A steady-state approach for inhibition of heterogeneous enzyme reactions

The kinetic theory of enzymes that modify insoluble substrates is still underdeveloped, despite the prevalence of this type of reaction both in vivo and industrial applications. Here, we present a steady-state kinetic approach to investigate inhibition occurring at the solid-liquid interface. We propose to conduct experiments under enzyme excess (E0 ≫ S0), i.e. the opposite limit compared with the conventional Michaelis-Menten framework. This inverse condition is practical for insoluble substrates and elucidates how the inhibitor reduces enzyme activity through binding to the substrate. We claim that this type of inhibition is common for interfacial enzyme reactions because substrate accessibility is low, and we show that it can be analyzed by experiments and rate equations that are analogous to the conventional approach, except that the roles of enzyme and substrate have been swapped. To illustrate the approach, we investigated the major cellulases from Trichoderma reesei (Cel6A and Cel7A) acting on insoluble cellulose. As model inhibitors, we used catalytically inactive variants of Cel6A and Cel7A. We made so-called inverse Michaelis-Menten curves at different concentrations of inhibitors and found that a new rate equation accounted well for the data. In most cases, we found a mixed type of surface-site inhibition mechanism, and this probably reflected that the inhibitor both competed with the enzyme for the productive binding-sites (competitive inhibition) and hampered the processive movement on the surface (uncompetitive inhibition). These results give new insights into the complex interplay of Cel7A and Cel6A on cellulose and the approach may be applicable to other heterogeneous enzyme reactions.