Extension to the weighted histogram analysis method: combining umbrella sampling with free energy calculations

Souaille, Marc; Roux, Benoı̂t

doi:10.1016/s0010-4655(00)00215-0

Cited by 868 publications

(956 citation statements)

References 20 publications

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“…68,69 The weighted histogram analysis method (WHAM) was then applied to the resulting data to obtain the potential of mean force (PMF). [70][71][72] Position dependent translation diffusion coefficients D(z) were determined using three approaches-one based on the Smoluchowski equation and two on the fluctuation-dissipation theorem. The first approach uses a numerical solution to the Smoluchowski equation as described by Bicout and Szabo 73 and as discussed by Hummer.…”

Section: Computationalmentioning

confidence: 99%

Permeation of the three aromatic dipeptides through lipid bilayers: Experimental and computational study

Lee

Kuczera

Middaugh

et al. 2016

The Journal of Chemical Physics

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The time-resolved parallel artificial membrane permeability assay with fluorescence detection and comprehensive computer simulations are used to study the passive permeation of three aromatic dipeptides—N-acetyl-phenylalanineamide (NAFA), N-acetyltyrosineamide (NAYA), and N-acetyl-tryptophanamide (NATA) through a 1,2-dioleoyl-sn-glycero-3-phospocholine (DOPC) lipid bilayer. Measured permeation times and permeability coefficients show fastest translocation for NAFA, slowest for NAYA, and intermediate for NATA under physiological temperature and pH. Computationally, we perform umbrella sampling simulations to model the structure, dynamics, and interactions of the peptides as a function of z, the distance from lipid bilayer. The calculated profiles of the potential of mean force show two strong effects—preferential binding of each of the three peptides to the lipid interface and large free energy barriers in the membrane center. We use several approaches to calculate the position-dependent translational diffusion coefficients D(z), including one based on numerical solution the Smoluchowski equation. Surprisingly, computed D(z) values change very little with reaction coordinate and are also quite similar for the three peptides studied. In contrast, calculated values of sidechain rotational correlation times τrot(z) show extremely large changes with peptide membrane insertion—values become 100 times larger in the headgroup region and 10 times larger at interface and in membrane center, relative to solution. The peptides’ conformational freedom becomes systematically more restricted as they enter the membrane, sampling α and β and C7eq basins in solution, α and C7eq at the interface, and C7eq only in the center. Residual waters of solvation remain around the peptides even in the membrane center. Overall, our study provides an improved microscopic understanding of passive peptide permeation through membranes, especially on the sensitivity of rotational diffusion to position relative to the bilayer.

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Section: Computationalmentioning

confidence: 99%

Permeation of the three aromatic dipeptides through lipid bilayers: Experimental and computational study

Lee

Kuczera

Middaugh

et al. 2016

The Journal of Chemical Physics

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“…To give these configurations x the proper weight proportional to p 0 (x), with x coming from different simulations with and without bias, one can for instance use a histogram-free version of the multidimensional weighted histogram analysis method (WHAM). [39][40][41] We first need to reweight the N -replica states in different simulations according to the reference distribution. By running N unbiased, uncoupled simulations according to p 0 (x 1 )p 0 (x 2 ) · · · p 0 (x N ) (or, simply, one unbiased simulation as a source for configurations x α that are then combined at random to form pseudo N -replica states) and one or several biased, coupled simulations (e.g., with different θ i ) according to p N (x 1 , .…”

Section: Bioen Methods Combining Replica Simulations With Erosmentioning

confidence: 99%

Bayesian ensemble refinement by replica simulations and reweighting

Hummer

Köfinger

2015

The Journal of Chemical Physics

211

394

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We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation.Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraint should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" (BioEn) method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of singlemolecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

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“…Then, the simulations are combined with a reweighting procedure since they are performed in biased ensembles. Two reweighting procedures are weighted histogram analysis method (WHAM) (Kumar et al 1992;Souaille & Roux, 2001) and umbrella integration (Kästner & Thiel, 2005). Using the final probability distribution of the configurations, the PMF and hence, the free energy profile of the system, is obtained.…”

Section: Equilibrium Methodsmentioning

confidence: 99%

Modeling and simulation of protein–surface interactions: achievements and challenges

Ozboyaci

Kokh

Corni

et al. 2016

Quart. Rev. Biophys.

184

199

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Abstract. Understanding protein-inorganic surface interactions is central to the rational design of new tools in biomaterial sciences, nanobiotechnology and nanomedicine. Although a significant amount of experimental research on protein adsorption onto solid substrates has been reported, many aspects of the recognition and interaction mechanisms of biomolecules and inorganic surfaces are still unclear. Theoretical modeling and simulations provide complementary approaches for experimental studies, and they have been applied for exploring protein-surface binding mechanisms, the determinants of binding specificity towards different surfaces, as well as the thermodynamics and kinetics of adsorption. Although the general computational approaches employed to study the dynamics of proteins and materials are similar, the models and force-fields (FFs) used for describing the physical properties and interactions of material surfaces and biological molecules differ. In particular, FF and water models designed for use in biomolecular simulations are often not directly transferable to surface simulations and vice versa. The adsorption events span a wide range of time-and length-scales that vary from nanoseconds to days, and from nanometers to micrometers, respectively, rendering the use of multi-scale approaches unavoidable. Further, changes in the atomic structure of material surfaces that can lead to surface reconstruction, and in the structure of proteins that can result in complete denaturation of the adsorbed molecules, can create many intermediate structural and energetic states that complicate sampling. In this review, we address the challenges posed to theoretical and computational methods in achieving accurate descriptions of the physical, chemical and mechanical properties of protein-surface systems. In this context, we discuss the applicability of different modeling and simulation techniques ranging from quantum mechanics through all-atom molecular mechanics to coarse-grained approaches. We examine uses of different sampling methods, as well as free energy calculations. Furthermore, we review computational studies of protein-surface interactions and discuss the successes and limitations of current approaches.

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Extension to the weighted histogram analysis method: combining umbrella sampling with free energy calculations

Cited by 868 publications

References 20 publications

Permeation of the three aromatic dipeptides through lipid bilayers: Experimental and computational study

Permeation of the three aromatic dipeptides through lipid bilayers: Experimental and computational study

Bayesian ensemble refinement by replica simulations and reweighting

Modeling and simulation of protein–surface interactions: achievements and challenges

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