Hydrophobicity of proteins and nanostructured solutes is governed by topographical and chemical context


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Hydrophobicity of proteins and nanostructured solutes
is governed by topographical and chemical context
Erte Xia,1, Vasudevan Venkateshwaranb,c,1, Lijuan Lib,c, Nicholas Regoa, Amish J. Patela,2, and Shekhar Gardeb,c,2

a Department of Chemical & Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104; b Howard P. Isermann Department of Chemical
and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180; and c Center for Biotechnology and Interdisciplinary Studies, Rensselaer
Polytechnic Institute, Troy, NY 12180

Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved October 26, 2017 (received for review March 23, 2017)

Hydrophobic interactions drive many important biomolecular self-
assembly phenomena. However, characterizing hydrophobicity at
the nanoscale has remained a challenge due to its nontrivial
dependence on the chemistry and topography of biomolecu-
lar surfaces. Here we use molecular simulations coupled with
enhanced sampling methods to systematically displace water
molecules from the hydration shells of nanostructured solutes and
calculate the free energetics of interfacial water density fluctua-
tions, which quantify the extent of solute–water adhesion, and
therefore solute hydrophobicity. In particular, we characterize the
hydrophobicity of curved graphene sheets, self-assembled mono-
layers (SAMs) with chemical patterns, and mutants of the pro-
tein hydrophobin-II. We find that water density fluctuations are
enhanced near concave nonpolar surfaces compared with those
near flat or convex ones, suggesting that concave surfaces are
more hydrophobic. We also find that patterned SAMs and pro-
tein mutants, having the same number of nonpolar and polar
sites but different geometrical arrangements, can display signif-
icantly different strengths of adhesion with water. Specifically,
hydroxyl groups reduce the hydrophobicity of methyl-terminated
SAMs most effectively not when they are clustered together but
when they are separated by one methyl group. Hydrophobin-II
mutants show that a charged amino acid reduces the hydropho-
bicity of a large nonpolar patch when placed at its center, rather
than at its edge. Our results highlight the power of water den-
sity fluctuations-based measures to characterize the hydrophobic-
ity of nanoscale surfaces and caution against the use of additive
approximations, such as the commonly used surface area models
or hydropathy scales for characterizing biomolecular hydropho-
bicity and the associated driving forces of assembly.

nanotube | curvature | chemical pattern | hydrophilicity | graphene

Hydrophobic interactions drive many important biolog-ical and colloidal self-assembly processes (1–6). Dur-
ing such assembly, the hydration shells of the associating
solutes are disrupted, replacing hydrophobic–water contacts with
hydrophobic–hydrophobic ones. Characterizing how strongly
water adheres to a given solute is, therefore, directly relevant
to the strength of hydrophobic interactions between solutes.
Macroscopically, surface–water adhesion is quantified by mea-
suring the water droplet contact angle on a surface. However,
such characterization does not translate usefully to proteins and
other nanoscale solutes. Indeed, characterizing how strongly or
weakly a protein surface or a specific patch on it adheres to water
(i.e., its hydrophobicity) is incredibly challenging and has neces-
sitated the use of simplifying assumptions.

To this end, simple surface area (SA) models have been used
to estimate the driving force for assembly, ∆G = γ∆A, where
∆A is the nonpolar SA buried upon assembly and γ is an appro-
priate surface tension (7–9). However, the value of γ used in pop-
ular models is nearly an order of magnitude lower than the oil–
water surface tension (10), and its temperature dependence is at
odds with that of biological assembly (11), reducing it to a fitting
parameter. Moreover, not just the magnitude but even the sign

of the best-fit γ can depend on the class of solutes used to esti-
mate it (12). As a result, for certain complex solutes the burial
of nonpolar SA can even be unfavorable, rendering such mod-
els ill-suited for characterizing the driving forces of nanoscale
assembly (13).

Other approximate approaches that use hydropathy scales (or
scoring functions) (14–18) assign an index (or a score) to an
amino acid residue based on some measure of its aversion to
water (e.g., water to oil transfer free energy) and estimate the
hydrophobicity of a protein patch as a sum of the hydrophobic-
ities of constituent amino acids (14). Many hydropathy scales
exist, and they differ significantly from each other (19, 20).
Importantly, while such methods can efficiently extract informa-
tion from large protein databases and classify them into mean-
ingful groups, they fail to predict the driving forces in specific
situations (21–23). Here we trace the failure of such approaches
to the assumption that the hydrophobicity of a protein patch can
be decomposed into a sum of its constituent parts (i.e., additiv-
ity), and that a unique hydrophobicity can be assigned to each
residue; our results contribute to the growing consensus that the
hydrophobicity of a residue is not unique but depends in a non-
trivial manner on its chemical and topographical context in a
protein.

