Kinetic Analysis of the Multistep Aggregation Mechanism of

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Kinetic Analysis of the Multi-Step Aggregation Mechanism of Monoclonal Antibodies Lucrèce Nicoud, Paolo Arosio, Margaux Sozo, Andrew Yates, Edith Norrant, and Massimo Morbidelli J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp505295j • Publication Date (Web): 13 Aug 2014 Downloaded from http://pubs.acs.org on August 21, 2014

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The Journal of Physical Chemistry

Kinetic Analysis of the Multi-step Aggregation Mechanism of Monoclonal Antibodies Lucrèce Nicoud1, Paolo Arosio2, Margaux Sozo1, Andrew Yates3, Edith Norrant3, Massimo Morbidelli1* 1

Department of Chemistry and Applied Biosciences, ETH Zurich, Switzerland 2

Department of Chemistry, University of Cambridge, England, UK 3

UCB Pharma, Braine l'Alleud, Belgium

* Corresponding author: Institute for Chemical and Bioengineering, Department of Chemistry & Applied Biosciences, ETH Zurich, Vladimir-Prelog-Weg 1, CH-8093 Zurich phone: +41 44 632 30 34, e-mail: [email protected]

Submitted to

Journal of Physical Chemistry B

ACS Paragon Plus Environment

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ABSTRACT We investigate by kinetic analysis the aggregation mechanism of two monoclonal antibodies belonging to the IgG1 and the IgG2 subclass under thermal stress. For each IgG, we apply a combination of Size Exclusion Chromatography and Light Scattering techniques to resolve the time evolution of the monomer, dimer and trimer concentrations, as well as the average molecular weight and the average hydrodynamic radius of the aggregate distribution. By combining the detailed experimental characterization with a theoretical kinetic model based on Population Balance Equations, we extract relevant information on the contribution of the individual elementary steps on the global aggregation process. The analysis shows that the two molecules follow different aggregation pathways under the same operating conditions. In particular, while the monomer depletion of the IgG1 is found to be rate-limited by monomeric conformational changes, bimolecular collision is identified as the rate-limiting step in the IgG2 aggregation process. The measurement of the microscopic rate constants by kinetic analysis allows the quantification of the protein-protein interaction potentials expressed in terms of the Fuchs stability ratio (W). It is found that the antibody solutions exhibit large W values, which are several orders of magnitude larger than the values computed in the frame of the DLVO theory. This indicates that besides net electrostatic repulsion, additional effects delay the aggregation kinetics of the antibody solutions with respect to diffusion-limited conditions. These effects likely include the limited efficiency of the collision events due to the presence of a limited number of specific aggregation-prone patches on the heterogeneous protein surface, and the contribution of additional repulsive non-DLVO forces to the protein-protein interaction potential, such as hydration forces. Keywords: Therapeutic Protein, Protein Stability, Kinetic Model, Smoluchowski Population Balance Equations, Fractal Aggregates, Interaction Potentials


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INTRODUCTION The understanding of the molecular mechanisms underlying protein aggregation is of great relevance in diverse research fields such as medicine 1, pharmacy 2, food science 3 and bionanotechnology 4. An important example is represented by the stability of therapeutic proteins in the biopharmaceutical industry, since the presence of aggregates in protein-based drugs must be strictly controlled to ensure drug efficacy and safety of the patient. Accelerated studies at elevated temperatures are commonly performed to assess product stability. The rationalization of the protein aggregation mechanism under thermal stress is a key requisite to evaluate the product shelf-life from these accelerated studies, yet it is difficult to achieve. In this work, we analyze the aggregation behavior under thermal stress of monoclonal antibodies (mAbs), which represent the largest part of the biopharmaceutical market 5-7. Despite aggregation has been observed with a large variety of proteins and in a wide range of operating conditions, most of the aggregation behaviors of therapeutic proteins can be described in the frame of a generalized Lumry-Eyring model, as proposed by Roberts and co-workers

8,9.

This multi-step aggregation scheme involves initially the formation of an

aggregation-prone intermediate in a non-native conformational state. This reactive intermediate promotes the nucleation of oligomers which is then followed by growth to larger aggregates. Despite the main steps involved in the aggregation process have been qualitatively identified 8,9 , the quantification of the relative importance of the individual steps in a specific system remains challenging. One of the main problems originates from the fact that typically only few quantities, such as the monomer conversion and the aggregate average molecular weight, are accessible experimentally. Kinetic analysis has been proven to be a powerful tool to complement experimental characterization and to quantify from macroscopic


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measurements the contribution of single microscopic events in the global aggregation process 10,11.

In this work, we apply this kinetic approach to gain insight into the aggregation mechanism of two model antibodies under thermal stress. The aggregate growth steps are described by Smoluchowski’s Population Balance Equations (PBE), which are conservation laws applicable to a variety of colloidal systems

12

including proteins. Recently, Population

Balance Equations have been applied to analyze the aggregation kinetics of urease 13,monoclonal

antibodies

14,

and amyloid fibril formation

11,15.

In this study, the aggregates

remain soluble for a sufficient time to allow the detection of both small oligomers and larger aggregates. By modifying the classical Smoluchowski’s PBE to include nucleation steps (i.e. protein unfolding, reversible oligomer formation and oligomer structural rearrangement), we are in a position to evaluate the connection between nucleus formation and aggregate growth, as well as to quantify the rates of these two steps. This quantification allows to estimate a coarse-grained (i.e. averaging protein surface heterogeneities) protein-protein interaction potential expressed in terms of the Fuchs stability ratio (W). In a wide range of systems, the colloidal stability of charged particles in suspension can be described in a semi-quantitative way by the DLVO (Derjaguin, Landau, Verwey, Oberbeek) theory, which takes into account electrostatic repulsion and Van der Waals attraction. Although many protein solutions share common features with sol colloidal dispersions, the DLVO theory has been proven to describe only to a limited extent the behavior of proteins in solution. For instance, Olsen and co-workers showed that the effect of salt and pH on the aggregation kinetics of model globular proteins exhibiting a random charge distribution can be realistically interpreted within the DLVO theory 16. However, the situation is more challenging for large and complex biomacromolecules such as mAbs. In most cases,


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the protein stability is controlled not only by electrostatic repulsion and Van der Waals attraction but also by additional interactions such as hydration forces, depletion forces or ion binding

17,18.

Moreover, the protein surface is generally highly heterogeneous and

aggregation-prone domains can be confined to a few hydrophobic patches whose exposition to the solvent depends strongly on protein conformation. As a consequence, protein aggregation depends not only on the protein colloidal stability, which is controlled by the type and strength of intermolecular interactions between two aggregating units, but also on the protein conformational stability 19, which is governed by the kinetics and thermodynamics of protein unfolding. In this work, we show that the antibody solutions under investigation exhibit large repulsive energy barriers, which cannot be explained within the DLVO theory. Additional effects, such as the limited efficiency of the collisions due to aggregation events confined to few surface patches or additional repulsive non-DLVO forces likely contribute to the large kinetic stability.

