A steady‐state theory for processive cellulases

Abstract

Processive enzymes perform sequential steps of catalysis without dissociating from their polymeric substrate. This mechanism is considered essential for efficient enzymatic hydrolysis of insoluble cellulose (particularly crystalline cellulose), but a theoretical framework for processive kinetics remains to be fully developed. In this paper, we suggest a deterministic kinetic model that relies on a processive set of enzyme reactions and a quasi steady-state assumption. It is shown that this approach is practicable in the sense that it leads to mathematically simple expressions for the steady-state rate, and only requires data from standard assay techniques as experimental input. Specifically, it is shown that the processive reaction rate at steady state may be expressed by a hyperbolic function related to the conventional MichaelisMenten equation. The main difference is a 'kinetic processivity coefficient', which represents the probability of the enzyme dissociating from the substrate strand before completing n sequential catalytic steps, where n is the mean processivity number measured experimentally. Typical processive cellulases have high substrate affinity, and therefore this probability is low. This has significant kinetic implications, for example the maximal specific rate (V max /E 0 ) for processive cellulases is much lower than the catalytic rate constant (k cat ). We discuss how relationships based on this theory may be used in both comparative and mechanistic analyses of cellulases.

Kinetics of Cellobiohydrolase (Cel7A) Variants with Lowered Substrate Affinity

“…that the concentration of attack sites for enzyme on the substrate surface is much larger than the enzyme concentration). This has previously been shown to be a reasonable assumption for conditions similar to those used here (22,23). We note that the main difference between the parameters for processive enzyme activity given in Equations 2 and 3 and the analogous parameters in the conventional Michaelis-Menten equation is the constant, ␤.…”

“…We have previously suggested (23,30) that experimental data for processive enzymes may be analyzed by a reaction scheme (Scheme 1), according to which the free enzyme, E, combines with a cellulose strand, C m , to form an activated complex, EC m . The enzyme subsequently moves along the strand, which is sequentially shortened by one cellobiose, moiety C, for each step (so the strand is converted to C m-1 , C m-2 , etc.).…”

“…At quasi-steady state, the rate of cellobiose production according to the processive reaction in Scheme 1, p V SS , attains the usual hyperbolic form (23),…”

“…n and may be interpreted as the probability that the enzyme will dissociate from the cellulose strand before completing the average number (n) of processive steps (23).…”

Specific Amyloid β Clearance by a Catalytic Antibody Construct

“…Small IgV concentrations were sufficient to hydrolyze particulate A␤, but diffusional restrictions decelerate enzymatic digestion of particulate substrates compared with soluble substrates (50,51). We acknowledge the potential of varying clearance rates for A␤ coaggregated with other proteins and A␤ aggregates containing post-translational chemical modifications.…”