The Role of Solute Attractive Forces in the Atomic-Scale Theory of

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The Role of Solute Attractive Forces in the Atomic-Scale Theory of Hydrophobic Effects Ang Gao, Liang Tan, Lawrence R. Pratt, Mangesh I. Chaudhari, Susan B. Rempe, Dilipkumar Asthagiri, and John D Weeks J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b01711 • Publication Date (Web): 16 May 2018 Downloaded from http://pubs.acs.org on May 16, 2018

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The Journal of Physical Chemistry

The Role of Solute Attractive Forces in the Atomic-Scale Theory of Hydrophobic Effects Ang Gao,† Liang Tan,‡ Mangesh I. Chaudhari,¶ D. Asthagiri,§ Lawrence R. Pratt,∗,‡ Susan B. Rempe,¶ and John D. Weeks† †Institute for Physical Science and Technology, and Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA ‡Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, LA 70118, USA ¶Center for Biological and Engineering Sciences, Sandia National Laboratories, Albuquerque, NM 87185, USA §Chemical and Biomolecular Engineering Rice University, Houston, TX USA E-mail: [email protected] Phone: 504-862-8929

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The role that van der Waals (vdW) attractive forces play in the hydration and association of atomic hydrophobic solutes like argon (Ar) in water is reanalyzed using the local molecular field (LMF) theory of those interactions. In this problem, solute vdW attractive forces can reduce or mask hydrophobic interactions as measured by contact peak heights of the ArAr correlation function compared to reference results for purely repulsive core solutes. Nevertheless, both systems exhibit characteristic hydrophobic inverse temperature behavior in which hydrophobic association become stronger with increasing temperature through a moderate temperature range. The new theoretical approximation obtained here is remarkably simple and faithful to the statistical mechanical LMF assessment of the necessary force balance. Our results extend and significantly revise approximations made in a recent application of the LMF approach to this problem, and, unexpectedly, support a theory of nearly 40 years ago.

Introduction The theory of hydrophobic effects has presented extended challenges to theoretical physical chemistry. 1–6 Attempts have been made to rationalize the peculiarities of aqueous solutions using intuitive notions of water structure and molecular bonding. But defensible statistical mechanics based theories of hydrophobic effects have often used concepts and approximations seemingly in conflict with standard intuitions and experiments. The Pratt-Chandler (PC) theory for hydrophobic interactions in a dilute solution of hydrophobic solutes 7 is a prime example of such a theory, 8–10 though recent work has provided a logically compelling reinterpretation. 11 The foremost experimental challenge of the PC theory, and an outstanding characteristic of hydrophobic interactions, is the inverse temperature behavior in which hydrophobic interactions or association as measured by the peak height of the solute-solute radial distribution function (RDF) increases with increasing temperature, 2


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for moderate temperatures. 9,10,12 The first analysis of that theoretical discrepancy focused on the influence of long-ranged attractive van der Waals (vdW) forces 13,14 involving the dilute hydrophobic solutes, interactions neglected by the PC theory. Nevertheless, those results have not been compelling, as discussed below. Here we revisit this issue, using modern developments in Local Molecular Field (LMF) theory, 3,15–19 which provide a quantitative framework for assessing the differing roles of short- and long-ranged interactions in nonuniform liquids. In particular, we consider the role of solute vdW attractions on both the inverse temperature behavior and the absolute peak height of relevant pair correlation functions. The system treated here, a dilute aqueous solution of argon (Ar), is simple and experimentally realizable. Results can be compared directly both to simulations using a Lennard-Jones (LJ) potential for Ar and to the repulsive core model system 20 considered by PC with only short-ranged repulsive Ar-Ar and Ar-water LJ core forces. This choice 21,22 puts simulation complexity in the background, statistical theory in the foreground, and should permit the best opportunity to secure physical lessons of broad relevance. [To simplify the presentation below, we denote the atomic Ar solute as A, the repulsive core solute as A0 , and the water oxygen as W.] Figure 1 gives new results from extended molecular dynamics simulations for the AA RDF in water for a range of temperatures, and the inset shows corresponding results for the A0 core model. The peak heights of the AA RDFs are about 60% of those of the core system, illustrating the reduction in the strength of hydrophobic interactions from attractive vdW forces. But both systems show strong inverse temperature behavior in their association. In contrast, Figure 2 shows that solute-water vdW attractions have little effect on hydrophobic hydration, as measured by the peak height of the AW and A0 W RDFs at 300K. Moreover, the inset shows that peaks are lower at higher temperatures, in further contrast to the inverse temperature behavior of gAA . The effects of solute attractive forces are clearly different in hydrophobic hydration and

