Predicting High-Concentration Interactions of Monoclonal Antibody

Jun 26, 2019 - Derivation of a simplification to the MSOS algorithm when using a sterics-only reference state; ... MSOS algorithms; and additional res...
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Article Cite This: J. Phys. Chem. B 2019, 123, 5709−5720

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Predicting High-Concentration Interactions of Monoclonal Antibody Solutions: Comparison of Theoretical Approaches for Strongly Attractive Versus Repulsive Conditions Cesar Calero-Rubio,†,§ Atul Saluja,‡,§ Erinc Sahin,‡ and Christopher J. Roberts*,† †

Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, United States Drug Product Science and Technology, Bristol-Myers Squibb, New Brunswick, New Jersey 08901, United States

‡

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S Supporting Information *

ABSTRACT: Nonspecific protein−protein interactions of a monoclonal antibody were quantified experimentally using light scattering from low to high protein concentrations (c2) and compared with prior work for a different antibody that yielded qualitatively different behavior. The c2 dependence of the excess Rayleigh ratio (Rex) provided the osmotic second virial coefficient (B22) at low c2 and the static structure factor (Sq=0) at high c2, as a function of solution pH, total ionic strength (TIS), and sucrose concentration. Net repulsive interactions were observed at pH 5, with weaker repulsions at higher TIS. Conversely, attractive electrostatic interactions were observed at pH 6.5, with weaker attractions at higher TIS. Refined coarse-grained models were used to fit model parameters using experimental B22 versus TIS data. The parameters were used to predict high-c2 Rex values via Monte Carlo simulations and separately with Mayer-sampling calculations of higher-order virial coefficients. For both methods, predictions for repulsive to mildly attractive conditions were quantitatively accurate. However, only qualitatively accurate predictions were practical for strongly attractive conditions. An alternative, higher resolution model was used to show semiquantitatively and quantitatively accurate predictions of strong electrostatic attractions at low c2 and low ionic strength.

1. INTRODUCTION The complex behavior of proteins in solution can be attributed to the contribution of molecular interactions between solvent, protein, buffer, and other cosolute molecules.1−5 These interactions can dictate solution properties and behaviors, including dynamic properties, such as native and non-native aggregation, phase separation (liquid−liquid separation, crystallization, etc.), opalescence, and elevated solution viscosity.1−15 These solution properties are monitored and controlled during the development and manufacturing of protein solutions for a range of health care, food, and other applications.2,5,7,16−20 Better understanding and control of the interactions among molecules in protein solutions can help to optimize the development and manufacturing of protein-based products, leading to a decrease in overall product and process development costs.2,21 However, the complex nature of the molecular-scale interactions makes it challenging to identify the key contributions that are needed to build tractable models to predict solution properties, particularly at high protein concentrations. Static light scattering (SLS) allows one to noninvasively measure and quantify the so-called “colloidal” or “weak” protein−protein interactions as a function of protein concentration (c2) in the form of Kirkwood−Buff (KB) © 2019 American Chemical Society

integrals, particularly the protein−protein KB integral, G22.4,22−26 In the remainder of this work, the notation of Casassa and Eisenberg will be employed: component 1 denotes solvent (water), 2 denotes protein along with the stoichiometric counterions needed to maintain electroneutrality, and 3, 4, and so forth denote additional solute species.23,27 In what follows, c2 denotes the mass concentration (in g/L or mg/mL) of protein in the solution of interest. G22 represents the KB integral between two protein molecules (i.e., “22” for the subscript), while also accounting for the presence of all other proteins and other molecules in solution. Consequently, G22 is dependent on the solution composition, including the protein concentration. In the limit of dilute conditions (low c2), the average distance between proteins is large compared to the range of the protein−protein interactions. Therefore, each protein interacts significantly with no more than one “near neighbor” protein at a given time, and G22 converges to its c2independent analogue, the second osmotic virial coefficient, B22.24,25,28 In general, the formal definitions of Bαβ and Gαβ are Received: April 22, 2019 Revised: May 31, 2019 Published: June 26, 2019 5709

DOI: 10.1021/acs.jpcb.9b03779 J. Phys. Chem. B 2019, 123, 5709−5720

The Journal of Physical Chemistry B ÄÅ w (c → 0, c → 0) ÉÑ ÅÅ αβ α β ÑÑ 1 ÅÅ − Ñ kBT ÅÅe Bαβ = − − 1ÑÑÑ dr dΩ1 dΩ 2 ÑÑ 2 r Ω1 Ω2 ÅÅÅ ÑÑÖ ÅÇ

Article

ionic strength values. The prior work showed an approach for combining low-c2 experimental interactions (via B22) with Monte Carlo (MC) simulations of multidomain CG MAb models to predict high-c2 protein−protein interactions (via Sq=0 or G22). The results below focus primarily on the accuracy of different CG MAb models and also different computational algorithms to predict high-concentration MAb interactions for a different antibody (termed MAb2) that displays strong electrostatically driven attractions for equivalent solution conditions such as those in the previous work.22 The results are compared with previously published data for MAb1.22 This work also explores the use of a higher resolution CG model to capture changes in colloidal stability caused by electrostatic interactions as a function of pH for both MAb1 and MAb2, but focused solely at low-c2 conditions, where predicting B22 is more tractable with higher-resolution models.

