Now suppose that in an enzymatic reaction the E enzyme must bind on $n$ sites to form complex C. The reaction scheme is now as follows: $$\text{E}+n\,\text{S }{\mathop{\rightleftharpoons}\limits_{k_{2}}^{k_1}} \text{ C}{\mathop{\longrightarrow} \limits_{}^{k_3}} \text{ E} + \text{P}$$ For the concentration $c$ of the complex C, we can then write: $$\frac{\dd c}{\dd t}=k_1s^ne - (k_2+k_{3})c$$ The pseudo steady state approximation implies $\frac{dc}{dt}=0$ and thus: $$k_1s^ne - (k_2+k_3)c=0$$ Substitution of $c+e=e_0$ and isolation of $c$ then gives $$c=\frac{e_0s^n}{K_m+s^n}$$ with the Michaelis-Menten constant $$K_m=\frac{k_2+k_3}{k_1}\tiny.$$ The reaction rate $r$ is then given by $$r=\frac{V_{\max}\cdot s^n}{K_m+s^n}$$ where $V_{\max}=n\,k_3e_0$. This is called the Hill equation.