††thanks: A.R.M. and A.S.-F. contributed equally to this work††thanks: A.R.M.
and A.S.-F. contributed equally to this work

Present address: ]Department of Food Technology, Lund University, SE-211 00
Lund, Sweden.

# Bayesian determination of the effect of a deep eutectic solvent on the
structure of lipid monolayers

A. R. McCluskey  a.r.mccluskey<EMAIL_ADDRESS>Department of Chemistry, University of Bath, Claverton Down, Bath, BA2 7AY, UK
Diamond Light Source, Harwell Campus, Didcot, OX11 0DE, UK  A. Sanchez-
Fernandez  [  Department of Chemistry, University of Bath, Claverton Down,
Bath, BA2 7AY, UK  European Spallation Source, SE-211 00 Lund, Sweden  K. J.
Edler  Department of Chemistry, University of Bath, Claverton Down, Bath, BA2
7AY, UK  S. C. Parker  Department of Chemistry, University of Bath, Claverton
Down, Bath, BA2 7AY, UK  A. J. Jackson  European Spallation Source, SE-211 00
Lund, Sweden  Department of Physical Chemistry, Lund University, SE-211 00
Lund, Sweden  R. A. Campbell  Division of Pharmacy and Optometry, University
of Manchester, Manchester, UK  Institut Laue-Langevin, 71 avenue des Martyrs,
38000, Grenoble, France  T. Arnold<EMAIL_ADDRESS>Department of
Chemistry, University of Bath, Claverton Down, Bath, BA2 7AY, UK  Diamond
Light Source, Harwell Campus, Didcot, OX11 0DE, UK  European Spallation
Source, SE-211 00 Lund, Sweden  ISIS Neutron and Muon Source, Science and
Technology Facilities Council, Rutherford Appleton Laboratory, Harwell Oxford,
Didcot, OX11 0QX, UK

###### Abstract

In this work, we present the first example of the self-assembly of
phospholipid monolayers at the interface between air and an ionic solvent.
Deep eutectic solvents are a novel class of environmentally friendly, non-
aqueous, room temperature liquids with tunable properties, that have wide-
ranging potential applications and are capable of promoting the self-assembly
of surfactant molecules. We use a chemically-consistent Bayesian modelling of
X-ray and neutron reflectometry measurements to show that these monolayers
broadly behave as they do on water. This method allows for the monolayer
structure to be determined, alongside the molecular volumes of the individual
monolayer components, without the need for water-specific constraints to be
introduced. Furthermore, using this method we are able to better understand
the correlations present between parameters in the analytical model. This
example of a non-aqueous phospholipid monolayer has important implications for
the potential uses of these solvents and for our understanding of how
biomolecules behave in the absence of water.

Usage

Electronic Supplementary Information (ESI) available: All analysis/plotting
scripts and figure files, allowing for a fully reproducible, and automated,
analysis workflow for the work presented is available at
https://github.com/arm61/lipids_at_airdes (DOI: 10.5281/zenodo.2577796) under
a CC BY-SA 4.0 license. Reduced experimental datasets are available at DOI:
10.15125/BATH-00548, under a CC-BY 4.0 license.

##  I Introduction

Deep eutectic solvents (DES) are green, sustainable liquids that are obtained
through the combination of ionic species with compounds that act as hydrogen
bond donors, such as sugars, alcohols, amines, and carboxylic acids Smith  _et
al._ (2014); Dai  _et al._ (2013). The resulting extensive hydrogen bonding
network is able to stabilise the ionic species and allows the eutectic mixture
to remain liquid at room temperature Hammond  _et al._ (2016, 2017); Araujo
_et al._ (2017). Through different combinations of the precursor materials, it
is possible to tune the solvent’s physicochemical properties, such as polarity
Pandey  _et al._ (2014), viscosity and surface tension Smith  _et al._ (2014),
network charge Zahn  _et al._ (2016), and hydrophobicity Ribeiro  _et al._
(2015); van Osch  _et al._ (2015). Recently DES have also been shown to
exhibit a “solvophobic” effect through the promotion of surfactant micelle
formation Sanchez-Fernandez  _et al._ (2016); Arnold  _et al._ (2015); Hsieh
and Liu (2018); Banjare  _et al._ (2018), phospholipid bilayer formation
Bryant  _et al._ (2017, 2016); Gutiérrez  _et al._ (2009), and the ability to
stabilise non-ionic polymer Sapir  _et al._ (2016) and protein conformations
Sanchez-Fernandez  _et al._ (2017).

Phospholipid monolayers at the air/water interface have been widely studied as
simplistic models for biological membranes. As such, they have been used to
gain insight into many biological processes that are technologically and
medically relevant. For example, investigations at the air/salt-water
interface have identified the importance that interactions between charged
phospholipid heads and ions present in solution have on the structure, monomer
packing and stability of the monolayer Mohwald (1990); Kewalramani  _et al._
(2010). However, the native environment for lipids _in-vivo_ is far from a
simple aqueous solution. In fact, it has been suggested Dai  _et al._ (2013);
Hammond  _et al._ (2017) that DES might form within the crowded cellular
environment and could assist in solubilizing biological species in an
intermediate environment between that of the hydrophobic phospholipid tails
and highly polar water-rich regions, thereby assisting survival under extreme
conditions such as freezing temperatures or drought where the water content of
cells is restricted. Despite the broad interest in these systems, the presence
of stable phospholipid monolayers at the interface between air and an ionic
solvent media has not been previously reported, to the best of the authors’
knowledge.

