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, 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 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].

At the top is figure 1.a which shows the overall enzymatic reaction. The enzymatic reaction is made up of different steps illustrated in the reaction from left to right, with the formation of enzyme-substrate as the first step in the overall reaction. This step goes both ways, with the reversed reaction being the dissociation of the enzyme-substrate into enzyme and substrate again. The next step is the dissociation of the enzyme-substrate into enzyme and product, which also goes both ways, allowing the formation of enzyme-substrate again from enzyme and product. Beneath is figure 1.b which shows a plot of initial rates of an enzymatic reaction plotted against the substrate concentration, which has substrate concentration on the x-axis and reaction rate on the y-axis. A Michaelis-Menten curve is fitted to the plot as a curve that increases fast and then plateaus shortly after. The data is marked with bullets and a line between them is drawn in blue. The graph shows that as the substrate concentration increases, so does the reaction rate. The reaction rate increase is rapid at the beginning of the reaction, but as the substrate concentration increases further, the reaction rate slows down and the curve starts plateauing. At this point, the reaction approaches its maximum velocity, which is marked on the graph as V max. ½ • V max is also marked on the graph, where the reaction has met 50% of its maximum velocity. A third variable on the graph is the k m which is equal to the substrate concentration where the reaction rate is ½ • 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]

This reaction implies that the rate of formation of products, i.e., 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]

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