Monoclonal Antibody Self-Association, Cluster Formation, and

in colloidal dispersions with competing interactions. P. Douglas Godfrin , N?stor E. Valadez-P?rez , Ramon Casta?eda-Priego , Norman J. Wagner , Y...
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Monoclonal Antibody Self-Association, Cluster Formation, and Rheology at High Concentrations Wayne G. Lilyestrom, Sandeep Yadav, Steven J. Shire, and Thomas M. Scherer* Late Stage Pharmaceutical Development, Genentech (a Member of the Roche Group), 1 DNA Way, South San Francisco, California 94080, United States S Supporting Information *

ABSTRACT: The rheological properties of macromolecular and colloidal suspensions are dependent on the thermodynamic and kinetic parameters that define viscous flow, and remain an active field of study with broad implications in cellular biophysics, soft-matter theory, and biopharmaceutical technology. Here we use static light scattering, small-angle Xray scattering, and viscosity measurements as a function of protein concentration to semiquantitatively correlate the oligomeric state of an IgG1 antibody (mAb1) with its rheological behavior at solution pH 6.0 and varying ionic strength (modified by 0.01−0.1 M Na2SO4). Solution SAXS characterization of 100 mM Na2SO4 solutions confirmed that mAb1 forms reversible dimers with extended structures in dilute solutions. Light-scattering measurements over a wide range of concentrations (1−175 mg/mL) provide detailed information on the equilibrium thermodynamic mAb1 interactions and their modulation by modest increases of Na2SO4. Through the use of interacting hard sphere models to fit light-scattering data, we establish that protein cluster formations consisting of 2−9 mAb1 molecules also increase the viscosity of 175 mg/mL IgG solutions from 52 up to 450 cP. The analysis of dilute and semidilute mAb1 solution rheology correlates linearly with the thermodynamic equilibrium cluster size, consistent with the viscosity behavior of elongated oligomeric structures that are not significantly dendrimeric or in a state of globular collapse. Furthermore, SAXS- and rheology-based structural modeling illustrate that only a small set of anisotropic interactions between complementary surfaces are required to nucleate and propagate protein clusters.

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INTRODUCTION With the aim of deriving an accurate understanding of the molecular and microscopic forces that determine the complex macroscopic behavior of fluids, colloidal suspension and protein solution rheology remains an active area of materials and softmatter physics research.1 The rheological behavior of macromolecular solutions and colloidal suspensions is increasingly understood as the product of several fundamental contributions. Hydrodynamic effects contribute to the formation of dynamic clusters that result in shear thickening,2,3 and entropic effects comprised of individual and collective particle diffusion can produce shear thinning.1,4 Contributions from excluded volume (steric repulsion) as well as attractive or repulsive interactions form the basis of thermodynamic effects, long thought to be important but still without a well-defined linkage for integration into modern fluid theories. In a study illustrating the rheological significance of thermodynamic contributions in a concentrated colloidal system, Zukoski and co-workers recently showed that, when thermodynamic effects were removed by normalization, the hydrodynamic contributions were essentially those of noninteracting hard spheres independent of the depletion attraction strength applied.5 However, for systems with interacting species a description of the macroscopic viscosities and moduli from knowledge of © XXXX American Chemical Society

molecular scale thermodynamic and kinetic parameters persists as a significant challenge.6 Highly concentrated solutions of proteins present a unique investigational window into the thermodynamic interaction and hydrodynamic contributions to the rheology and phase behavior of colloidal systems. Proteins are charged molecules with complex surface features consisting of an array of electrostatic and hydrophobic patches.7−9 The primary and higher-order structures of proteins enable a profound range of tuning with different types of amino acid sequences, surface features, sizes, and shapes. The result is that the intermolecular interactions of proteins are highly dependent on the location, anisotropy, and complementarity of their surface patches, helping to define their broad biological utility. In highly concentrated protein solutions, these interactions can take the form of weakly associated oligomers, often termed “clusters”.10 The osmotic second virial coefficient (A2) provides a quantitative measure of the protein−protein interactions, with each protein system subject to unique thermodynamic equilibrium properties that require a tailored approach to Received: January 24, 2013 Revised: March 25, 2013

A

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Rheological measurements as a function of protein concentration (or volume fraction) can be used to evaluate the hydrodynamic features and behavior of the protein molecules under the conditions of constant shear. In the absence of intermolecular interactions between the species in solution, the specific viscosity is dependent on particle shape, size, and volume fraction, all known to be important factors in colloidal and protein rheology.27,28 Both attractive and repulsive molecular interactions can lead to changes in shape, excluded volume, and density fluctuations that significantly increase the complexity of the flow properties of a solution.29−31 However, it is the roles of attractive colloidal/ protein interactions and clustering that provide particularly interesting tests to the developing models and theories of macroscopic rheological properties of the solutions.32,33 Several groups have studied the effects of weakly associated proteins and the formation of equilibrium clusters on protein gelation, crystallization, and other thermodynamic processes.34−37 These publications have increased our knowledge of the effects of protein clustering on the equilibrium behavior of these molecules in a variety of conditions. Recent efforts to understand dilute solution interactions of proteins in relation to the viscoelastic properties at high concentrations have also illustrated the difficulty of correlating 2-particle (pairwise) interactions to the inherently more complex multiparticle interactions and solution dynamics at high concentrations.31,38−40 To date, very little information exists that directly relates the effect of solution thermodynamics and macromolecular clustering of proteins at high concentrations to the solution rheological properties at the same conditions. In this contribution, SAXS and MALS measurements are used in conjunction with the rheological characterization of IgG1 antibody (mAb1) across a wide range of concentrations (1−175 mg/mL) to study the effects of equilibrium (thermodynamic) protein interactions on the dynamic, rheological properties of colloidal protein solutions. mAb1 is shown to self-associate forming oligomers/clusters of increasing size with higher Na2SO4 concentrations, through interpretation of solution light scattering with models of multiple interacting hard spheres. Characterization of dilute solutions (1−5 mg/ mL) with SEC-MALS and SAXS in conjunction with OEM analysis yielded structural information about the early stages of the oligomer assembly process. By sensitively tuning mAb1’s self-association with small increases in the solution ionic strength, the MALS and viscosity data show that increased solution viscosities are clearly correlated with the mAb1 oligomer states prevalent at high concentrations. Analysis of the rheological data alongside structure-based modeling provides evidence that mAb1 self-association results in elongated solution clusters at high concentrations. Collectively, the results demonstrate that mAb1 thermodynamic interactions at high concentrations strongly influence the dynamic rheological (hydrodynamic) behavior of the solutions, and that the contributions of attractive interactions remained unchanged by the system dynamics at the shear rate investigated.

