THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method

Kumar, Shankar; Bouzida, Djamal; Swendsen, Robert H.; Kollman, Peter A.; Rosenberg, John M.

doi:10.1002/jcc.540130812

Cited by 5,946 publications

(6,328 citation statements)

References 25 publications

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“…Thus, it provides a more stringent test on various REMD protocols' ability to enhance sampling. The weighted histogram analysis method (WHAM) was used to combine information from all temperatures to compute either the C v curves or various unbiased 1D and 2D probability distributions 48 . All the analysis was performed using a combination of the MMTSB toolset, CHARMM and in-house scripts.…”

Section: Simulation Protocols and Analysismentioning

confidence: 99%

Efficiency of Adaptive Temperature-Based Replica Exchange for Sampling Large-Scale Protein Conformational Transitions

Zhang

Chen

2013

J. Chem. Theory Comput.

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Temperature-based replica exchange (RE) is now considered a principal technique for enhanced sampling of protein conformations. It is also recognized that existence of sharp cooperative transitions (such as protein folding/unfolding) can lead to temperature exchange bottlenecks and significantly reduce the sampling efficiency. Here, we revisit two adaptive temperature-based RE protocols, namely, exchange equalization (EE) and current maximization (CM), that were previously examined using atomistic simulations (Lee and Olson, J. Chem. Physics 2011, 134, 24111). Both protocols aim to overcome exchange bottlenecks by adaptively adjusting the simulation temperatures, either to achieve uniform exchange rates (in EE) or to maximize temperature diffusion (CM). By designing a realistic yet computationally tractable coarse-grained protein model, one can sample many reversible folding/unfolding transitions using conventional constant temperature molecular dynamics (MD), standard REMD, EE-REMD, and CM-REMD. This allows rigorous evaluation of the sampling efficiency, by directly comparing the rates of folding/unfolding transitions and convergence of various thermodynamic properties of interest. The results demonstrate that both EE and CM can indeed enhance temperature diffusion compared to standard RE, by ∼3and over 10-fold, respectively. Surprisingly, the rates of reversible folding/unfolding transitions are similar in all three RE protocols. The convergence rates of several key thermodynamic properties, including the folding stability and various 1D and 2D free energy surfaces, are also similar. Therefore, the efficiency of RE protocols does not appear to be limited by temperature diffusion, but by the inherent rates of spontaneous large-scale conformational rearrangements. This is particularly true considering that virtually all RE simulations of proteins in practice involve exchange attempt frequencies (∼ps −1 ) that are several orders of magnitude faster than the slowest protein motions (∼μs −1 ). Our results also suggest that the efficiency of RE will not likely be improved by other protocols that aim to accelerate exchange or temperature diffusion. Instead, protocols with some types of guided tempering will likely be necessary to drive faster large-scale conformational transitions.

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Section: Simulation Protocols and Analysismentioning

confidence: 99%

Efficiency of Adaptive Temperature-Based Replica Exchange for Sampling Large-Scale Protein Conformational Transitions

Zhang

Chen

2013

J. Chem. Theory Comput.

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“…4 Specifically, we have developed an integrated path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method for computing KIEs, in which molecular dynamics simulations are first carried out to obtain the classical mechanical PMF using umbrella sampling. 47,48 Then, the nuclear coordinates of atoms associated with the chemical reaction are quantized by a path integral with the constraint that the centroid positions coincide with their corresponding classical coordinates. KIEs are evaluated by FEP between heavy and light atom masses, which is related to the quantized quasiparticle positions.…”

Section: Integrated Centroid Path Integral-free Energy Perturbation Amentioning

confidence: 99%

“…The effect of the biasing potential is subsequently removed when the separate simulation windows are combined to produce the overall PMF by using the weighted histogram analysis method. 48 For the proton transfer reaction, the classical reaction coordinate is defined as the difference in distance for the proton between the donor (α carbon of nitroethane) and the acceptor (an oxygen of the acetate ion) atom: Z PT = r(C α − H) − r(H − O). In the current simulations, 32 windows have been employed.…”