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6

4

T = 360K T = 320K T = 300K

5 4 3

3

2 1

2

0

gA0A0 (r) 0.3

0.4

0.5 0.6 r (nm)

0.7

0.8

1 gAA(r) 0

0.3

0.4

0.5

0.6 0.7 r (nm)

0.8

0.9

1.0

Figure 1: Radial distribution function of argon atoms (A) modeled as Lennard-Jones spheres in SPC/E water. Note the strong hydrophobic contact attraction, together with the clear inverse temperature behavior. The 97% confidence intervals for the T = 300K results, evaluated with GROMACS weighted-histogram (WHAM) bootstrap tools, 23 are smaller than the plotting symbols. The inset shows the radial distribution function of repulsive core A0 atoms, again showing strong inverse temperature behavior but with notably higher first peak heights. See Methods section below for procedural details. interaction phenomena. This differing behavior was predicted long ago in a subsequent paper by Pratt and Chandler (PC2). 14 That theory assumed a weak dependence of the hydrophobic hydration pattern on attractive solute forces, appropriate for small solutes, 24,25 just as seen in Figure 2. The observed sensitivity of the hydrophobic interactions (Figure 1) then was attributed to a competition between the strengths of the solute-water and solute-solute attractive forces suggested by a simple counting of nearest neighbors around the solutes. As they noted, this competition, relative to the behavior of repulsive solutes, differs from that considered in standard solution thermodynamic theories, e.g., the Flory-Huggins theory. 26,27 This compe-

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2.0

gWA(r) gWA0 (r)

1.5 T = 300K

1.0

2.0

360K 320K 300K

1.5

0.5

1.0

0.5

0.0 0.2

0.4

gWA(r) 0.3

0.4

0.5

0.6 0.8 r (nm)

0.6

1.0

0.7

0.8

1.2

Figure 2: WA radial distribution function gWA compared to that for a repulsive core A0 at 300K, showing that attractive interactions have little effect on the height of the first peak. The inset shows that the gWA also do not show the inverse temperature behavior. Thus, in contrast to Figure 1, the WA radial distribution functions are not naively symptomatic of hydrophobic interactions. tition was expressed in their approximation for the difference in the solute-solute potential of mean force w (cf. Eq. (11) or Eq. (15) of Ref. 14), which can be written as

wAA (r) − wA0 A0 (r) ≈ u1,AA (r) + 2

Z

dr 0 ρW|A0 A0 (r 0 |0, r) − ρW|A0 (r0 |0) u1,WA (r0 )

(1)

using notation explained in the theory section below. This combined PC2 theory, including an approximation to Eq. (1) for the effects of attractions, was confirmed by simulation 28 to be accurate quantitatively for the LJ-methane correlation function studied at a fixed temperature, though the fidelity of the LJ parameters PC used to model CH4 (aq) was disputed. Nevertheless, the overall picture remained unclear because the original PC theory was 5



not tested directly for the repulsive core case it targeted and in fact it is not quantitatively accurate in that case. 11 (The accuracy found in Ref. 28 probably arises because attractive interactions dominate for the solute model used.) The initial compelling molecular simulations of hydrophobic association also used full LJ interactions, 29,30 and did not separate competing effects from long-ranged vdW attractions and core repulsions. In the absence of a generally accepted statistical mechanical theory, the overall situation thus remained unresolved. Recent developments in LMF theory 3,15–19 provide a new statistical mechanics based framework that can clarify the role of solute attractive interactions in hydrophobic hydration and association. As recognized by Chaudhari, et al., 21 the theory takes an especially simple form in the infinite dilution limit considered by PC. Here we present a detailed treatment of this limit that strongly supports the ideas leading to Eq. (1). Our approach leads to even simpler and physically suggestive expressions for the difference in the potentials of mean force (see Eqs. (12)-(14) below) that are in good agreement with simulation results. This significantly revises some conclusions from the initial LMF treatment in Ref. 21, which found poor agreement arising from the use of an additional EXP approximation not consistent with Eq. (1), as explained below.

