The Michaelis-Menten Equation in biochemistry

The Michaelis-Menten Equation

In 1903, French physical chemist Victor Henri found that enzyme reactions were initiated by a bond (more generally, a binding interaction) between the enzyme and the substrate. His work was taken up by German biochemist Leonor Michaelis and Canadian physician Maud Menten, who investigated the kinetics of an enzymatic reaction mechanism, invertase, that catalyzes the hydrolysis of sucrose into glucose and fructose. In 1913, they proposed a mathematical model of the reaction. This reaction is known as The Michaelis-Menten Equation.

The Michaelis-Menten EquationLes 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.

  • It assumes that the ES complex is in rapid equilibrium with free enzyme E
  • Breakdown of ES to form products is assumed to be slower than
    (1) formation of ES and
    (2) breakdown of ES to re-form E and S

This may be represented schematically as,

E + S  ES →  E + P

Vo  = k2  [ES]

Rate of ES formation =  k1  [E][S]

= k1  ([Etotal] – [ES]) [S]

Rate of ES breakdown = k-1 [ES]  +  k2 [ES]

At steady state assumption:

Rate of ES formation   = Rate of ES breakdow

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]    Vo = Vmax   when  [Etotal] = [ES] (at saturation).      Therefore Vmax  = k2  [Etotal]

Enzyme Kinetics: Michaelis-Menton Equation

1.Characteristics of Km:

  • Km—the Michaelis constant—is characteristic of an enzyme and its particular substrate, and reflects the affinity of the enzyme for that substrate.
  • Km does not vary with the concentration of enzyme
  • Small Km:
    A numerically small (low) Km reflects a high affinity of the enzyme for substrate.
  • Large Km:
    A numerically large (high) Km reflects a low affinity of enzyme for substrat

2. Relationship of velocity to enzyme concentration:

  • The rate of the reaction is directly proportional to the enzyme concentration at all substrate concentrations.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

Double-Reciprocal or Lineweaver-Burk Plot

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