t) > 0 in (0, t3) ∪ (t4, +∞) and M (cid:48)(t) < 0 in (t3, t4). This finishes the proof of the case when x1 and x2 are complex valued. In the following, we assume that x1 and x2 are real valued. (1) We present the proof with the additional assumption that −x2 < a1 < a2 < δ < −x1 < a3, as the other cases can be dealt with by the same idea. Since
−x2 < a1 < a2 < δ < −x1 < a3 ⇒ β1 < 0, β2 > 0, β3 < 0, and βδ < 0,
by using (32) again, we obtain
(cid:2)ea2tM (cid:48)(t)(cid:3)(cid:48) = e(a2−a1)tg1(t), g1(t) = (a2 − a1)β1 + (a2 − δ)βδe(a1−δ)t + (a2 − a3)β3e(a1−a3)t, (40)
with f (0) = M (cid:48)(cid:48)(0) > 0 and limt→∞ g1(t) = (a2 − a1)β1 < 0. In terms of (39) and (40), we have (a2 − δ)(a1 − δ)βδ < 0 and (a2 − a3)(a1 − a3)β3 < 0, and so
f (cid:48)(t) = (δ − a2)(a1 − a2)β2e(δ−a2)t + (δ − a3)(a1 − a3)β3e(δ−a3)t < 0. Hence, there exists a t5 > 0 such that g1(t) > 0 in (0, t5), g1(t5) = 0, and g1(t) < 0 in (t5, +∞). For t > 0 sufficiently large, M (cid:48)(t), dominated by the term with exp(−a1) in (32), is negative. We also recall that M (cid:48)(t) > 0 for t > 0 sufficiently small. Thus, there exists a finite t6 > 0 such that M (cid:48)(t) > 0 in (0, t6), and M (cid:48)(t6) = 0. Then M (cid:48)(cid:48)(t6) ≤ 0, and (40) gives f (t6) = exp(a1t6)M (cid:48)(cid:48)(t6) ≤ 0. It follows that t6 ≥ t5 and f (t) < 0 for all t > t6. Hence, by using (40) again, for each t > t6, we have
M (cid:48)(t) = e−a2t
(cid:90) t
e(a2−δ)sf (s)ds < 0.
t6
(2) We present the proof for the case a1 < a2 < −x2 < δ < −x1 < a3, as the other cases can be handled similarly. With this specification, we have
β1 > 0, β2 < 0, β3 < 0, and βδ < 0. By (32) and (41), we obtain for all t > 0
(cid:2)ea1tM (cid:48)(t)(cid:3)(cid:48) = (a1 − δ)βδe(a1−δ)t + (a1 − a2)β2e(a1−a2)t + (a1 − a3)β3e(a1−a3)t > 0. As M (cid:48)(0) = 0, it shows that ea2tM (cid:48)(t) > 0, and so M (cid:48)(t) > 0 for all t > 0. (3) We give a short description for the proof with the additional condition that x1 < x2 < δ < a1 < a2 < a3, as the other cases can be proceeded in an analogous manner. Under this extra condition, (33) holds again. Thus the remaining discussion is the same as the proof given above for two complex valued x1 and x2, and we omit it here. 28
(39)
(41)
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CC-BY 4.0 International license . Calculation of M (t) for cross-talking n-state model
Following the standard procedure of [15,33,39] we obtain the master equations for the cross-talking n-state model, which further leads to the differential system of gene state probabilities and the average mRNA level M (t) as follows
o11(t) = −κ1Po11(t) + q1γPe(t), P (cid:48) P (cid:48) o2(t) = κ1Po11(t) − κ2Po2(t), P (cid:48) P (cid:48) · · ·
o12(t) = −λPo12(t) + q2γPe(t),
o3(t) = κ2Po2(t) − κ3Po3(t),
on−1(t) = κn−2Pon−2(t) − κn−1Pon−1(t), P (cid:48) P (cid:48) M
(cid:48)
(t) = vPe(t) − δM (t),
e(t) = λPo12(t) + κn−1Pon−1(t) − γPe(t),
Po11(0) = q1, Po12(0) = q2, Poj (0) = Pe(0) = M (0) = 0,
j = 2, 3, · · · , n − 1. |
Here Po11(t) and Po12(t) are probabilities of gene off 1 state selecting weak and signaling pathways, respectively. Poj (t), j = 2, 3, · · · , n − 1 are probabilities of gene off j states while the probability Pe(t) is for gene on state. Also, we consider the initial condition for which the gene is totally off with no transcripts at the initial time. For the special case of q2 = 0 which suggests that the gene activation is regulated by a single
