A generic rate law for surface‐active enzymes

Abstract

a b s t r a c tMany biochemical reactions are confined to interfaces, such as membranes or cell walls. Despite their importance, no canonical rate laws describing the kinetics of surface-active enzymes exist. Combining the approach chosen by Michaelis and Menten 100 years ago with concepts from surface chemical physics, we here present an approach to derive generic rate laws of enzymatic processes at surfaces. We illustrate this by a simple reversible conversion on a surface to stress key differences to the classical case in solution. The available area function, a concept from surface physics which enters the rate law, covers different models of adsorption and presents a unifying perspective on saturation effects and competition between enzymes. A remarkable implication is the direct dependence of the rate of a given enzyme on all other enzymatic species able to bind at the surface. The generic approach highlights general principles of the kinetics of surface-active enzymes and allows to build consistent mathematical models of more complex pathways involving reactions at interfaces.

Fractal Kinetic Behavior of Plasmin on the Surface of Fibrin Meshwork

“…Importantly, our numeric treatment of the model progress curves takes into account the variability in the plasmin concentration in the reactive layer through a randomizing factor based on independent measurements of plasmin activity retained at the fluid-fibrin interface, but even with this larger standard deviation (SD) allowance arising from the initial concentration (Table 1). Such a dependence of the apparent Michaelis constant on enzyme concentration in heterogeneous phase fibrinolysis is not unexpected in view of the recently developed generic rate law for surface-active enzymes (27). As elegantly demonstrated in this theoretical study, if a fluid-phase enzyme acts on a surface-bound substrate, the value of the Michaelis constant appears larger at increasing enzyme concentration, because the available area for absorption decreases monotonously when more enzyme is applied.…”

“…At stage I (initial) the more uniformly dispersed enzyme and the larger available area allow for higher rate of association to fibrin reflected in lower initial values of In conclusion, our study has substantiated in mechanistic terms a fractal kinetic model that describes satisfactorily the action of plasmin on fibrin surface. In this work earlier theoretical predictions for the behavior of surface-acting enzymes (18,27) and qualitative evidence for spatially constrained migration of plasmin in the network of fibrin fibers (28) this model could contribute to the rational design of better thrombolytic agents to combat cardioand cerebrovascular disease, the major morbidity and mortality cause in the world.…”

Modelling Reactions Catalysed by Carbohydrate-Active Enzymes

“…Building on such results, Kartal and Ebenhöh [24] have systematically derived a generic rate law for surface-active enzymes, which can be applied to enzymatic processes at the surface-bulk interface and can easily be generalised for specific enzymatic mechanisms. The authors demonstrated how different adsorption isotherms can be used to derive the enzyme kinetics and, due to the generality of their approach, could explain how different assumptions and different adsorption models influence the kinetic parameters, in particular the apparent Michaelis and maximal rate constants.…”

“…The various approaches to theoretically describe and simulate processes on substrate surfaces are very promising and it appears that the difficulties to include surface-active enzymes into pathways models can soon be overcome, in particular thanks to early pioneering work [46] and the development of more and more general rate laws for surface-active enzymes [48,49,24]. On the theoretical and modelling side, the key issues here will be to derive simplified but sufficiently accu-rate descriptions of the insoluble reactants and their surfaces, and to make plausible assumptions over the different adsorption models of the involved proteins, to simulate adequate available area functions, which are the key to correctly represent competition and crowding effects on the substrate surface.…”

Physical constrains and functional plasticity of cellulases: Linear scaling relationships for a heterogeneous enzyme reaction

“…Nevertheless, the kinetics of interfacial reactions is typically disregarded or fleetingly treated in textbooks [9][10][11][12][13] , and this state of affairs is quite different from conventional (non-biochemical) catalysis, where homogeneous and heterogeneous reactions are treated in parallel. Although insightful models and concepts of interfacial enzyme kinetics have been suggested [14][15][16] , no generally applied kinetic approach or rate equation currently exist. Neither is it clear whether progress in this field should be based on adaptation of conventional enzyme kinetic theory, or modifications of concepts and principles taken from inorganic heterogeneous catalysis.…”