Michaelis-Menten equation

Michaelis-Menten equation is a mathematical model that describes the kinetics of many enzyme-catalyzed reactions. Named after Leonor Michaelis and Maud Menten, the equation is derived from the law of mass action and is used to analyze the rates of enzymatic reactions.

Overview

The Michaelis-Menten equation is given by:

v = Vmax[S]/(Km + [S])

where:

• v is the reaction velocity,
• Vmax is the maximum reaction velocity,
• Km is the Michaelis constant,
• [S] is the substrate concentration.

The equation assumes that the enzyme-substrate complex is in a steady state, meaning that its concentration does not change over time. This assumption is valid when the substrate concentration [S] is much larger than the enzyme concentration [E].

Derivation

The Michaelis-Menten equation is derived from the law of mass action, which states that the rate of a chemical reaction is proportional to the product of the concentrations of the reactants. The derivation involves the following steps:

1. Write down the reaction scheme for the enzyme-catalyzed reaction. 2. Write down the rate equations for the reaction scheme using the law of mass action. 3. Assume that the enzyme-substrate complex is in a steady state. 4. Solve the rate equations for the reaction velocity v.

Applications

The Michaelis-Menten equation is used to analyze the rates of enzymatic reactions. It is particularly useful for determining the maximum reaction velocity Vmax and the Michaelis constant Km, which are characteristic parameters of the enzyme. The equation is also used in the design of drugs and in the diagnosis of diseases.

See also

• Enzyme kinetics
• Lineweaver-Burk plot
• Eadie-Hofstee diagram

References

Michaelis-Menten equation Resources
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