control the self-associative behavior. Toward this end, determination of A2 in the low-concentration regime (0.1 to ∼5.0 mg/mL) has been shown to correlate (albeit qualitatively) with phase behavior such as crystallization and gelation in the high concentration regime (>50 mg/mL).11−13 To account for the unique anisotropic, “patchy” electrostatic and hydrophobic features of real protein surfaces, Neal et al. incorporated orientation-specific interactions in calculating A2 by using Monte Carlo methods for the orientational integral.13,14 Providing a molecular basis for the qualitative correlation of A2 with protein crystallization, this groundbreaking effort illustrated that a small subset of orientations with surface complementarity and attractive interactions are responsible for a majority of the energetic contributions to the net attractive (A2) interactions experienced between protein molecules in solution. Although these advances have increased our knowledge of protein−protein interactions, they do not offer a complete picture of high-concentration protein solution behavior because two-particle interactions do not reflect the full complexity of intermolecular interactions present in concentrated systems.15−17 Protein interactions at high concentrations are not only the result of specific molecular binding or anisotropic pairwise interactions (as A2), but are also influenced by the simultaneous, non-specific long- and short- range interactions between many molecules arising from the molecular/chemical properties of both the solutes and solvent.15,16,18 Thus, while low-concentration measurements of A2 correspond to radially averaged pairwise interactions, measurements in dilute solutions cannot accurately predict the behavior of solutions at much higher concentrations or how the interactions scale when multiparticle interactions are involved. Fortunately, several biophysical methods can be applied to determine the strength and nature of attractive and repulsive forces between solute molecules in high concentration systems. Examples in the literature include osmotic pressure, sedimentation equilibrium, multi-angle light scattering (MALS), dynamic light scattering, NMR, small-angle X-ray scattering (SAXS), and other methods which can be used to gain information on highconcentration protein solutions.18−23 Of these techniques, the scattering methods are often considered the most versatile due to their simple sample preparation and robustness toward a broad range of solution conditions. Interpreting data collected from high-concentration scattering measurements poses unique challenges, since any weak attractive interactions are likely to be masked by the large nonspecific repulsions originating from excluded volume effects.17,24,25 These weak interactions are termed “hidden self-associations” and require special consideration during data analysis.26 Recently, the calculation of total scattering due to the presence of multiple interacting scattering species as a function of concentration was developed by Minton et al.24,25 In the interacting hard-sphere (IHS) models, macromolecular species are represented by equivalent hard convex particles with the mass of the macromolecule and size parameterized by a specific excluded volume that reflects both the hard steric core and short-ranged repulsive interactions with neighboring molecules. Importantly, this approach provides solutionaveraged information on the thermodynamic parameters that contribute attractive intermolecular interactions to form additional scattering species, and accounts for the net effects with association constants and association states.

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EXPERIMENTAL METHODS AND MATERIALS The monoclonal antibody mAb1 is based on a IgG1 framework and κ-light chain. mAb1 was expressed in Chinese hamster ovarian (CHO) cell lines and purified by a series of chromatography steps, including protein A and ion exchange chromatography methods. The purified antibody was then B