The study of lipid monolayers on a non-aqueous solvent like DES is relevant to
some potential new scientific areas or technological applications. For
example, it may be possible to study the interactions of proteins with model
membranes in a zero or low water environment, or even at low temperatures
where aqueous based model membranes are not practical. To enable such
experiments we must first understand how lipid monolayers are affected by a
non-aqueous environment. Published studies covering such non-aqueous systems
are, however, rather scarce mirroring the availability of solvents that show a
solvophobic effect comparable to water. In the absence of water, formamide has
been reported to support the formation of lipid monolayers Graner  _et al._
(1995); Weinbach  _et al._ (1993). Monolayers have also been observed at the
air-mercury interface Magnussen  _et al._ (1996); Kraack  _et al._ (2002),
although in this case, the similarity to water is somewhat limited. We have
recently shown that self-assembly of surfactant monolayers is possible for DES
with behaviour that is much more comparable to that seen in water Arnold  _et
al._ (2015); Sanchez-Fernandez  _et al._ (2018a).

In this work, we have investigated the structure of phospholipid monolayers at
the air-DES interface. To do this we have used the combination of both X-ray
and neutron reflectometry (XRR & NR), techniques that allow detailed
structures to be determined with near-atomic resolution. In order to interpret
our results, we have used a novel analysis method which allows us to
sufficiently constrain our model while using Bayesian inference Abelès (1948);
Parratt (1954) to properly quantify the errors and correlations inherent in
such models of reflectometry data. Specifically, we have constrained the model
to ensure that it is chemically self-consistent across multiple measurements
at various surface pressures. Four different phospholipids; 1,2-dipalmitoyl-
sn-glycero-3-phosphocholine (DPPC), 1,2-dimyristoyl-sn-
glycero-3-phosphocholine (DMPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine
(DLPC) and 1,2-dimyristoyl-sn-glycero-3-phospho-(1’-rac-glycerol) (sodium
salt) (DMPG), were studied at the interface between a 1:2 mixture of choline
chloride:glycerol and air. This has allowed a comparison of two chemically
distinct phospholipid head components, the zwitterionic phosphocholine (PC)
and the anionic phosphoglycerol (PG) to be probed in this ionic solvent
(Figure 1). In addition, the effect of the tail chain length in the assembly
of the Langmuir monolayer was explored by comparing molecules with
progressively increasing tail length (12, 14 and 16 carbon atoms in each of
the two hydrocarbon chains in each molecule). Our study is inevitably limited
in extent due to the limited availability of X-ray and neutron beamtime
together with the prohibitive expense of deuterated chemicals. However, we
believe that this work both hints at interesting differences in behaviour for
phospholipids monolayers on DES and demonstrates how our approach to fitting
can provide a quantitative understanding of this behaviour.

Figure 1: The two lipid classes with different head groups compared in this
study, where R indicates the hydrocarbon tail; (a) phosphatidylglycerol (PG),
(b) phosphocholine (PC).

Recent developments in computational resources and software have enabled
powerful methodologies and algorithms to be harnessed by those from non-expert
backgrounds. This has benefitted significantly from open-source software
projects such as the Python language van Rossum (1995) and the Jupyter
notebooks framework Kluyver  _et al._ (2016). In the area of NR and XRR, the
landscape of data-analysis software is diverse, with a range of software
packages available from a variety of sources; refnx Nelson and Prescott
(2019); Nelson  _et al._ (2018), MOTOFIT Nelson (2006), Rascal Hughes (2010)
Aurore Gerelli (2016), Refl1D Kienzle  _et al._ (2011), and GenX Björck and
Andersson (2007).

The use of a Python library, such as refnx, enables the implementation of
custom models that contain chemically-relevant information as well as the
application of probability distribution function (PDF) sampling techniques.
The Python library emcee Foreman-Mackey  _et al._ (2013) allows refnx to
access the Goodman & Weare Affine Invariant Markov chain Monte Carlo (MCMC)
Ensemble method Goodman and Weare (2010). This allows the sampling of the
high-dimensionality parameter space, relevant in reflectometry analysis, in a
Bayesian fashion, where the new samples are generated with consideration of
those sampled previously Sivia and Skilling (2006). Bayesian inference gives
an understanding of the PDF for the fitted parameters and therefore
estimations of their inverse uncertainties and inter-parameter correlations.

##  II Experimental Section

###  II.1 Materials

Choline chloride ($99\text{\,}\mathrm{\char 37\relax}$ %, Sigma-Aldrich) and
glycerol ($99\text{\,}\mathrm{\char 37\relax}$, Sigma-Aldrich), and d9-choline
chloride ($99\text{\,}\mathrm{\char 37\relax}$, $98\text{\,}\mathrm{\char
37\relax}$ D, CK Isotopes) and d8-glycerol ($99\text{\,}\mathrm{\char
37\relax}$, $98\text{\,}\mathrm{\char 37\relax}$ D, CK Isotopes) were
purchased and used without further purification. The DES was prepared by
mixing the precursors at a 1:2 ratio of choline chloride:glycerol, and heating
at $80\text{\,}\mathrm{\SIUnitSymbolCelsius}$ until a homogeneous, transparent
liquid formed Smith  _et al._ (2014). The solvent was equilibrated overnight
at $40\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and subsequently stored under a
dry atmosphere. Due to the limited availability of the deuterated precursors,
a fully protonated subphase (hDES) and a partially deuterated subphase (hdDES)
were prepared and used during the neutron reflectometry (NR) experiment. The
partially deuterated subphase was prepared using the following mixtures of
precursors: $1\text{\,}\mathrm{mol}$ of $0.38\text{\,}\mathrm{mol}$ fraction
of h-choline chloride/$0.62\text{\,}\mathrm{mol}$ fraction of d-choline
chloride; and $2\text{\,}\mathrm{mol}$ of $0.56\text{\,}\mathrm{mol}$ fraction
of h-glycerol/$0.44\text{\,}\mathrm{mol}$ fraction of d-glycerol. The
deuterated solvent was prepared following the procedure discussed above.

