Kinetics of Antibody Aggregation at Neutral pH and Ambient

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Kinetics of Antibody Aggregation at Neutral pH and Ambient Temperatures Triggered by Temporal Exposure to Acid Hiroshi Imamura, and Shinya Honda J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b05473 • Publication Date (Web): 18 Aug 2016 Downloaded from http://pubs.acs.org on August 19, 2016

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The Journal of Physical Chemistry

Kinetics of Antibody Aggregation at Neutral pH and Ambient Temperatures Triggered by Temporal Exposure to Acid Hiroshi Imamura, Shinya Honda* Biomedical Research Institute, National Institute of Advanced Industrial Science and Technology, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8566, Japan

ACS Paragon Plus Environment

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ABSTRACT

The purification process of an antibody in manufacturing involves temporal exposure of the molecules to low pH followed by neutralization—pH-shift stress—which causes aggregation. It remains unclear how aggregation triggered by pH-shift stress grows at neutral pH and how it depends on the temperature in an ambient range. We used static and dynamic light scattering to monitor the time-dependent evolution of the aggregate size of the pH-shift stressed antibody between 4.0 and 40.0 °C. A power-law relationship between the effective molecular weight and the effective hydrodynamic radius was found, indicating that the aggregates were fractal with a dimension of 1.98. We found that the aggregation kinetics in the lower-temperature range, 4.025.0 °C, were well described by the Smoluchowski aggregation equation. The temperature dependence of the effective aggregation rate constant gave 13 ± 1 kcal/mol of endothermic activation energy. Temporal acid exposure creates an enriched population of unfolded protein molecules that are competent of aggregating. Therefore, the energetically unfavorable unfolding step is not required and the aggregation proceeds faster. These findings provide a basis for predicting the growth of aggregates during storage under practical, ambient conditions.


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Introduction In pharmaceutical manufacturing of antibodies, affinity chromatography with immobilized protein A is a standard method for purification, where an acidic solution is used to elute the antibodies and inactivate viruses possibly contaminating the cell culture (clearance process). At the same time, however, the acid treatment inevitably leads to destabilization of the native state of the antibodies.1 The subsequent neutralization of pH of the solution produces antibody aggregates that grow over time.2 Monitoring and removing the aggregates is a prerequisite for the safe formulation of antibody drugs,3 because the aggregates are potentially immunogenic.4-7 Understanding the underlying mechanism of the aggregation triggered by temporal exposure to acid and subsequent neutralization—pH-shift stress—will aid in developing strategies for rational monitoring, removing, and preventing the aggregation. Previous studies aimed at examining the mechanisms of antibody aggregation have been carried out under severe conditions such as acidic pH,8,9 high temperature,10-12 and vigorous mechanical stress (shaking or stirring).13 Antibody molecules destabilized by such stresses serve as a source for spontaneous aggregation. Although these previous findings are intriguing, extrapolating them to aggregation processes under practical, ambient conditions is not straightforward because the native state is scarcely destabilized under ambient conditions. It still remains to be elucidated how the pH-shift stress-triggered aggregates emerge and grow at neutral pH and ambient temperatures. Possible mechanisms of aggregation of proteins including antibodies have been proposed. 1418

Observation of the aggregation phenomenon coupled with modeling the kinetics is an

attractive approach for finding or revising the underlying mechanism and for predicting the aggregation behavior under conditions of interest, e.g., long-term storage at room temperature or


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lower. In the present study, we monitored the time-dependent evolution of pH-shift stresstriggered aggregation at 4-40 °C by using static and a dynamic light scattering. By shifting the pH from acidic to neutral, a portion of the non-native molecules associated into oligomers, while the rest refolded into native ones. After that, the aggregates grew irreversibly. We performed modeling based on Smoluchowski aggregation kinetics,19 which is the basic equation of Brownian coagulation; applying these kinetics to polyclonal human immunoglobulin G has been proven successful by the pioneering work of Feder and colleagues.10,11 We found a master curve for pH-shift-triggered aggregation, which was the best approximation in a lowertemperature range of 4.0-25.0 °C. In addition, from the temperature dependence, we determined the endothermic activation energy for the aggregation, indicating that the pH-shift stressed antibody crosses a relatively low-barrier pathway to aggregation.

Materials and methods Sample preparation The antibody the present study used was a monoclonal humanized immunoglobulin G1 with a molecular weight of 148 kDa and with an isoelectric point of 8.5 that was calculated based on its sequence.20 The lyophilized powder was dissolved into a buffer solution containing 0.01 M sodium phosphate, 0.15 M NaCl, and 0.005% (v/v) polyoxyethylene (20) sorbitan monolaurate (pH 7.4) to a concentration of 11 mg/mL. The mother solution (pH 7.4) was dialyzed against 0.1 M glycine-HCl buffer solution (pH 2.0) with a membrane with a cut-off of 12-14 kDa (Scinova GmbH, Germany) for 22 ± 3 hours at 4 °C. The dialyzed solution was stored at 4 °C for 167 ± 5 hours before the following neutralization (within the time period of incubation, an increase in the protein size reached a plateau). The dialyzed protein solution (pH 2.1 ± 0.1) was diluted to 1.02


