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Cite this: Phys. Chem. Chem. Phys.,
2019, 21, 800

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Influence of glycerol on the cooling eﬀect of pairhydrophobicity in water: relevance to proteins’stabilization at low temperature†
Vikas Dubey

and Snehasis Daschakraborty*

Glycerol, as a cosolvent of water, stabilizes proteins under extreme conditions (both at high and low
temperatures). However, the mechanism of stabilization of proteins by glycerol at low temperature is
still elusive. Because the decrease of hydrophobic interactions at a lower temperature is one of the
crucial factors for the cold denaturation, we ask here whether glycerol protects the hydrophobic
interactions upon cooling and thereby acts against cold denaturation. Here, we have performed
potential of mean force (PMF) calculations, using the umbrella sampling technique, between a pair ofmethane hydrophobic solute molecules either in pure water or in binary mixtures of water and glycerol
for two diﬀerent compositions and each of them at four diﬀerent temperatures. We have found thatglycerol increases the pair hydrophobic interaction at all the temperatures studied and that theenhancement is more prominent at the lower temperatures studied here. Decomposition of the PMF
into the enthalpic and the entropic components and detailed molecular structural analyses give insight
Received 18th October 2018,
Accepted 4th December 2018

into the above observation. We have found that the enhancement of the hydrophobic interaction withincreasing glycerol concentration occurs primarily due to the strengthening of the glycerol–water inter-

DOI: 10.1039/c8cp06513f

action near the associated methane solute molecule pair and the tetrahedral ordering of the H-bonding
network being made uniform around the solute by the added glycerol molecules. These results indirectly

rsc.li/pccp

justify the efficacy of glycerol for the preservation of proteins against cold denaturation at low temperature.

1. Introduction
Glycerol is a versatile solvent having many biological andindustrial applications when mixed with water. It has eﬃcacy
in protecting living cells and tissues by preventing freezing of both
intracellular and extracellular fluid at subzero temperatures.1–5
Apart from the above colligative anti-freezing property of glycerol,
it can also act as an osmolyte to reduce the loss of cellular water.5–7
Strong hydrogen (H-) bonding between glycerol and water is
responsible for the water retention and cryoprotection activities ofglycerol.8–15 Apart from the above properties, glycerol stabilizes
Department of Chemistry, Indian Institute of Technology Patna, Bihar 801106,
India. E-mail: snehasis@iitp.ac.in† Electronic supplementary information (ESI) available: (1) Weighed histogram
showing the suﬃciency of sampling windows, (2) figures showing the convergenceof the PMF, (3) alternate way of presenting PMF curves, (4) decomposition ofentropy and enthalpy components of the PMF for T = 280 K and 300 K, (5) solvent
contribution towards the PMF for T = 280 K and 300 K, (6) table showing data offree energy, entropy and enthalpy at diﬀerent minima of the PMF, (7) the RDF
between methane solute C and solvent water OW in pure water at four diﬀerent
temperatures, (8) the RDF between the methane solute and solvent molecules at
T = 280 K and 300 K, and (9) the number of H-bonds per solvent water molecule as
a function of methane–methane separation for pure water at three different
temperatures. See DOI: 10.1039/c8cp06513f

800 | Phys. Chem. Chem. Phys., 2019, 21, 800--812

proteins under extreme conditions, like heat stress, cold shock,high pressure, etc.16–26 It has been observed that glycerol and someother protein stabilizers—e.g. trehalose, sucrose etc.—increase
the thermal denaturation temperature and decrease the cold
denaturation temperature of proteins.21 Also, the effect of protein
stabilizers on cold denaturation temperatures is much more
intense than the effect on thermal denaturation temperatures.21
Extensive theoretical and computer simulation studies havesignificantly contributed to the understanding of the generalmechanism of protein stabilization by glycerol (and some othersugar molecules) at ambient and higher temperatures.19,27–30
Macroscopic thermodynamic calculations indicated that glycerol
stabilizes the protein by increasing the free energy of the denatured
state more than the free energy of the native state and thereby
increases the free energy difference between the two states.19,28 This
happens due to an unequal preferential exclusion of the cosolvent
from the surface of the protein in native and denatured states due toa significant change of the surface area. This thermodynamic
justification has been indirectly evidenced in molecular theory
and simulation.27,29,30
Despite extensive studies on the stabilization mechanism ofproteins by glycerol at higher temperatures, much less attention
has been paid so far to the mechanism of protein stabilization