multi-step pathway, the system (42) reduces to
P (cid:48) o11(t) = −κ1Po11(t) + γPe(t), P (cid:48) P (cid:48) o3(t) = κ2Po2(t) − κ3Po3(t), P (cid:48) e(t) = κn−1Pon−1(t) − γPe(t), M
o2(t) = κ1Po11(t) − κ2Po2(t),
· · P (cid:48)
on−1(t) = κn−2Pon−2(t) − κn−1Pon−1(t),
(cid:48)
(t) = vPe(t) − δM (t),
Po11(0) = 1, Poj (0) = Pe(0) = M (0) = 0,
j = 2, 3, · · · , n − 1. The crucial step to solve the system (42) or (43) is to calculate the eigenvalues of the coefficient matrix for equations of gene state probabilities [33, 39]. Here we illustrate a simple case of κ1 = κ2 = · · · = κn−1 = κ in the system (43). Then its characteristic polynomial f (x) for gene state probabilities is expressed as
f (x) =
(cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12)
x + κ −κ ... 0 0
· · x + κ · · · ... · · · x + κ · · · ... 0 0 −κ
0
0 0 ...
−γ 0 ... 0 x + γ
(cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12)n×n
= (x + κ)n−1(x + γ) − κn−1γ. There is no standard method to solve the characteristic polynomial equation f (x) = 0 of degree n ≥ 5. However, the fundamental theorem of algebra shows that f (x) = 0 has n roots (eigenvalues) with complex roots always exhibiting in multiple pairs of conjugate complexes. 29
(42)
(43)
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available under a
CC-BY 4.0 International license . The second moment of mRNA distribution for cross-talking three-
state model (1)
By definition the second moment µ2(t) of the distribution of mRNA copy numbers is
µ2(t) =
∞ (cid:88)
m2Pm(t),
m=0
where Pm(t) is the solution of master functions (2)-(6). To derive µ2(t), we need first calculate the partial mRNA average levels at each gene state, defined by
M1j(t) =
∞ (cid:88)
mPm,o1j (t), j = 1, 2, M2(t) =
∞ (cid:88)
mPm,o2(t) and Me(t) =
∞ (cid:88)
mPm,e(t). m=0
m=0
m=0
By these definitions and (2)-(6) we can derive the equations of M11(t), M12(t), M2(t), Me(t) and µ2(t) [33, 39]
M (cid:48) M (cid:48) µ(cid:48)
11(t) = −(κ1 + δ)M11(t) + q1γMe(t), M (cid:48) 2(t) = κ1M11(t) − (κ2 + δ)M2(t), M (cid:48) 2(t) = −2δµ2(t) + δM (t) + vPe + 2vMe(t). 12(t) = −(λ + δ)M12(t) + q2γMe(t),
e(t) = λM12(t) + κ2M2(t) − (γ + δ)Me(t) + vPe(t),
Here we focus on the initial condition
(Po11(0), Po12(0), Po2(0), Pe(0), M (0), µ2(0)) = (q1, q2, 0, 0, 0, 0). |
To solve the first-order differential system (44)-(45), we denote by
LM1j (x) =
(cid:90) ∞
e−xtM1j(t)dt, j = 1, 2, LM2(x) =
(cid:90) ∞
e−xtM2(t)dt,
LMe(x) =
0 (cid:90) ∞
e−xtMe(t)dt,
and Lµ2(x) =
(cid:90) ∞
0
e−xtµ2(t)dt. 0
0
Then the application of Laplace transform to the first four equations of system (44) yields
0 = (x + κ1 + δ)LM11(x) − q1γLMe(x),
0 = (x + λ + δ)LM12(x) − q2γLMe(x),
0 = −κ1LM11(x) + (x + κ2 + δ)LM2(x),
vLe = −λLM12(x) − κ2LM2(x) + (x + γ + δ)LMe(x). 30
(44)
(45)
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CC-BY 4.0 International license . By applying Cramer’s rule in the theory of linear algebra to solve the above system, we obtain
LMe(x) =
v(x + κ1 + δ)(x + λ + δ)(x + κ2 + δ)Le(x) (x + δ)(x + a1 + δ)(x + a2 + δ)(x + a3 + δ)
,
where Le(x) is given by (20) while a1, a2 and a3 are given by (15)-(19) or by the separate (22), (24) and (26) for the corresponding cases. To solve the second moment µ2(t) from the system (44)-(45), we apply the Laplace transform
to the last equation of (44), and then substitute (46) to obtain
Lµ2(x) =
1 x + 2δ
(cid:18) vδ x + δ
+ v +
