View
23
Download
0
Category
Preview:
DESCRIPTION
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. - PowerPoint PPT Presentation
Citation preview
An improved hybrid An improved hybrid Monte Carlo method for Monte Carlo method for conformational sampling conformational sampling
of large biomoleculesof large biomolecules
Department of Computer Science Department of Computer Science and Engineeringand Engineering
University of Notre DameUniversity of Notre DameNotre Dame, IN 46556-0309Notre Dame, IN 46556-0309
Scott Hampton and Jesus A. Izaguirre
shampton@cse.nd.edu izaguirr@cse.nd.edu
SummarySummary
What is the problem?What is the problem? Why are we interested?Why are we interested? Why is it challenging?Why is it challenging?
Multiple-minima problemMultiple-minima problem Size of the moleculesSize of the molecules Multiple time scalesMultiple time scales
Our contributionOur contribution
Molecular SimulationMolecular Simulation
Molecular Molecular
DynamicsDynamics Monte Carlo Monte Carlo
methodmethod Sampling:Sampling:
f Ma
HMC AlgorithmHMC Algorithm
Start with some initial configuration Start with some initial configuration (q,p)(q,p)
Perform Perform cyclelengthcyclelength steps of MD, steps of MD, using timestep using timestep t,t, generating generating (q’,p’)(q’,p’)
Compute change in total energyCompute change in total energy H = H = H(q’,p’) - H(q’,p’) - H(q,p)H(q,p)
Accept new state based on Accept new state based on exp(-exp(- H H ))
Hybrid Monte CarloHybrid Monte Carlo
Hybrid Monte Carlo Method (HMC)Hybrid Monte Carlo Method (HMC) Combination of MD and MC methodsCombination of MD and MC methods Poor scalability of sampling rate with Poor scalability of sampling rate with
system size Nsystem size N Improvement with higher order Improvement with higher order
methods (Creutz, et. al.)methods (Creutz, et. al.) Our method scales better than HMCOur method scales better than HMC
Shadow HamiltonianShadow Hamiltonian
Based on work by Skeel and Hardy [1]Based on work by Skeel and Hardy [1] Hamiltonian: Hamiltonian: H=1/2pH=1/2pTTMM-1-1p + U(q)p + U(q) Modified Hamiltonian: Modified Hamiltonian: HHMM = H + O( = H + O(t t pp))
Shadow Hamiltonian: Shadow Hamiltonian: HHSS = H = HMM + O( + O(t t 2p2p)) Arbitrary accuracyArbitrary accuracy Easy to computeEasy to compute Stable energy graphStable energy graph
HH4 4 = H – f( q= H – f( qn-1n-1, q, qn-2n-2, p, pn-1n-1, p, pn-2n-2 ) )
Shadow HMCShadow HMC
Replace total energy Replace total energy HH with shadow with shadow energyenergy HHSS = = HHSS (q’,p’) - (q’,p’) - HHSS (q,p) (q,p)
Nearly linear scalability of sampling Nearly linear scalability of sampling raterate
Extra storageExtra storage Small overheadSmall overhead
Acceptance RatesAcceptance Rates
More Acceptance RatesMore Acceptance Rates
Sampling rateSampling rate
ConclusionsConclusions
SHMC has a much higher acceptance SHMC has a much higher acceptance rate, particularly as system size and rate, particularly as system size and timestep increasetimestep increase
SHMC discovers new conformations SHMC discovers new conformations more quicklymore quickly
SHMC requires extra storage and SHMC requires extra storage and moderate overhead.moderate overhead.
SHMC works best at relatively large SHMC works best at relatively large timestepstimesteps
Future WorkFuture Work
Are results valid?Are results valid? Theoretically validTheoretically valid BiasBias
What’s next?What’s next? Multiple Time Stepping (MTS)Multiple Time Stepping (MTS) Combining SHMC with other methodsCombining SHMC with other methods
AcknowledgementsAcknowledgements
This work was supported by NSF This work was supported by NSF Grant BIOCOMPLEXITY-IBN-Grant BIOCOMPLEXITY-IBN-0083653 and NSF CAREER award 0083653 and NSF CAREER award ACI-0135195ACI-0135195
SH was also supported by an Arthur SH was also supported by an Arthur J. Schmitt fellowship from the J. Schmitt fellowship from the University of Notre DameUniversity of Notre Dame
ReferencesReferences
1.1. R. D. Skeel and D. J. Hardy. R. D. Skeel and D. J. Hardy. Practical construction of modified Practical construction of modified Hamiltonians. Hamiltonians. SIAM J. on Sci. SIAM J. on Sci. Computing,Computing, 23(4):1172-1188, Nov. 23(4):1172-1188, Nov. 2001.2001.
2.2. GaSh00GaSh00
3.3. Sampling method paperSampling method paper
LeapfrogLeapfrog
Recommended