Salting In. The effect ofelectrostatic interactionson solubility can
be derived from the Debye–Hu ̈ckel theory, which is briefly discussed in
Section 2.3.2. It concerns electrostatic repulsion, not bond formation. A
compact globular protein can be considered as a large ion, and the theory
gives the activity coefficientg+of ions. The solubility of an ionic component
should be expressed as its activity at saturation; in other words,asatis fixed
at any temperature. Sincea¼c 6 g, a decrease ofg+ then leads to an
increase in solubility in terms of concentration (c). A relation forg+is given
in Eq. (2.28), but that is an oversimplification in the sense that all ions were
considered small and of roughly equal size. A protein molecule is relatively
large, and then a better approximation is given by
g+&exp 0 : 37 z^2 k
1 þkRð 7 : 8 Þwhich holds for water at room temperature. Here,zis valence,Rthe protein
radius in nm, andkthe Debye parameter (1/thickness of the electric double
layer) in nm^1 .kdepends on total ionic strengthI(molar), according to Eq.
(6.9b):k& 3 : 2 HI. A protein being a macroion,z^2 can be very large. Even at
the isoelectric pH it will not be zero, since it has to be averaged over all
molecules. Then
variation in charge; the root-mean-square value ofzwill often be about 2 at
the isoelectric pH. Some calculated examples are in Table 7.2. They are not
reliable for the highest ionic strength or for the highest valence.
Nevertheless, they clearly show that the activity coefficient will strongly
decrease, and thereby the solubility strongly increase, for a pH farther away
from the isoelectric point (largerjzj) and for a higher ionic strength. This is
TABLE7.2 Values of the Free Ion Activity Coefficient
ionic strength/millimolar
<z^2 >^1 =^2220200
2 0.86 0.75 0.60
4 0.55 0.32 0.20
8 0.09 0.011 0.002
Calculated according to Eq. (7.8) for various ionic strengths of the
solution and valence (z) of the macroion considered; its ionic radius
was taken as 3 nm.