Implementation and performance analysis of bridging Monte Carlo moves for off-lattice single chain polymers in globular states

Abstract Bridging algorithms are global Monte Carlo moves which allow for an efficient sampling of single polymer chains. In this manuscript we discuss the adaptation of three bridging algorithms from lattice to continuum models, and give details on the corrections to the acceptance rules which are required to fulfill detailed balance. For the first time we are able to compare the efficiency of the moves by analyzing the occurrence of knots in globular states. For a flexible homopolymer chain of length N = 1000 , independent configurations can be generated up to two orders of magnitude faster than with slithering snake moves.

[1]  Kurt Binder,et al.  Recent Developments in Monte Carlo Simulations of Lattice Models for Polymer Systems , 2008 .

[2]  Sidney Yip,et al.  Handbook of Materials Modeling , 2005 .

[3]  Peter Virnau,et al.  Detection and visualization of physical knots in macromolecules , 2010 .

[4]  D. Landau,et al.  Efficient, multiple-range random walk algorithm to calculate the density of states. , 2000, Physical review letters.

[5]  H. Stanley,et al.  Statistical physics of macromolecules , 1995 .

[6]  Kurt Binder,et al.  All-or-none proteinlike folding transition of a flexible homopolymer chain. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  E. J. J. Rensburg,et al.  TOPICAL REVIEW: Monte Carlo methods for the self-avoiding walk , 2009 .

[8]  P. Flory Principles of polymer chemistry , 1953 .

[9]  Peter Cifra,et al.  Persistence lengths and structure factors of wormlike polymers under confinement. , 2008, The journal of physical chemistry. B.

[10]  Steven J. Plimpton,et al.  Equilibration of long chain polymer melts in computer simulations , 2003, cond-mat/0306026.

[11]  K. Binder,et al.  Phase behavior of n-alkanes in supercritical solution: a Monte Carlo study. , 2004, The Journal of chemical physics.

[12]  Alfred Uhlherr,et al.  Monte Carlo Conformational Sampling of the Internal Degrees of Freedom of Chain Molecules , 2000 .

[13]  Rhonald C. Lua,et al.  Statistics of Knots, Geometry of Conformations, and Evolution of Proteins , 2006, PLoS Comput. Biol..

[14]  F. Mandel,et al.  Macromolecular dimensions obtained by an efficient Monte Carlo method: The mean square end‐to‐end separation , 1979 .

[15]  Long range moves for high density polymer simulations , 1997, cond-mat/9610116.

[16]  Nikos Ch. Karayiannis,et al.  Atomistic Monte Carlo simulation of strictly monodisperse long polyethylene melts through a generalized chain bridging algorithm , 2002 .

[17]  Kurt Binder,et al.  On the first-order collapse transition of a three-dimensional, flexible homopolymer chain model , 2005 .

[18]  J. Ilja Siepmann,et al.  Self-Adapting Fixed-End-Point Configurational-Bias Monte Carlo Method for the Regrowth of Interior Segments of Chain Molecules with Strong Intramolecular Interactions , 2000 .

[19]  Enzo Orlandini,et al.  The size of knots in polymers , 2009, Physical biology.

[20]  Thomas Wüst,et al.  Versatile approach to access the low temperature thermodynamics of lattice polymers and proteins. , 2009, Physical review letters.

[21]  Peter Virnau,et al.  Intricate Knots in Proteins: Function and Evolution , 2006, PLoS Comput. Biol..

[22]  K. Binder,et al.  Polymer + solvent systems : Phase diagrams, interface free energies, and nucleation , 2005 .

[23]  Peter Virnau,et al.  Protein knot server: detection of knots in protein structures , 2007, Nucleic Acids Res..

[24]  Vlasis G. Mavrantzas,et al.  Directed Bridging Methods for Fast Atomistic Monte Carlo Simulations of Bulk Polymers , 2001 .

[25]  K. Dill,et al.  A lattice statistical mechanics model of the conformational and sequence spaces of proteins , 1989 .

[26]  Marc L. Mansfield,et al.  Monte Carlo studies of polymer chain dimensions in the melt , 1982 .

[27]  Kurt Binder,et al.  A Guide to Monte Carlo Simulations in Statistical Physics , 2000 .

[28]  E. Shakhnovich,et al.  The role of topological constraints in the kinetics of collapse of macromolecules , 1988 .

[29]  V. G. Mavrantzas,et al.  Monte Carlo Simulation of Chain Molecules , 2005 .

[30]  Peter Virnau,et al.  Knots in globule and coil phases of a model polyethylene. , 2005, Journal of the American Chemical Society.

[31]  Doros N. Theodorou,et al.  Variable Connectivity Method for the Atomistic Monte Carlo Simulation of Polydisperse Polymer Melts , 1995 .

[32]  Wolfhard Janke,et al.  Surface effects in the crystallization process of elastic flexible polymers , 2009, 1002.2118.

[33]  Kurt Binder,et al.  Phase transitions of a single polymer chain: A Wang-Landau simulation study. , 2009, The Journal of chemical physics.

[34]  Doros N. Theodorou,et al.  Variable-Connectivity Monte Carlo Algorithms for the Atomistic Simulation of Long-Chain Polymer Systems , 2002 .

[35]  J. Wittmer,et al.  Static Rouse modes and related quantities: Corrections to chain ideality in polymer melts , 2007, The European physical journal. E, Soft matter.

[36]  Marc L. Mansfield,et al.  Knots in Hamilton Cycles , 1994 .

[37]  D W Sumners,et al.  Simulations of knotting in confined circular DNA. , 2008, Biophysical journal.

[38]  F. T. Wall,et al.  Macromolecular dimensions obtained by an efficient Monte Carlo method without sample attrition , 1975 .

[39]  Michel Mareschal,et al.  Bridging time scales: molecular simulations for the next decade , 2002 .

[40]  D. Stauffer Monte Carlo simulations in statistical physics , 1988 .

[41]  A. Sokal,et al.  The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk , 1988 .

[42]  G. Grest,et al.  Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation , 1990 .

[43]  Alexander Y. Grosberg,et al.  A few notes about polymer knots , 2009 .