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obtained as concentrated solutions from tangential flow filtration with added solution buffers and stabilizers, prior to being dialyzed into 20 mM L-histidine hydrochloride (His-Cl), pH 6.0, and the gravimetrically determined concentrated stock starting material at 175 mg/mL was stored at 2−8 °C until further use. mAb1 presented here is identical to mAb1 in another recent publication,41 but is not the same molecule referred to with the mAb1 designation elsewhere.12,18,31,40 The Na2SO4 and L-histidine hydrochloride of 99% minimum purity were obtained from Fisher Scientific (Fair Lawn, NJ). Small-Angle X-ray Scattering. SAXS data for mAb1 were measured at SIBYLS beamline (12.3.1) of the ALS using a Mar CCD area detector (diameter, 165 mM) at room temperature. Intensity curves were measured at concentrations of 1, 2.5, and 5 mg/mL for protein. Data images were subjected to circular integration, normalization, and subtraction of sample and buffer image files. The RG for each particle was approximated using PRIMUS42 to evaluate the Guinier equation and using GNOM27 to evaluate the p(r) function. The value of the maximum diameter of the particle Dmax was determined empirically by examining the quality of the fit to the experimental data for a range of Dmax values. The ensemble optimized fitting procedure of mAb1 dimers to the SAXS data was carried out in a fashion similar to that presented in Lilyestrom et al.41 The pool of IgG structures used to determine the best-fit minimal selected ensemble (MSE) of mAb1 was created in the following manner. First, 12 coordinate files of representatives of known IgG solution configurations were chosen from previously published data.41,43,44 Dimers of these coordinates were chosen at random and tested for combinations which best fit the SAXS data by exhaustively searching for form factors that matched the experimental scattering file with the program SASREF.45 The 10 best dimer combinations (as judged by χ2 < 2) were mobilized by applying normal-mode analysis with an 8 Å cutoff with the program ModeHunter (Willy Wrigglers, Biomachina.org). Several dozen coordinate files were generated for each of the initial dimer combinations in this manner and the final structural pool contained ∼1400 IgG dimers. The pool of IgG dimers was then combined with a similarly generated pool of ∼4000 IgG monomers41 and in total all the coordinates were used in searching for the final MSE that minimized the residuals between the modeled coordinates and the SAXS data. The MSE analysis was conducted with the program GAJOE.46 Estimates of the molecular/cluster volume (mL/g) were obtained from the measured RG determined by SAXS analysis as well as calculated RG values from computational models using the equation:

V=

N 4 π (R G)3 A 3 M

angles from 38 to 148°. Because the radius of gyration (RG) of mAbE is less than 10 nm, a dilute solution (1−2 mg/mL) of mAbE was used at each salt concentration to normalize the voltages of the photodiodes relative to the 90° detector using a photodiode detector gain setting of 21× at the end of each experiment. Measurement of SLS intensity was conducted as a function of mAb concentration from 0.5 to 175 mg/mL and as a function of Na2SO4 concentration (0−100 mM). Scattering data for each sample/vial were collected over an interval of 5− 10 min with a data collection frequency of 12 points/min. Astra 5.3.4.18 Software (Wyatt Technology Corp., Santa Barbara, CA) was used to acquire and process the SLS data, with a dn/dc value of 0.185 mL/g applied to calculations that could be exported as slice results. For a single scattering species at arbitrary concentration, the generalized equation for Rayleigh scattering intensity (R(θ,c)) reduces to eq 2.48 In this limiting case, which can be applied to systems of purified monodisperse molecules (e.g., many proteins), R(θ,c) is a function of the scattering angle θ and w/v concentration c, and is directly related to the mass of the scattering species (M), the molecular size through the radius of gyration, RG, and solute interactions described by the virial coefficients A2, A3, etc. as shown below. Kc 1 = [1 + 2A 2 Mc R (θ , c ) M ⎡ q 2R G 2 ⎢1 + + 3 ⎣

+ 3A3Mc 2 + ...] ⎤ ...⎥ ⎦

(2)

where K=

2 4π 2n2 ⎛⎜ dn ⎞⎟ ; NAλ 0 4 ⎝ dc ⎠

q=

4πn0(sin θ /2) λ0

The system constant K includes the solution refractive index (n),49 the wavelength of incident light (λ0), the refractive index increment of scattering solute (dn/dc), scattering vector q at scattering angle (θ) and the Avogadro constant (NA). In the limit of infinite dilution (c → 0) and the scattering vector q approaching 0, eq 1 yields the value of 1/M, the absolute molecular mass of the scattering species. In practice, lightscattering measurements are made at both finite concentrations and angles, extrapolating to one or both limiting conditions to obtain M. To simplify interpretation of the data directly obtained from light-scattering measurements, the value of apparent molecular mass (Mapp) is introduced and is defined at concentration c as R(0,c)/Kc in the limit of θ → 0. Modeling of Macromolecular Solution Nonideality with Thermodynamic Expressions for Self-Associating Hard Spheres. The use of scaled particle theory and thermodynamic models of up to three interacting species of hard spheres has been previously described in detail.25 Briefly, a generalized approach to the case of mixtures of interacting species is provided by the thermodynamically based fluctuation theory of light scattering.50,51 According to this theory, the average scattering intensity of a mixture of species is given by

(1)

where V represents an estimate of the hydrated cluster volume, RG is the radius of gyration from computational models as determined with the program CRYSOL,47 NA is Avogadro’s constant, and M is the molar mass of an IgG monomer. Static Light-Scattering Measurements. An 18-angle Dawn EOS light-scattering detector with a 30 mW solid-state laser (λ = 690 nm) from Wyatt Technology (Santa Barbara, CA) was used for all static light-scattering (SLS) measurements with a water-cooled Peltier temperature controller set at 23 °C. The instrument was calibrated with 99.9% toluene (chromatography grade). For a typical scintillation vial experiment, a detector gain setting of 1× was used for all photodiodes at fixed

R(θ , w) = K

∑ MiMj⟨ΔCiΔCj⟩

(3)

where Mi denotes the molecular weight of the ith scattering species, ⟨ΔCiΔCj⟩ denotes the average fluctuation correlation of the molar concentrations of scattering species i and j, and K is identical to the optical constant defined in eq 2. Expressions C

