Question

A straight forward answer please

Part A: For ing enzyme catalytic process Catalytic step E +P Substrate binding The forward rate constants are k1 and k2 and reverse rate constant is k.1 Express rate of complex [Enzyme.Substrate] formation and complex breakdown and determine the KM.

Answer 1

For the above equation, given that k₁ and k_-1 are the forward and reverse rate constants respectively. Let us take k₂ as the rate constant for the formation of the product P.

Now, the rate of the complex [ES] formation is = k₁ [E][S] ............. (1)

and rate of the complex [ES] breakdown is = k_-1 [ES] + k₂ [P][E]

Again, considering that the amount of enzyme is too small as compared to that of the substrate S, it may be assumed that [P][E] $\approx$   [ES]

Therefore equation (3), i.e., the rate of complex breakdown is = (k-1 + k2) [ES]...... (2)

From steady state approximation, d[ES]/dt = 0

Therefore, rate of complex [ES] formation is equal to the rate of complex breakdown

i.e., Equating equation (1) and (2) we have

k₁ [E][S] = (k_-1 + k₂) [ES]

or, [E][S] = (k_-1 + k₂) [ES] / k₁

or, [E][S] = K_M [ES]; where K_M = (k_-1 + k₂)/k₁

Therefore, K_M = [E][S] / [ES]....... (3) ; K_M is called Michaelis constant