Role of Cosolutes in the Aggregation Kinetics of Monoclonal

Article pubs.acs.org/JPCB

Role of Cosolutes in the Aggregation Kinetics of Monoclonal Antibodies Lucrèce Nicoud,† Margaux Sozo,† Paolo Arosio,‡ Andrew Yates,§ Edith Norrant,§ and Massimo Morbidelli*,† †

Department of Chemistry and Applied Biosciences, ETH Zurich, Zurich, Switzerland Department of Chemistry, University of Cambridge, Cambridge, England, United Kingdom § UCB Pharma, Braine l’Alleud, Belgium ‡

S Supporting Information *

ABSTRACT: We propose a general strategy based on kinetic analysis to investigate how cosolutes affect the aggregation behavior of therapeutic proteins. We apply this approach to study the impact of NaCl and sorbitol on the aggregation kinetics of two monoclonal antibodies, an IgG1 and an IgG2. By using a combination of size exclusion chromatography and light scattering techniques, we study the impact of the cosolutes on the monomer depletion, as well as on the formation of dimers, trimers, and larger aggregates. We analyze these macroscopic effects in the frame of a kinetic model based on Smoluchowski’s population balance equations modified to account for nucleation events. By comparing experimental data with model simulations, we discriminate the effect of cosolutes on the elementary steps which contribute to the global aggregation process. In the case of the IgG1, it is found that NaCl accelerates the kinetics of aggregation by promoting specifically aggregation events, while sorbitol delays the kinetics of aggregation by specifically inhibiting protein unfolding. In the case of the IgG2, whose monomer depletion kinetics is limited by dimer formation, NaCl and sorbitol are found respectively to accelerate and inhibit conformational changes and aggregation events to the same extent.

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INTRODUCTION Improving our understanding on the impact of cosolutes on protein stability is of fundamental relevance in a large variety of areas, including food science,1 medicine,2,3 bionanotechnology,2 and pharmacy.2,4 For example, in the bioprocessing of therapeutic proteins, excipients such as salts and sugars are commonly added to the protein solution during the final drug formulation step to provide physiological osmolality or hinder protein aggregation.5−7 Since aggregation represents the major degradation route of therapeutic proteins, the understanding of the effect of excipients on protein aggregation is of fundamental importance to optimize protein stability and guarantee suitable product shelf life. Accelerated studies at high temperature are commonly performed in an attempt to estimate in a short time the product shelf life under storage conditions. The proper extrapolation of stability studies from high to low temperature requires the mechanistic understanding of the impact of cosolutes on the aggregation process, which is challenging to achieve. Indeed, protein aggregation is a complex multistep process which involves several elementary steps such as protein unfolding, nucleation, and aggregate growth. In particular, two contributions can be distinguished in the aggregation propensity of a protein:8 (i) the protein conformational stability, related to the secondary and tertiary structures of the protein, and (ii) the protein colloidal stability, which results from the various © 2014 American Chemical Society

intermolecular forces acting between the protein molecules. These two contributions are strongly interconnected, since changes in the protein structure lead to changes in the intermolecular interactions. For instance, misfolding of the protein may induce the exposure of hydrophobic patches buried inside the native structure of the protein, thus promoting strong attractive hydrophobic interactions which trigger aggregation. The secondary and tertiary structures of a protein are dictated by the delicate balance between various intramolecular and solvation interactions, which is highly sensitive to the solution composition.1,2,9 Therefore, the presence of cosolutes affects both the intermolecular interactions and the protein structure in a complex way, and these two interconnected effects are difficult to characterize. Recently, we investigated the impact of salt on the oligomer formation of a monoclonal antibody under acidic conditions.10 It was shown that the salt effect on the selfassociation propensity is strongly ion specific and pH dependent, and that this effect is the result of the contribution of salt on protein conformation, charge screening, ion binding, and additional solvation forces.10 This complex effect can be hardly described by simplified theories such as the DLVO (Derjaguin, Landau, Verwey, Oberbeek) theory, Received: August 7, 2014 Revised: September 19, 2014 Published: September 22, 2014 11921

