Talk by William Duncan (Dept. of Mathematical Sciences, MSU)
02/04/2021 3:10-4:00pm WebEx Meeting
Abstract: In differential equation models of gene regulatory networks, interactions
between genes are often modeled by nonlinear sigmoidal functions. If these sigmoidal
functions are replaced by piecewise constant or switching functions, the dynamics
of the resulting system are completely determined by a finite number of inequalities
between parameters and can be computed efficiently. The expectation is that the equilibria
of the switching system correspond to equilibria of steep sigmoidal systems. However,
the sigmoidal system will have additional equilibria not present in the switching
system. In this talk, I will discuss results which show that all equilibria of steep
sigmoidal systems can be determined from the switching system inequalities. In the
case of ramp systems, a subclass of sigmoid systems, I discuss bifurcations of these
equilibria as the steepness of the functions decrease and give explicit bounds on
their slopes that guarantee the equilibria maintain their stability and numbers that
are predicted by the switching system.
