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Immunophysics

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Publications Immunophysics Division

2011

Modeling a self-propelled autochemotactic walker

Johannes Taktikos, Vasily Zaburdaev, Holger Stark

Physical Review E 84 (4) 041924 (2011) | Journal

We develop a minimal model for the stochastic dynamics of microorganisms where individuals communicate via autochemotaxis. This means that microorganisms, such as bacteria, amoebae, or cells, follow the gradient of a chemical that they produce themselves to attract or repel each other. A microorganism is represented as a self-propelled particle or walker with constant speed while its velocity direction diffuses on the unit circle. We study the autochemotactic response of a single self-propelled walker whose dynamics is non-Markovian. We show that its long-time dynamics is always diffusive by deriving analytic expressions for its diffusion coefficient in the weak-and strong-coupling case. We confirm our findings by numerical simulations.

Langevin Dynamics Deciphers the Motility Pattern of Swimming Parasites

Vasily Zaburdaev, Sravanti Uppaluri, Thomas Pfohl, Markus Engstler, Rudolf Friedrich, Holger Stark

Physical Review Letters 106 (20) 208103 (2011) | Journal

The parasite African trypanosome swims in the bloodstream of mammals and causes the highly dangerous human sleeping sickness. Cell motility is essential for the parasite's survival within the mammalian host. We present an analysis of the random-walk pattern of a swimming trypanosome. From experimental time-autocorrelation functions for the direction of motion we identify two relaxation times that differ by an order of magnitude. They originate from the rapid deformations of the cell body and a slower rotational diffusion of the average swimming direction. Velocity fluctuations are athermal and increase for faster cells whose trajectories are also straighter. We demonstrate that such a complex dynamics is captured by two decoupled Langevin equations that decipher the complex trajectory pattern by referring it to the microscopic details of cell behavior.

Perturbation Spreading in Many-Particle Systems: A Random Walk Approach

Vasily Zaburdaev, S. Denisov, P. Haenggi

Physical Review Letters 106 (18) 180601 (2011) | Journal

The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk where a single particle is traveling through an active, fluctuating medium. Employing two archetype ergodic many-particle systems, namely, (i) a hard-point gas composed of two unequal masses and (ii) a Fermi-Pasta-Ulam chain, we demonstrate that the corresponding perturbation profiles coincide with the diffusion profiles of the single-particle Levy walk approach. The parameters of the random walk can be related through elementary algebraic expressions to the physical parameters of the corresponding test many-body systems.

Contact

Immunophysics Division
Prof. Vasily Zaburdaev
Principal Investigator

Max-Planck-Zentrum für Physik und Medizin
Kussmaulallee 2
Room 02.116
91054 Erlangen, Germany
+49 9131 8284 102

vasily.zaburdaev@mpzpm.mpg.de

Silke Besold

Secretary

Friedrich-Alexander-Universität Erlangen-Nürnberg
Chair of Mathematics in Life Sciences
Kussmaulallee 2
Room 02.122
91054 Erlangen, Germany
+49 9131 8284 104

silke.besold@fau.de

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