From Cellular Function to Industrial Products
21
Binding between substrate and carrier is reversible, and the net rate of complex formation is
rm
Mass
balances for each of the membrane components are:
D,
d z1
=
0
(
1
)
D,
d 2cme
d z2
+ r
= 0
(
2
)
(3)
The total carrier concentration is
e,
= ~ [ { e + cme)dz
(4)
d
J0
To simplify the discussion we shall assume that
Ka
=
Kb = K.
This is not necessarily true: the partitioning
coefficient may be different at the outside face of the membrane and at the inside face since the
environment inside the cell is different from that in the abiotic phase. In derivation of Eq. (2.1 ) we also
implicitly assumed that the two partitioning coefficients were identical. We shall further take the three
diffusivities to be constant and equal to
D.
Finally we shall assume that both the forward and backward
reactions are much faster than the diffusion process. Effectively, this means that the chemical reaction is at
equilibrium everywhere:
c me
cm
+ e< r^cme
with equilibrium constant
K e
= —”—
(5)
Adding Eqs. (2) and (3) and integrating one obtains:
D
de
dz
dcme
dz
= k
i
(
6
)
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