∫∫ ∫

Gαβ =

ÄÅ w (c , c ) ÉÑ ÅÅ αβ α β ÑÑ ÅÅ − k T Ñ ÅÅe B − 1ÑÑÑ dr dΩ1 dΩ 2 ÑÑ Ω2 Å ÅÅÅ ÑÑÖ Ç

∫r ∫Ω ∫ 1

(1)

(2)

where wαβ represents the ensemble-averaged potential of mean force between molecular species α and β. wαβ is explicitly a function of the center-to-center distance (r) between a pair of molecules α and β, their relative orientations (Ωα and Ωβ), and their concentrations (cα, cβ). It is implicitly a function of the solution environment (solvent and other solute concentrations). kB is Boltzmann’s constant, and T is the absolute temperature.23,25,29 In the case of protein self-interactions (i.e., α = β = 2), these quantities are the direct manifestation of “weak” or “colloidal” interactions in solution such as: van der Waals forces between amino acids, relative to those between water and amino acids; hydrophobic interactions between amino acids; and screened electrostatic attractions and repulsions.22,24,28,30−32 In eq 1 using α = β = 2, w22 is evaluated in the dilute protein limit, which makes B22 a c2independent quantity. Conversely, w22 depends on c2 in eq 2 (α = β = 2), as G22 is inherently a c2-dependent quantity. In the limit of c2 → 0, B22 and G22 are formally equivalent except for the difference in sign and a factor of 1/2 based on eqs 1 and 2.25 At low and high concentrations, G22 is formally related to the zero-q static structure factor (Sq=0) via Sq=0 = 1 + c2G22.22,25,28 Therefore, Sq=0 provides a dimensionless measure of the deviation of the net protein−protein interactions from those in an ideal gas mixture (i.e., when Sq=0 = 1).22,25,33,34 Sq=0 values larger than 1 (i.e., G22 > 0) correspond to net attractions between proteins, and Sq=0 below 1 (i.e., G22 < 0) correspond to net repulsive interactions. Based on thermodynamic stability criteria, Sq=0 must be greater than zero. Determining protein−protein interactions experimentally can be costly in terms of time and protein material, particularly for therapeutic proteins such as antibodies. Accurate predictions of quantities such as G22 and Sq=0 can be useful at early stages of protein candidate selection and formulation design. Except for relatively small proteins and peptides, it is computationally intractable to simulate quantities such as B22 and G22 for most protein systems of interest with all-atom simulations and explicit solvent molecules.24,28,35,36 Coarsegrained (CG) molecular models provide faster computations at the expense of some degree of molecular definition.10,28,35−38 Simplified CG descriptions of protein solutions were historically employed primarily to retrospectively interpret experimental behaviors such as phase separation and aggregation. Recent work showed that CG models can be used to both simulate and quantitatively or semiquantitatively predict low- to high-c2 solution properties and net protein− protein interactions for a globular protein24 and for a monoclonal antibody (MAb)22 as a function of solution conditions such as pH and ionic strength. However, the results suggested that there may be challenges if one considers proteins and/or solution conditions where the net protein− protein interactions are strongly attractive.22,24,31,32 This report builds on the previous work that focused on a relatively stable MAb (termed MAb1 in what follows), in that MAb1 showed either strongly repulsive or weakly attractive protein−protein interactions across a range of solution pH and

2. MATERIALS AND METHODS 2.1. Sample Preparation. Sodium acetate buffer stock solutions were prepared by dissolving glacial acetic acid (Fisher Scientific) in distilled/deionized water (Milli-Q, MilliporeSigma) to reach 10 mM acetic acid, and titrated in a single stage to pH 5.1 ± 0.05 (termed pH 5 below) using a 5 M sodium hydroxide solution (Fisher Scientific). Similarly, 10 mM histidine buffer stock solutions were prepared by dissolving histidine hydrochloride (Sigma) in distilled/deionized water and titrating to pH 6.5 ± 0.05 (termed pH 6.5 below). A stock MAb2 solution was provided by Bristol-Myers Squibb at a starting protein concentration of ∼35 g/L. pH 5 and pH 6.5 protein stock solutions were filtered and dialyzed using a 10 kDa molecular weight cutoff (MWCO) Spectra/Por dialysis membrane (Spectrum Laboratories, Rancho Dominguez, CA) with the desired buffer using four 12 h buffer exchanges at 4 °C to remove any undesired solutes from the original stock solution. Cosolute stock solutions were prepared by dissolving sucrose (HPLC grade, Sigma) and/or NaCl (Fisher Scientific) in 10 mM buffer solutions (acetate for pH 5 and histidine for pH 6.5) to obtain final solutions of 30% w/w sucrose and/or 1.3 M NaCl. These solutions were titrated to the respective pH with small aliquots of 5 M sodium hydroxide stock solution. Final protein solutions were prepared gravimetrically by combining (1) protein stock solution, (2) pH-adjusted buffer, and (3) pH-adjusted cosolute stock solution with matching buffer. The proportions of (1), (2), and (3) were selected to achieve a constant cosolute concentration and pH as specified in Table 1. This was done for a series of increasing protein concentrations every 0.5 g/L up to a maximum of 5 g/L (for low-c2 interaction measurements) to ensure dilute protein behavior. For protein solutions above approximately 10 g/L (termed high-c2 conditions below), concentrated protein stock Table 1. Summary of Solution Conditions for Low-c2 Data added NaCl

5710

solution condition

at low c2

at high c2

pH 5, 10 mM acetate pH 5, 10 mM acetate + 5% w/w sucrose pH 6.5, 10 mM histidine pH 6.5, 10 mM histidine + 5% w/w sucrose

0−500 mM

0 mM & 100 mM

0−350 mM

DOI: 10.1021/acs.jpcb.9b03779 J. Phys. Chem. B 2019, 123, 5709−5720

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The Journal of Physical Chemistry B

