Michaelis–Menten kinetics

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Michaelis Menten S P E ES

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Michaelis–Menten kinetics describes the rate of enzyme-catalyzed reactions by relating the reaction rate to the concentration of a substrate. This model is named after Leonor Michaelis and Maud Menten, who proposed it in 1913. It is one of the best-known models of enzyme kinetics and forms the basis of understanding how enzymes function in biochemistry and molecular biology.

Overview

The Michaelis–Menten equation is given by:

\[ v = \frac{V_{max} [S]}{K_M + [S]} \]

where:

• \(v\) is the initial reaction velocity,
• \(V_{max}\) is the maximum reaction velocity,
• \([S]\) is the substrate concentration,
• \(K_M\) is the Michaelis constant, which represents the substrate concentration at which the reaction velocity is half of \(V_{max}\).

The equation assumes that the formation of the enzyme-substrate complex (\(ES\)) is in a steady state, meaning the formation and breakdown of \(ES\) are balanced.

Key Concepts

• Enzyme-Substrate Complex: The temporary complex formed when an enzyme binds to its substrate.
• V_max: The maximum rate of the reaction, occurring when all enzyme active sites are saturated with substrate.
• K_M (Michaelis Constant): A measure of the affinity of the enzyme for its substrate, with a low \(K_M\) indicating high affinity.
• Enzyme Inhibition: The process by which the activity of an enzyme is decreased, either by a reversible or irreversible inhibitor.

Derivation and Assumptions

The Michaelis–Menten equation is derived under the assumption that the enzyme-substrate complex formation and breakdown reach a steady state, which implies that the rate of formation of \(ES\) equals the rate of its breakdown. This derivation also assumes that the concentration of substrate is much greater than the concentration of enzyme, and that the reaction follows simple reversible kinetics.

Limitations

While the Michaelis–Menten model is widely used, it has limitations. It does not account for the complexities of many enzyme reactions, such as those involving:

• Multiple substrates,
• Allosteric effects,
• Cooperative binding,
• Reversible enzyme inhibition.

For these more complex scenarios, other models such as the Hill equation and allosteric regulation models are used.

Applications

Michaelis–Menten kinetics is fundamental in the fields of biochemistry and pharmacology, where it is used to understand drug metabolism and the effects of enzyme inhibitors on reaction rates. It also plays a crucial role in the design of enzyme assays and in the study of metabolic pathways.

See Also

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