# Enzyme Kinetics two enzymes in complex with one substrate

Given an enzyme reaction where two enzymes are required to form the complex, for example $\ce{2E +S-> E3S->2E +P}$, how would I calculate complex concentration assuming steady state approximation ($\frac{d\ce{E2S}}{dot}=0$). Does the 2 in front of $\ce{E}$ multiply the rate or is it the exponent when looking at the rates going into the complex?

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## 1 Answer

As this seems like a homework question (and may be closed), as an example consider the reaction $\ce{H2 + I2 = 2HI}$. The rate, r is $\displaystyle r=\frac{1}{2}\frac{d\mathrm{[HI]}}{dt}=k_1\mathrm{[H_2][I_2]}-k_2\mathrm{[HI]}^2$ where the rate constants $k_1,\;k_2$ are for the forward and reverse reactions respectively. (This assumes that the reaction occurs as written.) As steady state the intermediate or transient species has a rate of change of zero and you note in your question.

In the general case if the reaction is $aA+bB= dD+eE$ then $\displaystyle -\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=\frac{1}{d}\frac{d[D]}{dt}=-\frac{1}{e}\frac{d[E]}{dt}$