Talk by Dr. Shane Kepley (Dept. of Mathematics, Rutgers University)

03/04/2021

Abstract: 

Hill function models are widely used for modeling enzymatic reactions under a quasi-steady state assumption.  A major problem when using Hill models to study the dynamics of gene regulation is the rapid increase in the parameter dimension as additional gene interactions are added to the model. This presents a significant difficulty when studying equilibria in Hill models as their existence, location, and stability can vary wildly due to a variety of bifurcations. 

In this talk we introduce recent numerical techniques which have been developed for finding equilibria, saddle-node, and Hopf bifurcations in Hill models despite the high parameter dimension. These algorithms have been implemented in a Python library, HillCont, which has been developed for computing and continuing invariant sets and bifurcations in Hill models.