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mg/mL with the glycine buffer. A 12 µL aliquot of 1.0 M Tris-HCl (pH 8.0), placed onto the inner wall surface of a microtube, was mixed with 720 µL of the protein solution by tapping. This procedure was repeated 12 times and was completed just in 3 min. During neutralization, the sample solution was kept on ice. pH and the protein concentration of the resulting solution were 6.8 ± 0.2 and 0.85 mg/mL, respectively. Although the present procedure did not produce large protein aggregates immediately after neutralization, the solution was passed through a centrifugal filter unit with a pore size of 0.22 µm (Merck Millipore Ltd., Germany) to remove possible large particle impurities prior to transferring the solution into a quartz micro-cuvette. The quartz cuvette was embedded inside the thermo-regulating system, which had been equilibrated to a given temperature, at 5 min after the completion of neutralization. We also prepared a control that was utilized as an unstressed sample by diluting the mother solution 10 times with the buffer solution. Static and dynamic light scattering To probe the evolution of protein aggregates, static and a dynamic light scattering measurements were performed, which should provide the normalized time autocorrelation function of the scattering intensity for a given correlation time τ, g(2)(τ), defined by: g(2)(τ) = /2,

(1)

where I(t’) and I(t’ + τ) are the scattering intensities at time t’ and t’ + τ, respectively. The braces indicate averaging over time. The time-averaged (static) light scattering intensity is given by . g(2)(τ) is given in terms of the normalized electric field-field time autocorrelation function, g(1)(τ), via the following relation,: g(2)(τ) = B + β[g(1)(τ)]2,

(2)


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where B is the long-time value of g(2)(τ) and β is an instrumental parameter. In practice, B deviates slightly from the ideal value, i.e. one, because of a small amount of noise. The moment method by Frisken,21 which is a reformulated version of the method of cumulants, gives: g(1)(τ) = exp(−Γτ)(1 + (µ2/2!)τ2 − (µ3/3!)τ3),

(3)

where Γ is the mean decay rate and µm are the mth moments about the mean, which correspond directly to the mth cumulants in the method of cumulants.21 The functions of eq. (2) and eq. (3) with terms up to the second moment about the mean, µ2, were fitted to the experimental data. Γ is given by:

Γ = Ddifq2, (4) where Ddif is the diffusion constant of the particle(s) and q is the magnitude of the scattering vector. q is defined as: q = 4πnsin(θ/2)/λ,

(5)

where n is the refractive index of the solvent, θ is the scattering angle, and λ is the wavelength of the light. The diffusion constant, Ddif, is converted into the hydrodynamic radius of the particle, RH, via the Stokes-Einstein relation: RH = kBT/6πηDdif ,

(6)

where kB is the Boltzmann constant, T is the thermodynamic temperature, and η is the viscosity of the solvent. The refractive index and the viscosity of the solvent, a glycine-HCl solution containing Tris-HCl, were measured at the given temperatures (Supporting Information). We note that Γ, Ddif, and RH are expressed as effective values for particles with a size distribution. To probe the size distribution of the sample, we calculated the polydispersity index, Q,22 referred to as PDI elsewhere, defined by: Q = µ2 / Γ2.

(7)


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Since Γ and µ2 are the mean and the variance, respectively, Q reflects a “relative” shape of the distribution of the size.23 In addition, we performed another distribution analysis in which the autocorrelation function should represent a multiexponential decay. A size distribution weighted by light scattering intensity was obtained by using non-negative least squares (NNLS), a regularization method for numerical inversion of the Laplace transform. Here, we employed 0.01 for α, a so-called smoothing parameter, used in the regularization.24 The experiments were performed using a Zetasizer Nano S (Malvern Instruments Ltd., Worcestershire, U.K.) with θ = 173º and λ = 632.8 nm. Each of the measurements of g(2)(τ) was repeated 32 times using an acquisition time of 10 sec and averaged. Fractal dimension of the aggregates Under certain conditions, particles including protein molecules form aggregates with the character of a fractal.25 The fractal aggregate obeys the following relationship:26,27 D

i = (Ri / R0 ) f ,

(8)

where i is the number of a primary particle in a cluster, Ri is the radius of the cluster of an i-mer, and R0 is the radius of a primary particle. Here, the primary particle is a monomer. In the present study, we regarded the hydrodynamic radius (RH) as the radius. Df is the fractal dimension. Eq. (8) is rewritten as Ri = R0i1/D ; a larger Df represents a well-packed, more compact structure of the f

aggregates.28 The molecular weight of the i-mer, Mi, is given as: Mi = iM0,

(9)

where M0 is the molecular weight of the primary particle (monomer). According to eq. (8, 9), the effective number of primary particles, ieff, in a cluster with the size of RH is written as D ieff = (M eff / M 0 ) = (RH / R0 ) f ,

(10)


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where Meff is the effective molecular weight of the particles. The excess static light scattering from the protein particles, I, is determined by sol − solv, where the subscripts ‘sol’ and ‘solv’ denote a protein solution and a solvent, respectively. The relative excess light scattering intensity, I/I0, is calculated by: I/I0 = (n2I/cp) / (nm2Im/cp,m),

(11)

where cp, Im, cp,m, and nm are the mass concentration of the particle, the excess light scattering intensity from the primary (monomeric) particle, its mass concentration, and the refractive index of the dissolving solvent, respectively. For Rayleigh scattering, the excess light scattering intensity is rationalized by the Rayleigh ratio, R(θ): I ∝ R(θ).

