This chapter documents how kineticists have successfully treated important aspects of one-substrate enzyme-catalyzed reactions by applying rapid-equilibrium and steady-state approximations to obtain simple rate laws. The same rate behavior is observed with many hydrolases, simply because the concentration of the second substrate (water) cannot be varied in the course of most experiments. While rate parameters like Km, Vmax, and Vmax/Km provide valuable insights into the operation of one-substrate enzymes, initial rate analysis of enzymes provides an incomplete picture of catalysis, especially with regard to the nature of the rate-determining step(s) and the number of elementary reactions. We shall see in Chapter 9 that kinetic isotope effects provide a useful probe of the rate-determining step(s) and in Chapter 10 that fast reaction techniques are the best way to establish the number of elementary reactions and their rates of interconversion.
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