  Chemical Reaction Networks (CRNs) provide a useful abstraction of molecular
interaction networks in which molecular structures as well as mass conservation
principles are abstracted away to focus on the main dynamical properties of the
network structure. In their interpretation by ordinary differential equations,
we say that a CRN with distinguished input and output species computes a
positive real function $f : R+ $\rightarrow$ R+$, if for any initial
concentration x of the input species, the concentration of the output molecular
species stabilizes at concentration f (x). The Turing-completeness of that
notion of chemical analog computation has been established by proving that any
computable real function can be computed by a CRN over a finite set of
molecular species. Rate-independent CRNs form a restricted class of CRNs of
high practical value since they enjoy a form of absolute robustness in the
sense that the result is completely independent of the reaction rates and
depends solely on the input concentrations. The functions computed by
rate-independent CRNs have been characterized mathematically as the set of
piecewise linear functions from input species. However, this does not provide a
mean to decide whether a given CRN is rate-independent. In this paper, we
provide graphical conditions on the Petri Net structure of a CRN which entail
the rate-independence property either for all species or for some output
species. We show that in the curated part of the Biomodels repository, among
the 590 reaction models tested, 2 reaction graphs were found to satisfy our
rate-independence conditions for all species, 94 for some output species, among
which 29 for some non-trivial output species. Our graphical conditions are
based on a non-standard use of the Petri net notions of place-invariants and
siphons which are computed by constraint programming techniques for efficiency
reasons.