2.3. CG MAb Models and Interaction Parameters. 2.3.1. Low Resolution CG Models: HEXA and DODECA Models. Two different CG molecular models, termed HEXA and DODECA, were used to model low-c2 results and predict high-c2 experimental SLS behavior from the low-c2 results. These were a subset of the larger group of different CG models that were introduced in the previous work.28 These two models can provide an optimal balance between accuracy and computational burden.28 Figure 1 shows a schematic of the

solutions were prepared through membrane centrifugation at ∼3200 rcf using 10 kDa MWCO Amicon-Ultra centrifugal tubes (MilliporeSigma) and two buffer exchange steps. As expected, a pH shift was observed as the protein solution was concentrated from ∼35 to ∼165 g/L. Therefore, starting pH values of 4.3 and 5.9 were selected for the dialysis steps prior to centrifugal concentration steps. The resulting pH values were 5.06 ± 0.05 and 6.49 ± 0.05, respectively, for final 165 g/L solutions after centrifugal buffer exchange. This was performed similarly for MAb1 and MAb2 solutions. UV−vis spectrophotometry (Agilent 8453, Santa Clara, CA) was used to determine the concentration of the protein solutions at 280 nm using an extinction coefficient of 1.59 L g−1 cm−1 before and after dilutions from the concentrated stock solutions. Lower-concentration protein samples were then prepared by gravimetrically diluting the concentrated protein solution in the desired buffer to obtain c2 values ranging from 10 to 160 g/ L. 2.2. Static Light Scattering. Batch SLS experiments were conducted using a Wyatt Technology (Santa Barbara, CA) DAWN HELEOS II instrument with laser wavelength (λ) of 658.9 nm at 25.0 ± 0.1 °C. The average scattered intensity at 90° can be determined from SLS and used to calculate the excess Rayleigh ratio (R ex ) using methods described previously.4,13,22,24,39 Experimental values of Rex as a function of c2 can be used to quantify protein−protein interactions in the form of the protein−protein KB integral, G22 via22,25 Rex = M w,appc 2 + M w G22c 2 2 K

Figure 1. Schematic diagrams of the HEXA (left), DODECA (middle), and 1bAA (right) geometries. The solid-line connectors between Fab and Fc domains in the HEXA and DODECA models are guides to the eye; rigid Fab−Fc linkers were employed (see Materials and Methods).

HEXA and DODECA models. These models were developed and refined to resemble the overall shape of a MAb molecule, and use 6 (HEXA) or 12 (DODECA) beads per protein.22,28 Additional details for these models can be found in refs.22,28 In brief, they account for steric repulsions, short-ranged nonelectrostatic attractions, and screened charge−charge repulsions and attractions between the beads (domains) of the proteins, with the solvent treated implicitly. To compute theoretical valence values (qi), the standard Henderson−Hasselbalch equation was used in combination with pKa values of free amino acids in aqueous solution and the protein sequence.22,24,28,40 The amino acid sequence was partitioned into equal chain-length units to compute the charge of each HEXA or DODECA model bead following the methodology proposed in the previous work.22,28 In what follows, the terms valence and charge will be used interchangeably. Examples of the theoretical charge distribution for the DODECA model are shown in Figure 2 for MAb2 at the pH values in this work. All theoretical charge values are shown in Table 2 for pH 5 and 6.5 for both CG models, for both MAb1 and MAb2. 2.3.2. Higher Resolution CG Model: One-Bead-per-AminoAcid (1bAA) Model. A structurally higher resolution CG model was used to evaluate interactions between pairs of MAb1 or MAb2 molecules, as a function of pH, ionic strength, and a parameter (ψ) that estimates the degree of territorial ion binding (see below). A previously developed one-bead-peramino acid (1bAA) model was used to compute B22 values using the Mayer sampling (MS) with overlap sampling (MSOS) algorithm.24,31,32,41,42 The 1bAA force field allows one to evaluate the combination of the effects of short-ranged non-electrostatic interactions (e.g., hydrophobic and van der Waals attractions), electrostatic interactions, and protein excluded volume at the scale of individual amino acids while still being computationally tractable for B22 calculations; it is not tractable for simulating concentrated systems.28 Each amino acid is represented as a single bead, and the amino acid identity dictates the diameter of the bead, and relative well depth for short-ranged non-electrostatic attractions (εi). The charge (qi) for the ith amino acid resides at the center of that bead. Based on nominal pKa values, at pH 5, all

(3)

where Mw,app is the protein apparent molecular weight, and Mw is the protein true molecular weight. K is an optical constant for SLS and equal to 4π2n2(dn/dc2)2NA−1λ−4, where n is the refractive index of the solution, (dn/dc2) is the change in refractive index of the solution as a function of c2 (see below), and NA is Avogadro’s number.13,22,25,34 The zero-q limit for the structure factor (Sq=0) can be obtained by dividing the right hand side of eq 3 by c2Mw, with the canonical simplification that Mw,app ≈ Mw.4,22 Values of (dn/dc2) were determined using a J157HA refractometer (Rudolph Scientific, Hackettstown, NJ) for c2 values up to 5 g/L for each solution condition and by performing dilutions with matching dialysis buffer. An average value of 0.20(3) mL/g was obtained for buffer-only and NaCl solution conditions, whereas 0.22(4) mL/g was obtained for all solution conditions with 5% w/w sucrose. (dn/ dc2) values were found to be independent of solution pH, as expected.22 As noted above, G22 ≈ −2B22 in the limit of dilute protein concentration. In the present work, c 2 values below approximately 5 g/L resulted in sufficiently small values of |c2G22| ( 300 mM, MAb2 should be subject to weaker short-ranged non-electrostatic attractions in these solution conditions than MAb1 (at both pH 5 and pH 6.5). However, MAb2 displays a different pH dependence than MAb1 because B22/B22,ST at low TIS transitions from strong net electrostatic repulsions to strong net electrostatic attractions upon titration from pH 5 to pH 6.5. This is opposite to the behavior observed with most other MAbs reported in the literature.22,31,48 The reduction in repulsive interactions with an increase from pH 5 to 6.5 can be at least partially attributed to an overall decrease in effective protein surface charge as the pH approaches the pI of this molecule (computed as 7.55 for MAb2). However, this alone does not fully explain the unusual pH dependence for MAb2. If all charges on the protein surface were eliminated, the resulting B22/B22,ST value would be that obtained at TIS > 300 mM (around −0.25 for MAb2). Consequently, additional electrostatic effects are present at pH 6.5 for MAb2 that were not significant for MAb1. By analyzing the charge distribution of the molecule (cf., Figures 2 and S1 in the Supporting Information), one can see that there is a change in the sign of the net charge of the CH3 domain for both molecules by titrating from pH 5 to 6.5. However, the differences in charge values between the outermost domains (VH, VL at the top and CH2 and CH3 at the bottom) is more pronounced for MAb2 than for MAb1. Consequently, the presence of strong charge disparity can be conducive to strong electrostatic attractions as observed at pH 6.5 for MAb2.24,31,53 Although charge disparity might also be present on MAb1, the magnitude of these multipole effects does not appear to be as prominent for MAb1 as for MAb2. The experimental results are consistent with a colloidal interpretation where the net charge−charge repulsion dominates the B22 results for MAb1, leading to positive B22 values in contrast to the large negative B22 values for MAb2. Similar dipole or multipole dominated behavior can be observed for other MAb solutions and was also found for a globular protein in previous work.20,24,31,54 Finally, the addition of sucrose to MAb2 solutions also led to increases in B22 as observed previously for MAb1, and was most prominent at TIS > 300 mM. This suggests a change in the solvation shell(s) of MAb2 as was argued previously from the experimental results for MAb1.22,55 Insets in Figure 3 show the experimental Rex/K versus c2 (high-c2) results at pH 5 and pH 6.5 for the solution conditions presented in Table 1, and those that correspond to the B22/B22,ST measurements in the main panels. Additionally, the steric-only behavior for this molecule is shown as a