Section: Simulation Detailsmentioning

confidence: 99%

Combined QM/MM and path integral simulations of kinetic isotope effects in the proton transfer reaction between nitroethane and acetate ion in water

2007

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An integrated Feynman path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method has been used to investigate the kinetic isotope effects (KIEs) in the proton transfer reaction between nitroethane and acetate ion in water. In the present study, both nuclear and electronic quantum effects are explicitly treated for the reacting system. The nuclear quantum effects are represented by bisection sampling centroid path integral simulations, while the potential energy surface is described by a combined quantum mechanical and molecular mechanical (QM/MM) potential. The accuracy essential for computing KIEs is achieved by a FEP technique that transforms the mass of a light isotope into a heavy one, which is equivalent to the perturbation of the coordinates for the path integral quasiparticle in the bisection sampling scheme. The PI-FEP/UM method is applied to the proton abstraction of nitroethane by acetate ion in water through molecular dynamics simulations. The rule of the geometric mean and the Swain-Schaad exponents for various isotopic substitutions at the primary and secondary sites have been examined. The computed total deuterium KIEs are in accord with experiments. It is found that the mixed isotopic Swain-Schaad exponents are very close to the semiclassical limits, suggesting that tunneling effects do not significantly affect this property for the reaction between nitroethane and acetate ion in aqueous solution.

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“…An expression suited for obtaining the free energy decomposition into energy and entropy contributions ∆A(r) ) ∆E(r) -T∆S(r) by the weighted histogram analysis method 32,33 can be developed as follows. For simplicity, we use a scalar coordinate r for the derivation.…”

Section: Appendix Amentioning

confidence: 99%

Hamiltonian and Distance Replica Exchange Method Studies of Met-Enkephalin

Cukier

2007

J. Phys. Chem. B

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The conformational states of the zwitterionic form of the pentapeptide Met-enkephalin were explored with the use of explicit solvent molecular dynamics (MD). The N and C termini are ionized, as appropriate to polar solvent conditions, and consequently, there is a competition between open forms driven by polar solvation of the ammonium and carboxylate groups and closed forms driven by their salt-bridge formation. Normal MD started from an open state does not sample closed conformations. Sampling was enhanced with a distance replica exchange method (DREM) and with a Hamiltonian replica exchange method (HREM). The potential of mean force (PMF) along an end-to-end distance reaction coordinate was obtained with the DREM. The PMF shows a stable salt-bridge state and the presence of a large region of open states, as hypothesized for conformationally promiscuous small opiate peptides. The HREM systems differ by scaling the peptidepeptide and peptide-solvent electrostatic and Lennard-Jones potentials, with the goal of improving the sampling efficiency with a limited number of systems. A small number of systems were found to be sufficient to sample closed and open states. A principal component analysis (PCA) shows that the HREM-generated fluctuations are dominated by the first two principal modes. The first corresponds to the end-to-end reaction coordinate found in the DREM, and the first mode PMF is similar to the DREM PMF. The second mode describes the presence of two conformations, both of which correspond to the salt-bridge state distance. The conformers differ in the values of neighboring psi and phi dihedral angles, since such psi/phi compensation can still produce the same end-to-end distance. The two-dimensional PMF constructed from the first two PCA modes captures most of the significant backbone conformational space of Met-enkephalin.

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THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method

Cited by 5,946 publications

References 25 publications

Efficiency of Adaptive Temperature-Based Replica Exchange for Sampling Large-Scale Protein Conformational Transitions

Efficiency of Adaptive Temperature-Based Replica Exchange for Sampling Large-Scale Protein Conformational Transitions

Combined QM/MM and path integral simulations of kinetic isotope effects in the proton transfer reaction between nitroethane and acetate ion in water

Hamiltonian and Distance Replica Exchange Method Studies of Met-Enkephalin

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