Set-based parameter estimation for symmetric network motifs

Deriving a predictive model in systems biology is a complex task. One major problem is the typically large network size, which renders the analysis with standard methods difficult. Symmetry, as omnipresent in nature, was used in many applications to encounter this problem. In this work, we investigate the influence of symmetry on set-based parameter estimation. We show that the presence of symmetry in a model can be used to significantly simplify the parameter estimation problem. This is done by determining a symmetry-adapted basis, corresponding to a linear representation of a finite group, in which the problem size is of smaller dimension. We demonstrate the applicability of this approach for several common network motifs, as e.g. the Michaelis-Menten reaction and the feedforward motif.