2v2(x + κ1 + δ)(x + λ + δ)(x + κ2 + δ) (x + δ)(x + a1 + δ)(x + a2 + δ)(x + a3 + δ)
(cid:19)
Le(x). We note that Le(x) given by (20) can be simplified under the initial condition (12) or (45). The substitution of simplified Le(x) into (47) further gives
Lµ2(x) =
F (x) x(x + a1)(x + a2)(x + a3)(x + δ)(x + 2δ)(x + a1 + δ)(x + a2 + δ)(x + a3 + δ)
,
where F (x) takes the form of
F (x) = [q2λx2 + [q1κ1κ2 + q2λ(κ1 + κ2)]x + κ1κ2λ] ×[v(x + 2δ)(x + a1 + δ)(x + a2 + δ)(x + a3 + δ) + 2v2(x + λ1 + δ)(x + λ2 + δ)(x + λ3 + δ)]. Under the condition c2
1 < c2 where a1, a2 and a3 are all positive real numbers, we decompose
Lµ2(x) into the sum of partial fractions as
Lµ2(x) =
b0 x
+
b1 x + a1 b1,δ x + a1 + δ
+
+
+
b2 x + a2 b2,δ x + a2 + δ
+
b3 x + a3
+
bδ x + δ
+
b2,δ x + a3 + δ
. +
b2δ x + 2δ
Then the application of the inverse Laplace transform to Lµ2(x) readily leads to
µ2(t) = b0 + b1e−a1t + b2e−a2t + b3e−a3t + bδe−δt + b2δe−2δt
+b1,δe−(a1+δ)t + b2,δe−(a2+δ)t + b3,δe−(a3+δ)t,
31
(46)
(47)
(48)
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available under a
CC-BY 4.0 International license . with a1, a2 and a3 being given by (22) and the coefficients taking forms of
b0 =
F (0) 2a1a2a3δ2(a1 + δ)(a2 + δ)(a3 + δ)
,
b1 = −
F (−a1) a1δ(a2 − a1)(a3 − a1)(δ − a1)(2δ − a1)(a2 + δ − a1)(a3 + δ − a1)
,
b2 =
b3 =
−F (−a2) a2δ(a1 − a2)(a3 − a2)(δ − a2)(2δ − a2)(a1 + δ − a2)(a3 + δ − a2) −F (−a3) a3δ(a1 − a3)(a2 − a3)(δ − a3)(2δ − a3)(a1 + δ − a3)(a2 + δ − a3)
,
,
bδ =
b2δ =
−F (−δ) a1a2a3δ2(a1 − δ)(a2 − δ)(a3 − δ) F (−2δ) 2δ2(a1 − δ)(a2 − δ)(a3 − δ)(a1 − 2δ)(a2 − 2δ)(a3 − 2δ)
,
,
b1,δ =
b2,δ =
b3,δ =
−F [−(a1 + δ)] a1δ(a1 + δ)(a2 − α1)(a3 − α1)(δ − a1)(a2 − a1 − δ)(a3 − a1 − δ) −F [−(a2 + δ)] a2δ(a2 + δ)(a1 − a2)(a3 − a2)(δ − a2)(a1 − a2 − δ)(a3 − a2 − δ) −F [−(a3 + δ)] a3δ(a3 + δ)(a1 − α3)(a2 − a3)(δ − a3)(a1 − a3 − δ)(a2 − a3 − δ)
,
,
. |
Supporting Information
Table S1. Fitted system parameters for dynamical transcription data of mouse fibroblast genes. Fig. S1. Oscillatory dynamics of mRNA average level M (t) generated by a single pathway with multiple sequential steps (n-state model). The increase in the step number n − 1 prolongs the initial response lag and enhances the following damped oscillation for M (t). Parameters are the fitted rates of Cxcl1 gene in Table S1 with the average gene off duration Toff being constant under (a) κi = iκ1, i = 1, 2, · · · , n − 1; (b) κi = κ1, κj = 3κ1 for odd i and even j. Fig. S2. Oscillatory dynamics of mRNA average level M (t) generated by the cross-talking n-state model. The increase in the step number n − 1 in the basal pathway has nearly no impact on the initial quick up-and-down dynamics of M (t) but significantly enhances the following gentle and damped oscillatory behavior. Parameters are the fitted rates of Cxcl1 gene in Table S1 with the average gene off duration Toff being constant under (a) κi = iκ1, i = 1, 2, · · · , n − 1; (b) κi = κ1, κj = 3κ1 for odd i and even j. 32
bioRxiv preprint The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
doi:
https://doi.org/10.1101/2021.09.01.458497
;
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available under a
CC-BY 4.0 International license . Author Contributions
L.C. G.L. and F.J. designed and performed the research; F.J. wrote the paper. Acknowledgements
This work is supported by Natural Science Foundation of China grants (Nos. 11871174; 12001127;
