# Brillouin light scattering studies of aqueous E. coli cell lysate:
Viscoelastic properties of a multimacromolecular solution

D. F. Hanlon<EMAIL_ADDRESS>G. Todd Andrews  Department of Physics and
Physical Oceanography, Memorial University, St. John’s, NL, Canada, A1B 3X7
S. Heravi and V. Booth  Department of Biochemistry, Memorial University, St.
John’s, NL, Canada, A1C 5S7

###### Abstract

Brillouin spectroscopy was used to probe the viscoelastic properties of E.
coli bacterial cell lysate in aqueous solution at GHz-frequencies over the
range -5.0 ∘C $\leq T\leq$ 50.0 ∘C. This work offers a first temperature
dependent study on cell lysate by Brillouin light scattering. A single peak
was observed in the spectra and attributed to a longitudinal acoustic mode of
the solution. The speed of sound, bulk modulus, apparent viscosity and
hypersound attenuation were extracted from the frequency shift and FWHM of the
spectral peak. This study demonstrate that the behavior of complex
multimacromolecular solutions, as shown by E. coli lysate, can exhibit
viscoelastic properties closely akin to those observed in simple binary
aqueous protein solutions. Furthermore, our findings show that by analyzing
the raw spectral signature of the Brillouin spectra, it may be possible to
identify protein denaturation.

###### pacs:

Valid PACS appear here

††preprint: APS/123-QED

##  I Introduction

Cell lysate is a complex mixture of biomolecules that is released when cells
are ruptured. It finds wide application in various fields of research,
including fundamental biological studies and biotechnological applications
like protein purification Chiang  _et al._ (2005). Bacterial cell lysate, in
particular, has been extensively investigated in cell-free metabolic
engineering for producing target molecules and debugging pathways, offering
potential advantages for engineering bacterial cells such as the commonly used
lysate derived from Escherichia coli (E. coli) Kay and Jewett (2015). The
lysate derived from E. coli has been used extensively in the past due to its
well-characterized genetics, ease of cultivation, and relevance to both
environmental and clinical settings of the parent bacterium Macnab (1996). The
study of E. coli lysate has yielded valuable insights into the composition,
molecular interactions, and biochemical processes within bacterial cells,
thanks to the diverse assortment of biomolecules it contains Molloy  _et al._
(2000). These biomolecules, including proteins, nucleic acids, lipids,
carbohydrates, and associated metabolites, play crucial roles in essential
cellular functions like metabolism, gene expression, signal transduction, and
cell division Molloy  _et al._ (2000).

In the context of experimental fluids physics, cell lysate serves as a model
solute for studying aqueous multimacromolecular solutions commonly found in
biological systems. Understanding these solutions has proven challenging due
to their complex composition, however, their complexity also makes the system
interesting as it consists of a diverse array of molecules differing in size,
charge, and shape. To investigate the diffusivity of proteins and polymer
crowding agents in cell lysate solutions, nuclear magnetic resonance
techniques have been employed Trosel  _et al._ (2023); Wang  _et al._ (2010).
In one study, the rotational and translational diffusion of a 7.4 kDa test
protein, chymotrypsin inhibitor 2, was examined in the presence of synthetic
polymer crowders, protein crowders, and lysate Wang  _et al._ (2010). The
results indicated that artificial crowders like poly(vinylpyrrolidone) 40 and
Ficoll do not accurately replicate cellular environments due to the absence of
many non-covalent interactions that are present in real cells. Another study
investigated the effects of polymer crowders on polyethylene glycol in
bacterial cell lysate, revealing that polyethylene glycol is also unsuitable
as an excluded-volume crowding agent due to its strong association with lysate
components Trosel  _et al._ (2023). Rheology techniques have also been
employed to investigate the low-frequency viscoelasticity of cell lysate
solutions Wang  _et al._ (2010); Newton  _et al._ (2017); Trosel  _et al._
(2023). These studies focused on shear and storage moduli, as well as
viscosity in relation to shear rate. Interestingly, all of these parameters
exhibited a slight decrease with increasing shear rate. The high-frequency
viscoelastic properties of cell lysate solutions, however, have not been
examined. Such high-frequency viscoelastic characterization would inform the
testing and refinement of theoretical models based on simpler systems to
ensure that they capture the essential physics necessary to describe the
behavior of more complex systems.
This paper reports the results of Brillouin light scattering experiments with
an aqueous solution of E. coli cell lysate over the temperature range -5.0 ∘C
$\leq T\leq$ 50 ∘C. This is the first study to investigate the GHz-frequency
viscoelastic properties of a cell lysate solution. We determined the
hypersound velocity, bulk modulus, apparent viscosity and hypersound
attenuation as a function of temperature. The results of this work provide new
insight into the physics of complex multimacromolecular solutions that mimic
real-world biological systems.