MATERIALS AND METHODS Materials The two monoclonal antibodies used for this study are a glycosylated IgG1 and a nonglycosylated IgG2, which will be denoted in the following as mAb-1 and mAb-2, respectively. The theoretical isoelectric point (pI) of mAb-1 is between 8 and 9.2, while the theoretical pI of mAb-2 lies between 7.35 and 8.15. The antibody solutions were dialyzed at a protein concentration of 20 g/L against a 20 mM Histidine buffer at pH 6.5 using Slide A Lyzers cassettes from Thermo Fisher Scientific, with a cut-off molecular weight of 7 kDa. The volume of the dialysis buffer was five hundred-


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fold larger than the volume of the sample to be dialyzed. The buffer was renewed a first time after two hours, and a second time after four hours of dialysis. The dialysis was performed at 4°C under gentle stirring for at least 18 hours. The protein concentration of the stock solution after dialysis was checked by UV absorption at 280 nm. All the samples for this study were prepared by diluting the stock solution to the targeted concentration with a 20 mM Histidine buffer at pH 6.5. All the chemicals were purchased from Sigma, with the highest purity available. The buffers were filtered through a 0.1 μm cut-off membrane filter (Millipore).

Zeta Potential Measurements Zeta potential values () of proteins have been evaluated by a Zetasizer Nano (Malvern,

Worcestershire, UK) measuring the electrophoretic mobility via laser Doppler effect. From

the electrophoretic mobility the zeta potential is calculated according to the Henry equation: =

2 3

(1)

where ε and η are the dielectric constant and the viscosity of the medium, respectively. Measurements were performed at 25 °C and at a protein concentration of 1 g/L. Five repetitions of two independent samples were recorded for each condition and average values have been considered. The antibody net charge can be estimated from the measure of the zeta potential according to 20: =

4 (1 + )


(2)

6

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Where is the protein radius, is the elementary charge, is the medium electric

permittivity, and is the inverse Debye length.

Isothermal Aggregation Kinetics Isothermal aggregation kinetics were performed by incubating antibody samples at protein concentrations in the range from 1 g/L to 5 g/L at elevated temperatures in hermetically sealed HPLC vials containing 250 μl inserts (Agilent Technologies, part number 5182-0716, 5181-1270 and 5182-0721 for vials, inserts and caps, respectively). The vials were placed in a block-heater (Rotilabo H 250, Roth, Karlsruhe) for predetermined times. To improve heat transfer, 1 mL of aggregation buffer was added in the space delimited by the vial and the insert. Temperature was maintained by an oil bath at 70°C with less than ± 0.1°C variability, as verified with a thermocouple. Aggregated samples were quenched in an icewater bath for at least 3 min and analyzed immediately after by Size Exclusion Chromatography with inline Multi-Angle Light Scattering, or by batch Static Light Scattering. The high temperature of 70°C was selected in order to observe aggregation kinetics occurring under unfolding conditions which promote the aggregation process. Protein thermal stability was investigated by Circular Dichroism (CD) and Dynamic Light Scattering (DLS), as presented in Figure S1 of the Supplementary Material. CD experiments revealed that notable changes in the protein structure occur at around 70°C for both antibodies (Figure S1(a)), while DLS experiments showed that significant aggregation occurs above 70°C (Figure S1(b)), consistent with the changes in protein structure observed by CD.

Size Exclusion Chromatography with Inline Multi Angle Light Scattering Monomer conversion and oligomer formation was monitored by Size Exclusion Chromatography (SEC) with a Superdex 200 10/300 GL, 10 mm × 300 mm size-exclusion


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column (GE Healthcare, Uppsala, Sweden) assembled on an Agilent series HPLC unit (Santa Clara, CA, USA). The samples were eluted for 45 min at a constant flow rate of 0.5 mL/min using as mobile phase a 100 mM phosphate buffer containing 200 mM Arginine at pH 7.0, which has been shown to improve sample recovery

21.

The eluting species were detected by

UV at 280 nm and by Multi Angle Light Scattering (MALS) using a Dawn-Heleos II device (Wyatt, Santa Barbara, CA, USA). While the monomer peak was well resolved, the peaks corresponding to the dimer and trimer were partially overlapped with larger aggregates. The chromatograms were deconvoluted using OriginPro 8.5 (Academic) in order to determine the concentrations of monomer, dimer and trimer. Light scattering results were processed with the Astra software (Wyatt, Santa Barbara, CA, USA) to obtain the weight average molecular weight of the aggregate population (<

>). Figure S2 (Supplementary Material) shows

a representative example of a SEC chromatogram, with the applied peak deconvolution as well as the molecular weight determination from inline MALS. The data presented in the graphs correspond to the average and standard deviation (error bars) of at least two independent measurements. In order to assess the impact of lowering the temperature before analyzing the aggregated samples, the time evolution of the average hydrodynamic radius reconstructed from the population analyzed by off-line SEC-MALS analysis was compared with the values measured by in-situ Dynamic Light Scattering, as shown in the Figure S3 of the Supplementary Material. The two sets of data are in very close agreement, thereby proving that the aggregated samples of the systems under investigation were not significantly impacted by a change in temperature during the off-line analysis.


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Static Light Scattering and Evaluation of the Fractal Dimension Static Light Scattering measurements were performed using a goniometer BI-200SM

(Brookhaven Instruments, Holtsville, NY, USA) covering angles from =10° to 145°. A solidstate laser, Ventus LP532 (Laser Quantum, Manchester, UK) with a wavelength =532 nm was used as a light source. For clusters significantly larger than primary particles, the fractal dimension can be

estimated from the power-law regime of the structure factor, (!): (! )~! #$% &'(

1 1 ≪ ! ≪ < >

(3)

where is the radius of the primary particles inside the cluster, < > is the average radius of gyration of the cluster distribution and q is the scattering vector defined as: !=

4 * sin . / 2

(4)

where is the scattering angle, n is the refractive index of the solvent and the wavelength of the laser beam. For each sample, three measurements were recorded and average values were considered.

In-situ Dynamic Light Scattering The time evolution of the average hydrodynamic radius was followed by Dynamic Light

Scattering (DLS) in-situ at fixed angle = 173℃ using a Zetasizer Nano (Malvern). Briefly, the fitting of the autocorrelation function with the method of cumulants provides the average


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particle diffusion coefficient < 2 >, which is connected to the average hydrodynamic radius < 3 > by the Stokes-Einstein equation:

< 2 >=

45 6 6 < 3 >

(5)

Where 45 is the Boltzmann constant, 6 the temperature and the viscosity of the medium. The sample was incubated in a low volume quartz batch cuvette (ZEN 2112, Malvern). In order to prevent evaporation, a custom made plastic cap was added in the cuvette to reduce the air volume on top of the sample. The data presented in the graphs correspond to the average and standard deviation (error bars) of at least two independent measurements.