The water content of the DES was determined before and after each experiment
by Karl-Fischer titration (Mettler Toledo DL32 Karl-Fischer Coulometer,
Aqualine Electrolyte A, Aqualine Catholyte CG A) in order to ensure water
presence was kept to a minimum. Those measurements showed that the water
content of the solvent was kept below
$0.3\text{\,}\mathrm{w}\mathrm{t}\mathrm{/}\mathrm{\char 37\relax}$ during all
the experimental procedures presented here, which we assume to be negligible
and have to little impact on the characteristics of the DES Hammond  _et al._
(2016, 2017).

DPPC (C16 tails, $>99\text{\,}\mathrm{\char 37\relax}$), DMPC (C14 tails,
$>99\text{\,}\mathrm{\char 37\relax}$), and the sodium salt of DMPG (C14
tails, $>99\text{\,}\mathrm{\char 37\relax}$) were supplied by Avanti Polar
Lipids and, DLPC (C12 tails, $>99\text{\,}\mathrm{\char 37\relax}$) was
supplied by Sigma Aldrich and all were used without further purification.
Deuterated versions of DPPC (d62-DPPC, $>99\text{\,}\mathrm{\char 37\relax}$,
deuterated tails-only) and DMPC (d54-DPPC, $>99\text{\,}\mathrm{\char
37\relax}$, deuterated tails-only) were supplied by Avanti Polar Lipids and
used without further purification. These phospholipids were dissolved in
chloroform ($0.5\text{\,}\mathrm{mg}\text{\,}{\mathrm{mL}}^{-1}$) at room
temperature. PC indicates the molcule contains a phosphocholine head
component, where PG contains a phosphatidylglycerol head component, these are
shown in Figure 1.

In the XRR experiment, sample preparation was performed in situ using the
standard method for the spreading of insoluble monolayers on water: a certain
amount of the phospholipid solution was spread onto the liquid surface in
order to provide a given surface concentration. After the evaporation of the
chloroform, it is assumed that the resulting system is a solvent subphase with
a monolayer of phospholipid at the interface. Surface concentration was
modified by closing and opening the PTFE barriers of a Langmuir trough. In
order to minimise the volumes used in the NR experiment (to keep the cost of
deuterated compounds to a manageable level), it was not possible to use a
Langmuir trough. Instead, small Delrin adsorption troughs were used that did
not have controllable barriers. So, although the surface coverage was
nominally the same as used in the X-ray studies, the lack of precise control
over the surface pressure meant that it was not appropriate to co-refine XRR
and NR contrasts together.

###  II.2 Methods

XRR measurements were taken on I07 at Diamond Light Source, at
$12.5\text{\,}\mathrm{keV}$ photon energy using the double-crystal deflector
Arnold  _et al._ (2012). The reflected intensity was measured in a momentum
transfer range from
$0.018\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-1}0.7\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-1}$.
The data were normalised with respect to the incident beam and the background
was measured from off-specular reflection and subsequently subtracted. Samples
were equilibrated for at least one hour and preserved under an helium
atmosphere to minimise the adsorption of water by the subphase. XRR data were
collected for each of the lipids, DLPC, DMPC, DPPC and DMPG at four surface
pressures (DLPC: $20253035\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$,
DMPC: $20253040\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$, DPPC:
$15202530\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$, DMPG:
$15202530\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$, as measured with an
aluminium Wilhelmy plate; measurements were conducted at
$7\text{\,}\mathrm{\SIUnitSymbolCelsius}22\text{\,}\mathrm{\SIUnitSymbolCelsius}$.
The aluminium Wilhelmy plate was used over a traditional paper plate due to
the low wettability of paper by the DES.

The NR experiments were performed on FIGARO at the Institut Laue-Langevin
using the time-of-flight method Campbell  _et al._ (2011). Data at two
incident angles of $0.62\text{\,}\mathrm{\SIUnitSymbolDegree}$ and
$3.8\text{\,}\mathrm{\SIUnitSymbolDegree}$ were measured to provide a momentum
transfer range from
$0.005\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-1}0.18\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-1}$.
Two surface pressures for each system and contrast was measured (DMPC:
$2025\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$, DPPC:
$1520\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$). Similar to the X-ray
procedure, samples were given enough time to equilibrate (at least two hours),
kept under an inert atmosphere, and all measurements were conducted at
$22\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

###  II.3 Data analysis

The use of XRR and NR to analyse the structure of phospholipids on the surface
of water is well documented Mohwald (1990); Kewalramani  _et al._ (2010);
Bayerl  _et al._ (1990); Johnson  _et al._ (1991); Clifton  _et al._ (2012);
Helm  _et al._ (1987); Daillant  _et al._ (1990). The models used in the
rationalisation of XRR and NR data have varied significantly in numbers of
layers present, use of interfacial roughness, and the parameterisation of the
physical constraints applied. Frequently, these physical constraints include
the volumes of the phospholipid head and tail components, using values taken
from other techniques, such as those shown in Table 1. Additionally, a recent
evaluation of the applicability of different models for surfactant and
phospholipid monolayers from the NR perspective has been published Campbell
_et al._ (2018), that suggests possible oversights in the modelling of NR
data.

