Theory of the kinetics of reactions catalyzed by enzymes attached to the interior surfaces of tubes

A theoretical treatment is given of the kinetics of reactions catalyzed by enzymes attached to the inner surface of a tube, through which the substrate solution passes. A utilization factor, the ratio of the actual reaction rate to that in the absence of diffusional effects, is defined. A numerical procedure is proposed and numerical and approximate solutions for the utilization factor are given for five kinetic conditions: (a) Michaelis‐Menten behavior, (b) substrate inhibition, (c) product inhibition (competitive), (d) product, inhibition (non‐competitive), and (e) product inhibition (anticompetitive). When the enzyme chemically attached to a tube obeys a Michaelis‐Menten relationship, criteria for insignificant and significant diffusional effects are proposed.