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by glycerol against cold denaturation. Recent times have witnessed
an intense debate on the possible explanation for the observed
cold denaturation of proteins. While thermal denaturation ismuch more straightforward, the origin of cold denaturation is still
elusive. Denaturation of proteins at high temperature is generally
explained in the following two ways.31–39 (1) A large kinetic energy
value of the system at high temperature leads to a large fluctuationof the tertiary structure of the protein. (2) The thermal denaturation
can also be explained from a thermodynamic perspective. For thefolded (F) - unfolded (U) transformation of proteins, one canwrite the standard Gibbs free energy for the transformation as
DGF-U = DHF-U  TDSF-U. Here, DGF-U, DHF-U, and DSF-U
are the changes of the Gibbs free energy, the enthalpy, and theentropy for the F - U transformation. T is the temperature. It is
generally observed that both DHF-U and DSF-U are positive
during thermal denaturation occurrence. Therefore DGF-U
decreases with increasing temperature. This makes the denaturation process more and more thermodynamically favorable.
Above a certain temperature, when the entropy component
dominates over the enthalpy component, DGF-U becomes
negative. Therefore, above that temperature protein unfolding
becomes spontaneous and thus the protein denatures.
Unlike thermal denaturation, the origin of cold denaturationof proteins is not fully understood. Following are some views
existing in the literature. (1) The majority of experimental andcomputer simulation studies have suggested that the reductionof the hydrophobic interactions, which hold the tertiary structureof the protein together, due to lowering of temperature is thedriving force for cold denaturation.40–57 (2) Some other simulation
studies suggested that the increasing interaction between thehydrophilic residues of the protein and water with decreasing
temperature is mainly responsible for unfolding the tertiary
structure of the protein.58,59 (3) A Monte Carlo simulation study
found strong evidence that increasing water  water H-bondingat the protein interface with lowering temperature is a necessary
and sufficient condition for the protein’s cold denaturation.60
The above explanations for cold denaturation of proteins set
the stage for exploring the possible roles of glycerol in preserving
proteins’ structure and functionality at low temperature on afundamental level. It is possible that glycerol eﬀectively reduces
the impact of the above three factors of cold denaturation andthereby preserves the structure and function of a protein at low
temperature. In a recent paper, one of us has focused on how
glycerol and DMSO disrupt the H-bonding and tetrahedral
structure of solvent water around a model hydrophobic soluteat subzero temperatures.11 The above study implicitly addressedthat the similar disruption of the hydration structure near aprotein’s hydrophobic core by glycerol or DMSO could eﬀectively
assist in preserving the protein’s structure at low temperature.
In the present work, our primary goal is to see how glycerol
influences the pair hydrophobicity of two simple nonpolar
solute molecules in water and whether the hydrophobic interaction is somewhat retained against the observed reduction at alower temperature.53 This is motivated by earlier observations
that the reduction of the hydrophobic interactions in water at alower temperature is the key factor for cold denaturation if

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glycerol were capable of stabilizing the hydrophobic moiety at alower temperature. A number of studies have already focusedon how diﬀerent protein stabilizers aﬀect the pair hydrophobic
interaction between two nonpolar solute molecules in water atambient or higher temperatures.61–72 It was observed that withincreasing concentration of trehalose—a well-known protein
stabilizer—in water the dispersion of neopentane hydrophobic
solute molecules increases.61,62 It was argued that trehalosedecreases the neopentane–neopentane association constant value
by reducing the hydrophobic interaction between them.61,62 A
separate study, addressing the effect of trimethylamine N-oxide(TMAO) on pair hydrophobicity, did not see any role of TMAO.64
The above inert behavior of TMAO towards hydrophobicity wasthought to be the reason why TMAO is a good osmolyte. However,it has been recently found that upon addition of TMAO to water
the large favorable entropic contribution and the unfavorable
enthalpy, which are characteristic of hydrophobic interactions,decrease.63 These changes account for the strengthening of hydrophobic interactions when a particular force field model of TMAO is
considered. A molecular dynamics (MD) simulation study,70
addressing the effect of dimethyl sulphoxide (DMSO) concentration on pair hydrophobicity, observed the following.
The pair hydrophobic interaction between two nonpolar solute
molecules—measured by the depth of the first free energy
minimum—increases with increasing DMSO concentration inwater in the lower DMSO concentration regime.70 Similar
enhancement of pair hydrophobicity has recently been reportedwith increasing ethanol concentration in water up to a mole
fraction of 0.10.71 It has also been found, in a separate
theoretical study, that the direct interaction between cosolvent
molecules and nonpolar solute molecules can strengthenhydrophobic interactions and can contribute to stabilizing
collapsed globular structures.67 In addition to the importanceof the above work in understanding the fundamental role ofdifferent protein stabilizing agents in influencing hydrophobic
interactions in water, these studies connect their findings withthe stability issues of proteins in the presence of the above
additives.
The above studies have significantly contributed to theunderstanding of how a cosolvent does aﬀect the pair hydrophobic
interaction in water either at ambient or at higher temperatures.
Unfortunately, the eﬀect of those substances on pair hydrophobic
interactions at lower temperatures is not much explored, despite
its huge application in understanding the action of diﬀerent
protein stabilizers against cold denaturation at low temperature.
Retention of hydrophobic interactions at low temperature caneﬀectively prevent cold denaturation of the protein. Therefore,
we study here the eﬀect of glycerol on the pair hydrophobic
interaction between two methane molecules (a small hydrophobic
solute) for a wide range of temperatures. We have calculated the
PMF between a pair of methane hydrophobic solute molecules
using the umbrella-sampling method in all-atom MD simulations
at diﬀerent temperatures and compositions of the binary solvent
mixture of water and glycerol.
The outline for the remainder of this paper is as follows. The
molecular models and other simulation details are detailed

