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.