Free energy, entropy, and internal energy of hydrophobic interactions: Computer simulations

Smith, David Eugene; Haymet, A. D. J.

doi:10.1063/1.464809

Cited by 273 publications

(284 citation statements)

References 59 publications

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“…Figure 2A shows the free energy of association or PMF for two methane molecules in TIP4P water at 25 "C. As noted previously in similar calculations (Jorgenson et al, 1988), there is a pronounced minimum at contact, and a second minimum for a solvent-separated pair. A virtually identical curve was obtained previously (Smith & Haymet, 1993) using SPC water and molecular dynamics rather than Monte Carlo sampling: the minima and maxima are in precisely the same positions, and the differences in free energy between the solvent-separated and contact minima (0.59 t 0.06 kcal/ mol) are very similar. Thus, the methane methane PMF is not sensitive to the differences in the water models.…”

Section: Resultssupporting

confidence: 76%

A desolvation barrier to hydrophobic cluster formation may contribute to the rate‐limiting step in protein folding

1997

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To gain insight into the free energy changes accompanying protein hydrophobic core formation, we have used computer simulations to study the formation of small clusters of nonpolar solutes in water. A barrier to association is observed at the largest solute separation that does not allow substantial solvent penetration. The barrier reflects an effective increase in the size of the cavity occupied by the expanded but water-excluding cluster relative to both the close-packed cluster and the fully solvated separated solutes; a similar effect may contribute to the barrier to protein foldinghnfolding. Importantly for the simulation of protein folding without explicit solvent, we find that the interactions between nonpolar solutes of varying size and number can be approximated by a linear function of the molecular surface, but not the solvent-accessible surface of the solutes. Comparison of the free energy of cluster formation to that of dimer formation suggests that the assumption of pair additivity implicit in current protein database derived potentials may be in error. Keywords: hydrophobic interaction; potential of mean force; protein foldingThe hydrophobic interaction is extremely important in the folding and stabilization of proteins (Kauzmann, 1959;Dill, 1990), but is relatively poorly understood. In spite of this poor understanding, computer modeling of protein folding has developed substantially over the past IO years. One approach is to simulate protein folding in the presence of explicitly modeled water molecules, which, depending upon the accuracy of the water model, should at least in part reproduce the hydrophobic interaction. Molecular dynamics simulations with an explicit solvent model have provided valuable insights into possible foldinghnfolding trajectories (Daggett & Levitt, 1994;Karplus & Sali, 1995). However, because of the complexity of the processes being simulated and the absence of an obvious reaction coordinate, most studies have focused on qualitative features of the trajectories and not sought to calculate free energy changes (the study of Brooks and Boczko [I9951 is an exception). A second approach avoids the complexity and high computational demands of simulations with hundreds of explicit water molecules by deriving effective potentials from the distribution of amino acid residues in known protein structures (reviewed in Jones & Thornton, 1996). Although not modeled explicitly, the hydrophobic interaction dominates such "knowledge-based' potentials. These relationships are not true interaction potentials in a rigorous sense, but they have been extremely useful in a wide variety of applications, including protein fold recognition (Jones &

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Section: Resultssupporting

confidence: 76%

A desolvation barrier to hydrophobic cluster formation may contribute to the rate‐limiting step in protein folding

1997

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“…47,49,80,81,82,83,84,85 This free energy profile defines a PMF. We obtain the cavity contribution to the methane-methane PMF by calculating the excess chemical potential, µ ex (r), of a cavity volume described by two spheres each of radius d and separated by a distance r. The PMF is then defined as W (r) = µ ex (r) − lim s→∞ µ ex (s).…”

Section: B Methane-methane Potential Of Mean Force (Pmf)mentioning

confidence: 99%

“…Figure 7 shows a comparison of the cavity PMF calculated using IT with that obtained from explicit simulations by Smith and Haymet. 81 The flat default model has been used here and throughout this paper, unless otherwise noted. Also, an exclusion radius of d = 0.33 nm has been used for methane-size cavities corresponding to a distance where the methane-water oxygen radial distribution function reaches a value of 1.0 in commonly used models.…”