Kinetic Model The implementation of the PBE requires the definition of the aggregation rate constant

between two colliding aggregates containing 8 and 9 −monomeric units, respectively. In this work, we used the traditional Reaction Limited Cluster Aggregation kernel, which has been shown to successfully describe the aggregation kinetics of a large variety of colloidal systems 12,14.

The aggregation kernel is presented in equation (6) and a brief description of the various

terms is given in the following. 4A = 4>,@ = B C >,@ >,@ >,@ < 8 45 6 < 4A = < 3 < ,@ 4 8 F⁄$% 9 F⁄$% < C>,@ = (89)K < ≈ 1 − 1⁄ ;


(6)

10

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In the case where no repulsive barrier exists between the particles, the rate of particle aggregation is entirely controlled by Brownian motion, and each collision event leads to the formation of a larger aggregate. The corresponding aggregation kernel results from two contributions: the collision cross section of aggregates, which can be related to the aggregates mass by assuming a fractal geometry, and the diffusive mobility of the aggregates, which can be estimated from the aggregate size by the Stokes-Einstein relation (5). Based on these considerations, Smoluchowski derived the aggregation kernel for Diffusion Limited Cluster MNO = 4A × B>,@ . Aggregation (DLCA) 22: 4>,@

In contrast to DLCA, in the Reaction Limited Cluster Aggregation (RLCA) regime, the presence of a repulsive energy barrier between the particles delays the aggregation process. In this case, only a fraction of collisions is successful in forming larger aggregates and the reduced sticking efficiency can be expressed by the so-called Fuchs stability ratio, which can be computed from the expression of the total interaction potential between two primary particles, QR , as follows:

FF = 2 S

X

WYZ

exp .

QR (() ( / 45 6 ( W

(7)

This approach can be extended to the aggregation of two clusters of size 8 and 9 provided that the aggregate-aggregate interactions can be approximated to the interactions

between the two colliding primary particles, thus implying that FF can capture the interactions between two clusters, irrespective of their size. However, it is unlikely that this assumption holds true in the case of protein aggregation, where the reactivity strongly depends on protein conformation and on the accessibility of aggregation-prone patches, and thus changes significantly with aggregate size. Therefore, in the present study we introduced different values of the Fuchs ratio in order to characterize the stability of different sub-


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populations of species characterized by a similar reactivity. These sub-populations include monomer, oligomers, nucleus and larger aggregates. Finally, the rate of aggregation depends on the probability of having a primary particle on the external surface of a cluster, leading to an increase in reactivity with cluster size. This effect can be accounted for by the introduction of an additional factor C>,@ , for which several expressions have been proposed in the literature. In the absence of precise information about the correlation between aggregate size and reactivity, we selected the product kernel C>,@ = (89)K , which has been proven to describe well experimental data in a broad range of conditions

12.

Based on scaling arguments, Schmitt et al.

23

showed that the number of

primary particles located on the external surface of a fractal aggregate scales as 8 F#F⁄$% . This suggests that can be roughly estimated as ≈ 1 − 1⁄ .

Simulations were compared to experimental data by defining an objective function for each measurable quantity as defined in Supplementary Material. The weight average molecular weight of the simulated aggregate distribution was evaluated from the moments of the aggregate distribution and the average hydrodynamic radius of the overall population was computed as described by Lattuada et al. 24,25.

Computation of the Fuchs Stability Ratio within DLVO Theory As mentioned previously, the Fuchs stability ratio between two primary colloidal

particles, FF , can theoretically be computed from the expression of the interaction potential using equation (7). The DLVO theory 26,27, which accounts for the competing effects between Van der Waals attraction and electrostatic repulsion, has long been a cornerstone for the modeling of colloidal interactions.


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Assuming that proteins in solution can be modeled as spheres of radius , the Van der

Waals and electrostatic interaction potentials as a function of inter-particle distance ( can be

computed from the Hamaker expression (Equation (8)) and from the modified Hogg-HealyFursteneau expression (Equation (9)), respectively 28-31. Q[$\ (() = −

]^ 2 2 4 _ + + ln I1 − Ja W W 6 ((⁄ ) − 4 ((⁄ ) ((⁄ )W

4 d W ( Qbc (() = ln e1 + fg h− I − 2Jij (⁄

(8)

(9)

In the above equations, ]^ is the Hamaker constant, is the vacuum permittivity, is

the relative dielectric constant of the medium, d is the protein surface potential and is the Debye parameter, also called inverse Debye length. As most of the proteins have similar compositions, it can be assumed that proteins in aqueous solutions share similar Hamaker constants, which is expected to be in the order of 3 − 545 6 32,33, and was set here to ]^ = 345 6. The Debye parameter was computed as: =l

2 W mn o 45 6

(10)

Where mn is the Avogadro number, 45 is the Boltzmann constant, 6 is the temperature and o is the solution ionic strength defined as: o=

1 p @ W q@ r 2 >


(11)

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Where @ and q@ r are respectively the charge and bulk concentration of the various ionic species present in solution. Assuming that the distribution of all the ionic species present in the system can be described by the Poisson-Boltzmann equation, the protein surface potential can be estimated from the protein surface charge density s by solving the following equation 30: s = − t Where ℱ is the Faraday constant

@ d 2ℱ 45 6 p q@ r vexp .− / − 1wx

45 6 @

F/W

(12)

In this work, the protein surface charge density was computed from the value of the protein net charge estimated from the zeta potential measurements. The Fuchs stability ratio was then computed from the total interaction potential,

QR , according to equation (7), where QR is given by:

QR (() = Q[$\ (()+Qbc (()

(13)

RESULTS The aggregation kinetics of the two antibodies were performed at neutral pH under thermal stress (pH 6.5, 70°C) in the protein concentration range 1 - 5 g/L. The monomer depletion, the dimer and trimer formation as well as the aggregate weight average molecular weight were monitored by SEC-MALS, while the increase in average hydrodynamic radius of the non-fractionated population was followed by DLS in situ. As a representative example, the results of a mAb-1 sample incubated for 15 min at 70 °C and protein concentration of 2 g/L


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are shown in Figure S2 (Supplementary Material). The experimental monomer conversion has been analyzed to characterize the apparent reaction order, thus providing information on the rate-limiting step of the aggregation process. Then, experiments on diluted samples have been performed to probe for aggregate reversibility, and the fractal morphology of aggregates has been investigated by off-line Static Light Scattering. After the experimental analysis, we developed for each mAb a suitable aggregation kinetic scheme consistent with the experimental observations. The proposed kinetic models have been validated by fitting the model parameters at a reference protein concentration (2 g/L) and by predicting the aggregation kinetics at two different protein concentrations (1 g/L and 5 g/L). In the following, the results are reported for mAb-1 first, and then for mAb-2.

