This will be a non-technical talk. I will start by describing how Kolmogorov models dynamical systems and stationary processes so as to put them both into the same mathematical framework and some results that are made possible by this point of view.

These results lie on the chaotic side of dynamics.

On the rigid side of dynamics, I will describe the Kolmogorov-Moser twist theorem (part of KAM theory) and a generalization of that theorem.

I will discuss the very strong similarities between the stability properties of
chaotic and rigid systems.

In a recent article in APS News, John Hopfield, one of the founders of what has now become quantitative and systems biology, has defined physics as "The idea ... that the world is understandable." As a physicist working on biological problems, I pursue this understanding as the ultimate goal. Unfortunately, even for the simplest cellular networks, understanding their function is often obscured behind long and incomplete part lists of interaction partners, wiring diagrams, and differential equations. In this talk, I will describe how ideas of statistical physics and information theory allow us to make small steps towards formulation of and answers to questions like: What are the signal processing capabilities of stochastic biochemical networks? Which functions can they perform? How important is stochasticity? How can we understand network dynamics without microscopic simulations? While addressing these questions, I will also show examples of cross-fertilization between physics and systems biology: on the one hand, physics will suggest tools for faster simulation and deeper understanding of the networks dynamics, and, on the other, study of a biological problem will show an unexpected and illuminating connection between seemingly unrelated areas of theoretical physics.

Bistable systems are very common modules in natural biological systems. In this work, well-characterized biological components are used to construct a genetic toggle switch in S. cerevisiae through mutual inhibition. Mathematical modeling is combined with molecular biology to design and construct the genetic toggle switch. We show that, guided by modeling predictions, we can achieve bistability by tuning the system. I will illustrate the artificial "cell differentiation", both experimentally and mathematically, by starting the switch from a specific initial condition that expressions of both repressors are turned off.

This work demonstrates the use of synthetic gene networks to uncover general regulatory mechanisms in natural biological systems.

About the speaker: Dr. Xiao Wang is currently a Research Associate working with Dr. James Collins at Boston University's Center for BioDynamics. There he is developing mathematical models and computational algorithms to help understand and construct complex synthetic networks in eukaryotic cells from bottom up. Dr. Wang received his Ph.D. in Operations Research/ Bioinformatics & Computational Biology from The University of North Carolina at Chapel Hill in 2006. During his Ph.D., Dr. Wang also studied the yeast pheromone response pathway and used mathematical models to uncover novel regulatory roles of MAP kinase.