To study context-dependent hydrophobicity we use molecu-
lar dynamics (MD) simulations coupled with enhanced sam-
pling methods (24, 25) to systematically displace water molecules
from the solute hydration shell and quantify the corresponding

Significance

Numerous biological self-assembly processes, from protein
folding to molecular recognition, are driven by hydropho-
bic interactions, yet characterizing hydrophobicity at the
nanoscale has remained a major challenge, because it requires
understanding of the strength of protein–water interactions
and the ease with which they can be disrupted. Water near a
protein responds to its chemistry and topography in a man-
ner that is collective and complex and cannot be captured
by commonly used surface area models or hydropathy scales.
We demonstrate that water density fluctuations near proteins
can characterize protein hydrophobicity and reveal its depen-
dence on curvature and chemical patterns at the nanoscale.
Our approach opens new avenues for understanding and effi-
cient characterization of biomolecular interactions.

Author contributions: A.J.P. and S.G. designed research; E.X., V.V., L.L., N.R., and A.J.P.
performed research; E.X., V.V., L.L., N.R., and A.J.P. analyzed data; and E.X., V.V., A.J.P.,
and S.G. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.
1 E.X. and V.V. contributed equally to this work.
2 To whom correspondence may be addressed. Email: amish.patel@seas.upenn.edu or
gardes@rpi.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1700092114/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1700092114 PNAS | December 19, 2017 | vol. 114 | no. 51 | 13345–13350

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free energetic cost. The free energetics of interfacial water den-
sity fluctuations, and especially the rare ones that result in
opening of a cavity adjacent to the solute, then serve to quan-
tify hydrophobicity. Density fluctuations are enhanced and cor-
respondingly it is easier to create a cavity near a hydropho-
bic surface (26–29), consistent with the weaker surface–water
adhesion. Theory of inhomogeneous liquids connects water
density fluctuations to other quantities, such as water com-
pressibility, transverse water density correlations, and the free
energy of cavity formation, all of which can also serve as molec-
ular measures of context-dependent hydrophobicity (24, 26–
35). Such measures have been used previously to study as-
pects of context-dependent hydrophobicity of nanoscale surfaces
(35–48).

Here, we build on this work by characterizing the hydropho-
bicity of surfaces with systematic variations in curvature and
the chemical patterns they display. We show that concave non-
polar surfaces are more hydrophobic than convex ones. We
also show that hydrophobic patches with variations in chemi-
cal pattern and topography, whether on self-assembled mono-
layers (SAMs) or on the surface of a protein, hydrophobin-II,
can display significantly different hydrophobicity. Our work high-
lights the power of water density fluctuations-based measures to
characterize hydrophobicity of nanoscale surfaces and cautions
against the use of additive approximations, such as the com-
monly used SA models, hydropathy scales, and similar scoring
functions, for characterizing biomolecular hydrophobicity and
the associated driving forces of assembly.

Results and Discussion
Effect of Nanoscale Curvature on Surface Hydrophobicity. How cur-
vature influences the hydration of spherical hydrophobic solutes
is known. Highly curved solutes smaller than Rc ≈1 nm are
hydrated without significantly perturbing water’s hydrogen bond
network, whereas hydrating larger solutes requires the ener-
getically unfavorable breaking of hydrogen bonds (5, 49, 50).
Although typical proteins are larger than Rc, their surfaces
include bumps and crevices with different curvatures. To under-
stand how protein hydrophobicity is influenced by both the mag-
nitude and the sign of its local curvature we first study surfaces
with homogeneous chemistry and well-defined curvatures, hemi-
cylindrical nanotubes (Fig. 1A), which allows us to set one prin-
cipal curvature to zero and systematically vary the other, κ.

To sample concave (κ< 0) and convex (κ> 0) curvatures
we performed MD simulations of hemicylindrical open-ended

A B C D

Fig. 1. Effect of nanoscale curvature on hydrophobicity. (A) Simulation snapshot of a (16,16) hCNT in water. Only the water molecules in observation
volumes, v, near the concave (blue and white) and the convex (red and white) surfaces are shown for clarity. hCNT–water interactions are scaled by λ = 0.5.
(B) Compressibility of water in the first hydration shell normalized by its value near a flat graphene sheet, χ/χgraphene , as a function of the surface curvature,
κ. (C) Water density fluctuations, Pv (N), in cylindrical-shell volumes on the concave and convex sides of hCNTs computed using the INDUS method (25).
(D) Excess chemical potential, βµexv = − ln Pv (0), for creating a cavity of size and shape v near various hCNTs. These results show that concave nonpolar
surfaces are more hydrophobic than convex ones. Surface hydrophobicity is sensitive to and increases substantively with nanoscale curvature of concave
surfaces but is rather insensitive to curvature for convex surfaces (51).

(n,n) armchair carbon nanotubes (hCNTs) with n = 12, 16, and
24, as well as flat graphene sheets (κ = 0) in water. We system-
atically varied the strength of surface–water attractions using a
scaling factor λ, as described in SI Appendix. For λ = 0.5, the
wettability of the reference graphene surface is similar to that of
a CH3-terminated SAM surface, in that they both have similar
water droplet contact angles (SI Appendix). Fig. 1 shows results
for systems with λ = 0.5; results for other λ-values are included
in SI Appendix.