11631005), and by Program for Changjiang Scholars and Innovative Research Team in University
(No. IRT 16R16). The funders had no role in study design, data collection and analysis, decision
to publish, or preparation of the manuscript. Data Availability Statement
All relevant data are within the manuscript and its Supporting Information files. Competing interests
The authors declare no competing financial interests. References
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CC-BY-NC-ND 4.0 International license . Nematode Small RNA Pathways in the Absence of piRNAs
Maxim Zagoskin1,2,3*, Jianbin Wang1,2,3,4*,#, Ashley T. Neff1, Giovana M. B. Veronezi1, and
Richard E. Davis1,2#
1Department of Biochemistry and Molecular Genetics, University of Colorado School of Medicine, Aurora, CO
2RNA Bioscience Initiative, University of Colorado School of Medicine, Aurora, CO
3Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee, Knoxville, TN
4UT-ORNL Graduate School of Genome Science and Technology, University of Tennessee, Knoxville, TN
These authors contributed equally
#Corresponding Authors, [email protected], [email protected]
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was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under a
CC-BY-NC-ND 4.0 International license . Abstract
Small RNA pathways play diverse regulatory roles in the nematode C. elegans. However, our
understanding of small RNA pathways, their conservation, and their roles in other nematodes is limited. Here, we analyzed small RNA pathways in the parasitic nematode Ascaris. Ascaris has ten Argonautes
with five worm-specific Argonautes (WAGOs) that are associated with secondary 5’-triphosphate small
RNAs (22-24G-RNAs). These Ascaris WAGOs and their small RNAs target repetitive sequences (WAGO-
1, WAGO-2, WAGO-3, and NRDE-3) or mature mRNAs (CSR-1, NRDE-3, and WAGO-3) and are similar
to the C. elegans mutator, nuclear, and CSR-1 small RNA pathways. Ascaris CSR-1 likely functions to
“license” gene expression in the absence of an Ascaris piRNA pathway. Ascaris ALG-4 and its associated
26G-RNAs target and appear to repress specific mRNAs during meiosis in the testes. Notably, Ascaris
WAGOs (WAGO-3 and NRDE-3) small RNAs change their targets between repetitive sequences and
mRNAs during spermatogenesis or in early embryos illustrating target plasticity of these WAGOs. We
provide a unique and comprehensive view of mRNA and small RNA expression throughout nematode
spermatogenesis that illustrates the dynamics and flexibility of small RNA pathways. Overall, our study
provides key insights into the conservation and divergence of nematode small RNA pathways. Keywords: Nematode, small RNA pathways, Argonautes, WAGOs, CSR-1, NRDE-3, ALG-4, piRNAs,
22G-RNA, 26G-RNA, RdRP, spermatogenesis, germline, and Ascaris
2
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It is made
available under a
CC-BY-NC-ND 4.0 International license . Introduction
Small RNAs contribute to many regulatory processes. They are associated with diverse functions including
repressing foreign invaders and mobile elements, transcriptional regulation, mRNA translation and
degradation, DNA repair, chromatin regulation and epigenetic inheritance, and ciliate genome
rearrangements [1-5]. One of the first discoveries of small RNAs and their role in gene regulation was in
the free-living nematode Caenorhabditis elegans [6, 7]. Subsequent studies in C. elegans have revealed
