The Michaelis-Menten equations, as you have seen in the previous section, describes the rate of a 1-substrate enzyme-catalyzed reaction. The parameters Vmax and Km can be obtained experimentally for any given enzyme; however, they themselves provide very little information about the reaction mechanism, such as the number of discrete steps and their individual reaction rates. The reaction rate (V) is defined as the change in concentration over time. The rate can be expressed as either the rate of formation of products (P) or as the rate of consumption of reactants (the substrate, S) [1].

V = d[P]/dt = -d[S]/dt

Note that the rate of consumption of the substrate is equal to the negative change in the concentration of the substrate over time. The Michaelis-Menten equation described on the previous page is based on the reaction mechanism in Figure 1.a:

At the top is figure 1.a that illustrates 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 that shows another enzymatic reaction. This reaction is more extensive and has added another step to the process. After the formation of enzyme-substrate an additional step illustrates the formation of enzyme-product, which is then allowing the next step which is the dissociation of enzyme and product

Figure 1: Figure 1.a; Overall enzymatic reaction. Figure 1.b; Extended enzymatic reaction.

This mechanism includes 3 individual reactions with three different rate constants:

  • E + S → ES, formation of the enzyme-substrate complex, with the rate constant k1

  • ES → E + S, dissociation of the enzyme and the substrate, with the rate constant k-1

  • ES → E + P, dissociation of the enzyme and the product, with the rate constant k2

In the Michaelis-Menten model it is assumed that the third reaction is the rate-limiting step, and the associated rate constant k2 is also called the turnover number or kcat. For another reaction mechanism, the turnover number would be defined differently, for instance, in the reaction in Figure 1.b where the last step is the rate-limiting step. Here, kcat is equal to the rate constant of this step, i.e., kcat = k3. For reactions with more complicated reaction mechanisms, kcat can be a function of several rate constants. [2]

When measuring the reaction rate of a given enzymatic reaction, it is important to measure the initial reaction rate, which is the reaction rate at the beginning of the reaction.

References

  1. Atkins, Peter W.; de Paula, Julio; Friedman, Ronald (2009). Quanta, Matter, and Change: A molecular approach to physical chemistry. Oxford University Press. ISBN 978-0-19-920606-3.

  2. 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.

Michaelis-Menten equation

Initial reaction rate

Theory overview