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in Section 2. Section 3 presents the simulation results anddiscussion. Concluding remarks are oﬀered in Section 4.

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2. Method
2.1

Simulation details

All simulations are performed using the GROMACS package.73
Our simulation box contains a pair of methane molecules
dissolved in 2000 solvent molecules. The solvent is either purewater or binary mixtures of glycerol and water with mole fractionsof glycerol xG = 0.05 or 0.1. For each of the three compositions, wehave considered four diﬀerent temperatures, T = 260 K, 280 K,
300 K, and 320 K. Due to the fact that the freezing point of the
TIP4P/2005 water model (the force field model we have used in
the present work) is 252 K at atmospheric pressure, we have notchosen a temperature below 260 K. In addition, on further
lowering of the temperature below 260 K, the glycerol/water
mixture (even at xG = 0.1) becomes highly viscous and the
dynamics become much slower. Therefore, the PMF results are
expected to be erroneous and hence inconclusive. The rationaleof choosing the highest mole fraction of glycerol as 0.1 (equivalent
to a 0.36 weight fraction or 4.45 M concentration of glycerol) is asfollows. This binary mixture composition has suﬃcient cryoprotecting ability as the freezing point of the mixture decreases
by 20 degrees.74 Also, this composition of the glycerol/water
mixture was already seen to have eﬃcacy in thermal stabilizationof proteins.21,27–30 It is worth mentioning that a past experimentobserved that the cold denaturation temperature of a protein canbe decreased by 35 degrees at sucrose concentrations (anotherpolyol having strong protein stabilizing activity) as low as 0.9 M.21
All-atom modeling of a glycerol molecule is done by force
field parameters that were developed and modified by Chelli
et al.75 and Blieck et al.,76 respectively. Water molecules aremodeled by the TIP4P/2005 force field,77 the most eﬃcientmodel of water at all temperatures including the deeply supercooled region. (More popular models of water, like SPC/E etc.,
are not appropriate as these models do not provide a goodprediction of various microscopic and thermodynamic properties
specifically at subzero temperatures.) The above combination of
the force field models of water and glycerol has proven eﬃcacy inreproducing various thermodynamic, microscopic structural anddynamical properties for a wide range of temperatures including
sub-zero.78 Methane is modeled using OPLS/AA force fieldparameters.79
The equation of motion is solved every 2 fs using the leap-frog
algorithm. Long-range electrostatic interactions are handled by theparticle mesh Ewald summation technique. We first equilibrate
the system for a 50 ns simulation time using the isobaric–
isothermal (NPT) ensemble. The Nośe–Hoover thermostat80,81 isused for maintaining the system at a constant temperature. The
pressure is kept constant by the use of the Parrinello–Rahman
barostat.82 A coupling time of 0.5 ps is set for both the thermostat
and the barostat.
The PMF has been calculated using the umbrella sampling
method.83 We vary the separation between the pair of methane

