320
Chapter 8
Figure 8.1 Cell size distribution for
S. pombe.
The data points are measurements obtained using a Coulter
counter, and the line reflects model simulations. [Reprinted by permission from I. R. Kothari
et al.
(1972),
Estimation of parameters in population models for
Schizosaccharomyces pombe
from chemostat data,
Biotechnol. Bioeng,
14, 915-938.]
1
kf{m) dm ~ kn
(5)
where
(m)
is the average cell mass for the population (equal to Jt
Zn).
Since
k/(m j
i$ equal to the specific
growth rate for the population, Eq. (5) is equal to the standard expression for
qx.
Equation (5) shows that
when
r
is independent of
m,
the specific growth rate for the culture is a function of the average cell mass.
This would not be the situation with exponential growth of the individual cells, since here we find
qx
~j
km f(m
)
dm
=
k(m)n
=
kx
(6)
0
ffor evaluation of the integral, see Eq. (8.10)1.
Example 8.1 illustrates how the population balance can be used to examine the behavior of the
single cells in a culture: By comparison of the calculated distribution function with an
experimentally determined distribution function, different models for the behavior of the individual
previous page 343 Bioreaction Engineering Principles, Second Edition  read online next page 345 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off