Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 1: Statistical Physics of Biological Systems I (with BP, talks from DY)

DY 1.4: Talk

Monday, March 26, 2012, 10:15–10:30, MA 001

Spiral-wave prediction in a lattice of FitzHugh-Nagumo oscillators — •Miriam Grace and Marc-Thorsten Hütt — Jacobs University Bremen, Bremen, Germany

In many biological systems, variability of the components can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. The distribution of single-element properties should thus allow the prediction of features of such patterns. In a series of previous studies on established computational models of Dictyostelium discoideum pattern formation we demonstrated that the initial properties of potentially very few cells cells have a driving influence on the resulting asymptotic collective state of the colony [1,2]. One plausible biological mechanism for the generation of variability in cell properties and of spiral wave patterns is the concept of a "developmental path", where cells gradually move on a trajectory through parameter space. Here we review the current state of knowledge of spiral-wave prediction in excitable systems and present a new one-dimensional developmental path based on the FitzHugh-Nagumo model, incorporating parameter drift and concomitant variability in the distribution of cells embarking on this path, which gives rise to stable spiral waves. Such a generic model of spiral wave predictability allows new insights into the relationship between biological variability and features of the resulting spatiotemporal pattern.

[1] Geberth, D. and Hütt, M.-Th. (2008). Phys. Rev. E 78, 031917.

[2] Geberth, D. and Hütt, M.-Th. (2009). PLoS Computational Biology 5, e1000422.