Symmetry structures in dynamic models of biochemical systems

Symmetries provide a powerful concept for the development of mechanistic models by describing structures corresponding to the underlying dynamics of biological systems. In this paper, we consider symmetries of the non-linear Hill model describing enzymatic reaction kinetics, and derive a class of symmetry transformations for each order n of the model. We consider a minimal example consisting in the application of symmetry based methods to a model selection problem, where we are able to demonstrate superior performance compared to ordinary residual-based model selection. Finally, we discuss the role of symmetries in systematic model building in systems biology.