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Figure 1. MALS and SAXS analysis of mAb1 self-association at low concentrations. (A) SEC-MALS analysis of mAb1 self-association at 1, 2.5, 5.0, and 10.0 mg/mL in 20 mM His-Cl pH6.0, 100 mM Na2SO4. The elution profile of mAb1 in the absence of Na2SO4 in the mobile phase (gray trace) depicts a homogeneous molar mass of ∼150 kDa. Increasing the concentration injected mAb1 from 1 to 10 mg/mL (higher concentrations are darker red) increases the mobility, broadens the elution profile, and creates a heterogeneous molar mass of mAb1. (B) Batch-MALS experiments illustrate the concentration dependent self-association behavior of mAb1 under thermodynamic equilibrium. Increasing concentrations of mAb1 in 100 mM Na2SO4 increased the apparent molar mass significantly more than in the SEC-MALS experiments because samples were analyzed at higher constant concentrations. (C) SAXS scattering profiles of mAb1 exhibit an increase in the intensity of the low q values, reflecting an overall increase in RG. (D) The Fourier transformed P(r) functions were used to determine values of the average maximum dimension of the molecules within mAb1 solutions from the data presented in panel C. Increasing the concentration of mAb1 in the SAXS samples with 100 mM Na2SO4 results in a dramatic increase in the maximum dimension of the molecules in solution.

Rheological Measurements and Analysis. Measurements of mAb1 viscosity under the conditions described in this paper were completed using a Ta-AR G2 rheometer (TA Instruments, New Castle, DE) under constant shear rate of 1000/s using a 40 mm anodized aluminum cone with angle 1:0:50 (degree:minute:second) at 25 °C. Measurements of solution viscosity were averaged for 10 s for a total time of 2 min using 330 μL sample volumes. Viscosity measurements at the highest concentration (175 mg/mL) were obtained in duplicate and averaged to report the results. The solution rheology was characterized using the modified Ross and Minton equation:12,52

for average self- and heterofluctuation correlations as functions of species concentration ci and the partial derivatives of thermodynamic activity coefficients with respect to molar concentration (∂ ln γi/∂Cj) in mixtures of up to three scattering species have been presented elsewhere.24,25 In this model, the assumption is made that all species may be represented by equivalent hard spherical particles with identical specific excluded volume, so that the volume of each equivalent spherical particle is proportional to the mass of the oligomer represented. The association state(s) of the oligomer species (n and m) are obtained from fitting a model with monomer mass (M1), and association constants K1n and K1m for each solution condition. The effective hard-spherical model also employs an adjustable parameter Vex, referred to as the effective exclusion volume, which reduces to the actual partial specific volume in the absence of electrostatic repulsion (i.e., near the iso-ionic pH of the protein). More generally, Vex exceeds the mAb partial specific volume to provide a measure of the repulsive intermolecular interactions in concentrated solution.25 The data obtained for all angles at any single concentration were averaged to obtain an angle-independent value of R(0,c)/ K or simply R/K. Using scripts and functions written in MATLAB (R2011b, Mathworks, Natick, MA), nonlinear leastsquares modeling of the dependence of R/K upon the concentration of all scattering species (ctot) was carried out for each protein solution varying in Na2SO4 concentration.

ηinh =

ln(ηr ) c

=

k [η] ln(ηr ) + [η] v

(4)

where ηinh is the inherent viscosity, ηr is the relative solution viscosity, [η] is the intrinsic viscosity in mL/g, ν is the Simha shape parameter,53 k denotes the self-crowding factor, and c is the concentration in mg/mL. Equation 4 is an extension of Mooney’s semiempirical equation,54 applicable to the viscosity behavior of concentrated noninteracting spherical particles, where the volume excluded is the primary contribution to solution viscosity. According this equation, a plot of ηinh versus ln(ηr) should provide a linear relationship with an intercept equal to [η] and slope equal to [η]k/v. A deviation from linearity indicates that other mechanisms besides the excluded volume effect (hard-sphere model) also contribute to the D

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log Ka = 5.3−6.1 M−1 (depending on the model assumed). This detailed analysis of dilute solution mAb1 data in 100 mM Na2SO4 conditions is provided as Supporting Information, Figure S-1, and supports the hypothesis that dimerization may be a first step in the formation of higher-order oligomers in viscous protein solutions. Thus, at concentrations of 1−5.0 mg/ mL mAb1 is shown to form significant concentrations of reversible dimers. SAXS data of mAb1 in 20 mM His-Cl pH 6.0, 100 mM Na2SO4 at 1, 2.5, and 5.0 mg/mL protein concentrations reproduced the MALS results. The SAXS data (Figure 1C) illustrate increasing scattering intensity in the structure factors of each scattering pattern in a concentrationdependent manner. Similarly, the radius of gyration (RG) for each condition increases from 48.0 Å in the absence of Na2SO4 to 72.1 Å in 100 mM Na2SO4 and 5.0 mg/mL mAb1. Concurrent with the increase in RG, the maximum dimension (Dmax) of mAb1 increases from ∼152 Å in the absence of Na2SO4 to 268 Å with Na2SO4 and 5.0 mg/mL mAb1 (Figure 1D, Table 1). Mapp estimates from the SAXS data also suggest mAb1 forms dimers under these conditions, while the increase in Dmax of ∼116 Å suggests that these dimers have elongated form factors. We have previously determined the form factor of mAb1 under several conditions varying in salt concentration and salt type.41 Using the extensive characterization of mAb1 solution structures, we were able to apply rigid body modeling and molecular dynamics to search for the mAb1−mAb1 contacts that best reconstructed the overall SAXS scattering patterns of 1, 2.5, and 5.0 mg/mL mAb1 in the 20 mM His-Cl, pH 6.0, 100 mM Na2SO4 conditions. In order to determine approximate fractions of monomers and dimers in each solution condition, we searched for minimal selected ensembles (MSE) from an original pool containing 5400 structures of IgG monomers and dimers. Using MSE methods with the final ensemble size fixed to 10 coordinate files, it was determined that there are ∼40%(χ2 = 0.850), ∼50%(χ2 = 1.029), and ∼80%(χ2 = 1.479) dimers in the 1, 2.5, and 5.0 mg/mL mAb1 solutions, respectively. The mAb1 monomer conformations in the final MSE for each condition are similar to those that have been previously reported.41 Representative conformations of mAb1 dimers from this search are illustrated in Figure 2. The Dmax of mAb1 dimers that are included in the MSE vary from ∼260−314 Å (Figure 2A) and when subtracted from the experimental data produce residuals that are close to zero for all scattering angles (Figure 2B). The mAb1 dimer models (Figure 2C) suggest that both Fab−Fab and Fab−Fc interactions are present in solution and account for the increase in Mapp as well as increase in RG and Dmax that were determined in the MALS and SAXS experiments. The mAb1 dimer models from the MSE reconstruction of the SAXS scattering profile for at 5 mg/mL mAb1 with 100 mM Na2SO4 suggest that these complexes are elongated structures which appear to result from a limited number of anisotropic protein−protein interactions. Therefore, in the lowconcentration regime, the addition of Na2SO4 is sufficient to equilibrate interactions between mAb1 molecules in a way that increases the presence of higher-order associated species, which at 5 mg/mL can be dimeric. To gain more detailed insights into mAb1 solution interactions in the presence of Na2SO4, static light-scattering and rheological measurements of mAb1 over a concentration range of 1−175 mg/mL with 10, 20, 50, and 100 mM Na2SO4 cosolute were conducted. Figure 3 illustrates the increases in Mapp as a function of protein and Na2SO4 concentrations are

