3 Enzyme Kinetics

3.1 Introduction

Assaying Enzymes

To study an enzyme, an assay is necessary. The assay is a measurement of a chemical reaction, which might involve measuring the formation of the product. For example, b-galactosidase catalyzes the following reaction:

	             b-galactosidase
	lactose  ----------------------->  glucose  +  galactose

For this reaction, measuring the formation of glucose would constitute an assay. Because this is technically difficult, an easier way to follow the reaction is to use a substrate that gives a colored reaction product. b-galactosidase can catalyze many reactions of the following general type:

		      b-gal
	y-galactose  ----------->  y  + galactose

in the 'normal' reaction, y-galactose = lactose = glucose-galactose (y=glucose)
Two alternative substrates for b-galactosidase are:

ONPG = ONP-galactose (ONP = o-nitro-phenol)
X-gal = X-galactose (X = 4-chloro-3- bromo indole)

Both ONPG and X-gal are colorless, but when hydrolysed by b-galactosidase, they produce colored products:

	     b-gal
   ONPG --------------> galactose      +      ONP 
(colorless)	        (colorless)	     (yellow)

	      b-gal
   X-gal ---------------> galactose      +      4-Cl-3-Br-indigo 
(colorless)	         (colorless)             (deep blue)

These colored reaction products are much easier to detect and can be used to assay (measure) enzyme activity more easily that the 'normal' reaction catalyzed by b-galactosidase.

Enzyme catalysis

Here is an example of an enzyme catalyzed reaction:

The enzyme converts S to P (substrate to product). Initially, [P] is small, so the majority reaction is S-->P. Later, as [P] grows, the back reaction rate increases, until equilibrium is reached (enzymes catalyze BOTH forward AND reverse reactions).
To measure the kinetic properties of a given enzyme, you must perform many experiments like the one above. Keep the enzyme concentration constant and measure the initial rate of product formation (before the reaction is anywhere near equilibrium) at several different initial substrate concentrations. Then plot the initial velocity of the reaction: Vo, as a function of [S].

Some qualitative statements about this graph:

Velocity is dependent on [S]
The more enzyme added, the faster the reaction goes

Why isn't the graph linear? As [S] gets large, the enzyme becomes limiting - all enzyme molecules are 'busy' operating on the substrate and the rate of reaction depends on the amount of enzyme, not the amount of substrate.(And since the amount of enzyme used in this series of experiments is fixed, the rate asymptotically approaches a maximum.)

NOTE: the two preceding graphs look very similar, but mean quite different things! It is important to understand the difference between an individual reaction: [P] vs. t (from which you get Vo) and a kinetic graph of many such reactions: Vo vs. [S].This kinetic behavior can be modeled mathematically. That is what we discuss next, after a short review of chemical kinetics.

shanec@mit.edu