state) based on multibody simulations for HEXA or DODECA models was used as described in ref 22. This equation was used to compute Rex/K versus c2 as well as Sq=0 versus c2 for stericsonly reference systems and is a monoclonal antibody analogue to the so-called hard-sphere equation of state for spherical objects.22,29,50,52 Analogous to the analysis with B22/B22,ST at low concentrations, Rex/K and Sq=0 values above (below) the high-c2 steric-only values represent net-attractive (net-repulsive) behavior using a “sterics-only” reference state.

3. RESULTS AND DISCUSSION 3.1. Experimental “Weak” Protein−Protein Interactions for MAb2. The results presented and discussed below include previous results22 from MAb1 to compare with the solution behavior of MAb2 considered here. A primary focus of this section is on the experimental results for MAb2 because they have not been presented previously. SLS measurements were performed to determine Rex/K profiles of MAb2 for similar solution conditions as those in prior work.22 Figure 3

Figure 3. Main panels: Experimental B22/B22,ST values as a function of TIS for MAb 2 with added NaCl from 0 to 500 mM. Black symbols represent data with only buffer as the base solution condition, whereas red symbols represent the same buffer with 5% w/w added sucrose. Insets: High-c2 Rex/K values for buffer-only (black squares), buffer plus 5% w/w sucrose (red triangles), and buffer plus 100 mM NaCl (gray circles). Panel A corresponds to pH 5 and panel B to pH 6.5.

shows the experimental results of B22/B22,ST versus TIS for MAb2 at pH 5 and pH 6.5. The B22/B22,ST versus TIS profiles qualitatively differ between pH 5 and pH 6.5, and also when comparing the previous results for MAb1 with the current results for MAb2. At pH 5 (Figure 3A), B22/B22,ST values for MAb2 decrease from 1.9 (net-repulsive) to around −0.25 (netattractive) as TIS increases, whereas the same solution conditions resulted in values between 1.9 to around −0.5 for MAb1.22 Conversely at pH 6.5, the results in Figure 3B show qualitatively opposite behavior for MAb2 when compared to 5714

DOI: 10.1021/acs.jpcb.9b03779 J. Phys. Chem. B 2019, 123, 5709−5720

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Figure 4. Panels A,B: Comparison of B22/B22,ST as a function of TIS between experimental (symbols) and simulated values (shaded areas) using the DODECA model at pH 5 for buffer-only (A) and buffer with 5% w/w added sucrose (B) conditions. The insets correspond to response surfaces of ARD values as a function of εSR and ψ. Panels C,D: High-c2 predictions of Rex/K and Sq=0 from the DODECA simulations using parameters fitted to the data in panels A and B, respectively. Experimental values are given by symbols (black squares = buffer-only, red triangles = buffer with 5% w/w sucrose, gray circles = buffer with 100 mM NaCl). The blue dashed-line corresponds to the steric-only behavior.

c2, MAb2 experiences stronger attractions than does MAb1 (see discussion above and ref 22). This “reversal” when moving from low to high c2 conditions highlights the need to measure the interaction behavior of each molecule at the concentration of interest, and avoid the assumption that low-c2 interactions are directly predictive of high-c2 behavior.4,56,57 3.2. Simulations of “Weak” Protein−Protein Interactions for MAb2. Similar to a previous work,22,24 B22/B22,ST versus TIS values were compared between experiments and simulations using the HEXA and DODECA models. This allows one to reconstruct ARD versus [εSR, ψ] response surfaces to obtain parameters that capture the low-c2 SLS results. This was first done at pH 5, and the results are shown in Figure 4 for the DODECA model, where the experimental data and solution conditions are the same as those presented in Figure 3 and Table 1. Similar results were obtained for the HEXA model (see Figure S2 in the Supporting Information). The gray shaded areas represent the simulated B22/B22,ST versus TIS profiles obtained from ARD values below 20%. These parameter ranges were later used to predict high-c2 behavior at pH 5 and the solution conditions in Table 1. Figure 4 (panels C and D) shows a comparison of the experimental and predicted high-c2 Rex/K results as a function of c2 using the HEXA and DODECA models. Those are based on the TMMC simulations for the parameter space obtained by fitting low-c2 data as explained above. The shaded areas represent the model predictions including statistical uncertainty, and the symbols denote the experimental values. The results in Figures 4 and S2 show that the selected models (HEXA and DODECA) with the parameters from B22 (low-c2) behavior are able to semiquantitatively or quantitatively predict the high concentration behavior for solution conditions spanning from net repulsive to mildly net attractive interactions. This is consistent with the prior work with MAb1. However, the current approach (i.e., assuming low-c 2 parameters are constant and predictive of high-c2 conditions) is not always quantitatively accurate across molecules, solution