Fig. 1B shows the isothermal compressibility of interfacial
water near the curved hCNT surfaces, obtained by performing
MD simulations over a range of pressures and taking the pres-
sure derivative of the average number of waters, 〈Nv〉, in an
interfacial observation volume, v, using χ ≡ −(∂ ln〈Nv〉/∂P)T
(see SI Appendix for details). To compare different curvatures
on the same footing we deliberately selected subvolumes v, such
that they contain about the same number of water molecules,
〈Nv〉, on average. The hydration water near the concave sur-
face of the (12,12) hCNT is almost twice as compressible as that
near a flat graphene sheet. The hydration shell compressibility
decreases monotonically with κ as the surface becomes less con-
cave, and then increasingly convex, suggesting that concave non-
polar surfaces are more hydrophobic than convex surfaces of the
same curvature.

Our results for the convex surfaces are consistent with those
of Sarupria and Garde (34), who showed that the hydration shell
compressibility is the lowest near methane-sized hydrophobic
solutes and increases monotonically with increasing solute size
(decreasing curvature). For convex surfaces, results in Fig. 1B
are also in good agreement with those of Jabes et al. (52), who
found that hydration shell compressibility reduces by about 22%
near a hydrocarbon-coated cylinder with κ = 1.13 nm−1, rela-
tive to that near a flat plate. Our results highlight an asymmet-
ric dependence of hydration shell compressibility on the sign of
nanotube curvature. In particular, compressibility is more sensi-
tive to concave curvatures (i.e., the absolute value of slope |∂χ

∂κ
|

is higher for κ< 0 than for κ> 0). We note that this asymme-
try in slopes depends on the exact definition of curvature. As
shown in SI Appendix, Fig. S5 and discussed in SI Appendix, sec-
tion I-F, defining κ based on the curvature of liquid water inter-
face reduces the asymmetry; nevertheless, the observation that
compressibility of hydration water is higher near concave sur-
faces compared with convex ones holds true. This observation
suggests that introduction of both positive and negative curva-
tures (of equal magnitude) on an otherwise flat surface ought

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E F

D

B

Fig. 2. How chemical patterns influence surface hydrophobicity. (A) Top views of a CH3 -SAM containing n = 4 -OH head groups (red) separated by s = 0, 1, 2,
and 3 CH3 head groups (cyan), respectively. A 3 × 3 × 0.3-nm3 observation volume, v (white), is placed above the patches. (B) Free energies of emptying v
near the four patches in A. (C) Snapshot of the n = 4, s = 0 SAM surface (space-filled) illustrating the SAM–water interface, z(x, y), for a biased simulation
that displaces all but a fraction, ρv = 0.27, of waters from v. z is the vertical distance from the bottom of the SAM surface. (D) Top views of the interfaces
for n = 4 and s = 0, 1, and 2 for partially wet configurations (ρv = 0.47, 0.36, 0.27 from left to right). (E) Same as B for n = 7, and s = 0, 1, and 2. (F) Same as
D for n = 7, and s = 0 and 1.

to increase its hydrophobicity. Our assertion that a rugged non-
polar surface is more hydrophobic than a flat one is supported
by Mittal and Hummer (42), who find that the interfacial free
energy of a sinusoidal hydrophobic surface increases with its
amplitude.

Fig. 1C shows probability, Pv (N ), of observing N water
molecules in an interfacial observation volume, v. To compare
the various curved surfaces on an equal footing we varied the
axial length of v, such that they all contain roughly the same
number of waters on average, 〈Nv〉≈49. The Pv (N ) distribu-
tions, for all of the surfaces obtained using the INDUS method
(25), are Gaussian (parabolic) near the mean but display promi-
nent non-Gaussian low-N tails. Patel et al. (24, 27) have shown
that such low-N fat tails serve as an excellent signature of surface
hydrophobicity; the fatter the tail, the more hydrophobic the sur-
face. In qualitative agreement with the data for compressibility
(Fig. 1B), Fig. 1C shows that while the low-N tails of Pv (N ) are
rather insensitive to curvature for convex surfaces, curvature sig-
nificantly influences the tails, and thereby the hydrophobicity of
concave surfaces.

These low-N tails in Pv (N ) are directly connected to the work
required to create a cavity of the size and shape of v near the
surface (26, 28) through βµexv = − ln Pv (0). Fig. 1D shows the
dependence of βµexv on the absolute curvature of the hCNT. It
is far easier to create a cavity in the vicinity of concave surfaces
compared with convex ones, suggesting that concave nonpolar
surfaces are more hydrophobic and ought to bind hydrophobic
solutes more strongly than convex surfaces, consistent with the
results of Setny (53). These results point to an important short-

coming of SA models, which assume that the thermodynamic
driving forces for burying concave and convex hydrophobic areas
are identical.

