The rate of flow of substrate, rdif, or the rate of biocatalytic reaction, rkin, may play
predominant roles, depending on their relative magnitudes, as the lower step will be the
controlling step. As it can be seen from Figure 4.3 for a Michaelis-Menten kinetics, at
high bulk substrate concentrations when the reaction is zero order, robs will always be
equal to rmax and the reaction will be kinetically controlled. At lower bulk substrate
concentrations the reaction can be both kinetically or diffusionally controlled, depending
on the substrate modulus, μ. At low μ, when a » rmax/Km, mass transfer is much faster
than the biocatalytic reaction, but at high μ, when a « rmax/Km, the biocatalytic reaction
is much faster than the diffusion of substrate.
Figure 4.4 shows what happens for an inhibition kinetics. Again, the reaction can be
both kinetically or diffusionally controlled, depending on the substrate modulus, μ.
However, a major difference from Michaelis-Menten kinetics is that from a certain bulk
Figure 4.3 Roles of the rate of flow of
substrate, rdif, and the rate of enzyme
reaction, rkin, on the observed reaction
rate, robs, as function of the substrate
modulus for a Michaelis-Menten
kinetics. The heavy solid line refers to
rkin/rmax; the light solid lines refer to
robs/rmax and the broken lines refer to
rdif/rmax.
Design and modelling of immobilised biocatalytic reactors 99