##  II Methodology

###  II.1 Solution Preparation

A 500 mL flask containing 75 mL of Lysogeny Broth (LB) media, consisting of 5
g of yeast extract, 10 g of NaCl, and 10 g of tryptone fis , was closed with a
sponge plug and aluminum foil, and autoclaved for sterilization. After
reaching room temperature, overnight cultures of E. coli JM109 were prepared
by inoculating the 75 mL of LB media with 1 mL aliquots of frozen glycerol
cell stocks. The inoculated cultures were placed in a 30 ∘C incubator with
shaking at 150 rpm, protected with a foam stopper. Six 4 L flasks, each
containing 1 L of LB media, were pre-warmed to 37 ∘C. The following day, the
flasks were inoculated with 1 mL of overnight culture per 100 mL of fresh LB
media and incubated at 37 ∘C with shaking at 175 rpm. Each culture was
protected with a foam stopper.

Cells were harvested during the midlog phase at an absorption of 600 nm (A600)
ranging from 0.6 to 1.0. The absorption is a measure of the optical density
(OD) and is often used to characterize the concentration of cells in a
culture. The higher the OD implies a higher cell concentration Widdel (2007).
The harvested cells were centrifuged at 5670 g for 20 minutes at 4 ∘C. The
resulting pellet was subjected to three cycles of the French press at a
pressure of 10,000 psi (6.9 $\times$ 107 Pa) and maintained at 4 ∘C to
mechanically lyse the cells. This method of lysing the cell involves passing
the pellet through a tiny valve at extremely high pressures. As the cells
leave the valve, the pressure difference between the valve pressure and the
surrounding atmospheric pressure generates significant shear stress, which
eventually causes the cells to burst. The volume of cell lysate obtained was
approximately 30 mL. Once complete, the lysate was subject to lyophilization
to remove water. To begin this process, the lysate was stored in a freezer set
at -80∘C for 24 hours. Subsequently, the lysate is transferred into a vacuum
chamber, where it undergoes freeze-drying over the duration of 48 hours. Once
freeze-dried, the volume reduced to $\sim 5$ mL. The lyophilized cell lysate
was stored in a 15 mL falcon tube at -20 ∘C for future use.

To prepare the cell lysate solution, approximately 0.3 g of cell lysate was
carefully added to a glass sample cell. The lysate was dissolved in 4.0 $\pm$
0.1 ml of water. This gives a water concentration comparable to that inside
cells. The solution was then thoroughly mixed for approximately 10 minutes
using a stirring stick to promote uniform dispersion of the components.
Following the completion of the mixing step, Brillouin scattering experiments
were promptly initiated.

The density of the aqueous cell lysate solution was determined to be
$\rho=1.0\pm 0.1$ g/cm3, using the equation for a two-component solution

$\rho=\frac{m_{W}+m_{L}}{\frac{m_{W}}{\rho_{w}}+\frac{m_{L}}{\rho_{L}}},$ (1)

where $\rho_{W}=0.997$ g/cm3 is the density of water, $\rho_{L}=1.41$ g/cm3
(dried) Fischer  _et al._ (2004) is the density of cell lysate, and $m_{W}$
and $m_{L}$ are the mass of water and cell lysate (dried), respectively.

###  II.2 Brillouin Spectroscopy

Figure 1: Optical setup for Brillouin scattering used in this study. VNDF -
Variable neutral density filter, HWP - half wave plate, BS - beam splitter, M
- mirror, VNDF - variable neutral density filter, A - aperture L - lens, P -
prism, VTC - variable temperature chamber, PMT - photomultiplier tube.