(12)

R(θ) is expressed as:29 R(θ) ∝ MeffcpP(q)S(q),

(13)

where P(q) is the form factor, i.e. the intra-particle or the intra-cluster interference, and S(q) is the structure factor, i.e. the inter-particle or the inter-cluster interference. Here, we assumed P(q) = 1, which is a reasonable approximation when the size of a particle is smaller than q-1, i.e. qRH < 1.29,30 q-1 was 38 nm in the present experimental setup. The present experimental conditions under which the protein was sufficiently diluted satisfied S(q) = 1, where the inter-particle effect on the scattering is negligibly small. Accordingly, the excess light scattering intensity is proportional to the molecular weight: Eq. (10-13) gives I/I0 = (Meff / M0). Thus, the power-law relationship between the relative light scattering intensity and the relative radius is obtained as: log(I/I0) = Df log(RH/R0).

(14)

The slope of log(I/I0) gives the fractal dimension. Smoluchowski aggregation kinetics


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The Smoluchowski aggregation equation is formulated by considering that two diffusing particles collide and irreversibly coagulate with a given probability (see illustration in the right side of Fig. 5).19 The Smoluchowski equation gives the time-dependence of the concentration (the fraction or the population) of all i-mers: ∞ dni i−1 = ∑ Ai− j, j ni− j n j − 2∑ Ai, j ni n j , dτ s j=1 j=1

(15)

where ni is the i-mer concentration. The concentration is normalized to the initial primary particle concentration (∑iini = 1). Aij is the correction term of the probability that an i-mer and a j-mer collide by diffusion per unit time: 1 Aij = (i1/Df + j1/Df )(i−1/Df + j −1/Df ) , 4

(16)

where the original formula by Smoluchowski19 has been modified by introducing the concept of the fractal.10,11,27 τs is the reduced dimensionless time defined as τs = γt, where γ is the aggregation rate constant and t is the time. The time was set to zero when neutralization of the protein solution was completed. The differential equations were numerically solved. In the calculation, we considered clusters with i < 800, while the number should be theoretically infinite in eq. (15), since this number was enough to cover the present experimental range of the size distribution of the aggregates and conserve the total mass of the system in the simulation. RH/R0 and I/I0 were calculated according to:11 ∞

∞

∑n i

∑n i

2

i

RH / R0 =

=

i=1 ∞

∑ n i (R 2

i

i=1

0

2

i

/ Ri )

i=1 ∞

∑n i

2−1/D f

i

i=1

and I/I0 = Σii2n,

(17)


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respectively. Eq. (15-17) gives the time-dependent evolution of the effective hydrodynamic radius of the cluster and the excess light scattering intensity. The Smoluchowski equation per se describes the time-dependence of the fraction (population) of the i-mer, ini. Because the light scattering intensity is proportional to the number of primary particles, the normalized intensityweighted distribution of the i-mer, pi, is expressed as: pi = i2ni / Σii2ni.

(18)

The definition of the moment-generating function, M(−τ; Γ), of the distribution that is weighted by light scattering intensity is equivalent to g(1)(τ):22 M(−τ; Γ) ≡ Σi pi exp(−Γiτ) = g(1)(τ), (19) where Γi is the decay rate of the i-mer, which is calculated via eq. (4-6) and eq. (8). The series expansion of eq. (19), i.e., eq. (3), gives the Q value. We note that qR < 1 is violated when the aggregate grows over 38 nm in terms of the radius seen in the present experiment for longer time-periods, which requires more elaborate analysis than has been done in the present study. Size-exclusion chromatography Size-exclusion chromatography was performed on a Prominence HPLC system (Shimadzu Co., Kyoto, Japan) using a TSKgel SuperSW mAb HR column with 300 mm length × 7.8 mm internal diameter (Tosoh Co., Tokyo, Japan). 10 µL aliquots of the protein solution were loaded onto the column and eluted at a flow rate of 0.5 mL/min with a buffer solution of 0.1 M sodium phosphate and 0.2 M L-arginine hydrochloride (pH 6.9). The signal deriving from the ultraviolet absorption of the eluate was monitored at a wavelength of 280 nm. During the measurements, the liquid chromatography system and the samples were kept at the given temperatures.


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All analyses were performed by using IGOR Pro version 6.22A (WaveMetrics, Portland, OR), except for NNLS which was performed by using Zetasizer software version 7.02 (Malvern Instruments Ltd.).

Results and Discussion Irreversible aggregation triggered by pH-shift stress Fig. 1(a) shows that the autocorrelations, g(2)(τ) − 1, of the pH-shift stressed samples at 15.0 °C increased with the progression of time, indicating that the size of the protein aggregates increased with time. During the evolution of the size, the autocorrelations looked singleexponential rather than multiple-exponential. Indeed, each of the experimental autocorrelations was well described by the autocorrelation considering a mean decay with a small deviation as formulated in eq. (2-3), which are shown as the continuous solid lines in the figure. This suggests that the aggregates emerge and grow while keeping a unimodal distribution. The size distribution analyzed by NNLS shown in Fig. 1(b) supports this model. The aggregates kept growing over time. The process of aggregation was effectively irreversible; we found that visible particles or white precipitates emerged during continuous incubation for a period of less than 1 week. The deviation from the mean decay was also quantitatively assessed by using the polydispersity index, Q, as shown in Fig. 1(c). The Q values slightly exceeded the criteria for “nearmonodisperse”.31 It is of interest that Q values initially changed from 0.15~0.2, but became constant, shown as Q∞ in the figure, over a longer time. In addition, we found that the Q∞ values did not depend on temperature (data not shown).