802 | Phys. Chem. Chem. Phys., 2019, 21, 800--812

Papersolute molecules from 0.3 nm to 1.3 nm with a gap of 0.1 nm,
resulting in a total of 11 diﬀerent simulation systems for aparticular temperature and composition of the glycerol/water
mixture. This aggregates to a total of 132 simulation systems withvarying temperature and composition of the solvent mixture. For
each of the systems, we obtain the initial configuration with thedesired distance between the two methane solute molecules
using the pull code in GROMACS. Such a small interval is chosen
to ensure suﬃcient overlap between two neighboring windows.
Fig. S1 of the ESI† presents a representative figure, which shows
the overlap between the neighboring windows. Long simulations
are performed starting from the above initial configurations withthe distance between the methane molecules restrained by aharmonic potential with a force constant of 1000 kJ mol1 nm2.
Each configuration is simulated for a long time (50 ns for purewater and 100 ns for the two binary mixtures having xG = 0.05
and 0.1) to get suﬃcient sample points. This aggregates to a
total of 11.6 ms simulation time. The first 5 ns is not considered
for calculating the PMF. The weighed histogram analysis method(WHAM)84 at each window has been used to obtain the PMF as
a function of the separation between the two methane solute
molecules.
We have shown the convergence of the PMF for xG = 0.1 at
T = 260 K in Fig. S2 and S3 of the ESI.† Fig. S2 (ESI†) plots PMFs,
which are calculated from trajectories of increasing length. We
clearly see the convergence for trajectories having a duration of
more than 50 ns. We have also plotted, in Fig. S3 of the ESI,†
the PMF arising from the first 50 ns of the trajectory comparedwith the PMF obtained from the last 50 ns of the trajectory. The
convergence is absolutely clear in the above figures.
We decompose the PMF into enthalpic H(r) and entropic
terms S(r) using the finite diﬀerence (FD) method.53,71,85–88 In
this method, the entropy of association is obtained from thetemperature derivative of the PMF at each separation (r)between the two methane solute molecules.
SðrÞ ¼

Gðr; T þ DT Þ  Gðr; T Þ
DT(1)

The FD method is a widely used technique for obtaining theentropy contribution of the PMF with respect to temperature. It
was found that the FD approach performs similar to or better
than other alternative methods, like thermodynamic integration,
free energy perturbation, etc.89–91 Despite the great performanceof the FD approach there are limitations too. In order to ensurea statistically meaningful estimation of entropy, due to large
fluctuations in the complex systems one requires a large temperature gap (DT) between simulation systems under the assumption of
constant heat capacity. Although the assumption is generally good,
the FD approximation breaks down if DT is too large. Usually, DT ischosen as 20 K. In order to increase the accuracy, a large samplingof data is generally desirable. In this work, we have done enoughsampling in terms of the length of the individual trajectories. Our
trajectory lengths have a maximum of up to 100 ns, which is much
longer than generally collected. Good convergence of the PMF
plots, shown in Fig. S2 and S3 of the ESI,† is direct proof of theabove claim.

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In the present study, we chose DT to be 20 K. The enthalpy
contribution to the free energy H(r) at temperature T is estimated by
the following equation,

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H(r) = G(r) + TS(r).

(2)

The solvent contribution, Wsolv(r), to the PMF is calculated
by subtracting the solute–solute interaction energy Usol–sol(r) fromthe total PMF values at different r using the following equation
Wsolv(r) = G(r)  Usol–sol(r).

(3)

Wsolv(r) can be decomposed into the entropic Ssolv(r) and theenthalpic Hsolv(r) terms. While Ssolv(r) is actually identical to thetotal entropy,92
Ssolv(r) = S(r),(4)

the enthalpy from the solvent contribution, Hsolv(r), is calculated
by subtracting the solute–solute interaction in a vacuum, Usol–sol(r),from the total enthalpy of association, H(r), using the following
equation:
Hsolv(r) = H(r)  Usol–sol(r).

(5)

Hsolv(r) is further decomposed into two components: one is dueto the solute–solvent interaction Hsol–solv(r) and the remaining
part, Hrem(r), captures the change in solvent–solvent interactions as well as the mechanical pressure–volume (PDV) work.
Hsol–solv(r) is calculated directly from simulation, while Hrem(r)is obtained by subtracting Hsol–solv(r) from Hsolv(r)Hrem(r) = Hsolv(r)  Hsol–solv(r).

(6)

3. Results and discussion
3.1 Eﬀect of glycerol on the hydrophobic interaction at
diﬀerent temperatures
First, we see how glycerol influences the pair hydrophobic interaction between two methane solute molecules at the diﬀerent
temperatures considered here. We plot, in Fig. 1, the PMFs between
the pair of methane molecules either in pure water or in theglycerol/water binary mixture, varying the composition (xG = 0.05,
and 0.10) and temperature (T = 320 K, 300 K, 280 K, and 260 K) of
the system. The following is the procedure by which we put the
PMFs on one another in order to do comparative analysis. First, we
obtain the PMF using the WHAM analysis technique. Then, we set
the PMF to zero at r = 1.3 nm. We correct the entropic contribution
to the PMF due to rotation of the solute molecules by adding theterm 2kBT ln(r) to the PMF. The uncertainty in the PMF wascomputed by bootstrap analysis. An alternative presentation of the
PMF has also been shown in Fig. S4 of the ESI.†
Now we go back to the analysis of Fig. 1. Each PMF shows
three minima. The first one, situated at methane–methane
separation r B 0.4 nm, is the contact minimum (CM). The
second and the third minima occur approximately at r B 0.7 nm
and B1 nm separations, respectively. The second minimum isthe first solvent separated minimum (FSSM)53,71,93–97 as only
one solvent water layer can fit at this methane–methane separation.