Brillouin spectroscopy is a technique based on inelastic light scattering that
enables the investigation of thermal acoustic phonons within a medium. For a
$180^{\circ}$ backscattering geometry as used in the present work, application
of energy and momentum conservation to the scattering process reveals that the
phonon velocity, $v$, and frequency shift of the Brillouin peak, $f_{B}$, are
related by

$v=\frac{f_{B}\lambda_{i}}{2n},$ (2)

where $n$ is the refractive index of the target material at the incident light
wavelength $\lambda_{i}$. The refractive index of the cell lysate solution
used in the present work was taken to be equal to that of water, $n$ = 1.33.

The apparent viscosity $\eta=4\eta_{s}/3+\eta_{b}$, where $\eta_{s}$ and
$\eta_{b}$ are the shear and bulk viscosity, respectively, is related to the
full width at half maximum (FWHM) of the Brillouin peak due to the
longitudinal acoustic mode via Rouch  _et al._ (1976),

$\Gamma_{B}=\frac{16\pi^{2}n^{2}}{\rho\lambda_{i}^{2}}\left[\eta+\frac{\kappa}{C_{p}}(\gamma-1)\right],$
(3)

where $\rho$ is the density, $\kappa$ is the thermal conductivity, and
$\gamma=C_{p}/C_{v}$ is the ratio of specific heat at constant pressure to
that at constant volume. The second term in the brackets of this expression is
usually neglected for simple liquids, thus leaving the expression for
viscosity Rouch  _et al._ (1976),

$\eta=\frac{\rho\lambda_{i}^{2}}{16\pi^{2}n^{2}}\Gamma_{B}.$ (4)

Knowledge of the hypersound velocity and apparent viscosity permits the real
and imaginary parts of the complex longitudinal modulus,
$M=M^{\prime}+iM^{\prime\prime}$, to be determined through the relations

$M^{\prime}=\rho v^{2}$ (5)

and

$M^{\prime\prime}=2\pi\eta f_{B},$ (6)

where $M^{\prime}$ and $M^{\prime\prime}$ are referred to as the storage and
loss moduli, respectively Bailey  _et al._ .

The frequency-independent sound absorption coefficient may also be determined
from Brillouin data through Rouch  _et al._ (1976),

$\frac{\alpha}{f^{2}}=\frac{\Gamma_{B}}{2vf_{B}^{2}}.$ (7)

Brillouin spectra were collected using the $180^{\circ}$ backscattering setup
depicted in Fig. 1. A single-mode Nd:YVO4 solid-state laser (Coherent Verdi-2)
with an output power of 1.66 W and an emission wavelength of 532 nm served as
the incident light source. A half-wave plate (HWP) was used to rotate the
plane of polarization from vertical to horizontal. After leaving the half-wave
plate, the beam was divided into a reflected reference beam and a transmitted
sample probe beam by a beam splitter (BS). The reference beam is used in
conjunction with a mechanical shutter system to maintain interferometer
alignment and to prevent saturation of the photomultiplier tube (PMT) by
intense elastically scattered light from the sample. The transmitted beam was
reflected through an angle of 90∘ by front surface mirror (M1) and incident on
a right-angle prism (P) where it underwent total internal reflection. The
probe beam was then focused onto the sample using a camera lens (L1) with a
focal length of 5 cm and an f/# of 2.8. Two variable neutral density filters
(VNDF1 and VNDF2) were placed in the beam path to reduce the power at the
sample to $\sim 100$ mW. Scattered light was collected and collimated by the
same camera lens and subsequently focused onto the 450 $\mu$m-diameter input
pinhole of a six-pass tandem Fabry-Perot interferometer by a $f=40$ cm lens
(L2). The frequency-analyzed scattered light transmitted by the interferometer
was incident on the photocathode of a photomultiplier tube (PMT) where it was
converted to an electrical signal and sent to a computer for recording and
display.

