A benchmark for reaction coordinates in the transition path ensemble

Li, Wenjin; Ma, Ao

doi:10.1063/1.4945337

Cited by 22 publications

(59 citation statements)

References 51 publications

(62 reference statements)

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“…Here, the reactive current is localized in a narrower transition tube in the plane of φ and θ compared to the one in the plane of φ and ψ, which may be a plausible explanation to the observation that θ is more relevant to the reaction coordinate than ψ. 46,[61][62][63][64][65] In addition, our analyses indicated that the flow lines were not always located in the main transition tube in the plane of φ and θ. Most importantly, the direction of the time-lagged reactive current changes significantly and the forward current is not coincident with the backward one in the same plane, a phenomenon that is missing in the plane of φ and ψ.…”

Section: Illustrative Calculationsmentioning

confidence: 99%

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

2022

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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 ten years ago and so far its applications have been only illustrated in several low-dimensional systems. Given the transition path ensemble, expressions for calculating flux, current (a vector field), and principal curve 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 [W. Li, J. Chem. Phys. 156, 054117 (2022)]. 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: Illustrative Calculationsmentioning

confidence: 99%

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

2022

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“…Emergent potential energy was previously reported to quantify the relevance of a coordinate to the reaction coordinate. 17 For a system of n atoms with q ≡ (q 1 , · · · , q 3n ) being a complete and independent set of configuration coordinates, an infinitesimal change in the potential energy V(q) of the system can be decomposed as follows,…”

Section: Residue-residue Mutual Work Analysismentioning

confidence: 99%

Residue–Residue Mutual Work Analysis of Retinal–Opsin Interaction in Rhodopsin: Implications for Protein–Ligand Binding

2020

J. Chem. Theory Comput.

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crystal structure of Batho (chain A of PDB ID 2G87). 1 ASP83 and GLU122 were considered to be neutral 2 while all other charged amino acids were set to default protonation states. The spatial positions of Batho with respect to the lipid bilayer were taken from the Orientations of Proteins in Membranes (OPM) database. 3 All histidines were protonated either in the N position (HIS65, HIS152, HIS195, and HIS278) or in the N δ position (HIS100 and HIS211) 4 . The Schiff base linkage between the retinal and LYS296 was positively charged. The retinal and all crystallographic water molecules were preserved, other heteroatoms were removed.The CHARMM-GUI web-server 5 was used to embed the Batho system in an explicit membrane bilayer, and then immerse the resulted protein-lipid system in a box of explicit waters and ions at physiological concentration. Two palmitoyl chains bound to CYS322 and CYS323 were added to Batho before it was inserted in the membrane, which consisted of 128 palmitoyl-oleoyl-phosphatidyl choline (POPC) lipids. The final system was neutral and the size of the periodic box was approximately 71×71×92Å 3 with 8589 water molecules, 20 sodium ions, and 18 chloride ions (see Fig. S6).Simulation Details All simulations were performed with the software suite GROMACS-5.1.1. 6The c36 CHARMM force field 7 was used for protein and lipids. The force field parameters of retinal were adapted from recent literatures. 8,9 The TIP3P water model was used. The energy of the system was first minimized with very strong position restraints to heavy atoms of the protein (including retinal and two palmitoyl chains bound to rhodopsin). The position of the phosphorus atom and two dihedrals of lipids were also restrained strongly. Then, the system was under a series of equilibration with position and dihedral restraints were gradually released. The early stage of equilibration was performed in the NVE ensemble, then all the subsequent simulations were switched to the NPT ensemble. The system was coupled to a Berendsen thermostat with τ t =1.0 ps to keep the temperature constant at 303.15 K, and a semiisotropic Berendsen barostat with τ p =5.0 ps to keep the pressure constant at 1 bar. 10 An integration time step of 2 fs was used with constraints to bonds involving hydrogen atoms using the LINCS algorithm. 11 Lennard-Jones interactions were calculated using S2

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“…43,44 In the very recent endeavour to identify reaction coordinate from the TPE, the so-called emergent potential energy along a coordinate, a quantity estimated from the configurations of the TPE alone under the assist of forces on each atom (calculated by a rerun of the TPE without further sampling), was used to quantify the quality of a coordinate as the reaction coordinate and suggested a new energy decomposition scheme along the reaction coordinate. 45 Later, the equipartition terms in the TPE were calculated from both the position and momentum coordinates of the reactive trajectories and were suggested to be a promising quantity to appraise reaction coordinate. 46 In this paper, we are concerned with the extraction of reaction coordinate from the TPE with the conformational coordinates only.…”

Section: Introductionmentioning

confidence: 99%

Optimizing reaction coordinate by flux maximization in the transition path ensemble

2021

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Transition path ensemble is a collection of reactive trajectories, all of which largely keep going forward along the transition channel from the reactant state to the product one, and is believed to possess the information necessary for the identification of reaction coordinate. Previously, the full coordinates (both position and momentum) of the snapshots in the transition path ensemble were utilized to obtain the reaction coordinate (J. Chem. Phys. 2016, 144, 114103; J. Chem. Phys. 2018, 148, 084105). Here, with the conformational (or position) coordinates alone, it is demonstrated that the reaction coordinate can be optimized by maximizing the flux of a given coordinate in the transition path ensemble. In the application to alanine dipeptide in vacuum, dihderal angles ϕ and θ were identified to be the two best reaction coordinates, which was consistent with the results in existing studies. A linear combination of these two coordinates gave a better reaction coordinate, which is highly correlated with committor. Most importantly, the method obtained a linear combination of pairwise distances between heavy atoms, which was highly correlated with committor as well. The standard deviation of committor at the transition region defined by the optimized reaction coordinate is as small as 0.08. In addition, the effects of practical factors, such as the choice of transition path sub-ensembles and saving interval between frames in transition paths, on reaction coordinate optimization were also considered.

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A benchmark for reaction coordinates in the transition path ensemble

Cited by 22 publications

References 51 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

Residue–Residue Mutual Work Analysis of Retinal–Opsin Interaction in Rhodopsin: Implications for Protein–Ligand Binding

Optimizing reaction coordinate by flux maximization in the transition path ensemble

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