protein foldingHydrophobic association of {alpha}-helices, steric dewetting, and enthalpic barriers to

Justin L. MacCallum, Maria Sabaye Moghaddam, Hue Sun Chan, and D. Peter Tieleman

doi:10.1073/pnas.0605859104 published online Apr 2, 2007; PNAS

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Hydrophobic association of �-helices, stericdewetting, and enthalpic barriers to protein foldingJustin L. MacCallum*, Maria Sabaye Moghaddam†, Hue Sun Chan†§, and D. Peter Tieleman*§

*Department of Biological Sciences, Faculty of Science, University of Calgary, Calgary, AB, Canada T2N 1N4; and †Departments of Biochemistry andMedical Genetics and Microbiology, Faculty of Medicine, University of Toronto, Toronto, ON, Canada M5S 1A8

Edited by Jose N. Onuchic, University of California at San Diego, La Jolla, CA, and approved February 16, 2007 (received for review July 12, 2006)

Efficient protein folding implies a microscopic funnel-like multidimen-sional free-energy landscape. Macroscopically, conformational en-tropy reduction can manifest itself as part of an empirical barrier inthe traditional view of folding, but experiments show that suchbarriers can also entail significant unfavorable enthalpy changes. Thisobservation raises the puzzling possibility, irrespective of conforma-tional entropy, that individual microscopic folding trajectories mayencounter large uphill moves and thus the multidimensional free-energy landscape may not be funnel-like. Here, we investigate hownanoscale hydrophobic interactions might underpin this salient en-thalpic effect in biomolecular assembly by computer simulations ofthe association of two preformed polyalanine or polyleucine helicesin water. We observe a high, positive enthalpic signature at roomtemperature when the helix separation is less than a single layer ofwater molecules. Remarkably, this unfavorable enthalpy change,with a parallel increase in void volume, is largely compensated for bya concomitant increase in solvent entropy, netting only a small ornonexistent microscopic free-energy barrier. Thus, our findings sug-gest that high enthalpic folding barriers can be consistent with afunnel picture of folding and are mainly a desolvation phenomenonindicative of a cooperative mechanism of simultaneous formation ofmultiple side-chain contacts at the rate-limiting step.

cooperativity � energy landscape � folding transition state �heat capacity � solvation/desolvation

Generic properties of folding kinetics of proteins can offerdeep insights into their solvent-mediated energetics. Be-

cause many ostensibly mundane features of the folding processare not well accounted for by common notions, critical exami-nation of their biophysical basis has proven to be a productiveroute to fundamental advances. A prime example is the corre-lation between folding rate and native topology (1, 2) and thepossible connection of this behavior to folding cooperativity andspecific forms of many-body intraprotein interactions (3).

When folding is formulated in terms of a multidimensionalfree-energy landscape, the ‘‘vertical’’ axis denotes the potential ofmean force (PMF) of the protein, whereas all of the other dimen-sions represent the protein’s conformational degrees of freedom.For a protein to be able to fold, the landscape surface (4) isnecessarily funnel-like (5) because conformational search has to bedirected to circumvent the Levinthal paradox (6, 7). This picture isreadily reconcilable with the empirical folding barriers along one-dimensional free-energy profiles in traditional macroscopic descrip-tions (8) if the barriers arose solely from a reduction in conforma-tional entropy during folding, because restriction onconformational freedom appears, by definition, as decrease inmultidimensional surface area, rather than as barriers, on themicroscopic free-energy landscape (6, 9). However, experimentsindicate a significant enthalpic component in empirical foldingbarriers (10–14). Our interest in high enthalpic folding barriers ismotivated by two physical questions: (i) How does the existence ofthese barriers impact the folding funnel concept? (ii) What canthese barriers tell us about folding mechanisms (15)?

