Czaplewski, C.

Kalinowski, S.

Liwo, A.

Oldziej, S.

Scheraga, H. A.

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John von Neumann Institute for ComputingMultiplexed-Replica Exchange MolecularDynamics with the UNRES Force-Field as anEffective Method for Exploring theConformational Energy Landscape of Proteins.Cezary Czaplewski, Sebastian Kalinowski,Stanislaw Ołdziej, Adam Liwo, Harold A. Scheragapublished inNIC Workshop 2006,From Computational Biophysics to Systems Biology,Jan Meinke, Olav Zimmermann,Sandipan Mohanty, Ulrich H.E. Hansmann (Editors)John von Neumann Institute for Computing, Ju¨lich,NIC Series, Vol. 34, ISBN-10: 3-9810843-0-6,ISBN-13: 978-3-9810843-0-6, pp. 63-66, 2006.c© 2006 by John von Neumann Institute for ComputingPermission to make digital or hard copies of portions of this work forpersonal or classroom use is granted provided that the copies are notmade or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwiserequires prior specific permission by the publisher mentioned above.http://www.fz-juelich.de/nic-series/volume34Multiplexed-Replica Exchange Molecular Dynamics withthe UNRES Force-Field as an Effective Method forExploring the Conformational Energy Landscape ofProteins.Cezary Czaplewski1,2, Sebastian Kalinowski2, Stanisław Ołdziej1,2, Adam Liwo1,2,and Harold A. Scheraga11 Baker Laboratory of Chemistry and Chemical Biology,Cornell University, Ithaca, NY 14853-1301, U.S.A.,E-mail: has5@cornell.edu2 Faculty of Chemistry, University of Gdan´sk,Sobieskiego 18, 80-952 Gdan´sk, PolandThe theoretical prediction of the three-dimensional structures of proteins purely from an amino-acid sequence is a grand challenge of computational biophysics. Here, we present simulationsusing an effective search algorithm combined with the united residue force-field. In the replicaexchange method, the kinetic trapping problem is overcome by exchanging noninteracting repli-cas simulated at different temperatures. To enhance sampling, the replicas are multiplexedwith a number of independent molecular dynamics runs at each temperature. The simulatedfree-energy landscape is presented for 1CLB protein. Application of the multiplexed-replicaexchange algorithm to large-scale parallel computing is discussed.1 IntroductionEfficient conformational sampling algorithms are an essential component of methods forstudying protein structure and dynamics. Methods such as canonical Molecular Dynamics(MD) or Metropolis Monte Carlo (MC) can be used for estimating thermodynamic proper-ties as well as for a global search, but in practice they easily become trapped, and thus arenot effective methods for studying rough free-energy landscapes of proteins.One of the most effective sampling methods, the Replica Exchange method (alsoknown as Exchange MC1, or Parallel Tempering2), was initially developed to improve sam-pling in glassy systems in statistical physics. However, following Hansmann’s use of themethod in Monte Carlo simulations of a simple peptide, Met-enkephalin2 and Okamoto andSugita’s formulation of an MD version of the algorithm,3 the Replica Exchange method hasbeen applied extensively in protein-folding simulations.2 MethodsIn the united-residue physics-based UNRES model,4–6 a polypeptide chain is representedby a sequence of α-carbon (Cα) atoms linked by virtual bonds with attached united sidechains (SC) and united peptide groups (p) positioned in the middle between two consec-utive Cα atoms. The UNRES force field has been derived as a Restricted Free Energy(RFE) function decomposed into factors arising from interactions within and between a63given number of united interaction sites5. The selected parameters of the UNRES force-field were refined by hierarchical optimization6 of the potential-energy function.The Replica Exchange MD (REMD) method combines the idea of simulated annealingand Monte Carlo methods, and is one of the generalized-ensemble algorithms that performsa random walk in energy space due to a free random walk in temperature space. In theREMD method, n replica systems, each in the canonical ensemble, and each at a differenttemperature, are simulated. At given intervals, swaps, or exchanges, of the configurationalvariables between systems are accepted with the Metropolis criteria. In this paper, weare