Surfaces with the Same Chemistry but Different Patterns Can Have
Widely Varying Hydrophobicities. Flat SAMs provide excellent sys-
tems to analyze the effects of chemical patterns on hydrophobic-
ity without being encumbered by the effects of surface topogra-
phy (40, 54, 55). We study SAM surfaces with n hydrophilic sites
(–OH head groups) in a background of hydrophobic sites (–CH3
head groups) (see SI Appendix for details). We hold n constant
but vary the separation, s, the number of CH3 sites between adja-
cent OH sites (Fig. 2A). We studied seven patterns with n = 4
(s = 0, 1, 2, 3) and n = 7 (s = 0, 1, 2) and monitored water den-
sity fluctuations in cuboidal volumes, v, of width 0.3 nm placed
above a square 3-nm × 3-nm surface patch containing the chem-
ical patterns (Fig. 2A).

Which of the four patches in Fig. 2A is the most hydropho-
bic and which is the most hydrophilic? Additive models would
predict that all patterns are equally hydrophobic; however,
the answer is both nonintuitive and nontrivial. Fig. 2B shows
the hydrophilicity of the n = 4 patterns, as quantified by the
reversible work, µexv , required to empty the interfacial volume, v;
the higher the µexv , the more hydrophilic the patch. Although the
number of hydrophobic and hydrophilic sites is the same in the
four patches, µexv is different and varies nonmonotonically with s.
The s = 1 patch with –OH groups separated by one methyl group
is the most hydrophilic of the four. Thus, embedding a given
number of –OH groups in a hydrophobic background decreases

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hydrophobicity most effectively not when the –OH groups are
adjacent to one another in a cluster (s = 0), but when they are
separated by a methyl group (s = 1).

What leads to such a nonmonotonic response to the chemi-
cal context presented by the patch? To answer this question, we
visualize dewetting of the patches by following the average water
density field in INDUS simulations, where biasing potentials are
used to dewet v. For example, consider a biased simulation of
the n = 4, s = 0 SAM surface, which displaces all but a fraction,
ρv = 0.27, of waters in v on average; in Fig. 2C we show the cor-
responding SAM–water interface, z (x,y) [SI Appendix includes
details of the interface calculation (56)].

As v is dewetted for the s = 0 pattern (Fig. 2D, top row) the
interface detaches from the patch at the borders but remains
pinned to the central cluster, forming a doughnut-shaped cav-
ity above the patch. The s = 1 pattern (Fig. 2D, middle row) pins
the interface over a larger area, even when the observation vol-
ume is significantly dewetted, indicating the difficulty of dewet-
ting the region in its vicinity. Indeed, the work of cavity creation
µexv is several kBT larger for the s = 1 pattern than for s = 0.
Interestingly, as the –OH groups are further separated (s = 2)
the interface depins from the space between the hydrophilic sites,
making cavity formation easier, as reflected in lower µexv (Fig.
2B). The s = 2 pattern facilitates interface formation between
the OH sites as well as pins the interface outside v; thus, the
patch defined by v does not bear the full brunt of the pinning by
the hydrophilic sites. Therefore, v can be emptied more easily,
leading to the nonmonotonic dependence of hydrophobicity on
s. Patterns with seven –OH sites also display similarly context-
dependent hydrophobicity that varies nonmonotonically with s
(Fig. 2 E and F).

Collectively, these results highlight that even for simple flat
surfaces, surface–water adhesion strength depends on chemical
patterns in a manner that is complex and not anticipated by addi-
tive models. Our results are consistent with previous work on the

A B C

D E F

Fig. 3. Protein hydrophobicity is nonadditive. (A) Wild-type hydrophobin-II shown in space-fill representation (white, nonpolar; green, polar; red, anionic;
blue, cationic). Two residues, Leu-63 (gray, at the center) and Asp-59 (red, at the periphery of the patch), were swapped to create the mutant (Right). (B) Top
and front views of hydrophobin-II are shown along with the observation volume, v, that covers the hydrophobic patch and Asp-59. (C) The free energetics,
βGv (N) = − ln Pv (N), of observing N waters in v, is shown for wild type and swap mutant in units of the thermal energy, β−1 = kB T . (D) The difference in
Gv (N) for wild-type and mutant proteins is shown; the three lines are fits over the ranges 5–20, 30–100, and 110–150, respectively. (E) Interface encompassing
dewetted region (orange mesh) near wild-type and mutant proteins for a dewetted state with ≈ 20 (waters hidden for clarity). (F) βGv (N = 5) is significantly
larger for the mutant than for the wild type, highlighting the diminished hydrophobicity of the patch on the swap mutant.

hydration of patterned surfaces. For example, Luzar and Leung
(57) showed that in confined geometry a regularly spaced distri-
bution of hydrophilic sites is much more effective in slowing the
formation of vapor tubes that trigger the evaporation process.
Vanzo et al. (58) also found that uniformly distributing charges
(rather than segregating them) in a hydrophobic surface makes
the surface significantly more hydrophilic.

