Enzymes are essential molecules -- they catalyze the reactions that make life happen. Nature features a remarkable variety of enzymes that catalyze a wide variety of reactions. In comparing these enzymes, it can sometimes be helpful to consider them in terms of their catalytic efficiency, also called the specificity constant, which measures how efficiently the enzyme converts the substrate (the molecule it acts on) into the product. For enzymes that follow what biochemists call Michaelis-Menten kinetics, this constant can easily be calculated from experimental data.
Write down the Km and the kcat. These constants are determined experimentally, so you should already have it before you begin trying to calculate the specificity constant.
Recall that the Km represents (k-1 + k2) / k1, where k1 is the rate constant for the formation of an enzyme-substrate complex, k-1 is the rate constant for the breakup of that complex, and k2 is the rate constant for formation of product from the enzyme-substrate complex. Another (and perhaps more illuminating) way to define Km is as the concentration of substrate when the reaction is running at half the maximum velocity. If an enzyme has a large Km, it takes a lot of substrate to reach the enzyme's maximum rate, while a small Km means only a little substrate is needed to saturate the available enzyme.
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Recall that kcat is the rate constant for the rate-limiting step in the enzyme-catalyzed reaction. The rate-limiting step is the slowest step or the bottleneck that determines how fast overall the reaction can run.
Divide kcat by Km to get the specificity constant. For example, if kcat is 600 seconds^-1 and Km is 10 micromolar, then the catalytic efficiency is 60 microM^-1 s^-1.
Note that the rate of diffusion sets an upper boundary on the maximum catalytic efficiency, usually on the order of 10^8 to 10^9 M^-1 s^-1. Biochemists will sometimes say that an enzyme whose catalytic efficiency approaches this limit has achieved "catalytic perfection".
Catalytic efficiency isn't difficult to calculate from experimental data, but it's important to make sure you understand what it means (rather than just plugging numbers).