1. Leipzig, 17 May 20071 Markov Models of Protein Folding - Application to Molecular Dynamics Simulations Christian Hedegaard Jensen

2. Leipzig, 17 May 20072 Outline Markov Models and Molecular Dynamics Simulations Investigating Accelerated Molecular Dynamics

3. Leipzig, 17 May 20073 Outline Markov Models and Molecular Dynamics Simulations Investigating Accelerated Molecular Dynamics

4. Leipzig, 17 May 20074 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

5. Leipzig, 17 May 20075 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.

6. Leipzig, 17 May 20076 Calculating Mean First Passage Times

7. Leipzig, 17 May 20077 Cluster Variation

8. Leipzig, 17 May 20078 Sensitivity

9. Leipzig, 17 May 20079 Sensitivity

10. Leipzig, 17 May 200710 Sensitivity

11. Leipzig, 17 May 200711 Outline Markov Models and Molecular Dynamics Simulations Investigating Accelerated Molecular Dynamics

12. Leipzig, 17 May 200712 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.

13. Leipzig, 17 May 200713 Scaled Potentials Scale potential by constant Energy differences Assuming transition state theory: similar to changing temperature

14. Leipzig, 17 May 200714 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

15. Leipzig, 17 May 200715 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.

16. Leipzig, 17 May 200716 Thank you