\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,greek,english]{babel}



\usepackage{float}








\begin{document}

\title{Identification of Preferred Multimodal Ligand Binding Regions on IgG1 FC
using Nuclear Magnetic Resonance and Molecular Dynamics Simulations}



\author[1]{Ronak Gudhka}%
\author[1]{Camille Bilodeau}%
\author[1]{Scott McCallum}%
\author[2]{Mark McCoy}%
\author[2]{David Roush}%
\author[3]{Mark Snyder}%
\author[1]{Steven Cramer}%
\affil[1]{Rensselaer Polytechnic Institute}%
\affil[2]{Merck and Co., Inc.}%
\affil[3]{Bio-Rad Laboratories}%


\vspace{-1em}



  
  \date{May 25, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
In this study, the binding of multimodal chromatographic ligands to the
IgG1 FC domain were studied using nuclear magnetic resonance and
molecular dynamics simulations. Nuclear magnetic resonance experiments
carried out with chromatographic ligands and a perdeuterated 15N-labeled
FC domain indicated that while single mode ion exchange ligands
interacted very weakly throughout the FC surface, multimodal ligands
interacted with specific clusters of residues with relatively high
affinity, forming distinct binding regions on the Fc. The multimodal
ligand binding sites on the FC were concentrated in the hinge region and
near the interface of the CH2 and CH3 domains. Further, the multimodal
binding sites were primarily composed of positively charged, polar and
aliphatic residues in these regions, with histidine residues exhibiting
some of the strongest binding affinities with the multimodal ligand.
Interestingly, comparison of protein surface property data with ligand
interaction sites indicated that the patch analysis on FC corroborated
molecular level binding information obtained from the nuclear magnetic
resonance experiments. Finally, molecular dynamics simulation results
were shown to be qualitatively consistent with the nuclear magnetic
resonance results and to provide further insights into the binding
mechanisms. An important contribution to multimodal ligand-FC binding in
these preferred regions was shown to be electrostatic interactions and
pi-pi stacking of surface exposed histidines with the ligands. This
combined biophysical and simulation approach has provided a deeper
molecular level understanding of multimodal ligand-FC interactions and
sets the stage for future analyses of even more complex biotherapeutics.%
\end{abstract}%



\sloppy


\section*{Introduction}

{\label{introduction}}

A range of multimodal (MM) chromatographic systems have been developed
which exhibit enhanced selectivity as compared to single mode
interaction resins due to a combination of electrostatic, hydrophobic,
aromatic and/or hydrogen bonding interactions within a single ligand (S.
C. Burton, Haggarty, \& Harding, 1997; Simon Christopher Burton \&
Harding, 1997; Cramer \& Holstein, 2011; Ghose, Hubbard, \& Cramer,
2005; Holstein, Parimal, McCallum, \& Cramer, 2012; Johansson et al.,
2003; Melander, El Rassi, \& Horv\selectlanguage{ngerman}áth, 1989). Further, new prototypes of
MM resins that vary in solvent exposure and presentation of functional
groups as well as those having differences in linker length and
chemistry have been shown to have unique windows of selectivity
(Robinson, Snyder, et al., 2018; J. A. Woo et al., 2015; J. Woo,
Parimal, Brown, Heden, \& Cramer, 2015). The utility of MM
chromatography has also been demonstrated for important industrial
applications such as the capture of mAbs and related formats (Arakawa,
Kita, Sato, \& Ejima, 2009; Gagnon et al., 2010; Kaleas, Tripodi,
Revelli, Sharma, \& Pizarro, 2014; Pezzini et al., 2011) as well as for
challenging polishing steps such as removal of product related variants,
fragments and aggregates (Chen et al., 2010; Liu, Ma, Winter, \& Bayer,
2010; O'Connor et al., 2017).

In order to design novel chromatographic ligands and to facilitate
process development for downstream bioprocessing, a deeper understanding
of protein binding regions with chromatographic systems is important.
Several groups have contributed to the understanding of protein
interactions in single mode interaction systems and some representative
examples are presented here. Roush et al. identified patches on rat
cytochrome b\textsubscript{5} for interaction with an anion exchange
surface using a series of computational and experimental studies (Roush,
Gill, \& Willson, 1994). Yao et al. investigated the distribution of
charges on the surface of cytochrome c and its variants and explained
the retention behavior on cation exchange systems (Yao \& Lenhoff,
2004). Sun et al. employed a computational approach to predict preferred
binding orientations in both cation exchange (CEX) and hydrophobic
interaction systems (Sun, Welsh, \& Latour, 2005). Dismer et al.
utilized a lysine specific fluorescent dye (Cy5) to identify the binding
orientation of lysozyme on a cation exchange surface under various
mobile phase conditions (Dismer \& Hubbuch, 2007; Dismer, Petzold, \&
Hubbuch, 2008). Our group has previously employed amino acid specific
covalent labeling in combination with mass spectrometry (MS) to examine
the binding regions of protein libraries generated from lysozyme and
cytochrome C in a cation exchange system (Chung, Evans, et al., 2010;
Chung, Holstein, et al., 2010). Kittelmann et al. recently developed
QSAR models for predicting binding orientation of antibodies on CEX
chromatographic surfaces (Kittelmann, Lang, Ottens, \& Hubbuch, 2017).

Studies have also been carried out on understanding preferred binding
regions of proteins in more complex systems such as hydrophobic charge
induction (HCIC) and MM CEX. Zhang et al. performed a series of
molecular dynamics (MD) simulations to study the changes in binding
orientation of a \selectlanguage{greek}\emph{β-} \selectlanguage{english}barrel protein on HCIC surface as a function
of salt concentration (Zhang, Zhao, \& Sun, 2009). Yu et al. employed
coarse-grained simulations to investigate the preferred binding
orientation of lysozyme on a HCIC surface at different ligand densities
under a range of salt concentrations (Yu, Liu, \& Zhou, 2015). Our lab
has been actively involved in studying the preferred binding regions of
small proteins in MM CEX systems by employing protein libraries (Chung,
Hou, et al., 2010), MD simulations (Banerjee, Parimal, \& Cramer, 2017;
Freed, Garde, \& Cramer, 2011; Parimal, Garde, \& Cramer, 2015, 2017),
Atomic Force Microscopy (AFM) (Srinivasan et al., 2017) and Nuclear
Magnetic Resonance (NMR) (Chung, Freed, et al., 2010; Holstein, Chung,
et al., 2012; Holstein, Parimal, McCallum, \& Cramer, 2013; Srinivasan,
Parimal, Lopez, McCallum, \& Cramer, 2014).

Ligand-induced chemical shift perturbations (CSP) have been widely used
to identify binding regions on proteins (Clarkson \& Campbell, 2003).
The sensitivity of the chemical shifts to changes in the local
environment enables the identification of ligand complexation at an
atomic level, while also being able to accurately determine the residue
level binding affinity (Hong et al., 2009; Lu, Guo, Jin, \& Xiao, 2009;
Williamson, 2013). Previous work in our group employed 2D heteronuclear
single quantum correlation (HSQC) NMR experiments to identify binding
sites of single mode and MM CEX ligands on a small model protein,
ubiquitin, and its mutants (Chung, Freed, et al., 2010; Holstein, Chung,
et al., 2012). NMR was also employed to evaluate the effects of urea on
preferred binding regions in MM systems (Holstein et al., 2013).
Further, we have employed MM functionalized gold nanoparticles in
solution to identify binding regions on ubiquitin using NMR (Srinivasan
et al., 2014). We have also employed NMR in concert with MD simulations
to obtain more detailed molecular level information on protein
interactions in multimodal systems (Holstein, Chung, et al., 2012).

