Dynamics of the Aggregation of Cells with Internal Oscillators

Tilmann Glimm () and Daniel Gruszka
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Tilmann Glimm: Department of Mathematics, Western Washington University, Bellingham, WA 98225, USA
Daniel Gruszka: Department of Mathematics, Western Washington University, Bellingham, WA 98225, USA

Mathematics, 2025, vol. 13, issue 21, 1-16

Abstract: We investigate two closely related Lattice Gas Cellular Automata models of the interplay of aggregation of biological cells and synchronization of intracellular oscillations (“clocks”): clock-dependent aggregation, where the adhesive forces between cells depend on their relative clock phases (akin to so-called “swarmalators”), and simple adhesive aggregation, where they do not. Patterns of aggregation are similar for comparable ranges of parameters. However, while simple adhesive aggregation is quite similar to perikinetic aggregation, we show that clock-dependent aggregation differs in subtle ways. We found that it tends to inhibit coalescence of patterns and regularizes aggregate shapes, and, unintuitively, tends to enhance overall synchronization of clocks. Specifically, clock-dependent aggregation showed higher average circularity of aggregates and a larger value of Kuramoto’s r , measuring synchrony. Our results add to the growing literature on swarmalator models and give additional theoretical backing to the previously proposed idea that intracellular oscillatory processes may serve to regularize pattern formation, e.g., in chondrogenic condensation in embryonic chicken limbs. They thus contribute to a partial answer to the question: In the feedback between clocks and attraction in swarmalator models, how important is the effect of clocks on attraction? The detailed, systematic comparison of the results of these two types of aggregation is novel.

Keywords: swarmalators; synchronization; cell aggregation; pattern formation; Lattice-Gas Cellular Automata (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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