Weak Interactions Govern the Viscosity of Concentrated Antibody Solutions: High-Throughput Analysis Using the Diffusion Interaction Parameter

Abstract

Weak protein-protein interactions are thought to modulate the viscoelastic properties of concentrated antibody solutions. Predicting the viscoelastic behavior of concentrated antibodies from their dilute solution behavior is of significant interest and remains a challenge. Here, we show that the diffusion interaction parameter (k_D), a component of the osmotic second virial coefficient (B₂) that is amenable to high-throughput measurement in dilute solutions, correlates well with the viscosity of concentrated monoclonal antibody (mAb) solutions. We measured the k_D of 29 different mAbs (IgG₁ and IgG₄) in four different solvent conditions (low and high ion normality) and found a linear dependence between k_D and the exponential coefficient that describes the viscosity concentration profiles (|R| ≥ 0.9). Through experimentally measured effective charge measurements, under low ion normality where the electroviscous effect can dominate, we show that the mAb solution viscosity is poorly correlated with the mAb net charge (|R| ≤ 0.6). With this large data set, our results provide compelling evidence in support of weak intermolecular interactions, in contrast to the notion that the electroviscous effect is important in governing the viscoelastic behavior of concentrated mAb solutions. Our approach is particularly applicable as a screening tool for selecting mAbs with desirable viscosity properties early during lead candidate selection.

Introduction

The study of weak (i.e., nonspecific) protein-protein interactions is of significant interest given its immense relevance in terms of biological action, biochemical processes, and disease. Weak protein-protein interactions have been shown to influence protein aggregation, solution viscosity, and phase transitions (1–3). Intermolecular interactions coupled with conformational factors have been implicated in diseases such as cataract formation (4) and sickle-cell anemia (5), and in amyloid diseases such as systemic amyloidosis, amyotrophic lateral sclerosis, Alzheimer's disease, Parkinson's disease, and Huntington's disease (6,7). From a biopharmaceutical perspective, protein-protein interactions often become important during the development of concentrated monoclonal antibody (mAb)-based drug solutions.

mAbs are the most rapidly growing class of protein therapeutics being developed for the treatment of a wide spectrum of diseases ranging from cancer to arthritis (8). Currently >20 mAb drugs have been approved, and >400 are in clinical development worldwide (8). The increasing success of therapeutic mAbs can be attributed to their high target specificity, superior safety profiles compared with traditional small-molecule drugs, and long in vivo half-lives (9). Even with these unique advantages, high mAb doses (several mg/kg) are often necessary to achieve an adequate clinical effect. For some diseases, such as cancer, that are often treated in hospital settings, large doses (100–300 mg) of low- to moderate-concentration mAb solutions can be administered via intravenous injection/infusion. However, home-use applications for treating chronic inflammatory diseases, such as rheumatoid arthritis, necessitate the development of high-concentration mAb formulations (<1–1.5 mL) for patient self-administration (10). The development of suitable high-concentration mAb formulations can pose unique manufacturing and delivery challenges resulting from the high viscosity of such solutions.

mAbs exhibit peculiar and diverse viscosity-concentration profiles that reveal a sharp exponential increase in solution viscosity with increasing mAb concentration. Previous studies (2,3) that focused on understanding the origin of high viscosity in some high-concentration mAb solutions suggested that intermolecular interactions may be responsible for the sharp increases in solution viscosity in addition to excluded volume effects. It was proposed that in concentrated mAb solutions (>150 mg/mL), where intermolecular distances can be comparable to or even smaller than molecular dimensions, localized, weak intermolecular interactions between mAb molecules occur through exposed charged and hydrophobic patches. It was hypothesized that such interactions lead to the formation of long-range mAb networks, which suboptimally affect the mAb packing volume fraction and result in high solution viscosity. However, Salinas et al. (11) proposed that the increase in solution viscosity of mAbs may simply be a result of the electroviscous effect, in similarity to the effect observed in dilute solutions of charged colloids, wherein the high net surface charge (or ζ-potential) of particles under low ion normality can dominate viscoelastic behavior.

Here, we posed the following question: If the increase in viscosity of concentrated mAb solutions is caused by weak intermolecular interactions, to what extent would such interactions persist in low-concentration conditions, and could we detect them? The osmotic second virial coefficient (B₂) is an excellent measure of weak pairwise interactions; however, its measurement can be cumbersome and time-consuming (12). Although automated methods are emerging that may be able to increase throughput for B₂ determination (13), previous work showed that the diffusion interaction parameter (k_D), which is related to B₂ by the sedimentation interaction parameter (k_S), the partial specific volume $\left(\overline{\nu }\right)$, and the molecular mass (M) using the equation (14)

$$B_2=\frac{k_S+k_D+\overline{\nu }}{2M}$$ (1)

and is amenable to high-throughput measurement, is an equivalent measure of pairwise intermolecular interactions (1,15). To determine if high viscosity in concentrated mAb solutions can be explained by weak intermolecular interactions present under dilute conditions, we measured the k_D of 29 mAbs under four solvent conditions and examined its correlation to high-concentration mAb viscosity data. We also measured the effective charge of 19 mAbs in low-ion-normality solutions to determine whether the high viscosity of mAbs can be explained by the net charge (or ζ-potential) as incorporated in models describing the electroviscous effect.

