# Optimized Markov state models for metastable systems.

@article{Guarnera2016OptimizedMS, title={Optimized Markov state models for metastable systems.}, author={Enrico Guarnera and Eric Vanden-Eijnden}, journal={The Journal of chemical physics}, year={2016}, volume={145 2}, pages={ 024102 } }

A method is proposed to identify target states that optimize a metastability index amongst a set of trial states and use these target states as milestones (or core sets) to build Markov State Models (MSMs). If the optimized metastability index is small, this automatically guarantees the accuracy of the MSM, in the sense that the transitions between the target milestones is indeed approximately Markovian. The method is simple to implement and use, it does not require that the dynamics on the…

## Figures and Tables from this paper

## 16 Citations

Markov state models from hierarchical density-based assignment.

- Computer ScienceThe Journal of chemical physics
- 2021

This work proposes a variation on this typical workflow, taking advantage of hierarchical density-based clustering, and implements assignment of the data based on transitions between metastable states, resulting in a core-set MSM.

Markov state models from hierarchical density-based assignment

- Computer SciencebioRxiv
- 2021

This work proposes a variation on this typical workflow, taking advantage of hierarchical density-based clustering, and results are presented for a model potential and MD simulations of the alanine dipeptide and the FiP35 WW domain.

Hierarchical Markov State Model Building to Describe Molecular Processes.

- Computer ScienceJournal of chemical theory and computation
- 2020

The advantages of this Hierarchical Markov state model are that it is more realistic than the conventional chain-of-states approach as an ensemble of pathways rather than a single pathway is used to describe processes in high-dimensional systems, and it resolves the issue of poor sampling in Markov State model building when large free energy barriers are present.

On the removal of initial state bias from simulation data.

- Computer ScienceThe Journal of chemical physics
- 2019

This contribution analyzes the performance of MSMs in the thermodynamic reweighting task for a hierarchical set of systems and shows that MSMs can be rigorous tools to recover the correct equilibrium distribution for systems of sufficiently low dimensionality.

On the advantages of exploiting memory in Markov state models for biomolecular dynamics.

- BiologyThe Journal of chemical physics
- 2020

It is demonstrated that it is possible to construct quasi-Markov State Models (qMSMs) using MD simulations that are 5-10 times shorter than those required by MSMs, which opens the door to the study of conformational changes of complex biomolecules.

Quantifying Energetic and Entropic Pathways in Molecular Systems.

- PhysicsThe journal of physical chemistry. B
- 2022

When examining dynamics occurring at nonzero temperatures, both energy and entropy must be taken into account to describe activated barrier crossing events. Furthermore, good reaction coordinates…

What Markov State Models Can and Cannot Do: Correlation versus Path-Based Observables in Protein-Folding Models.

- PhysicsJournal of chemical theory and computation
- 2021

An extensive assessment of the ability of well-validated protein folding MSMs to accurately reproduce path-based observable such as mean first-passage times (MFPTs) and transition path mechanisms compared to a direct trajectory analysis and a recently proposed class of history-augmented MSMs (haMSMs) that exploit additional information not accounted for in standard MSMs.

Density-based cluster algorithms for the identification of core sets.

- Computer ScienceThe Journal of chemical physics
- 2016

The key point is to perform a hierarchical density-based clustering while monitoring the structure of the metric matrix which appears in the core-set method, which has a high spatial resolution and can distinguish between conformationally similar yet chemically different structures, such as register-shifted hairpin structures.

What Markov state models can and cannot do: Correlation versus path-based observables in protein folding models

- PhysicsbioRxiv
- 2020

An extensive assessment of the ability of well-validated protein folding MSMs to accuractely reproduce path-based observable such as mean first-passage times (MFPTs) and transition path mechanisms compared to a direct trajectory analysis and a recently proposed class of history-augmented MSMs (haMSMs) that exploit additional information not accounted for in standard MSMs.

A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)

- Computer Science
- 2016

It is proved that optimal milestoning permits the exact calculation of the mean first passage times (MFPT) between any two milestones.

## References

SHOWING 1-10 OF 141 REFERENCES

Markov state models based on milestoning.

- Computer ScienceThe Journal of chemical physics
- 2011

It is shown that Core Set MSMs can be used to extract phenomenological rate constants between the metastable sets of the system and to approximate the evolution of certain key observables.

On the Approximation Quality of Markov State Models

- MathematicsMultiscale Model. Simul.
- 2010

A sharp error bound for the difference in propagation of probability densities between the MSM and the original process on long timescales is provided for a rather general class of Markov processes ranging from diffusions in energy landscapes to Markov jump processes on large discrete spaces.

Statistical model selection for Markov models of biomolecular dynamics.

- Computer ScienceThe journal of physical chemistry. B
- 2014

Application of techniques that consider both systematic bias and statistical error on two 100 μs molecular dynamics trajectories of the Fip35 WW domain shows agreement with existing techniques based on self-consistency of the model's relaxation time scales with more suitable results in regimes in which those time scale-based techniques encourage overfitting.

Metastability and Markov State Models in Molecular Dynamics: Modeling, Analysis, Algorithmic Approaches

- Biology
- 2013

This book bridges the gap between mathematical research on molecular dynamics and its practical use for realistic molecular systems by providing readers with tools for performing in-depth analysis of simulation and data-analysis methods.

Metastability and Low Lying Spectra¶in Reversible Markov Chains

- Mathematics
- 2000

Abstract: We study a large class of reversible Markov chains with discrete state space and transition matrix PN. We define the notion of a set of metastable points as a subset of the state space ΓN…

On the assumptions underlying milestoning.

- Computer ScienceThe Journal of chemical physics
- 2008

This paper shows that sets of optimal milestones exist, i.e., sets such that successive transitions are indeed statistically independent, and explains why the time lags between transitions are not statistically independent even for optimal milestones, but it is shown that working with such milestones allows one to compute mean first passage times between milestones exactly.

Automatic Selection of Order Parameters in the Analysis of Large Scale Molecular Dynamics Simulations

- Computer ScienceJournal of chemical theory and computation
- 2014

This work introduces a method called clustering based feature selection (CB-FS) that combines supervised machine learning and feature selection with Markov state models to automatically identify the relevant degrees of freedom that separate conformational states and demonstrates the utility of this method in the evaluation of large-scale simulations.

Protein folded states are kinetic hubs

- BiologyProceedings of the National Academy of Sciences
- 2010

These models show that protein dynamics are dominated by stochastic jumps between numerous metastable states and that proteins have heterogeneous unfolded states yet often still appear two-state, and find that protein native states are hubs that can be reached quickly from any other state, however, metastability and a web of nonnative states slow the average folding rate.

Describing Protein Folding Kinetics by Molecular Dynamics Simulations. 1. Theory

- Chemistry
- 2004

A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study…

Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories.

- Computer ScienceJournal of chemical theory and computation
- 2012

A tree-based algorithm to partition conformations of biomolecules into sets of similar microstates, i.e., to coarse-grain trajectory data into mesostates is presented and it is demonstrated that the derived mesostate networks can preserve information regarding the free energy basins and barriers by which the system is characterized.