dx.doi.org/10.1021/jp508000w | J. Phys. Chem. B 2014, 118, 11921−11930

The Journal of Physical Chemistry B

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as mAb-1 and mAb-2, respectively, in agreement with the notation used in our previous study.34 The isothermal aggregation kinetic experiments were performed on dialyzed samples at the elevated temperature of 70 °C. The protein concentration was 1 g/L and the pH was set to 6.5 by using a 20 mM histidine buffer. Details about the sample preparation, isothermal aggregation kinetics, zeta potential, and aggregate fractal dimension determination, as well as size exclusion chromatography with inline light scattering measurements are reported in the main text of a previous work.34 The experimental procedure related to the evaluation of antibody aggregation thermal stability with dynamic light scattering is described in the Supporting Information of the aforementioned study.34 Kinetic Model. The kinetic mechanisms of mAb-1 and mAb-2 aggregation under thermal stress have been determined in a previous study34 and are summarized in Figure S1 of the Supporting Information. The two mAbs under investigation were shown to follow different aggregation mechanisms. While the monomer depletion of mAb-1 was found to be rate-limited by protein unfolding, the monomer depletion of mAb-2 was found to be rate-limited by bimolecular aggregation. Moreover, the aggregation mechanism of mAb-1 accounts for protein unfolding and irreversible aggregate growth, whereas the kinetic mechanism of mAb-2 includes reversible oligomer formation, irreversible oligomer structural rearrangement and irreversible aggregate growth. The parameters required to implement these kinetic schemes are briefly introduced below, while the detailed description of the kinetic models applied in this work can be found in our previous study.34 The aggregation rate constants between two colliding aggregates containing i and j primary particles were defined as follows, according to the formalism used to describe the aggregation of colloidal dispersions:33,35,36

which quantifies interparticle potentials in terms of electrostatic repulsion and van der Waals attraction. At low ionic strength (0−10 mM), the DLVO theory has been proven effective in describing quantitatively the increase in the aggregation propensity of several colloidal systems induced by charge screening upon salt addition.11−13 Attempts to apply this theory to proteins have been shown to be successful in rationalizing the impact of pH and salt on the colloidal stability of some small globular proteins which exhibit a random charge distribution.14 However, even at low ionic strength, strong discrepancies between the observed aggregation behaviors and predictions from DLVO theory are often observed, in particular due to the inability of the DLVO theory to account for ion specificity.15−17 These discrepancies are even more pronounced at increasing ionic strength where, in addition to charge-shielding effects, preferential binding of ions to the protein surface may occur.4,18−20 While salts are generally found to decrease protein colloidal stability, sugars and polyol sugars have been shown to reduce the aggregation propensity mostly by enhancing the protein conformational stability.21,22 Timasheff and Arakawa brought evidence of the preferential exclusion of sugars from the protein surface due to unfavorable protein−solvent interactions that favor compact protein conformations with respect to more open unfolded structures.23−25 While the impact of sugars and polyol sugars on the thermodynamic properties of protein solutions has been widely studied, their effect on the kinetic stability during non-native protein aggregation has been poorly considered. One particular challenge in studying the cosolute effect on protein aggregation is the discrimination of the impact of cosolutes on the protein structure stability and on the protein colloidal stability, since both contributions are strongly interconnected and are extremely difficult to investigate independently experimentally. In this work, we build on the power of chemical kinetics analysis to investigate the effect of cosolutes on the single elementary steps which contribute to the global aggregation mechanism. Chemical kinetics analysis is indeed increasingly emerging as a key tool to gain insights into the mechanisms of protein aggregation from macroscopic measurements.26−29 We illustrate this general procedure by considering the effect of NaCl and sorbitol on the aggregation behavior of monoclonal antibodies, which represent the largest growing part of therapeutic proteins in the biopharmaceutical market.30−32 By using a combination of size exclusion chromatography and light scattering techniques, we are able to follow both the nucleation of small oligomers and their growth to larger aggregates. We modify the classical Smoluchowski’s population balance equations (PBE), commonly applied to describe the aggregation kinetics of polymer colloids,33 to account for nucleation events occurring in the early stages of the process. By comparing experimental data with theoretical simulations, we are in a position to discriminate the effect of cosolutes on the elementary processes which contribute to the global aggregation rate, i.e. protein unfolding, oligomer formation, and growth to larger aggregates. Moreover, we are able to quantify the impact of cosolutes on effective protein interaction potentials expressed in terms of the Fuchs stability ratio.