To address these questions, we study solvent-mediated solute–solute interactions as mimics of the interactions between differ-

ent parts of a protein. The interaction free energies we considermodel contributions to a protein’s PMF that are represented bythe vertical axis of the microscopic multidimensional free-energylandscape. PMFs have temperature-dependent enthalpic andentropic components, because solvent degrees of freedom areaveraged. Here, we investigate what physical processes duringfolding may give rise to a significant increase in a PMF’senthalpic component. As our focus is on enthalpic barriers, wedo not consider conformational entropy of the protein mainchain (backbone). For this purpose, the scope of the presentstudy is restricted to solutes that are essentially rigid with respectto main-chain conformation. Hence the entropic components ofthe PMFs we computed originate largely from the solvent.

Atomic simulations of PMFs and other solvation effects areextremely useful for dissecting and rationalizing protein ther-modynamic data (16, 17). However, the relationship between thebehaviors of small solutes (18) and larger-length-scale biomo-lecular assembly is not always straightforward. Notably, whereasthe heat capacity of the protein folding transition state istypically lower than that of the unfolded state (11, 12), atomicsimulations indicate that the heat capacity at the desolvationbarrier of a pair of small nonpolar solutes is higher than thatwhen the pair is far apart (19, 20). These conflicting trends implythat the folding transition-state heat capacity cannot be under-stood as a simple summation of pairwise contributions fromcontacts between small-solute-like chemical groups (3). Nonad-ditivity is prevalent in many aspects of hydrophobicity (21),consistent with recent studies pointing to significant differencesin the molecular basis of hydrophobicity at small- and large-length scales (22–29). Therefore, based on this discrimination,we stipulate that an in-depth analysis of the macroscopic ther-modynamic signatures of folding kinetics could yield crucialinformation about the length scale and many-body nature of themicroscopic solvent-mediated interactions involved in the tran-sition state.

Results and DiscussionPursuing this investigative logic, we address whether high en-thalpic folding barriers signify large length scale (in contrast tosmall-solute-like) desolvation at the rate-limiting step by molec-ular simulations of two preformed polyalanine (A20) and twopolyleucine (L20) �-helices in a fixed relative orientation in water(Fig. 1). Calculating the separation-dependent free energy at

Author contributions: H.S.C. and D.P.T. designed research; J.L.M. and M.S.M. performedresearch; J.L.M. and M.S.M. analyzed data; and J.L.M., H.S.C., and D.P.T. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Freely available online through the PNAS open access option.

Abbreviations: PMF, potential of mean force; SASA, solvent-accessible surface area; MSA,molecular surface area.

§To whom correspondence may be addressed. E-mail: chan@arrhenius.med.toronto.edu ortieleman@ucalgary.ca.

This article contains supporting information online at www.pnas.org/cgi/content/full/0605859104/DC1.

© 2007 by The National Academy of Sciences of the USA

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multiple temperatures allows us to obtain the entropy, enthalpy,and heat capacity (see Methods).

Enthalpy–Entropy Compensation and Heat Capacity. Fig. 2 A and Fshows that the helices in the A20 and L20 two-helix systems preferto be in contact at 300 K. Because of the larger leucine sidechains, the contact free-energy minimum is at a larger separationand the well is deeper and broader for L20. As expected for thehydrophobic effect near room temperature (16, 17), the systemsdisplay a favorable entropy change at contact. A prominententhalpic barrier with a maximum �H0 � �60 kJ�mol�1 at 300K is observed for both A20 and L20 in Fig. 2 A and F at separationsslightly larger than that at contact (red curves), but the large andunfavorable enthalpy change in this region is almost completelycompensated for by a favorable entropy increase (green curves).The net result is only a small desolvation free-energy barrier forA20 (�G � �8 kJ�mol�1) and no free-energy barrier at all for L20(Fig. 2 A and F, black curves).

