Seminar at SMU Delhi
January 19, 2016 (Tuesday) ,
3:30 PM at Webinar
Understanding the long-term behavior of stochastic biochemical reaction networks: Analysis and Applications
Abstract of Talk
The internal dynamics of a living cell is generally very noisy. An important source of this noise is the intermittency of biochemical reactions among various molecular species in the cell. Commonly the role of this noise is studied using stochastic models for reaction networks, where the dynamics is described as a continuous-time Markov chain whose states represent the molecular counts of various species. In this talk we will discuss how the long-term behavior and stability properties of such Markov chains can be assessed using a blend of ideas from probability theory, linear algebra and optimisation theory. In particular we will describe a constructive framework for determining if the reaction dynamics is ergodic and if its statistical moments (means, variances etc.) converge to their steady-state values with time. Using these ideas we will show how living cells can maintain their internal state in uncertain and changing environments by employing feedback strategies that are similar to those in man-made systems like cars, airplanes etc. We shall demonstrate our results with many examples from Systems and Synthetic Biology.