# Structural Biochemistry/Enzyme/Michaelis constant
## Definition

The Michaelis Constant, K$_M$ is very important in determining enzyme-substrate interaction. This value of enzyme range widely and often dependent on environmental conditions such as pH, temperature, and ionic strength. The K$_M$ is able to detect two factors: One is the concentration of substrate when the reaction velocity is half that of the maximal velocity; thus, the Michaelis constant measures the concentration of substrate required for a significant catalysis to take place. Secondly, it is, in some cases, able to detect the strength of the enzyme-substrate complex (ES). When, and only when k$_2$ << k$_{-1}$, High K$_M$ indicates weak binding and low K$_M$ indicates strong binding. Under this special circumstance, K$_M$ is equal to the dissociation constant. Only then can the K$_M$ be used as a measurement of the strength of the ES complex.
There are cases where changes in the Michaelis constant are observed as is the case with inhibitors such as competitive, uncompetitive and noncompetitive inhibitors. In competitive inhibitors, the Michaelis constant increases because more active sites must be filled (either with competitive inhibitor or with substrate) to elicit the same Vmax. In uncompetitive inhibitors, the Michaelis constant decreases because the inhibitor only binds to the substrate-enzyme complex, creating an ESI complex. This drives the equilibrium reaction forward from E + S --> ES, where more inhibitor can bind. The Michaelis constant decreases more with the addition of inhibitors. In noncompetitive inhibition, the Michaelis constant remains the same.

## Determining K$_M$

The equation for the Michaelis Constant is K$_M$= (k$_{-1}$ + k$_2$)/k sometimes it can be seen as [ES] = [E][S]/K$_M$
From a graph one can determine the value of K$_M$. A graph with the reaction rate (V) on the Y axis plotted against the substrate concentration on the X axis allows one to find the value of K$_M$. K$_M$ is found at the substrate concentration when the reaction rate is half of its maximum value (V$_{max}$/2). Note that if K2 << k-1, then Km is equal to Kes, the rate constant for the disassociation of the enzyme-substrate complex.
File:Km.GIF
The values of K$_M$ and V$_{max}$ also give the fraction of active site filled (f$_{ES}$).

## Biological Examples

For many enzyme experimental evidence suggest that K$_M$ provide approximately substrate concentration in vivo. Physiological consequences of K$_M$ is exemplified in individuals sensitive to ethanol.
Normally in the liver, alcohol dehydrogenase converts ethanol into acetaldehyde. Acetaladehyde dehydrogenase, for example, has a low K$_M$ mitochondrial form and a high K$_M$ cytoplasmic form. In individuals sensitive to ethanol, the mitochondrial enzyme is less active due to substitution of a single amino acid and acetaldehyde is only processed by the cytoplasmic enzyme. Since cytoplasmic enzyme has high K$_M$, it can only achieve high catalysis at very high acetaldehyde concentrations. Consequently, less acetaldehyde is converted, and the excess escapes into the blood and causes symptoms such as facial flushing and rapid heart rate in sensitive persons.