Challenges for the identification of biological systems from in vivo time series data

Modern methods of high-throughput molecular biology render it possible to generate time series of metabolite concentrations and the expression of genes and proteins in vivo. These time profiles contain valuable information about the structure and dynamics of the underlying biological system. This information is implicit and its extraction is a challenging but ultimately very rewarding task for the mathematical modeler. Using a well-suited modeling framework, such as Biochemical Systems Theory (BST), it is possible to formulate the extraction of information as an inverse problem that in principle may be solved with a genetic algorithm or nonlinear regression. However, two types of issues associated with this inverse problem make the extraction task difficult. One type pertains to the algorithmic difficulties encountered in nonlinear regressions with moderate and large systems. The other type is of an entirely different nature. It is a consequence of assumptions that are often taken for granted in the design and analysis of mathematical models of biological systems and that need to be revisited in the context of inverse analyses. The article describes the extraction process and some of its challenges and proposes partial solutions.