Forum Numerica - Tomas Gedeon: Modeling complex phenotypes supported by gene regulatory networks

We describe a close connection between two seemingly disparate types of GRN models: ordinary differential equations and monotone Boolean maps. We show that switching (Glass) models connect the world of continuous dynamics of ODEs and discrete dynamics of Boolean maps by describing connection between collection of all parameterizations of switching systems and collections of monotone Boolean functions (MBFs) compatible with the network structure. This connection allows combinatorial (i.e. finite) description of ODE dynamics over parameter space and allows conceptualization of bifurcation theory of Boolean maps. The dynamics across the collection of MBFs describes the dynamical repertoire of the GRN.
We briefly discuss recent progress on iterative construction of the set of all monotone Boolean maps with $k$ inputs and then discuss applications to endocycling in yeast, a human developmental network, and pattern formation in the gap gene network in Drosophila.

Tomas Gedeon is a Professor of Mathematics at Montana State University who specializes in mathematical modeling of biological systems, especially those arising in cellular and molecular biology. His most recent interest is to develop new methods to understand behavior of gene regulatory networks with applications to apply understanding of cell cycle and behavior of developmental networks across time and space.
He obtained his undergraduate degree in Comenius University in his native Slovakia in 1989 and PHD in Mathematics from Georgia Institute of Technology in 1994.