Evaluation of effects of pH and ionic strength on colloidal stability of IgG solutionsby PEG-induced liquid-liquid phase separationRonald W. Thompson Jr., Ramil F. Latypov, Ying Wang, Aleksey Lomakin, Julie A. Meyer, Suresh Vunnum,and George B. Benedek Citation: The Journal of Chemical Physics 145, 185101 (2016); doi: 10.1063/1.4966708 View online: http://dx.doi.org/10.1063/1.4966708 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/145/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Influence of the pH value of a colloidal gold solution on the absorption spectra of an LSPR-assisted sensor AIP Advances 4, 031338 (2014); 10.1063/1.4869615 Intermediate range order and structure in colloidal dispersions with competing interactions J. Chem. Phys. 139, 154904 (2013); 10.1063/1.4824487 Phase transitions in human IgG solutions J. Chem. Phys. 139, 121904 (2013); 10.1063/1.4811345 Phase behavior of aqueous solutions containing dipolar proteins from second-order perturbation theory J. Chem. Phys. 120, 9859 (2004); 10.1063/1.1697387 Adhesion and liquid–liquid phase separation in globular protein solutions J. Chem. Phys. 116, 6826 (2002); 10.1063/1.1461358

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THE JOURNAL OF CHEMICAL PHYSICS 145, 185101 (2016)

Evaluation of effects of pH and ionic strength on colloidal stability of IgGsolutions by PEG-induced liquid-liquid phase separation

Ronald W. Thompson, Jr.,1,a) Ramil F. Latypov,1,a) Ying Wang,2,a),b) Aleksey Lomakin,2Julie A. Meyer,1,a) Suresh Vunnum,1 and George B. Benedek2,3,41Process and Product Development, Amgen Inc., Seattle, Washington 98119, USA2Materials Processing Center, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge,Massachusetts 02139, USA3Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge,Massachusetts 02139, USA4Center for Materials Science and Engineering, Massachusetts Institute of Technology, 77 MassachusettsAvenue, Cambridge, Massachusetts 02139, USA

(Received 12 August 2016; accepted 19 October 2016; published online 8 November 2016)

Colloidal stability of IgG antibody solutions is important for pharmaceutical and medicinal applica-tions. Solution pH and ionic strength are two key factors that affect the colloidal stability of proteinsolutions. In this work, we use a method based on the PEG-induced liquid-liquid phase separation toexamine the effects of pH and ionic strength on the colloidal stability of IgG solutions. We found thatat high ionic strength (≥0.25M), the colloidal stability of most of our IgGs is insensitive to pH, and atlow ionic strength (≤0.15M), all IgG solutions are much more stable at pH 5 than at pH 7. In addition,the PEG-induced depletion force is less efficient in causing phase separation at pH 5 than at pH 7. Incontrast to the native inter-protein interaction of IgGs, the effect of depletion force on phase separationof the antibody solutions is insensitive to ionic strength. Our results suggest that the long-rangeelectrostatic inter-protein repulsion at low ionic strength stabilizes the IgG solutions at low pH. Athigh ionic strength, the short-range electrostatic interactions do not make a significant contributionto the colloidal stability for most IgGs with a few exceptions. The weaker effect of depletion force atlower pH indicates a reduction of protein concentration in the condensed phase. This work advancesour basic understanding of the colloidal stability of IgG solutions and also introduces a practicalapproach to measuring protein colloidal stability under various solution conditions. Published by AIPPublishing. [http://dx.doi.org/10.1063/1.4966708]

I. INTRODUCTION

Antibodies, especially the IgG type, are an important classof proteins. They play a central part in the antibody-mediatedimmune system of human body.1 Pharmaceutical IgGs havebecome a major category of protein drugs for the treatment ofvarious diseases such as cancers and autoimmune disorders.2

Both antibody repertoire of human body and the antibodydrug candidates in portfolio of pharmaceutical companiescontain a large number of different antibody molecules. AllIgG molecules have roughly the same size and the Y-likeoverall shape as shown in Fig. 1. The IgG molecules ofthe same subclass also share large parts of their aminoacid sequence, but differ in the complementarity-determiningregions (CDRs) in the Fab domains (Fig. 1). The variationsof amino acid residues of CDRs could lead to a diversityin the inter-protein interactions. When these interactionsare attractive, one can expect the fully folded proteinmolecules to self-associate into protein condensed phases.

