A generalized bead-rod model for Brownian dynamics simulations of wormlike chains under strong confinement.

This paper is aimed to develop a Brownian dynamics simulation method for strongly confined semiflexible polymers where numerical simulation plays an indispensable role in complementing theory and experiments. A wormlike chain under strong confinement is modeled as a string of virtual spherical beads connected by inextensible rods with length varying according to the confinement intensity of the chain measured by the Odijk deflection length. The model takes hydrodynamic interactions into account. The geometrical constraints associated with the inextensible rods are realized by the so-called linear constraint solver. The model parameters are studied by quantitatively comparing the simulated properties of a double-stranded DNA chain with available experimental data and theoretical predictions.

[1]  W. Helfrich,et al.  Undulations, steric interaction and cohesion of fluid membranes , 1984 .

[2]  P. Ranjith,et al.  Dynamics of folding in semiflexible filaments. , 2002, Physical review letters.

[3]  S. Smith,et al.  Single-molecule studies of DNA mechanics. , 2000, Current opinion in structural biology.

[4]  J Langowski,et al.  A Brownian dynamics program for the simulation of linear and circular DNA and other wormlike chain polyelectrolytes. , 1998, Biophysical journal.

[5]  R. Lipowsky,et al.  Stretching of semiflexible polymers with elastic bonds , 2004, The European physical journal. E, Soft matter.

[6]  D. Ermak,et al.  Brownian dynamics with hydrodynamic interactions , 1978 .

[7]  S. Kabana,et al.  Antihelium-3 production in lead-lead collisions at 158 A GeV/c , 2003 .

[8]  R. Bhargava,et al.  Brownian Dynamics Simulation of a Polymer Molecule in Solution under Elongational Flow , 1998 .

[9]  E. Peters,et al.  Efficient Brownian dynamics simulation of particles near walls. II. Sticky walls. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  A. Khokhlov,et al.  Liquid-crystalline ordering in the solution of long persistent chains , 1981 .

[11]  Brownian dynamics simulations of bead-rod-chain in simple shear flow and elongational flow , 2004 .

[12]  Persistence length of a strongly charged rodlike polyelectrolyte in the presence of salt. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[14]  Huajian Gao,et al.  Spontaneous insertion of DNA oligonucleotides into carbon nanotubes , 2003 .

[15]  Berk Hess,et al.  LINCS: A linear constraint solver for molecular simulations , 1997 .

[16]  J. Skolnick,et al.  Electrostatic Persistence Length of a Wormlike Polyelectrolyte , 1977 .

[17]  A. Skvortsov,et al.  Statistical properties of confined macromolecules , 1995 .

[18]  H. Fujita,et al.  Wormlike Chains Near the Rod Limit: Translational Friction Coefficient , 1979 .

[19]  E. Siggia,et al.  Entropic elasticity of lambda-phage DNA. , 1994, Science.

[20]  Pascal Silberzan,et al.  From the Cover: The dynamics of genomic-length DNA molecules in 100-nm channels. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[21]  K. Richards,et al.  Mode of DNA packing within bacteriophage heads. , 1973, Journal of molecular biology.

[22]  Hiromi Yamakawa,et al.  Statistical Mechanics of Wormlike Chains , 1976 .

[23]  U. S. Agarwal Effect of initial conformation, flow strength, and hydrodynamic interaction on polymer molecules in extensional flows , 2000 .

[24]  Simulation of a semiflexible polymer in a narrow cylindrical pore , 2001, cond-mat/0106633.

[25]  T. Odijk Polyelectrolytes near the rod limit , 1977 .

[26]  A. Khokhlov,et al.  Liquid-crystalline ordering in the solution of partially flexible macromolecules , 1982 .

[27]  S. Quake,et al.  Dynamic Properties of an Extended Polymer in Solution , 1999 .

[28]  A. Lyulin,et al.  Brownian dynamics simulation of linear polymers under elongational flow: Bead–rod model with hydrodynamic interactions , 2002 .

[29]  Semjon Stepanow Statistical mechanics of semiflexible polymers , 2004 .

[30]  C. Wiggins,et al.  Relaxation dynamics of semiflexible polymers. , 2004, Physical review letters.

[31]  E A J F Peters,et al.  Efficient Brownian dynamics simulation of particles near walls. I. Reflecting and absorbing walls. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  DNA uptake into nuclei: numerical and analytical results , 2002, cond-mat/0212440.