In addition to probing the role of interactions as the general underlying mechanism that governs the viscosity of concentrated antibody solutions, our work has significant practical utility. Not only can high-concentration viscosities be severely limiting to the design of efficient ultrafiltration/diafiltration unit operations, they may also necessitate prohibitively high injection forces for delivery through a needle (16). Further, in the high-viscosity regime, small changes in mAb concentrations can lead to large changes in solution viscosity, causing additional process control challenges. Although it is possible to select for molecules with desirable (i.e., low) viscosity early in development, obtaining measurements with concentrated protein solutions by conventional techniques is time-consuming and often requires quantities of material that are not readily available during discovery and lead optimization. There remains a critical need for high-throughput methods that can facilitate rapid screening of molecules.

Materials and Methods

Solution preparation procedures

Twenty-nine full-length mAbs (mAb-1 through mAb-23) and charge-swap mutants for mAb-7 (M-1, M-2, and M-3), and mAb-15 (M-1, M-2, and M-3) with unique complementarity determining region (CDR) sequences were cloned, expressed in Chinese hamster ovary cell lines, and purified at Genentech (South San Francisco, California). The mAbs were constructed with an IgG₁ framework and κ light chains, with the following exceptions: mAb-4 and mAb-11 contained λ light chains, and mAb-13 was constructed with an IgG₄ framework. The numbering of these mAbs is related to the decreasing value of the interaction parameter (k_D) in low-ion-normality solution. Some of these mAbs, including the charge-swap mutants, were used in previous studies and are related to the previous nomenclature as follows: mAb-7 and mAb-15 are MAb2 and MAb1, respectively, in Liu et al. (16). Yadav et al. (17) described the sequence position and amino acids involved in the charge-swap mutations. The charge-swap mutants discussed previously are related to the current nomenclature as follows: mAb-15 (M-1) was labeled as M-7, mAb-15 (M-2) as M-5, mAb-15 (M-3) as M-6, and mAb-7 (M-2) as M-10 in Table 1 of Yadav et al. (17). The isoelectric points (pI) of the mAbs ranged from 7.7 to 9.6 as determined by capillary imaged isoelectric focusing experiments (data not shown). Antibody solutions were stored at 2–8°C before analysis.

The 20 mM histidine-acetate (His-OAc), 20 mM His-OAc with 200 mM arginine-chloride (Arg-Cl), 200 mM arginine-succinate (Arg-Succ), and 30 mM histidine-chloride (His-Cl) buffers were prepared with compendia-grade (USP, NP, EP) chemicals, and purified with deionized water via an Elga PURELAB Ultra (Celle, Germany) water purification system. The His-OAc buffer was prepared by adjusting a solution of 20 mM histidine to pH 5.5 with 18 mM acetic acid. The His-Cl solution was adjusted to pH 6.0 by combining 16.6 mM histidine-hydrochloride monohydrate and 13.3 mM histidine free-base. The Arg-Cl buffer was prepared by adjusting a solution of 20 mM histidine and 200 mM arginine to pH 5.0 with 218 mM hydrochloric acid. The Arg-Succ buffer was prepared by adjusting a solution of 200 mM arginine to pH 5.5 with 121 mM succinic acid.

The 29 mAbs were exhaustively dialyzed into His-OAc, His-Cl, Arg-Cl, and Arg-Succ buffers with the use of Pierce Slide-A-Lyzer dialysis cassettes or Millipore (Billerica, MA) Amicon Ultra centrifugation tubes (10 kD molecular mass cutoff), and the mAb stock solution pH was verified for each dialyzed sample. After dialysis, the samples were concentrated by ultrafiltration with the use of Amicon Ultra centrifugal filtration devices (10 kD molecular mass cutoff). We diluted the mAb stock solutions to the desired concentration with the respective buffer and filtered them through 0.1 μm Anopore membranes using Anotop 10 (Cat. No. 6809-1112) sterile syringe filters (Whatman International, Maidstone, UK) before obtaining viscosity and dynamic light scattering (DLS) measurements.

Determination of antibody concentration by UV spectroscopy

The mAb concentration in the stock solutions (>175 mg/mL) was measured without dilution by slope spectroscopy on a Varian Solo VPE (Bridgewater, NJ) spectrophotometer equipped with SoloVPE software (Bridgewater, NJ). The UV absorbance of a given sample was measured at 279 nm in a quartz cuvette as a function of pathlength using an initial pathlength of 150 μm and a terminal pathlength of 10 μm in 5-μm increments. Each sample measurement was corrected for absorbance at 320 nm and blanked against the appropriate buffer. SoloVPE software was used to determine an optimal (R² > 0.998) slope (m) of absorbance (A) as a function of pathlength (l) for each sample using six absorbance values between 0.5 and 1.0 AU. The slope and the absorptivity (α) were used to calculate mAb concentration (c) for each sample using the Beer-Lambert law:

$$m=\frac{d\left(A\right)}{d\left(l\right)}=\alpha \times c.$$ (2)

The mAb concentration in the diluted antibody solutions was measured with a SpectraMax M2^e microplate spectrophotometer (Molecular Devices, Sunnyvale, CA) equipped with SoftMax Pro software (Molecular Devices, Sunnyvale, CA). The UV absorbance of each sample was measured at 279 and 320 mm on a CoStar UV transparent 96-well plate. Protein concentration was calculated using the absorptivity of each antibody molecule. The absorptivities of the 29 mAbs ranged from 1.41 to 1.70 (mg/mL)⁻¹ cm⁻¹.

