Efficient Analysis of Chemical Reaction Networks Dynamics based on Input-Output Monotonicity

Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that rarely can be solved in closed-form, but that can instead be used to reason on the system dynamics. In this context, one of the possible approaches is to perform numerical simulations, which may require a high computational effort. In particular, in order to investigate some dynamical properties, such as robustness or global sensitivity, many simulations have to be performed by varying the initial concentration of chemical species. Results: In order to reduce the computational effort required when many simulations are needed to assess a property, we exploit a new notion of monotonicity of the output of the system (the concentration of a target chemical species at the steady-state) with respect to the input (the initial concentration of another chemical species). To assess such monotonicity behavior, we propose a new graphical approach that allows us to state sufficient conditions for ensuring that the monotonicity property holds. Our sufficient conditions allow us to efficiently verify the monotonicity property by exploring a graph constructed on the basis of the reactions involved in the network. Once established, our monotonicity property allows us to drastically reduce the number of simulations required to assess some dynamical properties of the CRN.