reference in the insets (see Materials and Methods). The results in the insets of Figure 3A (pH 5) show that Rex/K profiles for both buffer-only and buffer-with-sucrose solution conditions are net-repulsive (Rex/K values below the stericonly behavior) at lower-c2 conditions (below 80 g/L), but transition to net-attractive (Rex/K values above the steric-only behavior) at much higher c2 values (>80 g/L), with Rex/K profiles for sucrose less negative or positive (i.e., more repulsive) than those for buffer-only under all c2 values. The addition of 100 mM NaCl results in a substantial increase in Rex/K values to levels larger than those for steric-only behavior across the whole concentration range. Conversely, the results in Figure 3B (pH 6.5) show that all Rex/K profiles are netattractive. The buffer-only and buffer-with-sucrose solution conditions show a steep increase in Rex/K values, to the extent that solutions above 40 g/L could not be characterized because the scattering signal sharply increased above the limits of detection of the instrumentation. This rapid increase in Rex/K values with c2 correlates qualitatively with the measured B22 values, and is consistent with strongly attractive protein− protein interactions.24 The addition of 100 mM NaCl results in a large decrease in Rex/K values at pH 6.5. This indicates that the strong attractions are caused by electrostatic interactions, as short-ranged non-electrostatic attractions should not be affected by the addition of 100 mM NaCl, as discussed above and elsewhere.22,24,31 This observation is in good qualitative agreement with the B22 results for MAb1 and MAb2. Combining the results from low to high c2, the behavior for MAb2 shows some significant differences in comparison to MAb1.22 Similar quantitative B22 values were obtained for equivalent solution conditions at pH 5 for both molecules. Net-repulsive behavior was observed across the whole c2 range at pH 5 without added NaCl for MAb1. In addition, B22 was less attractive for MAb2 than for MAb1 at high TIS conditions. Based solely on B22 results, one might conclude that MAb2 is more colloidally stable (i.e., less prone to strong attractions) than MAb1 at high TIS. However, this is not the case. At high 5715

DOI: 10.1021/acs.jpcb.9b03779 J. Phys. Chem. B 2019, 123, 5709−5720

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Figure 5. Panels A,B: Comparison of B22/B22,ST vs TIS between experimental (symbols) and simulated (shaded areas) values using the DODECA model at pH 6.5 for buffer (A) and sucrose (B) conditions, with their respective ARD surface responses as a function of εSR and ψ in the insets. Panels C,D: High-c2 predictions of Rex/K and Sq=0 from low-c2 parameters with the DODECA model at pH 6.5 and for buffer-only (black squares), 5% w/w sucrose (red triangles), and 100 mM NaCl (gray circles). The blue dashed-line corresponds to the steric-only behavior.

incapable of capturing the complex nature of strong protein attractions, and the likely specific ion effects that the current models cannot account for. This can be addressed to some extent with higher resolution CG models, such as the one tested below. 3.3. TMMC Versus MSOS Simulations for Predicting High-c2 Interactions. The computational approach used to simulate high-c2 protein interactions used above relied on simulating hundreds to thousands of antibodies in an open box, and allowing for equilibration during a grand-canonical MC simulation.22,24,28 Although this is done to capture both the energy and entropy contributions to the solution as a function of c2 to better assess the effects of increasing c2, this approach might not be ideal if one is more interested in optimizing the time needed to obtain a predicted data set, rather than the overall accuracy of the prediction. In that context, the approach taken by the McMillan−Mayer solution theory becomes of interest, where a generic equation of state (EoS) can be created based on a polynomial expansion (i.e., the virial expansion), where the only parameters needed are the osmotic virial coefficients (see eq 5). These virial coefficients can be computed using the MSOS algorithm as explained in the Materials and Methods section. The viability of using such an approach to predict high-c2 behavior was tested for the present models, using results from the TMMC simulations for comparison. Figure 6 shows two illustrative cases from among the parameter sets obtained for the DODECA model. Sq=0 versus c2 profiles were computed using the TMMC algorithm or using the MSOS algorithm coupled with truncated versions of eq 5 (depending on the number of virial coefficients used) in conjunction with eq 6. Similar results were obtained for the HEXA model and are shown in Figure S3 (see the Supporting Information). Figures 6 and S3 illustrate that the MSOS approach can replicate the TMMC simulation if one uses up to the fourth (4th) virial coefficient and, in some situations, the fifth (5th) virial coefficient for conditions that exhibit netrepulsion (Figures 6A and S3A) to weak net-attraction (Figure

