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Michaelis-Menten

The Michaelis-Menten model is a simple model of an enzymatic reaction developed by Leonor Michaelis and Maud Menten in 1913. The model is based on the following 2 assumptions:

  • An enzymatic reaction proceeds in 2 steps: formation of an enzyme-substrate complex, ES E S , and dissociation of the enzyme and the product.
  • After a (very) short period of time, the concentration of the ES complex reaches a steady state, where the rate of formation of ES E S equals the rate of its consumption.

The first assumption implies that the enzymatic reaction is made up of 4 different reactions: formation of ES from E and S, dissociation of ES into E and S, dissociation of ES into E and P, and formation of ES from E and P. The rate of a reaction is usually measured in the beginning of the reaction, where no significant amount of P has been formed; therefore, the rate of formation of ES from E and P can be ignored. This results in the following overall reaction (Figure 1.a) [1]. E S from E and S, dissociation of E S into E and S, dissociation of E S into E and P, and formation of E S from E and P. The rate of a reaction is usually measured at the beginning of the reaction, where no significant amount of P has been formed; therefore, the rate of formation of E S from E and P can be ignored. This results in the following overall reaction, illustrated in Figure 1.a.

The top image, Figure 1.a, portrays the overall enzymatic reaction, displaying sequential steps from left to right. Initially, enzyme-substrate formation marks the first step, which is reversible, allowing enzyme-substrate dissociation back into enzyme and substrate. The subsequent step involves the reversible dissociation of enzyme-substrate into enzyme and product, facilitating the reverse formation of enzyme-substrate from enzyme and product. Below, Figure 1.b exhibits a plot with substrate concentration on the x-axis and initial rates of the enzymatic reaction on the y-axis. A Michaelis-Menten curve is fitted, illustrating a swift rate increase followed by a plateau. The graph highlights that higher substrate concentrations lead to elevated reaction rates until reaching V max. Additionally, the graph marks half of V max and k m, the substrate concentration where the reaction attains half of V max.

Figure 1: Figure 1.a: Overall enzymatic reaction; Figure 1.b: Plot of initial rates of an enzymatic reaction plotted against the substrate concentration, and a Michaelis-Menten curve fitted to this plot. At low substrate concentrations, the curve is steep; however, at higher concentrations, the curve reaches a plateau, and the rate approaches Vmax. The interpretation of km is also clear from the figure; km is equal to the substrate concentration where the reaction rate is ½ • Vmax [1]. V max. The interpretation of k m is also clear from the figure; k m is equal to the substrate concentration where the reaction rate is half of V max.

This reaction implies that the rate of formation of products, the reaction rate, is given by V = k2 • [ES]. When almost all the enzyme is part of the enzyme-substrate complex, the reaction approaches its maximum velocity (Vmax). In the above reaction, k2 is the rate-limiting step, and Vmax can therefore be expressed as [E] • k2. The rate-limiting rate constant is also called kcat, or the turnover number, and in the above reaction, kcat = k2. This means, that Vmax = kcat • [E] [1]. V equals k 2 times concentration of E S. When almost all the enzyme is part of the enzyme-substrate complex, the reaction approaches its maximum velocity, V max. In the above reaction, k 2 is the rate-limiting step, and V max can therefore be expressed as concentration of E times k 2. The rate-limiting rate constant is also called k cat, or the turnover number, and in the above reaction, k cat equals k 2. This means, that v max equals k cat times concentration of E.

References

  1. Lehninger, Albert L.; Nelson, David L.; Cox, Michael M. (2008). Principles of Biochemistry (5th ed.). New York, NY: W.H. Freeman and Company. ISBN 978-0-7167-7108-1.

Michealis-Menten equation

Theory overview

Referred from:

Article
Enzyme kinetic assay
Article
Enzyme Kinetics