Optimal sampling time selection for parameter estimation in dynamic pathway modeling

Systems Biology is an emerging research area, which considers mathematical representations of inter- and intra-cellular dynamics. Among the many research problems that have been addressed, dynamic modeling of signal transduction pathways has received increasing attention. The usual approach to represent intra-cellular dynamics are nonlinear, usually ordinary, differential equations. The purpose of the models is to test and generate hypothesis of specific pathways and it is therefore required to estimate model parameters from experimental data. The experiments to generate data are complex and expensive, as a consequence of which the time series available are usually rather short, with few if any replicates. Almost certainly, not all variables one would like to include in a model can be measured. Parameter estimation is therefore an important research problem in Systems Biology and the focus of this paper. In particular, we are interested in optimizing the sampling time selection in order to minimize the variance of the parameter estimation error. With few sampling time points feasible, their selection is of practical importance in experimental design. Finally, the theoretical results are supported with an application.