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An improved hybrid Monte Carlo method for conformational sampling of large biomolecules

An improved hybrid Monte Carlo method for conformational sampling of large biomolecules. Scott Hampton and Jesus A. Izaguirre shampton@cse.nd.edu izaguirr@cse.nd.edu. Department of Computer Science and Engineering University of Notre Dame Notre Dame, IN 46556-0309. Summary.

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An improved hybrid Monte Carlo method for conformational sampling of large biomolecules

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  1. An improved hybrid Monte Carlo method for conformational sampling of large biomolecules Scott Hampton and Jesus A. Izaguirre shampton@cse.nd.eduizaguirr@cse.nd.edu Department of Computer Science and Engineering University of Notre Dame Notre Dame, IN 46556-0309

  2. Summary • What is the problem? • Why are we interested? • Why is it challenging? • Multiple-minima problem • Size of the molecules • Multiple time scales • Our contribution

  3. Molecular Simulation • Molecular Dynamics • Monte Carlo method • Sampling:

  4. HMC Algorithm • Start with some initial configuration (q,p) • Perform cyclelength steps of MD, using timestep t, generating (q’,p’) • Compute change in total energy • H = H(q’,p’) - H(q,p) • Accept new state based on exp(- H )

  5. Hybrid Monte Carlo • Hybrid Monte Carlo Method (HMC) • Combination of MD and MC methods • Poor scalability of sampling rate with system size N • Improvement with higher order methods (Creutz, et. al.) • Our method scales better than HMC

  6. Shadow Hamiltonian Based on work by Skeel and Hardy [1] • Hamiltonian: H=1/2pTM-1p + U(q) • Modified Hamiltonian: HM = H + O(t p) • Shadow Hamiltonian: HS = HM + O(t 2p) • Arbitrary accuracy • Easy to compute • Stable energy graph • H4 = H – f( qn-1, qn-2, pn-1, pn-2 )

  7. Shadow HMC • Replace total energy H with shadow energy • HS = HS (q’,p’) - HS (q,p) • Nearly linear scalability of sampling rate • Extra storage • Small overhead

  8. Acceptance Rates

  9. More Acceptance Rates

  10. Sampling rate

  11. Conclusions • SHMC has a much higher acceptance rate, particularly as system size and timestep increase • SHMC discovers new conformations more quickly • SHMC requires extra storage and moderate overhead. • SHMC works best at relatively large timesteps

  12. Future Work • Are results valid? • Theoretically valid • Bias • What’s next? • Multiple Time Stepping (MTS) • Combining SHMC with other methods

  13. Acknowledgements • This work was supported by NSF Grant BIOCOMPLEXITY-IBN-0083653 and NSF CAREER award ACI-0135195 • SH was also supported by an Arthur J. Schmitt fellowship from the University of Notre Dame

  14. References • R. D. Skeel and D. J. Hardy. Practical construction of modified Hamiltonians. SIAM J. on Sci. Computing, 23(4):1172-1188, Nov. 2001. • GaSh00 • Sampling method paper

  15. Leapfrog

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