Determination of antibody effective charge by capillary zone electrophoresis

The electrophoretic mobility (μ) of 15 mAbs (mAb-1 to mAb-15) was measured with the use of a Beckman Coulter PA 800 plus Pharmaceutical Analysis System (18). The instrument was equipped with a Beckman Coulter eCAP amine capillary (65 cm, 50 μm inner diameter) and a UV detector module. Samples were prepared at 1 mg/mL concentrations in the 20 mM His-OAc, pH 5.5, solution. Dimethylsulfoxide (DMSO) was used as a neutral marker representing electroosmotic flow (EOF). The DMSO was prepared at a concentration of 0.02% (v/v) in water and injected immediately before the mAb sample using an applied pressure of 0.5 psi for 3 s. Detection was performed at 214 nm. Measurements were made in duplicate under applied voltages of 5000, 7000, and 10,000 V in reverse polarity. The apparent electrophoretic mobility of each protein (μ_p^∗) was determined from the slope of a graph that plotted the analyte velocity (V_p) as a function of the electric field (E) (18):

$$V_p=\frac{L_d}{t_p}$$ (3)

$$E=\frac{V}{L_t},$$ (4)

where L_d is the distance in centimeters from the capillary inlet to the detector, t_p is the sample migration time in seconds, V is the applied voltage, and L_t is the total length of the capillary. The same method was used to calculate the electrophoretic mobility of the EOF (μ_EOF) from the DMSO data. A corrected electrophoretic mobility (μ_p) was then determined for each sample by simply subtracting μ_EOF from μ_p^∗. The effective charge or apparent valence (z^∗) was determined by using the following relation (19):

$$z^{\ast }=\frac{{\mu }_p{k}_{\text{B}}T}{D_{0}e},$$ (5)

where k_B is Boltzmann's constant (1.3087 × 10⁻¹⁶ erg/°K), T is the absolute temperature (292 K), D₀ is the diffusion coefficient (average value of 4 × 10⁻⁷ cm²/s for an IgG antibody at infinite dilution as determined by DLS in low-ion-normality solution), and e is the elementary charge (1.60 × 10⁻¹⁹ coulombs).

Determination of antibody effective charge by electrophoretic light scattering

The electrophoretic mobility (μ) of 8 mAbs (mAb-2, mAb-7, mAb-7 (M-2), mAb-14, mAb-15, and mAb-15 (M-1, M-2, and M-3)) was measured with the use of a Malvern Zetasizer Nano Series (Worcestershire, UK). Samples were prepared at 5 mg/mL in the 30 mM His-Cl, pH 6.0, solution. The electrophoretic mobility measurements were made using laser Doppler velocimetry in a DTS1060 clear disposable folded capillary cell in fast field reversal mode. The ζ-potential (ζ) and effective net molecular charge (z^∗) were determined by using Henry's equation (Eq. 6) and a Debye-Hückel approximation of the Poisson-Boltzmann equation (Eq. 7) (20,21):

$$\zeta =\frac{3\eta {\mu }_p}{2\epsilon f\left(\kappa a\right)}$$ (6)

$$z^{\ast }=\frac{4\pi \epsilon a\left(1+\kappa a\right)\zeta }{e},$$ (7)

where η is the viscosity of the solvent (0.89 centipoise at 25°C is used for the purpose of this work), μ_p is the electrophoretic mobility, ε is the dielectric constant of the medium, e is the elementary charge (1.60 × 10⁻¹⁹ coulombs), κ is the Debye-Hückel parameter, α is the radius of a spherical particle, and f(κα) is Henry's function. The Debye-Hückel parameter $\left(\kappa \right)$, which describes the distance (in units of inverse length) across which two charged particles can interact, is a function of the molar ionic strength $\left(I\right)$ of the buffer:

$$\kappa =\sqrt{\frac{8\pi N_0{e}^2}{k_{\text{B}}T\epsilon }}\sqrt{I},$$ (8)

where ε is the solution dielectric constant, e is the electronic charge, T is temperature, $k_{\text{B}}$ is Boltzmann's constant, and $N_0$ is Avogadro's number (21). At a 15 mM solution ionic strength, an $f\left(\kappa a\right)$ value of 1.066 from the literature was used to calculate the ζ-potential (20,21). The Stokes hydrodynamic radius (R_h) calculated using the self-diffusion coefficients, D_s, from DLS measurements was used to determine the effective net molecular charge.

