The hydrophobic effect, and fluctuations: The long and the short of it


COMMENTARY

The hydrophobic effect, and fluctuations: The long
and the short of it
Erte Xia and Amish J. Patela,1

The hydrophobic effect, which is used to describe the
aversion of oil for water or the affinity of oily objects
for one another in water, plays an important role in
diverse disciplines (1). For example, by segregating
to the oil–water interface, amphiphilic molecules that
possess both hydrophobic and hydrophilic groups can
mitigate unfavorable oil–water interactions, thereby
stabilizing emulsions and facilitating detergency. Be-
cause roughly half the amino acids, which form the
basic building blocks of proteins, are hydrophobic,
the hydrophobic effect also plays a central role in bio-
physics. Owing to its ubiquity and its multifaceted
nature (2, 3), being able to accurately model the
hydrophobic effect is both important and challenging.
In PNAS, Vaikuntanathan et al. (4) provide important
insights into the essential ingredients required in a
minimal model of the hydrophobic effect.

The hydrophobic effect characteristically mani-
fests itself in very different ways at microscopic and
macroscopic length scales (1). Macroscopically, the
aversion of oil and water for one another is captured
by the large surface tension associated with the oil–
water interface. At this scale, the hydrophobic effect
drives the minimization of the unfavorable interfacial
area (for example, by the coalescence of oil droplets in
water). Although the macroscopic hydrophobic effect
is governed by the relatively straightforward physics of
interfaces, it can nevertheless lead to complex phe-
nomena, such as the nanobubble-mediated long-
ranged forces between extended hydrophobic sur-
faces (5), or the assembly of anisotropic particles at
curved interfaces (6). Interestingly, the thermody-
namic driving force for such hydrophobic assembly,
which is dictated by interfacial tension, decreases with
increasing temperature.

In contrast, at the molecular scale, the driving force
for hydrophobic assembly famously increases with
increasing temperature (1). In fact, whenever biomo-
lecular assembly occurs upon increasing temperature,
in seeming disregard for entropic considerations, the
hydrophobic effect is often the first suspect. A classic
example is the cold denaturation of proteins. Whereas
the denaturation or unfolding of proteins upon

heating is common, and is ascribed to the configura-
tional entropy of the macromolecule prevailing over
the favorable energy of the folded state, certain pro-
teins also denature upon cooling. Such cold denaturation
is explained by the fact that the molecular hydropho-
bic effect, which stabilizes the folded state of the pro-
tein, is weakened upon cooling, causing the protein
to unravel (7).

To understand these contrasting manifestations of
the hydrophobic effect, it is instructive to consider
how water structure is perturbed near small (molecu-
lar) and large (macroscopic) hydrophobic solutes.
Near a macroscopic hydrophobic object, such as an
oil droplet, interfacial water molecules are unable to
participate in four hydrogen bonds like their bulk
counterparts (8). This energetically unfavorable sce-
nario is responsible for the large oil–water surface ten-
sion and drives the minimization of interfacial area. In
the vicinity of molecular hydrophobes such as meth-
ane, the hydration waters are able to maintain all their
hydrogen bonds, but accommodating the hydro-
phobe severely constrains the hydrogen bonding net-
work of water (1). This strain on the hydrogen bonding
network is reflected in a large negative entropy of
hydration; it is this entropic penalty that causes molec-
ular hydrophobes to assemble more strongly as tem-
perature is increased. Thus, hydrophobic hydration
and assembly at the molecular level are not governed
by interfacial physics, but are fundamentally different.
Given these differences in hydrophobic hydration in
the molecular and macroscopic limits, at what size do
we cross over from one regime to the other?

Theory, simulation, and experiment all agree that
the cross-over occurs for solutes that are about 1 nm in
size (2, 9–13). This length scale emerges from a prod-
uct of the surface tension of water and its isothermal
compressibility, properties that respectively influence
the hydration of large and small solutes (1, 10, 12). The
1-nm length scale also plays a key role in numerous
molecular assemblies; for example, most amino acid
side chain residues are smaller than 1 nm, but folded
proteins are larger than 1 nm. Being able to quantita-
tively capture the length scale cross-over in hydrophobic

aDepartment of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104
Author contributions: E.X. and A.J.P. wrote the paper.
The authors declare no conflict of interest.
See companion article on page E2224 in issue 16 of volume 113.
1To whom correspondence should be addressed. Email: amish.patel@seas.upenn.edu.

www.pnas.org/cgi/doi/10.1073/pnas.1603014113 PNAS | April 26, 2016 | vol. 113 | no. 17 | 4549–4551

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www.pnas.org/cgi/doi/10.1073/pnas.1603014113


hydration is thus critical for understanding biophysical phenom-
ena such as protein folding and aggregation, and must be a
central requirement of any comprehensive theory of the
hydrophobic effect.

