Extended Surfaces Modulate Hydrophobic Interactions of Neighboring Solutes

Extended surfaces modulate hydrophobic interactions of neighboring solutes Amish J. Patela, Patrick Varillyb, Sumanth N. Jamadagnia,c, Hari Acharyaa, Shekhar Gardea,1, and David Chandlerb,1 aHoward P. Isermann Department of Chemical and Biological Engineering, and Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, Troy, NY 12180; bDepartment of Chemistry, University of California, Berkeley, CA 94720; and cProcter and Gamble Company, Beckett Ridge Technical Center, West Chester, OH 45069 Edited by B. J. Berne, Columbia University, New York, NY, and approved September 1, 2011 (received for review July 5, 2011) Interfaces are a most common motif in complex systems. To under- phobic surfaces will bind to and catalyze unfolding of proteins, stand how the presence of interfaces affects hydrophobic phenom- which we predict is relevant in the formation of amyloids and the ena, we use molecular simulations and theory to study hydration function of chaperonins. of solutes at interfaces. The solutes range in size from subnan- ometer to a few nanometers. The interfaces are self-assembled Models monolayers with a range of chemistries, from hydrophilic to hydro- Molecular Simulations. We simulate the solid–water interfaces of phobic. We show that the driving force for assembly in the vicinity self-assembled monolayers (SAMs) of surfactants (Fig. 1A) with of a hydrophobic surface is weaker than that in bulk water and a range of head-group chemistries, from hydrophobic (−CH3)to decreases with increasing temperature, in contrast to that in the hydrophilic (−OH) (8, 10). To study the size dependence of bulk. We explain these distinct features in terms of an interplay hydration at interfaces, we selected cuboid shaped (L × L × W) between interfacial fluctuations and excluded volume effects—the cavities, with thickness W ¼ 0.3 nm, and side L, varying from physics encoded in Lum–Chandler–Weeks theory [Lum K, Chandler small values comparable to the size of a water molecule to as D, Weeks JD (1999) J Phys Chem B 103:4570–4577]. Our results sug- large as 10 times that size. Thicker volumes will show qualitatively gest a catalytic role for hydrophobic interfaces in the unfolding of similar behavior, but will gradually sample the “bulk” region BIOPHYSICS AND proteins, for example, in the interior of chaperonins and in amyloid away from the interface. We model the monolayers and water formation. with reasonably realistic force fields. But to focus specifically on COMPUTATIONAL BIOLOGY solvent-induced hydrophobic interactions, we consider only idea- binding ∣ hydrophobicity ∣ thermodynamics lized solutes—cavities that simply expel water from the volume they occupy. Solute–solvent and solute–solute interactions be- ydrophobic effects are ubiquitous and often the most signif- yond those of excluded volume forces can further enrich our find- icant forces of self-assembly and stability of nanoscale struc- ings (5, 11, 12). H CHEMISTRY tures in liquid matter, from phenomena as simple as micelle formation to those as complex as protein folding and aggregation Theoretical Model. To rationalize the simulation results and obtain (1, 2). These effects depend importantly on length scale (3–5). additional physical insights, we developed a model based on Water molecules near small hydrophobic solutes do not sacrifice Lum–Chandler–Weeks (LCW) theory (4). LCW theory incorpo- hydrogen bonds, but have fewer ways in which to form them, lead- rates the interplay between the small length scale Gaussian den- ing to a large negative entropy of hydration. In contrast, hydrogen sity fluctuations and the physics of interface formation relevant bonds are broken in the hydration of large solutes, resulting in at larger length scales, and captures the length scale dependence an enthalpic penalty. For hydrophobic solutes in bulk water at of hydrophobic hydration in bulk water. Near hydrophobic sur- standard conditions, the cross-over from one regime to the other faces, LCW theory predicts the existence of a soft liquid– occurs at around 1 nm (3–6) and marks a change in the scaling of vapor-like interface, which has been confirmed by simulations the solvation free energy from being linear with solute volume to (7–9). being linear with exposed surface area. In bulk water, this cross- We model this liquid–vapor-like interface near a hydrophobic over provides a framework for understanding the assembly of surface, as an elastic membrane (Fig. 1B), whose energetics are small species into a large aggregate. governed by its interfacial tension and the attractive interactions Typical biological systems contain a high density of interfaces, with the surface. The free energy of cavity hydration, μex,is including those of membranes and proteins, spanning the entire related to the probability of spontaneously emptying out a cavity- spectrum from hydrophilic to hydrophobic. Whereas water near shaped volume, V. Such emptying can be conceptualized as a hydrophilic surfaces is bulk-like in many respects, water