While the understanding of small protein binding in multimodal
chromatographic systems is valuable, it is important to extend these
studies to more complex and industrially relevant biomolecules. One such
protein is the F\textsubscript{C} domain, which is highly conserved
across a given class of mAbs and which plays an important role in a
number of biotherapeutics such as bispecific antibodies and fusion
proteins (Shukla, Hubbard, Tressel, Guhan, \& Low, 2007). Robinson et
al. has examined the domain contributions of mAb binding using a
strategic set of chromatographic experiments and shown a shift in domain
dominance with pH and resin type (Robinson, Roush, \& Cramer, 2018,
2020). Gagnon et al. demonstrated that the binding of the
F\textsubscript{C} domain was driven by calcium affinity interactions in
hydroxyapatite (HA) chromatography (Gagnon, Cheung, \& Yazaki, 2009).
Lin et al. employed molecular simulations to identify preferred binding
sites of an HCIC ligand (MEP Hypercel) on single-chain
F\textsubscript{C} fragments (Lin, Tong, Wang, \& Yao, 2012). Even
though these studies have improved our understanding of
F\textsubscript{C} binding in MM systems, there is clearly a need to
develop a deeper understanding of these interactions at the molecular
level.

In the present study, we employ a combination of NMR and molecular
simulations to examine the interactions of chromatographic ligands with
the Fc. Transverse relaxation optimized spectroscopy
(\textsuperscript{15}N-TROSY) NMR titration experiments are carried out
using perdeuterated \textsuperscript{15}N-labeled F\textsubscript{C}with
both single mode and MM CEX ligands in free solution to identify primary
binding sites on the protein and to obtain residue specific binding
affinities to the ligands. We then examine the NMR results as they
compare to the protein surface property maps to develop a deeper
understanding of the relation between the binding regions and patches on
the protein surface. Finally, we employ MD simulations to provide
further insights into the intermolecular interactions and binding
mechanisms occurring with the F\textsubscript{C} in MM systems.

\section*{Materials \& Methods}

{\label{materials-methods}}

\subsection*{Materials}

{\label{materials}}

Perdeuterated \textsuperscript{15}N-labeled IgG1
F\textsubscript{C}domain (residues 1-228 corresponding to residues
220-447 in the IgG1) expressed in \emph{E. Coli} was provided by Merck
\& Co., Inc. (Kenilworth, NJ, 07033, USA). Disposable Zeba spin
desalting columns (7K MWCO, 0.5 mL) were purchased from Thermo Fisher
Scientific (Waltham, MA, 02451, USA). 1-propane sulfonic acid, 4-amino
hippuric acid, sodium acetate, acetic acid, sodium azide and
hydrochloric acid were purchased from Sigma-Aldrich (St. Louis, MO,
63103, USA). N-Benzoyl-dl-Methionine was purchased from Bachem Americas
Inc. (Torrance, CA, 90505, USA). Capto MMC chromatographic resin was
purchased from Cytiva (Uppsala, Sweden). Nuvia cPrime chromatographic
resin was donated by Bio-Rad Laboratories (Hercules, CA, 94547, USA).
Bruker\textsuperscript{TM}microbore NMR sample tubes were purchased from
Norell (Morganton, NC, 28680, USA). D\textsubscript{2}O was purchased
from Cambridge Isotope Laboratories, Inc. (Tewksbury, MA, 01876, USA).

\subsection*{Chromatography
Experiments}

{\label{chromatography-experiments}}

Chromatographic media were packed into a 5 x 50 mm column and
experiments were carried out on an \selectlanguage{ngerman}ÄKTA\selectlanguage{english} Explorer 100 (Cytiva, Upsella,
Sweden) controlled by UNICORN\selectlanguage{english} 5.1 software. The IgG1
F\textsubscript{C}domain was buffer-exchanged into buffer A (20 mM
sodium acetate, pH 5) using Zeba spin desalting columns and diluted with
buffer A to obtain a final protein concentration of 1 mg/mL. The
chromatographic columns were equilibrated with buffer A followed by a
100 \selectlanguage{greek}μ\selectlanguage{english}L pulse injection of the buffer-exchanged F\textsubscript{C}
solution. Bound protein was eluted with a linear salt gradient from
100\% buffer A to 100\% buffer B (20 mM sodium acetate, 1 M NaCl, pH 5)
over 40 column volumes (CV) at a flowrate of 1 CV/min. The column
effluent was monitored at 280 nm. The average of the first moments from
duplicate runs was used to determine the elution salt concentration.

\subsection*{Nuclear Magnetic Resonance
Experiments}

{\label{nuclear-magnetic-resonance-experiments}}

NMR spectra were obtained at 30\selectlanguage{ngerman}°C using a Bruker 800-MHz NMR
spectrometer equipped with
a\textsuperscript{1}H/\textsuperscript{15}N/\textsuperscript{13}C
cryoprobe with z-axis gradients. Data were acquired and processed using
TopSpin\selectlanguage{english} 3.2 software and the Sparky 3 software package (Goddard and
Kneller, University of California, San Francisco). Confirmation of the
backbone assignments was guided using published chemical shift values
(BMRB accession number 15514). Each sample had a constant protein
concentration of 0.12 mM in the NMR buffer (10 mM sodium acetate, pH
5.0, 10\% D\textsubscript{2}O and 0.02\% sodium azide). The ligands
employed in the NMR experiments to represent the SP Sepharose, Capto MMC
and Nuvia cPrime chromatographic resins are shown in Figure 1. A 1.0 M
stock solution of the SP Sepharose ligand (1-propane sulfonic acid) was
prepared in the NMR buffer. The Nuvia cPrime and Capto MMC ligands were
available as lyophilized powders and were dissolved in 0.12 mM
perdeuterated \textsuperscript{15}N-labeled protein solution prior to
titration. Due to the limited solubility of these ligands, the maximum
solution concentration of Nuvia cPrime and Capto MMC ligands was 60 and
3.2 mM, respectively. Since the commercial material for Capto MMC is
composed of immobilized enantiomers, a similar racemic mixture was used
in these solution-based NMR experiments.

Ligand-induced changes in chemical shift were recorded in a series
of\textsuperscript{15}N-TROSY experiments at a fixed
F\textsubscript{C}concentration (0.12 mM) and various
F\textsubscript{C}-ligand ratios (SP Sepharose, 1:1 to 1:800; Capto MMC,
1:0.5 to 1:25; and Nuvia cPrime, 1:0.5 to 1:320). Ligand-induced changes
in chemical shift were in fast exchange and at a population- weighted
average of the unbound and bound chemical shifts. The changes in
combined chemical shift (\selectlanguage{english}[?]\selectlanguage{greek}δ\selectlanguage{english}\textsubscript{NH}) upon ligand addition were
calculated using equation 1.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\delta_{\text{NH}}=\ \sqrt{\left(\delta_{H}\right)^{2}+\left(0.2*\delta_{N}\right)^{2}\ }\) & (1)\tabularnewline
\bottomrule
\end{longtable}

where \selectlanguage{greek}δ\selectlanguage{english}\textsubscript{H} and \selectlanguage{greek}δ\selectlanguage{english}\textsubscript{N} represent the change in
the chemical shift of the amide proton and nitrogen, respectively. A
weighting factor of 0.2 was employed to account for the difference in
sensitivity of proton and nitrogen chemical shifts of the amide group
(Rule \& Hitchens, 2005; Williamson, 2013). The binding dissociation
constant (K\textsubscript{D}) was calculated by fitting the changes
in\textsuperscript{1}H and \textsuperscript{15}N chemical shift as a
function of ligand concentration using the single-site binding model
(Rule \& Hitchens, 2005) as described in equation 2.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\delta_{\text{obs}}=\ \delta_{u}+\delta_{b}\frac{\left(K_{D}+\left[L\right]_{T}+[{P]}_{T}\right)-\ \sqrt{{(K_{D}+\left[L\right]_{T}+[{P]}_{T})}^{2}-(4*\left[L\right]_{T}[{P]}_{T})\ }}{2*[{P]}_{T}}\) & (2)\tabularnewline
\bottomrule
\end{longtable}

where K\textsubscript{D} is the apparent binding dissociation constant,
{[}L{]}\textsubscript{T} and {[}P{]}\textsubscript{T} are the total
ligand and protein concentrations used in the experiment and
[?]\selectlanguage{greek}δ\selectlanguage{english}\textsubscript{obs} is the observed change in chemical shift upon
ligand addition. [?]\selectlanguage{greek}δ\selectlanguage{english}\textsubscript{u} and [?]\selectlanguage{greek}δ\selectlanguage{english}\textsubscript{b} represent
the changes in chemical shift for the unbound and bound states,
respectively. Based on the K\textsubscript{D} 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 (Schr\selectlanguage{ngerman}ödinger).