The heat capacity change �CP is negative at contact and alsoat the enthalpic barrier for both A20 and L20 (Fig. 2 B and G).However, �CP is positive for some larger helix separations. Thistrend is somewhat similar to the association of small nonpolarsolutes (19, 20), but there is an important qualitative difference:The �CP peak for A20 is at a separation larger than that of thedesolvation free-energy barrier, rather than coinciding with thebarrier as for small nonpolar solutes (19–21).

Void Volumes Lead to Enthalpic Barriers to Helix–Helix Association.The origin of the enthalpic barrier is clear upon a dissection ofthe potential energies. As the two helices approach each other,the helix–water interaction energy rapidly becomes unfavorable(Fig. 2 C and H, orange curves). In contrast, the helix–helix (Fig.2 C and H, red curves) and water–water (Fig. 2 C and H, bluecurves) interactions are becoming favorable, but more gradually.This combination leads to a peak in total interaction energy (Fig.2 C and H, black curves) at an intermediate separation betweenthe helices.

Fig. 3 A and B shows an excellent correlation between the totalvolume and enthalpy changes in the system. Local water densityis sensitive to helix configuration (Fig. 3 C–H). Notably, Fig. 3D and G shows a void volume (central dark blue region) betweenthe helices at the desolvation free-energy barrier, because watermolecules cannot fit in the small intervening space when thehelices are not well packed against each other at this separation.A void volume implies a reduction in water–water interactions.In this light, it is clear that at least part of the enthalpic barrieroriginates from less favorable direct helix–helix and helix–waterinteractions relative to that when the two helices are, respec-tively, in tighter contact or farther apart.

CB

A

Fig. 1. Overview of the simulated system. (A) One helix (blue) is fixed, and theother helix (red) is free to move in the direction of the double arrows. The dashedlines show the simulation box. This snapshot displays the maximum helix–helixseparation of 2.4 nm. (B) A view showing the fixed helix–helix crossing angle. (C)Helix–helix packing for L20 at contact (r � 0.90 nm). The surfaces are solvent-accessible surfaces for a water-like spherical probe of radius 0.14 nm. The sidechains are shown as cyan (carbon) and white (hydrogen) sticks.

A F

B

C

D

G

H

I

E J

Fig. 2. Energetics of the A20 (Left) and L20 (Right) dimers. Thermodynamicand geometric properties are computed as functions of the spatial separationr between the centers of mass of the helices (horizontal axes). Changes in valueof the following properties (per mole of helix dimer), relative to those at larger, are plotted to characterize the association of each helix dimer. (A and F)Free-energy �G, i.e., PMF (black), enthalpy �H0 (red), and entropic free-energy�T �S0 (green) at 300 K. To facilitate comparisons, positions of the contactfree-energy minimum, the desolvation barrier, and the solvent-separatedminimum for each of the two helix dimer systems are marked by verticaldashed lines. (B and G) Heat capacity �CP. Error bars along the �H0, �T �S0, and�CP traces represent the standard error calculated as described in Methods. (Cand H) Components of the total potential energy. Selected contributions fromLennard–Jones (dotted curves), electrostatic (dashed curves), and the sum ofLennard–Jones and electrostatic (solid curves) terms of helix–helix (red),helix–water (orange), water–water (blue), and all (black) interactions areshown by separate curves. (D and I) Change in the total number of hydrogenbonds, defined by a distance �0.35 nm between the hydrogen and an accep-tor, and with a donor–hydrogen–acceptor angle �60°. (E and J) SASA (red)and MSA (black).

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Theoretical considerations (22) stipulated that a drying ordewetting transition is possible for extended nonpolar plates atseparations corresponding to multiple layers of water molecules.In contrast, Fig. 3 indicates only steric dewetting in helixdimerization. A single layer of water between the helices (Fig. 3E and H) appears to be stable on the time scale of oursimulations. This trend is consistent with recent investigations

(23, 25, 27, 29). For instance, a study of the collapse of thetwo-domain protein BhpC showed minimal dewetting untilthe onset of steric dewetting (23). A subsequent study of thehydrophobic collapse of a melittin tetramer revealed cleardewetting at separations corresponding to three or four layers ofwater (27), but the region that undergoes dewetting in this caseis tube shaped, which is unlike the open space between twohelices that is more accessible to stabilizing hydrogen bondingfrom bulk water.