Protein Hydrophobicity Is Context-Dependent and Nonadditive. We
use water density fluctuations-based measures to characterize
the hydrophobicity of a protein, hydrophobin II (Protein Data
Bank ID code 2B97) (59), which is a small globular (≈ 7 kDa)
fungal protein secreted in the extracellular environment. It dis-
plays a relatively large hydrophobic patch that makes the pro-
tein amphiphilic and surface active at the vapor–liquid inter-
face of water, enabling the formation of hydrophobic coatings
and sheaths that cover fungal spores (59). We note that when
viewed from the atomic-level hydrophobicity scale perspective
of Kapcha and Rossky (60) the patch appears actually quite
heterogeneous (SI Appendix). Acharya et al. (40) interrogated
the hydrophobin-II surface using binding of small methane-like
nonpolar solute probes present in an aqueous solution, which
revealed the hydrophobic patch referred to above. We have
also used the INDUS method to characterize the hydrophobic-
ity of hydrophobin-II using larger benzene-shaped probe vol-
umes. While the benzene-shaped probes also identified the
large hydrophobic patch, interestingly, we found that protein
hydrophobicity can also depend on the size and shape of probe
itself (29).

Here we study how altering the local context affects the
hydrophobicity of the patch. To this end, we created a swap
mutant by switching the positions of residues Asp-59 and Leu-
63 in the wild-type protein to Asp-63 and Leu-59 in the mutant
(Fig. 3A). Such a swap places a charged residue from the edge
to the center of the patch but does not perturb the overall

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structure of the protein; there are four disulfide bonds in the
protein, and the backbone root mean square deviation between
equilibrium wild-type and mutant structures are within thermal
fluctuations (see SI Appendix for simulation details). To study
the collective response of water to the swap we defined an
observation volume, v, of width 0.3 nm that envelopes a con-
tiguous region of nine nonpolar residues and Asp-59 (Fig. 3 A
and B) and contains roughly 140 waters on average. We calcu-
lated the free energetics of water density fluctuations, βGv (N ) =
− ln Pv (N ), near the wild-type and the swap mutant proteins
(Fig. 3C), allowing comparisons between two patches with the
same number and type of amino acids but having different geo-
metrical arrangement. It is clear that over the entire range of
water numbers one expends more work to dewet the patch in the
swap mutant compared with that in the wild-type protein, high-
lighting the decreased hydrophobicity of the patch in the swap
mutant.

The additional work, ∆Gv (N ), required to dewet the swap
mutant relative to the wild type (Fig. 3D) shows three approxi-
mately linear regimes. The one at high N arises from the slightly
different number of average water molecules in the volumes
near the two patches, whereas the differences in the low-N fat
tails are visible in the N range from 20 to 120 and reflect the
increased hydrophilicity of the mutant patch. Further depletion
in water numbers encroaches directly on the hydration shell of
the charged Asp-63 in the swap mutant, which is costly, leading
to the steep linear region for N < 20. Instantaneous interfaces
encompassing the dewetted regions near the wild-type and the
mutant proteins with roughly 20 water molecules in v (Fig. 3E)
show that a large cavity develops near the patch in both cases
(see SI Appendix for details). However, the cavity shape near the
wild-type hydrophobin-II is contiguous, whereas that near the
swap mutant is doughnut-shaped in that water remains pinned
to the central Asp-63. Importantly, it costs nearly 30 kBT less to
displace all but five waters from v and open the cavity near the
wild-type patch (Fig. 3F), consistent with the larger hydrophobic-
ity of the patch in the wild-type protein. Given that the number
and types of amino acid residues are identical in the two patches,
their disparate hydrophobicities are not be anticipated by addi-
tive models.

Conclusions and Outlook
Characterizing the hydrophobicity of heterogeneous nanoscale
surfaces has remained a major challenge. Additive and context-
independent descriptions of hydrophobicity are frequently used
by computational drug design approaches and implicit sol-
vent methods to estimate the hydrophobic contribution to
association (61). We showed that molecular measures based
on water-density fluctuations effectively capture the collective
response of water to complex surfaces and serve as robust
nanoscale measures of hydrophobicity. We used these mea-
sures to show that the hydrophobicity of proteins and nanos-
tructured solutes is strongly influenced by their chemistry and
topography in a manner that cannot be captured by additive
approaches.

In particular, by studying hemicylindrical nonpolar surfaces we
showed that concave nonpolar surfaces are more hydrophobic
compared with flat or convex surfaces, as reflected in the higher
water compressibility, larger water density fluctuations, and eas-
ier cavity formation in the vicinity of concave surfaces. The rel-
ative ease of displacing water from a concave region suggests an
important role for concave features (e.g., clefts or pockets) in
binding to hydrophobic solutes. Molecular details of water den-
sity fluctuations in a concave interfacial region and how they are
coupled to an approaching ligand are also known to be important
in ligand binding kinetics (62).

The asymmetric dependence of hydrophobicity of nonpolar
surfaces on curvature implies that introducing nanoscale topo-
graphical features on an otherwise flat nonpolar surface would
increase its hydrophobicity. Such features may be integral parts
of the structure of proteins and other macromolecules, or they
may appear fleetingly through conformational changes of a flex-
ible molecule or surface, suggesting that flexible nonpolar sur-
faces ought to be more hydrophobic than rigid ones. This expec-
tation is consistent with the results of Andreev et al. (63), who
showed that flexible nanotubes are more hydrophobic, expel
water from their interior, and reduce the flow of water through
them. Enhanced hydrophobicity as a result of flexibility should
also influence water phase behavior and evaporation rates under
nonpolar confinement. Indeed, Altabet and Debenedetti (64)
and Altabet et al. (65) have shown that water confined between
flexible nonpolar surfaces is less stable and evaporates signifi-
cantly faster relative to water confined between the correspond-
ing rigid surfaces.