Table 1:  Lipid component volumes extracted from different literature sources. $V_{l}$ corresponds to the total lipid volume, MD to molecular dynamics simulation, WAXS to wide-angle X-ray scattering, NB to neutral buoyancy and DVTD to differential vibrating tube densimetry. a The values for the head component in Kucerka _et al._ Kučerka  _et al._ (2004), were taken from Balgavý _et al._ Balgavý  _et al._ (2001). Lipid | DPPC |  |  | DMPC |  | DLPC |  | DMPG | POPG
---|---|---|---|---|---|---|---|---|---
Reference | Armen  _et al._ (1998) | Sun  _et al._ (1994) |  Kučerka  _et al._ (2004); Balgavý  _et al._ (2001)a | Armen  _et al._ (1998) |  Kučerka  _et al._ (2004); Balgavý  _et al._ (2001)a | Armen  _et al._ (1998) |  Kučerka  _et al._ (2004); Balgavý  _et al._ (2001)a | Pan  _et al._ (2012) | Kučerka  _et al._ (2012)
$V_{l}$/Å3 | $1287.3\pm 25.5$ | $1148\pm 2$ | $1264.2\pm 32.1$ | $1172.5\pm 25.1\textsterling$ | $1155.4\pm 30.0\textsterling$ | $1057.7\pm 24.7$ | $1046.6\pm 28.0$ | $1011.4$ | $1203$
$V_{t}$/Å3 | $966.4\pm 5.4$ | $829\pm 4$ | $924.7\pm 17.6$ | $851.5\pm 5.0\textsterling$ | $815.9\pm 15.5\textsterling$ | $736.8\pm 4.6$ | $707.1\pm 13.5$ | $720.4$ | $914$
$V_{h}$/Å3 | $320.9\pm 20.1$ | $319\pm 6$ | $339.5\pm 14.5$ | $320.9\pm 20.1$ | $339.5\pm 14.5$ | $320.9\pm 20.1$ | $339.5\pm 14.5$ | $291.0$ | $289$
Method | MD | WAXS | NB | MD | NB | MD | NB | DVTD | MD
T/∘C | 50 | 24 | 30 | 50 | 30 | 50 | 30 | 20 | 25

In Table 1, there appears to be a general consensus that the component volume
for the phosphocholine (PC) head is around
$320\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{3}360\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{3}$,
while the phosphatidylglycerol (PG) head is in the range
$289\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{3}291\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{3}$.
However, it is not clear that the head component volumes from the literature,
that are derived from water-based measurements, will be appropriate for this
work, which involves a non-aqueous solvent. The charged nature of the
zwitterionic or anionic lipid heads may have different interactions with the
polar, but neutral water as compared to the charged DES components Sanchez-
Fernandez  _et al._ (2018a), which will affect the phospholipid head component
volume. Therefore, herein we apply a chemically-consistent model that allows
for the co-refinement of reflectometry measurements at different surface
pressure and makes no assumption of the component volume for the lipid head,
$V_{h}$, or tail, $V_{t}$. Instead, these parameters were allowed to vary for
each lipid while being constrained to be self-consistent over different
surface pressures in the same phase; Liquid-Condensed (LC) for DPPC and
Liquid-Expanded (LE) for DMPC, DMPG, and DLPC. Furthermore, it is known that,
on water, increased surface pressure and the associated LE-LC phase
transitions lead to a compression of the lipid tail volume Marsh (2010); Small
(1984), and this compaction has not necessarily been accounted for in the
literature Campbell  _et al._ (2018). This model avoids this issue by making
no assumption about the molecular volumes and only considers surface pressures
that we believe to be in the same phase.

Our chemically-consistent model has been implemented in the Python library
refnx Nelson and Prescott (2019); Nelson  _et al._ (2018). This software
allows for the inclusion of a custom model to be defined, from which
parameters feed into the Abelès reflectivity model (a model that is widely
used to calculate reflectivity Abelès (1948); Parratt (1954)). This custom
model, along with a series of Jupyter notebooks showing, in full, the analysis
performed, can be found in the ESI and is available under a CC BY-SA 4.0
licence.

This model consists of two layers to define the lipid monolayer; the head
layer at the interface with the solvent and the tail layer at the interface
with the air. The head components have a calculated scattering length,
$b_{h}$, (found as a summation of the X-ray or neutron atomic scattering
lengths), and a component volume, $V_{h}$. These head components make up a
layer with a given thickness, $d_{h}$, and roughness, $\sigma_{h}$, within
which some volume fraction of solvent can intercalate, $\phi_{h}$. The tail
layer is defined in the same fashion, except that the thickness, $d_{t}$, is
limited such that it may be no greater than the maximum extended length of the
lipid tail (the Tanford length, $t_{t}$ Tanford (1980)), which is given in
Table 2, and that no solvent may intercalate into the layer (e.g.
$\phi_{t}=0$). The scattering length density (SLD) of the tail and head layers
used in the Abelès model can therefore be found as follows,

$\text{SLD}_{i}=\frac{b_{i}}{V_{i}}(1-\phi_{i})+\text{SLD}_{s}(\phi_{i}),$ (1)

where, $\text{SLD}_{s}$ is the scattering length density of the subphase
(DES), and $i$ indicates either the tail or head layer. To ensure that the
number density of head components and pairs of tail components is the same,
the following constraint was included in the model Braun  _et al._ (2017),

