How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 558

11.3. BIOMASS YIELD

To better describe growth kinetics in a simple fashion, we define some stoichiometrically
related parameters. Yield factors are defined based on the amount of consumption of
another material (Chapter 3). For example, the growth yield factor in a fermentation is
defined as

m G X
r S

dX j Growth

YF X=S ¼ ¼ (11.10)

dS

where m G is the true specific growth rate of the cells and more conveniently,

X X 0
S 0 S

Y X=S ¼ (11.11)

Note that the substrate change in Eqn (11.11) is the total substrate consumption, and the
biomass change is total or net change. This definition is of convenience when first used,
and it does have merits behind this definition as well. Sometimes, we refer to Y X/S in
Eqn (11.11) as the apparent growth yield. The apparent growth yield is easy to understand;
however, it is not a constant when a wide range of growth period is considered, in particular
when K S and K P are not identical, or when cell death also occurs during growth. The fact that
the apparent growth yield is not a constant makes its application difficult in kinetic studies.
On the other hand, the yield factor as defined in Eqn (11.10) is the true growth yield factor.
At the end of the batch growth period, we have an apparent growth yield factor (or growth
yield). Because culture conditions can alter patterns of substrate utilization, the apparent
growth yield factor is not a true constant. One can observe from Eqn (11.11) that there are
two quantities that affect the growth yield: perceived biomass change and the substrate
change. These two quantities are exclusively linked with each other. For example, with
a compound (such as glucose) that is both a carbon and energy source, substrate may be
consumed due to more than one purposes as:

DS ¼ DS Conversion

to biomass þ DS Growth

þ DS Maintenance
energy

þ DS Conversion
to extracellular
products

(11.12)

energy

although the net effect of each cell function is not independent for a clear distribution of the
substrate diversion. A growth yield accounts for the substrate consumption in the first two
terms on the right hand side of Eqn (11.12) would be more logical. Maintenance needs,
however, are required whether the cell is growing or simply staying functional (or viable),
although they can be growth rate dependent in some fashion. Conversion to extracellular
products may not be directly related to the cell biomass growth, although it is at least related
to maintenance needs. Therefore, if one defines the yield as the substrate consumption
directly attributed to the biomass assimilation, it might well be a constant. However, this ficti-
tious growth yield factor is not a factor that can be determined simply by examining the over-
all biomass yield and substrate consumption.
Cell functions are integral to the cell, and Eqn (11.12) is merely presented to elucidate the
various demands of the cell. The division of substrate uptake to biomass assimilation and