SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 45: Poster: Nonlinear Dynamics, Pattern Formation and Networks

DY 45.9: Poster

Donnerstag, 30. März 2023, 13:00–16:00, P1

Robust, precise, and modular solutions to the French flag problem in two dimensions without global signaling — •Lukas Zett, Stephan Kremser, Gabriel Vercelli, and Ulrich Gerland — Technical University of Munich

The formation of axial patterns with broad regions in multicellular systems has been conceptualized by Wolpert in his famous French flag problem. Both of Wolpert's proposed solutions, the balancing and gradient model, utilize long-range signaling between cells. Models relying on short-range signaling, based on cellular automata (CA) rules as modeling tool, have also computationally been shown to successfully solve the French flag problem in one dimension (1D). Here, we extend these models to two spatial dimensions (2D) to investigate whether the 1D solutions can be generalized to the 2D case and to search for novel solutions existing only in 2D. We dissect the 2D problem into two coupled, 1D pattern formation processes along and perpendicular to the axis of the French flag. Using evolutionary algorithms and consensus procedures as well as engineering approaches, CA dynamics which solve the French flag problem are found. We show that these solutions form more precise patterns and are in general more robust than their 1D counterparts, while still being able to scale with system size. Depending on the desired robustness and precision of the solution, different patterning modules along the two axes can be combined. Using the regulatory logics of these underlying modules could therefore serve as a basis for the design of synthetic patterning systems with a range of different specifications.