Determination of the diffusion interaction parameter k_D by DLS

The diffusion interaction parameter, k_D, for antibodies in dilute (up to 20 mg/mL) solutions was determined by means of DLS. Diffusion coefficients were measured as a function of protein concentration on a DynaPro PlateReader Plus (Wyatt, Santa Barbara, CA) at a laser wavelength of 828.88 nm. Aliquots (60 μm) of the filtered samples were transferred into sterile, 384-well, glass-bottom Greiner Sensoplates (Greiner Bio-One, Monroe, NC). Wyatt Technology Dynamics software was used to schedule and automate three 20-s acquisitions for each sample. Sample replicate (n = 4) data were averaged to reduce systematic error in the sample preparation and analysis. Measurements were performed at 25°C. The mutual diffusion coefficients, D_m, were determined for each mAb solution at protein concentrations of 1, 5, 10, 15, and 20 mg/mL in His-OAc, Arg-Cl, and Arg-Succ buffers. The diffusion coefficients for mAb-2, mAb-7, mAb-14, mAb-15, and the charge-swap mutants in 30 mM His-Cl buffer, pH 6.0, were measured using a Malvern Zetasizer Nano Series (Worcestershire, UK) at a laser wavelength of 632.8 nm as described previously (17).

The relationship of the mutual diffusion coefficient (D) with the diffusion interaction parameter (k_D) can be related by the self-diffusion coefficient (D₀), range 3.9–4.8 × 10⁻⁷ cm²/s), as a function of antibody concentration (c) using the following equation (14):

$$D=D_0\left(1+k_{D}c\right).$$ (9)

Thus, k_D was calculated by fitting the D versus C data to Eq. 9. The error for k_D was determined by calculating the propagation of the standard error of the coefficients from the linear regression.

Determination of the sedimentation interaction parameter k_S by AUC

The sedimentation interaction parameter (k_S) for antibodies in dilute solutions was determined by sedimentation velocity analytical ultracentrifugation (AUC) using a Beckman Coulter ProteomeLab XL-I analytical ultracentrifuge. Samples were centrifuged at 40,000 rpm at 20°C in 12-mm-pathlength cells equipped with charcoal-epon-filled centerpieces and sapphire windows. The Interference optical system was used to monitor mAb sedimentation. The weight-average sedimentation coefficients were determined from the $g\left(s^{\ast }\right)$ distribution using DCDT⁺ software (3). The sedimentation coefficients (s) were determined for seven mAbs (mAb-1, mAb-2, mAb-5, mAb-9, mAb-12, mAb-13, and mAb-15) at nominal protein concentrations of 1, 2, 5, 7.5, and 10 mg/mL in His-OAc buffer. Antibody concentrations were determined using the average fringe density from the DCDT⁺ software and a ratio of 3.3 fringes per mg/mL of protein. The sedimentation interaction parameter (k_s) was calculated by fitting the reciprocal sedimentation coefficient (1/s) versus antibody concentration (c) data to Eq. 10 (14):

$$\frac{1}{s}=\frac{1}{s_0}\left(1+k_{S}c\right),$$ (10)

where 1/s₀ is the reciprocal sedimentation coefficient at infinite dilution. The error for k_S was determined by calculating the propagation of the standard error of the coefficients from the linear regression.

Determination of the solution viscosity by cone-and-plate rheometry

Viscosity measurements were performed with the use of an Anton Paar Physica MCR 501 concentric cylinder cone and plate rheometer (Anton Paar, Graz, Austria) using an Anton Paar CP-25-1 measuring cell with a 25-mm diameter and 1.007° angle. The antibody solutions were adjusted to a target concentration of 175 mg/mL (± 5%) by diluting the respective stock solutions with the appropriate buffer. Then 70 μL of each sample protein solution were dispensed onto the sample plate and the cone was lowered to achieve uniform contact with the sample solution. Samples were protected from evaporation and temperature was controlled at 25 ± 0.1°C using an Anton Paar H-PTD200 Peltier system, which includes an evaporation hood and thermostat system. Sample viscosity was determined by measuring torque every second for 60 s using a constant shear rate of 1000 s⁻¹. Viscosity measurements are reported as an average of the stabilized viscosity measurements using three sample replicates. Sample analysis and data reporting were done with the use of Anton Paar RheoPlus software.

Determination of the osmotic second virial coefficient

B₂ was calculated using Eq. 1 for seven mAbs in His-OAc buffer, using the experimentally determined k_D, and k_S values, an average $\overline{\nu }$ value of 0.735 mL/g, and the molecular mass of an antibody (M =150,000 g/mol). The error for B₂ was determined by calculating the propagation of the error from k_D and k_S measurements.

Results and Discussion

Correlation of the diffusion interaction parameter with mAb viscosity in concentrated solutions

In ideal solutions, the relationship between the diffusion coefficient (D) and the frictional coefficient (f) of noninteracting Brownian particles can be described by the Stokes-Einstein equation:

$$D=\frac{k_{\text{B}}T}{f},$$ (11)

where k_B is Boltzmann's constant, and T is the absolute temperature.