a)Current addresses: SystImmune, Bellevue, WA 98005, USA (R.T.); Sanofi,Framingham, MA 01701, USA (R.L.); University of North Carolina, Wilm-ington, NC 28403, USA (Y.W.); and Eurofins Product Testing US, Bothell,WA 98011, USA (J.M.).

b)Author to whom correspondence should be addressed. Electronic mail:wangyy@uncw.edu

Indeed, numerous studies reported that IgG solutions undergovarious condensation phenomena including crystallization,liquid-liquid phase separation, aggregation, and gelation.3–13

These protein condensations involve folded globular proteinmolecules and thus are different manifestations of the colloidalinstability of protein solutions. In vivo condensation of naturalIgGs underlies the cryoglobulinemia complication in someblood cancers.10 Pharmaceutical IgGs with low colloidalstability are also a concern for antibody drug development.Therefore, evaluation of colloidal stability of IgG solutionsis important for medical and pharmaceutical applications. Inaddition, the universal Y-like shape of the IgG molecules andthe diversity of the inter-protein interactions make them aninteresting system for theoretical study of the phase behaviorof non-spherical colloidal particles.

The colloidal stability of an IgG solution is reflectedby its propensity to undergo crystallization, liquid-liquidphase separation, and colloidal aggregation. However, studiesof crystallization and aggregation are not always suitablefor evaluating colloidal stability of protein solutions. First,crystallization and aggregation are strongly controlled bykinetic factors that depend on specific experimental conditionsand are often difficult to predict. Also, IgGs, as largeand flexible protein molecules, are generally difficult tocrystallize. Aggregation is not associated with a well-defined

0021-9606/2016/145(18)/185101/9/$30.00 145, 185101-1 Published by AIP Publishing.

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FIG. 1. Crystallographic structure of an IgG molecule (DOI:10.2210/pdb1IGT/pdb in the Protein Data Bank). The graph is renderedusing VMD 1.9.1. Two identical heavy chains are shown in red, and twoidentical light chains are in blue. The three globular domains are two identical“antigen-binding domains” (Fab) and a “crystallizable domain” (Fc). Thecomplementarity-determining regions (CDRs) represent the hyper-variableparts of IgG.

quantity, like solubility, that can be used as a measure ofcolloidal stability. In contrast, liquid-liquid phase separationis a phase transition that occurs at well-defined solutionconditions. Liquid-liquid phase separation is not kineticallylimited because nucleation of the liquid condensed phase isusually fast and, at high degree of supersaturation, the spinodaldecomposition spontaneously occurs without nucleation.Moreover, liquid-liquid phase separation in protein solutions isthermodynamically metastable with respect to crystallizationand aggregation.7,12,14,15 From a thermodynamic perspective,when liquid-liquid phase separation occurs, the kineticallyhindered crystallization and aggregation will eventually occurgiven that there is sufficient time. In other words, liquid-liquid phase separation marks a higher limit of the chemicalpotential for a protein in crystals and colloidal aggregates.Therefore, the very nature of liquid-liquid phase separationmakes it useful for evaluating colloidal stability of IgGsolutions.

One practical challenge is that liquid-liquid phaseseparation is rarely observed in IgG solutions. For mostIgG solutions, the inter-protein attractive interactions are soweak that liquid-liquid phase separation does not occur attemperatures above the freezing point of an aqueous solution.One method to overcome this obstacle is to add a nonionicpolymer, polyethylene glycol (PEG), into the IgG solutions.PEG molecules in solution are sterically excluded from thevolume occupied by protein molecules. This exclusion effectcreates additional inter-protein attraction called depletionforce,16–20 which can cause protein phase separation above thefreezing point. Importantly, PEG normally does not interferewith the native inter-protein interactions, since PEG moleculesare excluded from the interaction areas of protein molecules.In practical applications, PEG is commonly used as a proteinprecipitant to promote protein precipitation or crystallization.In previous studies, we have demonstrated that PEG can be

used to induce liquid-liquid phase separation universally inIgG solutions.12 We also developed a method based on thePEG-induced liquid-liquid phase separation to evaluate thecolloidal stability of different IgGs at a physiological pH.11

