  Biological regulatory networks depend upon chemical interactions to process
information. Engineering such molecular computing systems is a major challenge
for synthetic biology and related fields. The chemical reaction network (CRN)
model idealizes chemical interactions, allowing rigorous reasoning about the
computational power of chemical kinetics. Here we focus on function computation
with CRNs, where we think of the initial concentrations of some species as the
input and the equilibrium concentration of another species as the output.
Specifically, we are concerned with CRNs that are rate-independent (the
computation must be correct independent of the reaction rate law) and
composable ($f\circ g$ can be computed by concatenating the CRNs computing $f$
and $g$). Rate independence and composability are important engineering
desiderata, permitting implementations that violate mass-action kinetics, or
even "well-mixedness", and allowing the systematic construction of complex
computation via modular design. We show that to construct composable
rate-independent CRNs, it is necessary and sufficient to ensure that the output
species of a module is not a reactant in any reaction within the module. We
then exactly characterize the functions computable by such CRNs as
superadditive, positive-continuous, and piecewise rational linear. Thus
composability severely limits rate-independent computation unless more
sophisticated input/output encodings are used.