\subsection*{Protein Surface
Properties}

{\label{protein-surface-properties}}

A structural model for the IgG1 F\textsubscript{C} domain was built by
homology modeling starting with the crystal structure for an
aglycosylated human IgG1 F\textsubscript{C} 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).

\subsection*{Molecular Dynamics
Simulations}

{\label{molecular-dynamics-simulations}}

MD simulations were performed with the two MM CEX ligands, Capto MMC and
Nuvia cPrime in free solution around the F\textsubscript{C} 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
F\textsubscript{C} 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/nm\textsuperscript{2} (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 F\textsubscript{C} 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\textsuperscript{-5} (consistent with default
parameters).

\section*{Results and Discussion}

{\label{results-and-discussion}}

\subsection*{\texorpdfstring{Chromatographic retention of the
F\textsubscript{C}domain}{Chromatographic retention of the FCdomain}}

{\label{chromatographic-retention-of-the-fc-domain}}

The linear salt gradient elution behavior of the IgG1
F\textsubscript{C}domain was evaluated on a CEX resin (SP Sepharose) and
two MM CEX systems (Capto MMC and Nuvia cPrime) and the resulting
elution salt concentrations are presented in Figure 3. As can be seen,
the F\textsubscript{C} domain was weakly retained on the CEX resin,
eluting at 0.12 M NaCl in the gradient. In contrast, the
F\textsubscript{C}domain exhibited significantly stronger retention on
the two MM CEX systems with 0.63 and 0.9 M NaCl required for the elution
from the Nuvia cPrime and Capto MMC resins, respectively. The higher
retention on Capto MMC as compared to Nuvia cPrime could be due to the
more solvent exposed aromatic moiety on the Capto ligand (Robinson,
Roush, et al., 2018; J. Woo et al., 2015). Further, the elevated salt
elution concentration seen in the MM resins as compared to the single
mode CEX system is likely due to more complex interactions occurring
with the F\textsubscript{C}domain. In order to gain further insight into
the interaction sites and binding mechanisms between these ligands and
the F\textsubscript{C}, TROSY titration experiments and MD simulations
were carried out.

\subsection*{NMR Chemical Shift Perturbation
Experiments}

{\label{nmr-chemical-shift-perturbation-experiments}}

The binding of individual chromatographic ligands to the
F\textsubscript{C} in solution was evaluated using NMR spectroscopy with
a perdeuterated \textsuperscript{15}N-labeled F\textsubscript{C}. The
ligands employed to represent the SP Sepharose, Capto MMC and Nuvia
cPrime resins are shown in Figure 1. As described in the Methods
section, ligands were titrated against a fixed concentration of the
labeled F\textsubscript{C} and the binding was monitored via the
resulting \textsuperscript{15}N-TROSY spectra. In the NMR spectra, the
amide groups on the \textsuperscript{15}N-labeled amide backbone of the
F\textsubscript{C} that were in close proximity to ligands were observed
to experience a change in the local electronic environment resulting in
chemical shift perturbations (CSPs). In the
resulting\textsuperscript{15}N-TROSY spectra, a single resonance peak
was observed for both the unbound and bound state of the protein for
each amide group. Thus, the observed peak was a population weighted
average of the two states and is defined by equation 3.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\delta_{\text{obs}}=\ f_{u}\delta_{u}+f_{b}\delta_{b}\) & (3)\tabularnewline
\bottomrule
\end{longtable}

where f\textsubscript{u} and f\textsubscript{b} are the fractions of the
unbound and bound protein, respectively, and \selectlanguage{greek}δ\selectlanguage{english}\textsubscript{u} and
\selectlanguage{greek}δ\selectlanguage{english}\textsubscript{b} are the chemical shift values of the unbound and
bound states of the protein. The linewidths were largely free of
exchange broadening and had ligand-dependent chemical shift values
similar to those without ligands. This was indicative of `fast-exchange'
behavior for protein-ligand interactions. The changes in combined
(\textsuperscript{1}H and \textsuperscript{15}N) chemical shift
([?]\selectlanguage{greek}δ\selectlanguage{english}\textsubscript{NH}) were then calculated using equation 1.

An important first step towards binding analysis was to evaluate the
CSPs for all the residues in the protein sequence. Accordingly, the
plots of the observed CSPs at the highest concentrations of the SP
Sepharose, Capto MMC and Nuvia cPrime ligands are presented in Figures
4a, b \& c, respectively (note: the Fc residues 1-228 correspond to the
IgG1 residues 220-447).The secondary structural elements of the
F\textsubscript{C} sequence are also shown at the bottom of Figure 4a.
The data were analyzed using the statistical method described by
Schumann et al. (Schumann et al., 2007) to determine the corrected
standard deviation \selectlanguage{greek}σ\selectlanguage{english}\textsubscript{0}. The residues with CSPs smaller
than \selectlanguage{greek}σ\selectlanguage{english}\textsubscript{0} were grouped as non-interacting (noise) and are
presented as grey bars in the Figures. Residues exhibiting large CSPs
are represented in red bars while residues with intermediate changes are
shown in a red-grey color gradient. As can be seen in Figure 4a, for
interactions of the SP Sepharose ligand to the F\textsubscript{C},
residues that experienced large changes in CSPs were spread across the
entire protein sequence and did not group into a specific region. In
addition, residues that exhibited intermediate changes were not
localized around residues that showed large CSPs. In contrast to the
single mode CEX ligand results, both the large and intermediate CSPs
associated with the binding of MM CEX ligands were clearly clustered in
specific regions in the F\textsubscript{C} sequence (Figures 4b \& c).
Interestingly, the residues experiencing these CSPs were primarily
located in clusters associated with more flexible regions of the
protein. For example, by comparing these data with the secondary
structural elements of the F\textsubscript{C}, it can be seen that the
clusters observed near residues 29-38 and 87-98 (Figures 4b \& c) were
associated with either loops or a combination of loops and \selectlanguage{greek}α-\selectlanguage{english}helices.
While the CSPs for the CEX and MM CEX systems were quite different, the
changes within the MM CEX systems for Capto MMC and Nuvia cPrime were
very similar. This was quantified by the Pearson correlation coefficient
which was calculated to be 0.15 \selectlanguage{ngerman}± 0.03 for the CEX and each of the MM
CEX systems and 0.85 for the Capto MMC and Nuvia cPrime systems (Figure
S1).

To further visualize these ligand-induced changes in combined chemical
shift, the CSPs for the residues were visualized on the protein surface
using the PyMol viewer. A cartoon and a surface representation of these
results for the three ligands studied are presented in Figures 5a and 6,
respectively. To facilitate the discussion, the color schemes used in
these figures are the same employed in Figure 4. As can be seen in
Figure 5a, for interactions of the SP Sepharose ligand with the
F\textsubscript{C}, residues that exhibited large and intermediate CSPs
were spread across the entire protein surface. Further, as expected for
a cation exchange ligand such as SP Sepharose, the residues that
experienced CSPs were often associated with positively charged (blue
colored) regions on the electrostatic potential (EP) map of the
F\textsubscript{C} shown in Figure 5b.