Side-Chain Size Effects on Helix–Helix Desolvation Energetics. Thenature of hydrophobicity in general can differ significantly forsmall and large nonpolar solutes (30–32). At room temperature,the hydration free energy of short linear alkanes is proportionalto the solvent-accessible surface area (SASA; see below) (33)with an effective surface tension of �10.5 kJ�mol�1�nm�2,whereas the surface tension for macroscopic water–oil interfacesis �31.4 kJ�mol�1�nm�2 (32). The crossover between a regime inwhich hydrogen bonding in water is hindered yet persists near thesolute and one with depleted hydrogen bonding (31) was pre-dicted to occur at a nanometer solute length scale (22, 34).

Here, upon helix dimerization, the number of water–waterhydrogen bonds increases by approximately five for L20 (Fig. 2I),whereas there is no increase for A20 (Fig. 2D). This finding is inline with the much more favorable enthalpy at contact for L20(red curve in Fig. 2F), driven mainly by favorable changes inwater–water electrostatic interactions (blue dashed curves in Fig.2H). This trend is consistent with the consensus that water canaccommodate small nonpolar solutes without significant disrup-tion to its hydrogen-bond network, whereas it cannot do so forlarge nonpolar solutes and hence some hydrogen bonds have tobe lost (22, 30–32, 34).

Our �-helix dimerization thermodynamics fits in a generalpattern of behavior of nanoscale hydrophobic solutes (i.e., withnanometer length scale). Several features we discover are quitesimilar to those observed recently in simulations of nonpeptidesolutes. For example, the desolvation free-energy barriers for apair of C60 fullerenes and a pair of C60H60 fulleranes at 298 Kwere found to be also quite low at �4 kJ�mol�1 and �12kJ�mol�1, respectively (26). A high desolvation enthalpic barrierof �500 kJ�mol�1 at 298 K was detected in a recent two-temperature study of the association of two parallel nonpolarplates of dimensions � 1.1 � 1.2 nm2 (60 carbon atoms each).Similar to the entropy–enthalpy compensation we ascertain fortwo �-helices, the positive enthalpy change for the nonpolarplates is almost completely compensated for by a favorableentropy change such that the resultant free-energy barrier isinsignificant (29).

Comparing Atomistic and Implicit Solvent Treatments: Insights andLimitations. Can simple notions of hydrophobicity capture theintricacy of nanoscale desolvation? Fig. 2 E and J shows thevariation of total SASA and molecular surface area (MSA) ofthe helices as they approach each other. SASA of a moleculeis the area of the surface traced by the center of a sphericalwater probe rolling on the van der Waals surface of the givenmolecule (see Fig. 1), whereas MSA is the area generated bythe part of probe surface facing the given molecule (35).

By construction, SASA measures the number of water moleculesthat can fit around the solutes; it decreases monotonically as rdecreases. Comparing Fig. 2 A and F with Fig. 2 E and J indicatesthat the SASA trend is similar to that of entropy, consistent with thenotion that reduction in water entropy is roughly proportional to thenumber of water molecules contacting the solutes. On the otherhand, MSA is a better measure of water–solute contact, hence it ismore suited for solvation enthalpy and related effects (36). Con-sistent with this expectation, the MSA profiles display peaks similarto the enthalpic barriers in Fig. 2 A and F that arise mainly from

A

B

C F

D G

E H

Fig. 3. Changes in volume and local water density during helix association.(A and B) Change in total volume �V (black) and enthalpy �H0 (red) for the A20

(A) and L20 (B) systems at 300 K. The positions of the contact minimum,desolvation barrier, and solvent-separated minimum configurations aremarked by vertical lines, with labels corresponding to C–H showing theoccupancy (local density) of water in a 0.05-nm slice passing through thecenter of mass of the two helices in these configurations. Molecular graphicswere produced by using VMD (57).