The sample was housed in a custom-built variable temperature chamber (VTC). A
Lakeshore Cryotronics temperature controller was used in conjunction with a
resistor and thermoelectric cooler to regulate sample temperature. Depending
on the target temperature for the experiment, either the heater or the cooler
was initially activated. Once the desired temperature was reached, the heater
and cooler worked in tandem to maintain the sample at that temperature. If the
temperature exceeded the desired setpoint, the heater was shut-off and the
cooler was switched on to reduce the temperature to the setpoint. Conversely,
when the sample dropped below the setpoint, the cooler was turned off and the
heater was activated to return the temperature to the setpoint. The accuracy
of this variable temperature chamber was $\pm 0.4$ ∘C. Further details can be
found in Ref. Hanlon  _et al._ (2023a).

##  III Results and Discussion

###  III.1 Brillouin Spectrum

####  III.1.1 General Features

Figure 2 shows Brillouin spectra collected from the E. coli lysate solution at
temperatures ranging from -5.0 ∘C to 50 ∘C. The chronological order in which
the spectra were collected is also indicated. A single Brillouin doublet was
observed in the spectra at $\sim\pm 7.2$ GHz and attributed to the
longitudinal acoustic mode of the cell lysate solution. Brillouin peak
frequency shifts and linewidths (FWHM) were obtained by fitting Lorentzian
functions to the Stokes and anti-Stokes Brillouin peaks and averaging the
resulting best-fit parameters. To obtain linewidths, the instrumental
linewidth of 0.3 GHz was subtracted from FWHM values obtained from the
Lorentzian fits. Estimated uncertainties in peak parameters (frequency shift
and FWHM) were obtained from the uncertainty in the Lorentzian fits.

####  III.1.2 Sedimentation Effects

It was noted that the frequency shifts of Brillouin peaks in the first three
spectra (obtained at 25 ∘C, 30 ∘C, and 35 ∘C and collected consecutively
within an hour after solution preparation) trended toward that of water,
raising concerns about the integrity of the data collected. The reason for
this was later discovered to be sedimentation of larger particles present in
the cell lysate, as made apparent by the presence of an $\sim 2$ mm-thick
white residue at the bottom of the sample cell when removed from the
temperature-controlled chamber at the conclusion of the experiment. These
larger particles likely include remnants of the bacterial cell wall
(characteristic size of $\sim 1$ $\mu$m Riley (1999); Huang  _et al._ (2008)),
and not molecular constituents such as proteins, nucleic acids, or lipids due
to the small sizes of the latter (see Table 1). There is also a small
percentage of smaller particles such as ions, metabolites, and polysaccharides
Johnson  _et al._ (2002) not included in Table 1 due to their minimal
abundance and significant variation in radii and density. This is in accord
with Stokes’ Law which predicts that the terminal velocity of a particle in a
fluid is proportional to the square of its radius Batchelor and Batchelor
(1967) (the strongest dependence on any parameter in this equation). With this
in mind, the sedimentation time was estimated by first stirring the solution
for approximately 10 minutes until homogeneous (as for the as-prepared
solution at the outset of the experiment) and then visually monitoring it
until the larger particles had settled. This time was found to be $\sim 45$
minutes. It is therefore likely that the spectra collected at 25∘C, 30∘C, and
35∘C were affected by sedimentation. This was considered when analyzing the
experimental results. It should also be noted that the probing incident laser
beam was not impeded by the settled residue.

Table 1: The approximate radius and density of cellular components in bacterial cells, along with their composition by weight Johnson  _et al._ (2002). Molecule | Radius | Mass Density | Abundance
---|---|---|---
| (nm) | (g/cm3) | % Dry weight
Proteins | 2 - 10 Zhdanov (2009) |  $\sim$ 1.35 Fischer  _et al._ (2004) | 50 - 55 Feijó Delgado  _et al._ (2013)
RNA | 7 - 10 Borodavka  _et al._ (2016) |  $\sim$ 2.00 Anderson  _et al._ (1966) | 20 Feijó Delgado  _et al._ (2013)
Phospholipids | 0.5 - 1 Nagle and Tristram-Nagle (2000) |  $\sim$ 1.01 Johnson and Buttress (1973) | 7 - 9 Feijó Delgado  _et al._ (2013)
DNA | 3 - 5 Sinden (1994) |  $\sim$ 1.70 Anderson  _et al._ (1966); Panijpan (1977) | 3 Feijó Delgado  _et al._ (2013)
Figure 2: Brillouin spectra of an E. coli bacterial cell lysate-water solution
collected at the temperatures indicated. Integer numbers (1-15) represent the
sequential order in which spectra were collected.

