# Structural Biochemistry/Enzyme/Uncompetitive Inhibitor
## Introduction

An uncompetitive inhibitor is an inhibitor that only binds to the enzyme-substrate complex. The formation of its binding site only forms when the enzyme and the substrate have interacted amongst themselves. The uncompetitive inhibition does not work when additional substrates are trying to be involved. The enzyme-substrate-inhibitor complex does not produce any product
E + S -> ES
ES + I -> ESI -X-> E + P
Uncompetitive inhibitor binds to enzyme-substrate complex to stop enzyme from reacting with substrate to form product, as such, it works well at higher substrate and enzyme concentrations that substrates are bonded to enzymes; the binding results in decreasing concentration of substrate binding to enzyme, Km, and Vmax, and increasing binding affinity of enzyme to substrate.
E + I -> (through S) ES + I -> E + P
where E is the enzyme, I is the inhibitor, ES is the enzyme-substrate complex, and P is the product.
This binding of the substrate modifies the structure of the enzyme making the inhibitor-binding site available. Uncompetitive inhibition decreases the maximum velocity as well as the K$_M$. K,$_M$ is the concentration of the substrate when the velocity is half of the maximum velocity based on the Michaelis-Menten Kinetics Model. Both V$_{max}$ and K$_M$ are reduced by equal amounts. V$_{max}$ will still be reduced even though the enzyme-substrate binding is enhanced because there are ESI complexes being formed. ESI complexes inhibit the formation of the product. An uncompetitive inhibitor will lower the K$_M$ and create a better enzyme-substrate binding because it only binds to ES complex. But the ES complex is constantly being depleted as the inhibitor binds, producing ESI complexes. Therefore, to maintain the equilibrium between ES and ESI complexes and following Le Chatelier's Principle, the reaction shifts toward more ES formation where it will bind more substrate to the enzymes to create more ES. Ultimately, this leads to a lower K$_M$. A reduced K$_M$ indicates a better enzyme-substrate binding because the enzyme can reach half its maximum velocity with less substrate concentration. In a sense, enzyme-substrate binding is very efficient because the enzyme and substrate have a high affinity and interact strongly.

## Kinetics of Uncompetitive Inhibitors

The first image depicts the basic theory behind uncompetitive inhibition and demonstrates what the inhibitor does to inactivate the enzyme and prevent it from forming the product. The second image shows what happens when the concentration of inhibitor is increased while enzyme concentration is constant. This shows how the V$_{max}$ of the enzyme decreases as the concentration of inhibitor goes up.

## Double-Reciprocal Plot of Uncompetitive Inhibition

The picture shows a double-reciprocal plot of V$_0$ and [S]. The x-intercept is equal to -1/K$_M$ while the y-intercept is 1/V$_{max}$. The slope of the line is K$_M$/V$_{max}$. Thus, the plot shows that K$_M$ is decreased and V$_{max}$ is also decreased.
The Michaelis-Menten equation becomes:
$\ 1/V_{o}={\frac {K_{m}}{V_{max}[S]}}+{\frac {1+[I]/K_{i}}{V_{max}}}$
As demonstrated in this equation, slope of the equation will be effectively the same as demonstrated by ${\frac {K_{m}}{V_{max}[S]}}$ but the y-axis on the double-reciprocal plot moves up by ${1+[I]/K_{i}}$ and as a consequence the shift causes the new line to be parallel to the original.

## Reference

Berg, Jeremy M., John L. Tymoczko, and Lubert Stryer. BIOCHEMISTRY. 6th ed. New York: W. H. FREEMAN AND COMPANY, 2007.