In contrast, the results for binding of the Capto MMC and Nuvia cPrime
ligands with the F\textsubscript{C}, indicated a more focused
interaction region as highlighted by the dotted blue ellipses of Figures
6a and b, respectively. Interestingly, the residues that interacted with
the MM ligands and were present in the flexible loops and alpha helices
(as discussed above for Figure 4) were located in the interface of the
C\textsubscript{H}2 and C\textsubscript{H}3 domains. Further, residues
that experienced ligand-induced CSPs were mostly identified to be
positively charged and/or aliphatic or aromatic in nature. In order to
examine this in more detail, the focused interaction region for the MM
ligands was also indicated on the EP and SAP maps presented in Figure 5b
and c. As can be seen in the figures, this region was associated with
both positive EP and some hydrophobicity which is expected for the
interactions of multimodal ligands (Karkov, Woo, Krogh, Ahmadian, \&
Cramer, 2015).

Interpretation of the CSP data does come with a few caveats. For
example, residues that are in close proximity of those directly
interacting with the ligands may also undergo significant changes in
chemical shift. In addition, residues interacting with a ligand may not
experience significant changes in electronic environment and thus may
not have a measurable CSP. In order to address these issues, the changes
in combined chemical shift during the titration experiments were
examined in more detail.

A few representative spectral overlays for the binding of the Nuvia
cPrime ligand to F\textsubscript{C} are presented in Figure 7 and the
corresponding CSPs as a function of ligand concentration are shown in
Figure S2. As can be seen in the figures, different trajectories of the
CSPs were observed with increasing ligand concentration for each of the
residues. For example, residue Asp 182 (Figures 7a and S2a) did not
exhibit any significant shift with increasing ligand concentration,
indicating that it likely did not participate in binding. For residues
that did show measurable CSPs, we observed primarily linear migrations
with both saturated and unsaturated behavior. As can be seen in Figures
7b and S2b, Val 178 exhibited linear migration without saturation, which
could be due to non-specific and/or weak interactions of the ligand with
this residue. On the other hand, for His 66 (Figures 7c \& S2c), a
saturating linear trajectory was observed which was indicative of a
simple two-state binding behavior that could be readily fit to the
Langmuir equation (equation 2) to determine the binding dissociation
constant (K\textsubscript{D}).

The CSP data at different ligand concentrations for all the
F\textsubscript{C} residues were fit to equation 2 using Matlab R2019b
with a maximum fitting error of 10\% in a 95\% confidence interval. For
interactions of the SP Sepharose ligand with the F\textsubscript{C},
residues that showed saturation behavior exhibited high
K\textsubscript{D} values (\textgreater{} 150 mM) which were indicative
of very weak interactions. Further, the SP Sepharose ligand was observed
to interact throughout the F\textsubscript{C} surface without clustering
into specific regions (results not shown).

Due to solubility constraints with the Capto MMC ligand (\selectlanguage{english}[?] 3.2 mM at pH
5), the K\textsubscript{D} determination with the multimodal ligands was
limited to the more soluble Nuvia cPrime ligand. The CSP data at
different Nuvia cPrime ligand concentrations for all the
F\textsubscript{C} residues were fit to equation 2 to determine the
residue specific K\textsubscript{D} values which are presented in Table
S1. Based on the maximum solubility of the Nuvia cPrime ligand (60 mM at
pH 5), only K\textsubscript{D} values below 40mM were able to be
accurately determined. As can be seen in the Table, the resulting
K\textsubscript{D} values were up to two orders of magnitude smaller
than those observed with the single mode SP Sepharose ligand. These
results qualitatively agree with the marked differences observed in the
elution salt concentrations, 0.12 and 0.63 M NaCl, for
F\textsubscript{C} in SP Sepharose and Nuvia cPrime chromatographic
systems, respectively.

The F\textsubscript{C} residues that exhibited saturation behavior for
interactions with the Nuvia cPrime ligand were color coded based on
their K\textsubscript{D} values and the resulting projections on the
protein surface are presented in Figure 8. As can be seen in the Figure,
residues interacting with a ``high'' binding affinity (1.2 \selectlanguage{english}[?]
K\textsubscript{D} \selectlanguage{english}[?] 10 mM) were primarily located in the hinge region
(green ellipse) and near the interface of the C\textsubscript{H}2 and
C\textsubscript{H}3 domains (blue ellipse) (note: these regions are the
same as those in Figure 6 which were based on the CSPs). The strong
interactions with a cluster of positively charged (His 66, His 5, Lys 3
and Lys 55) and polar (Thr 4, Thr 6 and Cys 7) residues in the hinge
region is indicative of this being a preferred binding region for the
ligand. However, it is important to note that interactions observed near
the flexible hinge region may be due to direct participation of the
residues in ligand binding and/or NMR shifts due to ligand binding
induced conformational changes in that region of the F\textsubscript{C}.
Further, while the hinge region was identified by NMR as a preferred
binding region for the ligand, steric affects would likely impact ligand
interactions with the F\textsubscript{C} when present in an intact mAb
and/or Fc fusion proteins.

As was observed with the CSP data (Figure 6), the
K\textsubscript{D}results also indicated that the interface of the
C\textsubscript{H}2 and C\textsubscript{H}3 domains was an important
preferred binding region for interacting with the Nuvia cPrime ligand
(Figure 8). Residues involved in binding to the Nuvia cPrime ligand in
this region are indicated in Table S1 with a \#. As can be seen in the
table, this contiguous MM ligand binding region was composed of
positively charged (His 214, Arg 36, His 210 and His 91), polar (Asn
215, Gln 219, Thr 31, Thr 218, Thr 37, Gln 92, Ser 221, Ser 35 and Gly
166) and aliphatic (Leu 32, Ile 34, Ala 159, Val 160 and Met 33)
residues. In this region, residue 214H interacted with one of the lowest
K\textsubscript{D} values (3.94 +- 2.1 mM), indicating relatively strong
binding to the ligand. Interestingly, this histidine residue has also
been shown to be one of the most important residues for binding of the
F\textsubscript{C}portion of IgG1 mAbs to Protein A resins (Idusogie et
al., 2000; Moiani et al., 2009). As can be seen in Table S1, a few
negatively charged residues (e.g. Glu 211 and Asp 93) also exhibited NMR
shifts which may be due to their proximity to the clusters of positively
charged and polar residues discussed above.

As was discussed above with the CSP results, this preferred binding
region at the interface of the C\textsubscript{H}2 and
C\textsubscript{H}3 domains (indicated by the blue ellipse) corresponded
to an overlapping region of positive EP and hydrophobicity (Figures 5b
and c). The fact that the K\textsubscript{D} results presented in Figure
8 are even more focused in this region lends further support to the
importance of both types of interactions in MM systems.

\subsection*{Molecular Dynamics
Simulations}

{\label{molecular-dynamics-simulations-1}}

The NMR experiments described so far provide a window into
protein-multimodal ligand interactions on a molecular level. While NMR
experiments yield molecularly-detailed data, they are time- and
resource-intensive making it difficult to quickly apply these tools to a
wide range of systems. In order to more deeply investigate the
F\textsubscript{C}-ligand interactions at the molecular level and to
explore some of the docked conformations of the Nuvia cPrime ligands, we
carried out MD simulations. As described in the Methods section,
simulations were performed with multiple ligand copies in free solution
with the protein, and throughout the simulation ligands were free to
reversibly interact from the protein surface. The free energy of a
ligand binding to a given region of the protein surface was calculated
as:\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(G_{\text{binding}}=-k_{B}\text{Tln}\left(\frac{\rho_{\text{bound}}}{\rho_{\text{bulk}}}\right)\) & (4)\tabularnewline
\bottomrule
\end{longtable}

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 1\selectlanguage{ngerman}Å spacing around the protein.

