  We study the model of continuous chemical reaction networks (CRNs),
consisting of reactions such as $A+B \to C+D$ that can transform some
continuous, nonnegative real-valued quantity (called a *concentration*) of
chemical species $A$ and $B$ into equal concentrations of $C$ and $D$. Such a
reaction can occur from any state in which both reactants $A$ and $B$ are
present, i.e., have positive concentration. We modify the model to allow
*inhibitors*, for instance, reaction $A+B \to^{I} C+D$ can occur only if the
reactants $A$ and $B$ are present and the inhibitor $I$ is absent. The
computational power of non-inhibitory CRNs has been studied. For instance, the
reaction $X_1+X_2 \to Y$ can be thought to compute the function $f(x_1,x_2) =
\min(x_1,x_2)$. Under an "adversarial" model in which reaction rates can vary
arbitrarily over time, it was found that exactly the continuous, piecewise
linear functions can be computed, ruling out even simple functions such as
$f(x) = x^2$. In contrast, in this paper we show that inhibitory CRNs can
compute any computable function $f:\mathbb{N}\to\mathbb{N}$.
