The Michaelis-Menton Equation has a very similar form to the Hill Equation but the key difference is that it deals with enzyme rates not ligand/receptor or drug/target interactions per se. Basically, it describes how fast an enzyme (E) makes its product (P) as a function of the total concentration of substrate ([*S*]* _{t}*). This rate of production formation (d[P]/dt) is proportional to the

*k*and the amount of complex ([ES]) which is exact what the Michaelis-Menton equation models. The Michaelis-constant (

_{cat}*K*= (

_{m}*k*+

_{off}*k*) /

_{cat}*k*) describes how tightly the substrate binds the enzyme and the

_{on}*k*is a rate-constant that describes how quickly the enzyme can make the product. Here,

_{cat}__denote concentrations and a t subscript indicates “total concentrations.”__

*brackets*

There are two parts to the Michaelis-Menton Equation. First, **the maximum velocity term ([ V]_{max})** which is equal to

*k*[

_{cat}*E*]

_{t}. This term represents the maximum rate at which the enzyme can produce product (basically when the enzyme is saturated with substrate). Second, we have a

**fractional term**which describes the shape of the dose-velocity curve in response to increasing concentrations of substrate. If you data is normalized to 100% then this fractional term is usually sufficient to describe your data.

On limitation of the Michaelis-Menton is that is only works when the receptor concentration is much lower than the Michaelis-constant (i.e. [*R*]* _{t}* <<

*K*). While this is often true experimentally (when very low concentrations of enzymes are ultilized), it is typically not true

_{m}*in vivo*and a more general, quadratic-equation must be used as is described in a previous post: Understanding Ligand-Receptor Dose-Response Curves.

**REFERENCES: **

- Michaelis, V.; Menten, M. Die Kinetik der Invertinwirkung (The Kinetics of Invertase Action).
*Biochemische Zeitschrift***1913**, 49, 33. - Johnson, K.; Goody, R. The Original Michaelis Constant: Translation of the 1913 Michaelis-Menten Paper.
*Biochemistry***2011**, 50, 8265-8269. - Lineweaver, H.; Burke, D. The determination of enzyme dissociation constants.
*J. Am. Chem. Soc.***1934**,56, 658-666. - Straus, O.H.; Goldstein, A.; Plachte, W. Zone Behavior of Enzymes.
*J. Gen. Physiol.***1943**, 26, 559-585. - Cha, S. Kinetic Behavior at High Enzyme Concentrations.
*J. Biol. Chem.***1970**, 245, 4814-4818. - Lauffenburger, D.A. Receptors: Models for Binding, Trafficking and Signalling, Oxford University Press
**1993**. - Segel, I.H. Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems, Wiley-Interscience,
**1993**

This work by Eugene Douglass and Chad Miller is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.