Predicting changes of reaction networks with partial kinetic information.

We wish to predict changes of reaction networks with partial kinetic information that lead to target changes of their steady states. The changes may be either increases or decreases of influxes, reaction knockouts, or multiple changes of these two kinds. Our prime applications are knockout prediction tasks for metabolic and regulation networks. In a first step, we propose a formal modeling language for reaction networks with partial kinetic information. The modeling language has a graphical syntax reminiscent to Petri nets. Each reaction in a model comes with a partial description of its kinetics, based on a similarity relation on kinetic functions that we introduce. Such partial descriptions are able to model the regulation of existing metabolic networks for which precise kinetic knowledge is usually not available. In a second step, we develop prediction algorithms that can be applied to any reaction network modeled in our language. These algorithms perform qualitative reasoning based on abstract interpretation, by which the kinetic unknowns are abstracted away. Given a reaction network, abstract interpretation produces a finite domain constraint in a novel class. We show how to solve these finite domain constraints with an existing finite domain constraint solver, and how to interpret the solution sets as predictions of multiple reaction knockouts that lead to a desired change of the steady states. We have implemented the prediction algorithm and integrated it into a prediction tool. This journal article extends the two conference papers John et al. (2013) and Niehren et al. (2015) while adding a new prediction algorithm for multiple gene knockouts. An application to single gene knockout prediction for surfactin overproduction was presented in Coutte et al. (2015). It illustrates the adequacy of the model-based predictions made by our algorithm in the wet lab.