Cell Metabolism - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 513

1. Referring to Fig. E10-4.1 , mass balance of lactose in the cell (area enclosed by the dotted
line) yields:

In Out þ Generation ¼ Accumulation

J S A c 0 þ r s V C ¼ 0 (E10-4.2)
where r s is the rate of generation of substrate in the cell based on the cell volume. This rate
is not convenient rate to use for engineering calculations because of the cell volume use.
For balanced growth, pseudo-steady state holds. There is no accumulation of substrate
inside the cell. Therefore, Eqn (E10-4.2) has the out flow and accumulation terms zero.
Equation (E10-4.2) can be rearranged to yield
J S A C ¼r s V C ¼r S V (E10-4.3)

where V is the volume of the culture (including cell and medium). The rate r S is a more
commonly used rate. Equation (E10-4.3) leads to

J S a ¼r S (E10-4.4)

where a is specific surface area of the cells,
a ¼ A C
V

(E10-4.5)

Substituting Eqn (E10-4.1) into (E10-4.4) , we obtain

S
K SE þ

S b
K SI þ

J S max a

S

¼r S (E10-4.6)

S b

which can be solved to give

K S I
1

S b ¼ (E10-4.7)

1

S
K SE þ

r S
J S max a

S þ

10 3 g/L, r S ¼ Since K SI ¼ 0.2 g/L, S ¼ 0.1 g/L, K SE ¼ 5 mg/L ¼ 5 0.65 g/(L $ h), and

¼

1.5 g/(L $ h), Eqn (E10-4.5) gives S b ¼ J Smax a 0.2158 g/L.

2. From part (a), we obtained that S b ¼ 0.2518 g/L. The lactose concentration in the biotic

phase is more than double that in the medium. One may think that the diffusion flux
would force the lactose out of the cell body as the concentration inside the cell body is
higher than that outside of the cell (in the medium). However, the mass transfer
is controlled by enzyme mediation. This is the reason that the transport of lactose is
apparently against the concentration gradient. Thus, the higher concentration of lactose
inside the biotic phase than that in the abiotic phase is correct.

10.6.2. Role of Cell Receptors in Metabolism and Cellular Differentiation
Almost all cells have receptors on their surfaces. These receptors can bind a chemical in
the extracellular space. Such receptors are important in providing a cell with information