# Tackling the construction of probability distributions arising in Bio-Chemical networks

**Vikram Sunkara
**

Institute for Applied and Numerical Mathematics

Department of Mathematics

Karlsruhe Institute of Technology

Karlsruhe, Germany

### Abstract:

Modern systems biology is working towards describing the interactions of processes in biology by networks, we refer to these as Bio-Chemical Reaction Networks (Biological Networks for short). Through advances in fluorescence techniques and sequencing technologies, biologists are able to scope deeper and describe critical biological processes as paths on a complex biological network. We are interested in a particular class of biological networks, that is, biological networks with paths which behave as jump Markov processes. The probability of observing any particular state the network is in at a particular point in time is given by solving the Chemical Master Equation (CME). For these particular class of networks, a variety of Monte Carlo based simulation methods have been proposed. However computing a probability distribution over all possible features of the network is computationally difficult. It has been shown that the computational complexity grows exponentially in the number of species in the system. In this talk we discuss the major issues that arise in computing probability distributions for large biological networks. We introduce and demonstrate some modern techniques inspired by adaptive domain selection and dimension reduction to help tackle our issues. We apply these techniques on real life examples to demonstrate their contribution.