MichaelisMentenmodellen

MichaelisMentenmodellen is a foundational mathematical framework in biochemistry for describing the rate of enzyme-catalyzed reactions with a single substrate under certain conditions. The rate equation expresses the reaction velocity v as a function of substrate concentration [S]: v = (Vmax [S])/(Km + [S]). Here Vmax is the maximal rate at saturating substrate and Km is the substrate concentration at which v is half of Vmax.

Vmax equals kcat [E]tot, where kcat is the turnover number (the number of substrate molecules converted per enzyme per unit time) and [E]tot is the total enzyme concentration. Km reflects the enzyme’s affinity for the substrate: a smaller Km indicates higher affinity. The model is derived under the steady-state approximation for the enzyme–substrate complex ES, assuming rapid formation and breakdown of ES relative to product formation, a constant total enzyme, and negligible reverse reaction under initial-velocity conditions. It is appropriate for reactions with a single substrate and where allosteric effects and multiple substrates are not significant.

Limitations include inapplicability to enzymes with multiple substrates, cooperative or allosteric effects, significant product inhibition, or when the reverse reaction cannot be neglected. Deviations occur at very high substrate concentrations or with tight-binding substrates.

Applications of the model include estimating kinetic parameters (Km, Vmax) and catalytic efficiency (kcat/Km), comparing enzymes or substrates, and interpreting enzyme inhibition. Data are commonly analyzed by fitting to the Michaelis-Menten curve or by linearized forms such as Lineweaver–Burk or Eadie–Hofstee, though nonlinear fitting is generally preferred today.

Historically, the model is attributed to Leonor Michaelis and Maud Menten, introduced in the early 20th century to describe basic features of enzyme kinetics.