Figure 9 shows the free energy plotted on the surface of the
F\textsubscript{C}. As can be seen, the Nuvia cPrime ligands had a
strong tendency to bind to the interface between the C\textsubscript{H}2
and C\textsubscript{H}3 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
C\textsubscript{H}2-C\textsubscript{H}3 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 F\textsubscript{C} binding sites for
interactions with the C1q and FcRgIII receptors. In the
C\textsubscript{H}2-C\textsubscript{H}3 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.

\section*{Conclusions}

{\label{conclusions}}

In this paper, a combination of NMR and MD simulations was employed to
develop a fundamental understanding of how single mode CEX and MM CEX
chromatographic ligands interact with the F\textsubscript{C} domain of
an IgG1 mAb. The NMR results provided insights into the interaction
sites of these ligands on the F\textsubscript{C}. Preliminary data
analysis of the NMR results based on CSPs revealed that, while the
single mode ligand interacted across the entire
F\textsubscript{C}surface, the MM ligands appeared to interact with
specific clusters of residues forming a concentrated binding region. In
order to obtain more quantitative information, the CSP data at different
ligand concentrations for each F\textsubscript{C} residue were fit to
the Langmuir equation to determine the residue specific binding
dissociation constants (K\textsubscript{D}). While the single mode CEX
ligand showed weak interactions over the F\textsubscript{C} surface with
high K\textsubscript{D} values (\textgreater{} 150 mM), the Nuvia cPrime
MM ligand exhibited up to two orders of magnitude smaller
K\textsubscript{D} values indicating significantly stronger binding to
the F\textsubscript{C}. The MM ligand binding sites on the
F\textsubscript{C} were concentrated in the hinge region and near the
interface of the C\textsubscript{H}2 and C\textsubscript{H}3 domains
which are relatively flexible regions of the F\textsubscript{C}. These
sites were also observed to consist of primarily positively charged,
polar and aliphatic residues on the F\textsubscript{C} surface.
Interestingly, histidine residues in these regions exhibited some of the
strongest binding to the MM ligand. Comparisons of the NMR results with
protein surface properties suggested that the MM ligand binding regions
were associated with overlapping regions of positive charge and
hydrophobicity on the F\textsubscript{C} surface. Finally, we presented
MD simulations to provide further insights into the binding mechanisms
these interactions. As was determined from the NMR analysis, the
simulations also indicated that the histidine residues in the interface
of the C\textsubscript{H}2 and C\textsubscript{H}3 domains were ``high
affinity'' binders. The simulations also indicated that these histidines
interacted with the MM ligands via electrostatic and pi-pi interactions.

This combined biophysical and simulations approach elucidates the MM
ligand interaction sites on the F\textsubscript{C} and sets the stage
for future analyses of even more complex biotherapeutics such as Fabs
and mAbs. While the current work was focused on only two MM ligands,
this method can readily be extended to other MM ligands that have been
recently shown to exhibit unique chromatographic selectivities for the
separation of complex multi-domain proteins (Robinson, Roush, 2018). The
molecular insights gained from this work can also potentially lead to
new protein molecular descriptors that may be useful for predicting the
multimodal chromatographic behavior of F\textsubscript{C} containing
molecules such as mAbs, bispecific Abs and fusion proteins. Future work
will also examine the interactions of the Fc with MM ligand-coated
nanoparticles in order to more fully account for co-operativity and
avidity effects in these systems.

\section*{Acknowledgements}

{\label{acknowledgements}}

This work was supported by the National Science Foundation (Grant number
CBET 1704745) as well as the ASC Graduate Fellowship Program from
Lawrence Livermore National Laboratory, Merck \& Co., Inc. (Kenilworth,
NJ, 07033, USA).and Bio-Rad laboratories (Hercules, CA, 94547, USA).
Work at the Lawrence Livermore National Laboratory (LLNL) was performed
under the auspices of the U.S. Department of Energy by Lawrence
Livermore National Laboratory under Contract DE-AC52-07NA27344.

\section*{References}

{\label{references}}

Arakawa, T., Kita, Y., Sato, H., \& Ejima, D. (2009). MEP chromatography
of antibody and Fc-fusion protein using aqueous arginine
solution.\emph{Protein Expression and Purification} , \emph{63} (2),
158--163. https://doi.org/10.1016/j.pep.2008.09.011

Baker, N. A., Sept, D., Joseph, S., Holst, M. J., \& Andrew McCammon, J.
(2001). \emph{Electrostatics of nanosystems: Application to microtubules
and the ribosome.} \emph{Proceedings of the National Academy of
Sciences, 98(18)} , 10037-10041. https://doi.org/10.1073/pnas.181342398.

Banerjee, S., Parimal, S., \& Cramer, S. M. (2017). A molecular modeling
based method to predict elution behavior and binding patches of proteins
in multimodal chromatography. \emph{Journal of Chromatography A}
,\emph{1511} , 45--58. https://doi.org/10.1016/j.chroma.2017.06.059

Bas, D. C., Rogers, D. M., \& Jensen, J. H. (2008). Very fast prediction
and rationalization of pK a values for protein2ligand
complexes.\emph{Proteins} , \emph{73} (3), 765--783.
https://doi.org/10.1002/prot.22102

Bayly, C. I., Cieplak, P., Cornell, W. D., \& Kollman, P. A.
(1993).\emph{A Well-Behaved Electrostatic Potential Based Method Using
Charge Restraints for Deriving Atomic Charges: The RESP Model} .
\emph{The Journal of Physical Chemistry, 97,} 10269-10280.

Bilodeau, C. L., Lau, E. Y., Cramer, S. M., \& Garde, S. (2019).
Conformational Equilibria of Multimodal Chromatography Ligands in Water
and Bound to Protein Surfaces. \emph{Journal of Physical Chemistry B,
123,} 4833-4843. https://doi.org/10.1021/acs.jpcb.9b01218

Burton, S. C., Haggarty, N. W., \& Harding, D. R. K. (1997). One step
purification of chymosin by mixed mode
chromatography.\emph{Biotechnology and Bioengineering} , \emph{56} (1),
45--55.
https://doi.org/10.1002/(SICI)1097-0290(19971005)56:1\textless{}45::AID-BIT5\textgreater{}3.0.CO;2-V

Burton, Simon Christopher, \& Harding, D. R. K. (1997). High-density
ligand attachment to brominated allyl matrices and application to mixed
mode chromatography of chymosin. \emph{Journal of Chromatography A}
,\emph{775} (1--2), 39--50.
https://doi.org/10.1016/S0021-9673(97)00515-3

Cheatham, T. E., Cieplak, P., \& Kollman, P. A. (1999). A Modified
Version of the Cornell et al. Force Field with Improved Sugar Pucker
Phases and Helical Repeat. \emph{Journal of Biomolecular Structure and
Dynamics} , \emph{16} (4), 845--862.
https://doi.org/10.1080/07391102.1999.10508297

Chen, J., Tetrault, J., Zhang, Y., Wasserman, A., Conley, G., DiLeo, M.,
\ldots{} Ley, A. (2010). The distinctive separation attributes of
mixed-mode resins and their application in monoclonal antibody
downstream purification process. \emph{Journal of Chromatography A}
,\emph{1217} (2), 216--224. https://doi.org/10.1016/J.CHROMA.2009.09.047

