The Michaelis-Menten model (*1*) is the
one of the simplest and best-known approaches to enzyme kinetics. It takes the
form of an equation relating reaction velocity to substrate concentration for a
system where a substrate *S* binds reversibly to an enzyme *E* to
form an enzyme-substrate complex *ES*, which then reacts irreversibly to
generate a product *P* and to regenerate the free enzyme *E*. This
system can be represented schematically as follows:

The Michaelis-Menten equation for this system is:

Here, *V*_{max}
represents the maximum velocity achieved by the system, at maximum (saturating)
substrate concentrations. *K _{M}* (the Michaelis constant;
sometimes represented as

This is a plot of the
Michaelis-Menten equation’s predicted reaction velocity as a function of substrate
concentration, with the significance of the kinetic parameters *V*_{max}
and *K _{M}* graphically depicted.

The best derivation of the
Michaelis-Menten equation was provided by George Briggs and J.B.S. Haldane in
1925 (*2*), and a version of it follows:

For the scheme previously
described, *k _{on}* is the bimolecular association rate constant of
enzyme-substrate binding;

Note that *k _{on}*
has units of concentration

Once these rate constants have been defined, we can write equations for the rates of change of all the chemical species in the system:

The last of these equations –
describing the rate of change of the *ES* complex – is the most important
for our purposes. In most systems, the *ES* concentration will rapidly
approach a steady-state – that is, after an initial burst phase, its
concentration will not change appreciably until a significant amount of
substrate has been consumed. This **steady-state approximation** is the first
important assumption involved in Briggs and Haldane’s derivation. This is also
the reason that well-designed experiments measure reaction velocity only in
regimes where product formation is linear with time. As long as we limit
ourselves to studying *initial* reaction velocities, we can assume that [*ES*]
is constant:

In order to determine the rate of
product formation (*d*[*P*]/*dt* = *k _{cat}*[

We now make a couple of
substitutions to arrive at the familiar form of the Michaelis-Menten equation. Since
*V*_{max} is the reaction velocity at saturating substrate
concentration, it is equal to *k _{cat}* [

Note that [*S*] here
represents the free substrate concentration, but typically is assumed to be
close to the total substrate concentration present in the system. This second
assumption is the **free ligand approximation**, and is valid as long the
total enzyme concentration is well below the *K _{M}* of the
system. If this condition is not met (for instance, with a very high-affinity
substrate), then the quadratic (or ‘Morrison’) equation must be used instead.

Comparing *K _{M}* [=
(

- Michaelis, L.,and Menten, M. (1913) Die kinetik der invertinwirkung,
*Biochemistry Zeitung**49*, 333-369. - Briggs, G. E., and Haldane, J. B. (1925) A Note on the Kinetics of Enzyme Action,
*Biochem J**19*, 338-339. - Van Slyke, D. D., and Cullen, G. E. (1914) The Mode of Action of Urease and of Enzymes in General,
*J Biol Chem**19*, 141-180.