####  III.1.3 Temperature Dependence

Figure 3: Plot of frequency shift and FWHM as a function of temperature for
water and an aqueous E. coli cell lysate solution. Error bars represent the
uncertainty in the spectral parameters.

Figure 3 shows the temperature dependence of the Brillouin peak frequency
shift for water and the cell lysate solution. In general, the frequency shift
for the lysate solution increases with increasing temperature. Previous
Brillouin scattering work on aqueous protein systems have consistently
reported a similar trend Bailey  _et al._ ; Comez  _et al._ (2012, 2016); Lupi
_et al._ (2011); Palombo and Fioretto (2019); Monaco  _et al._ (2001); Hanlon
_et al._ (2023a). Notably, at higher temperatures, the frequency shift for the
lysate solution has values that closely resemble those of water. For
temperatures below $T\sim 10$ ∘C, however, a noticeable difference develops
between the peak frequency shifts for water and the cell lysate solution.

Figure 3 also shows the Brillouin peak linewidth as a function of temperature
for water and cell lysate. Unlike the peak frequency shift, the FWHM for the
lysate solution is different from that of water over the entire temperature
range studied. This is a clear indication that even though larger particles in
the cell lysate have settled-out, smaller particles such as protein and lipid
molecules remain in solution. The FWHM begins to become appreciably different
from that of water for $T\leq 10$ ∘C, the same temperature range as noted
above for the Brillouin peak frequency shift.

###  III.2 Viscoelastic Properties

####  III.2.1 Temperature Dependence

Figure 4: Sound velocity, apparent viscosity, frequency-independent sound
absorption coefficient, storage, and loss modulus as a function of temperature
for an aqueous cell lysate solution. The uncertainty is approximately twice
the size of the symbols.

Figure 4 presents viscoelastic properties for water and cell lysate solution
over the range -5.0 ∘C to 50.0 ∘C determined from the Brillouin data using
equations given in Sec. II.2. As can be seen, the viscoelastic properties of
the cell lysate solution obtained from the first few post-sedimentation
spectra (#4 - #8 in Fig. 2, collected at $T>35$ ∘C), are nearly independent of
temperature and closely resemble those of water. In contrast, solution
viscoelastic properties obtained from spectra collected after those in this
“high-temperature” region (i.e., at $T\leq 20$ ∘C) are appreciably different
from those of water, as can be seen in Fig. 4 by comparison of values for the
lysate solution to those for water (direct or interpolated) at a given
temperature. A possible reason for this behaviour could be the irreversible
denaturation of proteins in the cell lysate solution at $T\sim 40$ ∘C Petsko
and Ringe (2004). If this is in fact the case, this result is very interesting
because it means that protein denaturation and configuration (folded or
unfolded) can be detected using Brillouin spectroscopy. This hypothesis is
also supported by the results of recent molecular dynamics simulations on
aqueous protein systems which show some convergence of sound velocity,
adiabatic bulk modulus, and shear viscosity toward values for water for
$T\gtrsim 40$ ∘C and a much reduced dependence of these quantities on
temperature in this range compared to that at lower temperatures Hanlon  _et
al._ (2023b).

The temperature dependence of several of the cell lysate solution viscoelastic
properties seems to display a weak anomaly at $T\sim 2$ ∘C, as indicated by
the dashed vertical line in Fig. 4. This anomaly is apparent in the velocity,
sound absorption, and storage modulus data, but barely discernible in the
temperature dependence of the apparent viscosity and loss modulus. Given that
a significant fraction of the cell lysate solution is water with a well-known
liquid-to-solid phase transition at 0 ∘C, this anomaly is not completely
unexpected and may in fact be a manifestation of a corresponding liquid-solid
phase transition in the lysate solution at approximately the same temperature.