Colloidal stability of a protein solution is determined notonly by the properties of the protein molecule but also bythe solution condition. Two important factors of the solutioncondition are pH and ionic strength. The solution pH affects thecharge state of the protein surface21 and thereby modulates themagnitude, polarity, and spatial distribution of the electrostaticinteractions between protein molecules. On the other hand,ionic strength regulates the range and the magnitude ofelectrostatic interactions by the ion screening effect.22 Asit is the case for regular colloids, pH and ionic strength couldmarkedly affect the stability of protein solutions. Therefore,in this work, we examined the effects of pH and ionic strengthon colloidal stability of IgG solutions by investigating thePEG-induced liquid-liquid phase separation. The pH and ionicstrength effects on colloidal stability can also be estimatedby measuring the zeta potentials of proteins. However, ourmethod provides two unique advantages over zeta potentialmeasurements: first, the propensity to undergo liquid-liquidphase separation directly characterizes the colloidal stabilityof protein solutions, while zeta potential measurements onlycapture the net surface charge of a protein molecule whichusually does not account for all inter-protein interactionsin the condensed phase; second, the PEG-induced liquid-liquid phase separation experiments are easier to perform asthey do not require any training or specialized equipment.Another way to study colloidal stability of protein solutionsis to determine virial coefficients by scattering techniques,including light scattering, X-ray scattering, and neutronscattering.23–26 Most scattering experiments measure pair-wiseinteractions between colloidal particles, i.e., the second virialcoefficient. On contrary, the PEG-induced phase separationexperiments measure the integrated overall interactions inthe condensed phase. In this regard, the phase separationmethod is complementary to the scattering methods. Whenthe scattering instruments are not available, the PEG-inducedphase separation provides an alternative method for rapidlyquantifying colloidal stability of protein solutions.

II. MATERIALS AND METHODS

A. Materials

Fully human monoclonal IgG antibodies mAb1, mAb2,mAb3, mAb4, mAb5, mAb6, mAb7, and mAb8 wereproduced at Amgen, Inc. All antibodies were in the monomericform with purity higher than 95%. mAb1-mAb4 belong to thehuman IgG2 subclass. mAb5-mAb8 belong to the human IgG1subclass. The isoelectric points of mAb1-mAb8 determinedby capillary isoelectric focusing were respectively 7.2, 8.8,6.8, 7.8, 9.0, 8.7, 8.9, and 7.5 (the cIEF data not shown). Theacetate buffers of different concentrations (0.02M, 0.15M,0.25M, 0.3M, and 0.5M) were prepared using sodium acetatesalt and glacial acetic acid. The 0.02M phosphate buffer wasprepared with Na2HPO4 and NaH2PO4 salts. Polyethyleneglycol with the molecular weight 8000 Da and purity greater

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than 99% (PEG8000, Sigma-Aldrich, St. Louis, MO) wasused.

B. Solubility measurement of PEG-inducedliquid-liquid phase separation

Stock solutions of 2 mg/ml and 4 mg/ml IgG wereprepared at a desired pH and ionic strength. Stock solutionsof PEG8000 were prepared at a 2 × higher concentration thanthe final PEG concentration. Note that the highly concentratedPEG increased the solution pH, especially at pH 5.2 and 5.4.Thus, it was necessary to adjust solutions to the desired pHwith glacial acetic acid following dissolution of PEG in theacetate buffer. Subsequently, equal volumes of protein andPEG stock solution were mixed at a room temperature. Whenthe initially transparent samples were brought to 4 ◦C, theyquickly became cloudy. The samples were then incubatedat 4 ◦C for 24 h to achieve equilibrium. After incubationthe white protein precipitate sedimented to the bottom ofthe test tubes. Each sample was briefly centrifuged at 4 ◦Cbefore an aliquot of the supernatant was carefully removedto determine the protein concentration. Supernatant proteinconcentrations were measured by a precalibrated 1100 SeriesHPLC system (Agilent Technologies, Santa Clara, CA) usinga ProPac WCX-10 analytical column (weak cation-exchange,4 mm × 250 mm; Dionex, Sunnyvale, CA) and a UV detector.3

Repeated measurements showed that the protein concentrationin the supernatant did not change after 24 and 48 h ofincubation. Therefore, the equilibrium protein concentrationafter a one-day incubation was taken as the solubility of theIgG solutions. We also found that the solubility of an IgGunder the same solution condition did not depend on the initialprotein concentration between 1 and 2 mg/ml.