conditions, and/or models, and this is in contrast with previous results with MAb1. However, in most cases for MAb2, there were strong attractions, and the models could only provide qualitatively or semiquantitatively accurate predictions. The results illustrate that the prior approach cannot quantitatively capture the interactions at both low and high c2 for strongly attractive conditions. This can be seen in Figure 5, where B22/B22,ST versus TIS values, and Rex/K and Sq=0 versus c2 at pH 6.5 were modeled using the DODECA model. Similar results were obtained for conditions with the HEXA model (not shown). In Figure 5A,B, the DODECA model is incapable of quantitatively capturing the experimentally measured B22/B22,ST versus TIS behavior, and no parameter set was found to result in less than 40% ARD for both panels. Consequently, only those parameters that minimized the ARD and fit the measured B22/ B22,ST values at either 0 mM NaCl (TIS = 10 mM) or 100 mM NaCl (TIS = 110 mM) were used to construct Figure 5C,D. In that case, the model is only able to qualitatively predict the intermediate-c2 behavior for both buffer-only and buffer + sucrose solution conditions, and is qualitatively incorrect at the highest concentrations. The model predictions are qualitatively correct at high concentrations with 100 mM NaCl added, but with large deviations that highlight limitations of the current HEXA and DODECA models. In terms of the expected basis of these deviations for MAb2, it is worth noting that these experimental conditions are highly attractive, with attractions being caused by strong electrostatic interactions. Similarly, side chain charges are physically located at the end of the side chain, and not in the geometrical center of the entire (sub-)domain, as assumed in the present models. This can also be seen by the unphysically high ψ values in the inset of Figure 5A,B. Values of ψ are expected to lie between 0 and 1, as this parameter is expected to represent the change in effective charge due to ion binding. Strong net-attractive behavior is highly dependent on molecular orientation, proximity, packing, and available volume, so low resolution models, such as the HEXA and DODECA models, are 5716

DOI: 10.1021/acs.jpcb.9b03779 J. Phys. Chem. B 2019, 123, 5709−5720

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The Journal of Physical Chemistry B Table 3. Viability of Using the MSOS Approach for Evaluated Solution Conditions and MAb Molecules molecule MAb1

MAb2

solution condition pH pH pH pH pH pH pH pH pH pH pH pH

5, buffer 5, sucrose 5, NaCl 6.5, buffer 6.5, sucrose 6.5, NaCl 5, buffer 5, sucrose 5, NaCl 6.5, buffer 6.5, sucrose 6.5, NaCl

B22/B22,ST 1.79 1.86 −0.18 0.72 0.87 −0.35 2.0 1.75 −0.06 −8.6 −7.1 −0.71

± ± ± ± ± ± ± ± ± ± ± ±

0.08 0.13 0.09 0.08 0.09 0.05 0.1 0.08 0.04 0.5 0.4 0.09

MSOS−TMMC? yes yes yes yes yes no yes yes yes no no no

High-c2 conditions require larger numbers of simulated molecules in the TMMC approach. This increases both the time to convergence and, thus, the total simulation time. Consequently, selecting one approach over the other must be based on the requirements of the user. Using the MSOS algorithm requires running a minimum of 4 or 5 molecular simulations (one for each virial coefficient), whereas the TMMC algorithm only requires a single but more comprehensive simulation. Additionally, slower algorithms might be required to better converge the MSOS calculations for strongly attractive conditions. Consequently, if the goal is to obtain a single c2 prediction, it would be more efficient to run a single TMMC simulation without the need to corroborate whether the MSOS approach is accurate. On the other hand, if a large series of concentrations is desired, it can be more efficient to use the MSOS algorithm, as this provides an analytical EoS. Finally, one needs to consider that the MSOS approach will not be able to provide additional information about the solution structure at very high c2, which will be the topic of a subsequent report. 3.4. Capturing B22 Behavior with a More Structurally Refined CG Model. B22/B22,ST was calculated as a function of ψ and TIS using the 1bAA model as explained above and in a previous work.24,28,31,32 This was done to assess whether the anisotropic surface distribution of charged residues can predict the transition from repulsive to strongly attractive electrostatic interactions from pH 5 to pH 6.5 for MAb2, and for comparison with MAb1, with more physically realistic values of ψ than what was needed with the DODECA and HEXA models. Figure S4 shows the results of evaluating B22/B22,ST as a function of the maximum hydrophobic well depth (termed εSR for ease of comparison with values for the DODECA and HEXA models) for simulations with no electrostatic contributions (i.e., ψ = 0). This allows one to set the value of εSR to match the experimental value at high TIS, as that value of B22/B22,ST is effectively independent of pH. After setting a value of εSR, response surfaces were constructed of B22/B22,ST as a function of ψ and TIS. These response surfaces are expected to show one of three limiting cases, depending on the degree of anisotropy of the surface charge distribution: (1) monopole-dominated behavior, such that B22/B22,ST is large and positive at low TIS, and decreases monotonically with increasing TIS (e.g., experimental results in Figure 3A); (2) dipole/multipole-dominated behavior, such that B22/B22,ST is large and negative at low TIS, and increases monotonically with increasing TIS (e.g., inset in Figure 3B);

Figure 6. Comparison of the MSOS and TMMC approaches for case studies using the DODECA model for net-repulsive (panel A) and net-attractive (panel B) conditions. Black solid lines represent the TMMC results, whereas red dashed, blue dotted, and green dashdotted represent the MSOS results with up to the 2nd, 3rd, and 4th virial coefficient, respectively. Insets correspond to the relative deviation as a function of c2 for each model using the TMMC results as the reference.

S3B) up to 150 g/L of protein concentration. However, adding more virial coefficients is needed to quantitatively capture conditions that exhibit stronger net attractions (Figure 6B). This is also in agreement with previous analyses of the shortcomings of using the virial EoS to capture solution behavior of concentrated systems.25,49 Additionally, MSOS simulations for A3, A4, and A5 for strongly attractive conditions (e.g., those exhibited by MAb2 at pH 6.5) were not successful due to lack of convergence with the MSOS algorithm with the present methodology. Consequently, the MSOS approach is limited in practice to net repulsive to weakly attractive conditions unless one further refines the execution of the MSOS algorithm. For instance, this could be achieved by using a different reference system that includes attractions added to the steric-only behavior. Doing so was outside the scope of the present work but is a target of future efforts. Based on the discussion above, Table 3 shows the measured B22/B22,ST values for each of the solution conditions in Figures 3−5, as well as for MAb1 in ref 22, and indicates whether or not the MSOS approach equals the TMMC approach up to 150 g/L within 10% relative deviation for those modeled conditions. Here, it can be seen that most conditions could be modeled with the MSOS algorithm, with the exception of conditions for MAb2 at pH 6.5. This suggests that the presence of strong electrostatic attractions may require higher structural resolution (see discussion above and refs22,24).22,24 In terms of practical convenience, it is challenging to recommend TMMC versus MSOS approaches because additional factors, such as sampling optimization and convergence, are difficult to predict for different c2 values. 5717

