1 / 15

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.

Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related