C. Measurement of phase separation temperatureof PEG-induced liquid-liquid phase separation

The phase separation temperatures of the IgG-PEGmixture solutions were determined by the turbidity mea-surement. The sample in a test tube was placed in athermostated light-scattering stage. A laser beam (He-Ne4 mW, 633 nm) was directed through the sample, and theintensity of transmitted light was measured by a photodiodeand recorded by a power meter (1936-C, Newport). Thetemperature of the sample was then lowered from a roomtemperature by 0.2 ◦C every 5 min. At a temperature, Tcloud,the sample became cloudy and the transmitted intensity rapidlydropped. This clouding marked the onset of phase separation.After clouding occurred, the temperature was raised andthe sample became clear at another temperature, Tclear. Theaverage of Tcloud and Tclear was taken as the estimate of theliquid-liquid phase separation temperature.

III. RESULTS AND DISCUSSION

A. PEG-induced liquid-liquid phase separationin IgG solutions

Upon addition of PEG we observed precipitation in ourIgG solutions at a constant temperature (Fig. 2(a)). The

FIG. 2. Liquid-liquid phase separation in a solution of 2 mg/ml mAb1 and12% (w/w) PEG8000 in 0.5 mM acetate buffer at pH 5.2 and 21◦C. (a) showsthe white precipitate. (b) is the picture of the liquid condensed phase taken bya light microscope at a room temperature.

resulting protein concentrations in the supernatants weresignificantly lower than those in the original solutions.Thus, the observed white precipitates were a protein-richphase. Under the light microscope, these precipitates werefound to be liquid droplets that coalesced when in contact(Fig. 2(b)). The precipitates completely dissolved when thesolution temperature was increased. The observed features ofthis thermally reversible protein condensation were consistentwith a typical liquid-liquid phase separation process. Analternative way to observe liquid-liquid phase separation is tolower the temperature of a homogenous IgG-PEG solution.When the temperature falls below a well-defined cloudingtemperature, the condensation occurs. When the temperatureis subsequently increased, the solution clears again. For all ofour IgGs, both clouding and clearing events occurred withinjust a few seconds. In contrast to the nucleation-dependentand relatively slow crystallization and aggregation, the fastkinetics of clouding and clearing of our samples was consistentwith liquid-liquid phase separation.

In previous studies,11,12 we have demonstrated that liquid-liquid phase separation can be universally induced in IgGsolutions at pH 7 by addition of PEG. Since most IgGs havebasic isoelectric points (pI from 6.5 to 10),27,28 pharmaceuticalIgGs are often formulated at a moderately low pH (pH 5-6)and ionic strength (<0.15M) for high colloidal stability.The colloidal stability is mostly due to the net repulsiveelectrostatic interactions between protein molecules. Indeed,we found that most IgG solutions in 20 mM acetate at pH 5.2remain transparent even in the presence of high concentrationsof PEG (up to 20% w/w PEG8000). To observe phaseseparation, we had to increase the concentration of buffersalts up to 0.5M. At the high ionic strength, the range and thestrength of electrostatic interactions were reduced due to thescreening effect of the counter-ions. Thereby, we were able toobserve the PEG-induced liquid-liquid phase separation in allof our IgG solutions over the pH range from 5.2 to 7.2 at theionic strength of 0.5M.

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In our experiments, we used sodium phosphate buffersfor solutions at pH 7.2, 6.6, and 6.0 and sodium acetatebuffers for solutions at pH 5.4 and pH 5.2. The ionicstrength of both buffers was 0.5 M. To examine the effectof the type of buffer salt on phase separation, we measuredthe clouding and clearing temperatures of the IgG-PEGmixture solutions in 0.5M acetate and phosphate buffersat pH 6.0. The phase separation temperatures in the twodifferent buffers were very similar (the difference was within0.5 ◦C, data not shown). Therefore, we did not considerthe effect of the type of buffer salts on phase separationhereafter.

