The multiscale coarse-graining method. X. Improved algorithms for constructing coarse-grained potentials for molecular systems.

The multiscale coarse-graining (MS-CG) method uses simulation data for an atomistic model of a system to construct a coarse-grained (CG) potential for a coarse-grained model of the system. The CG potential is a variational approximation for the true potential of mean force of the degrees of freedom retained in the CG model. The variational calculation uses information about the atomistic positions and forces in the simulation data. In principle, the resulting MS-CG potential will be an accurate representation of the true CG potential if the basis set for the variational calculation is complete enough and the canonical distribution of atomistic states is well sampled by the data set. In practice, atomistic configurations that have very high potential energy are not sampled. As a result there usually is a region of CG configuration space that is not sampled and about which the data set contains no information regarding the gradient of the true potential. The MS-CG potential obtained from a variational calculation will not necessarily be accurate in this unsampled region. A priori considerations make it clear that the true CG potential of mean force must be very large and positive in that region. To obtain an MS-CG potential whose behavior in the sampled region is determined by the atomistic data set, and whose behavior in the unsampled region is large and positive, it is necessary to intervene in the variational calculation in some way. In this paper, we discuss and compare two such methods of intervention, which have been used in previous MS-CG calculations for dealing with nonbonded interactions. For the test systems studied, the two methods give similar results and yield MS-CG potentials that are limited in accuracy only by the incompleteness of the basis set and the statistical error of associated with the set of atomistic configurations used. The use of such methods is important for obtaining accurate CG potentials.

[1]  Gregory A. Voth,et al.  Systematic coarse-graining of a multicomponent lipid bilayer. , 2009, The journal of physical chemistry. B.

[2]  J. Kress,et al.  Coarse-grained rigid blob model for soft matter simulations. , 2005, The Journal of chemical physics.

[3]  Alexander Lukyanov,et al.  Versatile Object-Oriented Toolkit for Coarse-Graining Applications. , 2009, Journal of chemical theory and computation.

[4]  Gregory A Voth,et al.  The multiscale coarse-graining method. IV. Transferring coarse-grained potentials between temperatures. , 2009, The Journal of chemical physics.

[5]  Kurt Kremer,et al.  Dual-resolution coarse-grained simulation of the bisphenol-A-polycarbonate/nickel interface. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  J. Andrew McCammon,et al.  A coarse grained model for the dynamics of flap opening in HIV-1 protease , 2005 .

[7]  Jeremy C. Smith,et al.  REACH coarse-grained biomolecular simulation: transferability between different protein structural classes. , 2008, Biophysical journal.

[8]  A polarizable coarse-grained water model for coarse-grained proteins simulations , 2009 .

[9]  Gregory A Voth,et al.  Efficient, Regularized, and Scalable Algorithms for Multiscale Coarse-Graining. , 2010, Journal of chemical theory and computation.

[10]  Michael L. Klein,et al.  A coarse grain model for n-alkanes parameterized from surface tension data , 2003 .

[11]  R. Larson,et al.  The MARTINI Coarse-Grained Force Field: Extension to Proteins. , 2008, Journal of chemical theory and computation.

[12]  S. Nosé.  A molecular dynamics method for simulations in the canonical ensemble , 1984 .

[13]  Jianpeng Ma,et al.  A minimalist network model for coarse-grained normal mode analysis and its application to biomolecular x-ray crystallography , 2008, Proceedings of the National Academy of Sciences.

[14]  Ruth Nussinov,et al.  Coarse-graining the Self-assembly of β-helical Protein Building Blocks , 2007 .

[15]  A. Mark,et al.  Coarse grained model for semiquantitative lipid simulations , 2004 .

[16]  Gregory A Voth,et al.  Peptide folding using multiscale coarse-grained models. , 2008, The journal of physical chemistry. B.

[17]  Avisek Das,et al.  The multiscale coarse-graining method. V. Isothermal-isobaric ensemble. , 2010, The Journal of chemical physics.

[18]  I. Bahar,et al.  Coarse-grained normal mode analysis in structural biology. , 2005, Current opinion in structural biology.

[19]  Robert E. Rudd,et al.  COARSE-GRAINED MOLECULAR DYNAMICS AND THE ATOMIC LIMIT OF FINITE ELEMENTS , 1998 .

[20]  R. C. Reeder,et al.  A Coarse Grain Model for Phospholipid Simulations , 2001 .

[21]  Jun-ichi Takimoto,et al.  A coarse-graining procedure for flexible polymer chains with bonded and nonbonded interactions , 2002 .

[22]  N. Go,et al.  Noninteracting local‐structure model of folding and unfolding transition in globular proteins. I. Formulation , 1981, Biopolymers.

[23]  Gregory A Voth,et al.  Coarse-grained peptide modeling using a systematic multiscale approach. , 2007, Biophysical journal.

[24]  M. Levitt.  A simplified representation of protein conformations for rapid simulation of protein folding. , 1976, Journal of molecular biology.

[25]  A. Liwo,et al.  Parametrization of Backbone−Electrostatic and Multibody Contributions to the UNRES Force Field for Protein-Structure Prediction from Ab Initio Energy Surfaces of Model Systems† , 2004 .

[26]  Klaus Schulten,et al.  Coarse grained protein-lipid model with application to lipoprotein particles. , 2006, The journal of physical chemistry. B.

[27]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[28]  Valentina Tozzini,et al.  Coarse-grained models for proteins. , 2005, Current opinion in structural biology.