ki , j = ks = Bi , j =

ks Bi , j Pi , j Wi , j 8 kBT 3 η

1 1/ d f (i + j1/ d f )(i−1/ d f + j−1/ d f ) 4 Pi , j = (ij)λ λ ≈ 1 − 1/df

(1)

where kB is the Boltzmann constant, T is the temperature, η is the medium viscosity, and df is the fractal dimension of the aggregates. The interparticle interaction potential is characterized by the so-called Fuchs stability ratio Wi,j, which represents the energy barrier that two approaching clusters must overcome before colliding. Briefly, the Fuchs stability ratio can be computed from the total interaction potential VT, as shown below for primary particles of radius Rp

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MATERIALS AND METHODS Sample Preparation and Experimental Characterization. The two model monoclonal antibodies used in this study were a glycosylated IgG1 and a nonglycosylated IgG2, which are both of industrial origin. In the following, they will be referred to

⎛ V (r) ⎞ dr exp⎜ T ⎟ 2 ⎝ kBT ⎠ r p

∞

W11 = 2R p

∫2R

(2)

The Fuchs stability ratio provides a quantification of the sum of all intermolecular forces, lumping together protein surface 11922



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heterogeneities. It is therefore a valuable parameter (which can be evaluated by fitting model simulations to experimental kinetics of aggregation) to assess in a coarse-grained manner the protein colloidal stability, as illustrated in this work. In the case of polymer colloids, Wi,j is assumed to be independent of cluster size (i.e., equal to W11). However, it is unlikely that this assumption holds true in the case of protein aggregation, where reactivity strongly depends on protein conformation and on the accessibility of aggregation-prone patches. Therefore, we introduced several Fuchs stability ratios characterizing the stability of the various species present in solution. In the case of mAb-1 aggregation, which involves the formation of a non-native aggregation-prone monomer, two classes of species were considered: the highly reactive monomer and the aggregates. Accordingly, three Fuchs stability ratios were defined to describe the three possible aggregation events: monomer− monomer (W11), monomer−aggregate (W1j), and aggregate− aggregate (Wij). These aggregation events correspond respectively to dimer formation, monomer addition, and cluster− cluster aggregation, and the expected order of reactivity is W11 < W1j < Wij. In the case of mAb-2 aggregation, which includes reversible oligomer formation, irreversible oligomer structural rearrangement, and aggregate growth, three kinds of aggregation events were also identified: aggregation events leading to tetramer formation, aggregation between the reactive nucleus (after tetramer structural rearrangement) and any other species, and all the other aggregation events, which lead to aggregate growth. These aggregation events were characterized by three Fuchs stability ratios, denoted as W11,W4*j, and Wij, respectively. On top of the Fuchs stability ratios, which describe aggregation events, additional parameters were introduced to describe nucleation events. In the case of mAb-1, protein unfolding was quantified by the unfolding rate constant kU, while the reversible tetramer formation and irreversible tetramer rearrangement involved in mAb-2 aggregation were described by the kinetic constants kr11, kr12, kr13, and knuc, as shown in Figure S1 of the Supporting Information. The parameter values describing the aggregation kinetics of mAb-1 and mAb-2 are summarized in Tables S1 and S2 of the Supporting Information, respectively. Details about the estimation of these parameters can be found in our previous study.34

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Figure 1. Impact of NaCl and sorbitol on mAb-1 (a) aggregation thermal stability and (b) aggregate fractal dimension. Impact of (c) NaCl and (d) sorbitol on the zeta potential values of mAb-1 and mAb-2.