MAb-1 Experimental Observations The measured concentrations of monomer, dimer and trimer, as well as the aggregate weight average molecular weight and the average hydrodynamic radius of the overall population at protein concentrations of 1 g/L, 2 g/L and 5 g/L are shown in Figure 1.


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Figure 1: Comparison between model simulations (represented by lines) and experimental data (represented by symbols) for mAb-1 solutions incubated at pH 6.5 and 70°C at three different protein concentrations. The parameters were determined at the reference protein concentration of 2 g/L based on the fittings to (a) the monomer depletion and oligomer formation determined from SEC, to (b) the aggregate weight average molecular weight determined from SEC with inline MALS and to (c) the average hydrodynamic radius monitored with DLS in-situ. The parameters determined at the intermediate protein concentration of 2 g/L were used to predict the data measured at 1 g/L (d-f) and 5 g/L (g-i). The estimated values of the corresponding kinetic parameters are summarized in Table I.

The analysis of the concentration dependence of the monomer depletion kinetics provides relevant information on the rate-limiting step of the aggregation mechanism under

investigation. For a first order kinetic, the depletion of the monomer concentration (qz ) can be described by the equation

${| $}

= −4n qz which can be integrated in ln ~ | = −4n , {

{

with q corresponding to the total protein concentration and 4n being independent of q .


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Figure 2(a) presents the logarithm of the residual monomer normalized by the total protein concentration as a function of time for three initial protein concentrations (1 g/L, 2 g/L and 5 g/L). All the experimental points are aligned on a single straight line, indicating that the monomer consumption follows a first order process and that 4n is independent of the

initial protein concentration. This observation suggests that the monomer consumption of mAb-1 is rate-limited by an unimolecular reaction step, i.e. protein unfolding from a native state to a non-native aggregation-prone conformational state.


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Figure 2: Apparent reaction rate order, reversibility and aggregate morphology in mAb-1 aggregation. (a) ( ⁄ ) as a function of time for three different protein concentrations (1 g/L, 2 g/L, 5 g/L), where represents the monomer concentration measured by SEC and

denotes the total protein concentration. This plot shows that the monomer depletion of mAb-1 follows a first order kinetics. (b) Dilution experiment showing that mAb-1 aggregates are irreversible. The aggregate distributions were determined from SEC for (1) a sample of mAb-1


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incubated 15 min at 70°C at a protein concentration of 5 g/L ; (2) the same as (1) but diluted ten times in the aggregation buffer and analyzed immediately after dilution; (3) the same as (2) but analyzed after 24 h. The sample was kept in the refrigerator to prevent further aggregation. ‘Other’ corresponds to all the aggregates larger than trimer. (c) Structure factor of aggregated samples at different incubation times. The average gyration radius of each sample is reported in the caption. From the fitting in the power-law regime, a fractal dimension of 1.85 can be evaluated.

The aggregate reversibility was then investigated by dilution experiments. Figure 2(b) shows the monomer and aggregate content of a 5 g/L sample of mAb-1 that was incubated at 70° C for 15 min and analyzed immediately after incubation. These values are compared to the results obtained after a ten times dilution. The ten times diluted sample was analyzed both immediately after dilution and after one day of storage in the refrigerator. It can be seen that the monomer concentration and the aggregate content were not affected by dilution, thus indicating that the formed aggregates are irreversible. The aggregate morphology was studied by SLS at various aggregation time points.

Figure 2(c) shows the structure factor (!) as a function of ! for five average aggregate sizes that were obtained by incubating a sample of mAb-1 at 70 °C at a protein concentration of 1 g/L for different times. The overlapping of the curves reveals that aggregates exhibit selfsimilarity and the power-law regime provides a fractal dimension value equal to = 1.85 ± 0.02.

Kinetic Model Development The experimental measurements indicate that (i) the monomer depletion of mAb-1 is rate-limited by protein unfolding and that (ii) mAb-1 aggregates are irreversible. Based on these observations, the aggregation kinetic scheme presented in Figure 3 is proposed.


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(M1-1)

m

Monomeric conformational changes

(M1-2)

Irreversible oligomer formation

(M1-3)

Irreversible aggregate growth by: monomer addition and cluster-cluster aggregation

Page 20 of 52

+ W

+ W

+ > >F 8 ≥ 3

> + @ >@ 8, 9 ≥ 2

Figure 3: Scheme of the kinetic mechanism proposed for mAb-1 aggregation

First, the monomer in its native form m unfolds to form , which is a denaturated conformational state of the monomeric protein. This step, denoted as (M1-1) in the kinetic scheme, is regarded as irreversible in this study. Indeed, can be considered as an

intermediate reactive species which is depleted by irreversible aggregation before it can refold. Therefore, aggregation is faster with respect to the possible backward reaction of unfolding, and the reversibility of the unfolding step can be neglected. The aggregation prone form of the protein, , can then aggregate to form oligomers, according to step (M1-2). Finally, aggregates grow irreversibly either by monomer addition or by cluster-cluster aggregation, as depicted in step (M1-3). The detailed population balance equations describing mAb-1 aggregation are reported in Supplementary Material. To account for the differences in reactivity of the various species present in solution, different Fuchs stability ratios are considered. In particular, the unfolded aggregation-prone

monomer is an unstable intermediate which has a very high reactivity compared to other


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aggregates species. Therefore, three types of aggregation events characterized by species with different reactivities can be identified: monomer-monomer, monomer-aggregate and

aggregate-aggregate. Accordingly, three Fuchs stability ratios are defined: FF , F> and >@ , which describe oligomer formation, aggregate growth by monomer addition and aggregate growth by cluster-cluster aggregation, respectively. It is worth precising that in order to reflect the high reactivity of the dimer, which is suggested by its low and nearly constant concentration, it is assumed that FW = FF. The aggregation rate constants for each aggregation event are then computed according to equation (6).

Model Validation The implementation of the proposed kinetic scheme requires the estimation of several parameters. Some of these parameters can be evaluated by independent measurements, while others can be estimated by fitting the suitable quantities to those measured experimentally as a function of time. Since the concentration of is low and nearly constant due to its high

reactivity, the unfolding rate constant 4 can be approximated to 4n , which is determined

from the linearization of the experimental monomer depletion (Figure 2(a)). The fractal dimension has been measured by SLS and the power law factor appearing in the aggregation

kernel (6) has been estimated as ≈ 1 − 1⁄

23.

The remaining parameters are the three

Fuchs ratios FF , F> and >@ which have been fitted to describe the time evolution of the

monomer, dimer and trimer concentrations as well as the aggregate weight average molecular weight and the average hydrodynamic radius of the overall population at the reference protein concentration of 2 g/L (Figure 1(a-c)). The parameters used for the simulations are summarized in Table I. Table I: Parameters used for the simulations of the kinetics of aggregation of mAb-1 at 70°C in the protein concentration range from 1 g/L to 5 g/L.


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Value

1×10-3 s-1 Slope

Source

a

Parameter

ln ~ vs a z

z

1.85

Indep. SLS Exp.

