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DY: Fachverband Dynamik und Statistische Physik

DY 24: Focus Session: New Trends in Nonequilibrium Physics – Conservation Laws and Nonreciprocal Interactions I

DY 24.7: Talk

Wednesday, March 20, 2024, 11:30–11:45, BH-N 243

Traveling waves and arrested coarsening in a simple model for protein patterns on biomembranes — •Benjamin Winkler¹, Sergio Alonso², and Markus Bär¹ — ¹Physikalisch-Technische Bundesanstalt, Berlin, Germany — ²UPC, Barcelona, Spain

The formation of protein patterns on membranes is important for spatial organization, growth and division of biological cells. In many cases these dynamics is described by coupled, mass-conserving reaction-diffusion equations. Here, we study the dynamics emergent from the coupling of two well-known, mass-conserved systems. System A is given by a simplified reaction-diffusion model for the emergence of cell polarity by proteins undergoing active phase separation. The proteins are fast-diffusing in the bulk of the cell and become activated when they bind to the cell membrane. System B is a Cahn-Hilliard-like equation describing the mixing dynamics of two different lipids. When introducing a coupling between system A and B due to a concentration-dependent interaction affinity, we observe the emergence of traveling waves in system A and likewise, a systematic slowing of the coarsening in system B depending on the coupling strength between the two systems. The primary linear instabilities of the homogeneous steady for the coupled system are all stationary, hence the traveling wave emerge from a secondary instability of a stationary pattern. Our results exemplify the interaction between pattern forming systems with well-separated length scales and illustrate how complex behavior in biological systems can arise from the coupling of simpler subsystems.