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During DLS measurement, we simultaneously performed size-exclusion chromatography of the pH-shift stressed samples to determine the existence of monomers and self-associated species as shown in Fig. 2. As the chromatogram of an unstressed sample indicates the retention time of monomeric species, the peaks of the stressed sample at 15.3, 13.3, and 10.4 min were identified as the monomer, dimer, and larger aggregates including oligomers, respectively. The peak areas derived from the protein detected by ultraviolet absorption from approximately 9 to 19 min increased with the progression of the aggregation reaction. The amount of the sample injected was not completely recovered through the chromatography, although the recovery improved with time. Indeed, incompleteness of the recovery (~20%) of the stressed sample was verified by comparison with the best recovery (~98%) of the unstressed sample. In light of the current situation where the aggregates evolved over time, physical trapping in the column due to large particle size would not be solely responsible, because it would not account for later improvement of recovery. Instead, the adsorption of a portion of the sample onto the column seems to be the reason, because non-native species of antibodies are prone to bind to columns according to previous reports.2,32 Non-native species were likely to refold into the native one during the course of several hours,2 which would explain the improvement of the recovery over time, because the monomeric antibody of the native state scarcely adsorbed onto the column. The increase in the native monomer during the aggregation suggests that the native monomer is not a major source for aggregation, in contrast to previous studies reporting a depletion of the monomer during spontaneous aggregation by heating or under acidic conditions.33,34 Accordingly, the content of the native monomer can be quantified. With the progression of time, the signal intensities of the peaks of the monomer increased and seemed to reach a plateau at ~7 h. We estimated the content of the monomer, those molecules not involved in the aggregation, to


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be 6% by comparing the relative peak area of the monomer of the stressed sample to that of the unstressed sample. We note that the retention time of the dimer (the peak showing a maximum at 13.3 min) in the pH-shift stressed sample was slightly delayed compared with 12.9 min for the dimer in the unstressed IgG1 as shown in the inset of Fig. 2. This is in accordance with previous reports,35 suggesting that the dimeric form of the pH-shift stressed sample is more compact than that of the unstressed one. Fig. 3 shows a pre-stage and an early stage of the aggregation monitored by the static light scattering intensities of pH-shift stressed samples. We calculated the relative excess light scattering intensity, I/I0. According to eq. (10-13) and with qRH < 1, I/I0 is proportional to the effective, apparent molecular weight of the (un)associated IgG1 samples. I/I0 at pH 2.0 was 2.0 ± 0.2 times larger than that of an unstressed, monomeric sample. Concurrent DLS measurements revealed that the effective hydrodynamic radius (RH) of the sample at pH 2.0 was 9.2 ± 0.1 nm with a polydispersity index (Q) of 0.10 ± 0.01, and that that of the unstressed sample was 5.2 ± 0.0 nm with a Q of 0.02 ± 0.01, where the errors are standard deviation for four independent experiments. The value of Q for the sample at pH 2.0, which is five times larger than that of the unstressed one, suggests that pH 2.0 made the sample slightly polydispersed rather than homogeneously dimeric, resulting in an effective molecular weight twice as large as that of the monomer with a larger effective RH. As shown in Fig. 3, pH-shift increased I/I0 to ~5.8 at ~10 min, at which the RH of the sample was determined to be 12.9 ± 0.03 nm with a Q of 0.20 ± 0.01 at 15.0 °C, indicating the formation of inhomogeneous oligomers in which ~3-6-mers were plausibly the major components. Initial increases in the light scattering intensities were significant compared with those seen later (Fig. 3)—the light scattering intensities linearly increased. Thus, evolution of the aggregates proceeds via two distinct phases: a rapid phase of


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formation of oligomers initiated by the neutralization of pH is followed by a slow phase of further growth of the aggregates, the mechanism of which will be discussed below. As shown in Fig. 4, the dependences of log(I/I0) on log(RH/R0) at all temperatures fall on linear lines, which were almost identical, indicating that the aggregates grown at neutral pH triggered by pH-shift stress can be described as fractals with the same fractal dimension (see the inset of Fig. 4). The slope of log(I/I0) against log(RH/R0) gave the fractal dimension; Df was 1.98 on average with a standard deviation of 0.01. The intercept was −0.02 on average with a standard deviation of 0.02. The intercept expressed as a power of 10, called the prefactor,36 was 0.95 (= 10–0.02) on average with a standard deviation of 0.05. The fractal dimension reflects not only the packing of monomers in the aggregate, i.e. compactness or morphology of the aggregate,28 but the mechanism of growth.27 The determined fractal dimension, Df = 1.98, is similar to Df = 2.05 for reaction-limited cluster aggregation (RLCA)27,37 rather than Df = 1.75 for diffusion-limited cluster aggregation (DLCA).38 The fractal dimension is close39 to and smaller9 than the values previously reported for antibodies. Here, we briefly summarize the effects of pH-shift stress on the antibodies as a scheme shown in Fig. 5. The acidic condition makes the antibody molecules non-native and renders them susceptible to self-association. By shifting the pH from acidic to neutral, the non-native, thermodynamically unstable species, transiently populated, refold into the native conformation or associate with each other to form oligomers. This scheme is consistent with a previous report by Filip et al.2 At a later stage, evolution of the aggregates proceeds irreversibly, probably without involving the refolded native species. In the next section, we further analyze the aggregation process in terms of modeling the kinetics. Modeling of the aggregation