a diverse and complex set of small RNAs, pathways, and associated Argonautes [8-11]. C. elegans small RNAs include miRNAs, 21U-RNAs (piRNAs) and small-interfering RNAs (siRNAs). C.
elegans miRNAs are involved in post-transcriptional gene regulation through regulation of mRNA
translation and degradation [12], but have also been associated with transcriptional activation [13]. C.
elegans can generate siRNAs against foreign elements, but also has a large repertoire of endogenous
siRNAs [8-11]. These C. elegans small RNAs are named based on their length and predominant first
nucleotide of the RNA, e.g., 21U-, 22G- and 26G-RNAs. 21U-RNAs have a 5’-monophosphate and 3’ 2’-
O-methylation [14-16]. They are primarily thought to identify foreign (non-self) RNA elements. The
identification of these foreign elements through RNA base-pairing leads to the subsequent synthesis of
secondary siRNAs that repress their targets. 22G-RNAs have a 5’-triphosphate [16-20]. These are
secondary siRNAs as they are generated in response to other small RNAs (21U-RNA, 26G-RNA, or other
siRNAs) [20, 21]. Thus, primary siRNAs base-pair with transcript targets, marking or identifying them for
the synthesis of the more abundant antisense, secondary 22G-RNAs by RNA-dependent RNA
polymerases (RdRPs) [18-23]. 22G-RNAs silence mobile elements, pseudogenes, non-annotated loci, and
select endogenous, germline genes [18]. They also serve to “activate or license”, “tune”, or repress gene
expression [24-27]. 26G-RNAs have a 5’ monophosphate [16, 19, 28, 29]. There are two classes of 26G-
RNAs in C. elegans, one is testis-specific and associated with the Argonautes ALG-3/4 [30-32], the other
is expressed in early embryos and associated with the Argonaute ERGO-1 [28, 29, 32, 33]. Like 21U-
RNAs, 26G-RNAs trigger or act to prime the synthesis of secondary siRNAs (22G-RNAs) through base-
pairing with targets [8-11]. Overall, C. elegans secondary 22G-RNAs are amplified responses to targets
identified by 21U- and 26G-RNAs and other primary siRNAs. Small RNAs are bound by effector Argonaute proteins. C. elegans Argonautes have undergone significant
expansion and diversification. Twenty-seven Argonaute genes were originally described [23]; 19 are
expressed (Julie Claycomb, personal communication). These include members of the AGO, PIWI, and
WAGO (Worm-specific Argonautes) Argonaute clades [34]. The C. elegans AGO clade Argonautes (5
AGOs) interact with miRNAs and 26G-RNAs, the PIWI clade (1 AGO) with 21U-RNAs (the worm piRNA
ortholog), and the WAGO clade (13 AGOs) with 22G-RNAs. |
Several of the WAGO clade Argonautes
function in the nucleus regulating transcription and heterochromatin formation [3, 11, 35, 36]. The largest
3
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was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under a
CC-BY-NC-ND 4.0 International license . expansion of C. elegans Argonautes is in the WAGO clade [23]. Many of these WAGOs are thought to
have redundant functions in C. elegans. Nematodes are an extremely diverse and abundant phylum adapted to a wide variety of lifestyles [37-39]. While extensive analyses of C. elegans Argonautes, small RNAs, and pathways have been carried out,
relatively little is known regarding the conservation, divergence, or function of these pathways in other
nematodes [8, 40, 41]. Nematodes have been divided into three major classes and five clades with C.