B. The pH effect on the PEG-induced liquid-liquidphase separation in IgG solutions

In our experiments, higher pHs favor the PEG-inducedliquid-liquid phase separation. Upon PEG-induced liquid-liquid phase separation, the protein concentration in theprotein-poor phase (the supernatant) drops to the equilibriumvalue after isothermal incubation. After incubation at 4 C, wemeasured the equilibrium IgG concentration in supernatantsfor samples with different PEG concentrations (Fig. 3).Fig. 3 shows that, at a given pH, the equilibrium proteinconcentration decreases as the PEG concentration increases.

FIG. 3. The IgG solubility via liquid-liquid phase separation as a function ofPEG concentration and pH at 4◦C.

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This result is expected since the depletion interaction(the additional inter-protein attraction) introduced by PEGincreases with PEG concentration. With the exception ofmAb8, the equilibrium protein concentration in Fig. 3decreases as pH increases. This result suggests that it ismore difficult to induce phase separation at low pH usingPEG.

The lower equilibrium protein concentration at higherpH indicates a stronger overall inter-protein attraction, whichconsists of native inter-protein interactions and the PEG-induced depletion force. It is important to note that theequilibrium concentrations of IgGs in our experiments areindependent of the protein concentration of the initial solution.From a theoretical perspective, this observation can only beexpected for phase separation in dilute protein solutions. Inall our experiments, the initial IgG solutions are quite dilute(<2 mg/ml). When phase separation occurs in a dilute IgGsolution, the protein concentration in the condensed phaseis generally very high (hundreds of mg/ml).9,12 Due to thesteric exclusion of the closely packed protein molecules,the condensed phase is essentially incompressible and thePEG molecules only stay in the protein-poor phase. In thislimiting case, the protein concentration in the supernatanthas a well-defined value at a given temperature and PEGconcentration. Hereafter, we will refer to the equilibrium IgGconcentration in supernatant as the protein solubility under thegiven solution condition. The solubility measurements enableus to obtain information on the native and PEG-induced inter-protein interactions. In an extensive body of historic work,the PEG-induced inter-protein interaction has been studiedboth experimentally and theoretically.16–20 With only a fewexceptions where specific PEG-protein interactions were seen,the PEG-induced inter-protein interaction is a purely entropicdepletion force.

To capture the physical meaning of the pH-dependenceof IgG solubility shown in Fig. 3, we have performedfollowing theoretical analysis based on the assumptions ofincompressible protein condensed phase and purely entropicdepletion interaction. In a previous work,11 we have shownthat, with these approximations, the IgG solubility measuredin our experiment, c1, as a function of the osmotic pressureproduced by PEG, Π2, can be expressed in a simple equation,

ln(

c1

c0

)=

ln

(M1

v0NAc0

)− εB

kT

+ (v0 − v) Π2

kT, (1)

where c0 ≡ 1 g/l, NA is the Avogadro’s number, k is theBoltzmann constant, T is the absolute temperature, and M1 isthe molecular weight of the protein (taken as 150 kg/mol).In this equation, there are three quantities that characterizethe properties of the protein-polymer mixtures undergoingphase separation: v is the volume excluded for PEG8000(i.e., the volume inaccessible to the mass center of PEGmolecules) by an IgG molecule in the dilute phase; v0 isthe excluded volume per IgG molecule in the condensedphase; and εB is the binding energy of an IgG moleculein the condensed phase (Fig. 4). When PEG moleculesare completely excluded from the condensed phase, theexcluded volume v0 is equal to the solution volume per IgGmolecule. The binding energy, εB, is an important parameter

FIG. 4. A schematic representation of the PEG-induced liquid-liquid phaseseparation in a dilute IgG solution. The volume excluded for PEG by an IgGmolecule in the dilute and condensed phases, v and v0, is illustrated by thedashed boundaries. The binding energy of IgG in the condensed phase is εB.Note that the concentration and configuration of IgG in the two phases are forillustrative purposes and do not reflect the real situation.

that characterizes the strength of interactions between nativeprotein molecules. The attractive inter-protein interactions thatdrive liquid-liquid phase separation could also result in otherprotein condensation phenomena such as colloidal aggregationand crystallization. In protein solutions, liquid-liquid phaseseparation is metastable with respect to crystallization andaggregation, i.e., the εB measured for liquid-liquid phaseseparation is the lower limit of the binding energy in the solidcondensed phases. Therefore, εB is a measure of the colloidalstability of protein solutions in a general sense.

