The Comparison of Monte Carlo Algorithms Applied for Off-Lattice Models of Polymer Chains
Kuriata Aleksander, Gront Dominik, Sikorski Andrzej *
Department of Chemistry, University of Warsaw
Pasteura 1, 02-093 Warszawa, Poland
*E-mail: sikorski@chem.uw.edu.pl
Received:
Received: 16 November 2016; revised: 23 November 2016; accepted: 24 November 2016; published online: 19 December 2016
DOI: 10.12921/cmst.2016.0000052
Abstract:
We designed two simplified models of macromolecular systems. Model chains were built of united atoms (statistical segments): the first one was a bead-spring model while in the second one beads were connected by bonds of constant length. The only potential introduced was the excluded volume and thus the system was athermal. Monte Carlo simulations of these models were carried out using Metropolis-like algorithms appropriate for each model: the one-bead displacement and the backrub algorithm. The scaling analysis of the chain’s static and dynamic properties was carried out. The universal behavior of the chain’s properties under consideration was found and discussed. The efficiency of both algorithms was compared and discussed.
Key words:
Backrub algorithm, computer simulation, Monte Carlo method, off-lattice models, polymer dynamics
References:
[1] J. Baschnagel, J.P. Wittmer, H. Meyer, Monte Carlo Simulation of Polymers:
Coarse-Grained Models, in: Computational Soft Matter: From Synthetic Polymers
to Proteins, Lecture Notes, N. Attig, K. Binder, H. Grubmüller, K. KremerG.J.
Strous, J. Dekker, Mucin-type glycoproteins, Crit. Rev. Biochem. Mol. Biol. 27,
57-92 (1992).
[2] D.J. Thornton, J.K. Sheehanm, From mucins to mucus: toward a more coherent
understanding of this essential barrier, Proc Am. Thorac. Soc. 1, 54-61 (2004).
[3] M. A.Hollingsworth, B.J. Swanson, Mucins in cancer: protection and control
of the cell surface, Nature Rev. Cancer 4, 45-60 (2004).
[4] P. Gniewek, A. Kolinski, Coarse-Grained Monte Carlo Simulations of Mucus:
Structure, Dynamics, and Thermodynamics, Biophys. J. 99, 3507-3516 (2010).
[5] K. Binder, A. Milchev, Off-lattice Monte Carlo methods for coarse-grained
models of polymeric materials and selected applications, J. Comput.-Aided
Mater. 9, 33-74 (2002).
[6] M.R. Betancourt, Efficient Monte Carlo trial moves for polypeptide
simulations, J. Chem. Phys. 123, 174905 (2005).
[7] M.R. Betancourt, Optimization of Monte Carlo trial moves for protein
simulations, J. Chem. Phys. 134, 014104 (2011).
[8] C.A. Smith, T. Kortemme, Backrub-like backbone simulation recapitulates
natural protein conformational variability and improves mutant side-chain
prediction, J. Mol. Biol. 380, 742-756 (2008).
[9] A.A. Podtelezhnikov, D.L. Wild, Exhaustive Metropolis Monte Carlo sampling
and analysis of polyalanine conformations adopted under the influence of
hydrogen bonds, Proteins: Struct., Funct., Bioinf. 61, 94-104 (2005).
[10] I.W. Davis, W.B. Arendall III, D.C. Richardson, J.S. Richardson, The
backrub motion: how protein backbone shrugs when a sidechain dances, Structure
14, 265-274 (2006).
[11] I. Teraoka, Polymer Solutions. An Introduction to Physical Properties,
Wiley-Interscience, New York 2002.
[12] B. Li, N. Madras, A.D. Sokal, Critical exponents, hyperscaling, and
universal amplitude ratios for two- and three-dimensional self-avoiding walks,
J. Stat. Phys. 80, 661-754 (1995).
[13] K. Binder, Applications of Monte Carlo methods to statistical physics,
Rep. Prog. Phys. 60, 487-559 (1997).
[14] C.F. Abrams, K. Kremer, The effect of bond length on the structure of
dense bead-spring polymer melts, J. Chem. Phys. 115, 2776-2785 (2001).
[15] C.F. Abrams, K. Kremer, Effects of excluded volume and bond length on the
dynamics of dense bead-spring polymer melts, J. Chem. Phys. 116, 3162-3165
(2002).
[16] D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical
Physics, 3rd edition, Cambridge University Press, Cambridge, chapter 6.6, 2009.
[17] P. Romiszowski, A. Sikorski, Dynamics of polymer chains in confined space.
A computer simulation study, Physica A 357, 356-363 (2005).
[18] P. Polanowski, J.K. Jeszka, A. Sikorski, Dynamic properties of linear and
cyclic chains in two dimensions. Computer simulation atudies, Macromolecules
47, 4830-4839 (2014).
[19] L. Harnau, R.G. Winkler, P. Reineker, On the dynamics of polymer melts:
Contribution of Rouse and bending modes, Europhys. Lett. 45, 488-494 (1999).
[20] D. Panja, Generalized Langevin equation formulation for anomalous polymer
dynamics, J. Stat. Mech. Theor. Exp. L02001 (2010).
