Question

Explain the meaning of the three assumptions for the Michaelis-Menten kinetics. Express each assumption in mathematical terms.

Answer 1

The Michaelis-Menten equation is based on three key assumptions.
(1) [S] is very large compared with [E], so that when all E is bound in the form ES, there is still an excess of S. : Each enzyme molecule is having more than one active sites at which the substrate must be bound so that the reaction takes place. At low concentrations of Substrate many active sites remain unoccupied thus lowering the rate of reaction. If most of these sites are occupied then the rate of reaction will eventually increase.

[E] << [S]

(2) Only initial velocity conditions are considered. Thus, there is very little accumulation of P, and the formation of ES from E + P is negligible: This approximation considers that the breakdown of ES into P is slower than the formation of ES from E and S. Thus the reaction of E+P is the rate limiting reaction.

Rate of the reaction = -d[P]/dt

(3) Steady-state assumption. The rate of breakdown of ES equals the rate of formation of ES.: Experiment shows that the true equilibrium would not be achieves in the fast step because the subsequent slow reaction would be constantly removing the intermediate enzyme-substrate complex, ES.

k₁[E][S] = k_-1[ES] + k₂[ES]