Tuesday, August 20th, 2013
3:00pm - 4:00pm, in Science 2-064

Chinmaya Gupta

University of Houston

Mathematical Models for Delayed Feedback in Gene Networks

Abstract: One of the principle aims of synthetic biology is to be able to engineer organisms with desired properties. In this context, mathematical models can provide valuable insights into mechanisms which give rise to these properties. I will discuss a mathematical model with delayed feedback that reveals a mechanism for building a biological oscillator that maintains a constant period over a range of ambient temperatures. This mechanism has been exploited to build a synthetic genetic oscillator in Escherichia coli that exhibits robust temperature compensation. In the absence of the compensation mechanism, Arrhenius scaling of biochemical reaction rates predicts that the period of oscillation should decrease with an increase in temperature. Delayed feedback can also have a strong stabilizing effect on the dynamics of bistable genetic switches. I will present a model of a general bistable genetic network that reveals the mechanism behind the stabilization: an increase in the number of failed transitions. The predictions from this model, and numerical verification from exact simulations, sometimes lead to conclusions that are different from those obtained from Langevin approximations. This leads to another question I will address: What are the appropriate Langevin approximations for describing the dynamics of gene networks with delayed feedback, and how good are these approximations?