# Mathematical Biology Seminar

### David Anderson

Department of Mathematics, University of Wisconsin-Madison

#### Stochastic analysis of biochemical reaction networks with absolute concentration robustness

#### Wednesday, January 15, 2014, at 3:05pm

LCB 219

It has recently been shown that structural conditions on the reaction network, rather
than a fine-tuning of system parameters, often suffice to impart "absolute concentration
robustness" on a wide class of biologically relevant, deterministically modeled mass-action
systems [Shinar and Feinberg, Science, 2010]. Many biochemical networks, however, operate
on a scale insufficient to justify the assumptions of the deterministic mass-action model,
which raises the question of whether the long-term dynamics of the systems are being
accurately captured when the deterministic model predicts stability. I will discuss recent
results that show that fundamentally different conclusions about the long-term
behavior of such systems are reached if the systems are instead modeled with stochastic
dynamics and a discrete state space. Specifically, we characterize a large class of
models which exhibit convergence to a positive robust equilibrium in the deterministic
setting, whereas trajectories of the corresponding stochastic models are necessarily
absorbed by a set of states that reside on the boundary of the state space
(i.e. an extinction event). The results are proved with a combination of methods from
stochastic processes and chemical reaction network theory.