0.46

1−

1

Page 22 of 52

¡

8.5×106

4×107

8×108

Fit b

Fit c

Fit d

This provides a good estimation of , provided that the concentration of unfolded monomer

is small due to its high reactivity. b The

same value was used for ¢

c

For ≥ £

d

For the aggregation events described neither by b nor by c

In Figure 1(a-c) it can be seen that the simulations are in excellent agreement with the experiments, indicating that the proposed kinetic model can successfully describe the aggregation of mAb-1 under the investigated conditions. To further validate the proposed kinetic scheme, the kinetics of aggregation were simulated at protein concentrations of 1 g/L and 5 g/L using the same set of values reported in Table I, with no additional parameters. In Figure 1(d-i), it can be seen that the model predictions agree very well with all experimental results, proving that the model is capable of predicting the concentration effect on the aggregation kinetics of mAb-1 in the concentration range from 1 g/L to 5 g/L. The simulated concentrations of the two monomeric states of mAb-1, m and are presented in Figure S4 (Supplementary Material), which shows the exponential depletion of m, and the formation of , which is then consumed by aggregation.

The comparison between the different Fuchs stability ratios estimated by the fitting to experimental data provides information on the relative reactivity of the various species


22

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involved in the aggregation process. Considering the values reported in Table I, it can be noticed that F@ ≪ >@ . This highlights that, for this system, aggregate growth by monomer

addition prevails over aggregate growth by cluster-cluster aggregation, probably due to the high reactivity of the unfolded monomer.

MAb-2 Experimental Observations After characterizing the aggregation mechanism of mAb-1, we show the strength of our approach by applying the same analysis to mAb-2. In Figure 4, we report the measured concentrations of monomer, dimer and trimer, as well as the aggregate weight average molecular weight and the average hydrodynamic radius as a function of time at protein concentrations of 1 g/L, 2 g/L and 5 g/L.


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Figure 4: Comparison between model simulations (represented by lines) and experimental data (represented by symbols) for mAb-2 solutions incubated at pH 6.5 and 70°C at three different protein concentrations. The parameters were determined at the reference protein concentration of 2 g/L based on the fittings to (a) the monomer depletion and oligomer formation determined from SEC, to (b) the aggregate weight average molecular weight determined from SEC with inline MALS, and to (c) the average hydrodynamic radius monitored with DLS in-situ. The parameters determined at the intermediate protein concentration of 2 g/L were used to predict the data measured at 1 g/L (d-f) and 5 g/L (g-i). The estimated values of the corresponding kinetic parameters are summarized in Table II.

In analogy with mAb-1, we evaluated the apparent reaction order from the concentration dependence of the experimental monomer depletion. This value has been found equal to 2, as shown in Figure 5(a) where the monomer conversion data are plotted in the linearized form ${| $}

F

{|

−

F

{

= −4n , which is the integrated solution of the mass balance

= −4n qz W . All experimental points fall on a single straight line passing through the

origin, showing that the monomer depletion of mAb-2 follows a second order process. This observation suggests that the monomer consumption of mAb-2 is rate-limited by bimolecular collisions, in contrast with the situation observed with mAb-1, where monomer consumption is rate limited by a monomolecular event, i.e. protein unfolding.


24

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Figure 5: Apparent reaction rate order, reversibility and aggregate morphology in mAb-2 aggregation. (a) ⁄ − ⁄ as a function of time for three different protein concentrations (1

g/L, 2 g/L, 5 g/L), where represents the monomer concentration measured by SEC and

denotes the total protein concentration. This plot shows that the monomer depletion of mAb-2 follows a second order kinetics. (b) Dilution experiment showing that mAb-2 aggregates are reversible. The aggregate distributions were determined from SEC for (1) a sample of mAb-2


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Page 26 of 52

incubated 15 min at 70°C at a protein concentration of 5 g/L ; (2) the same as (1) but diluted ten times in the aggregation buffer and analyzed immediately after dilution; (3) the same as (2) but analyzed after 24 h. The sample was kept in the refrigerator to prevent further aggregation. ‘Other’ corresponds to all the aggregates larger than trimer. (c) Structure factor of aggregated samples at different incubation times. The average gyration radius of each sample is reported in the caption. From the fitting in the power-law regime, a fractal dimension of 2.05 can be evaluated.

In Figure 5(b) we show the reversibility analysis by comparing the monomer and aggregate content of a 5 g/L sample of mAb-2 that was incubated at 70° C for 5 min and analyzed immediately after incubation with the results obtained with the same sample after a ten times dilution. The ten times diluted sample was analyzed both immediately after dilution and after one day of storage in the refrigerator. The results show that the monomer concentration is affected by dilution, thus suggesting that the oligomer formation of mAb-2 is reversible (Figure 5 (b)). It can be noticed that not only the dimer and trimer concentrations are reduced upon dilution, but also the concentration of larger oligomers. Since all aggregates larger than trimer elute from SEC in a single unresolved peak, the size of the largest reversible aggregate cannot be determined with accuracy. In the absence of precise information on the reversible oligomer formation, tetramer was assumed to be the largest reversible aggregate. Figure 5 (c) shows the structure factor (! ) as a function of ! for four average aggregate sizes. The overlapping of the curves reveals that, as in the case of mAb-1, aggregates exhibit self-similarity. The fractal dimension can be estimated from the power law regime equal to = 2.05 ± 0.02.


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Kinetic Model Development Based on the above experimental observations, we propose for mAb-2 the kinetic mechanism presented in Figure 6. (M2-1)

(M2-2)

Reversible oligomer formation

(M2-3)

Irreversible structural rearrangement

(M2-4)

¥¦§

: m ¨

Monomeric conformational changes

Irreversible aggregate growth

4FF ¬ + ⇄ W ª ® 4 FF ª ª 4FW ª + ⇄ W ª ® 4FW 4F « + ª ⇄ ¯ ® ª 4F ª 4WW ª ªW + W ⇄ ¯ ® © 4WW °±

¯ ² ¯ ∗

´∗

¯ ∗ + @ ² ¯@ 9 ≥ 1

> + @ >@ 8 ≥ 5, 9 ≥ 1

Figure 6: Scheme of the kinetic mechanism proposed for mAb-2 aggregation.

