# Toward Systems Biology

### May 30 - 31, June 1, 2011

### Grenoble

**Probabilistic Approximations of Bio-pathways Dynamics: Some Computational Aspects**

Systems of ordinary differential equations (ODEs) are often used to model bio-chemical networks. Such systems however are difficult to analyze. To get around this, we construct a discrete probabilistic approximation of the ODE dynamics. We do so by discretizing the value and the time domain and assuming a distribution of initial states w.r.t. the discretized value space. We next sample a representative set of initial states according to the initial distribution and generate a set of trajectories through numerical simulations. Finally, we encode these trajectories compactly as a dynamic Bayesian network.

Consequently, pathway properties can be analyzed efficiently through standard Bayesian inference techniques instead of resorting to a large number of ODE simulations. We have tested our method on a number of signaling pathway models. Specifically we have used it to study the regulatory mechanisms the complement system which is a key component of the human immune system. We are also currently developing a GPU-based implementation of our approximation algoritm.

**P S Thiagarajan** National University of Singapore