solution viscosity. The value of the slope divided by the intercept provides the effective crowding factor k/v. Following this analysis, the effective volume, [η], was obtained from linear extrapolations to intercept. In cases where the viscosity data did not fit the linearized eq 4 and showed a curvature, a linear extrapolation was performed from three to four terminal data points to obtain apparent effective volume [η]app in respective Na2SO4 conditions.

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RESULTS We chose mAb1, an IgG1 antibody with a significant number of surface-exposed hydrophobic residues in its complementarity determining region (CDR) and a general tendency to selfassociate under conditions of low to moderate ionic strength (with a variety of different salts), as a model to study the influence of ionic strength and protein concentration on weak, nonspecific protein intermolecular interactions and the rheological behavior of concentrated protein systems. Figure 1 illustrates mAb1’s self-association in 100 mM Na2SO4 as analyzed by SEC-MALS, MALS, and SAXS. Initially, mAb1 was noted for its tendency to elute at earlier times in SEC-MALS experiments as a function of protein concentration in the injection (1, 2.5, 5.0, and 10 mg/mL) when the mobile phase was 20 mM His-Cl pH 6.0 and 100 mM Na2SO4 (Figure 1A). Although the peak is clearly eluting ∼1 mL earlier volume in the SEC-MALS experiment, it also broadens from ∼0.9 mL in the experiment lacking Na2SO4 in the mobile phase to ∼1.3 mL in width in a profile that contains a significant shoulder in the 10 mg/mL injection with 100 mM Na2SO4. The apparent molecular weight (Mapp) values across the elution profile for each SEC-MALS experiment increase moderately with increasing protein concentration in the 1.0, 2.5, and 5.0 mg/ mL injections while the 10.0 mg/mL injection has an apparent molecular weight of ∼200 kDa in the elution profile’s leading edge. This chromatographic phenomenon is indicative of a weakly associated protein complex that dissociates with dilution as it passes through the SEC column. To confirm this result, the experiment was repeated with individual MALS measurements at fixed mAb concentrations/solution conditions; the same protein concentrations/solution conditions could be tested in the absence of the SEC column dilution effects. The result of the MALS experiment in Figure 1B illustrates the increase in Mapp when the protein concentration is constant during the course of each injection in the presence of 100 mM Na2SO4. Here, Mapp increases from ∼146 kDa in the absence of Na2SO4 at 1 mg/mL mAb1 to 230, 274, 308, and 382 kDa for 1.0, 2.5, 5.0, and 10 mg/mL concentrations, respectively, of mAb1 in 100 mM Na2SO4 (Table 1). Light-scattering measurements in dilute solutions were extended from 0.1 to 5 mg/mL to collectively provide monomer−dimer association constants of Table 1. Results from SAXS Data Analysis for mAb1 in 20 mM His-Cl, pH 6.0, and Increasing Concentrations of Na2SO4 [mAb1] (mg/mL)

Mapp (MALS)

Mapp (SAXS)

Guinier RG (Å)

Dmax (Å)

1 (NS) 1 2.5 5.0 10.0

146 230 274 308 382

144 218 246 301 −

48.0 59.7 64.0 72.1 −

152 180 225 268 − E

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Figure 2. Ensemble optimized fitting of mAb1 dimers to the SAXS scattering pattern. (A) The overall frequency of the maximum dimension of dimers within the ensemble (black line) is plotted along with the distribution of maximum dimension of the mAb1 dimers selected from the ensemble as best fit models. (B) The residuals (data − model) were used to determine the quality of the selected ensemble. (C) Two mAb1 dimer models from the minimal selected ensemble. One model illustrates a Fab−Fc interaction (left), while the other model illustrates a Fab−Fab interaction (right).

excluded volume effects in the higher-concentration regime, which result in the formation of thermodynamic equilibrium higher-order mAb1 clusters. While the increasing Mapp with increasing mAb1 and Na2SO4 concentration clearly establishes that the protein in this system self-associates, the extent to which mAb1 interacts at high concentrations requires more detailed analysis of the solution nonideality.26 Recently developed by Minton,25 scaled particle theory of multiple scattering species provides models that are able to account for the light scattering of up to three interacting species in solution. The interacting hard-sphere (IHS) models integrate the effects of excluded volume and attractive intermolecular interactions across a large concentration range with a minimum of adjustable parameters to semiquantitatively determine the extent of mAb1 self-association under the conditions used in Figure 3. The adjustable parameters of IHS models used to fit experimental data sets include the intermediate self-associated species (m-mer) and the higherorder associated species (n-mer) in terms of monomer units (Table 2, Figure 4), as well as the corresponding association constants (K1m and K1n) for each oligomer.

