# The Michaelis-Menten Equation in biochemistry

## The Michaelis-Menten Equation

Victor Henri, a French chemist in 1903, discovered that the responses of enzymes were initiated by a bond between the enzyme and the substrate (in general, a binding interaction). His research was undertaken by German biochemist Leonor Michaelis and Canadian physicist Maud Menten, who studied the kinetics of an enzymatic reaction system, invertase, which catalyzes sucrose hydrolysis into glucose and fructose. The mathematical model of the reaction was suggested in 1913. This reaction is known as The Michaelis-Menten Equation.

Let us consider an Enzyme E is binding with a substrate S. It assumes the formation of an enzyme-substrate complex ES. After that, the product P is released.

• The ES complex is assumed to be in fast balance with free enzyme E
• It is presumed that the breakdown of ES into products is slower than
(1) formation of ES and
(2) breakdown of ES to re-form E and S

This may be represented schematically as,

S + E  ES →  P + E

Vo  = k2  [ES]

ES formation rate =  k1  [E][S]

= k1  ([Etotal] – [ES]) [S]

ES breakdown rate = k-1 [ES]  +  k2 [ES]

ES formation rate = ES breakdow rate

k1  ([Etotal] – [ES]) [S]  =  k-1 [ES] +  k2 [ES]

k1 [Etotal][S] – k1[ES][S]  =  ( k-1  +  k2 )[ES]

k1 [Etotal][S]  =  (k1[S] +  k-1  +  k2 )[ES] We know, Vo  = k [ES] ⇒ Vmax  = k2  [Etotal]; Since, Vo = Vmax   when  [Etotal] = [ES] (at saturation).

## Enzyme Kinetics: Michaelis-Menton Equation ## 1.Characteristics of Km:

• Km — the constant Michaelis — is characteristic of an enzyme and its specific substratum, and represents the enzyme’s affinity to that substratum.
• Km does not differ with the enzyme concentration

## • Small Km:
A numerically tiny (low) kilometer represents a strong substrate enzyme affinity.
• Large Km:
A numerically big (elevated) kilometer represents a low substrate enzyme affinity

## 2. Relationship of velocity to enzyme concentration:

• The speed of response at all substrate levels is directly proportional to the concentration of the enzyme. For example, if the enzyme concentration is halved, the initial rate of the reaction (vo), as well as that of Vmax, are reduced to half that of the original.

## A Linear Form of the Michaelis-Menten Equation 