[21] K. Kremer, G.S. Grest, Dynamics of entangled linear polymer melts: A
molecular-dynamics simulation, J. Chem. Phys. 92, 5057-5086 (1990). (eds.),
John von NeumannInstitute for Computing, Jülich, Vol. 23, p. 83-140,2004.
We designed two simplified models of macromolecular systems. Model chains were built of united atoms (statistical segments): the first one was a bead-spring model while in the second one beads were connected by bonds of constant length. The only potential introduced was the excluded volume and thus the system was athermal. Monte Carlo simulations of these models were carried out using Metropolis-like algorithms appropriate for each model: the one-bead displacement and the backrub algorithm. The scaling analysis of the chain’s static and dynamic properties was carried out. The universal behavior of the chain’s properties under consideration was found and discussed. The efficiency of both algorithms was compared and discussed.
Key words:
Backrub algorithm, computer simulation, Monte Carlo method, off-lattice models, polymer dynamics
References:
[1] J. Baschnagel, J.P. Wittmer, H. Meyer, Monte Carlo Simulation of Polymers:
Coarse-Grained Models, in: Computational Soft Matter: From Synthetic Polymers
to Proteins, Lecture Notes, N. Attig, K. Binder, H. Grubmüller, K. KremerG.J.
Strous, J. Dekker, Mucin-type glycoproteins, Crit. Rev. Biochem. Mol. Biol. 27,
57-92 (1992).
[2] D.J. Thornton, J.K. Sheehanm, From mucins to mucus: toward a more coherent
understanding of this essential barrier, Proc Am. Thorac. Soc. 1, 54-61 (2004).
[3] M. A.Hollingsworth, B.J. Swanson, Mucins in cancer: protection and control
of the cell surface, Nature Rev. Cancer 4, 45-60 (2004).
[4] P. Gniewek, A. Kolinski, Coarse-Grained Monte Carlo Simulations of Mucus:
Structure, Dynamics, and Thermodynamics, Biophys. J. 99, 3507-3516 (2010).
[5] K. Binder, A. Milchev, Off-lattice Monte Carlo methods for coarse-grained
models of polymeric materials and selected applications, J. Comput.-Aided
Mater. 9, 33-74 (2002).
[6] M.R. Betancourt, Efficient Monte Carlo trial moves for polypeptide
simulations, J. Chem. Phys. 123, 174905 (2005).
[7] M.R. Betancourt, Optimization of Monte Carlo trial moves for protein
simulations, J. Chem. Phys. 134, 014104 (2011).
[8] C.A. Smith, T. Kortemme, Backrub-like backbone simulation recapitulates
natural protein conformational variability and improves mutant side-chain
prediction, J. Mol. Biol. 380, 742-756 (2008).
[9] A.A. Podtelezhnikov, D.L. Wild, Exhaustive Metropolis Monte Carlo sampling
and analysis of polyalanine conformations adopted under the influence of
hydrogen bonds, Proteins: Struct., Funct., Bioinf. 61, 94-104 (2005).
[10] I.W. Davis, W.B. Arendall III, D.C. Richardson, J.S. Richardson, The
backrub motion: how protein backbone shrugs when a sidechain dances, Structure
14, 265-274 (2006).
[11] I. Teraoka, Polymer Solutions. An Introduction to Physical Properties,
Wiley-Interscience, New York 2002.
[12] B. Li, N. Madras, A.D. Sokal, Critical exponents, hyperscaling, and
universal amplitude ratios for two- and three-dimensional self-avoiding walks,
J. Stat. Phys. 80, 661-754 (1995).
[13] K. Binder, Applications of Monte Carlo methods to statistical physics,
Rep. Prog. Phys. 60, 487-559 (1997).
[14] C.F. Abrams, K. Kremer, The effect of bond length on the structure of
dense bead-spring polymer melts, J. Chem. Phys. 115, 2776-2785 (2001).
[15] C.F. Abrams, K. Kremer, Effects of excluded volume and bond length on the
dynamics of dense bead-spring polymer melts, J. Chem. Phys. 116, 3162-3165
(2002).
[16] D.P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical
Physics, 3rd edition, Cambridge University Press, Cambridge, chapter 6.6, 2009.
[17] P. Romiszowski, A. Sikorski, Dynamics of polymer chains in confined space.
A computer simulation study, Physica A 357, 356-363 (2005).
[18] P. Polanowski, J.K. Jeszka, A. Sikorski, Dynamic properties of linear and
cyclic chains in two dimensions. Computer simulation atudies, Macromolecules
47, 4830-4839 (2014).
[19] L. Harnau, R.G. Winkler, P. Reineker, On the dynamics of polymer melts:
Contribution of Rouse and bending modes, Europhys. Lett. 45, 488-494 (1999).
[20] D. Panja, Generalized Langevin equation formulation for anomalous polymer
dynamics, J. Stat. Mech. Theor. Exp. L02001 (2010).
[21] K. Kremer, G.S. Grest, Dynamics of entangled linear polymer melts: A
molecular-dynamics simulation, J. Chem. Phys. 92, 5057-5086 (1990). (eds.),
John von NeumannInstitute for Computing, Jülich, Vol. 23, p. 83-140,2004.