It follows that smaller particles diffuse more rapidly than larger particles; thus, the diffusion coefficient for a molecular aggregate is generally lower than that of a monomer (23). Similarly, net attractive intermolecular interactions increase the correlation in motion between particles and yield a lower diffusion coefficient compared with that of a single particle; conversely, net repulsive intermolecular interactions yield a greater diffusion coefficient (1–3,14). To account for interactions between Brownian particles, the virial expansion can be used to express the concentration $\left(c\right)$ dependence of the diffusion coefficient by providing corrections for nonideality with a series of virial coefficients $\left(k_i\right)$ (14):

$$D=D_0\left[1+k_{D}c+k_3\left(c^2\right)+\cdots \right].$$ (12)

The diffusion interaction parameter (k_D) can be used as a first-order approximation of the concentration dependence of the mutual diffusion coefficient (D) (Eq. 9) to parameterize the measured deviations from solution ideality. In general, a positive k_D indicates net repulsive interactions and a negative k_D indicates net attractive interactions (2,3,15). For these reasons, the importance of k_D as a measure of intermolecular interactions is well established and numerous efforts have elucidated the relationship between k_D and biophysical properties, phase distribution, and aggregation of proteins (1–3). Previous studies showed that a high solution viscosity in concentrated mAb solution can result from reversible self-association (16,24). However, no comprehensive effort has been directed toward probing interactions that occur in dilute solutions and their relationship to the viscosity exhibited by concentrated solutions. Here, we selected 23 wild-type (WT) mAbs (designated as mAb-1 through mAb-23) and six charge-swapped mutant mAbs (designated as mAb 7 (M-1) through mAb 7 (M-3) and mAb 15 (M-1) through mAb 15 (M-3)) as model proteins to evaluate the utility of the diffusion interaction parameter (k_D), a dilute solution parameter, as a high-throughput tool for screening the viscosity of high-mAb-concentration (175 mg/mL) solutions. Due to material limitations, not all 29 mAbs were analyzed in all four solutions; however, large datasets were generated within each solution (His-OAc, n = 16; Arg-Cl, n = 16; His-Cl, n = 10; Arg-Succ, n = 8). The two solutions of low ion normality were His-OAc at pH 5.5 and His-Cl at pH 6.0. The two high-ion-normality solutions, 200 mM Arg-Cl and 200 mM Arg-Succ, were chosen because arginine salts were previously shown to be particularly effective in reducing mAb solution viscosity (16).

In the low-ion-normality His-OAc (Fig. 1 A) and His-Cl (Fig. 1 B) solutions, k_D values for 16 different mAbs varied over a wide range, from +35.7 mL/g to −22.5 mL/g. The positive values can be interpreted as weak repulsive interactions that exist between mAb molecules (mAb-1 to mAb-8, mAb-7 charge-swap mutants 1–3 and mAb-15 charge-swap mutants 1–2), whereas negative values would suggest weak attractive interactions to persist under these conditions. In the low-ion-normality condition, and in the absence of any electrostatic screening, a given mAb can be expected to experience significant electrostatic repulsion, giving rise to only repulsive interactions under these conditions. However, it is noteworthy that even under the low-ion-normality condition with electrostatic repulsion expected to be dominant (taking a simplistic view of mAbs being point charges), a significant subset of mAbs (mAbs 9–16 and mAb-15 (M-3)) exhibited net attractive interactions. Even more important is the relationship between k_D and mAb solution viscosity (measured at 175 mg/mL mAb). Positive k_D values correlated with lower solution viscosity, whereas negative k_D values correlated with higher viscosity. Correlation plots (Fig. 1, E and F) reveal a reasonable linear relationship between k_D and viscosity in His-OAc (|R|=0.76) and His-Cl (|R|=0.81) solutions. Similarly, a significant qualitative rank correlation between k_D and solution viscosity is observed from the column plots (Fig. 1, A and B).

Figure 1.

Bar plots comparing k_D (■) and mAb solution viscosity (□) in (A) 20 mM His-OAc, pH 5.5, (B) 30 mM His-Cl, pH 6.0, (C) 200 mM Arg-Cl, pH 5.0, and (D) 200 mM Arg-Succ, pH 5.5. Scatter plots display correlation between k_D and viscosity for the corresponding mAbs in (E) 20 mM His-OAc, pH 5.5, (F) 30 mM His-Cl, pH 6.0, (G) 200 mM Arg-Cl, pH 5.0, and (H) 200 mM Arg-Succ, pH 5.5. Viscosity was measured at 175 mg/mL by cone and plate rheometry.

In general, the k_D decreased with increasing ion normality and occupied a narrower range of values. In Arg-Cl and Arg-Succ solutions, the k_D values ranged from −21.0 to 3.8 mL/g and from −15.2 to 6.3 mL/g, respectively. Again, the more-positive or least-negative k_D values correlated with lower solution viscosity in both arginine-containing solutions, as demonstrated by their respective column plots (Fig. 1, C and D). A stronger correlation between k_D and viscosity was observed in the high-ion-normality Arg-Cl solution (Fig. 1 G, |R|=0.87). However, given the paucity (n = 4) of high-viscosity (>20 cP) mAbs to adequately test the strength of the correlation, eight additional mAbs for which the viscosity data span a wider range (7–80 cP) in 200 mM Arg-Succ solution, were chosen to function as a confirmatory training set. The correlation plot for mAbs in the Arg-Succ buffer revealed an even stronger linear dependence between these two parameters (Fig. 1 H, |R|=0.89).

