Parameter estimation and optimal experimental design.

Mathematical models are central in systems biology and provide new ways to understand the function of biological systems, helping in the generation of novel and testable hypotheses, and supporting a rational framework for possible ways of intervention, like in e.g. genetic engineering, drug development or treatment of diseases. Since the amount and quality of experimental 'omics' data continue to increase rapidly, there is great need for methods for proper model building which can handle this complexity. In the present chapter we review two key steps of the model building process, namely parameter estimation (model calibration) and optimal experimental design. Parameter estimation aims to find the unknown parameters of the model which give the best fit to a set of experimental data. Optimal experimental design aims to devise the dynamic experiments which provide the maximum information content for subsequent non-linear model identification, estimation and/or discrimination. We place emphasis on the need for robust global optimization methods for proper solution of these problems, and we present a motivating example considering a cell signalling model.