where KD is the apparent binding dissociation constant,
[L]T and [P]T are the total
ligand and protein concentrations used in the experiment and
∆δobs is the observed change in chemical shift upon
ligand addition. ∆δu and ∆δb represent
the changes in chemical shift for the unbound and bound states,
respectively. Based on the KD values and accounting for
fitting error, residues that were interacting with the ligands were
identified and clustered into binding sites. Curve fitting and
calculations were performed on Matlab R2019b and the protein surface
visualization was carried out on PyMol 2.3.5 viewer (Schrödinger).
Protein Surface
Properties
A structural model for the IgG1 FC domain was built by
homology modeling starting with the crystal structure for an
aglycosylated human IgG1 FC fragment (PDB code: 3S7G)
using Molecular Operating Environment (MOE 2018, Chemical Computing
Group). The electrostatic potential (EP) maps were calculated using the
adaptive Poisson-Boltzmann solver (APBS) (Baker, Sept, Joseph, Holst, &
Andrew McCammon, 2001) and surface aggregation propensity (SAP) maps
were calculated as described by Trout and co-workers (Chennamsetty,
Voynov, Kayser, Helk, & Trout, 2010). The EP map was calculated at pH
5.0 to match the experimental conditions. The resulting protein surface
maps were then visualized using the PyMol 2.0.6 viewer (Schrödinger).
Molecular Dynamics Simulations
MD simulations were performed with the two MM CEX ligands, Capto MMC and
Nuvia cPrime in free solution around the FC molecule, as
shown in Figure 2. Each simulation was performed for 200ns with a
timestep of 2fs and storing one frame every 1ps. The first 50ns were
taken as equilibration time and all analyses were performed using the
last 150ns. The simulation box dimensions were 8.5nm x 10nm x 13nm,
allowing for a buffer of roughly 1.5nm on each side of the protein. The
FC was prevented from rotating in each simulation by
restraining a single alpha carbon buried in the center of each of the
four Fc domains using a harmonic potential with a spring constant of
40,000kJ/mol/nm2 (Srinivasan et al., 2017). This
allowed the use of a rectangular simulation box without risking the
protein interacting with itself through periodic boundary conditions.
Additionally, each simulation contained sodium counterions for
electroneutrality and an excess of 18 sodium and chloride such that
there is a counterion for every charged side chain. A total of 61
ligands were included in each simulation, corresponding to a
concentration of 0.1 M. The FC was parameterized using
the AMBER Parm99 (Cheatham, Cieplak, & Kollman, 1999) forcefield and
PropKa (Bas, Rogers, & Jensen, 2008) was used to adjust the charge of
the side chains to reflect a pH of 5.0. Water was modeled explicitly
using the TIP3P (Jorgensen et al., 1981) water model and ligand atom
types and nonbonded interactions were parameterized using the General
AMBER Force Field (GAFF) (Wang, Wolf, Caldwell, Kollman, & Case, 2004).
Atomic partial charges were obtained using a GAUSSIAN (Frisch, M.J.E.A.,
Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman,
J.R., Scalmani, G., Barone, V., Mennucci, B., Petersson, 2009)
calculation with RESP (Bayly, Cieplak, Cornell, & Kollman, 1993; Wang,
Cieplak, & Kollman, 2000) assignment using the Antechamber tool of
AMBER (Wang, Wang, Kollman, & Case, 2001), as has been described
previously (Bilodeau, Lau, Cramer, & Garde, 2019). The resulting
topologies were converted into the GROMACS format using ACPYPE (Silva &
Vranken, 2012). In this work, partial negative charges on the carbons in
the phenyl ring were employed rather than explicit parameterizations to
reflect pi interactions.
Simulations were performed using GROMACS 4.5.3 (Hess, Kutzner, Van Der
Spoel, & Lindahl, 2008; Pronk et al., 2013) in the NPT ensemble. The
temperature and pressure were maintained at 298 K and 1 atm using a
Nosé-Hoover thermostat (Evans & Holian, 1985) and a Parrinello-Rahman
barostat (Parinello, M. and Rahman, 1980), respectively. Ligands,
protein, and water/ions were treated as three separate temperature
coupling groups. Electrostatic interactions were calculated using the
Particle-Mesh Ewald (Darden, York, & Pedersen, 1993) method with a grid
spacing of 0.1 nm, an order of 4 for the B-spline interpolation, and a
direct sum tolerance of 10-5 (consistent with default
parameters).