Although the data demonstrate that there is a strong (|R|>0.8) and statistically significant (p < 0.005) correlation between k_D and solution viscosity measured at high protein concentration (∼175 mg/mL), the correlation was the weakest (|R|=0.76 and |R|=0.81) in the low-ion-normality His-OAc and His-Cl solutions. We suspected that the relatively weaker correlation in His-OAc and His-Cl might stem from the increased error associated with measuring the concentration of highly viscous samples. At high mAb concentrations, small errors in concentration can lead to large variations in solution viscosity. If this were true, then the correlation with k_D could be further improved by accounting for the mAb concentration dependence of viscosity, which could be parameterized in terms of the exponential coefficient (k) of a simple exponential (Eq. 13):

$$\mathit{\eta }={\mathit{\eta }}_{\mathit{0}}{e}^{kc},$$ (13)

where η is the solution viscosity at any given mAb concentration c, and η₀ is the solution viscosity at infinite dilution. Due to the considerable material requirements for obtaining viscosity-concentration profiles, analysis was limited to select mAbs from each sample population in three solutions (His-OAc, n = 12 of 16; Arg-Cl, n = 7 of 16; His-Cl, n = 10 of 10). Using this approach (Fig. 2 A, R² range: 0.92–0.99; Fig. 2 B, R² range: 0.93–0.99; Fig. 2 C, R² range: 0.95–0.99), we observed a remarkable improvement in the correlation between k_D and k for His-OAc (Fig. 2 D, |R|=0.94), His-Cl (Fig. 2 E, |R|=0.89), and Arg-Cl (Fig. 2 F, |R|=0.96) solutions when compared with the correlations between k_D and absolute viscosity for the same three sample populations (His-OAc, |R|=0.77, n = 12; Arg-Cl, |R|=0.75, n = 7; and His-Cl, |R|=0.81, n = 10). These results demonstrate that the empirical coefficient k provides a more complete and accurate measure of antibody viscosity compared with a single point viscosity measurement at an arbitrarily chosen high protein concentration.

Figure 2.

Representative plots of solution viscosity as a function of mAb concentration along with corresponding fits in (A) 20 mM His-OAc, pH 5.5; (B) 30 mM His-Cl, pH 6.0; and (C) 200 mM Arg-Cl, pH 5.0. The scatter plot displays a correlation between k_D and the exponential coefficient, k, in (D) 20 mM His-OAc, pH 5.5; (E) 30 mM His-Cl, pH 6.0; and (F) 200 mM Arg-Cl, pH 5.0.

It is important to note that the diffusional interaction parameter (k_D) is a reasonably quantitative predictor of high concentration mAb solution viscosity within a given solvent system, so long as adequate data exist to provide a reference within each solvent system. For example, in our observation, arginine salts had a near universal effect in reducing the viscosity of the more viscous (>20 cP) concentrated mAb solutions with one exception, that of mAb-5 (Fig. 1, A and C, gray column). The mAb-5 solution viscosity (175 mg/mL) increased dramatically in the high-ion-normality solution containing Arg-Cl as compared with the low-ion-normality solution containing 20 mM His-OAc. In contrast to the other 15 mAbs, mAb-5 is predicted to have low viscosity in the His-OAc solution and high viscosity in the Arg-Cl solution based on its k_D values, which is confirmed by the corresponding viscosity measurements in the two respective solutions (Fig. 1, A and C).

In addition, the data demonstrate that k_D is also a good qualitative predictor of changes in solution viscosity after sequence-specific mutations in mAb-7 and mAb-15. For example, mAb-7 (WT) is predicted to have equivalent viscosity with charge-swap mutants mAb-7 (M-1, M-2, and M-3), which is confirmed by corresponding viscosity measurements (Fig. 1 B). In His-Cl solution, the k_D values for mAb-7 WT and mutants ranged from 5.69 to 11.09 mL/g, indicating weak repulsive interactions. Thus, the results indicate that charge substitutions in the framework and CDRs did not change the net molecular interactions from repulsive to attractive, and subsequently no increase in viscosity was observed for mAb-7 charge-swap mutants (M-1, M-2, and M-3).

More interestingly, mAb-15 (WT) is predicted to have higher viscosity than mAb-15 charge mutants (M-1, M-2, and M-3) in His-Cl solution based on their respective k_D values, which is confirmed by the corresponding viscosity measurements (Fig. 1 B). These results suggest that substitutions of charged residues only in the V_L (CDR1 and CDR3) or in both the V_L (CDR1) and V_H (CDR3) of mAb 15 (WT) resulted in a change from net attractive to net repulsive intermolecular interactions in mAb-15 (M-2) and mAb-15 (M-1), which resulted in corresponding decreases in solution viscosity. Similarly, substitutions of charged residues in V_H (CDR3) of mAb-15 (WT) showed net attractive intermolecular interactions for mAb-15 (M-3) with a slight increase in k_D and a decrease in solution viscosity (Fig. 1 B). Although increases in k_D have a strong quantitative correlation with the decreases in viscosity for mAb-15 mutants M-1 and M-2, the behavior of mAb-15 charge-swap mutant M-3, with a considerable lower viscosity than mAb-15 despite an only slightly increased k_D, illustrates a potential limitation of this method. Although k_D is capable of producing a good rank correlation, it fails to produce a strong quantitative correlation (|R|=0.73, n = 4) for mAb-15 and its charge-swap mutants. However, the quantitative correlation with k_D improves (|R|=0.77, n = 4) when the exponential coefficient for viscosity (Fig. 2 E) is used, as discussed previously.

