BNMC Seminar:  Biochemical Network Models with Really Big Matrices

Eric Mjolsness
Associate Professor, Department of Information and Computer Science
UC, Irvine

In this mostly theoretical talk, I will review how fully stochastic models of biochemical reaction networks can be expressed in terms of simple algebraic expressions built out of operators: infinite-dimensional matrices that move probability around between different possible states of the network. This formulation of the chemical master equation has several advantages. It allows some easy, small networks to be solved in an almost mechanical way. It allows solvable submodels to be used as subroutines inside of simulation algorithms for larger and more complicated networks. It admits a systematic approach to creating simulation algorithms based on the operator (matrix) exponential function. I will go on to show that there is a generalization of these ideas to parameter-bearing objects at multiple spatial scales, and not just molecules, which can serve as the foundation for a new general-purpose biological modeling language.