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We examine the growth of the aggregates based on Smoluchowski aggregation kinetics. The model describes irreversible clustering of particles of any size by diffusion and collision with a certain probability, the core idea of which is introduced in Lumry-Eyring with a nucleated polymerization model as an “aggregate growth via condensation” reaction.14,15 The following is a well-established characteristic of Smoluchowski aggregation kinetics:10,11,23,40-42 the aggregates grows while the relative shape of the distribution becomes constant over a longer time period (as seen in Fig. 1), resulting in a linear increase in the light scattering intensities as a function of time (as seen in Fig. 3). The current observations encourage the application of Smolchowski aggregation modeling to the present data of the aggregation behavior. Fig. 6 shows the time dependence of I/I0 and RH during the growth of the aggregates at 4.0, 15.0, 20.0, 25.0, 33.0, and 40.0 °C. As described in Fig. 3, rapid oligomerization at the early stage was followed by slow growth of the aggregates at the later stage. The later stage is initiated with the given mass distribution that the rapid aggregation at the early stage produces, i.e., the “initial distribution.” We generate the initial distribution of the i-mers by assuming the following: the rapid growth at the early stage obeys Smoluchowski aggregation kinetics eq. (1517) with an initial, homogeneous distribution consisting of monomers only, where I/I0, R0, and Df are 1, 5.2 nm, and 1.98, respectively. The initial (time-zero) distribution is illustrated with a black broken line in Fig. 6(c), which gives I/I0 = 6.4 and RH = 14.1 nm. The values are appropriate for describing the later phases, although they are slightly larger than the values at ~10 min, which may be due to a crossover between the earlier stage and the later stage. We found that 7% of the calculated initial distribution was the fraction of the monomer not involved in rapid aggregation, the value of which was close to 6%, the content of the monomer that escaped from aggregation estimated by SEC as shown in Fig. 2. The monomers surviving, which


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could be refolded, would not be involved in aggregation at the later stage. Thus, we assume Aij = 0 when i or j = 1, in the following calculation. In Fig. 6, we calculated the theoretical Smoluchowski aggregation curves numerically by eq. (15-17) to reproduce the experimental I/I0 and RH, where I0, R0, and Df were set to be 1, 5.2 nm, and 1.98, respectively. The aggregation rate constant γ is given by:

γ = (1/2)ksc0/W,

(20)

where ks is the Smoluchowski rate constant (ks = 8kBT/3η in units of cubic meter per second), c0 is the initial concentration of the primary particle (the initial number density of the monomer, here, 3.4 × 1021 m-3), and W is Fuchs stability ratio.43 We optimized the value of W as a variable parameter by using the non-linear least-squares Levenberg-Marquardt algorithm. It appears that the growth curves of the aggregation at 4.0, 15.0, 20.0, and 25.0 °C monitored by I/I0 and RH are well reproduced by Smoluchowski aggregation equation, while those at 33.0 and 40.0 °C are not. The curves of I/I0 are closer to linear at lower temperatures; when the curves are fitted to the function f(t) ∝ tz, where z is an exponent, with decreasing temperature, z approaches to 1, and is thus linear. A linear increase in light scattering intensity as a function of time is a hallmark of Smoluchowski aggregation kinetics; the exact analytical solution of the Smoluchowski aggregation equation of eq. (15) when Aij = 1 gives I/I0 = 1 + 2τs (τs = γt), which is also good approximation for Aij of eq. (16) proven by the numerical calculation by Feder et al (the linearity depends less on the fractal dimension).10,11 The present result demonstrates that the slow aggregation at the later stage can be modeled and is predictable at lower temperatures by Smoluchowski aggregation kinetics. In contrast, the growth kinetics of the aggregation at higher temperatures (33.0 and 40.0 °C) deviated from the theoretical curves. Calculation of the Smoluchowski equation with varying initial distributions, I0, R0, or Df, failed to reproduce the