$\phi_{h}=1-\bigg{(}\frac{d_{t}V_{h}}{V_{t}d_{h}}\bigg{)}.$ (2)

Based on the work of Campbell _et al._ Campbell  _et al._ (2018), a single
value for the interfacial roughness was fitted for all of the interfaces,
including the subphase (i.e. $\sigma_{h}$ = $\sigma_{t}$ = $\sigma_{s}$), as
there is only a single lipid molecule type in each monolayer. Therefore, any
capillary wave roughness at the air-DES interface is carried equally through
the layers. The interfacial roughness was constrained to be greater than
$3.3\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ in agreement with previous work
Sanchez-Fernandez  _et al._ (2016).

Table 2:  The invariant parameters within the chemically-consistent model. aValues obtained from the Tanford formula Tanford (1980). bValues obtained from Sanchez-Fernandez _et al._ Sanchez-Fernandez  _et al._ (2016). Component |  $b_{t}$/$\mathrm{fm}$ |  $b_{h}$/$\mathrm{fm}$ |  $t_{t}$/$\mathrm{\SIUnitSymbolAngstrom}$ |  SLD/$10^{-6}$${\mathrm{\SIUnitSymbolAngstrom}}^{-2}$
---|---|---|---|---
X-ray |  |  |  |
DLPC | 5073 | 4674 | 15.5a | –
DMPC | 5985 | 4674 | 18.0a | –
DPPC | 6897 | 4674 | 20.5a | –
DMPG | 5985 | 4731 | 18.0a | –
Air | – | – | – | 0
DES | – | – | – | 10.8b
Neutron |  |  |  |
d54-DMPC | 5329.8 | 602.7 | 18.0a | –
d62-DPPC | 6129.2 | 602.7 | 20.5a | –
h-DES | – | – | – | 0.43b
hd-DES | – | – | – | 3.15b

In order to justify the use of a single tail volume across many surface
pressures, it was necessary to ensure that the lipids remain in the same
phase. On water, this can be demonstrated with a Langmuir isotherm. However,
while we have confidence that the individual surface pressures measured were
reliable, we were unable to collect consistent Langmuir isotherm measurements,
due to the high viscosity of the DES. Instead, we have used grazing incidence
X-ray diffraction to confirm the phases of DMPC and DPPC at
$30\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$. DPPC was found to be in
the LC phase and DMPC in the LE phase at room temperature for the surface
pressures measured (see Section LABEL:sec:gixd in the ESI). We assume that
DMPG and DLPC are also in the LE phase since there is no reason to believe
that the phase behaviour in these systems differs significantly from DMPC at
the same temperature.

In the first of two steps, this custom model was used to co-refine the
component volume of the lipid head component, $V_{h}$, the volume of the tail
component, $V_{t}$, and the head thickness, $d_{h}$ across XRR measurements at
four different surface concentrations. In keeping with the work of Campbell
_et al._ Campbell  _et al._ (2018), a single value for the head thickness was
fitted for each lipid across all surface pressures, as the thickness of the
head layer was considered to be dependent on molecular dimensions only, and
has been shown to vary little with surface pressure Kewalramani  _et al._
(2010). The following parameters were allowed to vary; $d_{t}$, and
$\sigma_{t,h,s}$, independently across the surface pressures, while others,
shown in Table 2, were held constant at the values given. For each co-
refinement of four XRR measurements, there were, in total, eleven degrees of
freedom in the fitting process. Throughout all of the analyses, the
reflectometry scale factor was allowed to vary freely, while the background
was constrained to the intensity of either the largest or second-largest
$q$-value.

In the second step, the head and tail component volumes, and head layer
thickness determined from XRR were fixed for the refinement of the custom
model against the NR measurements. This approach means that the number of
variable parameters to fit the NR data can be reduced to two, namely the
thickness of the tail layer, $d_{t}$, and the interfacial roughness,
$\sigma_{t,h,s}$, for the co-refinement of two datasets. Table 2 also gives
the details of the scattering lengths and SLDs used as invariant parameters
for the NR fitting.

In both cases, the refinement of the custom model to the experimental data
involved the transformation of the reflectometry calculated from the model and
the data into $Rq^{4}$ such that the contribution of the Fresnel decay was
removed, before using the differential evolution method available to refnx
from the scipy library Jones  _et al._ (2001), to find the parameters that
gave the best fit to the data. The parameter space was then probed using the
MCMC method available through emcee Foreman-Mackey  _et al._ (2013), which
allowed for an estimate of the probability distribution function (PDF)
associated with each parameter. In the MCMC sampling, 200 walkers were used
over 1000 iterations, following equilibration of 200 iterations. The use of
MCMC sampling allowed for a Bayesian inference of the PDF for each of the
variables and their respective interactions and the Shapiro test to be used to
assess if each PDF was normally distributed. Parameters that were shown to be
normally distributed are given with symmetric confidence intervals, while
those that failed the Shapiro test are given with asymmetric confidence
intervals ($95\text{\,}\mathrm{\char 37\relax}$ confidence intervals in both
cases). However, it is important to note that these are not _true_ confidence
intervals, and account only for the uncertainty present in the data, i.e. they
do not account of systematic uncertainty in the measurement that is
underrepresented, or unrepresented, in the experimental dataset.