Section: B Methane-methane Potential Of Mean Force (Pmf)mentioning

confidence: 99%

Hydrophobic Effects on a Molecular Scale

et al. 1998

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A theoretical approach is developed to quantify hydrophobic hydration and interactions on a molecular scale, with the goal of insight into the molecular origins of hydrophobic effects. The model is based on the fundamental relation between the probability for cavity formation in bulk water resulting from molecular-scale density fluctuations, and the hydration free energy of the simplest hydrophobic solutes, hard particles. This probability is estimated using an information theory (IT) approach, incorporating experimentally available properties of bulk water -the density and radial distribution function. The IT approach reproduces the simplest hydrophobic effects: hydration of spherical nonpolar solutes, the potential of mean force (PMF) between methane molecules, and solvent contributions to the torsional equilibrium of butane. Applications of this approach to study temperature and pressure effects provide new insights into the thermodynamics and kinetics of protein folding. The IT model relates the hydrophobic-entropy convergence observed in protein unfolding experiments to the macroscopic isothermal compressibility of water. A novel explanation for pressure denaturation of proteins follows from an analysis of the pressure stability of hydrophobic aggregates, suggesting that water penetrates the hydrophobic core of proteins at high pressures. This resolves a long-standing puzzle, whether pressure denaturation contradicts the hydrophobic-core model of protein stability. Finally, issues of "dewetting" of molecularly large nonpolar solutes are discussed in the context of a recently developed perturbation theory approach.

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“…As a consequence, with increasing temperature the association of hydrophobic particles is found to be enhanced in order to minimise the solvation entropy penalty [8,9]. This entropy-driven association process is usually referred to as hydrophobic interaction and has been subject of numerous simulation studies [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. * dietmar.paschek@udo.edu; http://ganter.chemie.uni-dortmund.de/~pas/ Hydrophobic effects are considered to play an important role concerning protein stability and other self assembly phenomena [4,28,29].…”

Section: Introductionmentioning

confidence: 99%

Temperature dependence of the hydrophobic hydration and interaction of simple solutes: An examination of five popular water models

Paschek

2004

The Journal of Chemical Physics

273

326

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We examine five different popular rigid water models (SPC, SPCE, TIP3P, TIP4P and TIP5P) using molecular dynamics simulations in order to investigate the hydrophobic hydration and interaction of apolar Lennard-Jones solutes as a function of temperature in the range between 275 K and 375 K along the 0.1 MPa isobar. For all investigated models and state points we calculate the excess chemical potential for the noble gases and Methane employing the Widom particle insertion technique. All water models exhibit too small hydration entropies, but show a clear hierarchy. TIP3P shows poorest agreement with experiment whereas TIP5P is closest to the experimental data at lower temperatures and SPCE is closest at higher temperatures. As a first approximation, this behaviour can be rationalised as a temperature-shift with respect to the solvation behaviour found in real water. A rescaling procedure inspired by information theory model of Hummer et al. (Chem.Phys. 258, 349-370 (2000)) suggests that the different solubility curves for the different models and real water can be largely explained on the basis of the different density curves at constant pressure. In addition, the models that give a good representation of the water structure at ambient conditions (TIP5P, SPCE and TIP4P) show considerably better agreement with the experimental data than the ones which exhibit less structured O-O correlation functions (SPC and TIP3P). In the second part of the paper we calculate the hydrophobic interaction between Xenon particles directly from a series of 60 ns simulation runs. We find that the temperature dependence of the association is to a large extent related to the strength of the solvation entropy. Nevertheless, differences between the models seem to require a more detailed molecular picture. The TIP5P model shows by far the strongest temperature dependence. The suggested density-rescaling is also applied to the chemical potential in the Xenon-Xenon contact-pair configuration, indicating the presence of a temperature where the hydrophobic interaction turns into purely repulsive. The predicted association for Xenon in real water suggest the presence a strong variation with temperature, comparable to the behaviour found for TIP5P water. Comparing different water models and experimental data we conclude that a proper description of density effects is an important requirement for a water model to account correctly for the correct description of the hydrophobic effects. A water model exhibiting a density maximum at the correct temperature is desirable.

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Free energy, entropy, and internal energy of hydrophobic interactions: Computer simulations

Cited by 273 publications

References 59 publications

A desolvation barrier to hydrophobic cluster formation may contribute to the rate‐limiting step in protein folding

A desolvation barrier to hydrophobic cluster formation may contribute to the rate‐limiting step in protein folding

Hydrophobic Effects on a Molecular Scale

Temperature dependence of the hydrophobic hydration and interaction of simple solutes: An examination of five popular water models

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