[29]  Gregory A Voth,et al.  Allostery of actin filaments: molecular dynamics simulations and coarse-grained analysis. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Ioannis G. Kevrekidis,et al.  Equation-free: The computer-aided analysis of complex multiscale systems , 2004 .

[31]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[32]  Haruo Abe,et al.  Noninteracting local‐structure model of folding and unfolding transition in globular proteins. II. Application to two‐dimensional lattice proteins , 1981, Biopolymers.

[33]  Michael L. Klein,et al.  Coarse grain models and the computer simulation of soft materials , 2004 .

[34]  Syma Khalid,et al.  Coarse-grained molecular dynamics simulations of membrane proteins and peptides. , 2007, Journal of structural biology.

[35]  Vijay S. Pande,et al.  Screen Savers of the World Unite! , 2000, Science.

[36]  Avisek Das,et al.  The multiscale coarse-graining method. III. A test of pairwise additivity of the coarse-grained potential and of new basis functions for the variational calculation. , 2009, The Journal of chemical physics.

[37]  Zhiyong Zhang,et al.  Coarse-Graining Protein Structures With Local Multivariate Features from Molecular Dynamics , 2008, The journal of physical chemistry. B.

[38]  Pengyu Y. Ren,et al.  Generalized coarse-grained model based on point multipole and Gay-Berne potentials. , 2006, The Journal of chemical physics.

[39]  W. C. Swope,et al.  A computer simulation method for the calculation of equilibrium constants for the formation of physi , 1981 .

[40]  H. C. Andersen.  Molecular dynamics simulations at constant pressure and/or temperature , 1980 .

[41]  A. Lyubartsev,et al.  Calculation of effective interaction potentials from radial distribution functions: A reverse Monte Carlo approach. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[42]  T. Head-Gordon,et al.  Minimalist models for protein folding and design. , 2003, Current opinion in structural biology.

[43]  Gregory A Voth,et al.  Multiscale modeling of biomolecular systems: in serial and in parallel. , 2007, Current opinion in structural biology.

[44]  Zesheng Li,et al.  An automatic coarse-graining and fine-graining simulation method: application on polyethylene. , 2006, The journal of physical chemistry. B.

[45]  Berend Smit,et al.  Molecular Dynamics Simulations , 2002 .

[46]  Gregory A Voth,et al.  A multiscale coarse-graining method for biomolecular systems. , 2005, The journal of physical chemistry. B.

[47]  Gregory A Voth,et al.  The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models. , 2008, The Journal of chemical physics.

[48]  R. Jernigan,et al.  Estimation of effective interresidue contact energies from protein crystal structures: quasi-chemical approximation , 1985 .

[49]  G. Phillips,et al.  Optimization and evaluation of a coarse-grained model of protein motion using x-ray crystal data. , 2006, Biophysical journal.

[50]  Marcus Mueller,et al.  Biological and synthetic membranes: What can be learned from a coarse-grained description? , 2006 .

[51]  Gregory A Voth,et al.  Multiscale coarse-graining of ionic liquids. , 2006, The journal of physical chemistry. B.

[52]  J. Straub,et al.  Orientational potentials extracted from protein structures improve native fold recognition , 2004, Protein science : a publication of the Protein Society.

[53]  A. Liwo,et al.  Cumulant-based expressions for the multibody terms for the correlation between local and electrostatic interactions in the united-residue force field , 2001 .

[54]  W. Goddard,et al.  M3B: A Coarse Grain Force Field for Molecular Simulations of Malto-Oligosaccharides and Their Water Mixtures , 2004 .

[55]  Reinier L. C. Akkermans,et al.  A structure-based coarse-grained model for polymer melts , 2001 .

[56]  Sergei Izvekov,et al.  Multiscale Coarse-Graining of Mixed Phospholipid/Cholesterol Bilayers. , 2006, Journal of chemical theory and computation.

[57]  Magdalena A. Jonikas,et al.  Coarse-grained modeling of large RNA molecules with knowledge-based potentials and structural filters. , 2009, RNA.

[58]  Holger Gohlke,et al.  A natural coarse graining for simulating large biomolecular motion. , 2006, Biophysical journal.

[59]  Gregory A. Voth,et al.  The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models. , 2008, The Journal of chemical physics.

[60]  Carsten Kutzner,et al.  GROMACS 4:  Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. , 2008, Journal of chemical theory and computation.

[61]  R. Pandey,et al.  Residue energy and mobility in sequence to global structure and dynamics of a HIV-1 protease (1DIFA) by a coarse-grained Monte Carlo simulation. , 2009, The Journal of chemical physics.

[62]  Qiang Shi,et al.  Mixed atomistic and coarse-grained molecular dynamics: simulation of a membrane-bound ion channel. , 2006, The journal of physical chemistry. B.

[63]  William George Noid,et al.  Extended ensemble approach for deriving transferable coarse-grained potentials , 2009 .

[64]  Dirk Reith,et al.  Deriving effective mesoscale potentials from atomistic simulations , 2002, J. Comput. Chem..

[65]  G. Voth,et al.  A new perspective on the coarse-grained dynamics of fluids. , 2004, The Journal of chemical physics.

[66]  W. L. Jorgensen,et al.  Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids , 1996 .

[67]  Gregory A Voth,et al.  Systematic coarse-graining of nanoparticle interactions in molecular dynamics simulation. , 2005, The journal of physical chemistry. B.

[68]  Gregory A Voth,et al.  Multiscale coarse graining of liquid-state systems. , 2005, The Journal of chemical physics.