Using Mathematical Models to Help Understand Planar Cell Pol
3,681 views · Published 15 November 2007 · 51:04 · Indexed 26 September 2026
Channel: CITRIS and the Banatao Institute · 2007 · Education
March 7, 2007 In this talk, methods that we have designed to analyze and help to identify certain protein regulatory networks will be presented. Hybrid automata represent one suitable modeling framework, as the protein concentration dynamics inside each cell are modeled using linear differential equations; inputs activate or deactivate these continuous dynamics through discrete switches, which themselves are controlled by protein concentrations reaching given thresholds. We present an iterative refinement algorithm for computing discrete abstractions of a class of symbolic hybrid automata, and we apply this algorithm to a model of multiple cell Delta-Notch protein signaling. The results are analyzed to show that novel, non-intuitive, and biologically interesting properties can be deduced from the computation, thus demonstrating that mathematical modeling which extrapolates from existing information and underlying principles can be successful in increasing understanding of some biological systems.
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