Congrats Johannes and Frederik! One step closer in developing mechanistically correct models!
In this work, we present a symmetry-based method for classification of ODE models according to their symmetry groups. The mathematical framework for such methods is that of group theory and representation theory, and more generally differential geometry. The framework is well-established and enormously successful for model construction in mathematical physics, however, as an approach to model construction in systems biology in general, and reaction kinetics in particular, the symmetry framework is not widely used. By incorporating intrinsic properties of systems at all time scales, it could arguably represent and untapped potential for systems biology in both model development and analysis of dynamical models. By studying symmetries that a system obeys, it is possible to derive the corresponding dynamic models from those symmetries.
We have demonstrated the power of this method by deriving symmetries of the Hill models used in enzyme kinetics. We further validated our approach showing that the symmetries of the candidate models must be distinct, by implementing common translational symmetry. We show that symmetries reveal intrinsic properties of the system using only a single time series and that symmetry-based framework provides novel insights of the underlying mechanism. Finally, we demonstrated that symmetry-based methodology outperforms classic residual-based fitting, particularly in cases when few datasets are available, and can significantly contribute to the development of mechanistic models.
You can read the paper at: https://royalsocietypublishing.org/doi/10.1098/rsif.2020.0204