`
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`
`Biophysical journal
`V1103‘n0‘l (July 3 2012)
`General Collection
`
`2012-07-16 0943156
`W1 Bl8765
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`Volume 103
`
`Number 1
`
`July 3, 2012
`
`,
`
`@Nwwbiophysjnrg
`
`
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`5m
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`Biophysical S
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`Publlfhed by Cell Press
`for the Biophy5|cal Socnety
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`misrmfite'rialwascupiaed
`:figfitgggvmgtfiws
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`CSL EXHIBIT 1019
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`CSL EXHIBIT 1019
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`Page 2 of 12
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`
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`Page 2 of 12
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`

`

`Biophysical Journal Volume 103 July 2012 69 78
`
`69
`
`Weak Interactions Govern the Viscosity of Concentrated Antibody
`Solutions: High-Throughput Analysis Using the Diffusion Interaction
`Parameter
`
`†
`
`†
`
`†
`
`Barthe´ lemy Demeule,
`
`†
`
`‡
`Natalie Ciaccio,
`
`Jamie M. R. Moore,
`
`†
`
`Sandeep Yadav,
`Chris Petry,
`Brian D. Connolly,
`†
`†
`Steven J. Shire,
`and Yatin R. Gokarn
`*
`†
`Pharmaceutical Development, Genentech, Inc., South San Francisco, California; and
`Sciences, University of California, San Francisco, California
`
`‡
`Department of Bioengineering and Therapeutic
`
`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 (kD), 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 kD of 29 different mAbs (IgG1 and IgG4) in
`four different solvent conditions (low and high ion normality) and found a linear dependence between kD and the exponential
`coefficient that describes the viscosity concentration profiles (jRj 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 (jRj % 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 interac-
`tions 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 ther-
`apeutics being developed for the treatment of a wide spec-
`trum 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
`
`Submitted February 10, 2012, and accepted for publication April 24, 2012.
`
`*Correspondence: gokarn.yatin@gene.com or yatin gokarn@yahoo.com
`
`Editor: George Makhatadze.
`Ó 2012 by the Biophysical Society
`0006 3495/12/07/0069/10 $2.00
`
`cancer, that are often treated in hospital settings, large doses
`(100 300 mg) of low- to moderate-concentration mAb solu-
`tions can be administered via intravenous injection/infusion.
`However, home-use applications for treating chronic inflam-
`matory diseases, such as rheumatoid arthritis, necessitate
`the development of high-concentration mAb formulations
`(<1 1.5 mL) for patient self-administration (10). The devel-
`opment of suitable high-concentration mAb formulations
`can pose unique manufacturing and delivery challenges re-
`sulting from the high viscosity of such solutions.
`mAbs exhibit peculiar and diverse viscosity-concentra-
`tion profiles that reveal a sharp exponential increase in solu-
`tion 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 respon-
`sible for the sharp increases in solution viscosity in addition
`to excluded volume effects. It was proposed that in concen-
`trated mAb solutions (>150 mg/mL), where intermolecular
`distances can be comparable to or even smaller than molec-
`ular 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
`
`doi: 10.1016/j.bpj.2012.04.047
`
`Page 3 of 12
`
`

`

`70
`
`Connolly et al.
`
`surface charge (or z-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 inter-
`actions 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 (kD), which is related to B2 by the sedimentation
`interaction parameter (kS), the partial specific volume ðnÞ,
`B2 ¼ kS þ kD þ n
`
`2M
`
`(1)
`
`and the molecular mass (M) using the equation (14)
`
`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 con
`structed with an IgG1 framework and k light chains, with the following
`exceptions: mAb 4 and mAb 11 contained l 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 (kD) 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 posi
`tion 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
`
`C before analysis.
`not shown). Antibody solutions were stored at 2 8
`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 mm 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 mm and a terminal pathlength of 10 mm in 5 mm 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 path
`length (l) for each sample using six absorbance values between 0.5 and
`1.0 AU. The slope and the absorptivity (a) were used to calculate mAb
`concentration (c) for each sample using the Beer Lambert law:
`
`m ¼ dðAÞ
`dðlÞ ¼ a  c:
`
`(2)
`
`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 kD of 29 mAbs under four solvent conditions and exam-
`ined 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 z-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, ob-
`taining 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 facili-
`tate 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
`
`The mAb concentration in the diluted antibody solutions was mea
`sured with a SpectraMax M2e microplate spectrophotometer (Molecular
`
`Biophysical Journal 103(1) 69 78
`
`Page 4 of 12
`
`

