An Inverse Michaelis–Menten Approach for Interfacial Enzyme Kinetics

Abstract

Interfacial enzyme reactions are ubiquitous both in vivo and in technical applications, but analysis of their kinetics remains controversial. In particular, it is unclear whether conventional Michaelis–Menten theory, which requires a large excess of substrate, can be applied. Here, an extensive experimental study of the enzymatic hydrolysis of insoluble cellulose indeed showed that the conventional approach had a limited applicability. Instead we argue that, unlike bulk reactions, interfacial enzyme catalysis may reach a steady-state condition in the opposite experimental limit, where the concentration of enzyme far exceeded the molar concentration of accessible surface sites. Under this condition, an “inverse Michaelis–Menten equation”, where the roles of enzyme and substrate had been swapped, proved to be readily applicable. We suggest that this inverted approach provides a general tool for kinetic analyses of interfacial enzyme reactions and that its analogy to established theory provides a bridge to the accumulated understanding of steady-state enzyme kinetics. Finally, we show that the ratio of parameters from conventional and inverted Michaelis–Menten analysis reveals the density of enzyme attack sites on the substrate surface as probed by one specific enzyme. This density, which is an analogue to a molar substrate concentration for interfacial reactions, was shown to vary strongly even among related enzymes. This difference reflects how the enzyme discriminates between local differences in surface structure on the substrate.

Rate‐limiting step and substrate accessibility of cellobiohydrolase Cel6A from Trichoderma reesei

“…This method relies on the idea that the number of nonreducing ends from which the enzyme can initiate hydrolysis (attack sites), on the cellulose surface remains nearly constant in the initial part of the reaction, because new ends become exposed as the enzyme removes cellulose strands from the surface of the particle. Some experimental support of this assumption has been presented elsewhere , and if the density of attack site indeed remains nearly constant long enough to perform rate measurements, one can use another type of steady‐state analysis, which we call the inverse MM framework . In practice, this approach requires initial rate measurements at a fixed, low substrate load (low S 0 ) and at gradually increasing enzyme concentrations ( E 0 ).…”

The Role of Evolving Interfacial Substrate Properties on Heterogeneous Cellulose Hydrolysis Kinetics

“…31 The kinetics of cellulose hydrolysis are also highly dependent on solids loadings and enzyme-to-substrate ratios, and the apparent rate limiting factors can vary greatly depending on the chosen reaction conditions. 11,39,40 The effect of enzyme action on substrate properties limiting hydrolysis is largely uncharacterized. Often, attempts to understand the role of cellulose heterogeneity in rate decrease involves descriptions of more-and less-accessible fractions of substrate 41,42 , but understanding (1) adsorbs and complexes with an accessible cellulose chain (a productive binding site) resulting in hydrolysis.…”

“…Enzyme was constructed in PyMol 15 from (PDB 4C4C) 16 , (PDB 1CBH) 17 , and using the linker sequence from Badino et al 2017 18 . of the evolution of the accessible fraction-i.e., the productive binding capacity-throughout hydrolysis is limited. As the heterogeneous reaction takes place at the solid-liquid interface, it is reasonable to assume a surface ablation mechanism by which removal of productive binding sites from an accessible fraction exposes new sites from an inaccessible central core 13,17,32,39,40,[43][44][45][46][47][48][49][50] , and the initial cellulose surface area and concentration of productive binding sites has been shown to limit hydrolysis rates 8,11 , in support of this mechanism. However, mechanically increasing cellulose chain reducing end concentrations did not improve cellulose accessibility to TrCel7A (a reducing-end specific cellobiohydrolase) 48 , and the availability of reactive sites is not proportional to surface area or total reducing end concentrations 31,51 , indicating that the location of a cellulose chain on the surface of a cellulose particle alone is not a sufficient criterion to indicate accessibility.…”

“…It is, however, possible to use the enzyme as a reporter to estimate the concentration of productive binding sites. Using the ratio of specific maximum rates obtained at enzyme and substrate saturation, the concentration of productive binding sites has been estimated on Avicel 46 . Here, we use the rate of product released by Cel7A as a reporter of the concentration of binding sites, which at saturation directly correlates to the number of available productive Cel7A binding sites on cellulose, shown schematically in Figure 2.…”

pH profiles of cellulases depend on the substrate and architecture of the binding region

“…This can be expressed as in Scheme 1. We note that this approach was developed for soluble enzyme–substrate systems, but as argued elsewhere (Andersen, Kari, Borch, & Westh, ; Kari, Andersen, Borch, & Westh, ), an analogous treatment may be permissible for interfacial reactions provided that the usual requirement of substrate excess is fulfilled.

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