  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.
