Enzymatic Reaction of Silent Substrates:  Kinetic Theory and Application to the Serine Protease Chymotrypsin

Investigating the selectivity that an enzyme expresses toward its substrates can be technically challenging if reaction of these substrates is not accompanied by a conveniently monitored change in some physicochemical property. In this paper, we describe a simple method for determining steady-state kinetic parameters for enzymatic turnover of such “silent” substrates. According to this method, silent substrate S is allowed to compete for enzymic reaction with signal-generating substrate S*, whose conversion to product can be conveniently monitored. Full reaction progress curves are collected under conditions of [S*]o ≪ K m* and [S]o ≥ 3K m. Progress curves collected under these conditions are characterized by an initial lag phase of duration τ that is followed by the pseudo-first-order reaction of S*. Steady-state kinetic parameters for the silent substrate can be obtained by one of two methods. One method combines least-squares fitting with numerical integration of appropriate rate equations to analyze the progress curves, while the other method relies on direct graphical analysis in which K m is the value of [S]o that reduces the control velocity by a factor of 2 and V max is shown to simply equal the ratio [S]o/τ. We use these methods to analyze the α-chymotrypsin-catalyzed hydrolysis of silent substrate Suc-Ala-Phe-AlaNH2 with signal generator Suc-Ala-Phe-pNA. From the curve-fitting method, k c = 0.9 ± 0.2 s-1 and K m = 0.4 ± 0.1 mM, while by direct graphical analysis, k c = 1.1 ± 0.1 s-1 and K m = 0.51 ± 0.03 mM. As validation of this new method, we show agreement of these values with those determined independently by HPLC analysis of the hydrolysis of Suc-Ala-Phe-AlaNH2 by α-CT, where k c = 1.1 ± 0.1 s-1 and K m = 0.5 ± 0.1 mM.