web.pdx.edu/~rueterj/bi445/notes/regulation2.htm

Simple Regulation of Enzyme Activity

The simplest form of regulation is the inhibition of a single process in response to the product. This can be described in several ways.

Consider a pathway from A --> B --> C -->D that is catalyzed by three enzymes: ABase, BCase and CDase.

Simple on-off model:

IF the product, D, exceeds a set amount in the cell, THEN the rate of ABase will be stopped completely.

Example: Feedback inhibition of citrate on PFK would be of this general form. However, the mechanism would not be an on/off switch but rather the inhibition of the process above a concentration of citrate.

Graded model:

The rate of ABase is inhibited by [D].

This inhibition could be represented by Michaelis-Menten kinetics but including the inhibitor [D] as either a competitive or non-competitive inhibitor; affecting Ks or Vmax respectively.

The equation for competitive inhibition increases the apparent Km.

v = Vmax*S/(S + Km*([I]+ Ki)/[I]))

As the concentration of [I] is increased, the apparent Km will increase.

At [I] = 0 the Km is unaffected.

When [I] = Ki, there is a 2 fold increase in the apparent Km.

 

Example for competitive feedback inhibition: There is one, I just forget what it is right now -- succinate & malonate in Krebs cycle?

The equation for non-competitive inhibition decreases the apparent Vmax.

v =( Vmax/([I]+ Ki)/[I])) * S/(S + Km)

Example for non-competitive feedback inhibition: need one

 

Another useful model for inhibition is to use an allosteric enzyme.

v = Vmax * S^n/(S^n + K^n)

By shifting K in this model, the response can be set to operate at higher concentrations.

Example for allosteric feedback inhibition: This is the classical case of phospho-fructo-kinase with respect to ATP. As ATP increases in the cell above a particular level, the curve for PFK activity shifts to the right (lower velocity at the same substrate of F6P). The advantage of this type of inhibition is that it can keep the ATP in a usable lower range, and then have the inhibition "kick in" at higher ATP.