`

`Weak Interactions and mAb Viscosity
`
`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 anti
`body 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 (m) 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 mm 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 dupli
`cate under applied voltages of 5000, 7000, and 10,000 V in reverse polarity.
`The apparent electrophoretic mobility of each protein (mp*) was determined
`from the slope of a graph that plotted the analyte velocity (Vp) as a function
`of the electric field (E) (18):
`
`Vp ¼ Ld
`tp
`
`E ¼ V
`Lt
`
`;
`
`(3)
`
`(4)
`
`where Ld is the distance in centimeters from the capillary inlet to the
`detector, tp is the sample migration time in seconds, V is the applied voltage,
`and Lt is the total length of the capillary. The same method was used
`to calculate the electrophoretic mobility of the EOF (mEOF) from the
`DMSO data. A corrected electrophoretic mobility (mp) was then deter
`mined for each sample by simply subtracting mEOF from mp*. The effective
`charge or apparent valence (z*) was determined by using the following
`relation (19):
`
`;
`
`z ¼ m
`pkBT
`D0e
`where kB is Boltzmann’s constant (1.3087  10 16 erg/
`
`K), T is the abso
`lute 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).
`
`(5)
`
`Determination of antibody effective charge by
`electrophoretic light scattering
`
`The electrophoretic mobility (m) 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 (Worcester
`shire, 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 z potential (z) and effective
`net molecular charge (z*) were determined by using Henry’s equation
`(Eq. 6) and a Debye Huckel approximation of the Poisson Boltzmann
`equation (Eq. 7) (20,21):
`
`p
`
`z ¼ 3hm
`2ε fðkaÞ
`z ¼ 4pεað1 þ kaÞz
`
`;
`
`e
`
`71
`
`(6)
`
`(7)
`
`
`where h is the viscosity of the solvent (0.89 centipoise at 25
`C is used for
`the purpose of this work), mp is the electrophoretic mobility, ε is the dielec
`tric constant of the medium, e is the elementary charge (1.60  10 19
`coulombs), k is the Debye Huckel parameter, a is the radius of a spherical
`particle, and f(ka) is Henry’s function. The Debye Huckel parameter ðkÞ,
`which describes the distance (in units of inverse length) across which two
`s
`charged particles can interact, is a function of the molar ionic strength
`ðIÞ of the buffer:
`k ¼ 8pN0e2
`kBT ε
`
`p
`
`;
`
`I
`
`(8)
`
`where ε is the solution dielectric constant, e is the electronic charge, T is
`temperature, kB is Boltzmann’s constant, and N0 is Avogadro’s number
`(21). At a 15 mM solution ionic strength, an fðkaÞ value of 1.066 from
`the literature was used to calculate the z potential (20,21). The Stokes
`hydrodynamic radius (Rh) calculated using the self diffusion coefficients,
`Ds, from DLS measurements was used to determine the effective net molec
`ular charge.
`
`Determination of the diffusion interaction
`parameter kD by DLS
`
`The diffusion interaction parameter, kD, for antibodies in dilute (up to
`20 mg/mL) solutions was determined by means of DLS. Diffusion coeffi
`cients 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 mm) 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 prep
`
`C. The mutual
`aration and analysis. Measurements were performed at 25
`diffusion coefficients, Dm, 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 (Worcester
`shire, 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 (kD) can be related by the self diffusion coefficient
`(D0), range 3.9 4.8  10 7 cm2/s), as a function of antibody concentration
`D ¼ D0ð1 þ kDcÞ:
`
`(c) using the following equation (14):
`
`(9)
`
`Thus, kD was calculated by fitting the D versus C data to Eq. 9. The error
`for kD was determined by calculating the propagation of the standard error
`of the coefficients from the linear regression.
`
`Determination of the sedimentation interaction
`parameter kS by AUC
`
`The sedimentation interaction parameter (kS) for antibodies in dilute solu
`tions was determined by sedimentation velocity analytical ultracentrifugation
`
`Biophysical Journal 103(1) 69 78
`
`Page 5 of 12
`
`

`

`72
`
`Connolly et al.
`
`where kB 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 molec-
`ular 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
`ðcÞ dependence of the diffusion coefficient by providing
`corrections for nonideality with a series of virial coefficients
`
`
` þ /
`
`ðkiÞ (14):
`1 þ kDc þ k3
`
`:
`
`(12)
`
`D ¼ D0
`
`c2
`
`The diffusion interaction parameter (kD) can be used as
`a first-order approximation of the concentration dependence
`of the mutual diffusion coefficient (D) (Eq. 9) to parame-
`terize the measured deviations from solution ideality. In
`general, a positive kD indicates net repulsive interactions
`and a negative kD indicates net attractive interactions
`the importance of kD as
`(2,3,15). For
`these reasons,
`a measure of intermolecular interactions is well established
`and numerous efforts have elucidated the relationship
`between kD 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 relation-
`ship 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 (kD), 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 ¼ 16; Arg-Cl, n ¼ 16; His-Cl,
`n ¼ 10; Arg-Succ, n ¼ 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 re-
`ducing mAb solution viscosity (16).
`In the low-ion-normality His-OAc (Fig. 1 A) and His-Cl
`(Fig. 1 B) solutions, kD values for 16 different mAbs varied
`over a wide range, from þ35.7 mL/g to 22.5 mL/g.
`The positive values can be interpreted as weak repulsive
`
`(AUC) using a Beckman Coulter ProteomeLab XL I analytical ultracentri
`
`C in 12 mm pathlength
`fuge. Samples were centrifuged at 40,000 rpm at 20
`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
`gðs Þ distribution using DCDT
`þ
`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
`þ
`software and
`determined using the average fringe density from the DCDT
`a ratio of 3.3 fringes per mg/mL of protein. The sedimentation interaction
`parameter (ks) was calculated by fitting the reciprocal sedimentation coeffi
`cient (1/s) versus antibody concentration (c) data to Eq. 10 (14):
`
`(10)
`
`ð1 þ kScÞ;
`
`¼ 1
`s0
`
`1 s
`
`where 1/s0 is the reciprocal sedimentation coefficient at infinite dilution.
`The error for kS was determined by calculating the propagation of the stan
`dard 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
`
`angle. The antibody solutions were adjusted
`a 25 mm diameter and 1.007
`to a target concentration of 175 mg/mL (5 5%) by diluting the respective
`stock solutions with the appropriate buffer. Then 70 mL 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 5
`
`C using an Anton Paar H PTD200 Peltier system, which includes an
`0.1
`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 stabi
`lized viscosity measurements using three sample replicates. Sample anal
`ysis 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 kD, and kS values, an average n 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 kD and kS 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 noninter-
`acting Brownian particles can be described by the Stokes-
`Einstein equation:
`
`D ¼ kBT
`f
`
`;
`
`(11)
`
`Biophysical Journal 103(1) 69 78
`
`Page 6 of 12
`
`

