- TITLE: Stochastic Reachability Analysis in Complex Biological Networks
- AUTHOR: H. El-Samad, M. Fazel, X. Liu, A. Papachristodoulou, S. Prajna.
The impact of noise on cellular networks and its interplay with
their rich dynamics are increasingly being characterized as
important phenomena that must be thoroughly investigated for a
useful understanding of biological dynamics. At the same time, the
mathematical modeling and analysis of these networks in a stochastic
setting presents a number of challenges, such as the need for
a large number of computationally
expensive stochastic simulations to
collect statistics about the occurrence of important events
or correlate their occurrence with the noise intensity. In this paper, we
demonstrate the use of new techniques of stochastic reachability
analysis to address these problems. Specifically, we study the
problem of computing bounds on the probability of a biological
stochastic process to reach certain parts of the state space in a
finite time. The techniques presented are based on the algorithmic
construction of barrier certificates using convex optimization,
and are illustrated through the use of a biologically
important system: the bacteriophage $\lambda$ genetic switch.
- STATUS: To appear in Proceedings American Control Conference,
- ACC paper: pdf file
- DATE OF ENTRY: March 2006.