We also showed that patches with the same chemical composi-
tion but different geometrical arrangements, either on SAM sur-
faces or on proteins, can display significantly different hydropho-
bicities. Specifically, we showed that hydrophilic sites are most
effective in increasing the hydrophilicity of a nonpolar surface
not when they are clustered together but when they are sepa-
rated from each other by one hydrophobic site. Favorable direct
(electrostatic) interactions between polar or charged sites and
water can pin water molecules not only in direct contact with
the site but also in subsequent hydration shells. Thus, polar sites
separated by ∼ 1 nm can pin water effectively in the region
between them, and, similarly, a polar or charged site has a
larger impact on hydrophobicity and interactions when placed
at the center of a hydrophobic patch instead of at its periphery.
Such context dependence will play an important role in protein
engineering [for example, in engineering of antibodies to opti-
mize both affinity and specificity (66)] as well as in materials
design.

Finally, our work suggests that context-dependent hydra-
tion of protein surfaces can be characterized effectively using
water-density fluctuations and associated quantities. Such char-
acterization captures many-body effects that are missing in
additive models, which presents an important advantage, espe-
cially with regard to developing predictive approaches. The suc-
cess of bioinformatic approaches in predicting protein struc-
ture from sequence has relied on the availability of protein
sequence–structure information in the Protein Data Bank (67).
The sequence–structure relationship is nonadditive and com-
plex, similar to the relationship between chemistry and topog-
raphy, and hydrophobicity. If extensive data on the hydration
of diverse proteins were available, we speculate that data ana-
lytics approaches could be applied to estimate the hydropho-
bicity of protein surfaces. Such information about hydration
is not available in the Protein Data Bank, which contains
information about only the strongly localized crystal waters.
However, our approach using water-density fluctuations-based
characterization of hydrophobicity combined with advances in
high-performance computing provides a route to developing an
extensive “protein hydration data bank,” which could not only
support development of nonadditive predictive approaches but
also help efficient prediction of biomolecular interactions in
complex systems.

ACKNOWLEDGMENTS. We thank Cuyler Bates for preparation of nan-
otube coordinates. S.G. thanks the Center for Computational Innova-
tions at Rensselaer Polytechnic Institute for high-performance comput-
ing resources. This work was supported by National Science Foundation
Grants UPENN MRSEC DMR-1120901, CBET-1652646, and CBET-1511437
(to A.P.).

Xi et al. PNAS | December 19, 2017 | vol. 114 | no. 51 | 13349

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http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1700092114/-/DCSupplemental/pnas.1700092114.sapp.pdf
http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1700092114/-/DCSupplemental/pnas.1700092114.sapp.pdf


1. Pratt LR, Chandler D (1977) Theory of the hydrophobic effect. J Chem Phys 67:
3683–3704.

2. Tanford C (1973) The Hydrophobic Effect: Formation of Micelles and Biological Mem-
branes (Wiley, New York).

3. Kauzmann W (1959) Some factors in the interpretation of protein denaturation. Adv
Protein Chem 14:1–63.

4. Israelachvili J, Wennerström H (1996) Role of hydration and water structure in bio-
logical and colloidal interactions. Nature 379:219–225.

5. Chandler D (2005) Interfaces and the driving force of hydrophobic assembly. Nature
437:640–647.

6. Hillyer MB, Gibb BC (2016) Molecular shape and the hydrophobic effect. Annu Rev
Phys Chem 67:307–329.

7. Eisenberg D, McLachlan AD (1986) Solvation energy in protein folding and binding.
Nature 319:199–203.

8. Roux B, Simonson T (1999) Implicit solvent models. Biophys Chem 78:1–20.
9. Kang YK, Gibson KD, Nemethy G, Scheraga HA (1988) Free energies of hydration of

solute molecules. IV: Revised treatment of the hydration shell model. J Phys Chem
92:4739–4742.

10. Genheden S, Ryde U (2015) The MM/PBSA and MM/GBSA methods to estimate ligand-
binding affinities. Exp Op Drug Disc 10:449–461.

11. Chaudhari MI, Holleran SA, Ashbaugh HS, Pratt LR (2013) Molecular-scale hydropho-
bic interactions between hard-sphere reference solutes are attractive and endother-
mic. Proc Natl Acad Sci USA 110:20557–20562.

12. Mobley DL, Bayly CI, Cooper MD, Shirts MR, Dill KA (2009) Small molecule hydration
free energies in explicit solvent: An extensive test of fixed-charge atomistic simula-
tions. J Chem Theor Comput 5:350–358.

13. Harris RC, Pettitt BM (2014) Effects of geometry and chemistry on hydrophobic solva-
tion. Proc Natl Acad Sci USA 111:14681–14686.