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experimental data. We note that the quantitative inconsistency would not be solely due to the limitation of qRH < 1. Further work is needed to address the modeling of the curves at higher temperatures by the use of other kernels or by revising the reversibility of the elemental steps under the current conditions. In Fig. 6(d), we monitored the experimental Q and the theoretical Q calculated according to eq. (18-19) with the distribution by the Smoluchowski equations of Fig. 6(c). Both the Q values are invariant to time, indicating that the relative shape of the distribution of the size remains constant during the aggregation. This time-independent “self-preserving” of the distribution is well known as an inherent character of aggregation obeying Smoluchowski aggregation kinetics.41 However, the absolute values of Q are systematically different between the experiment and the calculation, which is a remaining question. The aggregation rate constant, γ, in eq. (20) is decreased by the factor 1/W, which is equivalent to the probability ε (= number of successful collisions / total number of collisions) introduced by Smoluchowski.19 By the fitting analysis, we determined W at the given temperatures. All the present aggregation curves apparently give W > 1, indicating that the aggregation progresses in the RLCA manner, consistent with the fractal dimension. The values of W determined for I/I0 at 4.0, 15.0, 20.0, and 25 °C were 1.3 (± 0.003) × 108, 7.6 (± 0.001) × 107, 5.6 (± 0.001) × 107, and 4.7 (± 0.003) × 107, which were consistent with the values determined for RH (with less than 11% difference). The values are almost ten times smaller than those reported in previous papers, where the heat-10,11 or acid9-induced spontaneous aggregation rate was analyzed, indicating low stability of dispersion of pH-shift triggered aggregation. W denotes ks/keff, where keff is the effective aggregation rate constant. According to the relation:10 keff = keff,0exp[−∆H*/(1/RT−1/RT0)],

(21)


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where keff,0 is keff at the reference temperature, T0, and R is the gas constant, we estimate the activation enthalpy for the aggregation to be ∆H* = 55 ± 3 kJ/mol (13 ± 1 kcal/mol) as shown in Fig. 7. Here, T0 is 298.15 K. The positive activation enthalpy indicates that aggregation involves an endothermic process. The value is almost ten times smaller than the previously reported value (502 ± 21 kJ/mol) for heat-induced aggregation of a polyclonal antibody.11 Jøssangg et al. pointed out that the value should be related to the denaturation.11 Indeed, the entire immunoglobulin G or its CH2 domain gives ca. 3 × 103 kJ/mol44 or ca. 3-4 × 102 kJ/mol45 for the enthalpy change upon heat-denaturation, respectively, values that are comparable to (or larger than) the previously reported activation enthalpy. A recent study has demonstrated that the unfolding contributes to increases in ∆H* for the growth of amyloid fibrils (the effect of nucleation being excluded).46 Accordingly, the smaller ∆H* observed in the present study indicates a lack of the unfolding-related contribution because the antibody molecules that are sufficiently unfolded by acid treatment before the pH-shift do not require further unfolding for aggregation. Fig. 5 contains a diagram in which the conversion of the aggregation-prone oligomers into the aggregates is energetically easier than that of the native species. By assuming that the activated state is in equilibrium, the Fuchs stability ratio or the probability is related to the Gibbs free energy of activation, ∆G*: 1/W = ε = exp(−∆G*/RT).

(22)

We found that ∆G* = 44 ± 13 kJ/mol and T∆S* = 11 ± 13 kJ/mol at 25.0 °C. The contribution of the entropic term in ∆G* (= ∆Η* − T∆S*) looks relatively small; the magnitude of T∆S* is almost zero to a half of that of ∆H*, which is obvious despite a large uncertainty. Desolvation of hydrophobic residues in the transition state has been recognized as a major contribution to an


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increase in T∆S*.46 In addition, the unfolding reaction increases T∆S*. We infer that the present T∆S* lacks the latter contribution. Fig. 8 shows that the experimental curves, which introduce the reduced dimensionless time,

τs (= γt), are collapsed onto a master curve. This indicates that the aggregation at neutral pH triggered by pH-shift stress is governed by a unique mechanism in the range of ambient, lower temperatures. There are potential implications for antibody drug stability under conditions of storage. In the present study, the situation was set to mimic storage conditions under which diffusing non-native species can encounter each other during their lifetime. This was accomplished through a transient increase in the population of unstable, non-native species by shifting pH. The fate of the nonnative species is the following: refolding into the native state or self-association by encountering each other. A small population of the non-native species would exist even at neutral pH and moderate temperatures. Although association of these two non-native species during their lifetime would be rare, practical, long-term storage of antibodies should offer enough time for accumulation of such rare association events. Thus, the procedure of the pH-shift stress would allow us to monitor the aggregation behavior of antibodies under ambient conditions without modulating thermodynamic states, e.g., heating. In summary, the aggregation of the antibody triggered by pH-shift stress proceeds via rapid aggregation followed by the slow clustering of aggregates. The aggregation is described by a fractal, the dimension of which is consistent with reaction-limited aggregation regime. The present study demonstrated that the latter slow clustering process well satisfied Smoluchowski aggregation kinetics when temperature was in a lower range (4.0-25.0 °C). This suggests that practical examination of aggregation propensity of antibodies under accelerated (heated)


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conditions does not give a good estimation. The relatively small endothermic activation enthalpy suggests that the temporal exposure of the antibody to acid, which induces unfolding, promotes aggregation by reducing the cost of activation energy. The determined parameters, c0, Df, ∆G*, and ∆H*, allow us to predict the growth of aggregates at a given lower temperature, which will contribute to improving the manufacturing process of the antibody drug. Furthermore, this could give insight into aggregation under more practical conditions, e.g., an estimation of the shelf life of antibody drugs.

ASSOCIATED CONTENT Supporting Information. Additional experimental procedures, figures, and references. This material is available free of charge via the internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]. Phone: +81-29-862-6737. Fax: +81-29-861-6194. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest.