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Fig. 1 PMF as a function of the distance between the pair of methane
molecules, dissolved either in pure water or in the glycerol/water binary
mixture, varying the composition (xG = 0.05, and 0.10), each at 4 diﬀerent
temperatures (T = 320 K, 300 K, 280 K, and 260 K).

Similarly, two water solvent layers can comfortably fit inside anr B 1 nm separation between the two methane molecules.
Therefore, the third minimum at r B 1 nm is also called thesecond solvent separated minimum (SSSM).53,71,93–97 Table S1 of
the ESI† lists the depths of the above three minima for systems
with differing temperature and solvent composition.
It is clear from Fig. 1a and Table S1 of the ESI† that for purewater at a 300 K temperature the depth of the CM and the
FSSM are B2.4 kJ mol1 and B0.5 kJ mol1 respectively.

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At r B 0.54 nm—in between the CM and FSSM—there exists thedesolvation barrier with a height of B3.2 kJ mol1. The SSSM israther a very shallow well with a depth of only B0.2 kJ mol1.
The SSSM is separated from the FSSM by the second barrier,occurring at r B 0.85 nm, with a height of B0.9 kJ mol1. All
the above numerical values are in good agreement with earlier
studies.53,93–97 Now, as we decrease the temperature of thesystem from 320 K to 260 K, the well-depth of the CM reducesfrom B3.0 kJ mol1 to B1.6 kJ mol1. The desolvation barrierheight also decreases from B4 kJ mol1 to B2.2 kJ mol1. This
indicates a significant reduction of the pair hydrophobicity ofmethane in water with decreasing the temperature. This isconsistent with an earlier temperature dependence study.53
However, very subtle changes are noticed in the depths of the
FSSM and SSSM, and the height of the second free energy
barrier. Similar changes in the depth of the CM and the heightof the barrier are observed for the methane–methane PMF in abinary mixture of glycerol and water with glycerol’s mole fraction
xG = 0.05. Interestingly, for xG = 0.10, the CM well depth is muchless sensitive towards the temperature.
The eﬀect of glycerol concentration on the depth of the CM
and the height of the desolvation barrier at all the four
temperatures is shown in Fig. 2. It is evident from Fig. 2a thatthe depth of the CM decreases almost linearly with decreasing
the temperature for pure water and for the glycerol/water binary
mixture for xG = 0.05. However, for xG = 0.10, the depth of thePaper

CM does not change appreciably below 280 K. With increasing
glycerol concentration in the mixture, the depth of the CM
increases at all the temperatures studied here. The increase ismuch more prominent at lower temperatures than at the higher
ones. For instance, while the depth of the CM increases fromB3 kJ mol1 (pure water) to B3.5 kJ mol1 upon increasingxG from 0.0 to 0.1 at T = 320 K, the same increase of glycerol
concentration increases the depth of the CM from B1.6 kJ mol1 to
B2.8 kJ mol1 at T = 260 K. This indicates that glycerol is eﬀective
for increasing the pair hydrophobicity between the pair of methane
molecules at all temperatures and that the eﬃciency significantly
increases at lower temperatures. This might be a molecular level
explanation for the experimental observation that glycerol prevents
cold denaturation more strongly than thermal denaturation ofproteins.21 In addition, it is evident from Fig. 2b that glycerol
increases the desolvation barrier height at all the temperatures
almost uniformly. In addition, Table S1 (ESI†) clearly shows that thefree energy diﬀerence between the CM and the FSSM increases withincreasing the glycerol concentration in the medium. This further
supports the fact that dissociation of two small hydrophobic solute
molecules becomes unfavorable as the glycerol concentration
increases in the medium. This gives a clear signature about thestrong eﬃcacy of glycerol in retaining the pair hydrophobic interaction between two hydrophobic molecules in water. From theabove observation, one can conjecture a fundamental mechanismof protein stabilization by glycerol at low temperature by retaining
the hydrophobic core of proteins in supercooled water. The above
results also corroborate with the fact that glycerol is a kosmotropeand therefore increases the hydrophobic interaction between two
nonpolar solute molecules in liquid water.98
3.2

Fig. 2 Temperature dependence of (a) CM well depths and (b) the
desolvation barrier height for three diﬀerent solvent compositions.