`

`Weak Interactions and mAb Viscosity
`
`
`
`"13"13"13"”13"13":313"”13"”6,13,15,33,?
`
`\QNN’O’NOJQ‘N '3’
`
`73
`
`|R| = 0.76
`
`Viscosity
`
`(CE)
`
`—20
`
`0
`
`20
`
`4O
`
` (d3)
` Ike
`
`Ausoosvx
`
`
`
`(d3)Ausoosm
`
`
`
`(d0)Ansoosm
`
`[IV
`
`'6
`sfssxssv"
`
`|R|= 0.81
`
`
`
`Vlscoslty(0P) 8
`
`UI
`
`|R|= 0.87
`
`Viscosity
`
`(cP)
`
`|R|= 0.89
`
` -2o
`
`o
`
`-10
`km (ml/9)
`
`10
`
`FIGURE 1 Barplots comparing kD(I) and mAb solution viscosity (CI) in (A) 20mM 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 1:.) 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 CI, pH 5.0, and (H) 200 mM Arg Succ, {H 5.5. Wscosity was measured at 175 myrnL by cone and
`plate rheometry.
`
`interactions that exist between mAb molecules (mAb-l to
`mAb-8, mAb-7 charge-swap mutants 1 3 and mAb-15
`charge-swap mutants l 2), whereas negative values would
`suggest weak attractive interactions to persist under these
`
`In the low-ion-nonnality condition, and in
`conditions.
`the absence of any electrostatic screening, a given mAb
`can be expected to experience significant electrostatic repul-
`sion, giving rise to only repulsive interactions under these
`
`Biophysical Journal 103(1) 69 7a
`
`Page 7 of 12
`
`

`

`74
`
`Connolly et al.
`
`conditions. However, it is noteworthy that even under the
`low-ion-normality condition with electrostatic repulsion ex-
`pected 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 interac-
`tions. Even more important is the relationship between kD
`and mAb solution viscosity (measured at 175 mg/mL
`mAb). Positive kD values correlated with lower solution
`viscosity, whereas negative kD values correlated with higher
`viscosity. Correlation plots (Fig. 1, E and F) reveal a reason-
`able linear relationship between kD and viscosity in His-
`OAc (jRj¼0.76) and His-Cl (jRj¼0.81) solutions. Similarly,
`a significant qualitative rank correlation between kD and
`solution viscosity is observed from the column plots
`(Fig. 1, A and B).
`In general, the kD decreased with increasing ion normality
`and occupied a narrower range of values. In Arg-Cl and
`Arg-Succ solutions, the kD 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 kD 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 kD and
`viscosity was observed in the high-ion-normality Arg-Cl
`solution (Fig. 1 G, jRj¼0.87). However, given the paucity
`(n ¼ 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,
`jRj¼0.89).
`Although the data demonstrate that there is a strong
`(jRj>0.8) and statistically significant (p < 0.005) correla-
`tion between kD and solution viscosity measured at high
`protein concentration (~175 mg/mL), the correlation was
`the weakest (jRj¼0.76 and jRj¼0.81) 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 kD could be further
`improved by accounting for the mAb concentration depen-
`dence of viscosity, which could be parameterized in terms
`of the exponential coefficient (k) of a simple exponential
`(Eq. 13):
`
`h ¼ h0ekc;
`
`(13)
`
`where h is the solution viscosity at any given mAb concen-
`tration c, and h0 is the solution viscosity at infinite dilution.
`Due to the considerable material requirements for obtaining
`
`Biophysical Journal 103(1) 69 78
`
`viscosity-concentration profiles, analysis was limited to
`select mAbs from each sample population in three solutions
`(His-OAc, n ¼ 12 of 16; Arg-Cl, n ¼ 7 of 16; His-Cl, n ¼ 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 kD and k for His-OAc (Fig. 2 D,
`jRj¼0.94), His-Cl
`jRj¼0.89), and Arg-Cl
`(Fig. 2 E,
`(Fig. 2 F, jRj¼0.96) solu