Cell Metabolism - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 511

I ¼ C AI ½

Protein M

C AMI ¼½ A $ Protein (10.32)

K AI þ C AI

where K AE is external binding affinity of the substrate, mol/m 3 and is equal to k -Eb /k Eb ; K AI is
internal binding affinity of the substrate, mol/m 3 and is equal to k

Ib /k Ib ; C AMI is the concen-
tration of species A in the membrane at the internal side interface; and C AME is the concen-
tration of species A in the membrane at the external side interface.
The flux of the target molecule into the cell depends on concentration gradient of species
A inside the membrane, that is,

d ðC AME C AMI Þ¼J Amax

J A ¼ D AM

C AE
K AE þ C AE

C AI
K AI þ C AI

(10.33)

where D AM is the diffusivity of the protein carrier bound with species A in the membrane,
and J Amax is the maximum flux rate of A, mol/(m 2 $ s). One can observe from equation

(10.33) that C AE < C AI does not necessarily mean a net flux out of the cell. Facilitated transport

of sugars and other low-molecular-weight organic compounds is common in eukaryotic
cells, but infrequent in prokaryotes. However, the uptake of glycerol in enteric bacteria
(such as E. coli) is a good example of facilitated transport.
Active transport is one particular type of facilitated transport in that active transport
occurs “against” a concentration gradient, i.e. C AE < C AI . The active transport is effected by

K AI > K AE . The intracellular concentration of a molecule may be a 100-fold or greater than

the extracellular concentration. The movement of a molecule (by itself) up a concentration
gradient is thermodynamically unfavorable and will not occur spontaneously; energy
must be supplied (or coupled with another reaction) for the binding to occur. In active trans-
port, several energy sources are possible: (1) the electrostatic or pH gradients of the proton-
motive force and (2) secondary gradients (for example, of Na þ or other ions) derived from the
proton-motive force by other active transport systems and by the hydrolysis of ATP.
The proton-motive force results from the extrusion of hydrogen as protons. The respiratory
system of cells (see section 10.7.4) is configured to ensure the formation of such gradients.
Hydrogen atoms, removed from hydrogen carriers (most commonly NADH) on the inside
of the membrane, are carried to the outside of the membrane, while the electrons removed
from these hydrogen atoms return to the cytoplasmic side of the membrane. These electrons
are passed to a final electron acceptor, such as O 2 . When O 2 is reduced, it combines with H þ
from the cytoplasm, causing the net formation of OH on the inside. Because the flow of H þ
and OH across the cellular membrane by passive diffusion is negligible, the concentration of
chemical species cannot equilibrate. This process generates a pH gradient and an electrical
potential across the cell. The inside of the cell is alkaline compared to the extracellular
compartment. The cytoplasmic side of the membrane is electrically negative, and the outside
is electrically positive. The proton-motive force is essential to the transport of many species
across the membrane, and any defect in the cellular membrane that allows free movement of
H þ and OH across the cell boundary can collapse the proton-motive force and lead to cell
death.
Some molecules are actively transported into the cell without coupling to the ion gradients
generated by the proton-motive force. By a mechanism that is not fully understood, the
hydrolysis of ATP to release phosphate bond energy is utilized directly in transport