804 | Phys. Chem. Chem. Phys., 2019, 21, 800--812

Decomposition of the PMF into enthalpy and entropy

In order to comprehend the above results on a more fundamental
level, we decompose the PMFs into the entropy (TS) and theenthalpy (H) contributions using eqn (1) and (2) respectively. In
the present study, we choose DT = 20 K in eqn (1) and hence thedecomposition of the PMF can be done only at three temperatures,
260 K, 280 K, and 300 K.
Fig. 3 plots the PMF and two components (H and TS) as
functions of methane–methane separation r for three different
solvent compositions at a 260 K temperature. The above resultsfor 280 K and 300 K temperatures are presented in Fig. S5 andS6 of the ESI† respectively. Table S1 of the ESI† lists thenumerical values of H and TS at the separations of the threeminima of the PMF. At the CM separation, TS is negative but
H is positive at all the temperatures for pure water. Therefore,
the hydrophobic association of the two methane solute molecules,
to form the contact pair, is entropically favorable but enthalpicallyunfavorable. On the other hand, TS is positive but H is negative
both at the FSSM and the SSSM separations. Therefore, boththe above minima of the PMF are enthalpically favorable
but entropically unfavorable. This is consistent with earlier
studies.53,63,71,85–88,92,93
Now, as glycerol is added to water, both the entropy andenthalpy decrease at the CM separation. A similar observation
was reported in recent work on hydrophobicity between two

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Fig. 3 PMF between the pair of methane solute molecules and its twocomponents, entropy (TS) and enthalpy (H), in (a) pure water, and water/
glycerol mixtures with (b) xG = 0.05, and (c) xG = 0.1 at a 260 K temperature.

neopentane molecules in a TMAO/water binary solvent mixture.72
While TS becomes less negative, the positive value of H
decreases. For xG = 0.1, both TS and H become negative at
the CM for T = 280 K and 260 K temperatures. Therefore, theCM of the PMF is favored both by the enthalpic and theentropic contributions. The above analysis implies that theobserved enhancement of the pair hydrophobic interaction,
particularly at the lower temperature, is due to the decrease ofenthalpy with the increase of glycerol concentration. Fig. 3 andTable S1 (ESI†) clearly show that at a 300 K temperature, theaddition of glycerol to water decreases the enthalpy of the CM
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ESI,† the above changes are much more prominent for the
lower temperatures. In addition, the decrease of H is slightly
more than that of  TS. These uneven changes of the enthalpic
and the entropic components result in the overall increase of
the CM well depth with increasing glycerol concentration.
To elucidate further, we calculate the solvent contribution to
the PMF, Wsolv, and decompose the same into the enthalpic(Hsolv) and the entropic (TSsolv) contributions using eqn (3)–(5).
They are presented in Fig. 4 for T = 260 K and in Fig. S7 and S8 of
the ESI† for T = 280 K and 300 K respectively. As expected, Wsolv
is also negative both at the CM and the FSSM separation at
all conditions. At the CM, Wsolv decreases with decreasing
temperature. This is due to the decrease of both the entropicTSsolv and the enthalpic Hsolv components at the CM. Hsolv has
contributions from methane solute–solvent (Hsol–solv) andsolvent–solvent interaction potentials and pressure–volume
work (PDV). We calculated Hsol–solv (directly from simulation)
as a function of r. We set Hsol–solv = 0 at an r = 1.3 nm separationand then subtract Hsol–solv from Hsolv to get the remaining
enthalpy contribution, Hrem.
Hsolv and its two components Hsol–solv and Hrem are plotted
as functions of r in Fig. 4d for T = 260 K. In all the situations,Hsol–solv is positive at the CM separation and decreases steadily
with r. This indicates that the methane–methane contact pairformation is disfavored by Hsol–solv. Hrem, which has contributions
from the solvent–solvent interaction and PDV work, makes a morethan 60% contribution to Hsolv at the CM for pure water. Hrem
decreases with decreasing the temperature. This could be becauseof the strengthening of the water solvent–solvent interaction near
the hydrophobic solute.11,99–108
Now, we discuss the eﬀect of glycerol on the above components.
Fig. 4 presents Wsolv, Hsolv, TS, Hsol–solv, and Hrem as functionsof r for different solvent compositions for a 260 K temperature.
(See Fig. S7 and S8 of the ESI† for the results at the two othertemperatures.) Similar to the PMF, Wsolv also increases withincreasing glycerol concentration at the CM at all the temperatures
studied here. The decomposition of Wsolv into the enthalpic andthe entropic terms clearly shows that the decrease of Wsolv at the
CM separation arises from the decrease of Hsolv, which is again
caused by the drop of Hrem for higher glycerol concentration.
We will see in the next subsection that the above decrease of
Hrem is a direct consequence of the local solvent structure
augmentation around the hydrophobic solute in presence ofthe glycerol cosolvent in water.
3.3

Analysis of the solvent structure around the solute

In this section, we discuss how glycerol influences the solvation
structure around the methane hydrophobic solute and thereby
explain the observations of the preceding sections from a more
fundamental perspective.
Tetrahedral order parameter. We calculate the tetrahedral
order parameter q for the solvent molecules separately at theinterface and in the bulk using the following equation:109,110

3 X
4 
3X
1 2
q¼1
cos yjk þ(7)
8 j¼1 k¼jþ1
3

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Fig. 4 Solvent contribution of the PMF, Wsolv, and its two components (entropy (TS) and enthalpy (Hsolv)) as functions of methane–methane separationr in solvent with three different compositions: (a) xG = 0.0, (b) xG = 0.05, and (c) xG = 0.1 at a T = 280 K temperature. Hsolv and its two components,
Hsol–solv and Hrem, at various r values for (d) xG = 0.0 (e) xG = 0.05, and (f) xG = 0.1 at a 260 K temperature.