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uncompensated losses of favorable water–solute interactions (Fig.2 C and H). Here, the position of the MSA peak matches that of theenthalpic barrier accurately for A20, but not so for L20, likelybecause the present MSA treatment does not account for side-chainflexibility. These comparisons indicate that while ‘‘implicit-solvent’’area measures such SASA and MSA can provide valuable physicalinsights (17, 35), perhaps no single area measure can provideadequate predictions for the spatial dependence of a broad rangeof thermodynamic signatures of hydrophobic association (19, 21).

Fitting �G at the contact minima in Fig. 2 A and F to thecorresponding SASA changes in Fig. 2 E and J yields surfacetensions of 11.2 and 13.6 kJ�mol�1�nm�2, respectively, for A20 andL20. Both values are far from the macroscopic limit of �30kJ�mol�1�nm�2 (see above); nonetheless, the effective surface ten-sion for L20 is �20% higher than that for A20. Thus, consistent withits larger size, the behavior of L20 is slightly more macroscopic-likethan that of A20. The negative �CP at contact is larger for L20 thanfor A20 (Fig. 2 B and G); this difference follows from L20’s largerdecrease in surface area upon contact (Fig. 2 E and J) and that the�CP per SASA decrease is approximately twice as large for L20 asfor A20 (�0.14 versus �0.07 kJ�mol�1�K�1�nm�2).

Helix–Helix Association Thermodynamics and Water Distribution. Fig.3 C–H examines the distribution of water around the helices.When the helices are in contact, there is tight packing andinterdigitation of side chains along the helix–helix interface (Fig.3 C and F). When the helices are a little apart, Fig. 3 D and Gshows the development of a void volume, i.e., steric dewetting,that leads to a high enthalpic desolvation barrier (see above).

For A20, a relatively shallow (� �5 kJ�mol�1) solvent-separatedfree-energy minimum is observed at separations slightly larger thanthat at the desolvation barrier (Fig. 2A). The absence of a corre-sponding solvent-separated �G minimum for L20 is likely caused bythe tendency of the flexible leucine side chains to smooth out subtlefeatures. At the solvent-separated minimum of A20, the localdensity plot (Fig. 3E) shows that in between the two helices thereare individual water molecules with occupancy much higher thanbulk, suggesting that they are localized. Thus, the favorable enthalpyin this region likely results from the packing of the two helices witha layer of water molecules fitting tightly in between. In contrast, atthe corresponding separation for L20 (Fig. 3H), the water betweenthe two helices displays occupancy closer to the bulk value, sug-gesting that the water molecules are less confined. For the lessflexible A20 system, an additional free-energy barrier (secondmaximum at r �1.30 nm) and an additional free-energy minimum(at r �1.46 nm) can be discerned, echoing a similar, but moredramatic, pattern observed in simulations of two smooth hydro-phobic surfaces (25).

Ramifications for the Transition States of Protein Folding. The resultsabove on nanoscale hydrophobic interactions provide perspectiveson the critical role of water (37–41) and the nature of transitionstates (42, 43) in protein folding and help resolve at least twopuzzles. First, as stated above, the change in heat capacity �CP fromthe unfolded to transition state is usually negative, but the �CPtrend for small nonpolar solutes such as methane is opposite(19–21), indicating basic physical differences between the twoprocesses. Now, in view of the negative �CP at the desolvationbarrier for a pair of helices (Fig. 2 B and G), protein unfolded-to-transition state �CP may be rationalized, at least in part, bydesolvation of nanoscale hydrophobic surfaces.

