Tube Translocation of a Herniating Chain
Żurek Sebastian, Drzewiński Andrzej
Institute of Physics,
University of Zielona Góra,
ul. Prof. Z. Szafrana 4a,
65-516 Zielona Góra, Poland
e-mail: S.Zurek@if.uz.zgora.pl; A.Drzewinski@proton.if.uz.zgora.pl
Received:
Received: 23 March 2010; accepted: 1 July 2010; published online: 24 August 2010
DOI: 10.12921/cmst.2010.16.02.211-215
OAI: oai:lib.psnc.pl:733
Abstract:
Translocation is modeled with the Rubinstein-Duke rules for hopping reptons along a one-dimensional lattice (tube). Identification of some coupled states guarantees a semi-periodicity of the process. The chain is driven through the pore by a bias potential promoting the transition of stored length in one direction. Accounting exactly for all allowed states the translocation time of polymers up to the 10-links length is determined. The crossover from reptation to faster dynamics through gradually allowing hernia creation and annihilation is found. Some computational details are presented.
Key words:
Rubinstein-Duke model, semi-periodic stochastic model, translocation
References:
[1] B. Albert, D. Bray, J. Lewis, M. Raff, K. Roberts, J.D. Watson, Molecular Biology of the Cell. (Garland, New York, 1994).
[2] J.J. Kasianowicz, E. Brandin, D. Branton, D.W. Deamer, Characterization of individual polynucleotide molecules using a membrane channel. Proc. Natl. Acad. Sci. USA 93, 13770 (1996).
[3] A. Meller, L. Nivon, D. Branton, Voltage-Driven DNA Translocations through a Nanopore. Phys. Rev. Lett. 86, 3435 (2001).
[4] V.V. Lehtola, R.P. Linna, K. Kaski, Critical evaluation of the computational methods used in the forced polymer translocation. Phys. Rev. E78, 061803 (2008).
[5] A. Drzewiński, J.M.J. van Leeuwen, Crossover from reptation to Rouse dynamics in a one-dimensional model, Phys. Rev. E73, 061802 (2006).
[6] B. Widom, J.L. Viovy, A.D. Defontaines, Repton model of gel electrophoresis and diffusion. J. Phys. I France 1 (1991).
[7] J.M.J. van Leeuwen, A. Drzewiński, Stochastic Lattice Models for the Dynamics of Linear Polymers. Phys. Rep. 475, 53 (2009).
[8] E. Gabriel, G.E. Fagg, G. Bosilca, T. Angskun et al., Open MPI: Goals, Concept, and Design of a Next Generation MPI Implementation. Proceedings of the 11th European PVM/MPI Users’ Group Meeting, 2004.
[9] X.S. Li, J.W. Demmel, SuperLU DIST: A Scalable Distributed- Memory Sparse Direct Solver for Unsymmetric Linear Systems. ACM Trans. Mathematical Software 29, 2 (2003).
Translocation is modeled with the Rubinstein-Duke rules for hopping reptons along a one-dimensional lattice (tube). Identification of some coupled states guarantees a semi-periodicity of the process. The chain is driven through the pore by a bias potential promoting the transition of stored length in one direction. Accounting exactly for all allowed states the translocation time of polymers up to the 10-links length is determined. The crossover from reptation to faster dynamics through gradually allowing hernia creation and annihilation is found. Some computational details are presented.
Key words:
Rubinstein-Duke model, semi-periodic stochastic model, translocation
References:
[1] B. Albert, D. Bray, J. Lewis, M. Raff, K. Roberts, J.D. Watson, Molecular Biology of the Cell. (Garland, New York, 1994).
[2] J.J. Kasianowicz, E. Brandin, D. Branton, D.W. Deamer, Characterization of individual polynucleotide molecules using a membrane channel. Proc. Natl. Acad. Sci. USA 93, 13770 (1996).
[3] A. Meller, L. Nivon, D. Branton, Voltage-Driven DNA Translocations through a Nanopore. Phys. Rev. Lett. 86, 3435 (2001).
[4] V.V. Lehtola, R.P. Linna, K. Kaski, Critical evaluation of the computational methods used in the forced polymer translocation. Phys. Rev. E78, 061803 (2008).
[5] A. Drzewiński, J.M.J. van Leeuwen, Crossover from reptation to Rouse dynamics in a one-dimensional model, Phys. Rev. E73, 061802 (2006).
[6] B. Widom, J.L. Viovy, A.D. Defontaines, Repton model of gel electrophoresis and diffusion. J. Phys. I France 1 (1991).
[7] J.M.J. van Leeuwen, A. Drzewiński, Stochastic Lattice Models for the Dynamics of Linear Polymers. Phys. Rep. 475, 53 (2009).
[8] E. Gabriel, G.E. Fagg, G. Bosilca, T. Angskun et al., Open MPI: Goals, Concept, and Design of a Next Generation MPI Implementation. Proceedings of the 11th European PVM/MPI Users’ Group Meeting, 2004.
[9] X.S. Li, J.W. Demmel, SuperLU DIST: A Scalable Distributed- Memory Sparse Direct Solver for Unsymmetric Linear Systems. ACM Trans. Mathematical Software 29, 2 (2003).