In Eq. (1), the bracketed term characterizes the nativeinter-protein interaction in the condensed phase: ln

(M1

v0NAc0

)is the translational entropy of a protein molecule; the bindingenergy, εB, represents all other parts of free energy includingenergetic and entropic components. The second term on theright side of Eq. (1) describes the effect of depletion forceinduced by the addition of PEG. It is easy to see that (v0 − v) Π2is the volumetric work done by the osmotic pressure of PEGin the process to move an IgG molecule from the dilute phaseto the condensed phase. The osmotic pressure of PEG, Π2,can be calculated from the weight fraction of PEG, c2, usinga semi-empirical equation of state,29

Π2

NAkT=

ρ

M2c2

1 + 0.49

(c2

c∗2

)5/4. (2)

Here ρ � 1 g/ml is the density of the solution, and M2is the molecular weight of PEG, and c∗2 ≡ ρσ−0.8/v2 is thedilute-semidilute crossover concentration of PEG, where σ isthe number of ethylene glycol units in a PEG molecule andv2 = 0.825 ml/g is the partial specific volume of PEG.

Eq. (1) shows that pH could affect the protein solubilitythrough altering the free energy of native inter-proteininteractions and changing the work done by the PEG-induced

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depletion force. Using the data in Fig. 3, we plotted ln (c1/c0)versus Π2/NAkT as shown in Fig. 5. According to Eq. (1),one can fit the data in Fig. 5 using a linear function. Theslope, NA (v0 − v), and the intercept, ln

(M1

v0NAc0

)− εB

kT, of the

linear fit respectively characterize the effect of depletion forceand native inter-protein interactions on phase separation. Asshown in Fig. 4, the excluded volume, v , in the dilute phaseonly depends on the geometry of IgG molecules and thesize of PEG. Since all IgG molecules have similar shape andsize, v is approximately a constant for a given PEG. In aprevious study,11 we have analyzed the dependence of v onthe PEG molecular weight and estimated that v � 387 nm3

for PEG8000. Knowing the value of v , the excluded volumein the condensed phase, v0, can be deduced from the slopeof the linear fits in Fig. 5, and the binding energy εB canthen be deduced from the intercept. We wrote the binding

energy at a given pH as εB = εB0 + bδpH, where εB0 is thebinding energy at a reference pH, δpH is the change of pHwith respect to the reference pH, and b is the proportionalitycoefficient. Using this expression of εB and Eq. (1), we wereable to simultaneously fit the data in each graph of Fig. 5 (thegoodness of fit, R2 > 0.97). The resulting values of v0 and εB0are summarized in Fig. 6. Alternatively, one can use Eq. (1)to fit the data individually without the constraint of εB (Fig.S1 of the supplementary material). The results thus obtainedare similar to Fig. 6.

In Fig. 6(a), for all of our IgGs, v0 increases as pHdecreases below 6. The pH dependence of v0 suggests thatthe protein concentration in the condensed phase decreaseswhen pH is lowered. Intuitively, one can expect a lessdense condensed phase at a lower pH, since the electrostaticinteractions between IgG molecules become less attractive

FIG. 5. ln(c1/c0) as a function of the normalized PEGosmotic pressure Π2/NAkT . The plots are made basedon the data in Fig. 3. The solid lines are the linear fitsusing Equation (1).

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FIG. 6. The volume per IgG molecule v0 (a) and the binding energy of an IgGmolecule εB (b) in the condensed phase as a function of pH. These valueswere obtained by fitting the data in Fig. 5 using Eq. (1). The uncertaintiesof v0 and εB associated with the fitting are respectively within 10 nm3 and0.5 kJ/mol.

as pH shifts away from their isoelectric point. However, thelower density of condensed phase cannot be attributed to theoverall repulsion between net surface charges on IgGs. Inour experiments, the ionic strength was high (0.5 M) and therange of electrostatic interaction was short (Debye length is∼0.45 nm). This length of ionic interactions is much shorterthan the distance between the centers of IgG molecules in thecondensed phase ( 3√v0 is ∼7 nm). Therefore, the increase ofv0 at low pH is due to the changes of localized electrostaticinteractions between the protein surfaces. Indeed, previousneutron scattering studies have shown that concentrated IgGsolutions can have very different solution structures.26,30 Formost of our IgGs, v0 is insensitive to pH changes above pH6.0. This observation is in agreement with the fact that thepKa values of ionic groups of amino acid residues are mostlyfar from pH 7.

