Michaelis Menten equation

Michaelis Menten equation describes enzyme kinetics by relating reaction rate to substrate concentration in pharmacology.

• The Michaelis-Menten equation describes the kinetics of enzyme-catalyzed reactions, first proposed by Leonor Michaelis and Maud Menten in 1913.
• It expresses the relationship between reaction rate (V) and substrate concentration ([S]):

$V = \frac{V_{\text{max}} \,[S]}{K_m + [S]}$

Where:

• V = reaction rate at a given substrate concentration
• Vmax = maximum reaction rate when the enzyme is fully saturated with the substrate
• [S] = substrate concentration
• Km = Michaelis constant, representing the substrate concentration at which the reaction rate is half of Vmax (i.e., Vmax/2), indicating enzyme affinity for the substrate

This equation assumes a steady-state condition for the enzyme-substrate complex and is useful in determining enzyme kinetics, such as affinity and catalytic efficiency.

Explanation with Examples of Drugs

1. Phenytoin:

   • A classic example of a drug displaying nonlinear (dose-dependent) pharmacokinetics due to saturable hepatic enzyme metabolism.
   • Even small increases in dose can cause disproportionately high increases in plasma levels and prolonged half-life.

2. Theophylline:

   • At therapeutic doses, metabolism can become saturated, leading to unpredictable increases in plasma concentrations if dose adjustments are not carefully managed.

3. Ethanol:

   • At moderate to high concentrations, the alcohol dehydrogenase pathway saturates, causing a constant elimination rate (i.e., zero-order kinetics over a certain range).

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