RESULTS Impact of Cosolutes on Aggregation Thermal Stability, Aggregate Morphology, and Electrostatic Interactions in mAb Solutions. We first evaluated the impact of NaCl and sorbitol on the aggregation thermal stability (i.e., the aggregation propensity upon temperature increase) of the antibody solutions by recording the increase in the solution scattered intensity as a function of temperature with dynamic light scattering (DLS). An increase in the solution scattered intensity is indeed an indication of the increase in size and/or number of aggregates. Figure 1a shows the DLS intensity as a function of temperature for mAb-1 in the absence and in the presence of NaCl and sorbitol. The results show that NaCl and sorbitol have a destabilizing and a stabilizing effect, respectively, on the aggregation propensity of mAb-1. Similar results were obtained in the case of mAb-2 (data not shown). The aggregate morphology was then investigated by static light scattering (SLS), as shown in Figure 1b for mAb-1.

The aggregates were found to exhibit fractal geometry, and a fractal dimension value could be estimated from the power-law regime of the plot of the structure factor S(q) as a function of the q vector. The results indicate that the presence of NaCl leads to an increase in the fractal dimension, i.e. salt leads to the formation of more compact aggregates. One possible explanation is that the presence of salt makes the protein surface more uniform due to screening of heterogeneous charges. The value of df = 2.05 in the presence of 10 mM of salt is indeed consistent with fractal dimension values usually reported in the case of uniformly charged spheres aggregating under reaction limited conditions, while the lower value of df = 1.85 in the absence of salt may indicate some patchiness of the protein surface, as proposed by Wu et al.37 Unfortunately, the impact of salt on the fractal 11923



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dimension value could not be investigated in the case of mAb-2 due to the precipitation of large aggregates occurring during the cooling required by the off-line scattering experiments. The presence of sorbitol, instead, does not impact the aggregate fractal dimension, neither in the case of mAb-1 (df = 1.85, Figure 1b) nor in the case of mAb-2 (df = 2.05, data not shown). The impact of cosolutes on effective protein charge was then assessed by zeta potential measurements. Figure 1c,d shows the protein zeta potential as a function of NaCl and sorbitol concentration, respectively, for both antibodies. The zeta potential measurements quantify the electric potential at the double layer, which is related to the protein surface charge and the nondiffusive counterions located in the layer around the particle. Charged cosolutes may affect the zeta potential value by binding to the opposite charged groups on the surface of the protein and by modifying the electrostatic interactions in the double layer. By adding salt, the zeta potential of mAb-1 decreases from 5.7 mV to a value close to zero (Figure 1c), while the zeta potential value of mAb-2 is already close to zero in the absence of salt and is therefore less sensitive to the addition of NaCl. It can be observed in Figure 1d that the presence of sorbitol does not significantly affect the zeta potential values of both antibodies. It is interesting to observe that changes in aggregate structure correlate with changes in electrostatic interactions: the presence of salt decreases the net repulsive electrostatic interactions and induces the formation of more compact aggregates characterized by a larger fractal dimension value (Figure 1). On the other hand, the presence of sorbitol does not affect the electrostatic interactions and does not impact aggregate morphology (Figure 1). Impact of Cosolutes on the Kinetics of Aggregation. After characterizing the impact of the cosolutes on the macroscopic properties of the aggregation process, we analyze their effects on the elementary processes in the aggregation mechanisms described in Figure S1 of the Supporting Information. For both antibodies, the monomer depletion, dimer and trimer formation, as well as the aggregate weightaverage molecular weight were followed by size exclusion chromatography coupled with an inline multiangle light scattering detector. The experimental data were then compared with model simulations to extract information on the impact of cosolutes on the microscopic reaction rates. The obtained results are discussed in the following, with reference first to mAb-1 and then to mAb-2. mAb-1. Impact of NaCl. Figure 2 shows the experimental results on the kinetics of aggregation of mAb-1 in the absence of salt as well as in the presence of 5 mM and 10 mM NaCl. It can be observed that the salt significantly accelerates the increase in aggregate molecular weight during time (Figure 2d), while it has only a slight impact on the monomer depletion kinetics (Figure 2a). In Figure 2e, we show the average aggregate molecular weight as a function of monomer conversion. It can be seen that, at a given monomer conversion, the presence of NaCl induces the formation of larger aggregates, with respect to the situation without salt. This experimental observation suggests that the presence of salt decreases the characteristic time of aggregate growth, while it does not change the characteristic time of monomer depletion, which has been previously shown to be rate-limited by monomeric conformational changes.34 Therefore, the analysis of the impact of NaCl on the aggregation kinetics reveals that the unfolding rate constant is not affected by the presence of salt, while the aggregation rate