At the considered high temperature a population of partially unfolded conformational states of the antibody is likely present. However, since the monomer consumption is limited by bimolecular collisions, the applied set of characterization techniques does not provide information on the kinetics and thermodynamics of the unfolding step. It is therefore not possible to determine which monomeric form is involved in the aggregation process. For the sake of generality, we consider reversible monomeric changes from the native state (m) to a


27


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Page 28 of 52

non-native state of the protein (), as schematized in step (M2-1) of the reaction scheme, and we introduce a generic aggregation-prone intermediate () in the aggregation kinetic scheme. This generic intermediate is able to represent in a coarse-grained approach all the possible unfolding scenarios. Two limiting cases consistent with the observed second order kinetics of the monomer depletion could occur: the protein could react (i) in its native form

( = m) or (ii) in a denaturated state ( = ) provided that the generation of is fast compared to its consumption by aggregation. Besides these two limiting cases, another

intermediate situation could occur where only a fraction & of the monomer would be prone to aggregate. In this case, the dimerization and monomer addition rate constants can be computed as apparent reaction rate constants 4FF = & W × 4FF and 4F@ = & × 4F@ which

contain the actual reaction rate constant, reflecting the colloidal stability of the protein, and the fraction of the reactive monomeric species, which takes into account the protein conformational stability

34.

Another possible mechanism compatible with the observed

second order kinetics would involve protein assisted unfolding, where a reversible complex formation is followed by rate-limiting unfolding and aggregation of the unfolded state. However, since evidence about protein assisted unfolding is limited, we did not consider further this hypothesis in the following. The reactive monomeric state can form a nucleus by reversible oligomerization followed by irreversible structural rearrangement, according to the steps (M2-2) and (M2-3) in Figure 6, respectively. As mentioned above, tetramer has been assumed to be the largest reversible species. The complete description of reversible tetramer formation requires eight parameters (four forward reactions and four backward reactions). The reversibility experiments showed that the aggregates are not equally reversible, and in particular the trimer appears to be the least reversible species. In order to reduce the number of fitting


28

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parameters, we assumed that oligomer formation can be described by a single Fuchs stability ratio, i.e. FF = FW = F = WW . In addition, we assumed that each bound inside the

® ® tetramer can break with equal probability, and therefore 4F ≈ 24WW , since the probability

that a tetramer breaks into one monomer and one trimer is two times higher than the probability to form two dimers. Consequently, the number of parameters describing ® ® ® reversible oligomerization is reduced from eight to four (FF , 4FF , 4FW , 4F ).

Finally, the step (M2-4) in the reaction scheme represents aggregate growth, which can occur either by monomer addition or by cluster-cluster aggregation. In order to account for the differences in reactivity of the various populations present in solutions, three different Fuchs ratios have been considered: one for oligomer formation (FF ), one for nucleus consumption (¯∗ @ ), and one for cluster-cluster aggregation (>@ ). The detailed population balance equations describing mAb-2 aggregation can be found in Supplementary Material. Model Validation As in the case of mAb-1, the fractal dimension was measured by independent SLS

experiments and was estimated as ≈ 1 − 1⁄ . All the other kinetic parameters

® ® ® (FF , ¯∗ @ , >@ , 4FF , 4FW , 4F , 4µ{ ) were estimated by fitting the model simulations to five

independent sets of experimental data (monomer, dimer and trimer concentrations as well as aggregate weight molecular weight and average hydrodynamic radius of the overall population) at the reference protein concentration of 2 g/L. In Figure 4(a-c) we present the comparison between experimental and simulated kinetics of aggregation of mAb-2. It can be seen that the simulations are in very close


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Page 30 of 52

agreement with all experimentally accessible quantities. The parameter values used for the simulations are summarized in Table II. Table II: Parameters used for the simulations of the kinetics of aggregation of mAb-2 at 70°C in the protein concentration range from 1 g/L to 5 g/L. Parameter

Value

2.05

Source

a

Indep. SLS Exp.

0.51 1−

1

¶∗ ·

¡·

¸

¸¢

¸£

¹

2.7×107

1×106

4×108

4.4×10-3

1.4×10-4

1.3×10-2

3.7×10-3

Fit a

Fit b

Fit c

Fit

Fit

Fit d

Fit

It was assumed that = ¢ = £ = ¢¢

b

For ≥

c

For the aggregation events described neither by a nor by b

d

It was assumed that ¸¢¢ = ¢ ¸£

With the parameters determined at the reference protein concentration of 2 g/L we then simulated the aggregation kinetics at 1 g/L and 5 g/L, thus testing the capability of the model to predict the concentration dependence of the aggregation rate. Figure 4(d-i) compares the predicted kinetics with experimental results at protein concentrations of 1 g/L and 5 g/L. The model predictions of the monomer depletion, dimer and trimer formation, as well as the aggregate weight average molecular weight and average hydrodynamic radius of the non-fractionated population are in good agreement with the experimental data, confirming the validity of the proposed kinetic model. As in the case of mAb-1, the ranking of the Fuchs stability ratios provides information on the relative reactivity of the different species present in the system. Considering the values


30

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of reported in Table II, the various species involved in the kinetic mechanism can be classified according to their reactivity in the following order: nucleus > oligomers > large aggregates. This observation is consistent with the definition of nucleus as the least stable species present in the system.


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DISCUSSION Comparison Between the Two Antibodies The kinetics of aggregation of two monoclonal antibodies, which differ in terms of IgG subclass, glycosylation and net charge, were followed at neutral pH under thermal stress. The comparison between experimental and simulated kinetic data allowed the identification of the key steps involved in the aggregation mechanism of the two proteins. The two mAbs were found to exhibit different aggregation behaviors under the same operating conditions. In Figure 7, we present a scheme of the aggregation mechanism proposed for each mAb and we highlight the identified rate limiting step for monomer consumption in each aggregation pathway. The kinetic mechanism proposed for mAb-1 includes protein unfolding, which is the rate limiting step, followed by irreversible oligomer formation and aggregate growth, which is dominated by monomer addition and accompanied by cluster-cluster aggregation.

The

mechanism of mAb-1 aggregation significantly differs from the aggregation pathway identified for mAb-2, which was found to be rate-limited by bimolecular collisions and includes reversible oligomer formation followed by irreversible tetramer rearrangement and aggregate growth.


32

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Figure 7: Scheme of the mechanisms of mAb-1 and mAb-2 aggregation. The aggregation mechanism

of

mAb-1

includes

monomeric

conformational

changes,

irreversible

oligomerization and irreversible aggregate growth, whereas the aggregation mechanism of mAb-2 includes monomeric conformational changes, nucleus formation and irreversible aggregate growth. While the monomer depletion is limited by protein unfolding in the case of


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Page 34 of 52

mAb-1, bimolecular collision leading to dimer formation is the rate limited step in the case of mAb-2.