Figure 3. Light scattering as a function of mAb1 concentration presented in the form of apparent molecular weight. The data illustrate the increasing tendency of mAb1 to self-associate as a function of Na2SO4 concentration.

Table 2. Best Fit Parameters for mAb1 Modeled by Multicomponent Equilibrium Association with Solution Nonideality

visibly nonlinear. The data show that, in the absence of salt, mAb1’s Mapp values decrease rapidly with higher protein concentrations, illustrative of net repulsive protein intermolecular interactions. In contrast, with increasing Na2SO4, mAb1’s Mapp increases to a maximum of ∼460 kDa at ∼25− 30 mg/mL in 100 mM Na2SO4 and then decreases to ∼90 kDa at concentrations above 150 mg/mL. Overall, the data obtained for mAb1 solutions with 10−100 mM Na2SO4 suggest increasingly attractive interactions at low to moderate concentrations of protein with contributions from the repulsive F

[Na2SO4] (mM)

mol wt (Da)

m-mer

log K1m

n-mer

log K1n

Vex

0 10 20 50 100

140000 150000 150000 150000 150000

2 2 2 2 4

0.1 4.2 3.6 4.9 12.5

3 3 4 6 9

3.2 9.4 13.5 23.7 33.6

2.6 2.1 2.1 2.2 2.5

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Figure 4. Concentration dependence of scattering intensity (data and calculated best fit of nonideal monomer, m-mer, n-mer interacting hard-sphere models) for mAb1 in 20 mM HisCl with (A) 0 mM (no added salt), (B) 10 mM, (C) 20 mM, (D) 50 mM, and (E) 100 mM Na2SO4.

Modulating Na2SO4 concentration in this system clearly is an effective method of tuning the strength and range attractive interactions between mAb1 molecules, and these interactions result in the formation of oligomers or clusters at high concentrations. Thermodynamic interactions and equilibrium structure associations are proposed to have a more influential role than hydrodynamic interactions in determining the rheological behavior of solutions or colloidal suspensions with increasing volume fraction (Φ).5,55 Colloidal systems with short-range attraction (like mAb1) often display increases in solution viscosity, or jam with increasing Φ and crowding effects until the phase transition critical point (Φc) is reached to form gels.30 The high-concentration light-scattering measurements provide compelling thermodynamic evidence of mAb1’s self-association and cluster formation, and offer the opportunity of studying the rheological effects of sensitively tuning the attractive interactions between mAb1 molecules. Therefore, solutions of mAb1 were prepared with a wide range of protein concentrations (1−175 mg/mL) and Na2SO4 conditions (0, 10, 20, 50, 100 mM Na2SO4) identical to those used for highconcentration MALS experiments) with 20 mM His-Cl, pH 6.0, prior to determining its viscosity under constant shear rate (1000 s−1). Figure 5A illustrates the solution viscosities in centipoise (cP) as a function of concentration for mAb1 in each salt condition. The viscosity of mAb1 solutions clearly increases as a function of both protein and Na2SO4 concentration. To directly relate the rheology of mAb1 solution as a function of Na2SO4 to the prevalent oligomers (n = 2−9) present at the highest concentrations, solution viscosities of mAb1 at 175 mg/ mL were determined in duplicate and plotted as a function of oligomer size n (Figure 5B). mAb-E viscosity at 175 mg/mL is included as reference point for IgG1 solutions existing as monomeric species across the concentration range, due to strong net repulsive electrostatic interactions at the low ionic strength 20 mM His-Cl, pH 6 buffer experimental conditions.18,40 Error bars associated with mAb1 solution viscosity at 175 mg/mL are comparable to the symbol size, while the error bar for n = 2 reflects uncertainty in the average oligomer size present in 0 mM Na2SO4 as well as for n = 9 where the IHS modeling analysis with n = 8−10 provided equivalent results with similar degrees of fit to the 100 mM Na2SO4 mAb1 solution data. An essentially linear relationship between the increasing oligomer size (n) and solution viscosity (cP) is obtained in a manner consistent with Staudinger’s rule.28 This correlation unmistakably demonstrates the importance of the attractive intermolecular interactions in determining solution viscosity.