Theory We consider a uniform dilute solution of A solute atoms with a bulk number density ρA > 0 in water (W) with a bulk density ρW , anticipating the limit of infinite dilution as ρA → 0. Figure 3 depicts the system of interest and the notation used below. The vdW interactions between a solute A and another A or a W (oxygen) a distance r away are given by LJ pair potentials. This potential can be separated according to the sign of the force 20 into a repulsive core component u0 and a longer-ranged attractive component u1 . To relate properties of the repulsive core system to those of the full system we consider partially coupled solutes Aλ for

6


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0 ≤ λ ≤ 1 with LJ interactions given by uWAλ (r) = u0,WA (r) + λu1,WA (r)

(2)

uAλ Aλ (r) = u0,AA (r) + λu1,AA (r) .

(3)

and

The radial distribution function gAλ Aλ (r) = e−βwAλ Aλ (r) .

(4)

introduces also the potential of mean force wAλ Aλ (r). The potential of mean force may be obtained from the free energy change, wAλ Aλ (r) = Ωrλ − Ω∞ λ ,

(5)

when two infinitely separated Aλ solutes are moved to a relative separation r. Here Ωrλ denotes the grand free energy when the two Aλ solutes are at a fixed relative distance r as in the right panel of Figure 3. With that geometrical definition, our development of Eq. (5) will center on the density distortion δρW|Aλ Aλ (r 0 |0, r) = ρW|Aλ Aλ (r 0 |0, r) − ρW .

(6)

where ρW|Aλ Aλ (r 0 |0, r) ≡ ρW gW|Aλ Aλ (r 0 |0, r) is the conditional W (oxygen) density at r 0 given that the Aλ solutes are fixed at 0 and r. Differentiating these free energies with respect to the energy scaling parameter λ yields

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an exact, formal result for infinitely dilute solutes ∂wAλ Aλ (r) = u1,AA (r) + ∂λ

Z

dr 0 δρW|Aλ Aλ (r 0 |0, r) u1,WA (ra0 ) + u1,WA (rb0 ) Z − lim dr 0 δρW|Aλ Aλ (r 0 |0, r) u1,WA (ra0 ) + u1,WA (rb0 ) . (7) r→∞

This can be exactly rewritten as ∂wAλ Aλ (r) = u1,AA (r) + 2 ∂λ

Z

dr 0 δρW|Aλ Aλ (r 0 |0, r) − δρW|Aλ (r0 |0) u1,WA (r0 ) ,

(8)

because the density perturbations from the solutes add independently, δρW|Aλ Aλ (r 0 |0, r) ≈ δρW|Aλ (ra0 |0) + δρW|Aλ (rb0 |0) ,

(9)

when r → ∞. If we assume, as in PC2, a small dependence of the WA density perturbations δρW|Aλ Aλ and δρW|Aλ on the attractive forces, integrating over λ leads directly to Eq. (1). Consulting Figure 2, this is a accurate approximation for small A solutes. Thus, Eq. (8) clarifies the notation and approximations leading to Eq. (1). Eq. (8) still contains three-body conditional densities and further approximations are needed for simple results. In the original PC2 applications, 7,14 a RISM calculation provided a practical two-body contraction. That procedure is a trivial numerical effort, and should be accurate. Here we use LMF based arguments 3,15–19 to obtain accurate and even simpler approximations to Eq. (8). Eq. (9) is exact at large separations. We expect its use when convoluted with the slowly varying u1,WA in Eq. (8) should still yield accurate results at smaller solute separations, though with increasing error for decreasing r. Eq. (9) is also reminiscent of the proximity approximation 31–33 and those ideas may provide additional support for its use here. 8


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W

$** (()

W

W +, − + = +,0

+, = +,.

A#

$%&%& (()

A#

A#

1

+

A# 2

Figure 3: Notation used in our derivation. The left panel shows the interactions of the partially coupled solute Aλ and water W with LJ potentials uWAλ (r) and uAλ Aλ (r) given in Eqs. (2) and (3) respectively. The right panel shows the coordinates for Aλ and W. The two solutes are denoted as a and b respectively, and their relative displacement is r. The displacements of a particular water oxygen relative to the two solutes are denoted as r 0a and r 0b respectively. Using Eq. (9) to approximate the term in braces in Eq. (8), we find ∂wAλ Aλ (r) ≈ u1,AA (r) + 2 ∂λ

Z

dr 0 δρW|Aλ (r0 |0)u1,WA (|r 0 − r|) .