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ACKNOWLEDGMENTS This research was partially supported by the developing key technologies for discovering and manufacturing pharmaceuticals used for next-generation treatments and diagnoses both from the Ministry of Economy, Trade and Industry, Japan (METI) and from Japan Agency for Medical Research and Development (AMED). The authors thank Dr. Takashi Shimizu (AIST, Tsukuba, Japan) and Dr. Seiki Yageta (The University of Tokyo, Tokyo, Japan) for stimulating discussion and comments. ABBREVIATIONS IgG1, Immunoglobulin G1; DLS, dynamic light scattering; SEC, size-exclusion chromatography; NNLS, non-negative least squares.

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Protein Downstream Processing; Labrou, N. E., Ed.; Humana Press: Totowa, NJ, 2014; Vol. 1129. Filipe, V.; KüKrer, B.; Hawe, A.; Jiskoot, W. Transient Molten Globules and Metastable Aggregates Induced by Brief Exposure of a Monoclonal IgG to Low pH. J. Pharm. Sci. 2012, 101, 2327–2339. Vázquez-Rey, M.; Lang, D. A. Aggregates in Monoclonal Antibody Manufacturing Processes. Biotechnol. Bioeng. 2011, 108, 1494–1508. Rosenberg, A. S. Effects of Protein Aggregates: an Immunologic Perspective. AAPS J. 2006, 8, E501–E507. Guidance for Industry: Immunogenicity Assessment for Therapeutic Protein Products; Food and Drug Administration, Center for Drug Evaluation and Research (CDER), Center for Biologics Evaluation and Research (CBER), 2014. Hernandez, R. Detecting Protein Aggregates and Evaluating Their Immunogenicity. BioPharm International 2015, 28, 22–26. Moussa, E. M.; Panchal, J. P.; Moorthy, B. S.; Blum, J. S.; Joubert, M. K.; Narhi, L. O.; Topp, E. M. Immunogenicity of Therapeutic Protein Aggregates. J. Pharm. Sci. 2016, 105, 417–430. Arosio, P.; Barolo, G.; Müller-Späth, T.; Wu, H.; Morbidelli, M. Aggregation Stability of a Monoclonal Antibody During Downstream Processing. Pharm. Res. 2011, 28, 1884–1894.


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Berne, B. J.; Pecora, R. Dynamic Light Scattering: with Applications to Chemistry, Biology, and Physics; Jhon Wiley Sons, Inc.: New York, 1976. Johnson, C. S.; Gabriel, D. A. Laser Light Scattering; DOVER PUBLICATIONS, INC.: New York, 1994. Baalousha, M.; Lead, J. R. Nanoparticle Dispersity in Toxicology. Nature Nanotech 2013, 8, 308–309. Arakawa, T.; Ejima, D.; Li, T.; Philo, J. S. The Critical Role of Mobile Phase Composition in Size Exclusion Chromatography of Protein Pharmaceuticals. J. Pharm. Sci. 2010, 99, 1674–1692. Arosio, P.; Rima, S.; Morbidelli, M. Aggregation Mechanism of an IgG2 and Two IgG1 Monoclonal Antibodies at Low pH: From Oligomers to Larger Aggregates. Pharm. Res. 2012, 30, 641–654. Nicoud, L.; Arosio, P.; Sozo, M.; Yates, A.; Norrant, E.; Morbidelli, M. Kinetic Analysis of the Multistep Aggregation Mechanism of Monoclonal Antibodies. J. Phys. Chem. B 2014, 118, 10595–10606. Paul, R.; Graff-Meyer, A.; Stahlberg, H.; Lauer, M. E.; Rufer, A. C.; Beck, H.; Briguet, A.; Schnaible, V.; Buckel, T.; Boeckle, S. Structure and Function of Purified Monoclonal Antibody Dimers Induced by Different Stress Conditions. Pharm. Res. 2012, 29, 2047–2059. Sorensen, C.; Roberts, G. The Prefactor of Fractal Aggregates. J. Colloid Interface Sci. 1997, 186, 447–452. Weitz, D. A.; Huang, J. S.; Lin, M. Y.; Sung, J. Limits of the Fractal Dimension for Irreversible Kinetic Aggregation of Gold Colloids. Phys. Rev. Lett. 1985, 54, 1416– 1419. Weitz, D. A.; Oliveria, M. Fractal Structures Formed by Kinetic Aggregation of Aqueous Gold Colloids. Phys. Rev. Lett. 1984, 52, 1433–1436. Nicoud, L.; Sozo, M.; Arosio, P.; Yates, A.; Norrant, E.; Morbidelli, M. Role of Cosolutes in the Aggregation Kinetics of Monoclonal Antibodies. J. Phys. Chem. B 2014, 118, 11921–11930. Vicsek, T.; Family, F. Dynamic Scalling for Aggregation of Clusters. Phys. Rev. Lett. 1984, 52, 1669–1672. Sorensen, C.; Taylor, T. Dynamic Light Scattering as a Probe of the Evolution of a SelfPreserving Size Distribution in a Fractal System. Phys. Rev., A 1986, 33, 1411–1413. Oster, G. Light Scattering From Polymerizing and Coagulating Systems. J. Colloid Sci. 1947, 2, 291–299. Fuchs, N. Über Die Stabilität Und Aufladung Der Aerosole. Phys. Z. 1934, 89, 736–743. Vermeer, A. W. P.; Norde, W. The Thermal Stability of Immunoglobulin: Unfolding and Aggregation of a Multi-Domain Protein. Biophys. J. 2000, 78, 394–404. Ionescu, R. M.; Vlasak, J.; Price, C.; Kirchmeier, M. Contribution of Variable Domains to the Stability of Humanized IgG1 Monoclonal Antibodies. J. Pharm. Sci. 2008, 97, 1414–1426. Buell, A. K.; Dhulesia, A.; White, D. A.; Knowles, T. P. J.; Dobson, C. M.; Welland, M. E. Detailed Analysis of the Energy Barriers for Amyloid Fibril Growth. Angew. Chem. Int. Ed. Engl. 2012, 51, 5247–5251.