It would be of great relevance to correlate the observed aggregation behaviors with antibody properties (such as IgG subclass, glycosylation pattern or protein charge). However, such an attempt is extremely challenging since it requires detailed information on the protein structure. Regarding the two antibodies under examination in this study, we summarized in Table III the main differences between the two molecules in terms of both structures and aggregation behaviors. Although correlating antibody structure with aggregation behaviors is beyond the scope of this study, the two following remarks can be formulated. First, it can be noted that the antibody which is the more resistant to aggregation (i.e. mAb-1, whose monomer depletion kinetics is rate limited by protein unfolding) is also the one which is glycosylated and which carries the highest net charge. Second, it can be observed that the antibody carrying a larger net charge (i.e. mAb-1) forms relatively open aggregates

characterized by a fractal dimension value of = 1.85, which is lower than the one expected

under RLCA conditions ( = 2.05). This suggests that aggregation is confined only to a few aggregation-prone patches, possibly due to charge heterogeneities. On the other hand, the antibody whose net charge is screened (i.e. mAb-2) forms more compact aggregates

characterized by a fractal dimension of = 2.05. This observation can be possibly explained by the charge screening, which makes the protein surface more uniform, thus leading to the fractal dimension value expected in the case of uniformly charged polymer colloids, as already suggested by Wu et al. 35. Table III: Comparison between the two antibodies in terms of their structure and aggregation behaviors at pH 6.5 and 70 °C.


34

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mAb-1

mAb-2

Antibody subclass

IgG1

IgG2

Glycosylation

Yes

No

Zeta Potential

5.71 ± 3.51 mV

0.53 ± 0.75 mV

Protein charge (from eq. (2))

+4

+ 0.4

Apparent order

1

2

R.L.S.a for monomer depletion

Monomeric unfolding

Bimolecular aggregation

Reversibility

No

Yes

Fractal dimension

1.85±0.02

2.05±0.02

a

Rate-Limiting Step

Characteristic Times From the estimated kinetic rate constants, we can compute the characteristic times of the different microscopic events involved in the aggregation process, thus allowing the quantification of the time scales over which the various phenomena occur. The calculated characteristic times at the reference protein concentration of 1 g/L are presented in Supplementary Material. For both proteins, the characteristic time of diffusion in this system

is in the order of 10#º » while aggregation occurs on a time scale of minutes. This indicates that diffusion is not the rate-limiting step for monomer depletion. In the case of mAb-1, the production of an aggregation-prone monomer by the unfolding reaction occurs on a time scale of approximately 20 min, while its disappearance by aggregation has a characteristic time of only 1 min, which is consistent with the finding that mAb-1 aggregation is unfolding ratelimited.


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DLVO Theory Alone Cannot Describe the Interaction Potential of Antibody Solutions The kinetic approach used in this study allows the quantification of the inter-particle interaction potentials, expressed in terms of the Fuchs stability ratio (WFF), from the reaction rate constants estimated by fitting to the experimental kinetics of aggregation. The Fuchs stability ratio quantifies the fraction of collisions which are successful in forming larger aggregates, providing a measure of the extent to which the aggregation kinetics is delayed with respect to diffusion limited conditions. The Fuchs stability ratio can be directly related to the protein-protein interaction potential, as shown in equation (7). It quantifies proteinprotein interactions in a coarse-grained manner, averaging protein surface heterogeneities over space. It is of great interest to compare the Fuchs stability value obtained by fitting to experimental kinetics of aggregation to the theoretical value computed with equation (7). As illustrated in the next paragraph, this comparison allows to identify some gaps between theories dealing with colloidal stability (such as the DLVO theory) and experimental observations. In the following, the values of the Fuchs stability ratio evaluated by fitting to

experimental kinetics of aggregation are denoted by FF , while the values computed

MN[½ theoretically in the frame of the DLVO theory are referred to as FF .

The values of the Fuchs stability ratio estimated by fitting to experimental kinetics of

aggregation are in the order of FF ~10¾ (Table I and Table II). This large value indicates the presence of a high energy barrier that particles must overcome before colliding, which reduces the collision efficiency and thus delays the aggregation process with respect to diffusion limited conditions. On the other hand, the very low values of zeta-potential of the antibody solutions (see Table III) suggest that at the considered pH of 6.5, the antibody net charge is close to zero and net electrostatic stabilization is thus expected to be small. Figure 8


36

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shows the computed contribution of the Van der Waals attraction and of the electrostatic repulsion to the total protein-protein interaction potential as a function of the inter-particle distance, as computed from equations (8) to (13) for mAb-1 and mAb-2. Based on these MN[½ calculations, from equation (7) we computed FF ≈ 1 for the two antibodies. These low

computed values of the Fuchs stability ratio, which correspond to the DLCA regime, reflect the low net charge of the antibody solutions under these conditions, and are several orders of magnitude smaller than the values estimated by kinetic analysis. This difference between the measured and the calculated Fuchs stability ratio values is striking, and it is not affected by potential inaccuracies in the assessment of the net protein charge from zeta potential measurements (partly due to fact that zeta potential measurements were carried out at room temperature, while aggregation kinetics were performed under thermal stress). Indeed, an increase in the protein net charge of mAb-1 by a factor of three would result in a change in the

MN[½ MN[½ computed Fuchs ratio from FF = 1 to FF = 2.3, which is still much lower than the

value obtained by kinetic analysis. Moreover, to obtain a value of Fuchs stability ratio of MN[½ = 8.5 × 10¿ , which is equal to the value obtained by fitting to the experimental data, FF

an unreasonable change in the charge from = +4 to = +43 would be required.


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Figure 8: Electrostatic repulsion alone is not responsible for the large energy barrier that protein molecules must overcome before colliding. Computed protein-protein interaction potential (À) of mAb-1 (a) and mAb-2 (b) in the frame of the DLVO theory as a function of

intermolecular distance ¸/ÁÂ , where ÁÂ is the particle radius. The Fuchs stability ratios computed from the integration of the interaction potentials are close to 1 for both mAbs. This

value is several orders of magnitude lower than the values of obtained by the estimated reaction rate constants.

Therefore, our results strongly indicate that the colloidal stability of antibody solutions cannot be rationalized only in the frame of the DLVO theory, which considerably underestimates the repulsive energy barrier between two approaching molecules. The DLVO theory may underestimate the colloidal stability of antibody solutions for several reasons


38

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including: (i) the low collision efficiency due to the heterogeneous protein surface, which may provide only a limited number of aggregation-prone patches and thus requires specific geometrical orientation of the two aggregating molecules, in contrast with sticking homogeneous spherical colloids; (ii) additional repulsive non-DLVO repulsion forces, such as hydration forces, which further contribute to the interaction potential.

CONCLUSIONS We investigated by kinetic analysis the aggregation behavior under thermal stress of two monoclonal antibodies belonging to the IgG1 and IgG2 subclass. By applying a combination of Size Exclusion Chromatography and Light Scattering techniques, we characterized the time evolution of the monomer, dimer and trimer concentrations, as well as the average molecular weight of the aggregate distribution and the average hydrodynamic radius of the non-fractionated population. For each mAb, based on the experimental observations, we proposed an aggregation mechanism and we derived a kinetic model based on Smoluchowski’s Population Balance Equations. The classical Smoluchowski’s PBE were modified to account for the nucleation events, which are essential in the description of the protein aggregation process. Remarkably, the proposed models were able to describe well the different sets of experimental data and to predict the concentration dependence of the aggregation kinetics in the range from 1 to 5 g/L. The combination of experimental data and theoretical kinetic analysis allowed us to quantify the contribution of the single microscopic steps on the global aggregation rate. We demonstrated that the two mAbs exhibit different aggregation mechanisms under the same operating conditions. In particular, it was found that the monomer depletion kinetics of mAb-


39


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Page 40 of 52

1 is rate-limited by unimolecular protein unfolding, while bimolecular aggregation was identified as the rate-limiting step for the monomer depletion of mAb-2. From the measurement of the microscopic kinetic rate constants, we quantified the protein-protein interaction potentials expressed in terms of the Fuchs stability ratio and we showed that DLVO theory considerably underestimates the colloidal stability of the antibody solutions under investigation. This result is possibly due to the reduced efficiency of collisions related to the presence of a limited number of specific aggregation-prone patches on the heterogeneous protein surface, as well as the contribution of additional repulsive non-DLVO forces to the protein-protein interaction potential, such as hydration forces.

