# 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

**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 _{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 ½ • V_{max} [1].

This reaction implies that the rate of formation of products, the reaction rate, is given by *V = k _{2} • [ES]*. When almost all the enzyme is part of the enzyme-substrate complex, the reaction approaches its maximum velocity (

*V*). In the above reaction, k

_{max}_{2}is the rate-limiting step, and V

_{max}can therefore be expressed as

*[E] • k*. The rate-limiting rate constant is also called k

_{2}_{cat}, or the turnover number, and in the above reaction, k

_{cat}= k

_{2}. This means, that

*V*[1].

_{max}= k_{cat}• [E]*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

- 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.