Optimizing reaction coordinate by flux maximization in the transition path ensemble

Li, Wenjin

doi:10.1101/2021.11.18.469181

Cited by 3 publications

(14 citation statements)

References 52 publications

(22 reference statements)

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“…62 Later, a different viewpoint was suggested in the flux maximization approach. 63 Noting that each reactive trajectory in the TPE is actually one unit of flux from the reactant state to the product one and the largest possible net flux along a coordinate is the number of transition paths, which equals the flux along the true reaction coordinate, the flux maximization approach quantifies the relevance of a coordinate to the reaction coordinate with a density-weighted average flux along…”

Section: Introductionmentioning

confidence: 99%

Time-Lagged Flux in the Transition Path Ensemble: Flux Maximization and Relation to Transition Path Theory

2022

J. Phys. Chem. A

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The transition path ensemble is of special interest in reaction coordinate identification as it consists of reactive trajectories that start from the reactant state and end in the product one. As a theoretical framework for describing the transition path ensemble, the transition path theory has been introduced more than 10 years ago, and so far, its applications have only been illustrated in several low-dimensional systems. Given the transition path ensemble, expressions for calculating flux, current (a vector field), and principal curves are derived here in the space of collective variables from the transition path theory, and they are applicable to time series obtained from molecular dynamics simulations of high-dimensional systems, i.e., the position coordinates as a function of time in the transition path ensemble. The connection of the transition path theory is made to a density-weighted average flux, a quantity proposed in a previous work to appraise the relevance of a coordinate to the reaction coordinate [Li, W. J. Chem. Phys. 2022, 156, 054117]. Most importantly, as an extension of the existing quantities, time-lagged quantities such as flux and current are also proposed. The main insights and objects provided by these time-lagged quantities are illustrated in the application to the alanine peptide in vacuum.

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Section: Introductionmentioning

confidence: 99%

Time-Lagged Flux in the Transition Path Ensemble: Flux Maximization and Relation to Transition Path Theory

2022

J. Phys. Chem. A

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“…We suggest that a few coordinates in close relevance to reaction coordinates can be first identified from flux maximization 28 or one-dimensional free energy analogues with the EDARC approach, 40 which do not require the calculation of partial derivative of potential energy with respect to coordinates (an independent and complete set), and then the relative importance of these relevant coordinates and a one-dimensional reaction coordinate as a (possibly curvilinear) function of them can be constructed by visual inspection of in subspaces of various combinations of CVs.…”

Section: Discussionmentioning

confidence: 99%

“…The software package GROMACS (version 5.1.1) 47 was employed for all-atom MD simulations with an integration time step of 0.5 fs. The same simulation setup as the ones in previous publications 27,28 was used. Three non-equilibrium ensembles of short trajectories were collected: (1) TPE: The TPE for the transition from C 7eq to C 7ax harvested with transition path sampling, in which the definitions of two stable states ( C 7eq and C 7ax ) were given based on the backbone dihedrals ϕ and ψ .…”

Section: Methodsmentioning

confidence: 99%

“…Then, we illustrate the applications of such a theoretical framework in the C 7eq → C 7ax isomerization of the alanine dipeptide in vacuum, a system that has been intensively studied previously. 23,27,28,30,39,[41][42][43] The viability of this approach is tested on several non-equilibrium ensembles of short trajectories that we have examined previously using EDARC. 40 Finally, some concluding remarks are given at the end of the article.…”

Section: Introductionmentioning

confidence: 99%

“…Li used the equipartition terms in the TPE along a coordinate to appraise the relevance of the coordinate to reaction coordinates and the maximization of equipartition terms reproduced a good one-dimensional representation of reaction coordinates. 27 Later on, a density-weighted average of the flux along a coordinate over the TPE was demonstrated to be a promising quantity to rank reaction coordinates 28 and its relation to the transition path theory, a statistical theory for describing the TPE pioneered by Weinan and Vanden-Eijnden, 29 was clarified thereafter. 30 On the other hand, the committor can be efficiently estimated by methods other than shooting many unconstrained trajectories with random assignment of momenta and then committor-based approaches can be applied to identify reaction coordinates.…”

Section: Introductionmentioning

confidence: 99%

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Potential Energy Weighted Reactive Flux and Total Rate of Change of Potential Energy: Theory and Illustrative Applications

2022

Preprint

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Reactive flux can be largely non-zero in a nonequilibrium ensemble of trajectories and provide insightful information for reactive transitions from the reactant state to the product state. Based on the reactive flux, a theoretical framework is proposed here for two quantities, the potential energy weighted reactive flux and the total rate of change of potential energy, which are useful for the identification of mechanism from a nonequilibrium ensemble. From such quantities, two multidimensional free energy analogues can be derived in the subspace of collective variables and they are equivalent in the regions where the reactive flux is divergence-free. These free energy analogues are assumed to be closely related to the free energy in the subspace of collective variables and they are reduced in the one-dimensional case to be the ensemble average of the potential energy weighted with reactive flux intensity, which was proposed recently and could be decomposed into energy components at the per-coordinate level. In the subspace of collective variables, the decomposition of the multidimensional free energy analogues at the per-coordinate level is theoretically possible and is numerically difficult to be calculated. Interestingly, the total rate of change of potential energy is able to identify the location of the transition state ensemble or the stochastic separatrix, in addition to the locations of the reactant and product states. The total rate of change of potential energy can be decomposed at the per-coordinate level and its components can quantify the contribution of a coordinate to the reactive transition in the subspace of collective variables. We then illustrated the main insights and objects that can be provided by the approach in the application to the alanine peptide in vacuum in various nonequilibrium ensembles of short trajectories and the results from these ensembles were found to be consistent.

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Committor-Consistent Variational String Method

Chipot

Roux

2022

J. Phys. Chem. Lett.

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The treatment of slow and rare transitions in the simulation of complex systems poses a great computational challenge. A powerful approach to tackle this challenge is the string method, which represents the transition path as a one-dimensional curve in a multidimensional space of collective variables. Commonly used strategies for pathway optimization include aligning the tangent of the string to the local mean force or to the mean drift determined from swarms of short trajectories. Here, a novel strategy is proposed, allowing the string to be optimized based on a variational principle involving the unidirectional reactive flux expressed in terms of the time-correlation function of the committor. The method is illustrated with model systems and then probed with the alanine dipeptide and a coarse-grained model of the barstar-barnase protein complex. Successive iterations variationally refine the string toward an optimal transition pathway following the gradient of the committor between two metastable states.

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Optimizing reaction coordinate by flux maximization in the transition path ensemble

Cited by 3 publications

References 52 publications

Time-Lagged Flux in the Transition Path Ensemble: Flux Maximization and Relation to Transition Path Theory

Time-Lagged Flux in the Transition Path Ensemble: Flux Maximization and Relation to Transition Path Theory

Potential Energy Weighted Reactive Flux and Total Rate of Change of Potential Energy: Theory and Illustrative Applications

Committor-Consistent Variational String Method

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