elegans and its relatives as members of Clade V [42-45]. The nematode Ascaris is a parasite of humans
(and pigs) infecting upwards of 800,000 people [46-48]. Ascaris is a Clade III nematode estimated to have
diverged from C. elegans approximately 365-400 million years ago [49, 50]. Previous studies in Ascaris
indicated that piRNAs and PIWI Argonautes are absent in Ascaris [51]. PIWI Argonautes and piRNAs play
a key role in repressing mobile elements in the germline. C. elegans piRNAs have been proposed to serve
in identifying and defining foreign genetic elements acting upstream of secondary siRNA pathways [52-
56]. Thus, they have been described as defining self vs. non-self [57]. The WAGO-associated 22G
secondary RNAs function in silencing and can maintain silencing of the foreign elements over generations
in C. elegans [8, 11]. To counteract silencing, it has been proposed that 22G-RNAs associated with the C.
elegans CSR-1 function to ‘license”, identify self, or protect germline genes from repression and allow for
their expression [24, 26, 58]. Given the key role of piRNAs in many organisms, and their role in C. elegans,
the absence of piRNAs and PIWI in Ascaris raises the question of how Ascaris small RNA pathways have
adapted to the absence of piRNAs and PIWI (e.g., self vs non-self). Does Ascaris still need small RNA
pathways to “license” gene expression without the presence of piRNAs? How are self vs non-self elements
determined? Here, we generated antibodies to Ascaris Argonaute proteins and carried out Argonaute IP and small RNA
sequencing to characterize small RNA pathways in several developmental stages. Ascaris has Argonautes
that are highly specific for binding miRNAs (AsALG-1) and 26G-RNAs (AsALG-4). AsWAGO Argonautes
bind 5’-triphosphate small RNAs (22-24G-RNAs). These small RNAs target repetitive sequences including
mobile elements, but they also target mRNAs and likely “license”, “tune”, and/or repress gene expression. |
Two Ascaris WAGOs change their genomic targets (mRNAs vs repetitive sequences) in different
developmental stages. We exploited the long ~1 meter Ascaris male germline to obtain discrete regions of
the testis and analyzed Ascaris Argonautes and their small RNAs throughout spermatogenesis. These
analyses provide a unique and comprehensive timeline for the expression of Argonautes, their bound small
RNAs and targets, and changes in expression of their corresponding genomic or mRNA targets throughout
nematode spermatogenesis. Our study suggests that in the absence of piRNAs and with extensive
evolutionary divergence from C. elegans, several Ascaris small RNA pathways and Argonautes appear to
bind similar small RNAs, have similar targets, and in many cases appear to serve similar roles in both
4
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was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under a
CC-BY-NC-ND 4.0 International license . nematodes. Therefore, the potential “licensing” of gene expression in another nematode by Ascaris CSR-
1 does not appear to be a consequence or counter response to the presence of piRNAs. Overall, our
studies illustrate the conservation, loss of Argonautes, and divergence of small RNA pathways that
illustrate the flexibility and adaptability of Argonautes and small RNA pathways in nematodes. 5
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available under a
CC-BY-NC-ND 4.0 International license . Results
Ascaris Argonautes
We previously identified 10 Ascaris Argonautes [51]. Alignment and phylogenetic analyses of these
Argonautes indicates the presence of 5 AGO clade and 5 WAGO (Worm-specific Argonautes) Clade
Argonautes, but the absence of PIWI Argonautes (Figure 1A). Of the 5 Ascaris AGOs, two (AsALG-1 and
AsALG-6) cluster with C. elegans miRNA associated Argonautes and one (AsALG-4) with C. elegans ALG-
