Abstract

Many questions in biology can be formulated as a direct problem: Given a biochemical system, can one deduce some of its properties? However, in the field of synthetic biology and DNA computing, the central problem is an inverse one: Given a property, can one design a biochemical system that displays this property? Given a biochemical system, can one introduce additional molecular species to control properties of the original system? In this talk, I will present mathematical methods for systematic design and control of biochemical systems using two modelling approaches: (i) less-detailed deterministic models, taking form of ordinary differential equations for concentrations of molecular species, and (ii) more-detailed stochastic models, taking form of the Gillespie stochastic simulation algorithm for copy-numbers of molecular species. I will demonstrate the mathematical methods by constructing relatively simple biochemical systems displaying exotic dynamics, such as multi-stability, oscillations, chaos, specific bifurcation structures and noise-induced phenomena.