ACKNOWLEDGEMENTS Financial support from the Fondation Claude et Giuliana and from the Swiss National Foundation (grant No. 200020_147137/1) is gratefully acknowledged. We also thank UCB Pharma (Braine l'Alleud, Belgium) and Merck Serono (Vevey, Switzerland) for material supplying and financial support.

ASSOCIATED CONTENT Protein thermal stability investigated with Circular Dichroism and Dynamic Light Scattering, representative SEC chromatogram of an aggregated sample, comparison between off-line and in-situ measurements, simulated time evolution of the native and unfolded monomer concentrations involved in mAb-1 aggregation, Population Balance Equations, computation of the characteristic times.


40

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Lattuada, M.; Sandkuhler, P.; Wu, H.; Sefcik, J.; Morbidelli, M. Aggregation Kinetics of

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TABLE OF CONTENTS IMAGE


45

FITTINGS

fb) fc) The Journal of Physical Chemistry Page 46 of 52 20

10

20

600

k[nm]

15

800

10

400

5

200 0

10

20

30

Timek[min]

0 0

10

20

30

10

20

30

10

20

30

Timek[min]

PREDICTIONS

ff)

fe)

10

20

Timek[min]

20

1000

600

5

200

fh) Monomer Dimer Trimer

10

400

0

30

15

800

k[nm]

Monomer Dimer Trimer

10

20

30

Timek[min]

0 0

fi)20

Timek[min]

1000 15

800 600

k[nm]

Concentrationk[g/L]

30

Timek[min]

Concentrationk[g/L]

1 1 2 0.5 3 4 00 5 6 fd) 7 1 8 0.8 9 0.6 100.4 110.2 12 0 13 0 fg) 5 14 15 4 16 3 17 2 18 1 19 0 20 0

1000

MWwAggk[kDa]


1.5

MWwAggk[kDa]

2

MWwAggk[kDa]

Concentrationk[g/L]

fa)

10

400 ACS Paragon Plus Environment 5

10

20

Timek[min]

30

200 0

10

20

30

Timek[min]

0 0

Timek[min]

1

Page 47 Theof Journal 52 of Physical Chemistry 1)g/L (a)

S(q)

Content0[%]

ln(cM/c0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

2)g/L 5)g/L

0 -1 1st order

-2

dcM/dt0~0cM

-3 0

100

10

(b)

20

30

Time0[min]

40

(1))Before)dilution (2))After)10x)dilution (3))After)10x)dilution)+)24)h

80 60

Irreversible

40

aggregates

20 0

10

0

10

-1

1 2 3 4 Monomer Dimer Trimer Other

(c)

Rg

35)nm d =)1.85 60)nm f 100)nm 140)nm -2 ACS 210)nm Paragon Plus Environment 10 -1 0 10 10

qRg0[-]

10

1

FITTINGS

fb) 1600 Chemistry fc)4048 of 52 The Journal of Physical Page

10

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20

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k[nm]

1000

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PREDICTIONS

ff)40

1600 1400

30

1200 1000

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800 600

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400 200

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Timek[min]

0

fh) Monomer Dimer Trimer

k[nm]

fe) Monomer Dimer Trimer

10

20

30

Timek[min] 1600

0 0

fi)

Timek[min]

40

1400

k[nm]

Concentrationk[g/L]

30

1200

200

Concentrationk[g/L]

1 1 2 0.5 3 4 00 5 6 fd) 1 7 8 0.8 9 0.6 100.4 110.2 12 0 13 0 fg) 5 14 15 4 16 3 17 2 18 1 19 0 20 0

1400

MWwAggk[kDa]


1.5

MWwAggk[kDa]

2

MWwAggk[kDa]

Concentrationk[g/L]

fa)

30

1200 1000

20

800

600 ACS Paragon Plus Environment 10 400 200 10

20

Timek[min]

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Timek[min]

0 0

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Page 49 Theof Journal 52 of Physical Chemistry 1-g/L (a)

1/cML-L1/c0L[L/g]

6

S(q)

ContentL[%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

2-g/L 5-g/L

2nd order

5

dcM/dtL~Lc2M

4 3 2 1 0 0

100

10

(b)

20

TimeL[min]

30

(1)-Before-dilution (2)-After-10x-dilution (3)-After-10x-dilution-+-24-h

80

Reversible

60

aggregates 40 20 0

1 2 3 4 Monomer Dimer Trimer Other

10

0

10

-1

-2

(c)

Rg

30-nm 170-nm 360-nm 480-nm

df =-2.05

Paragon Plus Environment 10ACS -1 0 10 10

qRgL[-]

10

1

The Journal of Physical Chemistry Page 50 of 52 (a) mAb-1 r.l.s. 1 I. Monomeric 2 conformational 3 changes 4 5 6 II. + 7 Irreversible oligomerization 8 9 10 III. + 11 Irreversible aggregate growth 12 13 14 15 16 17 18 I. 19Monomeric conformational 20 changes 21 22 23 r.l.s. 24 II. ... + 25Reversible oligomerization 26 27 28 III. 29 Irreversible rearrangement 30 31 32 IV. Irreversible 33 + aggregate growth 34 35 36 37 ACS Paragon Plus Environment 38 rate limiting step for monomer depletion r.l.s.: 39 40

(b) mAb-2

(a)

Page 51 The 52 of Physical Chemistry 2 ofJournal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

V(r)/kBT [-]

mAb-1 WDLVO ~1 11

1 0 -1 -2

Electrostatic Van der Waals Total 2

2.5

3

3.5

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0 -1

Electrostatic Van der Waals Total

-2 ACS Paragon Plus Environment 2 2.5 3

r/Rp [-]

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Monomer

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MWwAgg [kDa]

Concentration [g/L]

2

Dimer Trimer he1.5Journal of Physical Page 52 Chemist of 52 800 1

600 400

0.5 1 200 200 0 10 20 30 10 20 30 Time [min] Time [min] 3 4 5 6 Paragon ACS Plus Environmen + 7 + 8

Kinetic Analysis of the Multistep Aggregation Mechanism of

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