Relation of the diffusion and sedimentation interaction parameters with the osmotic second virial coefficient

The osmotic second virial coefficient (B₂) is often employed as a convenient measure of the nature and magnitude of pairwise protein-protein interactions (25). Although its definition stemming from its relationship to the osmotic pressure (Eq. 14) is well known,

$$\Pi =RTc\left(\frac{1}{M}+B_{2}c+B_3{c}^2+\cdots \right),$$ (14)

the B₂ is also related to the diffusion and sedimentation interaction parameters (Eqs. 9 and 10) by Eq. 1 (14).

From a molecular perspective, positive B₂ values are interpreted to result from net repulsive protein-protein interactions, and conversely, negative B₂ values reflect net attractive protein-protein interactions (25,26). Because of the insights that B₂ provides into the strength and nature of intermolecular interactions, investigators have made numerous efforts to interpret how these intermolecular interactions measured by the osmotic second virial coefficient relate to the biophysical properties, solution behavior, and colloidal stability of proteins (1,12,27,28). Numerous studies have shown a correlation between the osmotic second virial coefficient (B₂) and various measures of protein phase behavior (e.g., solubility, crystallization, and liquid-liquid phase separation) and protein stability (e.g., aggregation and precipitation). Although direct measurements of B₂ require osmotic pressure measurements that can be obtained by membrane osmometry (25,26), a variety of orthogonal approaches, such as static light scattering (SLS) (15), DLS and sedimentation velocity (1,14), sedimentation equilibrium (29), DLS (3), self-interaction chromatography (29), size-exclusion chromatography (27), and cross-interaction chromatography (30), have been reported to provide equivalent measures of B₂—even though negative values for B₂ measured by light-scattering techniques have been shown to include contributions from nonassociative interactions (e.g., excluded volume and protein-solute effects) that exist in protein solutions and can vary with ionic strength and pH (29). To further investigate the importance of k_D and B₂ with respect to protein-protein interactions as they relate to solution viscosity, we determined B₂ for seven mAbs (mAb-1, mAb-2, mAb-5, mAb-9, mAb-12, mAb-13, and mAb-15) that exhibit a broad range of both positive and negative k_D values in low-ion-normality solution (His-OAc). We determined the k_S values using the sedimentation velocity, and calculated k_S, k_D, and partial specific volume (assuming a standard value of 0.735 mL/g) to calculate the osmotic second virial coefficient using Eq. 1.

Fig. 3 A demonstrates that the qualitative rank correlation of k_D is comparable to k_S and B₂ for each of the seven mAbs assessed. The data demonstrate that values obtained independently for k_D (DLS) and k_S (AUC) have a strong linear dependence, and thus so do k_D and B₂. In fact, the data demonstrate a strong linear dependence between k_D and B₂ (Fig. 3 B) consistent with that reported recently for IgG₁s (1,12,15). In particular, Lehermayr et al. (15) established the linear dependence of k_D with B₂ (independently obtained from SLS using a set of IgG₁ and IgG₄ mAbs) described by the empirical equation k_D = 1.06B₂M − 8.9, where M is the molecular mass. In our studies, conducted with different IgG₁s, the linear dependence of k_D and B₂ (obtained from DLS/AUC) can be described by the empirical equation $k_D=1.33B_{2}M-8.2$. Recently, similar results were also reproduced by Saito et al. (12). The two correlations are in excellent agreement, especially considering that the measurements were made independently using different methods for the B₂ determination (SLS versus DLS/AUC), different solution conditions, and different IgG₁ molecules. The excellent correlation between k_D and B₂ for IgG₁ mAbs demonstrates that the two parameters are proportional measures of solution nonideality, and thus that k_D is an equivalent measure of protein-protein interactions as compared with the osmotic second virial coefficient. We must point out that the empirical relationship between k_D and B₂ is not universal but limited to molecular types with similar shapes (e.g., IgGs). Determination of B₂ across molecular types will necessitate an independent determination of both k_D and k_S, as described previously (1).

Figure 3.

(A) Bar plots comparing k_D (■), k_s (□), and B₂ () of the mAb solutions sorted by viscosity in His-OAc buffer. Error in k_D, k_s, and B₂ measurements presented as error bars. (B) Correlation of B₂ (DLS/AUC) with k_D (DLS) for 8 mAbs (●) in low-ionicity solution (20 mM His-OAc, pH 5.5) compared with correlation of B₂ (SLS) with k_D (DLS) for 16 mAbs (○) reported by Lehermayr et al. (15).

