18
Chapter 2
Mw
is the molecular weight of the compound, and
K°pL
is the olive oil water-partitioning coefficient
for the compound;
P
has the unit cm s'1
. The correlation has been obtained from measurements on a
large number of different compounds. When using the correlation one should, however, recognize
that for some compounds
P
might deviate by a factor of 10 from the value predicted by the
correlation; see, e.g., Stein (1990). When calculating a value for the permeability coefficient it is
important to consider an appropriate lipid membrane system, since by its definition the
permeability coefficient is inversely proportional to the membrane thickness. Strictly speaking, Eq.
(2.2) therefore holds only for the system for which it was derived, namely the plant cell
Chara
ceratophylla
, but lacking better information it may be used also for other cell types.
In order to calculate the net rate of transport the flux given by Eq. (2.1) is multiplied by the specific
surface area of the cell acd] (unit: area per cell dry weight, e.g., m2 (g DW) *):
r = J a ceii = P a c e n (c a
- c j
(2.3)
For a spherical cell with a water content
w
(g (g cell) ‘) and cell density P^,, (g m 3), the specific
surface area is «<*„= 6/(dcdl(l -w,)Pcei1). Thus, with a few parameters the rate of free diffusion can
easily be calculated for a given compound.
The most important compounds transported by free diffusion are oxygen, carbon dioxide, water,
organic acids, and a lcoh ols. In their d isso cia ted form , sm all organ ic acid s are p ractically in so lu b le
in the lipid membrane, and one should therefore replace their total concentrations in Eq. (2.1) with
the concentrations of the undissociated acid on each side of the membrane. These can be calculated
from
c
i tundiss
ci
K o10pHi
+ 1
(2.4)
where
Ka
is the acid dissociation constant. It is seen that the pH in the aqueous phase at the
membrane surface has an influence on ciundiss, and since extra- and intracellular pH are often
different, it is therefore possible to have a flux of the acid across the membrane even when
ca=cb.
Example 2.1 Free diffusion of organic acids
Maintenance of intracellular pH is very important for overall cell function, and the cell is equipped with
specific enzymes located in the cytoplasmic membrane that ensures that the intracellular pH is kept
constant by pumping protons out of the cell. This proton pumping is an active process, and involves
consumption of Gibbs free energy in the form of ATP (hereby the name ATPases for these proton
pumping enzymes). In the presence of high concentrations of organic acids it has been found that there is
a substantial drain of ATP to maintain the intracellular pH, and this is due to an increased flux of protons
into the cell via rapid diffusion of the undissociated acids. This effect has been illustrated in a study of
Verduyn
et al.
(1992), who analyzed the influence of benzoic acid on the respiration of
Saccharomyces
cerevisiae.
They found that the biomass yield on glucose decreased with increasing concentration of the
acid. At the same time the specific uptake rates of glucose and oxygen increased. Thus, there is a less
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