Michaelis-Menten kinetics is based on the following reaction scheme: E + S k_2 k
ID: 533807 • Letter: M
Question
Michaelis-Menten kinetics is based on the following reaction scheme: E + S k_2 k--1 ES ES k_z rightarrow P + E The rate law for this process can be derived using either a pre-equilibrium approximation or a steady state approximation. a.) Describe these two approximations in words and specify the conditions that make each approximation applicable. b.) Both derivations incorporate a mass-balance relationship ([E]_0 = [E] + [ES]) for all enzyme species. Why is it not necessary to use a mass-balance equation for the substrate? c.) Derive the rate law for the Michaelis-Menten reaction scheme using either the pre-equilibrium or the steady state approximation. Clearly specify your choice.Explanation / Answer
a) In pre-equilibrium approximation we assume that the reactants and intermediates formed are in
equilibrium whereas in steady state approximation we assume that the intermediates are removed
right after their production.
b) This is derived to identify the enzyme at the end and to study its kinetics therefore we do not require
a mass balance equation for the substrate.
c) Using steady state approximation,
assumptions : [S] = [So] ; [Eo] = [E] + [ES]
formation rate = consumption rate
K-1[ES] + K2[ES] = K1 [E] [S]
[ K-1 + K2 ] / K1 = [E] [S] / [ES]
Let Km = [ K-1 + K2 ] / K1
Km = ( [Eo] - [ES] ) [S] /[ES]
multiply with [ES] on both sides and rearrange as,
[ES] = [Eo] [S] / ( Km + [S] )
Now dp/dt = vo = K2 [ES]
vo = K2 [Eo] [S] / ( Km + [S] )
when [ES] = [Eo] ; vmax = K2 [Eo]
dp/dt = vo = vmax [S] / ( Km + [S] )