2009 Math Biology Seminar - 12

Nonlinear dynamical systems are prevalent in systems biology, where they are often used to represent a biological system. Its dynamical behaviour is often impossible to understand by intuition alone without such mathematical models. Ideas and methods from systems and control engineering can help us to understand how the pathway architecture and parameter choices produce the desired performance and robustness in the observed dynamics. In this talk, we first show the direct interaction of a theoretical analysis with efficiently setting up experiments. We present the application of tools from engineering for designing biological experiments to elucidate the signalling pathway in the chemotactic system of /Rhodobacter sphaeroides/. In the second part, we focus on the problem of finding experimental setups that allow for full state observability and parameter identifiability of a nonlinear dynamical system; that is, whether the values of system states and parameters can be deduced from output data (experimental observations). This is an important question to answer as often observability and identifiability are assumed, which might lead to costly repetitions of experiments. We present a novel approach to check a priori for parameter identifiability and use new, state of the art computational tools for the implementation. Examples from biology are used to illustrate our method.