Figure 2: The XRR profiles (left) and SLD profiles (right) for each of the
four lipids; (a) DLPC, (b) DMPC, (c) DPPC, and (d) DMPG, at the four measured
surface pressures; see legend above each plot. The different surface pressure
XRR profiles have been offset in the $y$-axis by an order of magnitude and SLD
profiles offset in the $y$-axis by
$5\text{\times}{10}^{-6}\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-2}$, for
clarity.

##  III Results & Discussions

The chemically-consistent model was co-refined across the four surface
pressure XRR measurements for each lipid. Although lipid monolayers on water
often reach values above $50\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$,
signifying a decrease in surface tension to ca.
$20\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$ upon addition of lipid, it
was not possible to reach those values for the monolayers on DES Mohwald
(1990). The surface tension of pure choline chloride:glycerol has been
previously reported to be
$63.5(5)\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$ Sanchez-Fernandez  _et
al._ (2016). This means that a surface pressure of ca.
$40\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$ iin choline
chloride:glycerol will also result in a reduction to ca.
$20\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$ in the surface tension.
Interestingly, the absolute values of surface tension in both water and
choline chloride:glycerol after addition of lipid are similar. Therefore,
surface pressures of up to $40\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$
were measured for the monolayers on DES, when possible. The resulting XRR
profiles and associated SLD profiles are shown in Figure 2. Table III gives
details of all varied parameters for each lipid at
$30\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$, as well as the details of
$\phi_{h}$ which was determined from Eqn. 2 (the same details for the other
surface pressures are available in Section LABEL:sec:xrrpara of the ESI).

Table 3:  The best-fit values, and associated $95\text{\,}\mathrm{\char
37\relax}$ confidence intervals for the varying parameters in the XRR models,
at the $30\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$. The values for
$\phi_{h}$ was obtained from the appropriate use of Eqn. 2.

Lipid | DLPC | DMPC | DPPC | DMPG
---|---|---|---|---
$\sigma$/$\mathrm{\SIUnitSymbolAngstrom}$ |  |  |  |

& $3.86\pm{0.00}$ $4.90\pm{0.00}$ $4.44\pm{0.01}$
$d_{t}$/$\mathrm{\SIUnitSymbolAngstrom}$ $9.52^{+0.03}_{-0.04}$
$13.72\pm{0.01}$ $16.91\pm{0.01}$ $13.99^{+0.01}_{-0.01}$
$V_{t}$/${\mathrm{\SIUnitSymbolAngstrom}}^{3}$ $624.92\pm{3.51}$
$718.76\pm{0.52}$ $765.29^{+0.37}_{-0.38}$ $734.01\pm{0.62}$
$V_{h}$/${\mathrm{\SIUnitSymbolAngstrom}}^{3}$ $331.48\pm{0.58}$
$339.55\pm{0.28}$ $322.01\pm{0.24}$ $329.95^{+0.32}_{-0.33}$
$d_{h}$/$\mathrm{\SIUnitSymbolAngstrom}$ $10.98^{+0.13}_{-0.12}$
$13.21\pm{0.04}$ $12.69\pm{0.03}$ $13.95\pm{0.04}$ $\phi_{h}$/$\times 10^{-2}$
$54.03^{+1.04}_{-0.95}$ $50.93\pm{0.23}$ $43.94\pm{0.22}$ $54.92\pm{0.20}$

Following the initial structural determination of the monolayer by XRR, NR was
used to confirm the structure and show the applicability of the chemically-
consistent model for DPPC and DMPC. The resulting NR profiles and associated
SLD profiles, at a surface pressure of 20 mNm-1 are given in Figure 3 (the
other NR and SLD profiles can be found in Figure LABEL:fig:sineutron of the
ESI). Table III gives details of the varied parameters at each surface
pressure as well as $\phi_{h}$ as determined from NR.

Figure 3: The NR and SLD profiles at a surface pressure of 20 mNm-1 for two
contrasts, the solid line identifing the hdDES contrast and the dashed line
the hDES contrast; (a) DMPC, (b) DPPC. The NR profiles have been offset in the
$y$-axis by an order of magnitude and SLD profiles offset in the $y$-axis by
$5\text{\times}{10}^{-6}\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-2}$, for
clarity.

Table 4:  The best-fit values, and associated 95 % confidence intervals for
the varying parameters in the co-refined NR models. The values of $\phi_{h}$
were found using Eqn. 2.

& $3.31^{+0.01}_{-0.02}$ $4.27\pm{0.17}$ $3.98\pm{0.10}$
$d_{t}$/$\mathrm{\SIUnitSymbolAngstrom}$ $13.98\pm{0.15}$
$17.97^{+0.05}_{-0.01}$ $12.32\pm{0.13}$ $15.56\pm{0.10}$ $\phi_{h}$/$\times
10^{-2}$ $50.00^{+0.54}_{-0.54}$ $35.72^{+0.04}_{-0.16}$
$59.16^{+0.43}_{-0.43}$ $48.40^{+0.33}_{-0.33}$

###  III.1 Effect of compression on monolayer thickness

From Tables III and III, we can see that, as expected and as found in previous
work Mohwald (1990); Vaknin  _et al._ (1991), the thickness of the tail layer
increases as the number of carbon atoms in the tail chain increases.
Furthermore, the thickness of the tail layers in these monolayers appears to
agree well with values found for water-analogues; $13.72\pm{0.01}$ Å at 30
mN/m in DES compared with $d_{t}=15.8$ $\mathrm{\SIUnitSymbolAngstrom}$ at
$30\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$ in water for DMPC Johnson
_et al._ (1991), and $16.91\pm{0.01}$ $\mathrm{\SIUnitSymbolAngstrom}$ at
$30\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$ in DES compared with
$d_{t}=16.7$ $\mathrm{\SIUnitSymbolAngstrom}$ at
$40\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$ in water for DPPC Helm  _et
al._ (1987).