Chennamsetty, N., Voynov, V., Kayser, V., Helk, B., \& Trout, B. L.
(2010). Prediction of Aggregation Prone Regions of Therapeutic
Proteins.\emph{Journal of Physical Chemistry B, 114,} 6614--6624.
https://doi.org/10.1021/jp911706q

Chung, W. K., Evans, S. T., Freed, A. S., Keba, J. J., Baer, Z. C.,
Rege, K., \& Cramer, S. M. (2010). Utilization of lysozyme charge
ladders to examine the effects of protein surface charge distribution on
binding affinity in ion exchange systems. \emph{Langmuir} , \emph{26}
(2), 759--768. https://doi.org/10.1021/la902135t

Chung, W. K., Freed, A. S., Holstein, M. A., Mccallum, S. A., Cramer, S.
M., Designed, S. M. C., \& Performed, M. A. H. (2010). Evaluation of
protein adsorption and preferred binding regions in multimodal
chromatography using NMR. \emph{Proceedings of the National Academy of
Sciences, 107(39)} , 16811--16816.
https://doi.org/10.1073/pnas.1002347107

Chung, W. K., Holstein, M. A., Freed, A. S., Evans, S. T., Baer, Z. C.,
\& Cramer, S. M. (2010). Ion exchange chromatographic behavior of a
homologous cytochrome C variant library obtained by controlled
succinylation. \emph{Separation Science and Technology} , \emph{45}
(15), 2144--2152. https://doi.org/10.1080/01496395.2010.507432

Chung, W. K., Hou, Y., Holstein, M., Freed, A., Makhatadze, G. I., \&
Cramer, S. M. (2010). Investigation of Protein Binding Affinity and
Preferred Orientations in Ion Exchange Systems Using a Homologous
Protein Library. \emph{Journal of Chromatography A} , \emph{1217} (2),
191--198. https://doi.org/10.1016/j.chroma.2009.08.005

Clarkson, J., \& Campbell, I. D. (2003). Studies of protein-ligand
interactions by NMR. \emph{Biochemical Society Transactions} ,\emph{31}
(Pt 5), 1006--1009. https://doi.org/10.1042/

Cramer, S. M., \& Holstein, M. A. (2011). Downstream bioprocessing:
recent advances and future promise. \emph{Current Opinion in Chemical
Engineering} , \emph{1} , 27--37.
https://doi.org/10.1016/j.coche.2011.08.008

Darden, T., York, D., \& Pedersen, L. (1993). Particle mesh Ewald: An
N\&sdot;log(N) method for Ewald sums in large systems. \emph{The Journal
of Chemical Physics} , \emph{98} , 5648.
https://doi.org/10.1063/1.464397

Dismer, F., \& Hubbuch, J. (2007). A novel approach to characterize the
binding orientation of lysozyme on ion-exchange resins. \emph{Journal of
Chromatography A} , \emph{1149} , 312--320.
https://doi.org/10.1016/j.chroma.2007.03.074

Dismer, F., Petzold, M., \& Hubbuch, J. (2008). Effects of ionic
strength and mobile phase pH on the binding orientation of lysozyme on
different ion-exchange adsorbents. \emph{Journal of Chromatography A}
,\emph{1194} (1), 11--21. https://doi.org/10.1016/J.CHROMA.2007.12.085

Evans, D. J., \& Holian, B. L. (1985). The Nose-Hoover
thermostat.\emph{The Journal of Chemical Physics} , \emph{83} (8),
4069--4074. https://doi.org/10.1063/1.449071

Freed, A. S., Garde, S., \& Cramer, S. M. (2011). Molecular simulations
of multimodal ligand-protein binding: Elucidation of binding sites and
correlation with experiments. \emph{Journal of Physical Chemistry B}
,\emph{115} (45), 13320--13327. https://doi.org/10.1021/jp2038015

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, G. and N. (2009). Gaussian 09, Revision a. 02.\emph{Gaussian.
Inc., Wallingford, CT} , \emph{200} . Retrieved from
https://gaussian.com/g09citation/

Gagnon, P., Cheung, C.-W., Lepin, E. J., Wu, A. M., Sherman, M. A.,
Raubitschek, A. A., \& Yazaki Pete Gagnon, P. J. (2010).\emph{Minibodies
and Multimodal Chromatography Methods: A Convergence of Challenge and
Opportunity} . \emph{Bioprocess International} 8(2), 26-35.

Gagnon, P., Cheung, C., \& Yazaki, P. J. (2009). Cooperative multimodal
retention of IgG , fragments , and aggregates on
hydroxyapatite.\emph{Journal of Separation Science, 32} , 3857--3865.
https://doi.org/10.1002/jssc.200900055

Ghose, S., Hubbard, B., \& Cramer, S. M. (2005). Protein interactions in
hydrophobic charge induction chromatography (HCIC). \emph{Biotechnology
Progress} , \emph{21} (2), 498--508. https://doi.org/10.1021/bp049712+

Hess, B., Kutzner, C., Van Der Spoel, D., \& Lindahl, E. (2008). GROMACS
4: Algorithms for Highly Efficient, Load-Balanced, and Scalable
Molecular Simulation. \emph{Journal of Chemical Theory and Computation,
4,} 435-447. https://doi.org/10.1021/ct700301q

Holstein, M. A., Chung, W. K., Parimal, S., Freed, A. S., Barquera, B.,
McCallum, S. A., \& Cramer, S. M. (2012). Probing multimodal ligand
binding regions on ubiquitin using nuclear magnetic resonance,
chromatography, and molecular dynamics simulations. \emph{Journal of
Chromatography A} , \emph{1229} , 113--120.
https://doi.org/10.1016/j.chroma.2011.12.101

Holstein, M. A., Parimal, S., McCallum, S. A., \& Cramer, S. M. (2012).
Mobile phase modifier effects in multimodal cation exchange
chromatography. \emph{Biotechnology and Bioengineering} , \emph{109}
(1), 176--186. https://doi.org/10.1002/bit.23318

Holstein, M. A., Parimal, S., McCallum, S. A., \& Cramer, S. M. (2013).
Effects of urea on selectivity and protein-ligand interactions in
multimodal cation exchange chromatography. \emph{Langmuir} ,\emph{29}
(1), 158--167. https://doi.org/10.1021/la302360b

Hong, Y.-H., Ahn, H.-C., Lim, J., Kim, H.-M., Ji, H.-Y., Lee, S.,
\ldots{} Lee, B.-J. (2009). Identification of a novel ubiquitin binding
site of STAM1 VHS domain by NMR spectroscopy. \emph{FEBS Letters}
,\emph{583} (2), 287--292. https://doi.org/10.1016/j.febslet.2008.12.034

Idusogie, E. E., Presta, L. G., Totpal, K., Wong, P. Y., Meng, Y. G., \&
Mulkerrin, M. G. (2000). Mapping of the C1q Binding Site on Rituxan, a
Chimeric Antibody with a Human IgG1 Fc. \emph{Journal of Immunology}
,\emph{164} , 4178--4184. https://doi.org/10.4049/jimmunol.164.8.4178

Johansson, B.-L., Belew, M., Eriksson, S., Glad, G., Lind, O., Maloisel,
J.-L., \& Norrman, N. (2003). Preparation and characterization of
prototypes for multi-modal separation media aimed for capture of
negatively charged biomolecules at high salt conditions. \emph{Journal
of Chromatography A} , \emph{1016} , 21--33.
https://doi.org/10.1016/S0021-9673(03)01140-3

Jorgensen, W. L. (1981). Transferable Intermolecular Potential Functions
for Water, Alcohols, and Ethers. Application to Liquid
Water1.\emph{Journal of American Chemical Society, 103,} 335-340.

