Self-propelled particles with fluctuating speed and direction of motion in two dimensions.

We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion, and assume that both processes can be described by independent characteristic time scales. We show the occurrence of a complex transient that can exhibit a series of alternating regimes of motion, for two different angular dynamics which correspond to persistent and directed random walks. We also show additive corrections to the diffusion coefficient. The characteristic time scales are also exposed in the velocity autocorrelation, which is a sum of exponential forms.

[1]  Tojo,et al.  Correlated random walk in continuous space. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  M. Schienbein,et al.  Random walk and directed movement: Comparison between inert particles and self-organized molecular machines. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Werner Ebeling,et al.  Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems , 2005 .

[4]  F. Schweitzer.  Brownian Agents and Active Particles , 2003, Springer Series in Synergetics.

[5]  D. Lauffenburger,et al.  A high-throughput migration assay reveals HER2-mediated cell migration arising from increased directional persistence. , 2006, Biophysical journal.

[6]  G. Danuser,et al.  Two Distinct Actin Networks Drive the Protrusion of Migrating Cells , 2004, Science.

[7]  Jason M. Haugh,et al.  Quantitative elucidation of a distinct spatial gradient-sensing mechanism in fibroblasts , 2005, The Journal of cell biology.

[8]  H. Othmer,et al.  Models of dispersal in biological systems , 1988, Journal of mathematical biology.

[9]  G. Viswanathan,et al.  Necessary criterion for distinguishing true superdiffusion from correlated random walk processes. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Henrik Flyvbjerg,et al.  Cell motility as persistent random motion: theories from experiments. , 2005, Biophysical journal.

[11]  G. Gaudiosi,et al.  171 , 2006 .

[12]  A. Libchaber,et al.  Particle diffusion in a quasi-two-dimensional bacterial bath. , 2000, Physical review letters.

[13]  P. A. Prince,et al.  Lévy flight search patterns of wandering albatrosses , 1996, Nature.

[14]  Lutz Schimansky-Geier,et al.  RANDOM WALK THEORY APPLIED TO DAPHNIA MOTION , 2004 .

[15]  M. Footer,et al.  Biophysical parameters influence actin-based movement, trajectory, and initiation in a cell-free system. , 2004, Molecular biology of the cell.

[16]  Dennis Bray,et al.  Cell Movements: From Molecules to Motility , 1992 .

[17]  Sheng-You Huang,et al.  Directed random walks in continuous space. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion , 1930 .

[19]  A. Czirók,et al.  Exponential Distribution of Locomotion Activity in Cell Cultures , 1998, physics/9902022.

[20]  Richard B. Dickinson,et al.  Optimal estimation of cell movement indices from the statistical analysis of cell tracking data , 1993 .

[21]  Motion of an adhesive gel in a swelling gradient: a mechanism for cell locomotion. , 2003, Physical review letters.

[22]  Christian Bracher.  Eigenfunction approach to the persistent random walk in two dimensions , 2003, cond-mat/0304241.