The variation of the tail layer thickness in the models with surface pressure
is given for each lipid in Figure 4(e). As is commonly observed for lipid
monolayers at the air-water interface, an increase in surface pressure results
in an increase in the thickness of the tail layer. The variation of this
parameter differs for each of the lipids. For DLPC and DMPC a gradual increase
in the thickness is observed at the surface pressures measured here. For DMPC
and DPPC however, after a gradual increase in thickness between
$15\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}25\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$,
a plateau is reached. This is indicative of the formation of a compacted
monolayer where further compression does not produce further changes in the
thickness of the tail layer. This behaviour has been seen for DMPC and DPPC
monolayers, where the formation of the condensed phases is reached at high
surface concentrations Mohwald (1990).

Figure 4: The PDFs of the head volume for each of the four lipids; (a) DLPC,
(b) DMPC, (c) DPPC, and (d) DMPG, and the variation of the tail layer
thickness (e) and volume fraction of solvent in the head layer (f); DLPC
(circles), DMPC (squares), DPPC (triangles), and DMPG (crosses), trend lines
have been added between the points to guide the eye.

###  III.2 Effect of compression on solvent concentration

In Figure 4(f), it is clear that for all four lipids, as the surface pressure
is increased there is a corresponding decrease in the percentage solvent
present in the lipid head layer. This can be rationalised by considering that
when the surface pressure is increased, the free volume available to the
solvent between the lipid head components reduces forcing the solvent out of
the lipid head layer and into the bulk. A similar effect has been observed
when increasing the surface pressure from
$11\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$ to
$31\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$ for a DMPC/DMPG monolayer
at the air-water interface Bayerl  _et al._ (1990).

###  III.3 Effect of compression on the lipid tail component volumes

It can be seen by comparing Tables 1 and III that the volumes of the lipid
tails are significantly lower in the current measurements than found
previously, by other techniques. It is unlikely that this is a result of the
DES subphase, due to the hydrophobic nature of the lipid tails. However, this
reduction has been shown previously Campbell  _et al._ (2018), where it was
rationalised by the compaction of the monolayer at elevated surface pressure.
In that work, the optimal value of the tail component volume for DPPC was
found to be $772\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{3}$ at a surface
pressure of $35$ mNm-1, this agrees well with the value of
$765.29^{+0.37}_{-0.38}$ ${\mathrm{\SIUnitSymbolAngstrom}}^{3}$ found in this
work at surface pressures of
$15202530\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$.

In this work, a single tail component volume was fitted to each lipid for all
four surface pressures that were measured. This is based on the assumption,
that at all four surface pressures, the lipids adopt the same phase and
therefore any variation in the structure with surface pressure would manifest
only as a change in the tail thickness. It is clear when comparing Tables 1
and III that some of the tail component volumes are also reduced in the
current XRR measurements compared to those determined previously. The
reduction was found to be between $8\text{\,}\mathrm{\char
37\relax}12\text{\,}\mathrm{\char 37\relax}$ for DPPC, DMPC and DLPC when
compared with literature sources at
$24\text{\,}\mathrm{\SIUnitSymbolCelsius}30\text{\,}\mathrm{\SIUnitSymbolCelsius}$,
this is in good agreement with the maximum compression percentage of
$15\text{\,}\mathrm{\char 37\relax}$ noted by Small and coworkers Small
(1984). DMPG shows a small increase in the tail volume relative to the
literature value quoted at a lower temperature. Notably, this value is similar
to that found in this work for DMPC, which has the same tail structure and
suggests that our results are at least self-consistent.

###  III.4 Solvent effect on lipid head component volumes

Figure 4 shows the PDFs determined for the head component volume for each of
the four lipids. The three lipids with the PC head component are consistent,
giving values of $\sim 330$ Å3, regardless of tail component. This agrees well
with the values found for the same head component in water, shown in Table 1.
Interestingly, the component volume for the PG head is similar to that for the
PC head with a value of $329.95^{+0.32}_{-0.33}$
${\mathrm{\SIUnitSymbolAngstrom}}^{3}$. The PG head component volume in water,
from either DMPG using differential vibrating tube densimetry Pan  _et al._
(2012) or POPG using molecular dynamics simulations Kučerka  _et al._ (2012),
is noticeably smaller. This indicates that there may be some effect arising
from the solvation in choline chloride:glycerol causing an apparent increase
in the PG component volume when compared with water. However, this has only
been shown for a single PG-lipid at the air–DES interface.

The major difference between the two head groups of the lipids is that the PG
is present as a sodium salt, whereas the PC is zwitterionic. When in solution
the anionic PG head is expected to associate with cations in solution, as it
does in water Grigoriev  _et al._ (1999) where such interactions depended on a
variety of factors including the ionic strength. In the case of a DES, the
environment is inherently ionic and therefore the interaction of an anionic
lipid head may be more complex. As well as interacting with the sodium, the
head is likely to interact with the choline cations, similar to behaviour
reported previously for surfactant micelles Sanchez-Fernandez  _et al._
(2018b). The extent of interaction with each of the cations is unclear, but
regardless it seems likely that the solvation of the PG head is improved in
the DES relative to water. This better solvation would explain the apparent
increase in the volume of the PG head since it would result in a swelling of
this group through its strong interactions with the solvent. In the case of
PC, the proximity of a local cation within the molecule results in the same
folding of the head group seen in water because this interaction is less
transient than the equivalent interactions with the solvent.

