Towards an Efficient Verification Method for Monotonicity Properties of Chemical Reaction Networks

One of the main goals of systems biology is to understand the behaviour of (bio)chemical reaction networks, which can be very complex and difficult to analyze. Often, dynamical properties of reaction networks are studied by performing simulations based on the Ordinary Differential Equations (ODEs) models of the reactions' kinetics. For some kinds of dynamical properties (e.g. robustness) simulations have to be repeated many times by varying the initial concentration of some components of interest. In this work, we propose sufficient conditions that guarantee the existence of monotonicity relationships between the variation of the initial concentration of an "input" biochemical species and the concentration (at all times) of an "output" species involved in the same reaction network. Our sufficient conditions allow monotonicity properties to be verified efficiently by exploring a dependency graph constructed on the set of species of the reaction network. Once established, monotonicity allows us to drastically restrict the number of simulations required to prove dynamical properties of the chemical reaction network.