Kaleas, K. A., Tripodi, M., Revelli, S., Sharma, V., \& Pizarro, S. A.
(2014). Evaluation of a multimodal resin for selective capture of
CHO-derived monoclonal antibodies directly from harvested cell culture
fluid. \emph{Journal of Chromatography B} , \emph{969} , 256--263.
https://doi.org/10.1016/j.jchromb.2014.08.026

Karkov, H. S., Woo, J., Krogh, B. O., Ahmadian, H., \& Cramer, S. M.
(2015). Evaluation of selectivity in homologous multimodal
chromatographic systems using in silico designed antibody fragment
libraries. \emph{Journal of Chromatography A} , \emph{1426} , 102--109.
https://doi.org/10.1016/j.chroma.2015.11.047

Kittelmann, J., Lang, K. M. H., Ottens, M., \& Hubbuch, J. (2017).
Orientation of monoclonal antibodies in ion-exchange chromatography: A
predictive quantitative structure--activity relationship modeling
approach. \emph{Journal of Chromatography A} , \emph{1510} , 33--39.
https://doi.org/10.1016/j.chroma.2017.06.047

Lin, D.-Q., Tong, H.-F., Wang, H.-Y., \& Yao, S.-J. (2012). Molecular
Insight into the Ligand\selectlanguage{english}-IgG Interactions for 4-Mercaptoethyl-pyridine
Based Hydrophobic Charge-Induction Chromatography. \emph{Journal of
Physical Chemistry B, 116,} 1393-1400. https://doi.org/10.1021/jp206817b

Liu, H. F., Ma, J., Winter, C., \& Bayer, R. (2010). mAbs Recovery and
purification process development for monoclonal antibody
production.\emph{MAbs} , \emph{2} (5), 480--499.
https://doi.org/10.4161/mabs.2.5.12645

Lu, R. C., Guo, X. R., Jin, C., \& Xiao, J. X. (2009). NMR studies on
binding sites and aggregation-disassociation of fluorinated surfactant
sodium perfluorooctanoate on protein ubiquitin. \emph{Biochimica et
Biophysica Acta - General Subjects} , \emph{1790} (2), 134--140.
https://doi.org/10.1016/j.bbagen.2008.10.009

Melander, W. R., El Rassi, Z., \& Horvath, C. (1989). Interplay of
hydrophobic and electrostatic interactions in biopolymer
chromatography\selectlanguage{english} : Effect of salts on the retention of
proteins.\emph{Journal of Chromatography A} , \emph{469} , 3--27.
https://doi.org/10.1016/S0021-9673(01)96437-4

Moiani, D., Salvalaglio, M., Cavallotti, C., Bujacz, A., Redzynia, I.,
Bujacz, G., \ldots{} Fassina, G. (2009). Structural Characterization of
a Protein A Mimetic Peptide Dendrimer Bound to Human IgG. \emph{Journal
of Physical Chemistry B} , \emph{113} (50), 16268--16275.
https://doi.org/10.1021/jp909405b

O'Connor, E., Aspelund, M., Bartnik, F., Berge, M., Coughlin, K.,
Kambarami, M., \ldots{} Wang, W. (2017). Monoclonal antibody fragment
removal mediated by mixed mode resins. \emph{Journal of Chromatography
A} , \emph{1499} , 65--77. https://doi.org/10.1016/j.chroma.2017.03.063

Parimal, S., Garde, S., \& Cramer, S. M. (2015). Interactions of
Multimodal Ligands with Proteins: Insights into Selectivity Using
Molecular Dynamics Simulations. \emph{Langmuir, 31,} 7512-7523.
https://doi.org/10.1021/acs.langmuir.5b00236

Parimal, S., Garde, S., \& Cramer, S. M. (2017). Effect of guanidine and
arginine on protein--ligand interactions in multimodal cation-exchange
chromatography. \emph{Biotechnology Progress} , \emph{33} (2), 435--447.
https://doi.org/10.1002/btpr.2419

Parinello, M. and Rahman, A. (1980). Crystal Structure and Pair
Potentials: A Molecular-Dynamics Study, \emph{The American Physical
Society, 45(14),} 1--22.

Pezzini, J., Joucla, G., Gantier, R., Toueille, M., Lomenech, A. M., Le
Senechal, C., \ldots{} Cabanne, C. (2011). Antibody capture by
mixed-mode chromatography: A comprehensive study from determination of
optimal purification conditions to identification of contaminating host
cell proteins. \emph{Journal of Chromatography A} , \emph{1218} (45),
8197--8208. https://doi.org/10.1016/j.chroma.2011.09.036

Pronk, S., Pall, S., Schulz, R., Larsson, P., Bjelkmar, P., Apostolov,
R., \ldots{} Lindahl, E. (2013). GROMACS 4.5: A high-throughput and
highly parallel open source molecular simulation
toolkit.\emph{Bioinformatics} , \emph{29} (7), 845--854.
https://doi.org/10.1093/bioinformatics/btt055

Robinson, J., Roush, D., \& Cramer, S. (2018). Domain contributions to
antibody retention in multimodal chromatography systems. \emph{Journal
of Chromatography A} , \emph{1563} , 89--98.
https://doi.org/10.1016/j.chroma.2018.05.058

Robinson, J., Roush, D., \& Cramer, S. M. (2020). The effect of pH on
antibody retention in multimodal cation exchange chromatographic
systems. \emph{Journal of Chromatography A} , \emph{1617} , 460838.
https://doi.org/10.1016/j.chroma.2019.460838

Robinson, J., Snyder, M. A., Belisle, C., Liao, J., Chen, H., He, X.,
\ldots{} Cramer, S. M. (2018). Investigating the impact of aromatic ring
substitutions on selectivity for a multimodal anion exchange prototype
library. \emph{Journal of Chromatography A} , \emph{1569} , 101--109.
https://doi.org/10.1016/J.CHROMA.2018.07.049

Roush, D. J., Gill, D. S., \& Willson, R. C. (1994). \emph{Electrostatic
Potentials and Electrostatic Interaction Energies of Rat Cytochrome b5
and a Simulated Anion-Exchange Adsorbent Surface.} \emph{Biophysical
Journal, 66,} 1290-1300. https://doi.org/10.1016/S0006-3495(94)80924-5

Rule, G. S., \& Hitchens, T. K. (2005). \emph{Fundamentals of protein
NMR spectroscopy} . Dordrecht, Netherlands: Springer.

Schumann, F. H., Hubert, A. E., Ae, R., Maurer, T., Wolfram, A. E., Ae,
G., \ldots{} Kalbitzer, R. (2007). Combined chemical shift changes and
amino acid specific chemical shift mapping of protein-protein
interactions. \emph{Journal of Biomolecular NMR} , \emph{39} , 275--289.
https://doi.org/10.1007/s10858-007-9197-z

Shukla, A. A., Hubbard, B., Tressel, T., Guhan, S., \& Low, D. (2007).
Downstream processing of monoclonal antibodies-Application of platform
approaches. \emph{Journal of Chromatography B} , \emph{848} , 28--39.
https://doi.org/10.1016/j.jchromb.2006.09.026

Silva, D., \& Vranken, B. F. (2012). \emph{ACPYPE-AnteChamber PYthon
Parser interfacE} . \emph{BMC Research Notes, 5,} 1-8.