(10)

Figure 4 gives simulation results for the system of interest showing that this approximation for the last term remains remarkably accurate even at small r provided that the solute cores do not significantly overlap. We also expect smooth changes in δρW|Aλ in Eq. (10) from the slowly varying u1 as λ is varied. PC2 neglected those changes, but a better approximation, consistent with the assumption of Gaussian fluctuations, takes the simplest linear approximation, δρW|Aλ (r0 |0) ≈ δρW|A0 (r0 |0) + λ δρW|A (r0 |0) − δρW|A0 (r0 |0) .

(11)

Eq. (10) can then be integrated over 0 ≤ λ ≤ 1 to obtain wAA (r) − wA0 A0 (r) ≈ u1,AA (r) +

Z

dr 0 δρW|A (r0 |0) + δρW|A0 (r0 |0) u1,WA (|r 0 − r|) . (12) 9



3

0.5 0.4

2

0.3 0.2

gAA(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1

0.1 0.0 0

0.2

0.4 0.6 r (nm)

0.8

0 1.0

Figure 4: The red simulation results curve gives for T0 = 300K and p = 1 atm corR circle 0 0 0 responding to β dr δρ (r |0, r) − δρ (r |0) u1,WA (r ). The solid black curve gives W|AA W|A R 0 0 0 β dr δρW|A (r |0)u1,WA (|r − r|). Both curves are scaled by kB T , and their difference is less than 0.08 for separations greater than 0.3 nm, where the AA RDF gAA (r) (blue dotted curve) is substantially different from zero. The Gaussian approximation in Eq. (12) can account for soft interface fluctuation effects around large hydrophobic solutes 18,24,25 and previous work 19,34 has shown it is accurate for both small and large solutes. Quasi-chemical theory 35 offers another perspective where such fluctuation effects are typically taken into account. In the small solute case considered here, the original PC assumption of small changes in the solute-solvent correlation function from attractive interactions is accurate and further approximations can be made. Thus replacing δρW|A in Eq. (12) by δρW|A0 we arrive at a striking simplification of Eq. (1) involving only pair correlations between a single truncated solute and water:

wAA (r) − wA0 A0 (r) ≈ u1,AA (r) + 2

Z 10

dr 0 δρW|A0 (r0 |0)u1,WA (|r 0 − r|) .


(13)

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Results for the last term in Eq. (13) are shown as magenta circles in Figure 5 The opposite replacement where δρW|A0 in Eq. (12) is replaced by δρW|A gives

wAA (r) − wA0 A0 (r) ≈ u1,AA (r) + 2

Z

dr 0 δρW|A (r0 |0)u1,WA (|r 0 − r|) .

(14)

The last term in Eq. (14) is plotted as a red chain-dotted line in Figure 5. At 0.4 nm it differs from the results of Eq. (13) by only 0.11kB T. This approximation needs only full solute-water pair correlations, and in principle experimental data could be used. The EXP approximation considered previously in Ref. 21 generated exactly the same functional forms as in Eq. (14), but without the crucial explicit factor of 2 in the last term. The authors noted that the poor results they found were probably associated with the asymmetric treatment of correlations around the a and b solutes produced by EXP. In the LMF treatment here, and in the original work of PC2, this symmetry and the factor of 2 appears naturally and much more accurate results are found.

Discussion This study extends and revises recent reconsiderations of the effects of solute attractive forces on hydrophobic interactions. 21 Unexpectedly, the present study supports the outlook of nearly 40 years ago: 14,29 solute attractive forces can mask hydrophobic interactions as traditionally conceived, 22,35 indeed possibly leading to “. . . results that contradict the conventional wisdom on hydrophobic interaction . . . ” 29 This masking leads to basic physical conclusions that deserve emphasis for molecular modeling of aqueous solution phenomena. Firstly, although net hydrophobic effects from core steric/packing effects can stabilize compact and aggregated biomolecular structures, the remaining hydration effects may loosen the aggregate if intra-aggregate attractive interactions are fully included. We believe this conclusion is consistent with the body of biomolecular simulation results. 36,37 Such effects can be illustrated dramatically in the dilute solution limit considered here for 11