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Figure 7. B22/B22,ST response surface of the 1bAA CG model as a function of ψ and TIS for MAb1 (panels A,C: εSR = 0.5 kBT) and MAb2 (panels B,D: εSR = 0.44 kBT). Panels A,B correspond to pH 5, and panels C,D correspond to pH 6.5.

and (3) B22/B22,ST shows a transition between monopole- and multipole-dominated regions as ψ increases. The shape of the response surface should depend on the solution pH as well as the protein sequence and structure. Because these are CG models using implicit solvent, the effective values for ψ and εSR can be modified experimentally by changing the properties of the solutione.g., by adding additional cosolutes that mediate protein−protein interactions, as well as by specific-ion effects that lead to preferential exclusion or accumulation of ions near the protein surface.22,55,58−61 Figure 7 shows the response surfaces for pH 5 and pH 6.5, for MAb1 and MAb2 based on the 1bAA CG model. Figure 7 shows that both molecules exhibit monopoledominated behavior (case 1, above) at pH 5, and this behavior also occurs for MAb1 at pH 6.5. However, MAb2 exhibits multipole-dominated behavior at pH 6.5 (case 2, above). These results are in quantitative or semiquantitative agreement with measured B22/B22,ST values, and provide further evidence that the charge distribution of both molecules are dominating their interaction behavior as discussed above. Additionally, the 1bAA was capable of quantitatively or semiquantitatively matching the measured B22 results for both molecules; with larger deviations for MAb2 at pH 6.5 due to strong electrostatic attractions (see Figure S5 in the Supporting Information). The magnitude of the attractive interactions observed for MAb2 at pH 6.5 and low TIS conditions can be conducive of phase separation, high solution viscosity, and other physicochemical instabilities.20,24,31,62−64 It is desirable to avoid such conditions during the development of protein-based solutions. The results in Figure 7 suggest that this type of response surface approach with the 1bAA model has the potential to be used more generally as a tool to assess how anisotropic surface-charge distributions affect protein−protein interactions without arbitrary definitions of charge “patches” or other geometric measures of anisotropic interactions that are difficult to generalize, and allows one to better infer the effect of point mutations in the overall colloidal stability of the molecule.24,28,31,42,43,65 This could provide an additional tool to evaluate protein colloidal stability during the candidate

selection steps during the development of protein-based products, as illustrated recently with other MAb candidates under only low-c2 conditions.31

4. SUMMARY AND CONCLUSIONS SLS was used to quantify “weak” protein−protein interactions of a MAb (termed MAb2) as a function of protein concentration (c2) for a range of pH and TIS and sucrose concentration. These included conditions that resulted in both net-repulsive and net-attractive protein interactions at low TIS, and under low- to high-c2 conditions. By comparison with previous results for a different antibody (termed MAb1), lowc2 results showed that both molecules exhibit net-repulsive behavior at low TIS and pH 5, which transitions to netattractive behavior as the solution TIS increases. At pH 6.5, MAb1 showed weakly net-attractive behavior from low to high TIS, whereas MAb2 showed strong net-attractive behavior at low TIS caused by strong electrostatic attractions. At high TIS (>300 mM), statistically equivalent behavior was found at both pH conditions, with weaker attractions observed for MAb2 in high ionic strengths. For all measured pH and TIS conditions, the addition of 5% w/w sucrose to the solution induced weaker net attractions with increasing TIS. This behavior was also observed at high c2, where solution conditions with 5% w/w sucrose always resulted in more repulsive behavior. For conditions without sucrose present and at high c2, bufferonly conditions shifted from net-repulsive behavior (relative to steric-only interactions) at pH 5 to net-attractive at pH 6.5, whereas solution conditions with 100 mM NaCl resulted in net-attractive behavior relative to steric contributions at both pH values and for both molecules. Two CG molecular models were tested to evaluate their potential to predict excess Rayleigh profiles and zero-q structure factors at high c2. In terms of model predictions from low to high c2, the quantitative differences between the models were not statistically significant for net-repulsive to weakly net-attractive conditions, and therefore both models could be used to accurately predict high-c2 behavior depending on the requirements of the user (e.g., computational burden and molecular features). However, the HEXA and DODECA 5718

