scholarly journals Transition path theory from biased simulations

2018 ◽  
Vol 149 (7) ◽  
pp. 072336 ◽  
Author(s):  
G. Bartolucci ◽  
S. Orioli ◽  
P. Faccioli
Keyword(s):  
Transition Path ◽  
Transition Path Theory

scholarly journals Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics

2020 ◽  
Vol 30 (6) ◽  
pp. 3321-3366
Author(s):  
Luzie Helfmann ◽  
Enric Ribera Borrell ◽  
Christof Schütte ◽  
Péter Koltai
Keyword(s):  
Finite Time ◽  
Social Dynamics ◽  
Transition Path ◽  
Time Dynamics ◽  
Transition Path Theory ◽  
Periodically Driven ◽  
Statistical Behavior ◽  
Ergodic Limit ◽  
Dynamical Regimes ◽  
Time Systems

Abstract Given two distinct subsets A, B in the state space of some dynamical system, transition path theory (TPT) was successfully used to describe the statistical behavior of transitions from A to B in the ergodic limit of the stationary system. We derive generalizations of TPT that remove the requirements of stationarity and of the ergodic limit and provide this powerful tool for the analysis of other dynamical scenarios: periodically forced dynamics and time-dependent finite-time systems. This is partially motivated by studying applications such as climate, ocean, and social dynamics. On simple model examples, we show how the new tools are able to deliver quantitative understanding about the statistical behavior of such systems. We also point out explicit cases where the more general dynamical regimes show different behaviors to their stationary counterparts, linking these tools directly to bifurcations in non-deterministic systems.

scholarly journals Full Kinetics of CO Entry, Internal Diffusion, and Exit in Myoglobin from Transition-Path Theory Simulations

2015 ◽  
Vol 137 (8) ◽  
pp. 3041-3050 ◽  
Author(s):  
Tang-Qing Yu ◽  
Mauro Lapelosa ◽  
Eric Vanden-Eijnden ◽  
Cameron F. Abrams
Keyword(s):  
Internal Diffusion ◽  
Transition Path ◽  
Transition Path Theory ◽  
Kinetics Of

scholarly journals Analyses of Multi-dimensional Single Cell Trajectories Quantify Transition Paths Between Nonequilibrium Steady States

2020 ◽  
Author(s):  
Weikang Wang ◽  
Jianhua Xing
Keyword(s):  
Single Cell ◽  
Epithelial To Mesenchymal Transition ◽  
A549 Cells ◽  
Time Lapse ◽  
State Theory ◽  
Nonequilibrium Steady States ◽  
Transition Path ◽  
Mesenchymal Transition ◽  
Transition Path Theory ◽  
Cell Trajectories

ABSTRACTA problem ubiquitous in almost all scientific areas is escape from a metastable state, or relaxation from one stationary distribution to a new one1. More than a century of studies lead to celebrated theoretical and computational developments such as the transition state theory and reactive flux formulation. Modern transition path sampling and transition path theory focus on an ensemble of trajectories that connect the initial and final states in a state space2, 3. However, it is generally unfeasible to experimentally observe these trajectories in multiple dimensions and compare to theoretical results. Here we report and analyze single cell trajectories of human A549 cells undergoing TGF-β induced epithelial-to-mesenchymal transition (EMT) in a combined morphology and protein texture space obtained through time lapse imaging. From the trajectories we identify parallel reaction paths with corresponding reaction coordinates and quasi-potentials. Studying cell phenotypic transition dynamics will provide testing grounds for nonequilibrium reaction rate theories.

scholarly journals Microscopic interpretation of folding ϕ-values using the transition path ensemble

2016 ◽  
Vol 113 (12) ◽  
pp. 3263-3268 ◽  
Author(s):  
Robert B. Best ◽  
Gerhard Hummer
Keyword(s):  
Transition Path ◽  
Transition Path Sampling ◽  
Mutant Proteins ◽  
Transition Path Theory ◽  
Folding Rates ◽  
Small Proteins ◽  
Versus Transition ◽  
Microscopic Interpretation ◽  
Dynamics Simulations ◽  
Substantial Heterogeneity

All-atom molecular dynamics simulations now allow us to create movies of proteins folding and unfolding. However, it is difficult to assess the accuracy of the folding mechanisms observed because experiments cannot yet directly resolve events occurring along the transition paths between unfolded and folded states. Protein folding ϕ-values provide residue-resolved information about folding mechanisms by comparing the effects of mutations on folding rates and stability, but determining ϕ-values by separately simulating mutant proteins would be computationally demanding and prone to large statistical errors. Here we use transition path theory to develop a method for computing ϕ-values directly from the transition path ensemble, without the need for additional simulations. This path-based approach uses the full transition path information available from equilibrium folding and unfolding trajectories, or from transition path sampling, and does not require identification of folding transition states. Applying our approach to a set of simulations of 10 small proteins by Shaw and coworkers [Lindorff-Larsen K, Piana S, Dror RO, Shaw DE (2011) Science 334(6055):517–520; Piana S, Lindorff-Larsen K, Shaw DE (2011) Biophys J 100(9):L47–L49; and Piana S, Lindorff-Larsen K, Shaw DE (2013) Proc Natl Acad Sci USA 110(15):5915–5920], we find good agreement with experiments in most cases where data are available. We can further resolve the contributions to fractional ϕ-values coming from partial contact formation versus transition path heterogeneity. Although in some cases, there is substantial heterogeneity of folding mechanism, in others, such as Ubiquitin, the mechanism is strongly conserved.

Direct generation of loop-erased transition paths in non-equilibrium reactions

2016 ◽  
Vol 195 ◽  
pp. 443-468 ◽  
Author(s):  
Ralf Banisch ◽  
Eric Vanden-Eijnden
Keyword(s):  
Detailed Balance ◽  
Computational Procedure ◽  
Direct Access ◽  
Transition Path ◽  
Sampling Schemes ◽  
Transition Path Theory ◽  
Equilibrium Reactions ◽  
Reactive Trajectories ◽  
Transition Paths ◽  
Non Equilibrium

A computational procedure is proposed to generate directly loop-erased transition paths in the context of non-equilibrium reactions, i.e. reactions that occur in systems whose dynamics is not in detailed balance. The procedure builds on results from Transition Path Theory (TPT), and it avoids altogether the need to generate reactive trajectories, either by brute-force calculations or using importance sampling schemes such as Transition Path Sampling (TPS). This is computationally advantageous since these reactive trajectories can themselves be very long and intricate in complex reactions. The loop-erased transition paths, on the other hand, are shorter and simpler because, by construction, they are pruned of all the detours typical reactive trajectories make and contain only their productive pieces that carry the effective current of the reaction. As a result they give direct access to the reaction rate and mechanism.

Transition Path Theory for Markov Jump Processes

2009 ◽  
Vol 7 (3) ◽  
pp. 1192-1219 ◽  
Author(s):  
Philipp Metzner ◽  
Christof Schütte ◽  
Eric Vanden-Eijnden
Keyword(s):  
Jump Processes ◽  
Transition Path ◽  
Markov Jump ◽  
Transition Path Theory ◽  
Markov Jump Processes
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