3. CELLULAR ASPECTS OF ACTIVE TRANSPORT
189
The ratio of the two forms determines the value of the permeability
coefficient of the membrane to the ionic species considered.
The ratio X
2 ~/CaX is evidently a function of the Ca concentration
in the medium and of the affinity of X
2- for Ca as defined by the constant
Κ (Eq. 14).
If we consider the system just defined in its relationship with a complex medium, e.g., the extracellular fluid, different types of variations
may be considered: (a) Another cation may, by true competition, form
a complex with X
2 ~; or (b) this cation will form a complex with X
2without occupying the sites of the alkaline earth, but with the result that
displacement of the equilibrium defined by Eq. 14 occurs (noncompetitive inhibition); or (c) the value of Κ defined in Eq. 14 may be directly
related to the ionic strength of the medium.
In the first case, we may define a new constant Kf for any other
alkaline cation, Κ for instance, and
Whatever the mechanism in effect, the amount of CaX will be directly
related not only to the value of Κ and the Ca concentration, but also to
the cationic composition of the medium bathing X
2 ~.
In order to illustrate these propositions, let us consider the case of
Elodea cells (200). In a solution of NaCl or KCl they rapidly lose their
Ca. By progressively adding Ca to the solution, it is possible to determine the concentration corresponding to a fixation of Ca by the cell.
This occurs when the ratios Ca:Na are close to 200. With MgCl 2 the
ratio has a value of about 20. That there is a fixation of Ca on a cellular
structure is well demonstrated by the fact that the total amount of Ca
present in the cell can be completely extracted only in the presence of
citrate. Note that the minimum quantity of Ca which cannot be extracted
without citrate is not very different when expressed in terms of membrane surface area, if we compare yeast cells, Elodea cells, or Arbacia
eggs. It is also interesting to consider the results of Danielli (201, 202)
showing that the ratio Na:Ca at the surface of many cells (red cells,
leukocytes, Asteria eggs) is close to 1 while it is around 100 in the
medium, thereby suggesting a different affinity of the cellular structures
involved for the various cations.
This difference in affinity can be best explained if the ions form salts
of various strength. The ion forming the weakest salt will be more
readily bound. In the case of Elodea, Ca has an affinity 100 times greater
than Na, or Na changes the affinity of the structure for Ca following one
of the mechanisms described above.
2(K+)(X
2 ~)
(K 2 X)
(15)
189
The ratio of the two forms determines the value of the permeability
coefficient of the membrane to the ionic species considered.
The ratio X
2 ~/CaX is evidently a function of the Ca concentration
in the medium and of the affinity of X
2- for Ca as defined by the constant
Κ (Eq. 14).
If we consider the system just defined in its relationship with a complex medium, e.g., the extracellular fluid, different types of variations
may be considered: (a) Another cation may, by true competition, form
a complex with X
2 ~; or (b) this cation will form a complex with X
2without occupying the sites of the alkaline earth, but with the result that
displacement of the equilibrium defined by Eq. 14 occurs (noncompetitive inhibition); or (c) the value of Κ defined in Eq. 14 may be directly
related to the ionic strength of the medium.
In the first case, we may define a new constant Kf for any other
alkaline cation, Κ for instance, and
Whatever the mechanism in effect, the amount of CaX will be directly
related not only to the value of Κ and the Ca concentration, but also to
the cationic composition of the medium bathing X
2 ~.
In order to illustrate these propositions, let us consider the case of
Elodea cells (200). In a solution of NaCl or KCl they rapidly lose their
Ca. By progressively adding Ca to the solution, it is possible to determine the concentration corresponding to a fixation of Ca by the cell.
This occurs when the ratios Ca:Na are close to 200. With MgCl 2 the
ratio has a value of about 20. That there is a fixation of Ca on a cellular
structure is well demonstrated by the fact that the total amount of Ca
present in the cell can be completely extracted only in the presence of
citrate. Note that the minimum quantity of Ca which cannot be extracted
without citrate is not very different when expressed in terms of membrane surface area, if we compare yeast cells, Elodea cells, or Arbacia
eggs. It is also interesting to consider the results of Danielli (201, 202)
showing that the ratio Na:Ca at the surface of many cells (red cells,
leukocytes, Asteria eggs) is close to 1 while it is around 100 in the
medium, thereby suggesting a different affinity of the cellular structures
involved for the various cations.
This difference in affinity can be best explained if the ions form salts
of various strength. The ion forming the weakest salt will be more
readily bound. In the case of Elodea, Ca has an affinity 100 times greater
than Na, or Na changes the affinity of the structure for Ca following one
of the mechanisms described above.
2(K+)(X
2 ~)
(K 2 X)
(15)