How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 593

11.14.2.2.2. SUBSTITUTABLE SUBSTRATES
When two or more substrates of similar functionality are limiting, the contributions of the
substrates to the microbial growth are additive:

X

N SS

m maxj S j
K S j þ S j

m G ¼

1 a j

(11.74)

j¼

where N SS is the number of limiting substrates that are substitutive and a j is the frac-
tional rate contribution of substrate j. For example, glucose, xylose, and mannose are
substitutive. The quantity a j is a function of the concentrations of the substrate mixture
and

X

N SS

1 a j ¼

1 (11.75)

j¼

That is, the total amount of enzymes in a cell is constant. However, the distribution of the
enzymes that can assist the uptake and conversion of each substrate can change according
to the growth and medium conditions.

11.14.2.2.3. MIXED TYPES OF SUBSTRATES
When both complimentary and substitutive substrates are present, the overall growth rate
is more completed and will depend on the combination of the substrates. For example, with
one type of substrate being substitutive and all the others being complementary, the micro-
bial growth rate is given by:

N SC

Y X

N SS

S j
K S j þ S j

1 a l m max l S l

m G ¼ (11.76)

K S l þ S l

j¼ 1 l¼

11.14.3. Simplest Reaction Network (or Simplest Metabolic) Model
The simplest reaction network that has the potential to capture the transitional effects (or
unbalanced growth) is given below

k 1
k 1

k 1c YF P=S P þ

S þ E S$ E YF X=S X þ E (11.77a)

% /

k 2
k 2 n E E

X % (11.77b)

This is the simplest approximation to a metabolic pathway. It has the potential to describe
balanced as well as unbalanced growth.
The approximation is not only on the number of steps involved in metabolism and cell
generation but also on the elementary steps. Clearly, at least two steps in Eqn (11.77) are
not elementary, where stoichiometrical coefficients are not restricted to integers between
0 and 3.