near two-step process in which interfacial fluctuations of the mem- hydrophobic surfaces is different, akin to that near a liquid–vapor brane can empty out a large fraction of V in the first step, with interface (3–5, 7–9). Here, we consider how these interfaces alter the remaining volume v emptied out via a density fluctuation hydrophobic effects. Specifically, to shed light on the thermo- (Fig. 1C). When v is small, the probability that it contains N dynamics of hydration at, binding to, and assembly at interfaces, waters is well approximated by a Gaussian (8, 13, 14). The cost we study solutes with a range of sizes at various self-assembled of emptying v can then be obtained from the average and the monolayer interfaces over a range of temperatures using molecular simulations and theory. Author contributions: A.J.P., S.G., and D.C. designed research; A.J.P., P.V., S.N.J., and H.A. Our principal results are that, although the hydration thermo- performed research; A.J.P., P.V., and S.N.J. contributed new reagents/analytic tools; A.J.P., dynamics of hydrophobic solutes at hydrophilic surfaces is similar P.V., S.N.J., and H.A. analyzed data; and A.J.P., P.V., S.G., and D.C. wrote the paper. to that in bulk, changing from entropic to enthalpic with increas- The authors declare no conflict of interest. ing solute size, it is enthalpic for solutes of all length scales near This article is a PNAS Direct Submission. hydrophobic surfaces. Further, the driving force for hydrophobi- 1To whom correspondence may be addressed. E-mail: [email protected] or chandler@ cally driven assembly in the vicinity of hydrophobic surfaces is berkeley.edu. weaker than that in bulk and decreases with increasing tempera- This article contains supporting information online at www.pnas.org/lookup/suppl/ ture, in contrast to that in bulk. These results suggest that hydro- doi:10.1073/pnas.1110703108/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1110703108 PNAS Early Edition ∣ 1of6 Downloaded by guest on September 28, 2021 A B C DE F Fig. 1. Size-dependent hydrophobic hydration at interfaces. (A) A schematic of a cuboidal cavity (green) at the SAM–water interface. The SAM head groups (black and white), alkane tails (gray), and water (red and white, partially cut out for clarity) are shown. (B) A typical configuration of the model membrane, color coded by its distance from the model surface (gray). (C) Important volumes in estimating the free energy, μex, of emptying the probe volume V (green) using the theoretical model. The region above the membrane is the volume B (blue), and the intersection of V and B is v (dark green). (D) Length-scale dependence of the cavity hydration free energy per unit area, μex∕A, in bulk water and at interfaces, at T ¼ 300 K, obtained from molecular dynamics simulations. (E) Theoretical model estimates of μex∕A, near surfaces with different attraction strengths, η.(F) Connecting the microscopic binding free energy of a cavity to an interface, to the macroscopic surface wettability. The cos θ values were obtained from molecular dynamics simulations of a water droplet on SAM γ surfaces (10). Lines are predictions using Eq. 1 with size-dependent LV taken from D. variance of the number of waters in v, which are evaluated by next to the SAM surfaces are captured well by this model, parti- assuming that water density responds linearly to surface–water cularly for the hydrophobic surfaces (with η around one), where adhesive interactions. the potential UðrÞ closely mimics the effect of the real SAM We tune the strength of the model surface–water attraction, on the adjacent water, and the agreement between theory and UðrÞ, using a parameter η, where η ≈ 1 corresponds to a hydro- simulation is nearly quantitative. For the more hydrophilic SAMs, phobic −CH3 SAM-like surface, with higher values representing the comparison is qualitative, because the simple form for UðrÞ increasingly hydrophilic surfaces. The representation of hydro- does not represent dipolar interactions well. philic surfaces in our theoretical model lacks the specific details Fig. 1D also indicates that μex becomes favorable (smaller) of hydrogen bonding interactions (e.g., between the hydrophilic with increasing surface hydrophobicity. The difference in μex at − η Δμex μex − μex OH SAM surface and water), so comparisons between high- an interface and in the bulk, ¼ int bulk, quantifies the model surfaces and hydrophilic SAM surfaces in simulations hydration contribution to the experimentally measurable free are qualitative in nature. Equations that put the above model energy of binding of solutes to interfaces. Because the solvation on a quantitative footing are given in Appendix and the details of large solutes is governed by the physics of interface formation, of its exact implementation are included in SI Text. both in bulk and at the SAM surfaces, we can approximate Δμex γ − γ − γ 2 ¼ Acð SV SL LVÞ, where Ac ¼ L is the cross-sectional Size-Dependent Hydrophobic Hydration at, and Binding to Interfaces.

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