[33]  Dynamics of small loops in DNA molecules , 2000 .

[34]  Öttinger,et al.  Brownian dynamics of rigid polymer chains with hydrodynamic interactions. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[35]  Theo Odijk,et al.  Physics of tightly curved semiflexible polymer chains , 1993 .

[36]  Gang Bao,et al.  Mechanics of biomolecules , 2002 .

[37]  Robert H. Austin,et al.  Bending and twisting dynamics of short linear DNAs. Analysis of the triplet anisotropy decay of a 209 base pair fragment by Brownian simulation , 1989 .

[38]  Tamar Schlick,et al.  Inertial stochastic dynamics. II. Influence of inertia on slow kinetic processes of supercoiled DNA , 2000 .

[39]  Hiromi Yamakawa,et al.  Helical Wormlike Chains in Polymer Solutions , 1997 .

[40]  Theo Odijk,et al.  The statistics and dynamics of confined or entangled stiff polymers , 1983 .

[41]  P. G. de Gennes,et al.  Dynamics of Entangled Polymer Solutions. I. The Rouse Model , 1976 .

[42]  Rob Phillips,et al.  Mechanics of DNA packaging in viruses , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[43]  M. Fixman,et al.  Simulation of polymer dynamics. I. General theory , 1978 .

[44]  S. Smith,et al.  Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads. , 1992, Science.

[45]  D. Frenkel,et al.  Confinement free energy of semiflexible polymers , 1993 .

[46]  Alasdair C Steven,et al.  Encapsidated Conformation of Bacteriophage T7 DNA , 1997, Cell.

[47]  J. García de la Torre,et al.  A second‐order algorithm for the simulation of the Brownian dynamics of macromolecular models , 1990 .

[48]  R. Pecora,et al.  DNA: a model compound for solution studies of macromolecules , 1991, Science.

[49]  Thomas T. Perkins,et al.  Dynamical scaling of DNA diffusion coefficients , 1996 .

[50]  D. Dupré,et al.  Liquid crystalline properties of solutions of persistent polymer chains , 1991 .

[51]  M. Muthukumar,et al.  Brownian dynamics simulation of bead–rod chains under shear with hydrodynamic interaction , 1999 .

[52]  R. Lewis,et al.  Brownian dynamics simulations of a three‐subunit and a ten‐subunit worm‐like chain: Comparison of results with trumbell theory and with experimental results from DNA , 1988 .

[53]  Huajian Gao,et al.  SIMULATION OF DNA-NANOTUBE INTERACTIONS , 2004 .

[54]  P. Gennes Dynamics of Entangled Polymer Solutions. II. Inclusion of Hydrodynamic Interactions , 1976 .

[55]  Erwin Frey,et al.  Statics and dynamics of single DNA molecules confined in nanochannels. , 2005, Physical review letters.

[56]  P. Gennes Reptation of a Polymer Chain in the Presence of Fixed Obstacles , 1971 .

[57]  Hiromi Yamakawa,et al.  Modern Theory of Polymer Solutions , 1971 .

[58]  D. Thirumalai,et al.  Pulling-speed-dependent force-extension profiles for semiflexible chains. , 2004, Biophysical journal.

[59]  R. Pecora,et al.  Dynamics of low molecular weight DNA fragments in dilute and semidilute solutions , 1991 .

[60]  P. Dimitrakopoulos Longitudinal relaxation of initially straight flexible and stiff polymers. , 2004, Physical review letters.

[61]  Stuart A. Allison,et al.  Brownian dynamics simulation of wormlike chains. Fluorescence depolarization and depolarized light scattering , 1986 .

[62]  T. Norisuye Semiflexible polymers in dilute solution , 1993 .

[63]  Tamar Schlick,et al.  A Combined Wormlike-Chain and Bead Model for Dynamic Simulations of Long Linear DNA , 1997 .

[64]  T. Odijk Stiff chains and filaments under tension , 1995 .

[65]  I. Neelov,et al.  Brownian Dynamics Simulations of Dendrimers under Elongational Flow: Bead−Rod Model with Hydrodynamic Interactions , 2003 .

[66]  Tamar Schlick,et al.  Macroscopic modeling and simulations of supercoiled DNA with bound proteins , 2002 .