title: 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 Michaelis-Menten 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)/E₀) 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.
authors.affiliation: Department of Science, Systems and Models, Research Unit for Functional Biomaterials, Roskilde University, Roskilde, Denmark.
authors.forename: Nicolaj
authors.initials: N
authors.lastname: Cruys-Bagger
authors.forename: Jens
authors.initials: J
authors.lastname: Elmerdahl
authors.forename: Eigil
authors.initials: E
authors.lastname: Praestgaard
authors.forename: Kim
authors.initials: K
authors.lastname: Borch
authors.forename: Peter
authors.initials: P
authors.lastname: Westh
mesh_terms: D000465:Algorithms; D002475:Cellobiose / Q000378:metabolism; D044602:Cellulases / Q000378:metabolism*; D002482:Cellulose / Q000737:chemistry / Q000378:metabolism*; D043366:Cellulose 1,4-beta-Cellobiosidase / Q000378:metabolism; D005656:Fungal Proteins / Q000378:metabolism; D006868:Hydrolysis; D035901:Hypocrea / Q000201:enzymology / Q000378:metabolism; D007700:Kinetics; D008958:Models, Molecular; D020075:Phanerochaete / Q000201:enzymology / Q000378:metabolism; D012995:Solubility
chemical_list: D005656:Fungal Proteins; D002475:Cellobiose; D002482:Cellulose; D044602:Cellulases; D043366:Cellulose 1,4-beta-Cellobiosidase
keywords: cellobiohydrolase; deterministic model; enzyme kinetics; rate-limiting step; sequential-step mechanism