Figure 2. Comparison between simulated (lines) and experimental (symbols) aggregation kinetics of mAb-1 incubated at 70 °C at a protein concentration of 1 g/L in the absence and presence of 5 and 10 mM NaCl. (a) Monomer, (b) dimer, (c) trimer concentrations, and (d) aggregate weight-average molecular weight versus time and (e) aggregate weight-average molecular weight versus monomer conversion, defined as the nonaggregated fraction of the initial protein content. Parameter values used in the simulations are summarized in Table 1.

constants increase upon salt addition, indicating a decrease of the net repulsive intermolecular forces, in agreement with the changes in zeta potential and aggregate morphology described in the previous paragraph (Figure 1). We can quantify this behavior with the kinetic model developed in a previous work,34 which considers several Fuchs stability ratios to account for the different reactivities of the two populations present in solution, i.e. the unfolded monomer, which is a highly reactive aggregation-prone intermediate, and the aggregates. Accordingly, W11, W1j, and Wij have been introduced to describe dimer formation, monomer addition, and cluster−cluster aggregation, respectively. In order to simplify the fitting procedure, we assumed that salt has the same impact on all the aggregation rate constants. Thus, we introduced a parameter α1, which was defined as the ratio between each aggregation rate constants in the presence of cosolute divided by the corresponding value in the absence of cosolute. Since the aggregation rate constants are inversely proportional to the Fuchs stability ratios, α1 is defined as α1 =

−CS W11 +CS W11

=

W1−j CS W1+j CS

=

W ij−CS W ij+CS

(3)

where −CS and +CS denote the situations without and with cosolute, respectively. At each salt concentration, the parameter α1 was evaluated by fitting to the experimental data. Regarding the other parameters, the fractal dimension was measured by independent SLS experiments and the power law factor λ was estimated as λ ≈ 1 − 1/df. The unfolding rate constant kU was assumed to be unchanged as compared to the situation without cosolute. The parameter values used for the simulations are summarized in Table 1. In particular, we found α1 = 0.29 in the presence of 11924



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Table 1. Parameter Values Used in the Simulations of the Aggregation Kinetics of mAb-1 in the Presence of Cosolutesa cosolute 5 mM NaCl 10 mM NaCl 250 mM sorbitol 500 mM sorbitol

λ

df b

1.94 2.05b 1.85b 1.85b

c

0.48 0.51c 0.46c 0.46c

ku (s−1)

α1

10 × 10−4 d 10 × 10−4 d 6.7 × 10−4 e 3.5 × 10−4 e

0.29e 0.14e 1.00d 1.00d

The parameter α1 is defined as the ratio between the aggregation rate constants in the presence and in the absence of cosolute (see eq 3). The parameter values in the absence of cosolutes are reported in Table S1 (Supporting Information). bMeasured by independent SLS experiments. cEstimated from λ = 1 − 1/df. dSame values as those evaluated in the absence of cosolute. eFitted to experimental data. a

