UC Riverside Undergraduate Research Journal

Computational Prediction of Association Free Energies for the C3d-CR2 Complex and Comparison to Experimental Data
Alexander S. Cheung
magnitude of the excess charge in CR2 by 1e, a decrease
in ΔΔG solvation is observed. Additionally, when a basic
residue is mutated to an acidic residue, an even greater
decrease in ΔΔG solvation is observed since such a mutation
decreases the magnitude of the excess charge in CR2 by 2e.
Intuitively, these results correlate well to those
illustrated in Fig. 4A. In Fig. 4A, a proportional relationship
is observed between ΔΔG solvation and association ability.
In Fig. 5A,B, an increase in ΔΔG solvation was observed
when the mutation increased the magnitude of the excess
charge on the component (e.g. mutation of a basic amino
acid to a neutral amino acid in C3d), while a decrease in
ΔΔG solvation was observed when the mutation diminished
the magnitude of the excess charge on the component (e.g.
mutation of and acidic amino acid to a neutral amino acid in
C3d). Because C3d and CR2 have opposite excess charge,
an increase in the magnitude of the excess charge on
either component can increase the long-range electrostatic
attraction between the two components, speeding up
formation of the encounter complex and thus ultimately
resulting in an increase in binding ability.
Similar plots have been generated in which the change
in ΔΔG solvation is plotted against the distance between
Arg390, the CR2 residue at the association site (not shown;
data in Table 1). Trends similar to Fig. 5 were observed.
Discussion
The interaction of complement protein fragment C3d
with the first two modules of CR2 has been the subject of
many intensive studies among immunologists, because it is an
essential link between innate and adaptive immunities. Earlier
efforts by the Morikis Group have focused on shedding light
on the underlying structural and physicochemical properties
underlying C3d-CR2 association [3,5]. In particular, a twostep
model was proposed according to which electrostatics
drive the nonspecific recognition between C3d and CR2 and
contribute to their specific binding. An earlier study by Zhang
et al [5] presented calculations of ionization free energy
differences as a function of pH, ionic strength, and mutations,
which compared favorably with experimental data.
In the present study, we examine the effect of
solvation on the electrostatic free energies of association.
We have calculated electrostatic free energies of association
using two different methods. The first calculation
produced a difference between electrostatic free energy of
association and Coulombic free energy of association in
vacuum, using the complete thermodynamic cycle of Fig.
3, which incorporates solvation effects (vertical processes)
in the calculation. The second calculation produced the
electrostatic free energy of association in solution by using
the bottom horizontal process only, which does not account
for solvation. We have performed our calculations for the
parent complex and the same mutants as in [5] for which
there are published experimental association data [6,9]. We
have demonstrated that the inclusion of solvation effects
is necessary to accurately predict association abilities, by
comparing our theoretical data to the experimental data.
This is shown in Fig. 4 where a positive correlation is
observed between the predicted solvation free energy
differences and the experimental binding ability data (Fig.
4A). In contrast, no correlation is observed when solvation
effects are not taken into account (Fig. 4B).
Moreover, we compare our calculated solvation free
energy differences to the ionization free energy differences
of Zhang et al [5] (Fig. 6). A solid correlation is observed
between the two sets of data, with a correlation coefficient
of -0.8. The negative sign indicates that solvation effects are
unfavorable while ionization free energies are favorable.
Inclusion of favorable Coulombic interactions (top horizontal
process in the thermodynamic cycle) are expected to produce
overall electrostatic free energies of association, which, when
compared to the ionization free energy differences, will yield
Figure 6. ΔΔG ionization versus ΔΔG solvation . ΔΔG ionization is from [5]. A
linear fit is drawn in red.
20 UCR Un d e r g r a d u a t e Re s e a r c h Jo u r n a l