Srinivasan, K., Banerjee, S., Parimal, S., Sejergaard, L., Berkovich,
R., Barquera, B., \ldots{} Cramer, S. M. (2017). Single Molecule Force
Spectroscopy and Molecular Dynamics Simulations as a Combined Platform
for Probing Protein Face-Specific Binding. \emph{Langmuir} , \emph{33} ,
10851-10860. https://doi.org/10.1021/acs.langmuir.7b03011

Srinivasan, K., Parimal, S., Lopez, M. M., McCallum, S. A., \& Cramer,
S. M. (2014). Investigation into the molecular and thermodynamic basis
of protein interactions in multimodal chromatography using
functionalized nanoparticles. \emph{Langmuir} , \emph{30} (44),
13205--13216. https://doi.org/10.1021/la502141q

Sun, Y., Welsh, W. J., \& Latour, R. A. (2005). Prediction of the
Orientations of Adsorbed Protein Using an Empirical Energy Function with
Implicit Solvation. \emph{Langmuir, 21,} 5616-5626.
https://doi.org/10.1021/la046932o

Wang, J., Cieplak, P., \& Kollman, P. A. (2000). How Well Does a
Restrained Electrostatic Potential (RESP) Model Perform in Calculating
Conformational Energies of Organic and Biological
Molecules?\emph{Journal of Computational Chemistry} , \emph{21} (12),
1049--1074.
https://doi.org/10.1002/1096-987X(200009)21:12\textless{}1049::AID-JCC3\textgreater{}3.0.CO;2-F

Wang, J., Wang, W., Kollman, P. A., \& Case, D. A.
(2001).\emph{Antechamber, An Accessory Software Package For Molecular
Mechanical Calculations. Journal of American Chemical Society, 222,} 41.

Wang, J., Wolf, R. M., Caldwell, J. W., Kollman, P. A., \& Case, D. A.
(2004). Development and testing of a general Amber force
field.\emph{Journal of Computational Chemistry} , \emph{25} (9),
1157--1174. https://doi.org/10.1002/jcc.20035

Williamson, M. P. (2013). Progress in Nuclear Magnetic Resonance
Spectroscopy Using chemical shift perturbation to characterise ligand
binding. \emph{Progress in Nuclear Magnetic Resonance Spectroscopy}
,\emph{73} , 1--16. https://doi.org/10.1016/j.pnmrs.2013.02.001

Woo, J. A., Chen, H., Snyder, M. A., Chai, Y., Frost, R. G., \& Cramer,
S. M. (2015). Defining the property space for chromatographic ligands
from a homologous series of mixed-mode ligands. \emph{Journal of
Chromatography A} , \emph{1407} , 58--68.
https://doi.org/10.1016/j.chroma.2015.06.017

Woo, J., Parimal, S., Brown, M. R., Heden, R., \& Cramer, S. M. (2015).
The effect of geometrical presentation of multimodal cation-exchange
ligands on selective recognition of hydrophobic regions on protein
surfaces. \emph{Journal of Chromatography A} , \emph{1412} , 33--42.
https://doi.org/10.1016/j.chroma.2015.07.072

Yao, Y., \& Lenhoff, A. M. (2004). Electrostatic Contributions to
Protein Retention in Ion-Exchange Chromatography. 1. Cytochrome c
Variants. \emph{Analytical Chemistry} , \emph{59} (3), 6743.
https://doi.org/10.1021/ac049327z

Yu, G., Liu, J., \& Zhou, J. (2015). Mesoscopic Coarse-Grained
Simulations of Hydrophobic Charge Induction Chromatography ( HCIC ) for
Protein Purification. \emph{AIChE Journal} , \emph{61} (6), 2035--2047.
https://doi.org/10.1002/aic

Zhang, L., Zhao, G., \& Sun, Y. (2009). Molecular Insight into Protein
Conformational Transition in Hydrophobic Charge Induction
Chromatography: A Molecular Dynamics Simulation. \emph{J. Phys. Chem. B}
, \emph{113} , 6873--6880. https://doi.org/10.1021/jp809754k

\textbf{Figure Legends}

Figure 1: The Ligands employed in NMR experiments to represent the
chromatographic resins; (a) SP Sepharose, (b) Nuvia cPrime and (c) Capto
MMC ligands.

Figure 2: Snapshot from MD simulation of F\textsubscript{C} surrounded
by Capto MMC ligands in free solution. Protein is shown in a surface
representation in grey, water is shown in wireframe and colored based on
atom type, and ligands and ions are shown in a licorice representation
and colored based on atom type. Color scheme: hydrogen, white; oxygen,
red; carbon, cyan; nitrogen, blue; and sulfur, yellow.

Figure 3: Chromatographic Retention of the F\textsubscript{C} domain on
single mode SP Sepharose and MM CEX systems. 40 CV linear salt gradient
from 0 to 1M NaCl at pH 5.

Figure 4: Residue specific ligand-induced changes in combined chemical
shift for binding of (a) SP Sepharose, (b) Capto MMC and (c) Nuvia
cPrime ligands to the F\textsubscript{C} domain. Secondary structure of
the F\textsubscript{C} domain at the bottom of a. Numbered regions 2-14;
25-38; 61-70; 87-98; 119-127; 154-157; 211-216; represent the loops \&
\selectlanguage{greek}α-\selectlanguage{english}helices. (Note: different y-axis scale for Nuvia cPrime).

Figure 5: (a) A colored cartoon and surface representation of residue
specific ligand induced changes in combined chemical shift upon binding
of SP Sepharose ligand to the F\textsubscript{C} domain. (b)
Electrostatic Potential (EP) map at pH 5 and (c) Surface Aggregation
Propensity (SAP) map of the F\textsubscript{C} domain. (Note: numbered
regions 1-13; 25-38; 87-98; 119-127; 211-216; represent the loops \&
\selectlanguage{greek}α-\selectlanguage{english}helices).

Figure 6: A colored cartoon and surface representation of residue
specific ligand induced changes in chemical shift for binding of (a)
Capto MMC and (b) Nuvia cPrime ligands to the F\textsubscript{C} domain.
(Note: numbered regions 1-13; 25-38; 87-98; 119-127; 211-216; represent
the loops \& \selectlanguage{greek}α-\selectlanguage{english}helices).

Figure 7: Representative \textsuperscript{15}N-TROSY peaks from the
Nuvia cPrime titration experiments for residues (a) Aspartate 182, (b)
Valine 178 and (c) Histidine 66 at 0 (purple), 5 (magenta), 10(cyan), 20
(green), 40 (pink) mM ligand concentrations

Figure 8: Nuvia cPrime binding sites on F\textsubscript{C} domain as
determined by NMR with color coded dissociation constant
(K\textsubscript{D}) for non-interacting, grey; and strong, red;
intermediate, salmon; and weak, pink; binding residues. Residues located
in the hinge and C\textsubscript{H}2-C\textsubscript{H}3 interface
regions are highlighted in green and blue ellipses, respectively.

Figure 9: Nuvia cPrime binding hotspots on the F\textsubscript{C} as
determined by MD simulations.

Figure 10: The dual role of protonated histidines in the (a) flexible
hinge region and (b) interface of the C\textsubscript{H}2 and
C\textsubscript{H}3 domains.

Figure S1: Comparison of the CSP data between (a) Nuvia cPrime and SP
Sepharose, blue; (b) Capto MMC and SP Sepharose, brown; and (c) Capto
MMC and Nuvia cPrime, purple; ligand systems.

Figure S2: Representative ligand induced changes in chemical shift as a
function of Nuvia cPrime ligand concentration and the resulting fits for
residues (a) Aspartate 182, (b) Valine 178 and (c) Histidine 66.

Table S1: A List of residues on the F\textsubscript{C} surface
interacting with Nuvia cPrime ligand, associated binding dissociation
constant (K\textsubscript{D}) with the standard error of fitting and the
coefficient of determination (R\textsuperscript{2}). Residues located in
the hinge and C\textsubscript{H}2-C\textsubscript{H}3 interface regions
are indicated by * and \#, respectively.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Free-ligand-NMR-paper-figures/Free-ligand-NMR-paper-figures}

\end{center}
\end{figure}

\selectlanguage{english}
\FloatBarrier
\end{document}

