Methods for biochemical model decomposition and quantitative submodel comparison

Comparing alternative models for a given biochemical system is in general a very difficult problem: the models may focus on different aspects of the same system and may consist of very different species and reactions. The numerical setups of the models also play a crucial role in the quantitative comparison. When the alternative designs are submodels of a reference model, e.g. knockdown mutants of a model, the problem of comparing them becomes simpler: they all have very similar, although not identical, underlying reaction networks, and the biological constraints are given by the ones in the reference model. In the first part of our study we review several known methods for model decomposition and for quantitative comparison of submodels. We describe the knockdown mutants, elementary flux modes, control-based decomposition, mathematically controlled comparison and its extension, local submodels comparison and a discrete approach for comparing continuous submodels. In the second part of the paper we present a new statistical method for comparing submodels that complements the methods presented in the review. The main difference between our approach and the known methods is related to the important question of how to chose the numerical setup in which to perform the comparison. In the case of the reviewed methods, the comparison is made in the numerical context of the reference model, i.e., in each of the alternative models both the kinetics of the reactions and the initial values of all variables are chosen to be identical to those from the reference model. We propose in this paper a different approach, better suited for response networks, where each alternative model is assumed to start from its own steady state under basal conditions. We demonstrate our approach on a case study focusing on the heat shock response