Inference of chemical reaction networks based on concentration profiles using an optimization framework.

Understanding the structure of reaction networks along with the underlying kinetics that lead to particular concentration readouts of the participating components is the first step toward optimization and control of (bio-)chemical processes. Yet, solutions to the problem of inferring the structure of reaction networks, i.e., characterizing the stoichiometry of the participating reactions provided concentration profiles of the participating components, remain elusive. Here, we present an approach to infer the stoichiometric subspace of a chemical reaction network from steady-state concentration data profiles obtained from a continuous isothermal reactor. The subsequent problem of finding reactions consistent with the observed subspace is cast as a series of mixed-integer linear programs whose solution generates potential reaction vectors together with a measure of their likelihood. We demonstrate the efficiency and applicability of the proposed approach using data obtained from synthetic reaction networks and from a well-established biological model for the Calvin-Benson cycle. Furthermore, we investigate the effect of missing information, in the form of unmeasured species or insufficient diversity within the data set, on the ability to accurately reconstruct the network reactions. The proposed framework is, in principle, applicable to many other reaction systems, thus providing future extensions to understanding reaction networks guiding chemical reactors and complex biological mixtures.