Turing instability, localised patterns and plant cell polarity formation

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• Alan Champneys, University of Bristol
• Wednesday 05 February 2020, 14:00-15:00
• Engineering ENG-G29.

If you have a question about this talk, please contact Fabian Spill.

In this talk I shall describe recent work inspired by problems in cell biology, namely how the dynamics of small G-proteins underlies polarity formation. Their dynamics is such that their active membrane-bound form diffuses more slowly. Hence you might expect Turing patterns. Yet how do cells form backs and fronts or single isolated patches? In understanding these questions we shall show that the key is to identify the parameter region where Turing bifurcations are sub-critical. What emerges is a unified 2-parameter bifurcation diagram containing pinned fronts, localised spots, localised patterns. This diagram appears in many canonical models such as Schnakenberg and Brusselator, as well as biologically more realistic systems. A link is also found between theories of semi-strong interaction asymptotics and so-called homoclinic snaking. I will close with some remarks about relevance to root hair formation and pavement cells to the importance of sub-criticality in biology.

This talk is part of the Applied Mathematics Seminar Series series.

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• Applied Mathematics Seminar Series
• Engineering ENG-G29
• School of Mathematics Events

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