Biological Physics

The following is a list of some recent papers on topics related to our activities in the area of biological physics.

Generic modeling of cooperative growth patterns in bacterial colonies

Eshel Ben-Jacob, Ofer Shochet, Adam Tenenbaum, Inon Cohen, András Czirók and Tamás Vicsek

Published in: Nature 368, 46 (1994).

ABSTRACT In nature, bacterial colonies often must cope with hostile environmental conditions. To do so, they have developed sophisticated cooperative behavior and intricate communication channels on all levels. It has been shown that bacterial colonies can exhibit complex growth patterns similar to those observed during growth processes in non living systems. Some qualitative features of the complex morphologies may be accounted for by invoking ideas from pattern formation in non-living systems together with a simplified model of chemotactic "feedback". Here we present a non-local, communicating walkers model to study the effect of local bacterium-bacterium interaction and communication via chemotaxis signaling. We demonstrate how communication enables the colony to develop complex patterns in response to adverse growth conditions. Efficient response of the colony requires self-organization on all levels, which can be achieved only via cooperative behavior of the bacteria. It can be viewed as the action of an interplay between the micro-level (the individual bacterium) and the macro-level (the colony) in the determination of the emerging pattern.

Statistical theory of muscle contraction: new analytic results versus experiments

Imre Derényi and Tamás Vicsek

ABSTRACT Myosin is an ATPase enzyme that converts the chemical energy stored in ATP molecules into mechanical work. During muscle contraction, the myosin cross-bridges attach to the actin filaments and exert force on them yielding a relative sliding of the actin and myosin filaments. In this paper we present a simple mechanochemical model for the cross-bridge interaction involving the relevant kinetic data and providing simple analytic solutions for the mechanical properties of muscle contraction, such as the force-velocity relationship or the relative number of the attached cross-bridges. Thus, our model connects the mechanical data with the kinetic data and the concentration of the ATP and ATPase products analytically. So far the only analytic formula which could be fitted to the measured force-velocity curves has been the well known Hill equation, but the microscopic background of its parameters has remained unclear. The analytic results of our model also agree extremely well with the experimental curves, however, its parameters have clear microscopic meaning.

The kinesin walk: a dynamic model with elastically coupled heads

Imre Derényi and Tamás Vicsek

Published in: Proc. Natl. Acad. Sci. USA 93, 6775 (1996).

ABSTRACT Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. In this paper we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads showing all of these properties. The analytic and numerical treatment of our model results in a very good fit to the experimental data and practically has no free parameters. Changing the values of the parameters in the restricted range allowed by the related experimental estimates has almost no effect on the shape of the curves and results mainly in a variation of the zero load velocity which can be directly fitted to the measured data. In addition, the model is consistent with the measured pathway of the kinesin ATPase.

Lattice-gas model for collective biological motion

Zoltán Csahók and Tamás Vicsek

Published in: Phys. Rev. E 52, 5297 (1995).

ABSTRACT One of the most interesting aspects of evolution is the emergence of multicellular organisms due to the appearance of cooperation and differentiation of eucariotes. Although much research has been done along this line, some of the related basic questions are still open. As a natural step towards the understanding of the physical and physico-chemical background of self-organization of microorganisms several authors considered relatively simple systems such as the development of bacterial colonies. In this paper we present a simple lattice gas model for the collective motion of self-driven particles. Similar approach has been applied to traffic systems which also belong to the class of self-driven systems. We show both numerically and theoretically that weakly first order phase transition takes place in our system separating the phase with zero net transport and the ordered phase with non-zero average velocity. We find the critical exponents differ from the ones of the q=6 Potts model and from mean field values. This difference can be attributed to the fact that although we have similarities with spin systems our model differs in a very specific way: the spins in our model are moving and this spatial dynamics is coupled to the spin dynamics.

  1. E. Ben-Jacob, O. Shochet, A. Tenenbaum, I. Cohen, A. Czirok and T. Vicsek: "Communication, regulation and control during complex patterning of bacterial colonies", Fractals 2, 15 (1994).
  2. E. Ben-Jacob, O. Shochet, A. Tenenbaum, I. Cohen, A. Czirok and T. Vicsek: "Fractal patterns and complexity during diffusive growth of bacterial colonies", Symmetry 4, 303 (1994).
  3. Tamás Vicsek, András Czirók, Eshel Ben-Jacob, and Inon Cohen: "Novel type of phase transition in a system of self-driven particles", Phys. Rev. Lett. 75, 1226 (1995).
  4. Imre Derényi and Tamás Vicsek: "Cooperative transport of Brownian particles", Phys. Rev. Lett. 75, 374 (1995).
  5. Eshel Ben-Jacob, Inon Cohen, Ofer Shochet, András Czirók and Tamás Vicsek: "Cooperative formation of chiral patterns during growth of bacterial colonies", Phys. Rev. Lett. 75, 2899 (1995).
  6. Eshel Ben-Jacob, Inon Cohen, Ofer Shochet, András Czirók and Tamás Vicsek: "Response of bacterial colonies to imposed anisotropy", Phys. Rev. E 53, 1835 (1996).
  7. A. Czirók, H.E. Stanley and T. Vicsek: "A Possible Origin of Power-Law Behavior in n-Tuple Zipf Analysis", Phys. Rev. E 53, 6371 (1996).
  8. A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet and T. Vicsek: "Formation of complex bacterial colonies via self generated vortices", Phys. Rev. E 54, 1791 (1996).

Zoltán Csahók, November 1996.