###  III.5 Refinement of neutron reflectometry

The ability to fit the NR data, as shown in Figure 3 indicates that the value
found for the head component volume is consistent between the pair of
measurements for the same system. It is clear, that again stable monolayers of
the lipids are forming at the air-DES interface, and that the component
volumes determined from XRR measurements are robust enough to be used in the
modelling of NR data. Furthermore, the trends observed with increasing surface
pressure in the XRR models, pertaining to the increasing tail thickness and
decreasing solvent concentration in the head components are consistent with
that found in the NR models.

###  III.6 Interparameter correlations

The use of Bayesian inference and MCMC sampling allowed for the probing of the
probability distribution function for each parameter individually. However, it
also enables the pairwise inter-parameter PDFs to be investigated, an example
for DMPC at $30\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$ is shown in
Figure 5 (similar plots for the other XRR datasets and the NR datasets are
available in Figures LABEL:fig:dlpc1 \- LABEL:fig:dppcn2 of the ESI). These
two-dimensional PDFs give important information about the correlations that
are present between the parameters of the chemically-consistent model. The
less circular in nature that the 2D PDF is, the greater the correlation that
is present between the parameters, e.g. a north-east/south-westerly skewed PDF
indicates a positive correlation (where an increase in one parameter
correlates an increase in the other) while a north-west/south-easterly skewed
PDF indicates a negative correlation (an increase in one correlates with a
decrease in the other).

Figure 5: The multi-parameter PDFs for the chemically-consistent model of DMPC
XRR data at $30\text{\,}\mathrm{mN}\text{\,}{\mathrm{m}}^{-1}$.

Substantial correlations are present in the parameters fitted to the XRR
datasets, indicating important uncertainty that must be considered. In
particular, as can be seen in Figure 5, there is a positive correlation
between the lipid head thickness, $d_{h}$, and the solvent concentration in
the head layer, $\phi_{h}$. This correlation can be rationalised as a result
of the SLD of the solvent and the head layer (which is $\sim
50\text{\,}\mathrm{\char 37\relax}$ solvated) being similar, and therefore the
boundary between the two is not easy to define. Such correlations are
unavoidable without considering many neutron contrasts of the lipid and
solvent, due to the solvophilic nature of the lipid heads. Another important
correlation is that between the head thickness and the tail thickness,
$d_{t}$, again this is due to the lack of a well-defined boundary between the
head and tail layers. This is partially driven by the interfacial roughness
that is present between the layers, with the correlation being more pronounced
for phospholipids with shorter tails (e.g. there is a greater correlation for
DLPC than DPPC).

##  IV Conclusions

For the first time, stable phosphocholine and phosphatidylglycerol lipid
monolayers have been observed and characterised on an ionic solvent surface.
Until the emergence of ionic liquids and DES, only a limited number of
molecular solvents exhibited the ability to promote self-assembly and, to the
best of our knowledge, only water and formamide among those had demonstrated
the formation of phospholipid monolayers at the air-liquid interface.

A physically and chemically constrained modelling approach and Bayesian
analysis method was used to rationalise these measurements showing that the
structures are remarkably similar at the air-DES interface to those previously
observed at the air-water interface. This has the important implication that
DES, therefore, offer the possibility of performing studies of model membranes
in the absence of water. Such applications may include fundamental
investigations of phospholipid monolayers in extreme environments (total or
partial absence of water, cryogenic temperatures), protein-membrane
interactions and development of new technologies for drug delivery. However,
the PG component did show a significant difference; having a larger head
component volume than observed for the same system in water. This suggests
that the transfer of lipids to a DES is not just a simple substitution of the
subphase. In this specific case, we have proposed an explanation based on the
dissociation of the PG head component salt and the subsequent interaction with
the DES. Finally, the use of MCMC sampling of the reflectometry model
parameter space gives insight into the correlations present in XRR data
modelling, that should be considered in work of this nature.

The ability to determine the head component volume was facilitated by access
to easy to use, open-source software that allowed for the straightforward use
of a custom, chemically-consistent model within the analysis of the XRR and NR
measurements. Furthermore, to our knowledge, this work presents the first use
of a chemically-consistent parameterisation to co-refine XRR measurements at
different surface concentrations.

##  V Author Contributions

T.A., A.J.J., A.S.-F. and K.J.E. were involved in the experimental design and
conducted the experiments along with R.A.C..

A.R.M. developed the chemically-consistent model and analysed the data, with
input from S.C.P, A.S.-F., T.A., and R.A.C..

A.R.M., A.S.-F. and T.A. wrote the manuscript, with input from all authors.

###### Acknowledgements.

The authors thank Andrew Nelson for useful discussions & assistance with the
refnx software. Additionally, we thank Oliver Hammond for insightful
discussions regarding the effect of the DES. A.R.M. is grateful to the
University of Bath and Diamond Light Source for co-funding a studentship
(Studentship Number STU0149). Thanks also to the European Spallation Source
and the University of Bath Alumni Fund for supporting A.S.-F. We also thank
Diamond Light Source (Experiment number SI10546-1) and Institut Laue-Langevin
(DOI: 10.5291/ILL-DATA.9-13-612) for the awarded beamtime.

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