The electroviscous effect may not be dominant in governing viscosity at high mAb concentrations

The electroviscous effect, first proposed by Smoluchowski (31), describes the relationship between the specific viscosity (η_s) and the ζ-potential as a function of volume fraction (ϕ) of charged colloidal particles suspended in a dilute electrolyte solution:

$${\eta }_s=2.5\left[1+\frac{1}{\kappa {\eta }_0{a}^2}{\left(\frac{\zeta \delta }{2\pi }\right)}^2\right]\phi ,$$ (15)

where η_o is the solvent viscosity, a is the particle radius, κ is the specific conductivity or inverse Debye length, and δ is the dielectric constant. Thus, with other factors kept constant, particles with larger electrostatic potentials would be expected to have greater effects on specific viscosity under conditions of low ion normality when the electrical double layer is comparable to the particle radius. This effect was previously shown to apply, at least qualitatively, to dilute protein solutions of bovine serum albumin and ribonuclease A (32,33). However, a recent study with concentrated BSA solutions showed that intermolecular interactions, and not net charge, dominate the solution viscosity under these conditions (34). Because of their similar sizes (Stokes radii ∼5 nm) and shapes, mAbs are good models in which to examine the effects of net protein charge on viscosity under conditions of low ion normality. To date, no systematic effort has been made to elucidate the role of the electroviscous effect on mAb viscosity. However, a previous study invoked the electroviscous effect as a plausible explanation for the drop in mAb solution viscosity with increasing ionic strength (11). To investigate the importance of the electroviscous effect in modulating viscosity at high mAb concentrations, we measured the effective charge of 15 mAbs and 4 mAb charge-swap mutants (Fig. 4) in low-ionic-strength buffers (20 mM His-OAc, pH 5.5; and 30 mM His-Cl, pH 6.0). Due to material limitations, analysis was limited to select mAbs from each sample population in two low-ion-normality solutions (His-OAc, n = 15 of 16; His-Cl, n = 8 of 10). A very weak (|R|≤0.5), statistically insignificant (p ≥ 0.2) correlation between effective charge and solution viscosity is observed in His-Ace (Fig. 4 A, |R|=0.37) and His-Cl (Fig. 4 B, |R|=0.48) solutions. Although the quantitative correlation with effective charge improves (|R|=0.57 and |R|=0.49) when the exponential coefficient for viscosity is used (data not shown), the correlation is still much weaker than that observed with k_D (Fig. 2, D and E, |R|=0.94 and |R|=0.89) under identical solution conditions. Our data demonstrate that the electroviscous effect, based on the net charge, may not be dominant, and that nonspecific protein-protein interactions play a more important role in governing the viscosity of concentrated mAb solutions.

Figure 4.

Correlation of mAb effective charge (z^∗) and viscosity in low-ionicity solutions (A) 20 mM His-OAc, pH 5.5, and (B) 30 mM His-Cl, pH 6.0.

Weak protein-protein interactions govern viscosity at high mAb concentrations

Previous work suggests that high viscosity in concentrated mAb solutions may result from reversible mAb self-association (10,16,24). This hypothesis is consistent with the results from our experiments. Our results demonstrate that there is a strong correlation (|R| ≥0.8) between k_D and viscosity, which improves (|R|≥0.9) when the exponential coefficient for viscosity (k) is used. The sign and magnitude of k_D represent the sum of all the interactions (e.g., electrostatic interactions, van der Waals interactions, hydrogen bonds, and hydrophobic interactions) that can exist between mAbs. It has been proposed that these nonspecific interactions can lead to weak self-assemblies of ordered or networked mAbs in solution, which in turn leads to suboptimal antibody packing, causing high solution viscosity.

Although the effective charge is not correlated to viscosity at high mAb concentration (|R|≤0.6, p ≥ 0.2), it is clear that electrostatic attractive interactions contribute significantly to the net nonspecific intermolecular interactions measured by k_D. Upon addition of ionic excipients, the intermolecular attractions present in low-ion-normality solution (Fig. 1, A and B) can be disrupted, resulting in a decrease in solution viscosity (Fig. 1, C and D). The increased ion normality (>15 mM) effectively shields the attractive charge-charge interactions between mAbs that may result from surface charge asymmetry (and not net charge). At high mAb concentrations (>100 mg/mL), the average surface-to-surface interseparation distance, calculated from the inverse cube root of protein number density (ρ_n^−1/3), is of the order of a few (<5) nanometers, which is comparable to the Debye screening length (κ⁻¹) at 15 mM ion normality of ∼2.5 nm. This essentially brings the molecular surfaces into close proximity at mAb concentrations, and intermolecular interactions stemming from the heterogeneity of the surface charge distribution are likely to become important.

Certainly, the intermolecular interactions between mAbs are best studied in the concentrated regime where the high viscosity actually manifests, as demonstrated by Scherer et al. (35). However, our results provide compelling evidence that such intermolecular interactions persist in the concentration regime (≤20 mg/mL) employed for k_D determination, as measured in terms of pairwise two-body interactions. This is a significant finding because k_D is amenable to throughput formats and can be determined rapidly on parallelized, plate-based DLS instruments (36) using small quantities of protein (1–3 mg), and low concentrations (10–20 mg/mL). Thus, k_D may be particularly effective as a screening tool for selecting mAbs with desirable viscosity properties early during lead candidate selection.

Conclusions

We have shown that weak intermolecular interactions that persist in dilute solution correlate with the viscosity of concentrated mAb solutions. Our results demonstrate that both the diffusion interaction parameter (k_D) and the osmotic second virial coefficient (B₂) are proportional measures of intermolecular interactions, and that the k_D is an excellent predictor of mAb viscosity properties in solutions of low and high ion normality. Because DLS is amenable to parallelized, high-throughput formats and requires small quantities of protein, we anticipate that k_D will be more useful than k_S or B₂ in screening candidates for multiple desirable pharmacological and pharmaceutical properties during lead candidate selection.