5 mM NaCl and α1 = 0.14 in the presence of 10 mM NaCl. These values correspond to a decrease in the Fuchs stability ratio by factors of 3.5 and 7, respectively. In Figure 2, we compare the model simulations with the experimental data. It can be seen that the model is capable of describing well the time evolution of the different sets of experimental data. In particular, it is worth noticing that the slight acceleration in the monomer depletion kinetics in the presence of salt (Figure 2a) can be explained by a decrease in the value of the Fuchs stability only (i.e., without changes in the unfolding rate constant), as proven by model simulations. Moreover, the fact that one single fitting parameter α1 is capable of describing the decrease in protein stability upon salt addition suggests that NaCl affects the reactivity of the reactive monomer and of the clusters to the same extent. In summary, our results show that in the investigated range of salt concentration the presence of NaCl increases the aggregation kinetics of mAb-1 only by promoting the aggregation events, i.e., by reducing the repulsive energy barrier between two colliding particles, without impacting the kinetics of formation of the aggregation prone monomer, i.e., the unfolding step. mAb-1. Impact of Sorbitol. Figure 3 shows experimental kinetics data of mAb-1 in the absence of polyol sugar and in the presence of 250 and 500 mM sorbitol. It can be seen that sorbitol significantly delays the monomer depletion while it has almost no impact on the increase in the aggregate molecular weight. Therefore, at a given monomer conversion, the presence of sorbitol induces the formation of larger aggregates compared to the situation without polyol sugar, as can be seen in Figure 3e. This result suggests that the presence of sorbitol increases the characteristic time of monomer depletion, which corresponds to the characteristic time of protein unfolding, to a larger extent than the characteristic time of aggregate growth. Moreover, it was reported that sorbitol neither impacts the protein net charge nor the aggregate morphology of mAb-1 (Figure 1), suggesting that sorbitol does not impact protein reactivity. In agreement with these experimental observations, in the model simulations we considered the same values of the Fuchs stability ratios estimated in the absence of cosolute. Moreover, the fractal dimension was measured by independent SLS experiments and the power law factor λ was estimated as λ ≈ 1 − 1/df. The only fitting parameter was therefore the unfolding rate constant kU. The parameters used for the simulations are summarized in Table 1. It can be seen in Figure 3 that the results of the model simulations are in very close agreement with the experimental data. In particular, it is worth noticing that the slight delay observed in the kinetics of aggregate growth in the presence of

Figure 3. Comparison between simulated (lines) and experimental (symbols) aggregation kinetics of mAb-1 incubated at 70 °C at a protein concentration of 1 g/L in the absence, and presence of 250 and 500 mM sorbitol. (a) Monomer, (b) dimer, (c) trimer concentrations, and (d) aggregate weight-average molecular weight versus time and (e) aggregate weight-average molecular weight versus monomer conversion, defined as the nonaggregated fraction of the initial protein content. Parameter values used in the simulations are summarized in Table 1.

sorbitol (Figure 3d) can be explained by a decrease in the unfolding rate constant only (i.e., without changes in the Fuchs stability ratio), as proven by model simulations. This analysis reveals that sorbitol delays the kinetics of mAb-1 aggregation only by delaying the kinetics of formation of the aggregationprone monomer without impacting protein reactivity, i.e. sorbitol slows down protein unfolding while it has a negligible impact on the energy barrier that colliding particles must overcome in order to aggregate. Sorbitol is known to favor a compact native conformation of the protein, which exposes a small surface area to the solvent, with respect to more open unfolded structures. Sorbitol has indeed been shown to impart thermodynamic stability to protein solutions due to a preferential exclusion effect.23,24,38 Here, we show that sorbitol also increases the kinetic stability of the mAb solution under investigation by delaying the kinetics of formation of the partially unfolded aggregation-prone monomer. mAb-2. Impact of NaCl. The same approach used for mAb-1 was applied to investigate the impact of cosolutes on the aggregation mechanism of mAb-2. Figure 4 shows the experimental data of mAb-2 aggregation in the absence of salt as well as in the presence of 10 and 50 mM NaCl. Larger NaCl concentrations were used for mAb-2 with respect to mAb-1 in order to observe an appreciable impact of the salt on the aggregation kinetics. The lower zeta potential value of mAb-2 with respect to mAb-1 indeed suggests that the protein net charge is lower. Therefore, mAb-2 molecules experience less electrostatic repulsion and the charge screening by NaCl addition might thus have less impact on the aggregation kinetics of mAb-2. In Figure 4, it can be observed that NaCl accelerates both the kinetics of monomer depletion and of aggregate growth. In addition, at a given monomer conversion, the aggregate weight-average molecular weight (Figure 4e), the dimer and 11925