In a seminal contribution, Lum, Chandler, and Weeks (LCW)
introduced the key theoretical principles necessary for reconciling
hydrophobic hydration at small and large length scales (2). The
LCW theory of hydrophobicity prescribed decomposing the spa-
tial variations in water density, which arise from the presence of a
hydrophobic solute, into two separate components. The first com-
ponent, ρlðrÞ, is governed by interfacial physics and displays only
gentle variations over molecular length scales; LCW used a Landau–
Ginzburg density functional to describe the free energetics of
this component. The second component, ρsðrÞ, incorporates
the small-amplitude, short-wavelength fluctuations in molecular
density. Importantly, the statistics of such small fluctuations in
water density are Gaussian, a fact that underpins liquid-state
theories (14, 15) and has been confirmed by molecular simulations
(16). LCW theory leverages the Gaussian statistics of the small
length scale fluctuations to integrate out ρsðrÞ, thereby providing
a renormalized and coarse-grained description of the free ener-
getics of ρlðrÞ. In particular, ρlðrÞ remains close to its bulk liquid
value, ρbulk, within and near molecular solutes, because the small
ρsðrÞ fluctuations are sufficient to vacate the region occupied by
the solute. In contrast, vacating waters from a region larger than
1 nm (for the solute to occupy) requires nucleation of an interface,
with ρlðrÞ vanishing within the solute region and approaching
ρbulk outside.

The original LCW paper used a variational formalism to
evaluate ρlðrÞ in the mean-field limit (2). To incorporate fluctua-
tions in ρlðrÞ, subsequent LCW-inspired treatments (17, 18) used
simple models capable of capturing interfacial physics, such as the
lattice gas model. In the lattice gas model, variations in density
between adjacent lattice sites carry an energetic penalty, «, which
along with the lattice spacing, δ, determines the interfacial tension,
γ. However, the formation of a water–vapor interface at ambient
conditions is associated not only with an energetic penalty, but
also with entropically favorable interfacial fluctuations (Fig. 1A);
indeed, the statistics of such long-wavelength capillary wave fluc-
tuations are well understood (19). Vaikuntanathan and Geissler
(20) recognized that for the lattice gas model to appropriately
capture capillary wave fluctuations, only a small range of « values
could be used. If « is too small, we approach the critical point, and
the bulk liquid and vapor phases display large density fluctua-
tions; however, if « is too large, interfacial fluctuations are sup-
pressed. With the optimally parameterized lattice gas for ρlðrÞ, the

authors’ LCW-inspired model was able to quantitatively capture,
without any adjustable parameters, the length scale cross-over in the
hydration free energies of idealized hydrophobes of various shapes.
Remarkably, their model was also able to capture subtle features of
the interfacial free energetics, such as a preference for droplets over
bubbles (20, 21), highlighting the importance of capillary fluctua-
tions even for nanoscale interfaces (Fig. 1 B and C).

In their recent study, Vaikuntanathan et al. (4) subject their
LCW-inspired model to another stringent test, that of quantifying
the statistics of water density fluctuations; such fluctuations, char-
acterized by the probability, PvðNÞ, of observing N waters in a
probe volume, v, have provided numerous insights into the mul-
tifaceted nature of the hydrophobic effect (3, 16, 23, 24). For
example, low-N fluctuations are significantly enhanced near a hy-
drophobic surface, situating the interfacial waters at the edge of
dewetting transition (Fig. 1D) and making them sensitive to pertur-
bations (2, 24). Using their LCW-inspired model, Vaikuntanathan
et al. (4) obtain not just qualitative, but also quantitative,
agreement with molecular simulations, in their estimates of
PvðNÞ for probe volumes in bulk water, at interfaces, and in
hydrophobic confinement. Furthermore, this quantitative agree-
ment is lost if either the small length-scale Gaussian fluctuations or
the large length-scale interfacial fluctuations are not included in
the model.

By identifying capillary fluctuations as an essential ingredient
of a minimal model of the hydrophobic effect, Vaikuntanathan
et al. (4) have laid the groundwork for studying aqueous systems
using a coarse-grained representation of water, which has the
accuracy of molecular simulations but exacts a tiny fraction of
the computational cost. Given the importance of solvent fluctua-
tions in modulating dewetting barriers and the kinetics of hydro-
phobic interactions (25–27), their model could conceivably be
used to study not only the thermodynamics, but also the kinetics
of complex self-assemblies. Another important application is the
study of biomolecules, which are too large to model using explicit
water. Along with hydrophobic interactions, electrostatic interac-
tions also play an important role in the biomolecular context. We
hope that the success of LCW-inspired models motivates the de-
velopment of minimal models that efficiently incorporate fluctua-
tions in both the short- and long-wavelength water polarization
response to charged moieties (28, 29).

Acknowledgments
This work was supported by National Science Foundation Grants
UPENN MRSEC DMR 11-20901 and CBET 1511437, and the Charles
E. Kaufman Foundation Grant KA2015-79204.

A B C D

Fig. 1. Long-wavelength interfacial fluctuations can be seen in simulation snapshots of (A) the liquid–vapor interface, (B and C) nanoscopic vapor
bubbles in bulk water, and (D) at a hydrophobic surface. The work of Vaikuntanathan et al. (4) and Vaikuntanathan and Geissler (20) highlights
the importance of such fluctuations and provides a way to incorporate them into a minimal model of the hydrophobic effect. The average
interface in each case is either flat (A and D) or spherical (B and C), and the color represents deviation away from the average interface toward
(red) or away (blue) from water (cyan). The instantaneous interfaces were computed using the algorithm outlined in ref. 22.

4550 | www.pnas.org/cgi/doi/10.1073/pnas.1603014113 Xi and Patel

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