Electrostatics in Macromolecular Solutions - Food Colloids: Self-Assembly and Material Science - page 149

number of authors through experiment 32-35 and theoretical modelling. 36-38
The strength of the interaction is to a large extent regulated by electro-
static interactions, as governed by key parameters such as pH and salt
concentration.
A particularly interesting observation is the apparently paradoxical forma-
tion of soluble complexes under conditions where the net charges of the protein
and the polyelectrolyte have the same sign. The experimental studies of Dubin,
de Kruif, and their co-workers, 33,36,39 have demonstrated this special feature of
polymer-protein complexation. The expression 'complexation on the wrong
side' has sometimes been used, meaning that a polyanion forms a complex with
a protein at a pH above the isoelectric point of the protein. The molecular
interpretation of such studies has focused on the assumption of 'charged
patches' on the protein surface. 30,37,40,43
A formal way to describe the interaction between oppositely charged patches
on two macromolecules is in terms of a multipole expansion. That is, for two
neutral protein molecules, the leading terms would be dipole dipole, dipole-
quadrupole, etc. Other electrostatic properties of the protein, however, may be
more important, and already in 1952 Kirkwood and Shumaker 20 demonstrated
theoretically that fluctuations of residue charges in two proteins can result in an
attractive force. Recently, we have used MC simulations and the charge
regulation theory described in the previous section in order to explain pro-
tein-polyelectrolyte association in a purely electrostatic model. 41 A charge
regulation mechanism was also suggested by Cohen Stuart and Biesheuvel. 42
We can use simulated capacitances and dipole moments in order to calculate
analytically the ion-induced-charge and ion-dipole contributions to the interac-
tion-free energy according to Equation (17). The results indicate that the regu-
lation term is by far the most important term for lysozyme, while for
a-lactalbumin and b-lactoglobulin the two terms are of comparable magnitude.
The curves in Figure 14 should, of course, be regarded as qualitative and not
quantitative. However, they still give, as will be seen below, a correct picture of the
behaviour of the three proteins. The contact separation has been defined as
protein radius+polyelectrolyte radius, R p + R pe . The latter has been chosen as
half of the end-to-end separation of the corresponding neutral ideal polymer.
Both protein and polyelectrolyte radii are approximate, but even with a rather
generous variation of these values the general picture of Figure 14 will remain the
same. The regulation term decays slower than the ion dipole term, which means
that it will gain in relative importance at larger separations, as shown in Figure 14.
This means that, even if the two terms are comparable at contact, the regulation
term can still dominate the contribution to the second virial coefficient.
We have performed four different simulations for each protein-polyelectro-
lyte complex:
(A) the 'neutral' protein (all charges set to zero),
(B) the protein with fixed charges at each amino-acid residue,
(C) the protein with an ideal dipole at its centre of mass, and
(D) the protein with titrating amino-acid residues.