Thermodynamics of a conformational change using a random walk in energy-reaction coordinate space: Application to methane dimer hydrophobic interactions

Morozov, Alexander N.; Lin, Sheng Hsien

doi:10.1063/1.3077658

Cited by 15 publications

(21 citation statements)

References 51 publications

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“…While it is challenging to study the association process in experiments, it has been extensively studied through molecular simulations. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] The water models in these studies encompass ab initio modeling using density functional theory (DFT), 16,17 classical fully atomistic models, [18][19][20][21][22][23][24][25][26] anisotropic coarse-grained models, 30,32 and isotropic coarse-grained models. 31 Three features of the free energy of methane-methane interaction have been well established by these studies: (i) a global minimum in the free energy when the methane pair is in contact, which is referred to as contact pair (CP), (ii) a second lowest free energy state when the methane pair is separated by a shell of water, which a) Author to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic and structural signatures of water-driven methane-methane attraction in coarse-grained mW water

Molinero¹

2013

The Journal of Chemical Physics

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Hydrophobic interactions are responsible for water-driven processes such as protein folding and self-assembly of biomolecules. Microscopic theories and molecular simulations have been used to study association of a pair of methanes in water, the paradigmatic example of hydrophobic attraction, and determined that entropy is the driving force for the association of the methane pair, while the enthalpy disfavors it. An open question is to which extent coarse-grained water models can still produce correct thermodynamic and structural signatures of hydrophobic interaction. In this work, we investigate the hydrophobic interaction between a methane pair in water at temperatures from 260 to 340 K through molecular dynamics simulations with the coarse-grained monatomic water model mW. We find that the coarse-grained model correctly represents the free energy of association of the methane pair, the temperature dependence of free energy, and the positive change in entropy and enthalpy upon association. We investigate the relationship between thermodynamic signatures and structural order of water through the analysis of the spatial distribution of the density, energy, and tetrahedral order parameter Qt of water. The simulations reveal an enhancement of tetrahedral order in the region between the first and second hydration shells of the methane molecules. The increase in tetrahedral order, however, is far from what would be expected for a clathrate-like or ice-like shell around the solutes. This work shows that the mW water model reproduces the key signatures of hydrophobic interaction without long ranged electrostatics or the need to be re-parameterized for different thermodynamic states. These characteristics, and its hundred-fold increase in efficiency with respect to atomistic models, make mW a promising water model for studying water-driven hydrophobic processes in more complex systems.

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Section: Introductionmentioning

confidence: 99%

Thermodynamic and structural signatures of water-driven methane-methane attraction in coarse-grained mW water

Molinero¹

2013

The Journal of Chemical Physics

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“…In a Wang-Landau-type simulation, the convergence of the density of the states and the saturation of the error present potential issues [10][11][12][13][14]. The original implementation [9] used a flatness criterion for the histogram of the visits to the various energy levels: when the histogram is flat within some tolerance, we assume that g(E) at that level of iteration has converged.…”

Section: The Numerical Density Of Statesmentioning

confidence: 99%

“…We use a fitting function of the form Universality arguments [23,24] suggest that c 3 = 0. Nevertheless, a correction at this order is due to the fact that we use the finite-volume estimator (14), as it can be shown with a simple saddle point argument [26]. A fit of the data according to Eq.…”

Section: Interface Tensionsmentioning

confidence: 99%

Numerical method for determining the interface free energy

Hietanen

Lucini

2011

Phys. Rev. E

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We propose a general method (based on the Wang-Landau algorithm) to compute numerically free energies that are obtained from the logarithm of the ratio of suitable partition functions. As an application, we determine with high accuracy the order-order interface tension of the four-state Potts model in three dimensions on cubic lattices of linear extension up to L = 56. The infinite volume interface tension is then extracted at each β from a fit of the finite volume interface tension to a known universal behavior. A comparison of the order-order and order-disorder interface tension at βc provides a clear numerical evidence of perfect wetting.

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“…However, as this criterion has been found to be quite arbitrary by several subsequent studies [29][30][31][32][33], we use the criterion discussed in [33] to lower ln f . Another modification we adopted here is the one suggested by Zhou et al [34] that for continuous systems the DOS should be linearly interpolated if the energy falls between the centers of two energy bins.…”

Section: Models and The Wang-landau Methodsmentioning

confidence: 99%

Dynamical traps in Wang-Landau sampling of continuous systems: Mechanism and solution

2015

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We study the mechanism behind dynamical trappings experienced during Wang-Landau sampling of continuous systems reported by several authors. Trapping is caused by the random walker coming close to a local energy extremum, although the mechanism is different from that of critical slowing down encountered in conventional molecular dynamics or Monte Carlo simulations. When trapped, the random walker misses entire or even several stages of Wang-Landau modification factor reduction, leading to inadequate sampling of configuration space and a rough density-of-states even though the modification factor has been reduced to very small values. Trapping is dependent on specific systems, the choice of energy bins, and Monte Carlo step size, making it highly unpredictable. A general, simple, and effective solution is proposed where the configurations of multiple parallel Wang-Landau trajectories are inter-swapped to prevent trapping. We also explain why swapping frees the random walker from such traps. The efficacy of the proposed algorithm is demonstrated.

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Thermodynamics of a conformational change using a random walk in energy-reaction coordinate space: Application to methane dimer hydrophobic interactions

Cited by 15 publications

References 51 publications

Thermodynamic and structural signatures of water-driven methane-methane attraction in coarse-grained mW water

Thermodynamic and structural signatures of water-driven methane-methane attraction in coarse-grained mW water

Numerical method for determining the interface free energy

Dynamical traps in Wang-Landau sampling of continuous systems: Mechanism and solution

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