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Reaction coordinates and rates from transition paths.

ABSTRACT: The molecular mechanism of a reaction in solution is reflected in its transition-state ensemble and transition paths. We use a Bayesian formula relating the equilibrium and transition-path ensembles to identify transition states, rank reaction coordinates, and estimate rate coefficients. We also introduce a variational procedure to optimize reaction coordinates. The theory is illustrated with applications to protein folding and the dipole reorientation of an ordered water chain inside a carbon nanotube. To describe the folding of a simple model of a three-helix bundle protein, we variationally optimize the weights of a projection onto the matrix of native and nonnative amino acid contacts. The resulting one-dimensional reaction coordinate captures the folding transition state, with formation and packing of helix 2 and 3 constituting the bottleneck for folding.

SUBMITTER: Best RB

PROVIDER: S-EPMC1100744 | biostudies-literature | 2005 May

REPOSITORIES: biostudies-literature

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Reaction coordinates and rates from transition paths.

Best Robert B RB Hummer Gerhard G

Proceedings of the National Academy of Sciences of the United States of America 20050406 19

The molecular mechanism of a reaction in solution is reflected in its transition-state ensemble and transition paths. We use a Bayesian formula relating the equilibrium and transition-path ensembles to identify transition states, rank reaction coordinates, and estimate rate coefficients. We also introduce a variational procedure to optimize reaction coordinates. The theory is illustrated with applications to protein folding and the dipole reorientation of an ordered water chain inside a carbon n ...[more]

PMID: 15814618

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Project description:The free energy of a process is the fundamental quantity that determines its spontaneity or propensity at a given temperature. In particular, the binding free energy of a drug candidate to its biomolecular target is used as an objective quantity in drug design. Recently, binding kinetics-rates of association (k on) and dissociation (k off)-have also demonstrated utility for their ability to predict efficacy and in some cases have been shown to be more predictive than the binding free energy alone. Some methods exist to calculate binding kinetics from molecular simulations, although these are typically more difficult to calculate than the binding affinity as they depend on details of the transition path ensemble. Assessing these rate constants can be difficult, due to uncertainty in the definition of the bound and unbound states, large error bars and the lack of experimental data. As an additional consistency check, rate constants from simulation can be used to calculate free energies (using the log of their ratio) which can then be compared to free energies obtained experimentally or using alchemical free energy perturbation. However, in this calculation it is not straightforward to account for common, practical details such as the finite simulation volume or the particular definition of the "bound" and "unbound" states. Here we derive a set of correction terms that can be applied to calculations of binding free energies using full reactive trajectories. We apply these correction terms to revisit the calculation of binding free energies from rate constants for a host-guest system that was part of a blind prediction challenge, where significant deviations were observed between free energies calculated with rate ratios and those calculated from alchemical perturbation. The correction terms combine to significantly decrease the error with respect to computational benchmarks, from 3.4 to 0.76 kcal/mol. Although these terms were derived with weighted ensemble simulations in mind, some of the correction terms are generally applicable to free energies calculated using physical pathways via methods such as Markov state modeling, metadynamics, milestoning, or umbrella sampling.

Dataset Information

Reaction coordinates and rates from transition paths.

Publications

Reaction coordinates and rates from transition paths.

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