Electrostatics in Macromolecular Solutions - Food Colloids: Self-Assembly and Material Science - page 151

Figure 15 The free energy of interaction A(R) between the centres of mass of the protein
and the polyelectrolyte at low salt concentration obtained from MC simula-
tions with titrating amino acids (model D). The curves have been calculated at
the respective isoelectric points for lysozyme (no symbols), a -lactalbumin
(filled circles) and b -lactoglobulin (filled squares)

repulsive, indicating that the 'wrapping' of the chain around the proteins is an
entropically unfavourable structure.
The attractive minimum in the protein-polyelectrolyte potential is reduced
upon addition of salt 37 and we can use the minima of A(R) in Figure 15 in order
to estimate the critical ionic strength. Assuming that the salt screening can
be described by simple DH theory, and that the complex can be defined
as 'dissolved' when the interaction is less than kT, we get the following
relation:

exp( 2 k R min )|A(R min )| r kT. (23)

The factor of two in the exponent of Equation (23) comes from the fact that the
second-order terms dominate the interaction. Following this recipe, we find
that approximately 10-20 mM salt is sufficient to dissociate the a-lactalbumin-
polymer or b-lactoglobulin-polymer complexes, respectively.
Thus, we have shown that a polyanion can form a complex with a neutral
protein molecule. Next we make a numerically more rigorous partitioning of the
contributions to the free energy of interaction shown in Figure 15. We can deduce
that the minimum for lysozyme is solely due to charge regulation [Figure 16(a)].
If the charge distribution on lysozyme is considered fixed, then the polyanion-
lysozyme interaction is essentially everywhere repulsive. Replacing the detailed
charge distribution with an ideal dipole at the mass centre has a small effect on
the free energy. This means that the ion-dipole interaction gives a very small
attractive contribution, while the effect from higher order moments is negligible.