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

@article{Grazioli2015AdvancementsIM, 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}, year={2015} }

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…

#### References

SHOWING 1-10 OF 15 REFERENCES

Advancements in Milestoning I: Accelerated Milestoning via "Wind" Assisted Re-weighted Milestoning (WARM)

- Physics, Mathematics
- 2015

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.

- Chemistry, MedicineThe Journal of chemical physics
- 2007

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.

- MedicineThe Journal of chemical physics
- 2015

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.

- Physics, MedicineThe Journal of chemical physics
- 2004

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.

- Mathematics, MedicineThe Journal of chemical physics
- 2006

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.

- Computer Science, MedicineThe Journal of chemical physics
- 2009

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

- Mathematics, Computer ScienceMultiscale Model. Simul.
- 2008

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

- Mathematics, Physics
- 2005

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.

- Computer Science, MedicineAnnual review of physical chemistry
- 2002

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

- Mathematics
- 1998

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…