Second, although simulations of small nonpolar solutes haverevealed a compensation between enthalpy and solvent entropy atthe desolvation barrier, the height of the enthalpic desolvationbarrier of small solutes is too small to account for the much higherenthalpic protein folding barriers. For example, at 25°C, the en-thalpic folding barrier �H‡�D (in the original notation) �30kJ�mol�1 for chymotrypsin inhibitor 2 (CI2) (11) and �32 kJ�mol�1

for cold shock protein CspB (12); but the enthalpy peak is only �7.5kJ�mol�1 for three-methane association at room temperature (21).A recent simulation of protein A (38) found that the enthalpychange from an unfolded to a transition regime is negative at thetransition temperature, consistent with experiment (14), but con-ditions corresponding to lower experimental temperatures withpositive enthalpic folding barriers were not explored. Here, Fig. 2A and F shows that the ��60 kJ�mol�1 enthalpic barrier for helixdimerization is comparable and can be even higher than that forprotein folding at 300 K. For L20, the �CP around the desolvationbarrier is also similar to the �CP

‡-D � �1.3 kJ�mol�1�K�1 reportedfor CI2 (11). All in all, the desolvation of the L20 dimer displaysthermodynamic signatures that are qualitatively and quantitativelysimilar to the folding transition states of small two-state proteins.

In our two-helix systems, the unfavorable enthalpy increase atdesolvation is concomitant with a favorable solvent entropy in-crease as water is released from the interhelix interface. Conse-quently, there is no free-energy barrier for L20 and the free-energybarrier is much lower than the enthalpic barrier for A20. Thesedramatic compensations lend credence to the idea that the unfa-vorable enthalpic signature of the folding transition state does notnecessarily contradict the funnel picture of the microscopic free-energy landscape (15), which allows for low barriers on mildlyrugged, overall downhill slopes (6, 7). By the same token, theheights of experimental enthalpic folding barriers, which signifi-cantly exceed the enthalpic barriers of small-solute association, maybe viewed as evidence that the folding rate-limiting step generallyinvolves desolvating many side chains in a cooperative, essentiallysimultaneous manner. In this perspective, it is noteworthy that theenthalpic folding barriers of some proteins are lower than theenthalpic desolvation barriers for A20 and L20 (see above). Thisfinding suggests that, for these proteins, the degree of cooperativityin simultaneous side-chain desolvation at the folding rate-limitingstep could be somewhat lower than that in the present helixdimerization models.

OutlookThis study is based on models with fixed main-chain helical con-formations that are designed to explore transient nanoscale eventsat the folding rate-limiting step. The above analysis underscoreshow length-scale dependence of solvent-mediated effects in con-junction with macroscopic thermodynamic data may be used toprovide microscopic energetic and structural information about thefolding transition state. Our results rationalize several generic, yetpuzzling, phenomena in folding kinetics; they also raise intriguingquestions. For instance, while our approach is suggestive of collec-tive dynamics similar to that in the ‘‘diffusion-collision’’ model (44),our helix dimerization model does not address the stability ofisolated helices because their unfolding is precluded. Therefore,results reported here can also be consistent with a folding scenarioin which the cooperative formation of multiple side-chain contactsoccurs between extremely transient helices. To tackle a broaderrange of folding questions, studies with more relaxed conforma-tional restrictions will be necessary to explore, for example, apossible cooperative interplay between local structural propensityand nonlocal contacts (3).

MethodsThe starting structures were generated by simulated annealing(45). Both of the two-helix starting structures adopt a coiled-coilantiparallel geometry with a crossing angle � � �27° for A20 and�28° for L20. One helix was fixed in space by harmonic restraintson the �-carbons; the other helix had restraints applied in onlytwo dimensions (hence the helical conformation and � werefixed) and was free to slide along the helix–helix vector to varythe separation r (Fig. 1). The side chains and water moleculeswere not restrained. The helices were placed in a rectangular boxof �6 � 4.5 � 4.5 nm3, and solvated with 3,867 and 3,778 water

