Theory of the kinetics of reactions catalyzed by enzymes attached to membranes

A theoretical treatment has been worked out for the kinetics of solid‐supported enzyme systems, with diffusive and electrostatic effects taken into account. A utilization factor, defined as the ratio of the actual reaction rate to the rate of substrate consumption in the outer solution, is defined, and equations to evaluate the utilization factor are given for five kinetic conditions: (a) Michaelis‐Menten behavior, (b) substrate inhibition, (c) product inhibition (competitive), (d) product inhibition (noncompetitive), and (e) product inhibition (anticompetitive). When the solid‐supported enzymes obey a Michaelis‐Menten relationship, an equation for the apparent Michaelis constant is given and a criterion for insignificant diffusion effects is shown. A substrate‐inhibited enzyme reaction may display multiple steady‐state behavior, and a criterion for uniqueness is presented. In the case of product‐inhibited enzyme reactions, the utilization factor is always less than that which corresponds to a Michaelis‐Menten relationship. Equations to evaluate the apparent Michaelis and inhibition constants are given.

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