where \(\rho_{\text{bound}}\) and \(\rho_{\text{bulk}}\) are the ligand
density in the bound and bulk regions respectively, \(k_{B}\) is the
Boltzmann constant and T is the temperature. The free energy was
calculated at every grid point with 1Å spacing around the protein.
Figure 9 shows the free energy plotted on the surface of the
FC. As can be seen, the Nuvia cPrime ligands had a
strong tendency to bind to the interface between the CH2
and CH3 regions as well as the hinge region. These
hotspots are qualitatively consistent with those observed using NMR.
Previous work in our group has shown that free ligand MD simulations can
qualitatively predict hotspots observed in NMR experiments for small
model proteins (Holstein, Chung, et al., 2012; Parimal et al., 2015).
Here, we have shown for the first time that this is also true for large,
therapeutically relevant proteins.
MD simulations are also valuable in that they can directly elucidate the
mechanism of binding. To illustrate this, Figures 10a and b show example
poses of Nuvia cPrime bound to the hinge region and the
CH2-CH3 interface, respectively. In the
hinge region (shown in Figure 10a) Nuvia cPrime interacts with a
combination of histidines and hydrophobic methionines. Interestingly,
the cluster of residues (Tyr 81, Lys 3, His 49 and Met 1) that were
identified to interact with the Nuvia cPrime ligand are also a part of
the natural complementary FC binding sites for
interactions with the C1q and FcRgIII receptors. In the
CH2-CH3 interface (Figure 10b), ligands
appeared to interact with the histidines through two mechanisms: direct
positive (histidine)-negative (carboxylic acid) interactions, and pi-pi
stacking (between the phenyl ring and histidine ring). Previous work in
our group has shown that pH can be used as an effective tool for
modulating the interactions of Fc with multimodal chromatographic
supports (Robinson et al., 2020). The simulation results presented here
suggest that this may be due to the strong ligand-histidine
interactions, which would be significantly affected by a change in pH
from 5 to 7.