On Extreme Concentrations in Chemical Reaction Networks with Incomplete Measurements

Abstract

A fundamental problem in the analysis of chemical reactions networks consists of identifying concentration values along time or in steady state which are coherent with the experimental concentration data available. When concentration measurements are incomplete, either because information is missing about the concentration of a species at a particular time instant, or even there is no information at all on the concentration of a species, then the problem becomes ill-defined, and then different concentration curves are compatible with existing data. In this paper we address the problem of finding the extreme (highest and lowest) concentrations under incomplete data measurements; as a byproduct of our approach, the model parameters associated with such extreme concentrations are obtained. These extreme concentrations provide valuable information on the impact that incomplete measurements have on the theoretical reconstruction of concentrations from experimental data. To obtain such concentrations range, mathematical optimization problems are formulated, solvable by a variety of global optimization approaches, such as, for example, the stochastic global optimization method suggested.