14. Kyte J, Doolittle RF (1982) A simple method for displaying the hydropathic character
of a protein. J Mol Biol 157:105–132.

15. Ferrara P, Gohlke H, Price DJ, Klebe G, Brooks CL (2004) Assessing scoring functions
for protein-ligand interactions. J Med Chem 47:3032–3047.

16. Bonella S, Raimondo D, Milanetti E, Tramontano A, Ciccotti G (2014) Mapping the
hydropathy of amino acids based on their local solvation structure. J Phys Chem B
118:6604–6613.

17. Eisenberg D (1984) Three-dimensional structure of membrane and surface proteins.
Annu Rev Biochem 53:595–623.

18. Rose GD, Wolfenden R (1993) Hydrogen bonding, hydrophobicity, packing, and pro-
tein folding. Annu Rev Biophys Biomol Struct 22:381–415.

19. Cornette JL, et al. (1987) Hydrophobicity scales and computational techniques for
detecting amphipathic structures in proteins. J Mol Biol 195:659–685.

20. Granick S, Bae SC (2008) A curious antipathy for water. Science 322:1477–1478.
21. Kortemme T, Baker D (2002) A simple physical model for binding energy hot spots in

protein–protein complexes. Proc Natl Acad Sci USA 99:14116–14121.
22. Kollman PA, et al. (2000) Calculating structures and free energies of complex

molecules: Combining molecular mechanics and continuum models. Acc Chem Res
33:889–897.

23. Kister AE, Phillips JC (2008) A stringent test for hydrophobicity scales: Two proteins
with 88% sequence identity but different structure and function. Proc Natl Acad Sci
USA 105:9233–9237.

24. Patel AJ, Varilly P, Chandler D (2010) Fluctuations of water near extended hydropho-
bic and hydrophilic surfaces. J Phys Chem B 114:1632–1637.

25. Patel AJ, Varilly P, Chandler D, Garde S (2011) Quantifying density fluctuations in
volumes of all shapes and sizes using indirect umbrella sampling. J Stat Phys 145:
265–275.

26. Godawat R, Jamadagni SN, Garde S (2009) Characterizing hydrophobicity of inter-
faces by using cavity formation, solute binding, and water correlations. Proc Natl
Acad Sci USA 106:15119–15124.

27. Patel AJ, et al. (2011) Extended surfaces modulate hydrophobic interactions of neigh-
boring solutes. Proc Natl Acad Sci USA 108:17678–17683.

28. Patel AJ, et al. (2012) Sitting at the edge: How biomolecules use hydrophobicity to
tune their interactions and function. J Phys Chem B 116:2498–2503.

29. Patel AJ, Garde S (2014) Efficient method to characterize the context-dependent
hydrophobicity of proteins. J Phys Chem B 118:1564–1573.

30. Lee CY, McCammon JA, Rossky P (1984) The structure of liquid water at an extended
hydrophobic surface. J Chem Phys 80:4448–4455.

31. Lee SH, Rossky PJ (1994) A comparison of the structure and dynamics of liquid water
at hydrophobic and hydrophilic surfaces—A molecular dynamics simulation study. J
Chem Phys 100:3334–3345.

32. Giovambattista N, Rossky PJ, Debenedetti PG (2006) Effect of pressure on the phase
behavior and structure of water confined between nanoscale hydrophobic and
hydrophilic plates. Phys Rev E 73:041604.

33. Mittal J, Hummer G (2008) Static and dynamic correlations in water at hydrophobic
interfaces. Proc Natl Acad Sci USA 105:20130–20135.

34. Sarupria S, Garde S (2009) Quantifying water density fluctuations and compress-
ibility of hydration shells of hydrophobic solutes and proteins. Phys Rev Lett 103:
037803.

35. Jamadagni SN, Godawat R, Garde S (2011) Hydrophobicity of proteins and interfaces:
Insights from density fluctuations. Annu Rev Chem Biomol Engg 2:147–171.

36. Bratko D, Curtis RA, Blanch HW, Prausnitz JM (2001) Interaction between hydrophobic
surfaces with metastable intervening liquid. J Chem Phys 115:3873–3877.

37. Giovambattista N, Debenedetti PG, Rossky PJ (2007) Hydration behavior under con-
finement by nanoscale surfaces with patterned hydrophobicity and hydrophilicity. J
Phys Chem C 111:1323–1332.

38. Bratko D, Daub CD, Leung K, Luzar A (2007) Effect of field direction on electrowetting
in a nanopore. J Am Chem Soc 129:2504–2510.

39. Giovambattista N, Lopez CF, Rossky PJ, Debenedetti PG (2008) Hydrophobicity of
protein surfaces: Separating geometry from chemistry. Proc Natl Acad Sci USA 105:
2274–2279.

40. Acharya H, Vembanur S, Jamadagni SN, Garde S (2010) Mapping hydrophobicity at
the nanoscale: Applications to heterogeneous surfaces and proteins. Faraday Discuss
146:353–365.

