Electrostatics in Macromolecular Solutions - Food Colloids: Self-Assembly and Material Science - page 150

Figure 14 The contribution to the free energy of interaction, A(x), as a function of
reduced separation x ¼ R/ s from the charge-induced-charge term (solid lines)
and the ion-dipole term (dashed lines). Lines without symbols denote lys-
ozyme, filled circles denote a -lactalbumin and filled squares denote b -lacto-
globulin. The free energies are calculated from Equation (17) using simulated
capacitances and dipole moments. Note that the ion-dipole terms for a -
lactalbumin and b -lactoglobulin coincide
The first set of simulations (A) describes only the shape of the protein, and so
the free energy of interaction is, of course, everywhere repulsive. The second set
(B) uses fixed fractional charges on all residues, which has been determined in a
separate simulation of the isolated protein at the appropriate pH. In the next
set (C), the charge distribution of the protein is replaced by an ideal dipole.
And, in the fourth and final set (D), the amino acids are allowed to titrate, and
so this simulation contains all electrostatic contributions including the ion-
induced-charge term. The difference between the results from sets B and
C indicates the importance of higher order electrostatic moments (quadrupole,
octupole, etc.) in the protein, while the comparison of set C with set D reveals
the importance of the regulation mechanism.
The calculated free energy of interaction, A(R), for the three proteins at their
respective pI values all show a clear minimum (Figure 15). The relative depths
of the minima are in qualitative agreement with perturbation calculations
(see Figure 14), though the actual numbers are approximately half the values
predicted by second-order perturbation theory. The minima appear at roughly
the same separation despite the fact that the b-lactoglobulin molecule is more
than twice as big as the other two. This can be explained by the elongated shape
of the former, which also results in a more long-ranged attraction. The
separation R can approach zero, which corresponds to a situation where the
polyelectrolyte wraps around the protein. We note here, however, that A(0) is