3/4 Argonautes. The two additional Argonautes (AsALG-5 and AsALG-7) cluster with 26G-RNA-like
Argonautes or RDE-1 (Figure 1). Four of these five Ascaris AGOs have conserved RNase H, catalytic
tetrad residues that confer slicer activity except for AsALG-6. The 5 Ascaris WAGOs were named AsCSR-1, AsWAGO-1, AsWAGO-2, AsWAGO-3, and AsNRDE-3
based on expression pattern, their sequence and phylogenetic similarity to C. elegans, and the small RNAs
associated with these Argonautes (see below)(Figure 1). Two C. elegans WAGOs function in nuclear RNAi
and are expressed in different stages, HRDE-1 (germline) and NRDE-3 (soma) [59, 60]. Our phylogenetic
analysis suggests one Ascaris WAGO, named AsNRDE-3, is related to these C. elegans nuclear WAGOs. |
It is expressed in zygotes and early embryos and present both in the cytoplasm and nuclei of embryos. We note that with only one Ascaris nuclear WAGO, AsNRDE-3 may also serve functions similar to C.
elegans HRDE-1. Only AsCSR-1 and AsWAGO-3 have the RNase H, catalytic tetrad residues that confer
slicer activity. Ascaris has three RdRPs (Figure 1B and 4B). One is clearly orthologous to C. elegans RRF-3 (RdRP-3)
and is expressed in the germline, oocytes, zygotes, and during early development. In the male germline,
RdRP-3 RNA expression is highest at M5 when the initiation of 26G-RNAs occurs and likely plays a major
role in their biogenesis. The other two Ascaris RdRPs are similarly orthologous to either C. elegans EGO-
1 or RRF-1 and are expressed in the germlines (Table S1). No ortholog of C. elegans RRF-2 appears
present in Ascaris. Additional Ascaris orthologous proteins likely associated with small RNA pathways in
C. elegans are provided in Table S1. Ascaris Argonautes are dynamically expressed throughout the male and female germlines, early
development, larvae, and adult tissues (Figure 1B; rpkm values less than 5 are considered low or
background levels of expression). The most abundant Argonaute in all these stages is the Ascaris CSR-1
ortholog, AsCSR-1 (Figure 1B), which is expressed in the male and female germlines, zygotes prior to
pronuclear fusion (where the maternal to zygotic transition occurs) [61], and through the 4-cell stage of
early development suggesting a pivotal role of AsCSR-1 and its small RNAs in germline development, the
maternal-zygotic transition and early embryogenesis. AsCSR-1 is not expressed in late embryos, larvae
or somatic tissues and the gene becomes heavily marked with H3K9me3 in 32-64 cell embryos when its
6
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was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
available under a
CC-BY-NC-ND 4.0 International license . expression ceases (Figure S1). Two isoforms of CSR-1 protein are present in C. elegans that vary in the
first exon and thus amino-terminus [62-65]. The C. elegans CSR-1a isoform with the extended amino-
terminus is expressed during spermatogenesis [64]. RNA-seq, ISO-seq, or PRO-seq analysis in Ascaris
did not identify RNAs that differ in exon 1 and the AsCSR-1 has the extended amino-terminal end similar
to C. elegans CSR-1a. Other Ascaris WAGOs are also primarily expressed in germline and embryos, with
AsWAGO-1 expression at higher levels than the others. Interestingly, AsWAGO-1 and AsWAGO-3 are
also expressed in somatic tissues such as intestine and carcass (cuticle, body wall muscle, hypodermis,
and some nervous tissue). Their targets and functions in these tissues remain to be determined. For AGO-clade Ascaris Argonautes, the miRNA Argonautes (AsALG-1 and AsALG-6) are expressed in
both the male and female germline, early development, and larvae but are present at much lower levels in
somatic tissues including the muscle, intestine, and carcass. |
Subsets and Splits