Fit-Preserving Data Refinement of Mass-Action Reaction Networks

The systematic development of large biological models can benefit from an iterative approach based on a refinement process that gradually adds more details regarding the reactants and/or reactions of the model. We focus here on data refinement, where the species of the initial model are substituted with several subspecies in the refined one, each with its own individual behavior in the model. In this context, we distinguish between \emph{structural refinement}, where the aim is to generate meaningful refined reactions, and \emph{quantitative refinement}, where one looks for a data fit at least as good as that of the original model. The latter generally requires refitting the model and additional experimental data, a computationally expensive process. A \emph{fit-preserving refinement}, i.e. one that captures the same species dynamics as the original model, can serve as a suitable alternative or as initialization for parameter estimation routines. We focus in this paper on the problem of finding all numerical setups that yield fit-preserving refinements of a given model and formulate a sufficient condition for it. Our result suggests a straightforward, computationally efficient automation of the quantitative model refinement process. We illustrate the use of our approach through a discussion of the Lotka-Volterra model for prey-predator dynamics.