Despite the fact that the goal of SSF processes is product formation, the
modeling of production has received little attention. The products produced in
SSF can be quite different in the way they are related to growth activities. Simple
approaches which have been taken to modeling the production of a catabolic
end product, extracellular enzymes, and secondary metabolites are described
below.
Sato and Yoshizawa [119] modeled the production of ethanol, a catabolic end
product, during SSF of Saccharomyces cerevisiae. The rate of ethanol production was assumed to be directly proportional to the rate of carbon dioxide
formation, which had both growth and non-growth associated terms as shown
in Eq. (18). The non-growth associated term represented maintenance metabolism and the non-growth associated rate constant was assumed to decrease
exponentially as the ethanol concentration increased, in order to describe the
inhibitory effect of ethanol on its own production.
Enzyme production kinetics in SSF have the potential to be quite complex,
with complex patterns of induction and repression resulting from the multisubstrate environment. As a result, no mechanistic model of enzyme production in SSF has yet been proposed. Ramesh et al. [120] modeled the production
of a-amylase and neutral protease by Bacillus licheniformis in an SSF system.
They showed that production profiles of the two enzymes could be described by
the logistic equation. However, although they claimed to derive the logistic
equation from first principles, the derivation was based on a questionable initial
assumption about the form of the equation describing product formation
kinetics: They did not justify why the rate of enzyme production should be
independent of biomass concentration but directly proportional to the multiple
of the enzyme concentration and the substrate concentration. As a result their
equation must be considered as simply empirical.
Perez-Correa and Agosin [121] modeled growth and production of gibberellic acid, a secondary metabolite, by Gibberella fujikuroi. Equation (18) was used
to characterize gibberellic acid production. The non-growth associated rate
constant was modeled as depending on the nitrogen concentration according to
the Monod equation with a substrate inhibition term. Since the growth rate was
also related to the nitrogen concentration by a Monod equation, these equations
described the observed behavior that the gibberellic acid production is very
slow until nitrogen is largely depleted, and then there is a period of production
until the nitrogen is totally exhausted. As nitrogen concentration falls growth
slows and the substrate inhibition of gibberellic acid production is progressively alleviated, but then as the nitrogen concentration falls to zero then both
the growth and non-growth associated production terms fall to zero.
4.4
Intraparticle Diffusion of Enzymes, Nutrients, Hydrolysis Products,
and Oxygen
It has been noted several times in the preceding sections that growth activities
lead to intraparticle concentration gradients, with consequences for bioreactor
performance. No attention has been paid to intraparticle product concentra92
D.A. Mitchell et al.
modeling of production has received little attention. The products produced in
SSF can be quite different in the way they are related to growth activities. Simple
approaches which have been taken to modeling the production of a catabolic
end product, extracellular enzymes, and secondary metabolites are described
below.
Sato and Yoshizawa [119] modeled the production of ethanol, a catabolic end
product, during SSF of Saccharomyces cerevisiae. The rate of ethanol production was assumed to be directly proportional to the rate of carbon dioxide
formation, which had both growth and non-growth associated terms as shown
in Eq. (18). The non-growth associated term represented maintenance metabolism and the non-growth associated rate constant was assumed to decrease
exponentially as the ethanol concentration increased, in order to describe the
inhibitory effect of ethanol on its own production.
Enzyme production kinetics in SSF have the potential to be quite complex,
with complex patterns of induction and repression resulting from the multisubstrate environment. As a result, no mechanistic model of enzyme production in SSF has yet been proposed. Ramesh et al. [120] modeled the production
of a-amylase and neutral protease by Bacillus licheniformis in an SSF system.
They showed that production profiles of the two enzymes could be described by
the logistic equation. However, although they claimed to derive the logistic
equation from first principles, the derivation was based on a questionable initial
assumption about the form of the equation describing product formation
kinetics: They did not justify why the rate of enzyme production should be
independent of biomass concentration but directly proportional to the multiple
of the enzyme concentration and the substrate concentration. As a result their
equation must be considered as simply empirical.
Perez-Correa and Agosin [121] modeled growth and production of gibberellic acid, a secondary metabolite, by Gibberella fujikuroi. Equation (18) was used
to characterize gibberellic acid production. The non-growth associated rate
constant was modeled as depending on the nitrogen concentration according to
the Monod equation with a substrate inhibition term. Since the growth rate was
also related to the nitrogen concentration by a Monod equation, these equations
described the observed behavior that the gibberellic acid production is very
slow until nitrogen is largely depleted, and then there is a period of production
until the nitrogen is totally exhausted. As nitrogen concentration falls growth
slows and the substrate inhibition of gibberellic acid production is progressively alleviated, but then as the nitrogen concentration falls to zero then both
the growth and non-growth associated production terms fall to zero.
4.4
Intraparticle Diffusion of Enzymes, Nutrients, Hydrolysis Products,
and Oxygen
It has been noted several times in the preceding sections that growth activities
lead to intraparticle concentration gradients, with consequences for bioreactor
performance. No attention has been paid to intraparticle product concentra92
D.A. Mitchell et al.