using multiplex REMD (MREMD) introduced by Pande7. In MREMD, to enhancesampling, the replicas are multiplexed with a number of independent molecular dynamicsruns at each temperature. Exchanges of configurations only between random replicas withneighboring temperatures are tried.3 Results and DiscussionThe free energy is the most important quantity for the description of equilibrium propertiesof proteins. An example of the simulated free-energy landscape for the 1CLB protein isshown in Figure 1.Figure 1. Free energy landscape of 1CLB protein as a function of rmsd and radius of gyration, and representativestructures from low free-energy regions.To calculate free energy profiles, we used the densities of states obtained from themulti-histogram analysis of MREMD trajectories.8 From the densities of states, we calcu-lated the microcanonical entropy, S(Ei) = kBln[n(Ei)], for all conformations collectedfrom the simulations, and used it to compute the microcanonical free energies with the64following expression: F (Ei, T ) = Ei − TS(Ei). To plot the free energy as a functionof rmsd (r) and radius of gyration (ρ), we calculated the free energy by evaluating thefollowing expression for each grid point:F (r, ρ, T ) = −kBT ln∑Ei∈N(r,ρ)exp(−F (Ei, T )kBT)(1)where the index i enumerates conformations within the histogram bins, N(r, ρ), for givenranges of rmsd and radius of gyration.Parallelization of the MREMD method has been enhanced by removing the synchro-nization step. The exchanges of configurations between random replicas with neighboringtemperatures are tried, not at the same number of MD steps for each replica but are forcedby the replica with the lowest temperature independent of the number of steps performedby the other replicas. The improved algorithm scales almost linearly up to 1,000 processorswith over 80% average performance.AcknowledgmentsSupport from the National Institutes of Health (grant GM-14312), the National ScienceFoundation (grant MCB00-03722), the NIH Fogarty International Center (grant TW7193),the Polish Ministry of Education and Science (grant 3 T09A 032 26) as well as use of su-percomputing resources at the National Science Foundation Terascale Computing Systemat the Pittsburgh Supercomputer Center is gratefully acknowledged.References1. K. Hukushima and K. Nemoto. Exchange monte carlo method and application to spinglass simulations. J. Phys. Soc. Jpn., 65:1604–1608, 1996.2. U. H. E. Hansmann. Parallel tempering algorithm for conformational studies ofbiological molecules. Chem. Phys. Lett., 281:140–150, 1997.3. Y. Sugita and Y. Okamoto. Replica-exchange molecular dynamics method for proteinfolding. Chem. Phys. Lett., 314:141–151, 1999.4. A. Liwo, S. Ołdziej, M. R. Pincus, R. J. Wawak, S. Rackovsky, and H. A. Scher-aga. A united-residue force field for off-lattice protein-structure simulations. I.functional forms and parameters of long-range side-chain interaction potentials fromprotein crystal data. J. Comput. Chem., 18:849–873, 1997.5. A. Liwo, C. Czaplewski, J. Pillardy, and H. A. Scheraga. Cumulant-based expressionsfor the multibody terms for the correlation between local and electrostatic interactionsin the united-residue force field. J. Chem. Phys., 115:2323–2347, 2001.6. S. Ołdziej, J. Ła¸giewka, A. Liwo, C. Czaplewski, M. Chinchio, M. Nanias, and H. A.Scheraga. Optimization of the unres force field by hierarchical design of the potential-energy landscape. 3. use of many proteins in optimization. J. Phys. Chem. B,108:16950–16959, 2004.7. Y. M. Rhee and V. S. Pande. Multiplexed-replica exchange molecular dynamicsmethod for protein folding simulation. Biophys. J., 84:775–786, 2003.658. M. Nanias, C. Czaplewski, and H. A. Scheraga. Replica exchange and multicanonicalalgorithms with the coarse-grained united-residue (UNRES) force field. J. Chem.Theor. Comput., 2:513–528, 2006.66

Multiplexed-Replica Exchange Molecular Dynamics with the UNRES Force-Field as an Effective Method for Exploring the Conformational Energy Landscape of Proteins.

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Multiplexed-Replica Exchange Molecular Dynamics with the UNRES Force-Field as an Effective Method for Exploring the Conformational Energy Landscape of Proteins.

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