Fig. 5 exhibits the distributions of q (p(q)) for three diﬀerent
solvent systems, each at three diﬀerent temperatures, 300 K,
280 K, and 260 K. q has been calculated for the solvent
molecules (both water and glycerol) around a central watermolecule, which is either at the interface or in the bulk region.
Note that the interface (up to r B 5.5 Å) and the bulk (outside
the distance r B 11 Å) are identified by the radial distributionfunction (RDF) between the methane solute and solvent water,presented in Fig. S9 of the ESI.† Fig. 5 clearly shows thatp(q) has a maximum at q B 0.83 and a shoulder at q B 0.50 under
all conditions. While the peak at q B 0.83 corresponds to an almost
perfect tetrahedral structure, the shoulder at q B 0.50 corresponds
to the trigonal pyramidal geometry of water molecules with missing
water from one vertex of the tetrahedron.11
A closer inspection of Fig. 5 further reveals that p(q) forinterfacial water molecules has a slightly more intense peak at

806 | Phys. Chem. Chem. Phys., 2019, 21, 800--812

q B 0.83 than that for the bulk water molecules. This is
prominent for the pure water case. Therefore, the interfacial
water molecules are more tetrahedrally ordered than the bulk
ones at all the temperatures studied for xG = 0.0. This ispopularly known as hydrophobic iceberg formation of water
adjacent to an hydrophobe.99–108 So, when two hydrophobic
solute molecules approach towards each other to form a contact
pair, some water molecules are released from the interface dueto the excluded volume effect. Now, as we add glycerol to water,
both the interfacial and the bulk solvent become less tetrahedral. This is common for all the temperatures studied. This
indicates that the added glycerol molecules decrease the tetrahedral order of water both at the hydrophobic solute interface
and in the bulk. A closer view of Fig. 5 further reveals that p(q)for the interfacial water closely resembles that of the bulk waterat a 0.1 mole fraction of glycerol. This suggests that glycerolThis journal is © the Owner Societies 2019

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compositions. (The pictures for the other two temperatures arepresented in Fig. S10 and S11 of the ESI†) Fig. 6a clearly showsthat for pure water the first peak intensity decreases as thesolute pair molecules approach closer to each other. This
reduction of the first peak intensity of the RDF confirms the
exclusion of some solvent water molecules from the interface
because of the reduced volume of the interfacial layer. The
above exclusion of water molecules from the interface—due tothe hydrophobic association of the two methane solute molecules—results in an overall loss of H-bond strength. (The Hbond number per solvent water molecule is plotted, in Fig. S12of the ESI,† as a function of distance from the solute.) Therefore, the hydrophobic association leads to an increase of theenthalpy of the system and the association becomes anenthalpy-disfavored process. Therefore, the exclusion of theinterfacial water molecules due to the association of the hydrophobes actually results in an increase of enthalpy.
Fig. 6b and c suggest that the decrease of the first peakintensity of the methane–water RDF, as discussed in the above
paragraph, is almost insensitive to the glycerol concentration.
However, the RDF between methane and glycerol molecules issomething interesting. Here, the first peak intensity increases
slightly as two methane solute molecules form a contact pairstarting from the dissociated state. This suggests that the
reduction of the interfacial solvation shell width (due to theassociation of the solute pair) does not affect the coordination
number of glycerol molecules around the methane solute.
Therefore, the hydrophobic association process triggers theinclusion of glycerol molecules from the bulk. This can be
explained using the preferential interaction of glycerol with themethane solute via the hydrophobic interaction between
them.11 The inclusion of glycerol molecules in the interfacial
layer, when two methane solute molecules aggregate together
to form a contact pair, must increase the glycerol–glycerol andglycerol–water interactions and thereby decreases the enthalpy
at the CM.

