Neuter Reactants: What do they do?
There are reactions similar to the one you show, which is straightforward catalysis, these are autocatalytic reactions such as $\ce{A + B\to 2B}$ or $\ce{A + 3B\to 3B}$ which lead to interesting non-linear behaviour. Of more importance is the Michaelis-Menten scheme  $\ce{E + S\leftrightharpoons ES \to P + E}$ where E is an enzyme , S a substrate, ES a complex of both, and P the product.