Analysis of the MALS scattering intensity (R/K) data with IHS models reveals that additional details of the mAb1 selfassociation behavior at high concentrations can be deconvoluted and interpreted. Figure 4 illustrates the IHS model fits to the concentration dependent scattering data and the effects of increasing association of mAb1 in 10, 20, 50, and 100 mM Na2SO4. Best-fit parameters included a fixed molecular weight of 150 kDa and Vex of ∼2.2 mL/g for mAb1 within conditions that contained Na2SO4 (Table 2). Electrostatic repulsions likely dominate the net repulsive interactions between mAb1 molecules in the absence of Na2SO4 and may account for the differences in the best-fit values for that data in Table 2. Remarkably, even small increases in solution ionic strength (20−200 mM) with Na2SO4 resulted in dramatic increases in mAb1 self-association to form dimer and higher-order oligomers. The solution scattering in the presence of Na2SO4 can be accounted for by the thermodynamic reversible association of mAb1 to form equilibrium oligomers of stoichiometry n = 2−9 depending on salt concentrations. Although the ability of the IHS models to fit the data quantitatively with three scattering species does not necessarily indicate the presence of a single higher oligomer or “n-mer”, such fitting parameters could reflect a distribution of higherorder oligomers centered about the value of n. However, using a limited number of scattering species generally facilitates identification of the best fit and discrimination between several models of association; as the number of fitting parameters/ species increases, so does the number of acceptable fits and the complexity of identifying the most appropriate model. Regardless, the data unequivocally illustrate that increasing Na2SO4 concentrations from 10 to 100 mM leads to an increase in oligomer (cluster) size and association constant (log K1n, Table 2). While m-mer (intermediate oligomer) association constants did not increase significantly (log K1m = 3.6−12.5 M−1) across the salt range studied, the association constants for the n-mer species increased from log K1n values of 3−34 M−1, coinciding with the increasing cluster sizes required to fit the light-scattering data. Simulations of the mass fraction compositions for the three scattering species (monomer, mmer, and n-mer) as a function of total protein concentration were made using the association constants and oligomer states obtained from IHS best fit results. Such calculations determined that, in each scattering experiment, n-mer clusters comprise a majority (>90% by mass) of scattering species at the highest concentrations (175 mg/mL) as shown in the Supporting Information, Figure S-2. Collectively, the light-scattering results lead to the conclusion that larger, more tightly bound mAb1 oligomers are formed with increasing Na2SO4 concentrations. G

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Figure 6. Solution inherent viscosity vs ln(ηr) plotted in accordance with eq 4, for mAb1 in the presence of increasing Na 2 SO 4 concentration and hard spheres ηinh calculated from the viscosity data reported for glass beads.54 For hard spheres, a linear fit to the viscosity data is obtained as expected from theory. The data for a similar IgG1 mAb (●) (mAb-E, from ref 40) are also well described by a linear fit, providing an example of rheological behavior regulated by repulsive excluded volume effects for a molecular analogue. In contrast, mAb1 data are nonlinear and progressively moreso with increasing Na2SO4 levels. The [η]app obtained for mAb1 at high concentrations for various Na2SO4 concentrations are detailed in Figure S-2 in the Supporting Information.

mAb1 solution rheology. The hard-sphere data shows the expected linearity as a function of volume fraction; linear regression analysis provides an intercept of 2.5 mL/g for the apparent effective volume ([η]app), matching the theoretical intrinsic viscosity of a sphere, while a constant slope of 1.37 establishes the viscosity behavior of particles in the absence of attractive or repulsive interactions. In contrast, the rheological data for mAb1 have significant curvature as a function of the relative viscosity that increased with Na2SO4 concentration. Due to the obvious nonlinearity in mAb1 inherent viscosity data, the apparent effective volume was determined from the yaxis intercept using linear regression analysis of the 3−4 highest protein concentrations data points for each Na2SO4 solution condition (Supporting Information, Figure S-3). The results are summarized in Figure 7A and show large increases the apparent molecular volumes, which ranged from 10 to 35 mL/g as a function increasing Na2SO4 concentration. Even in the absence of Na2SO4 mAb1 viscosity data shows a degree of curvature. Although low concentration analysis of [η]app results in a value ∼7 mL/g typical for an IgG1 monomer,57,58 at higher mAb1 concentrations in 0 mM Na2SO4 [η]app ∼10 mL/g, suggesting that reversible dimer species may be present to some extent at high concentrations due to weak mAb1 self-association. The increase in the effective rheological volumes as a function of ionic strength corroborates the increasing cluster sizes observed by light scattering at high mAb1 concentrations. The open squares also shown in Figure 6 illustrate data for a similar IgG1 mAb, mAb-E, as presented previously.40 In contrast to mAb-1, mAb-E viscosity analysis displays a linear trend to indicate that its solution behavior is determined primarily by the excluded volume effects of a single species at all concentrations. Two important observations from the rheological analysis are worth noting. First, the nonlinear solution rheology clearly

Figure 5. Effect of mAb1 cluster size and on mAb1 viscosity. (A) Viscosity profiles of mAb1 in 0, 10, 20, 50, 100 mM Na2SO4 collected for various concentrations in the range of 1−175 mg/mL (up to volume fraction ∼0.25). The profiles illustrate the dependence of mAb1 viscosity on Na2SO4 concentration and, therefore, mAb1 cluster size. (B) Viscosity vs cluster size (n) for mAb1 at volume fraction 0.25 (175 mg/mL concentration) where the MALS data analysis demonstrates average mAb1 oligomer sizes of 2−10 exist as a function of increasing Na2SO4 concentrations. Error bars associated with viscosity are comparable to the symbol size, while error bars for cluster size at n = 2 and n = 9 reflect analytical uncertainty in the average oligomer size present for these two data points. The first-order relationship between viscosity and mAb1 cluster size suggests that these larger mAb1 oligomers exist as end-to-end associated and semiextended structures (e.g., random-walk chains) in solution, instead of branched, compact clusters or collapsed globules.

