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Markov Models of Protein Folding

- Application to Molecular Dynamics Simulations

Christian Hedegaard Jensen

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Outline

• Markov Models and Molecular Dynamics Simulations

• Investigating Accelerated Molecular Dynamics

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Outline

• Markov Models and Molecular Dynamics Simulations

• Investigating Accelerated Molecular Dynamics

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Basic Idea

• Do many Molecular Dynamics Simulations

• Cluster the trajectories into discrete states

• Combine the information about transitions from all the trajectories into a single Markov model transition matrix.

• This allows for highly parallel simulations. E.g. Folding@Home

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How Sensitive is the Dynamics to Clustering

• Investigate a small peptide VPAL• 500ns MD simulation with explicit

water at 300k• How sensitive are the mean first

passage times between states, to the clustering of the states.

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Calculating Mean First Passage Times

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Cluster Variation

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Sensitivity

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Sensitivity

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Sensitivity

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Outline

• Markov Models and Molecular Dynamics Simulations

• Investigating Accelerated Molecular Dynamics

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Accelerated Molecular Dynamics

• Modify the potential energy landscape to speed up transitions between states.

D. Hamelberg, J. Mongan, and J. A. McCammon. Accelerated molecular dynamics: a promising and e±cient simulation method for biomolecules. Journal of Chemical Physics, 120(24):11919-11929, 2004.A. F. Voter. Hyperdynamics: Accelerated molecular dynamics of infrequent events. Physical Review Letters, 78(20):3908-3911, 1997.A. F. Voter. A method for accelerating the molecular dynamics simulation of infrequent events. Journal of Chemical Physics, 106(11):4665-4677, 1997.

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Scaled Potentials

• Scale potential by constant

• Energy differences

• Assuming transition state theory: similar to changing temperature

10 ~ VV

2121 VVVV

TkEB

r *exp

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Scaled Potentials

• Possible use 1:– Do a simulation with <1

• Possible use 2:– Start with =1– For every e.g. 10ps in same minima change =

0.9*– When in new minima reset =1

• This means that the potentials are modified just enough (and no more) to escape a minima within a reasonable time

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Scaled Potentials

• Do calculations with different and investigate the change in mean first passage times between states.

• Compare to simulations done at different temperatures.

• If there is a significant speedup implement algorithm.

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Thank you