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Figure captions

Figure 1. Time dependence of dynamic light scattering of a pH-shift stressed IgG1 sample at 15.0 °C after neutralization. (a) Time dependence of the normalized time autocorrelation functions. The solid lines were generated by fitting analysis. (b) Intensity-weighted distribution of the size determined by NNLS analysis on the autocorrelations at 15.0 °C. (c) Time dependence of the polydispersity index, Q, at 15.0 °C. The error bars show the uncertainties of the values in the fitting analysis. Q∞ indicates the average between 15 and 25 h. The time shown is the progression after neutralization of the protein solution.

Figure 2. Time dependence of the size-exclusion chromatograms of pH-shift stressed IgG1 samples. Inset is a chromatogram of unstressed IgG1 (pH 7.4).

Figure 3. Time dependence of relative excess static light scattering. Unstressed IgG1 at pH 7.4 (blue, filled circle); IgG1 at pH 2.0 just before neutralization (red, filled circle); and pH-shift stressed IgG1 samples at 4.0 (red, open circle), 15.0 (dark orange, open square), and 20.0 °C (green triangle) are shown. The solid linear lines are drawn for visual guide. Error bars for relative excess light scattering of IgG1 at pH 2.0 represent the standard deviation determined by seven independent experiments.

Figure 4. Power-law relationships between light scattering intensities and the hydrodynamic radius. Data are shown for pH-shift stressed IgG samples at 4.0 (red circle), 15.0 (dark orange square), 20.0 (green triangle), 25.0 (cyan inverted triangle), 33.0 (magenta diamond), and 40.0 °C (purple cross). The solid line represents a slope of 1.98 with an intercept of −0.02 ± 0.02. The


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inset indicates the values of the fractal dimension at the given temperatures determined by fitting to eq. (14). The error bars indicate the uncertainties of the values in the fitting analysis. We applied the fitting analysis to the data-region of RH < 38 nm to satisfy qR < 1. The experiments were performed twice at 15.0 and 25.0 °C, each of which gave consistent Df values within the error range.

Figure 5. Schematic illustration of the effect of pH-shift stress on the antibody in terms of free energy. Purple Y-shaped objects and orange spheres represent native and non-native antibody molecules, respectively.

Figure 6. Modeling of the aggregation of pH-shift stressed IgG1 based on the Smoluchowski aggregation equation. (a) and (b) show the time dependence of the static light intensities and the hydrodynamic radius, respectively, of pH-shift stressed IgG1 sample aggregates at 4.0 (red circles), 15.0 (dark orange squares), 20.0 (green triangles), 25.0 (cyan inverted triangles), 33.0 (magenta diamonds), and 40.0 °C (purple crosses). The dotted lines indicate the curves calculated by the Smoluchowski aggregation equation with Df = 1.98 and R0 = 5.2 nm and optimized W. (c) indicates the time dependence of the distribution of the i-mers corresponding to the theoretical curve in (a) at 4.0 °C. The black broken line shows the initial (time-zero) distribution, which gives I/I0= 6.4 and RH = 14.1 nm. (d) shows the experimental polydispersity index, Q, at 4.0 °C (red open circles), compared with Q calculated using Smoluchowski’s theoretical distribution (solid line).

Figure 7. Temperature dependence of the effective aggregation rate constant, keff (=ks/W). keff was determined by the relative excess light scattering intensities, I/I0 (red, open circles), and by the hydrodynamic radius, RH (black, filled circles). The error bars represent the uncertainties of the values in the fitting analysis. The lines are the fitting line as per eq. (21) in the range between


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4.0 and 25.0 °C (solid lines) and in the range between 15.0 and 25.0 °C (broken line), where the colors, red and black, are for the light scattering intensity and for the hydrodynamic radius, respectively. The experiments were performed twice at 15.0 and 25.0 °C, which gave consistent W values within an error of 17% and 3%, respectively.

Figure 8. A master curve of the evolution of aggregates of pH-shift stressed IgG1 samples. The experimental data in terms of (a) the relative excess static light intensities, I/I0, and (b) the relative hydrodynamic radius, RH/R0, at 4.0 (red circles), 15.0 (dark orange squares), 20.0 (green triangles), and 25.0 °C (cyan inverted triangles) are displayed as a function of the dimensionless time, τs (= γt). The dotted lines represent the master curve determined by the Smoluchowski aggregation equation with Df = 1.98 and R0 = 5.2 nm.

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Kinetics of Antibody Aggregation at Neutral pH and Ambient

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