Patterns in discrete spatial systems: a Boolean Delta-Notch model

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Date/heure
Date(s) - 28/01/2019
11 h 00 min - 12 h 00 min

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Lateral signalling is a pervasive mechanism capable of explaining cell differentiation. Spatial Boolean models of signalling have previously been formulated and studied. Because of the inherent combinatorial explosion, their computational analysis has proven to be challenging. In this talk, we discuss some properties of a Boolean Delta-Notch model in multi-cell systems with arbitrary neighbourhood relations. We show that the fixed points have a simple characterisation in terms of vertex covers of the graph encoding the chosen neighbourhood relation. We then proceed to investigate trap spaces and the reachability of fixed points, and interpret the results in terms of robustness of patterns. Building on the theory of Boolean networks, the approach can serve as a starting point for the analysis of more complex models of pattern formation.

http://www.mi.fu-berlin.de/en/math/groups/dibimath/staff/tonello.html

Olivier CHABROL
Posts created 14

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