Population Balance Equations
321
cells can be evaluated. In their analysis, Kothari
et al
(1972) used the cell mass distribution
function, which can be obtained using a Coulter counter or other size-distribution measurement
system. Today it is also possible to obtain distribution functions for many other cellular properties
by flow cytometry [see, e.g., Bailey and Ollis (1986) for a description]. With this technique one
may measure the single-cell content of macromolecules like proteins, chromosomal DNA,
carbohydrates,
and
plasmid
DNA
by
applying
specific
fluorescent
dyes
that
label
the
macromolecular pool of interest. Furthermore, by measuring the accumulation of an intracellular
fluorescent product formed by the action of a certain enzyme, it is possible to quantify the cellular
content of a specific enzyme. In addition to measurement of the cellular content by fluorescent
techniques, it is also possible to measure the cell size by light scattering, and most modem flow
cytometers are equipped with both light-scattering and fluorescent-measurement facilities whereby
a two-dimensional distribution function for a population can be obtained (see Fig. 8.1).
With measurements of both cell size and cell composition it is possible to calculate the distribution
function, based on mass fractions
y/(X)
from the two-dimensional distribution function
f(y,m) (y
is
the content of the measured component in grams per cell). Cells with the composition
X
(grams per
gram dry weight) are found on the curve
y-X m
in the
y-m
plane, and the total concentration o f cells
with a composition
X
is therefore given by
Figure 8.2 Two-dimensional distribution function for a population of recombinant
S. cerevisiae.
The
fluorescence intensity is correlated to the content of plasmid DNA and the light-scattering intensity is
correlated to the cell size. It is observed that the plasmid-free and plasmid-containing cells are easily
distinguished. [Reprinted by permission from J. E. Bailey and D. F. Ollis (1986),
Biochemical Engineering
Fundamentals,
McGraw-Hill.]
39
31
23
15
07
00
*
------------
Fluorescence
intensity
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