Fig. 5 Glycerol concentration depenedence of the distribution of tetrahedral order parameter q for interfacial (solid line) and bulk (dashed line)
solvent with diﬀerent compositions: xG = 0.0 (black), xG = 0.05 (red), and
xG= 0.10 (blue) at three temperatures (a) T = 300 K, (b) T = 280 K, (c) T = 260 K.
The ratio of averaged q between the interfacial and the bulk solvent, hqIi/hqBi, ateach temperatures is shown in the inset as a function of xG.

symmetrizes the tetrahedral ordering of the solvent across spacearound the hydrophobic solute and that directly impacts theincreasing entropy for contact pair formation. The water molecules, released from the interface, do not increase the overall
entropy of the system. This explains the decreasing value of  TS
at the CM with increasing glycerol concentration.
Radial distribution function. Now, we turn our focus toexplaining the reason for decreasing enthalpy H at the CM withincreasing glycerol concentration. Fig. 6 shows the RDF
between the methane solute and solvent molecules at T =260 K as a representative temperature for three diﬀerent solvent

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4. Conclusion
Here, we have systematically studied the eﬀect of glycerol onpair hydrophobicity in water at diﬀerent temperatures ranging
from 320 K to 260 K using the umbrella sampling technique inall-atom MD simulations. The PMF has been calculated at
diﬀerent separations of the methane solute pair. Addition ofglycerol to water increases the well-depth of the CM of the PMF
between the pair of methane solute molecules at all thetemperatures studied. The desolvation barrier between the
CM and FSSM also increases with glycerol’s concentration.
The above action of glycerol is more prominent at a lower
temperature than that at the higher ones. This shows thatglycerol has greater eﬃcacy in preserving the hydrophobic
interaction at a lower temperature, which otherwise decreases
with decreasing temperature of the medium. This result has animportant implication in understanding the mechanism ofstabilization of proteins at low temperature by preventing cold

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Fig. 6 Radial distribution functions between the methane solute (C atom) and the solvent molecules (water’s OW and glycerol’s CG atom) for three
diﬀerent solvent compositions xG = 0.0, 0.05, and 0.1, at T = 260 K.

denaturation, which is supposed to occur via reduction ofhydrophobic interactions at a lower temperature.40–56
In order to obtain further insight, we have separated out theenthalpic (H) and the entropic (TS) contributions of the PMF
by the FD method. From these analyses, we have understoodthat at the separation of the CM, TS increases and H decreases
with increasing glycerol concentration. However, the above changes
are not exactly the same as each other. The larger decrease of H than
the increase of  TS ultimately increases the CM well depth of the
PMF with an increase of glycerol concentration. Further analyses
of various components of H terms and more detailed solvation
analyses show that the reduction of the H value at the CM
separation originally comes from the increase of the solvent–solvent interaction near the hydrophobic solute molecules as they
aggregate together to form a contact pair. In addition, glycerol

808 | Phys. Chem. Chem. Phys., 2019, 21, 800--812

induces symmetrization of the tetrahedral ordering of the solvent
across the space surrounding the hydrophobic solute. The above
symmetrization causes a reduction of the entropy contribution of
the PMF at the CM separation.
Lastly, one can question the transferability of the findings ofthe present study to a more complex system, like a protein. The
question is pertinent because our choice of the nonpolar solute,methane, is diﬀerent from a protein, which is bigger and much
more complex. A number of studies (see for example, ref. 64 and
111–117) extensively studied the solute length scale dependenceof hydrophobic hydration. Drying of the extended nonpolar
surface was observed once the size of a hydrophobic solute goesbeyond a certain length scale (1 nm size).111 Interestingly, thesmall-to-large crossover length scale can be varied by different
means, like the addition of some cosolvents. For example, theThis journal is © the Owner Societies 2019

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molecular simulation by Garde et al.114 reported a significant
reduction of the crossover length scale from B1 nm for purewater to the size of a small molecule on the addition of an
ethanol like cosolvent to water. This is relevant in the present
study as we consider here binary mixtures of water and glycerol(a polyol compound). Therefore, we presume a significant
shortening of the small-to-large crossover distance to the sizeof a small solute, like methane, for the mixtures. Furthermore, arecent molecular simulation study118 further justifies our choiceof the solute in the present study. The objective of the above
study was to understand whether proteins behave like a small
non-polar solute or a larger one. Quite surprisingly, the simulation
has shown that proteins, having sizes of more than 1 nm, canbehave as ‘small’ particles on the whole in terms of the hydrophobic effect. The above study also indicated that the proximity ofpolar and nonpolar residues of proteins makes the protein hydration structure very similar to that of a small nonpolar solute.
Therefore, we expect that the key findings of the present work arewell transferable to a more complex system with practical interest.

Conflicts of interest
There are no conflicts to declare.

Acknowledgements
VD acknowledges IIT Patna for a research fellowship. We
acknowledge Dr Biman Jana for fruitful discussion. We acknowledge IIT Patna for computational support. This paper is dedicatedto Sahitya, the newborn baby of the Daschakraborty family.

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