Understanding cell physiology from protein, DNA and RNA interactions represents a daunting challenge to the biological and modeling communities. Although a biologist may have his own idea about which proteins and interactions are important in a particular context, and a modeler may have his favorite abstraction for a given modeling problem, these choices are rather difficult to justify objectively. Therefore, comprehensive models of cell physiology are built with the idea that every detail matters. Model reduction provides strategies to extract the essential features of a complex model and use them for model identification and model analysis.
In this talk, we present model reduction methods with applications in computational biology. We focus on deterministic biochemical reactions networks with ordinary differential equations kinetics. Multiscale simplifications of such networks can be obtained by graph reconstruction operations, such as pooling and pruning reactions and species. Tropical geometry and analysis, new branches of mathematics coping with the asymptotic behavior of systems of equations, offer a natural framework for multiscale model reduction. In particular, by using the concept of tropical equilibration, one can find the sets of species and reactions to pool and to prune. We also discuss backward pruning machine learning strategies, in which model reduction is used for model identification.