The pH-dependence of v0 has a strong effect on thework done by the PEG-induced depletion force. As shownin Eq. (1), the strength of the depletion force is associatedwith the difference between v and v0. The change in v0 ismore significant with respect to v − v0 than that of v0 itself.

Therefore, the slope in Fig. 5 is expected to be sensitive tothe change in v0. In contrast, the ln(v0) term of the intercept isonly marginally affected. Note that the condensed phase is stillhighly concentrated even at low pH. Direct measurement of theprotein concentration in the condensed phase is impracticalbecause the amount of the condensed phase is very small,and the contamination from the dilute bulk phase duringthe liquid handling is almost inevitable. Nevertheless, thev0 measured in our experiments can be used to estimate theprotein concentration in the condensed phase: cI I

1 = M1/NAv0.The largest v0 in Fig. 6 (∼330 nm3) corresponds to the IgGconcentration ∼750 mg/ml. Therefore, the condensed phasein all of our experiments is very crowded, which is consistentwith our initial assumptions.

While the work of the depletion force in phase separationexhibits significant dependency on pH, we found that themagnitude of the overall native inter-protein interactions forthe majority of our IgG is essentially independent of pH. Withthe exceptions of mAb7 and mAb8, the intercepts of the linearfits in Fig. 5 do not change with pH within the experimentalerror. Similarly, Fig. 6(b) shows that the binding energy, εB, ofIgGs (mAb1-mAb6) in the condensed phase exhibits little pHdependence. This result suggests that the average inter-proteininteraction of the IgGs in the condensed phase is insensitive topH, even though the changes in v0 suggest that the less-denseconfigurations of protein molecules are favored at low pH. Incontrast, the binding energies, εB, of mAb7 and mAb8 showstrong pH dependency in opposite directions. Apparently, astronger pH dependence of εB indicates that the proteinshave more ionic groups with pKa close to the pH range of5.2-7.2. On the other hand, the isoelectric points of mAb7 andmAb8 are within the pH range of other IgGs. Therefore, thepH dependence of εB of mAb7 and mAb8 demonstrates theimportance of localized electrostatic interactions, instead ofthe net interactions signified by zeta potential, for colloidalstability of protein solutions at high ionic strengths. The IgGswith abnormal inter-protein interactions are likely to presentchallenges for biopharmaceutical development or even play arole in in vivo pathological condensation in diseases such ascryoglobulinemia.

C. The effect of ionic strength on the PEG-inducedliquid-liquid phase separation in IgG solutions

Ionic strength of a solution is another important factorthat controls the electrostatic interactions between proteinmolecules. We examined the pH dependence of v0 and εB formAb1 at two lower ionic strengths (0.3 M and 0.25 M) bymeasuring the protein solubility in PEG-induced liquid-liquidphase separation. (Fig. 7) Interestingly, we found that v0 andεB did not strongly depend on ionic strength. Their variationswere within the experimental error. The experiments on mAb2(Fig. S2 of the supplementary material) showed similar resultsto mAb1. On the other hand, we already knew that the PEG-induced phase separation showed a very different behavior ationic strengths lower than 0.15 M. At pH 5.2 and ionic strength0.15 M, we could not induce liquid-liquid phase separationfor any of our IgGs using up to 20% w/w PEG8000. At pH7 and 0.15 M ionic strength, liquid-liquid phase separation

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FIG. 7. The volume per IgG molecule v0 (a) and the binding energy of anIgG molecule εB (b) in the condensed phase as a function of pH for mAb1 atdifferent ionic strengths, 0.5 M, 0.3 M, and 0.25 M.

