- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Relation between cooperative molecular motors and active Brownian particles

Clément Touya, Tilo Schwalger, and Benjamin Lindner*

  • Max-Planck-Institut für Physik komplexer Systeme, Nöthnizer Straße 38, D-01187 Dresden, Germany

  • *Corresponding author: benji@pks.mpg.de
PDF

Phys. Rev. E 83, 051913 – Published 16 May, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.051913

Abstract

Active Brownian particles (ABPs), obeying a nonlinear Langevin equation with speed-dependent drift and noise amplitude, are well-known models used to describe self-propelled motion in biology. In this paper we study a model describing the stochastic dynamics of a group of coupled molecular motors (CMMs). Using two independent numerical methods, one based on the stationary velocity distribution of the motors and the other one on the local increments (also known as the Kramers-Moyal coefficients) of the velocity, we establish a connection between the CMM and the ABP models. The parameters extracted for the ABP via the two methods show good agreement for both symmetric and asymmetric cases and are independent of N, the number of motors, provided that N is not too small. This indicates that one can indeed describe the CMM problem with a simpler ABP model. However, the power spectrum of velocity fluctuations in the CMM model reveals a peak at a finite frequency, a peak which is absent in the velocity spectrum of the ABP model. This implies richer dynamic features of the CMM model which cannot be captured by an ABP model.

    View figure in article

      Article Text

      References (21)

      1. J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer Associates, Sunderland, MA, 2001).
      2. D. Bray, Cell Movements (Garland, New York, 2001).
      3. H. Chaté, F. Ginelli, G. Gregoire, F. Peruani, and F. Raynaud, Eur. Phys. J. B 64, 451 (2008).
      4. S. Ramaswamy, Annu. Rev. Conden. Ma. P. 1, 323 (2010).
      5. T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. 75, 1226 (1995).
      6. M. Schienbein and H. Gruler, Bull. Math. Biol. 55, 585 (1993).
      7. F. Schweitzer, W. Ebeling, and B. Tilch, Phys. Rev. Lett. 80, 5044 (1998).
      8. U. Erdmann, W. Ebeling, L. Schimansky-Geier, and F. Schweitzer, Eur. Phys. J. B 15, 105 (2000).
      9. F. Schweitzer, Brownian Agents and Active Particles (Springer, New York, 2002).
      10. Yu. L. Klimontovich, Statistical Theory of Open Systems (Kluwer Academic Publishers, Dordrecht-Boston-London, 1995).
      11. B. Lindner, New. J. Phys. 9, 136 (2007).
      12. D. Selmeczi, S. Mosler, P. H. Hagedorn, N. B. Larsen, and H. Flyvbjerg, Biophys. J. 89, 912 (2005).
      13. D. Selmeczi, L. Li, L. I. I. Pedersen, S. F. Norrelykke, P. H. Hagedorn, S. Mosler, N. B. Larsen, E. C. Cox, and H. Flyvbjerg, Eur. Phys. J-Spec. Top. 157, 1 (2008).
      14. C. A. Yates, R. Erban, C. Escudero, I. D. Couzin, J. Buhl, I. G. Kevrekidis, P. K. Maini, and D. J. T. Sumpter, Proc. Natl. Acad. Sci. USA 106, 5464 (2009).
      15. M. Badoual, F. Jülicher, and J. Prost, Proc. Natl. Acad. Sci. USA 99, 6696 (2002).
      16. F. Jülicher and J. Prost, Phys. Rev. Lett. 75, 2618 (1995).
      17. B. Lindner and E. M. Nicola, Phys. Rev. Lett. 101, 190603 (2008).
      18. S. Endow and H. Higuchi, Nature 406, 913 (2000).
      19. P. Reimann, Phys. Rep. 361, 57 (2002).
      20. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1989).
      21. D. T. Gillespie, J. Chem. Phys. 113, 297 (2000).

      Outline

      Information

      Phys. Rev. E 83, 051913– Published 16 May, 2011
      • Received 2 November 2010

      ©2011 American Physical Society

      Sign In to Your Journals Account

      Filter

      Filter

      Article Lookup

      Enter a citation