Eric Siggia – Rockefeller University
Wednesday, April 3rd, 10:45AM EDT
Geometry and Genetics
The classic phenomena of canalization in developmental biology, that outcomes are discrete and biologically interpretable, is a license to treat phenomenological models by geometric methods. Papers of Smale and others from 1961-70’s prove that the Waddington topographical metaphor for developmental of cells or embryos moving down hill and bifurcating into lineages, is rigorously true for gene network models. We (Rand et al PNAS 2021) extend these results to classify all generic two dimensional parameter spaces for such models. Results extend to spatial patterns as well as intracellular gene networks. The geometric interpretation of dynamical systems is in accordance with basic notions of classical embryology. Biological data from directed differentiation of embryonic stem cells and vertebrate development will be interleaved into the presentation.