It is also interesting to note the qualitative similarity of the temperature
dependence of some lysate solution viscoelastic properties to those of simple
aqueous protein systems obtained using molecular dynamics simulations (see
Fig. 4 in this paper and Figs. 2, 4 and 5 in Ref. Hanlon  _et al._ (2023b)).
Despite considerable differences in composition, the sound velocity and
storage modulus for the lysate solution and nearly all of the model systems
show an overall increase with increasing temperature over the range from a few
∘C to $\sim 40-45$ ∘C and a much weaker dependence for higher temperatures,
with some convergence of values toward those for water in this upper range. In
addition, the overall decrease in shear viscosity with increasing temperature
for the simulated protein-water systems mimics that of the apparent viscosity
of the cell lysate solution. Interestingly, similar behaviour was found for
the temperature dependence of sound velocity, storage modulus, and apparent
viscosity of natural snail mucus, a system comprised primarily, but not only,
of water and glycoproteins Hanlon  _et al._ (2023a). When considered together,
these results suggest that the underlying physical mechanisms responsible for
the bulk viscoelasticity of simple aqueous protein solutions are also at play
in multimacromolecular solutions. Consequently, it may be possible to predict
the viscoelastic behaviour of complex macromolecular solutions, such as found
in biological systems, using rather simple models.

####  III.2.2 Activation Energy

Figure 5 shows the natural logarithm of the apparent viscosity as a function
of inverse temperature. The apparent viscosity for the entire temperature
region depends linearly on $1/T$ so we fit an Arrhenius relationship of the
form

$\eta=\eta_{0}e^{E_{a}/k_{B}T}$ (8)

to the data. The activation energy for the cell lysate was determined to be
$E_{a}=17.1$ kJ/mol, which is approximately 20% higher than the activation
energy for water and other polymer-water systems Lupi  _et al._ (2011); Comez
_et al._ (2012); Hanlon  _et al._ (2023a). Notably, the observed data
exhibited a linear relationship, indicating a negligible thermal dependence of
both the activation entropy ($\eta_{0}$) and enthalpy ($E_{a}$) across the
entire temperature range studied. In contrast to other systems, no evidence of
a transition to non-Arrhenius behavior was observed. In other aqueous protein
solutions, the apparent viscosity typically follows an Arrhenius behavior in
the high-temperature region ($T\geq 20$ ∘C), which is associated with the
onset of cooperative motions at the molecular level and is often described by
a power law or a Vogel–Fulcher relationship Lupi  _et al._ (2011); Hanlon  _et
al._ (2023a).

Figure 5: Natural logarithm of viscosity for an aqueous solution of bacterial
cell lysate as a function inverse temperature. Dashed lines represent best
fit. The uncertainty is approximately twice the size of the symbols.

##  IV Conclusion

In this study the GHz-frequency viscoelastic properties of an aqueous solution
of E. coli cell lysate were probed by Brillouin spectroscopy across a
temperature range of -5.0 ∘C to 50 ∘C. We find that the observed behaviour in
the frequency shift and FWHM, and consequently the speed of sound, viscosity
and sound absorption closely resembles that of simple aqueous solutions
containing only a single protein or polymer species. For instance, previous
Brillouin scattering studies Bailey  _et al._ ; Comez  _et al._ (2012, 2016);
Lupi  _et al._ (2011); Palombo and Fioretto (2019); Monaco  _et al._ (2001);
Hanlon  _et al._ (2023a) have shown the general increase in frequency shift
and decrease in FWHM with increasing temperature. This could have potentially
important implications for computer simulations and theoretical work on
multimacromolecular systems because it demonstrates that the viscoelasticity
of a complex systems can, at least in some cases, be accurately modelled using
much simpler systems. The quantitative nature of the results obtained in this
work also highlight the potential of Brillouin light scattering spectroscopy
as a potent tool for examining the viscoelasticity of complex biological
systems, as the influence of proteins on the viscoelastic properties of these
systems is still in some ways poorly understood.

## Disclosure Statement

No potential conflict of interest was reported by the authors.

## Acknowledgments

This work was partially supported by Memorial University Seed, Bridge and
Multidisciplinary Fund through grant 216354-46314-2000.

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