How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 591

If a single-substrate enzyme-catalyzed reaction is the rate-limiting step in microbial growth,
then inhibition of the enzyme activity results in inhibition of microbial growth by the same
pattern. Since the Monod equation is an approximate growth rate equation, one is not able to
differentiate the maximum growth rate and saturation constant from the noninhibited case.
The kinetic constants are merely correlation coefficients. Therefore, only the noncompetitive
substrate inhibition is presented here:

m max

m G ¼ 1 1 (11.65)

K S
S

S
K I

þ þ

which is most general form of substrate inhibited growth rate equation if Monod growth
prevails.

11.14.2.1.2. PRODUCT INHIBITION
High concentration of extracellular product can be inhibitory for microbial growth.
Product inhibition may be competitive or noncompetitive, and in some cases when the
underlying mechanism is not known, the inhibited growth rate is approximated to exponen-
tial or linear decay expressions.
Competitive product inhibition:

m max S

1

m G ¼ (11.66)

P
K P

K S þ þ S

Noncompetitive product inhibition:

m max S

1

m G ¼ (11.67)

P
K P

ðK S þ SÞ þ

Ethanol fermentation from glucose by yeasts is a good example of noncompetitive product
inhibition, and ethanol is the inhibitor at concentrations above about 5%. Other rate expres-
sions used for ethanol inhibition are

1 n

m max S
K S þ S

P
P m

m G ¼ (11.68)

where P m is the product concentration at which growth stops, or

m max S

K S þ S e P=K P

m G ¼ (11.69)

where K P is the product inhibition constant.

11.14.2.1.3. CELL INHIBITION
Perhaps, the most common inhibition is the cells themselves. In most cases, there is no
limitation on the space for the cells to occupy; however, it can become an issue for batch