If the rate of reaction, $\nu$, is expressible in the form: $$\nu =(k_0+\sum _{\begin{array}{c}i\end{array}}{k}_i[C_i{]}^{n_i})[A{]}^{\alpha }[B{]}^{\beta }...$$ where A, B, ... are reactants and $C_i$ represents one of a set of catalysts, then the proportionality factor $k_i$ is the catalytic coefficient of the particular catalyst $C_i$. Normally the partial order of reaction $n_i$ with respect to a catalyst is unity, so that $k_i$ is an $(\alpha +\beta +...+1)$th order rate coefficient. The proportionality factor $k_0$ is the $(\alpha +\beta +...)$th order rate coefficient of the uncatalysed component of the total reaction. For example, if there is catalysis by hydrogen and hydroxide ions, and the order of reaction can be expressed in the form: $$k=k_0+k_{{\text{H}}^{+}}[{\text{H}}^{+}]+k_{{\text{OH}}^{-}}[{\text{OH}}^{-}]$$ then $k_{H^{+}}$ and $k_{{\text{OH}}^{-}}$ are the catalytic coefficients for H⁺ and OH⁻, respectively. The constant $k_0$ relates to the uncatalysed reaction.