SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 35: Statistical Physics of Biological Systems I (joint session BP/DY)

DY 35.8: Vortrag

Donnerstag, 30. März 2023, 11:45–12:00, TOE 317

Stochastic wavelength selection and pattern fixation — •Tom Burkart1,2, Anastasiia Petrova2,3, Laeschkir Würthner1,2, Claudia Veigel2,3, and Erwin Frey1,2,41Arnold Sommerfeld Center for Theoretical Physics (ASC), Department of Physics, LMU München, Munich, Germany — 2Center for NanoScience, LMU München, Munich, Germany — 3Department of Cellular Physiology, Biomedical Center (BMC), LMU München, Planegg-Martinsried, Germany — 4Max Planck School Matter to Life, Munich, Germany

Biological pattern-forming processes are typically driven by a chemical fuel (out-of-equilibrium systems) or by a relaxation towards a thermodynamic equilibrium (phase separation). In these cases, pattern wavelength selection results from translational shifts of high-density regions and mass redistribution in between such regions. Here, we study how a pattern with a characteristic wavelength can form when high-density regions can only grow, but neither mass redistribution nor translation are allowed. The corresponding wavelength selection mechanism relies on thermal fluctuations, irreversible fixation of randomly occurring high-density regions, and long-ranged interactions between these regions. To model the density dynamics and the long-ranged interaction, we derive a set of reaction-diffusion equations from a free energy functional. In addition, we derive the statistics of pattern wavelengths from order statistics, emphasising the stochastic nature of the underlying mechanism. Our results constitute an alternative path to pattern formation next to out-of-equilibrium dynamics and phase separation processes.

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