# Enzyme Inhibition

A substrate cannot always be turning into product. The activity of the enzyme has to be regulated by the cell.  To combat this, the cell contains natural molecules that act as inhibitors to these enzymes. Many drugs are simply inhibitors of specific enzymes.

There are three classes of Inhibitors

The first is Competitive Inhibitors, which bind to the enzyme to prevent binding to the substrate. The formation and dissociation of both EI and ES have their own rates.

Prediction: when we add a given amount of substrate, we will have formation of both EI and ES => [ES] will be lower in the presence of its inhibitor => the E will have a lower affinity for its S => Km will increase.

Secondly, as [S] increases, [EI] will increase too, thus creating a competition between the binding of the S and the binding of the inhibitor. Because [I] is constant then as we increase [S], the S will outcompete the inhibitor. Thus the maximum velocity will be unchanged in the presence of an inhibitor. Vmax will not change.

Recall that Km = [E][S]/[ES] = (k-1 + k2)/ k1 for steady state conditions. The steady state also applies to an enzyme and its inhibitor. The rate of formation of the rate of the formation of the enzyme inhibitor complex is equal to the rate of the degradation of this complex. We define the concentration of the inhibitor, Ki = [E][I]/[EI].

When Ki is high, [EI] is low and thus the enzyme has a low affinity for the inhibitor.
When Ki is low, [EI] is high and thus the enzyme has a high affinity for the inhibitor.

Rearranging terms in a similar manner as before using a new term, α = 1 + [I]/ Ki we can get V0 with a competitive inhibitor as:

V0 = Vmax[S]/(α*Km+[S])

The term, α*Km, is called the apparent Km.

From this, we form the Lineweaver-Burke with a competitive inhibitor.

1/V0 =  (αKm/Vmax)(1/[S] ) + 1/Vmax

Comparing slopes with the non-inhibitor version, we see that here the slope is necessarily larger making the line steeper. Similarly, the x-intercept will be closer to the y-axis and thus Km will be larger.

An example is Aspirin (acetylsalicylate), which inhibits the enzyme COX-2. COX-2 catalyzes the first step in the synthesis of prostaglandins, which produces pain.