Cardini, Gianni

Chelli, Riccardo

Giovannelli, Edoardo

Procacci, Piero

Signorini, Giorgio Federico

English

Florence Research

Implementations of nonequilibrium methods for free energy calculations: forthcomingdevelopments of the ORAC molecular dynamics simulation codeRiccardo Chelli,∗ Gianni Cardini, Edoardo Giovannelli, Giorgio F. Signorini, and Piero Procacci†Dipartimento di Chimica, Universita` di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy(Dated: May 20, 2015)ORAC is a FORTRAN suite to simulate complexbiosystems at the atomistic level[1, 2]. The program’sengine is supplemented by multiple time steps integra-tion, smooth particle mesh Ewald method, constant pres-sure and constant temperature algorithms. Quite re-cently, several advanced techniques for enhanced sam-pling in atomistic systems have been implemented,including replica exchange with solute tempering[2],metadynamics[2], steered molecular dynamics[2], serialgeneralized ensemble simulations[3, 4] and nonequilib-rium alchemical transformations[5]. All these computa-tional technologies have been devised for parallel archi-tectures using the standard MPI communication proto-col.Further instances are being implemented in the ORACcode, concerning algorithms aimed at improving speedupof nonequilibrium molecular dynamics simulations. Inparticular, two quite recent computational schemes,called path-breaking[6, 7] and dynamical freezing[8], arecurrently under study. The former approach is specif-ically addressed to unidirectional nonequilibrium simu-lations for the calculation of free energy differences viaJarzynski’s equality[9]. The method faces one of themost important drawbacks of unidirectional nonequilib-rium simulations, which deals with the large amount ofrealizations necessary to reach suitable convergence ofthe work exponential average featuring the Jarzynski’srelation. In this respect, a significant improvement ofthe performances has been obtained by finding a way ofstopping nonequilibrium simulation trajectories, featuredby negligible contribution to the work exponential aver-age, before their normal end. This is just achieved withpath-breaking schemes, which are essentially based onperiodic checks of the work dissipated during the pullingtrajectories. Such schemes can be based either on break-ing trajectories whose dissipated work exceeds a giventhreshold or on breaking trajectories with a probabilityincreasing with the dissipated work. In both cases, thecomputer time needed to carry out a series of nonequilib-rium trajectories is reduced up to a factor ranging from 2to more than 10, for processes of almost different nature,such as the helix-coil transition of deca-alanine and thepulling of the distance between two methane molecules inwater solution (simulation tests can be found in Ref. [6]).The efficiency of the method depends on several aspects,such as the nature of the considered process, the numberof check-points along the pathway and the pulling rateas well.Path-breaking into ORAC is being devised to make af-fordable calculations on different typologies of computingarchitectures. The first target, which is currently underdevelopment, is to design a code for a distributed com-puting grid made of non-homogeneous cores, with negli-gible inter-core communications. The second possibilityis to implement path-breaking under Message Passing In-terface environment, eventually suitable for calculationson High Performance Computing platforms.Combination of path-breaking with bidirectionalnonequilibrium simulations for free energy calculations[7]is also possible and will be addressed in future develop-ments of the ORAC project.The other nonequilibrium technique (dynamical freez-ing) under study for implementation in the ORAC codeis based on a different concept, even if it also deals withthe difficulties of nonequilibrium pulling simulations inrecovering free energy differences, especially due to thepoor convergence of path-ensemble averages. As alreadystated, a large number of nonequilibrium trajectories isnecessary to achieve free energy estimates with accept-able accuracy. Dynamical freezing improves free energyestimates by lowering the computational cost of steeredmolecular dynamics simulations employed to realize suchtrajectories. This is accomplished by generating trajecto-ries where the particles not directly involved in the drivenprocess are dynamically frozen. Such a freezing is dy-namical rather than thermal because it is reached by asynchronous scaling of atomic masses and velocities keep-ing the kinetic energy of each particle unchanged. Theforces between dynamically frozen particles can then becalculated rarely. Thus, it is possible to generate realiza-tions of a process whose computational cost is not cor-related with the size of the whole system, but only withthat of the reaction site. The method is on the up gradeby borrowing the concept of configurational freezing, im-plemented for Monte Carlo simulations[10]. A sphere ofmobility of established radius is enforced around the siteof the process, while all other particles are fixed. Bothapproaches, path-breaking and dynamical freezing, areplanned to be integrated with nonequilibrium alchemicaltransformations already implemented in the ORAC code.ORAC is an open-source program distributed free ofcharge under the GNU general public license (GPL)http://www.chim.unifi.it/orac.∗ riccardo.chelli@unifi.it † piero.procacci@unifi.itVIRT&L-COMM.7.2015.7ISSN: 2279-87732[1] P. Procacci, T. A. Darden, E. Paci, and M. Marchi.Orac: A molecular dynamics program to simulate com-plex molecular systems with realistic electrostatic inter-actions. J. Comput. Chem., 18:1848, 1997.[2] S. Marsili, G. F. Signorini, R. Chelli, M. Marchi, andP. Procacci. Orac: a molecular dynamics simulation pro-gram to explore free energy surfaces in biomolecular sys-tems at the atomistic level. J. Comput. Chem., 31:1106,2010.[3] R. Chelli. Optimal weights in serial generalized-ensemblesimulations. J. Chem. Theory Comput., 6:1935, 2010.[4] R. Chelli and G. Signorini. Serial generalized ensemblesimulations of biomolecules with self-consistent determi-nation of weights. J. Chem. Theory Comput., 8:830, 2012.[5] P. Procacci and C. Cardelli. Fast switching alchemicaltransformations in molecular dynamics simulations. J.Chem. Theory Comput., 10:2813, 2014.[6] R. Chelli, C. Gellini, G. Pietraperzia, E. Giovannelli, andG. Cardini. Path-breaking schemes for nonequilibriumfree energy calculations. J. Chem. Phys., 138:214109,2013.[7] E. Giovannelli, C. Gellini, G. Pietraperzia, G. Cardini,and R. Chelli. Combining path-breaking with bidirec-tional nonequilibrium simulations to improve efficiencyin free energy calculations. J. Chem. Phys., 140:064104,2014.[8] P. Nicolini and R. Chelli. Improving fast-switching freeenergy estimates by dynamical freezing. Phys. Rev. E,80:041124, 2009.[9] C. Jarzynski. Nonequilibrium equality for free energydifferences. Phys. Rev. Lett., 78:2690, 1997.[10] P. Nicolini, D. Frezzato, and R. Chelli. Exploiting con-figurational freezing in nonequilibrium monte carlo sim-ulations. J. Chem. Theory Comput., 7:582, 2011.VIRT&L-COMM.7.2015.7ISSN: 2279-8773

Implementations of nonequilibrium methods for free energy calculations: forthcoming developments of the ORAC molecular dynamics simulation code

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Implementations of nonequilibrium methods for free energy calculations: forthcoming developments of the ORAC molecular dynamics simulation code

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