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molecules, respectively, for A20 and L20. Simulations were per-formed under essentially atmospheric pressure (1 bar � 0.987atm) at five temperatures ranging from T � 275 to 350 K, usingthe GROMACS software package (46), the OPLS all-atom forcefield (47, 48), the TIP3P water model (49), and a time step of 2fs. Bonds were constrained to their equilibrium lengths by theSETTLE algorithm (50) for water and the LINCS algorithm (51)for other molecules. The Lennard–Jones interactions were eval-uated by using a 0.9/1.4-nm twin-range cutoff. Electrostaticinteractions were evaluated by using the smooth particle meshEwald algorithm (52, 53) with 0.9-nm real space cutoff, 0.12-nmFourier spacing, and tinfoil boundary conditions. An umbrellasampling protocol was used to sample in the range of r � 0.64to 2.4 nm for A20 and 0.8 to 2.4 nm for L20, using a harmonicbiasing potential with a spacing of 0.1 nm and a force constantof 3,000 kJ�mol�1�nm�2. The results were unbiased with theweighted histogram analysis method (54). The simulations wereperformed as part of the Canadian Internetworked ScientificSupercomputer Project in essentially 1 day on all academicsupercomputers in Canada (55). For each r at a given T, 6 ns ofmolecular dynamics was simulated, with data from the first 1 nsdiscarded to ensure equilibration. The remaining 5 ns was splitinto five 1-ns blocks, which were treated independently on thebasis of rapid fluctuations in r and in water density (data notshown). A total of 3.2 �s of simulation time was collected.

PMFs of helix–helix association at several Ts are shown insupporting information (SI) Fig. 4. The heat capacity function wasobtained by linear fit to the equation:

�Cp�r �d

dT�U�T, r, [1]

where �U(T, r) is the change in total potential energy at T, froma large helix–helix separation of 2.4 nm to separation r. The

enthalpy and entropy at T � T0 were then obtained by fitting tothe standard relation:

�G�T, r � �H0�r � T�S0�r � �Cp�r�T � T0

� T�Cp�r ln�T�T0 [2]

with �CP(r) held fixed at the value obtained from Eq. 1, and T0chosen to be 300 K. Fits were performed by Mathematica 5.1from Wolfram Research, (Champaign, IL) using the Regress andNonlinearRegress functions. Standard errors were obtained bytreating each 1-ns block as an independent sample and taking theasymptotic standard error (as returned by NonlinearRegress).

As a consistency check, we also computed �H0 directly fromthe potential energies; the results are in good agreement with Eq.2 (SI Fig. 5). To assess robustness of our results across differentforce fields, as has been ascertained for small nonpolar solutes(20), we repeated the PMF and volume calculations for L20 byusing the GROMOS ffG53a5 force field (56). The similarity ofthe predictions from the two force fields (SI Fig. 6 and SI Fig.7) provides evidence that our results are representative ofgeneral physical trends in nanoscale hydrophobic interactions.

We thank Paul Lu of University of Alberta for help with matters related tothe Third Canadian Internetworked Scientific Supercomputer Project(CISS-3) distributed computing effort and Walter Ash for preparing thestarting structures used in this study. J.L.M. is supported by the NaturalSciences and Engineering Research Council, Alberta Ingenuity, and KillamTrust studentships. M.S.M is supported in part by a Premier’s ResearchExcellence Award (Ontario) to H.S.C., who holds a Canada Research Chairin Proteomics, Bioinformatics, and Functional Genomics. D.P.T. is a SeniorScholar of the Alberta Heritage Foundation for Medical Research, aCanadian Institutes of Health Research New Investigator, and a SloanFoundation Fellow. This research was also supported by grants from theCanadian Institutes of Health Research (to H.S.C. and D.P.T.). Computa-tions for this work were made possible by the Third Canadian Internet-worked Scientific Supercomputer Project (CISS-3) and WestGrid.

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