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Huan-xiang Zhou - One of the best experts on this subject based on the ideXlab platform.

  • electrostatic enhancement of diffusion controlled protein protein association comparison of theory and experiment on barnase and barstar
    Journal of Molecular Biology, 1998
    Co-Authors: M Vijayakumar, Kwan Y Wong, Gideon Schreiber, Alan R Fersht, Attila Szabo, Huan-xiang Zhou
    Abstract:

    Abstract The electrostatic enhancement of the association rate of barnase and barstar is calculated using a transition-state theory like expression and atomic-detail modeling of the protein molecules. This expression predicts that the rate enhancement is simply the average Boltzmann Factor in the region of configurational space where association occurs instantaneously in the diffusion-controlled limit. Based on experimental evidence, this “transition state” is defined by configurations in which, relative to the stereospecifically bound complex, the two proteins are shifted apart by ∼8 A (so a layer of water can be accommodated in the interface) and the two binding surfaces are rotated away by 0° to 3°. The values of the average Boltzmann Factor, calculated by solving the Poisson-Boltzmann equation, for the wild-type complex and 16 complexes with single mutations are found to correlate well with experimental results for the electrostatic rate enhancement. The predicted rate enhancement is found to be somewhat insensitive to the precise definition of the transition state, due to the long-range nature of electrostatic interactions. The experimental ionic strength dependence of the rate enhancement is also reasonably reproduced.

  • correlation between rate of enzyme substrate diffusional encounter and average Boltzmann Factor around active site
    Biopolymers, 1998
    Co-Authors: Huan-xiang Zhou, James M Briggs, Sylvia Tara, Andrew J Mccammon
    Abstract:

    The utility of the average Boltzmann Factor around the active site of an enzyme as the predictor of the electrostatic enhancement of the substrate binding rate is tested on a set of data on wild-type acetylcholinesterase and 18 charge mutants recently obtained by Brownian dynamics simulations. A good correlation between the average Boltzmann Factors and the substrate binding rate constants is found. The effects of single charge mutations on both the Boltzmann Factor and the substrate binding rate constant are modest, i.e., < 5 fold increase or decrease. This is consistent with the experimental results of Shafferman et al. but does not support their suggestion that the overall rate of the catalytic reaction is not limited by the diffusional encounter of acetylcholinesterase and its substrate.

  • Brownian dynamics study of the influences of electrostatic interaction and diffusion on protein-protein association kinetics
    Biophysical journal, 1993
    Co-Authors: Huan-xiang Zhou
    Abstract:

    A unified model is presented for protein-protein association processes that are under the influences of electrostatic interaction and diffusion (e.g., protein oligomerization, enzyme catalysis, electron and energy transfer). The proteins are modeled as spheres that bear point charges and undergo translational and rotational Brownian motion. Before association can occur the two spheres have to be aligned properly to form a reaction complex via diffusion. The reaction complex can either go on to form the product or it can dissociate into the separate reactants through diffusion. The electrostatic interaction, like diffusion, influences every step except the one that brings the reaction complex into the product. The interaction potential is obtained by extending the Kirkwood-Tanford protein model (Tanford, C., and J. G. Kirkwood. 1957. J. Am. Chem. Soc. 79:5333–5339) to two charge-embedded spheres and solving the consequent equations under a particular basis set. The time-dependent association rate coefficient is then obtained through Brownian dynamics simulations according an algorithm developed earlier (Zhou, H.-X. 1990. J. Phys. Chem. 94:8794–8800). This method is applied to a model system of the cytochrome c and cytochrome c peroxidase association process and the results confirm the experimental dependence of the association rate constant on the solution ionic strength. An important conclusion drawn from this study is that when the product is formed by very specific alignment of the reactants, as is often the case, the effect of the interaction potential is simply to scale the association rate constant by a Boltzmann Factor. This explains why mutations in the interface of the reaction complex have strong influences on the association rate constant whereas those away from the interface have minimal effects. It comes about because the former mutations change the interaction potential of the reaction complex significantly and the latter ones do not.

William A Goddard - One of the best experts on this subject based on the ideXlab platform.

  • the continuous configurational Boltzmann biased direct monte carlo method for free energy properties of polymer chains
    Journal of Chemical Physics, 1997
    Co-Authors: Jiro Sadanobu, William A Goddard
    Abstract:

    We develop here a highly efficient variant of the Monte Carlo method for direct evaluation of the partition function, free energy, and other configurational dependent physical properties for long polymer chains. This method (CC–BB) combines continuous configurational biased sampling with Boltzmann Factor biased enrichment. To illustrate the efficiency and to validate the bias correction for weighting the torsion and chain enrichments, we applied this model to isolated single chains using a united atom force field. For a 50 monomer polymer chain CC–BB with 400 chains leads to an accuracy of 0.1% in the free energy whereas simple sampling direct Monte Carlo requires about 109 chains for this accuracy. This leads to cost savings by a Factor of about 350 000. CC–BB is easily extended to multichain systems, to the condensed state, to more realistic force fields, and to evaluating the mixing free energy for polymer blends.

De La Cruz, Monica Olvera - One of the best experts on this subject based on the ideXlab platform.