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0.8 0.6

2

0.4 0.2

R

dr′ δρW|A (r ′ |0)βu1,WA (|r′ − r|)

theory net

β [wAA (r) − wA0 A0 (r)]

0.0 −0.2 −0.4

T = 300K

βu1,AA (r)

0.4

0.6 r (nm)

0.8

Figure 5: Comparison of theory with simulation utilizing the last term in Eq. (13) (magenta circles) and in Eq. (14) (red chain-dotted line). The solid black curve is the simulation result of Ref. 21. The dashed-black curve is the sum of the red and blue curves and is the present estimate of the net theory. The red and blue curves have opposite signs, emphasizing that the theory balances opposing effects. These results should be compared to those in Figure 4 of Ref. 21. the simple single-site Girifalco model of C60 solutes in water studied in Ref. 18. Simulations show there is strong hydrophobic association of two model repulsive core fullerenes in water. In contrast, fullerenes with realistic attractive LJ attractions are hydrophilic and experience no attractive solvent-induced association forces, even though there is a minimum at contact from the strong direct solute-solute vdW attractions. Secondly, when the modeling and theoretical problems are cast in the context that the external aqueous solution is integrated-out — as in osmotic problems — the strengths of the remaining attractive forces effects can come together in an unfamiliar pattern. We have noted above such a distinction of the present work with Flory-Huggins theory. Indeed the 12


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Flory-Huggins interaction parameter involved in aqueous solutions of water-soluble polymers may have concentration dependences that are not anticipated by text-book derivations of that basic theoretical approach. 27

Models and Simulation Methods The simulations were carried-out with the GROMACS package, 38 the SPC/E model of the water molecules, 39 and the OPLS force field. GROMACS selects the SETTLE 40 constraint algorithm for rigid SPC/E water molecules. The same constraint algorithm was used in previous simulations involving water. 11,41 Parameters for the Ar LJ interactions were εWA = 0.798 kJ/mol, σWA = 0.328 nm, εAA = 0.978 kJ/mol, and σAA = 0.340 nm. Some cases treated A0 atoms which exerted only LJ repulsive forces, the traditional WCA reference case, on the water O atoms. That modification was implemented with tabulated potentials following the GROMACS manual. Standard periodic boundary conditions were employed, with particle mesh Ewald utilizing a cutoff of 1 nm and long-range dispersion corrections applied to energy and pressure. The Parrinello-Rahman barostat controlled the pressure at 1 atm, and the Nose-Hoover thermostat was used to maintain the temperature. Two Ar atoms were hydrated in 1000 SPC/E water molecules. The solute-solute separation spanning 0.33 nm to 1.23 nm was stratified using a standard windowing approach and the results combined using the weighted histogram analysis method (WHAM). 23 This involved 19 windows (and simulations) for window separations r ranging from 0.33 nm to 1.23 nm.

Acknowledgement Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Secu13



rity Administration under contract DE-NA0003525. This work was supported by Sandia’s LDRD program (MIC and SBR) and by the National Science Foundation, Grant CHE1300993. This work was performed, in part, at the Center for Integrated Nanotechnologies (CINT), an Office of Science User Facility operated for the U.S. DOE’s Office of Science by Los Alamos National Laboratory (Contract DE-AC52-06NA25296) and SNL.