41. Daub CD, Wang J, Kudesia S, Bratko D, Luzar A (2010) The influence of molecular-
scale roughness on the surface spreading of an aqueous nanodrop. Faraday Discuss
146:67–77.

42. Mittal J, Hummer G (2010) Interfacial thermodynamics of confined water near molec-
ularly rough surfaces. Faraday Discuss 146:341–352.

43. Bratko D, Daub CD, Luzar A (2009) Water-mediated ordering of nanoparticles in an
electric field. Faraday Discuss 141:55–66.

44. Wang J, Bratko D, Luzar A (2011) Probing surface tension additivity on chemi-
cally heterogeneous surfaces by a molecular approach. Proc Natl Acad Sci USA 108:
6374–6379.

45. Fennell CJ, Dill KA (2011) Physical modeling of aqueous solvation. J Stat Phys 145:
209–226.

46. Factorovich MH, Molinero V, Scherlis DA (2015) Hydrogen-bond heterogeneity boosts
hydrophobicity of solid interfaces. J Am Chem Soc 137:10618–10623.

47. Ma CD, Wang C, Acevedo-Vélez C, Gellman SH, Abbott NL (2015) Modulation of
hydrophobic interactions by proximally immobilized ions. Nature 517:347–350.

48. Garde S (2015) Physical chemistry: Hydrophobic interactions in context. Nature
517:277–279.

49. Lum K, Chandler D, Weeks JD (1999) Hydrophobicity at small and large length scales.
J Phys Chem B 103:4570–4577.

50. Rajamani S, Truskett TM, Garde S (2005) Hydrophobic hydration from small to large
lengthscales: Understanding and manipulating the crossover. Proc Natl Acad Sci USA
102:9475–9480.

51. Cheng YK, Rossky PJ (1998) Surface topography dependence of biomolecular
hydrophobic hydration. Nature 392:696–699.

52. Jabes BS, Bratko D, Luzar A (2016) Universal repulsive contribution to the solvent-
induced interaction between sizable, curved hydrophobes. J Phys Chem Lett 7:
3158–3163.

53. Setny P (2008) Hydrophobic interactions between methane and a nanoscopic pocket:
Three dimensional distribution of potential of mean force revealed by computer sim-
ulations. J Chem Phys 128:125105.

54. Acharya H, Mozdzierz NJ, Keblinski P, Garde S (2012) How chemistry, nanoscale rough-
ness, and the direction of heat flow affect thermal conductance of solid–water inter-
faces. Ind Eng Chem Res 51:1767–1773.

55. Mrksich M, Whitesides GM (1996) Using self-assembled monolayers to understand the
interactions of man-made surfaces with proteins and cells. Annu Rev Biophys Biomol
Struct 25:55–78.

56. Willard AP, Chandler D (2014) The molecular structure of the interface between water
and a hydrophobic substrate is liquid-vapor like. J Chem Phys 141:18C519.

57. Luzar A, Leung K (2000) Dynamics of capillary evaporation. I. Effect of morphology
of hydrophobic surfaces. J Chem Phys 113:5836–5844.

58. Vanzo D, Bratko D, Luzar A (2012) Tunable wetting of surfaces with ionic functional-
ities. J Phys Chem C 116:15467–15473.

59. Hakanpää J, Linder M, Popov A, Schmidt A, Rouvinen J (2006) Hydrophobin HFBII in
detail: Ultrahigh-resolution structure at 0.75 Å. Acta Crystallogr Sect D Biol Crystallogr
62:356–367.

60. Kapcha LH, Rossky PJ (2014) A simple atomic-level hydrophobicity scale reveals pro-
tein interfacial structure. J Mol Biol 426:484–498.

61. Jorgensen WL (2004) The many roles of computation in drug discovery. Science
303:1813–1818.

62. Setny P, Baron R, Kekenes-Huskey PM, McCammon JA, Dzubiella J (2013) Solvent
fluctuations in hydrophobic cavity–ligand binding kinetics. Proc Natl Acad Sci USA
110:1197–1202.

63. Andreev S, Reichman D, Hummer G (2005) Effect of flexibility on hydrophobic behav-
ior of nanotube water channels. J Chem Phys 123:194502.

64. Altabet YE, Debenedetti PG (2014) The role of material flexibility on the drying tran-
sition of water between hydrophobic objects: A thermodynamic analysis. J Chem Phys
141:18C531.

65. Altabet YE, Haji-Akbari A, Debenedetti PG (2017) Effect of material flexibility on the
thermodynamics and kinetics of hydrophobically induced evaporation of water. Proc
Natl Acad Sci USA 114:E2548–E2555.

66. Julian M, Li L, Garde S, Wilen R, Tessier P (2017) Efficient affinity maturation of anti-
body variable domains requires co-selection of compensatory mutations to maintain
thermodynamic stability. Sci Rep 7:45259.

67. Baker D, Sali A (2001) Protein structure prediction and structural genomics. Science
294:93–96.

13350 | www.pnas.org/cgi/doi/10.1073/pnas.1700092114 Xi et al.

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