Corpus ID: 52831911

Advancements in Milestoning II: Calculating Autocorrelation from Milestoning Data Using Stochastic Path Integrals in Milestone Space

  title={Advancements in Milestoning II: Calculating Autocorrelation from Milestoning Data Using Stochastic Path Integrals in Milestone Space},
  author={Gianmarc Grazioli and Ioan Andricioaei},
  journal={arXiv: Statistical Mechanics},
The Milestoning method has achieved great success in the calculation of equilibrium kinetic properties such as rate constants from molecular dynamics simulations. The goal of this work is to advance Milestoning into the realm of non-equilibrium statistical mechanics, in particular, the calculation of time correlation functions. In order to accomplish this, we introduce a novel methodology for obtaining flux through a given milestone configuration as a function of both time and initial… 

Figures from this paper


Advancements in Milestoning I: Accelerated Milestoning via "Wind" Assisted Re-weighted Milestoning (WARM)
The Milestoning algorithm created by Ron Elber et al. is a method for determining the time scale of processes too complex to be studied using brute force simulation methods. The fundamental objects
Extending molecular dynamics time scales with milestoning: example of complex kinetics in a solvated peptide.
The kinetics of a conformational transition in a blocked alanine is computed and shown to be accurate, more efficient than straightforward molecular dynamics by a factor of about 9, and nonexponential.
Exact milestoning.
A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are
Computing time scales from reaction coordinates by milestoning.
An algorithm is presented to compute time scales of complex processes following predetermined milestones along a reaction coordinate in which the velocities are uncorrelated in time (but spatial memory remains).
On the calculation of time correlation functions by potential scaling.
It is shown that the exact value of the time correlation functions of the original system can be obtained, in principle, using an action-reweighting scheme based on a stochastic path-integral formalism.
Markovian milestoning with Voronoi tessellations.
This paper explains how to estimate the rate matrix of transitions between the milestones from data collected from the MD trajectories in the Voronoi cells, and shows how this rate matrix can be used to compute mean first passage times between milestones and reaction rates.
Transition Path Theory for Markov Jump Processes
The framework of TPT for Markov chains is developed in detail, and the relation of the theory to electric resistor network theory and data analysis tools such as Laplacian eigenmaps and diffusion maps is discussed as well.
Elaborating transition interface sampling methods
We review two recently developed efficient methods for calculating rate constants of processes dominated by rare events in high-dimensional complex systems. The first is transition interface sampling
Transition path sampling: throwing ropes over rough mountain passes, in the dark.
This article reviews the concepts and methods of transition path sampling. These methods allow computational studies of rare events without requiring prior knowledge of mechanisms, reaction
Transition path sampling and the calculation of rate constants
We have developed a method to study transition pathways for rare events in complex systems. The method can be used to determine rate constants for transitions between stable states by turning the