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Rheology at High Concentrations. J. Phys. Chem. B 2013, 117, 6373−6384. (4) Ghosh, R.; Calero-Rubio, C.; Saluja, A.; Roberts, C. J. Relating Protein-Protein Interactions and Aggregation Rates from Low to High Concentrations. J. Pharm. Sci. 2016, 105, 1086−1096. (5) Wang, W.; Roberts, C. J. Aggregation of Therapeutic Proteins; John Wiley & Sons, Inc., 2010. (6) Rakel, N.; Bauer, K. C.; Galm, L.; Hubbuch, J. From Osmotic Second Virial Coefficient (B22) to Phase Behavior of a Monoclonal Antibody. Biotechnol. Prog. 2015, 31, 438−451. (7) Andrews, J. M.; Weiss, W. F.; Roberts, C. J. Nucleation, Growth, and Activation Energies for Seeded and Unseeded Aggregation of αChymotrypsinogen A†. Biochemistry 2008, 47, 2397−2403. (8) Barnett, G. V.; Razinkov, V. I.; Kerwin, B. A.; Hillsley, A.; Roberts, C. J. Acetate- and Citrate-Specific Ion Effects on Unfolding and Temperature-Dependent Aggregation Rates of Anti-Streptavidin IgG1. J. Pharm. Sci. 2016, 105, 1066−1073. (9) Tessier, P. M.; Lenhoff, A. M.; Sandler, S. I. Rapid Measurement of Protein Osmotic Second Virial Coefficients by Self-Interaction Chromatography. Biophys. J. 2002, 82, 1620−1631. (10) George, A.; Wilson, W. W. Predicting Protein Crystallization from a Dilute Solution Property. Acta Crystallogr., Sect. D: Biol. Crystallogr. 1994, 50, 361−365. (11) Chaudhri, A.; Zarraga, I. E.; Yadav, S.; Patapoff, T. W.; Shire, S. J.; Voth, G. A. The Role of Amino Acid Sequence in the SelfAssociation of Therapeutic Monoclonal Antibodies: Insights from Coarse-Grained Modeling. J. Phys. Chem. B 2013, 117, 1269−1279. (12) Raut, A. S.; Kalonia, D. S. Pharmaceutical Perspective on Opalescence and Liquid-Liquid Phase Separation in Protein Solutions. Mol. Pharm. 2016, 13, 1431−1444. (13) Piazza, R. Interactions in Protein Solutions near Crystallisation: A Colloid Physics Approach. J. Cryst. Growth 1999, 196, 415−423. (14) Godfrin, P. D.; Valadez-Pérez, N. E.; Castañeda-Priego, R.; Wagner, N. J.; Liu, Y. Generalized Phase Behavior of Cluster Formation in Colloidal Dispersions with Competing Interactions. Soft Matter 2014, 10, 5061−5071. (15) Li, L.; Kumar, S.; Buck, P. M.; Burns, C.; Lavoie, J.; Singh, S. K.; Warne, N. W.; Nichols, P.; Luksha, N.; Boardman, D. Concentration Dependent Viscosity of Monoclonal Antibody Solutions: Explaining Experimental Behavior in Terms of Molecular Properties. Pharm. Res. 2014, 31, 3161−3178. (16) Wang, W. Protein Aggregation and Its Inhibition in Biopharmaceutics. Int. J. Pharm. 2005, 289, 1−30. (17) Weiss, W. F.; Young, T. M.; Roberts, C. J. Principles, Approaches, and Challenges for Predicting Protein Aggregation Rates and Shelf Life. J. Pharm. Sci. 2009, 98, 1246−1277. (18) Dear, B. J.; Hung, J. J.; Truskett, T. M.; Johnston, K. P. Contrasting the Influence of Cationic Amino Acids on the Viscosity and Stability of a Highly Concentrated Monoclonal Antibody. Pharm. Res. 2017, 34, 193−207. (19) Neergaard, M. S.; Kalonia, D. S.; Parshad, H.; Nielsen, A. D.; Møller, E. H.; van de Weert, M. Viscosity of High Concentration Protein Formulations of Monoclonal Antibodies of the IgG1 and IgG4 Subclass - Prediction of Viscosity through Protein-Protein Interaction Measurements. Eur. J. Pharm. Sci. 2013, 49, 400−410. (20) Singh, S. N.; Yadav, S.; Shire, S. J.; Kalonia, D. S. Dipole-Dipole Interaction in Antibody Solutions: Correlation with Viscosity Behavior at High Concentration. Pharm. Res. 2014, 31, 2549−2558. (21) Roberts, C. J. Therapeutic Protein Aggregation: Mechanisms, Design, and Control. Trends Biotechnol. 2014, 32, 372−380. (22) Calero-Rubio, C.; Ghosh, R.; Saluja, A.; Roberts, C. J. Predicting Protein-Protein Interactions of Concentrated Antibody Solutions Using Dilute Solution Data and Coarse-Grained Molecular Models. J. Pharm. Sci. 2018, 107, 1269−1281. (23) Ben-Naim, A. Statistical Thermodynamics for Chemists and Biochemists; Plenum Press, 1992. (24) Woldeyes, M. A.; Calero-Rubio, C.; Furst, E. M.; Roberts, C. J. Predicting Protein Interactions of Concentrated Globular Protein

models failed to predict high-c2 interactions based only on lowc2 parameters for strongly attractive conditions (e.g., MAb2 at pH 6.5). An additional approach using the MSOS algorithm to compute osmotic virial coefficients was tested and found to mimic the results from the TMMC algorithm for conditions where B22/B22,ST was larger than approximately −1. The simulations showed that both the HEXA and DODECA models were able to quantitatively or semiquantitatively predict the experimental data based solely on parameters obtained by combining B22 versus TIS experimental and simulated data collected at low c2, if the conditions were net repulsive or mildly net attractive relative to steric-only interactions. Finally, a more structurally refined CG 1bAA model was used to identify if anisotropic charge distributions were responsible for strong attractions for the MAb2 at pH 6.5 and low protein concentrations. The results obtained from the 1bAA model semiquantitatively and qualitatively agree with those measured experimentally, and demonstrated this as an alternative approach to predict when electrostatic interactions will transition from net repulsive to net attractive as a function of pH.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.9b03779.

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Derivation of a simplification to the MSOS algorithm when using a sterics-only reference state; charge distribution of Mab1; HEXA simulations for Mab2 with TMMC and MSOS algorithms; and additional results from 1bAA simulations for Mab1 and Mab2 (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 302-831-1048. ORCID

Christopher J. Roberts: 0000-0001-9978-2767 Present Address §

Biologics Drug Product Development and Manufacturing, Sanofi, Framingham, Massachusetts 01701, USA. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS C.C.-R. and C.J.R. gratefully acknowledge Bristol-Myers Squibb, the National Science Foundation (CHEM 1213728), and the National Institutes of Health (R01 EB006006) for financial support.

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