Kinetics is the science of movement within reactions, or of the operation of a catalyst. Here we are going to study the operations of enzymes and of their inhibitors.

We start out with a particular enzymatic reaction. It might be the fizzing of the breakdown of hydrogen peroxide by the enzyme catalase, or it might be the conversion of ONPG to a yellow color by lactase, or it might be any one of thousands of other examples. As we record our data, we note that as time goes by more product is made (more oxygen accumulates in the catalase reaction, or the spectrophotometer indicates that more yellow is being formed in the lactase reaction, etc.). At first the product builds up at a rather steady rate, but then the increase begins to taper off and finally plateau as there is no more substrate to be converted.

In kinetic studies we are interested in "initial velocities" of our reactions - those times when product is being made at a constant rate - before any tapering off. (Actually, this is a tricky way of looking at the reaction when we know what the substrate concentration really is.) So we start our reaction and immediately begin taking notes on how much product is produced at timed intervals. This is then graphed, as shown on the right. We have thus worked hard collecting data just to get one answer: how fast was that reaction at that particular substrate concentration and that particular enzyme concentration. And that answer, V_o, is obtained by taking a ruler and laying it down on our graph and drawing in a straight line that is our best visual guess as to the initial slope of the reaction curve.

BUT you want to run this reaction several times - but at different initial substrate concentrations. Each time you run the reaction, you make a new graph like the one above. Yes, a lot of graph paper gets used! And each on produces only one bit of data: the initial velocity (V_o)of the reaction at that particular substrate concentration ([S]).

So now we have a lot of V_o's with their companion [S]'s. What shall we do with them? Years ago, two scientists, Michaelis and Menton, decided to graph that sort of data. What they plotted looked like the figure at the right.

It thus became obvious that the reaction had a maximum velocity, V_max, that was gloriously an immutable constant for that particular enzyme. Scientists like constants! Furthermore, after using a lot of sophisticated algebra, which we shall not get into here - but it exhaustively outlined in almost every biochemistry text, they determined another constant, K_M, which is called the Michaelis constant. It is merely the division of V_max by 2.

But this K_M had special importance because it was the relationship of the rates of the forward reactions in the overall reaction equation and the backward reaction. And this has special meaning because it reflects the stability of the enzyme-substrate complex.

However we are interested in the effects of inhibitors on the enzymatic reaction. In particular, we want to know if the inhibitor competes with the substrate, or does it act elsewhere on the enzyme to cause a misfolding or other deleterious configuration to occur that diminishes the efficiency of the enzyme's active site, where the substrate is converted to product. Michaelis and Menton (and others) then ran an assortment of inhibited reactions and found the following information, where "normal" is the uninhibited reaction, "CI" is one in which a "competitive inhibitor" is working, and "other" is when other sorts of inhibitors are present - such as allosteric inhibitors.

HOWEVER, while Michaelis and Menton were picking up laurels, another group of scientists was not happy with the curves in the graphs they were seeing. Straight lines are among scientists' dreams. Lineweaver and Burk juggled the Michaelis math and found that if they made a double inversion of the two axes, they came up with straight lines. On the right is shown one such reaction curve. Taking a close look at this "Lineweaver-Burk Plot" we see that at the origin, both the substrate and velocity are ideally infinite, and get smaller as one moves away from the origin.

Very importantly it should be noticed that when a reaction's line crosses the vertical axis, it crosses at 1/V_max. See the beauty of straight lines? All you have to do is get a few points on the graph and use a straightedge to find 1/V_max. No guessing at where Michaelis' rounded curve asymptotes. Other mathematical manipulations show that the intercept of the line with the horizontal axis is at the negative reciprocal of K_M. So Lineweaver and Burk showed a better way to calculate those two values.

Returning to the effects of inhibitors, they have clear distinctions on this kind of plot. Competitive inhibitors always intersect with the 1/V_max point on the graph. The other types of inhibitors either intersect elsewhere or not at all - merely forming parallel lines.

SUMMARY. By merely running a reaction several times at different substrate and inhibitor concentrations, one can ascertain both the maximum velocity of a reaction, and the affinity that the enzyme has for the substrate. These values are important when concocting new chemotherapeutics.