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A universal robustness to spatio-temporal variation in pattern formation

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ADIW02 - Mathematical and Computational Modelling of Anti-Diffusive Phenomena

Biological systems use spatio-temporally varying input signals to self-organise into macroscale structures (patterns) that are vital for many physiological processes. As observed by Turing in 1952, these patterns are in a state of continual development, and are usually transitioning from one pattern into another. How can this self-organising process be robust in the presence of confounding effects caused by unpredictable or heterogeneous environments? Through multiscale analysis, I present a general theory of pattern formation in the presence of spatio-temporal input variations, and show how biological systems can generate non-standard dynamic robustness for ‘free’ over physiologically relevant timescales. I apply this theory to paradigmatic pattern-forming systems, and predict that they are robust with respect to non-physiological variations in input signal. More broadly, I show how the dynamics of pattern-forming systems with spatio-temporally varying parameters can be classified based on the bifurcations in their governing equations.

MP Dalwadi and P Pearce (2021), Emergent robustness of bacterial quorum sensing in fluid flow, Proc Nat Acad Sci, 118(10):e2022312118 (10.1073/pnas.2022312118) MP Dalwadi and P Pearce (2023), Universal dynamics of biological pattern formation in spatio-temporal morphogen variations, Proc R Soc A: 479: 20220829 (10.1098/rspa.2022.0829)

This talk is part of the Isaac Newton Institute Seminar Series series.

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