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Literature DB >> 27239166

A MATHEMATICAL FRAMEWORK FOR EXACT MILESTONING.

David Aristoff¹, Juan M Bello-Rivas², Ron Elber³.

Abstract

We give a mathematical framework for Exact Milestoning, a recently introduced algorithm for mapping a continuous time stochastic process into a Markov chain or semi-Markov process that can be efficiently simulated and analyzed. We generalize the setting of Exact Milestoning and give explicit error bounds for the error in the Milestoning equation for mean first passage times.

Entities: Chemical Disease Species

Keywords: accelerated molecular dynamics; long-time dynamics; semi-Markov processes; stationary distribution

Year: 2016 PMID： 27239166 PMCID： PMC4879838 DOI： 10.1137/15M102157X

Source DB: PubMed Journal: Multiscale Model Simul ISSN： 1540-3459 Impact factor: 1.930

13 in total

1. Transition path sampling: throwing ropes over rough mountain passes, in the dark.

Authors: Peter G Bolhuis; David Chandler; Christoph Dellago; Phillip L Geissler
Journal: Annu Rev Phys Chem Date: 2001-10-04 Impact factor: 12.703

2. Computing time scales from reaction coordinates by milestoning.

Authors: Anton K Faradjian; Ron Elber
Journal: J Chem Phys Date: 2004-06-15 Impact factor: 3.488

3. Simulations of thermodynamics and kinetics on rough energy landscapes with milestoning.

Authors: Juan M Bello-Rivas; Ron Elber
Journal: J Comput Chem Date: 2015-08-12 Impact factor: 3.376

4. Umbrella sampling for nonequilibrium processes.

Authors: Aryeh Warmflash; Prabhakar Bhimalapuram; Aaron R Dinner
Journal: J Chem Phys Date: 2007-10-21 Impact factor: 3.488

5. Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics.

Authors: John D Chodera; Nina Singhal; Vijay S Pande; Ken A Dill; William C Swope
Journal: J Chem Phys Date: 2007-04-21 Impact factor: 3.488

6. Exact rate calculations by trajectory parallelization and tilting.

Authors: Eric Vanden-Eijnden; Maddalena Venturoli
Journal: J Chem Phys Date: 2009-07-28 Impact factor: 3.488

7. Exact milestoning.

Authors: Juan M Bello-Rivas; Ron Elber
Journal: J Chem Phys Date: 2015-03-07 Impact factor: 3.488

8. A replica exchange transition interface sampling method with multiple interface sets for investigating networks of rare events.

Authors: David W H Swenson; Peter G Bolhuis
Journal: J Chem Phys Date: 2014-07-28 Impact factor: 3.488

Review 5. Dissecting Multiple Pathways in the Relaxation Dynamics of Helix <==> Coil Transitions with Optimum Dimensionality Reduction.

Authors: Gouri S Jas; Ed W Childs; C Russell Middaugh; Krzysztof Kuczera
Journal: Biomolecules Date: 2021-09-12

5 in total

A MATHEMATICAL FRAMEWORK FOR EXACT MILESTONING.

1. Transition path sampling: throwing ropes over rough mountain passes, in the dark.

2. Computing time scales from reaction coordinates by milestoning.

3. Simulations of thermodynamics and kinetics on rough energy landscapes with milestoning.

4. Umbrella sampling for nonequilibrium processes.

5. Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics.

6. Exact rate calculations by trajectory parallelization and tilting.

7. Exact milestoning.

8. A replica exchange transition interface sampling method with multiple interface sets for investigating networks of rare events.

9. Revisiting and computing reaction coordinates with Directional Milestoning.

10. MOIL-opt: Energy-Conserving Molecular Dynamics on a GPU/CPU system.

1. Committors, first-passage times, fluxes, Markov states, milestones, and all that.

2. Value of Temporal Information When Analyzing Reaction Coordinates.

3. Conformational Free Energy Changes via an Alchemical Path without Reaction Coordinates.

4. Long-Time-Scale Predictions from Short-Trajectory Data: A Benchmark Analysis of the Trp-Cage Miniprotein.

Review 5. Dissecting Multiple Pathways in the Relaxation Dynamics of Helix <==> Coil Transitions with Optimum Dimensionality Reduction.