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(19) Remsing, R. C.; Liu, S.; Weeks, J. D. Long-ranged Contributions to Solvation Free Energies from Theory and Short-ranged Models. Proc. Nat. Acad. Sci. USA 2016, 113, 2819–2826. (20) Weeks, J. D.; Chandler, D.; Andersen, H. C. Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids. J. Chem. Phys. 1971, 54, 5237–5247. (21) Chaudhari, M. I.; Rempe, S. B.; Asthagiri, D.; Tan, L.; Pratt, L. R. Molecular Theory and the Effects of Solute Attractive Forces on Hydrophobic Interactions. J. Phys. Chem. B 2016, 120, 1864–1870. (22) Pratt, L. R.; Chaudhari, M. I.; Rempe, S. B. Statistical Analyses of Hydrophobic Interactions: A Mini-review. J. Phys. Chem. B 2016, 120, 6455–6460. (23) Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swedsen, R. H.; Kollman, P. A. The Weighted Histogram Analysis Method for Free-Energy Calculation on Biomolecules. I. The Method. J. Comp. Chem. 1992, 13, 1011–1021. (24) Lum, K.; Chandler, D.; Weeks, J. Hydrophobicity at Small and Large Length Scales. J. Phys. Chem. B 1999, 103, 4570–4577. (25) Chandler, D. Interfaces and the Driving Force of Hydrophobic Assembly. Nature 2005, 437, 640–647. (26) Doi, M. Introduction to Polymer Physics; Oxford University Press, 1996. (27) Chaudhari, M.; Pratt, L.; Paulaitis, M. E. Concentration Dependence of the FloryHuggins Interaction Parameter in Aqueous Solutions of Capped PEO Chains. J. Chem. Phys. 2014, 141, 244908. (28) Smith, D. E.; Haymet, A. D. J. Free Energy, Entropy, and Internal Energy of Hydrophobic Interactions: Computer Simulations. J. Chem. Phys. 1993, 98, 6445–6454.

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(29) Watanabe, K.; Andersen, H. C. Molecular-Dynamics Study of the Hydrophobic Interaction in an Aqueous-Solution of Krypton. J. Phys. Chem. 1986, 90, 795 – 802. (30) Pangali, C.; Rao, M.; Berne, B. J. A Monte Carlo Simulation of the Hydrophobic Interaction. J. Chem. Phys. 1979, 71, 2975. (31) Garde, S.; Hummer, G.; Garc´ıa, A. E.; Pratt, L. R.; Paulaitis, M. E. Hydrophobic Hydration: Inhomogeneous Water Structure Near Nonpolar Molecular Solutes. Phys. Rev. E 1996, 53, R4310. (32) Ashbaugh, H. S.; Paulaitis, M. E. Effect Of Solute Size and Solute-Water Attractive Interactions on Hydration Water Structure around Hydrophobic Solutes. J. Am. Chem. Soc. 2001, 123, 10721–10728. (33) Ashbaugh, H. S.; Pratt, L. R.; Paulaitis, M. E.; Clohecy, J.; Beck, T. L. Deblurred Observation of the Molecular Structure of an Oil-Water Interface. J. Am. Chem. Soc. 2005, 127, 2808–2809. (34) Gao, A. Manipulating and Simplifying the Intermolecular Interactions in Liquid Mixtures. ProQuest Dissertations and Theses 2017, (35) Asthagiri, D.; Merchant, S.; Pratt, L. R. Role of Attractive Methane-Water Interactions in the Potential of Mean Force between Methane Molecules in Water. J. Chem. Phys. 2008, 128, 244512. (36) Tomar, D. S.; Weber, V.; Pettitt, B. M.; Asthagiri, D. Importance of Hydrophilic Hydration and Intramolecular Interactions in the Thermodynamics of Helix–Coil Transition and Helix–Helix Assembly in a Deca-Alanine Peptide. J. Phys. Chem. B 2015, 120, 69–76. (37) Asthagiri, D.; Karandur, D.; Tomar, D. S.; Pettitt, B. M. Intramolecular Interactions

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Overcome Hydration to Drive the Collapse Transition of Gly15. J. Phys. Chem. B 2017, 121, 8078–8084. (38) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory. Comput. 2008, 4, 435–447. (39) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Missing Term in Effective Pair Potentials. J Phys Chem 1987, 91, 6269–6271. (40) Miyamoto, S.; Kollman, P. A. SETTLE: An Analytical Version of the Shake and Rattle Algorithm for Rigid Water Models. J. Comp. Chem. 1992, 13, 952–962. (41) Chaudhari, M. I.; Sabo, D.; Pratt, L. R.; Rempe, S. B. Hydration of Kr(aq) in Dilute and Concentrated Solutions. J. Phys. Chem. B 2015, 119, 9098–9102.

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TOC graphic

0.8 masking hydration effect 0.4 kB T

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theory

MD simulation

0.0 T = 300K −0.4

bare LJ attraction 0.4

0.6 r (nm)

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0.8

The Role of Solute Attractive Forces in the Atomic-Scale Theory of

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