Michaelis Menten equation

• It denotes the relationship between substrate concentration and enzymatic reaction rate quantitively.

E+ S ( K1/K2)⇌ ES (K3)à E+ P—- i)

Vformation = K1 [E][S] – ii)

V breakdown = K2 [ES] + K3 [ES] = ES ( K2 + K3)

At equilibrium, V formation = V breakdown

Hence,

K1 [E][S] = ES (K2 + K3)

Or, [E][S] = [ES] ( K2 + K3)/ K1 — iii)

Or, [E] [S] = [ES] Km — iv) [ Where , Km = K2+ K3/K1]

Since, [E] = ([Et] – [ES])

Putting the value of [E] in equation (iv), we get,

( [Et] – [Es]) [S] = [ES] Km

Or, [Et] [S] – [ES][S] = [ES] Km

Or, [Et] [S] = [ES] ( Km + [S])

Or, [ES] = [Et][S]/ Km + [S] —–v)

Again, we can determine V₀ in terms of [ES] by following the equation,

V₀ = K3 [ES]

Or, [ES] = V₀/ K3 ——- vi)

Putting the value of [ES] in equation v), we get

V₀/ K3 = [Et][S] / Km + [S]

Or, V₀ = K3 [Et][S] / Km + [S]——— vii)

Since, V_max  = K3 [Et] —– viii)

Now,

V₀ = Vmax [S]/ Km + [S] —- ix) [ Where, v= velocity, V₀ = initial velocity, Vmax = maximum velocity]

This equation (ix) is the Michaelis-Menten equation.

Note: Michaelis-Menten equation is mainly used to characterize the enzymatic rate at different substrate concentrations and to characterize the elimination of chemicals.