# A Bayesian method for construction of Markov models to describe dynamics on various time scales

## Abstract/Contents

- Abstract
- The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This thesis presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (t, P, T), where t is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N x N transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. 1. The method uses Bayesian analysis to determine the partition as well as the transition probabilities. 2. The method allows the construction of a Markov model for any chosen mesoscopic time scale t. 3. It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a 'consistent mesoscopic Markov model' (or CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P, T) for any chosen t. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time scale t was generated by the CMMM specified by (P, T). An optimization algorithm is used to find the most probable CMMM for the chosen mesoscopic time step. We applied this method of Markov model construction to several toy systems (random walks in one and two dimensions) as well as the dynamics of alanine dipeptide in water and of trpzip2 in water. The resulting Markov state models were indeed successful in capturing the dynamics of our test systems on a variety of mesoscopic time scales.

## Description

Type of resource | text |
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Form | electronic; electronic resource; remote |

Extent | 1 online resource. |

Copyright date | 2011 |

Publication date | 2010, c2011; 2010 |

Issuance | monographic |

Language | English |

## Creators/Contributors

Associated with | Rains, Emily Kathleen |
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Associated with | Stanford University, Department of Chemistry |

Primary advisor | Andersen, Hans, 1941- |

Thesis advisor | Andersen, Hans, 1941- |

Thesis advisor | Fayer, Michael D |

Thesis advisor | Pande, Vijay |

Advisor | Fayer, Michael D |

Advisor | Pande, Vijay |

## Subjects

Genre | Theses |
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## Bibliographic information

Statement of responsibility | Emily Kathleen Rains. |
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Note | Submitted to the Department of Chemistry. |

Thesis | Ph.D. Stanford University 2011 |

Location | electronic resource |

## Access conditions

- Copyright
- © 2011 by Emily Kathleen Rains
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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