To evaluate the molecular and solution structural implications of protein self-association on the rheology at high concentrations, mAb1 viscosity data were analyzed using the modified Mooney equation.52 This approach offers quantitative analysis of the behavior of mAb1 under dynamic conditions of shear, in terms of the apparent volume occupied by mAb1 species in each salt condition. Figure 6 presents the analysis of solution inherent viscosity (ln(ηr)/c) versus the relative viscosity (ln(ηr)) for mAb1 in 0−100 mM Na2SO4 in accordance with eq 4. The hard-sphere rheological model was obtained from the work of Vand et al. on monodisperse suspensions of glass spheres56 and is shown for comparison to H

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Figure 7. Experimental data and computational models of the effective molecular volume of mAb1. (A) Shown in green columns are [η]app obtained from the experimental data (Supporting Information, Figure S-2) at high concentrations, while the values derived from computational models are represented by blue columns. (B−E) Computational models of mAb1 trimer, tetramer, hexamer, and nonamer species corresponding to the equilibrium oligomeric states determined with MALS as well as the apparent volumes determined from the rheological characterization of solutions. The mAb1 model structures were assembled on the basis of localized Fab−Fab and Fab−Fc interactions and are shown with superimposed gray spheres (origins positioned at each model’s center of mass) that illustrate the radii of gyration and the apparent volumes of each oligomer.

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DISCUSSION The evidence for equilibrium formation of protein cluster species has long been anticipated as a nanoscale feature of transitions between soluble species and phase-separated protein gels, crystals, and metastable liquid concentrates. To date, the evidence of protein cluster formation in high concentration is primarily based on SANS measurements of lysozyme solutions which have been the subject of considerable debate.7,35,59 Transient cluster formations that are induced by shear, on the other hand, have been unambiguously shown to cause shearthickening rheological behavior in systems of noninteracting colloidal suspensions.1 The work presented here details the experimental characterization of the self-association and solution rheological behavior of an IgG1 monoclonal antibody that has been observed to form gels and crystalline phases with a variety of ionic strength conditions and salt types. Solutions of mAb1 varying in protein concentration and ionic strength modulated by Na2SO4 were used as a model system to observe the formation of equilibrium protein clusters, and to correlate mAb1 cluster size (n-mer) to solution rheology at a fixed (low) shear rate. Furthermore, analysis of both mAb1 equilibrium and rheological solution behavior provides information on the thermodynamic and apparent dynamic size and shape of mAb1 clusters across a broad range of concentrations. During the course of investigating the general relationship between mAb

indicates the presence of contributions from intermolecular interactions to the solution rheology of mAb1. At any given value of ln(ηr) the inherent viscosity (ln(ηr)/c) increases as a function of the salt concentration, demonstrating that the interactions between mAb1 species are increasing in strength under dynamic conditions of shear in parallel to the observations at equilibrium. Second, the observed curvature in the rheological analysis indicates effective structures of species changed throughout the concentration-dependent rheology as well. The parameter k/v from the modified Mooney equation accounts for the rheological effects of excluded volume and particle shape: for mAb1, the evident curvature in Figure 6 shows that k/v is not constant, while analyses of typical (low viscosity) mAbs such as mAb-E provide a constant value of k/v at similar concentrations. We attribute the decreasing value of k/v for mAb1 to an increasingly large shape parameter (v), which would suggest a progressively asymmetric shapes or extended structures as a function of both increasing protein and Na2SO4 concentrations. Collectively, the rheological analysis establishes a linkage between attractive intermolecular interactions and the effects on solution viscosity at high protein concentrations, supporting the conclusion that mAb1 thermodynamic molecular-scale interactions have a dominant contribution to the solution dynamic behavior of bulk solution viscosity. I

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ing end-to-end oligomer formation in clusters would result in a higher extension and asymmetry compared to a side−side association, consistent with the analysis of the rheological effects of mAb1 self-association that indicate increasing volume exclusion on the dynamic behavior of the molecules. Equilibrium (thermodynamic) mAb1 clusters with extended structures in solution are proposed to form the stress-bearing chains that influence mAb solution rheology, dramatically increasing the viscosity in proportion with the strength of intermolecular attractions and cluster size. Such a mechanism for the influence of clusters formed by thermodynamic attractive interactions on solution rheology, we note, contrasts with the dense “aggregated” clusters of HS colloids formed by hydrodynamic forces under shear.2,3 We speculate that the higher-order structure of IgG antibodies incorporates several inherent features which can also contribute to their complex rheological and thermodynamic solution behavior as purified proteins. mAbs consist of a multi-dentate overall structure (2 Fabs & 1 Fc binding domain), when combined with the highly flexible range of motion of the Fabs, the potential for complementary surface patches, and the extended/exposed location of CDRs at the termini, render these protein structures especially effective at engaging in intermolecular self- and hetero-interactions.

intermolecular interactions (clustering) and mAb solution rheology, several interesting facets of the system were found to yield additional insights into the molecular details of mAb1 colloidal solution behavior. While the extent of mAb1 self-association behavior is salttype dependent (data not shown, manuscript in preparation), mAb1 solubility was observed to be highly dependent on the solution ionic strength in general. Thus, the tendency of mAb1 to interact with itself appears to be a 2-fold consequence of increased charge screening by salts. Primarily, the increasing salt concentrations minimize the repulsive electrostatic interactions that dominate at low ionic strength conditions (e.g., 0 mM salt). The modification of solution ionic strength with Na2SO4 also appears to facilitate greater hydrophobic attractive contributions to the net interactions between mAb1 molecules. In dilute solutions