was observed in our IgG solutions by addition of as littleas ∼6% w/w PEG8000. These results suggested that theeffect of ionic strength on the PEG-induced liquid-liquidphase separation can be divided into two distinct regions:(1) below 0.15M, the repulsion between surface charges ofIgGs at low pH completely prevents phase separation, andthe PEG-induced depletion force is not sufficient to overcomethe repulsion; (2) above 0.25M, the repulsion is screenedby the counter-ions, but further increases in the ionicstrength impose only an insignificant effect on the overallinter-protein interaction. That is to say, there is a criticalionic strength between 0.15M and 0.25M. One plausibleexplanation for this sharp transition of the ionic strengtheffect is the following: below the critical ionic strength, therange of the electrostatic repulsion is longer than the rangeof the depletion force induced by PEG, which thereby createsa long-range energy barrier which cannot be overcome byincreasing the strength of the short-range depletion force.Above the critical ionic strength, the electrostatic interactionsare short-range with respect to the depletion force and arerelatively weak compared to other types of short-range inter-

protein interactions. Thus, a further increase of ionic strengthhas only a marginal effect on the total inter-protein interaction.To elucidate this transition, we calculated the Debye-Hückellength of charge carriers in our solutions.31 The Debye lengthincreases from 0.4 nm to 0.8 nm as the ionic strength ofsolution decreases from 0.50M to 0.15M. For comparison,the range of depletion interaction of PEG is approximately0.5Rg,17,18 where Rg ≈ 0.0287M2

0.55 is the radius of gyrationof PEG and M2 is the molecular weight of PEG.16 Therange of depletion interaction for PEG8000 is about 1.3 nm.Assuming the effective range of electrostatic interaction isproportional to the Debye length, the electrostatic repulsioncan outrange the depletion interaction as ionic strengthdecreases.

IV. CONCLUSION

We have previously demonstrated that liquid-liquid phaseseparation can be universally induced in IgG antibodysolutions by the addition of PEG.12 Liquid-liquid phaseseparation provides a means to probe the attractive interactionsbetween the native folded antibody molecules. In a previousstudy,11 we established a method based on the PEG-inducedliquid-liquid phase separation at neutral pH to quantifythe colloidal stability of different IgG antibodies, i.e., thepropensity of the native proteins to undergo liquid-liquid phaseseparation as well as the closely related colloidal aggregationand crystallization. In this work, we demonstrated that thismethod can also be used at mildly acidic pH to comparethe stability of different therapeutic IgGs which are typicallyformulated between pH 5 and 6. We also evaluated theeffects of pH and ionic strength on the native inter-proteininteractions of IgGs and the PEG-induced depletion force.We found that, at ionic strength above 0.25M, pH (from5.2 to 7.2) has little effect on the strength of the nativeinter-protein interactions for most of our IgGs. However, thePEG-induced depletion force is less efficient in causing phaseseparation when pH is far away from an isoelectric point ofthe protein. At ionic strength lower than 0.15M, the PEG-induced liquid-liquid phase separation is prevented at acidicpH, but restored at high pH. The results of our experimentssuggest that at a low ionic strength, the electrostatic repulsionbetween protonated IgGs at acidic pH has a longer rangecompared to the depletion force; at a high ionic strength, theshort-range repulsion does not make significant contributionto the total interaction but it results in a decrease ofprotein concentration in the condensed phase. This workprovides insights into the basic rules that govern colloidalstability of IgG antibodies under different solution conditions.This knowledge is valuable for practical applications suchas formulation development of pharmaceutical antibodies.Our results also shed light on the effects of depletioninteraction on phase transitions in solutions of highly chargedproteins. Along the line of this study, future research onthe interplay between the range of electrostatic repulsion(ionic strength) and the range of depletion interaction(depending on PEG molecular weight) could yield interestingresults.

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185101-9 Thompson, Jr. et al. J. Chem. Phys. 145, 185101 (2016)

SUPPLEMENTARY MATERIAL

See supplementary material for Figures S1 and S2.

ACKNOWLEDGMENTS

R.W.T. performed the research; R.F.L. designed theresearch, analyzed data, and wrote the paper; Y.W. designedthe research, analyzed data, and wrote the paper; A.L. designedthe research and analyzed data; J.A.M. performed the research;S.V. analyzed data; and G.B.B. designed the research andwrote the paper.

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