  • Multicanonical Monte Carlo ensemble growth algorithm
    'American Physical Society (APS)', 2020
    Co-Authors: Vernizzi Graziano, Nguyen, Trung Dac, Orland Henri, De La Cruz, Monica Olvera
    Abstract:

    7 pages, 6 figures; Added references and figures, corrected typos, improved notationInternational audienceWe present a novel Ensemble Monte Carlo Growth method to sample the equilibrium thermodynamic properties of random chains. The method is based on the multicanonical technique of computing the density of states in the energy space. Such a quantity is temperature independent, and therefore microcanonical and canonical thermodynamic quantities, including the free energy, entropy, and thermal averages, can be obtained by re-weighting with a Boltzmann Factor. The algorithm we present combines two approaches: the first is the Monte Carlo ensemble growth method, where a "population" of samples in the state space is considered, as opposed to traditional sampling by long random walks, or iterative single-chain growth. The second is the flat-histogram Monte Carlo, similar to the popular Wang-Landau sampling, or to multicanonical chain-growth sampling. We discuss the performance and relative simplicity of the proposed algorithm, and we apply it to known test cases

  • Multicanonical Monte Carlo Ensemble Growth Algorithm
    'American Physical Society (APS)', 2020
    Co-Authors: Vernizzi Graziano, Nguyen, Trung Dac, Orland Henri, De La Cruz, Monica Olvera
    Abstract:

    We present a novel Ensemble Monte Carlo Growth method to sample the equilibrium thermodynamic properties of random chains. The method is based on the multicanonical technique of computing the density of states in the energy space. Such a quantity is temperature independent, and therefore microcanonical and canonical thermodynamic quantities, including the free energy, entropy, and thermal averages, can be obtained by re-weighting with a Boltzmann Factor. The algorithm we present combines two approaches: the first is the Monte Carlo ensemble growth method, where a "population" of samples in the state space is considered, as opposed to traditional sampling by long random walks, or iterative single-chain growth. The second is the flat-histogram Monte Carlo, similar to the popular Wang-Landau sampling, or to multicanonical chain-growth sampling. We discuss the performance and relative simplicity of the proposed algorithm, and we apply it to known test cases.Comment: 7 pages, 6 figures; Added references and figures, corrected typos, improved notatio

Daniel Zwanziger - One of the best experts on this subject based on the ideXlab platform.

  • fundamental modular region Boltzmann Factor and area law in lattice gauge theory
    Nuclear Physics B - Proceedings Supplements, 1994
    Co-Authors: Daniel Zwanziger
    Abstract:

    Abstract The thermodynamic limit of lattice gauge theory is derived in a gauge which is optimized to make all link variables as close to unity as possible. The derivation rests upon (1) a precise bound on the fundamental modular region and (2) a direct evaluation of the functional integral of the Wilson lattice by the saddle-point method that is valid in the thermodynamic limit. The result confirms the calculational scheme obtained previously, which differs from the Faddeev-Popov scheme by the incorporation of non-perturbative effects, but which remains perturbatively renormalizable. The lattce Faddeev-Popov propagator, which appears in the modified action, acquires a dipole singularity at zero momentum, characteristic of long-range correlations. This is sufficient to produce an area law for Wilson loops, provided that unevaluated terms to not cancel the effect found.

  • fundamental modular region Boltzmann Factor and area law in lattice theory
    Nuclear Physics, 1994
    Co-Authors: Daniel Zwanziger
    Abstract:

    Abstract The thermodynamic limit of lattice gauge theory is derived in a gauge which is optimized to make all link variables as close to unity as possible. The derivation rests upon (1) a precise bound on the fundamental modular region and (2) a direct evaluation of the functional integral of the Wilson lattice by the saddle-point method that is valid in the thermodynamic limit. The result confirms the calculational scheme obtained previously, which differs from the Faddeev-Popov scheme by the incorporation of non-perturbative effects, but which remains perturbatively renormalizable. The lattice Faddeev-Popov propagator, which appears in the modified action, acquires a dipole singularity at zero momentum, characteristic of long range correlation. This is sufficient to produce an area law for Wilson loops, provided that unevaluated terms do not cancel the effect found.

Jiro Sadanobu - One of the best experts on this subject based on the ideXlab platform.

  • the continuous configurational Boltzmann biased direct monte carlo method for free energy properties of polymer chains
    Journal of Chemical Physics, 1997
    Co-Authors: Jiro Sadanobu, William A Goddard
    Abstract:

    We develop here a highly efficient variant of the Monte Carlo method for direct evaluation of the partition function, free energy, and other configurational dependent physical properties for long polymer chains. This method (CC–BB) combines continuous configurational biased sampling with Boltzmann Factor biased enrichment. To illustrate the efficiency and to validate the bias correction for weighting the torsion and chain enrichments, we applied this model to isolated single chains using a united atom force field. For a 50 monomer polymer chain CC–BB with 400 chains leads to an accuracy of 0.1% in the free energy whereas simple sampling direct Monte Carlo requires about 109 chains for this accuracy. This leads to cost savings by a Factor of about 350 000. CC–BB is easily extended to multichain systems, to the condensed state, to more realistic force fields, and to evaluating the mixing free energy for polymer blends.