Biomedical Engineering Reference
In-Depth Information
TABLE 11.7
Values of Monod Saturation Constant for Oxygen Limited Growth of Several Types of Cells
Microorganism
T
,
C
Cell size,
m
K
S
, mmol/L-O
2
m
10
5
Micrococcus candicans
20.2
0.5
1.1
10
5
Aerobacter aerogenes
19.0
0.6
3.1
10
5
Escherichia coli
19.2
0.6
2.22
10
5
Serratia marescens
18.8
0.7
3.60
10
4
Azotobacter indicum
19.6
1.6
3.00
10
4
Bacillus megatherium
19.2
2.0
5.97
10
4
Bacillus megatherium (LiCl)
20.0
2.4
7.07
10
3
Acetobacter suboxydans
19.2
2.7
1.57
10
3
Bacillus megatherium (glycine)
20.6
4.0
3.12
Data source: J. Longmuir, Biochem. J., 57: 81, 1954.
In other words, Monod equation still holds. However, the saturation constant K
S
is modified.
The saturation constant is higher when mass transfer effect is pronounced. Apart from the
discussion in
11.4, this derivation gives us a clue why the Monod equation is the approxi-
mate growth rate equation for a complicated metabolic pathway when pseudosteady state
(balanced growth) holds.
Since the mass transfer coefficient increases with increasing agitation (convection),
temperature, and particle (cell) size (surface area decrease with cell size), one can expect
the (apparent) saturation constant K
S
to vary with these parameters.
Table 11.7
shows typical
values of saturation constant for oxygen limited growth as a function of cell size. One does
observe a trend in cell size dependence.
While Monod equation is the most widely used cell growth model, it has its limitations.
For example, balanced growth conditions (pseudosteady state), dilute substrate concentra-
tions, dilute cell concentration, no inhibitory substances present in the medium, and single
limiting substrate (with all other required substrates in excess) are the most severe limita-
tions. Some of these limitations can be relaxed by adding additional terms.
x
11.14.2.1. Modification of Monod Equation with Growth Inhibitors
At high concentrations of substrate or product and in the presence of inhibitory substances
in the medium, growth becomes inhibited, and growth rate depends on inhibitor concentra-
tion. The inhibition pattern of microbial growth is analogous to enzyme inhibition. If a single-
substrate enzyme-catalyzed reaction is the rate-limiting step in microbial growth, then
kinetic constants in the rate expression are biologically meaningful. Often, the underlying
mechanism is complicated, and kinetic constants do not have biological meanings and are
obtained from experimental data by curve fitting.
11.14.2.1.1. SUBSTRATE INHIBITION
At high substrate concentrations, microbial growth rate is inhibited by the substrate. As
in enzyme kinetics, substrate inhibition of growth may be competitive or noncompetitive.
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