Origin of Entropy Convergence in Hydrophobic Hydration and Protein Folding

Garde, Shekhar; Hummer, Gerhard; Garcı́a, Angel E.; Paulaitis, Michael E.; Pratt, Lawrence R.

doi:10.1103/physrevlett.77.4966

Cited by 262 publications

(389 citation statements)

References 19 publications

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“…It seems likely that the entropy change for these large-scale hydrophobic plates converges around T s , similar to the behavior observed for the hydration of small hydrophobic solutes and for the folding of proteins. 14,19,20 At this temperature, the driving force for plate association is only enthalpic. The entropic contribution increases as the temperature decreases.…”

Section: Resultsmentioning

confidence: 96%

Temperature Dependence of Dimerization and Dewetting of Large-Scale Hydrophobes: A Molecular Dynamics Study

2008

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We studied by molecular dynamics simulations the temperature dependence of hydrophobic association and drying transition of large-scale solutes. Similar to the behavior of small solutes, we found the association process to be characterized by a large negative heat capacity change. The origin of this large change in heat capacity is the high fragility of hydrogen bonds between water molecules at the interface with hydrophobic solutes; an increase in temperature breaks more hydrogen bonds at the interface than in the bulk. With increasing temperature, both entropy and enthalpy changes for association strongly decrease, while the change in free energy weakly varies, exhibiting a small minimum at high temperatures. At around T ) T s ) 360 K, the change in entropy is zero, a behavior similar to the solvation of small nonpolar solutes. Unexpectedly, we find that at T s , there is still a substantial orientational ordering of the interfacial water molecules relative to the bulk. Nevertheless, at this point, the change in entropy vanishes due to a compensating contribution of translational entropy. Thus, at T s , there is rotational order and translational disorder of the interfacial water relative to bulk water. In addition, we studied the temperature dependence of the drying-wetting transition. By calculating the contact angle of water on the hydrophobic surface at different temperatures, we compared the critical distance observed in the simulations with the critical distance predicted by macroscopic theory. Although the deviations of the predicted from the observed values are very small (8-23%), there seems to be an increase in the deviations with an increase in temperature. We suggest that these deviations emerge due to increased fluctuations, characterizing finite systems, as the temperature increases.

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Section: Resultsmentioning

confidence: 96%

Temperature Dependence of Dimerization and Dewetting of Large-Scale Hydrophobes: A Molecular Dynamics Study

2008

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“…Simulations on the isolated helix III fragment show that helix III unfolds at Ϸ420 K. This large stability comes from strong side chain contacts in helix III that are consistent with a helix conformation. The use of a constant volume in the REMD simulations overstabilizes hydrophobic contact formation at high T and may be partially responsible for the high transition T (42)(43)(44). The high transition T should be of no major concern because the folding temperature is extremely sensitive to the detailed cancellation between entropy and enthalpy.…”

Section: Resultsmentioning

confidence: 99%

Folding a protein in a computer: An atomic description of the folding/unfolding of protein A

Garcı́a

Onuchic

2003

Proc. Natl. Acad. Sci. U.S.A.

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322

334

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We study the folding mechanism of a three-helix bundle protein at atomic resolution, including effects of explicit water. Using replica exchange molecular dynamics we perform enough sampling over a wide range of temperatures to obtain the free energy, entropy, and enthalpy surfaces as a function of structural reaction coordinates. Simulations were started from different configurations covering the folded and unfolded states. Because many transitions between all minima at the free energy surface are observed, a quantitative determination of the free energy barriers and the ensemble of configurations associated with them is now possible. The kinetic bottlenecks for folding can be determined from the thermal ensembles of structures on the free energy barriers, provided the kinetically determined transition-state ensembles are similar to those determined from free energy barriers. A mechanism incorporating the interplay among backbone ordering, sidechain packing, and desolvation arises from these calculations. Large ⌽ values arise not only from native contacts, which mostly form at the transition state, but also from contacts already present in the unfolded state that are partially destroyed at the transition. T he energy landscape theory and the funnel concept, along with a new generation of experiments, have created a ''new view'' of protein folding (1-4). Folding is best described as an ensemble of converging pathways toward the native structure. For good folding sequences, these paths are all energetically very similar with barriers between them on the k B T energy scale. Minor fluctuations due to environmental or mutational changes may vary the path probabilities, but the overall global landscape flow will be only weakly altered. This leads to a key result of the energy landscape theory: protein folding dynamics can be properly understood as the diffusion of an ensemble of protein configurations over a low-dimensional free energy surface, which may be constructed by using many different order parameters.In this article, we describe the free energy landscape for protein folding simulated with full atomic details of both protein and solvent, over a broad range of temperatures. For our studies, a natural choice is the 10-55 helical fragment B of protein A from Staphylococcus aureus, using the replica exchange molecular dynamics (REMD) algorithm described by Sugita and Okamoto (5). Protein A folds into a simple three-helix bundle (6) whose folding has been widely studied by using minimalist and all-atom simulations (7-17) as well as experiments (18,19). All of these different studies provided some information about the folding mechanism and the nature of the transition-state ensemble (TSE). The study presented here aims to establish a quantitative picture by integrating the earlier qualitative findings with detailed simulations. We simulated 82 replicas of the water-protein system, with temperature, T, ranging from 277 to 548 K, and each replica was started from a different configuration spanning the space of folde...

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“…To quantify the different factors contributing to the entropy convergence, 14 we use the approximate Gaussian representation eq 20 for p 0 with mean m = n = ρv and variance σ 2 = n 2 − n 2 . This results in an estimate of the chemical potential,…”

Section: B Origin Of Entropy Convergence In Hydrophobic Hydration Anmentioning

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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Origin of Entropy Convergence in Hydrophobic Hydration and Protein Folding

Cited by 262 publications

References 19 publications

Temperature Dependence of Dimerization and Dewetting of Large-Scale Hydrophobes: A Molecular Dynamics Study

Temperature Dependence of Dimerization and Dewetting of Large-Scale Hydrophobes: A Molecular Dynamics Study

Folding a protein in a computer: An atomic description of the folding/unfolding of protein A

Hydrophobic Effects on a Molecular Scale

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