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Table 2. Parameter Values Used in the Simulations of the Aggregation Kinetics of mAb-2 in the Presence of Cosolutesa cosolute

df

λ

α2

10 mM NaCl 50 mM NaCl 250 mM sorbitol 500 mM sorbitol

2.05d 2.05d 2.05b 2.05b

0.51c 0.51c 0.51c 0.51c

1.20e 1.60e 0.60e 0.35e

The parameter α2 is defined as the ratio between the kinetic rate constants measured in the presence of cosolute divided by those measured in the absence of cosolute (see eq 4). The parameter values in the absence of cosolutes are reported in Table S2 (Supporting Information). bMeasured by independent SLS experiments. cEstimated from λ = 1 − 1/df. dSince df could not be measured in the presence of NaCl due to sample precipitation, it was assumed to be equal to the value measured in the absence of salt in the simulations. e Fitted to experimental data. a

kinetic analysis confirms that NaCl accelerates in a concentration dependent manner all the elementary steps involved in the aggregation scheme to the same extent. mAb-2. Impact of Sorbitol. Finally, the impact of sorbitol on the aggregation kinetics of mAb-2 was investigated. Experimental data are presented in Figure 5, showing that sorbitol is capable of

Figure 4. Comparison between simulated (lines) and experimental (symbols) aggregation kinetics of mAb-2 incubated at 70 °C at a protein concentration of 1 g/L in the absence, and presence of 10 and 50 mM NaCl. (a) Monomer, (b) dimer, (c) trimer concentrations, and (d) aggregate weight-average molecular weight versus time and (e) aggregate weight-average molecular weight versus monomer conversion, defined as the nonaggregated fraction of the initial protein content. Parameter values used in the simulations are summarized in Table 2.

trimer concentrations (data not shown) are independent of salt concentration. This important observation indicates that the aggregate distribution obtained at a given monomer conversion is independent of salt concentration. Since specific promotion of nucleation or growth events would affect in a different way the aggregate distribution at a given monomer conversion, the analysis provides evidence that NaCl does not impact specific steps of the reaction scheme but rather accelerates all the elementary processes of the aggregation process, i.e., nucleation and growth to a similar extent. Based on these considerations, we introduced a parameter α2 defined as the ratio of the value of each kinetic rate constant (corresponding either to an aggregation, dissociation or nucleation event) in the presence of cosolute divided by the corresponding value in the absence of cosolute (which are reported in Table 2). Since the aggregation rate constants are inversely proportional to the Fuchs ratios, α2 is defined as α2 =

−CS W11 +CS W11

=

W 4−*CS j W 4+*CS j

=

W ij−CS W ij+CS

=

r +CS k11 r −CS k11

=


=


=

Figure 5. Comparison between simulated (lines) and experimental (symbols) aggregation kinetics of mAb-2 incubated at 70 °C at a protein concentration of 1 g/L in the absence, and presence of 250 and 500 mM sorbitol. (a) Monomer, (b) dimer, (c) trimer concentrations, and (d) aggregate weight-average molecular weight versus time and (e) aggregate weight-average molecular weight versus monomer conversion, defined as the nonaggregated fraction of the initial protein content. Parameter values used in the simulations are summarized in Table 2.

+CS k nuc −CS k nuc

(4)

where −CS and +CS denote the situation without and with cosolute, respectively. At each salt concentration, the parameter α2 was evaluated by fitting to the experimental data. Due to sample precipitation at large aggregate sizes, the fractal dimension of mAb-2 aggregates in the presence of salt could not be measured experimentally and was thus assumed to be the same as the one estimated in the absence of salt. The parameter values used for the simulations are summarized in Table 2. In particular, we obtained α2 = 1.2 and α2 = 1.6 at 10 and 50 mM NaCl, respectively. As shown in Figure 4, the model simulations are in very good agreement with the set of experimental data. Therefore, the

delaying both the monomer depletion and the aggregate growth kinetics. As in the case of NaCl, the aggregate weight-average molecular weight (Figure 5e) as well as the dimer and trimer concentrations (data not shown) obtained at a given monomer conversion are not affected by the presence of sorbitol. This suggests that the presence of sorbitol does not impact the aggregate distribution at a given monomer conversion, indicating that sorbitol does not impact specific steps of the reaction 11926



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scheme but rather delays all the elementary steps of the aggregation process to the same extent. Similarly to the approach used in the case of NaCl, we performed the simulations of the inhibited aggregation kinetics in the presence of sorbitol by considering the set of kinetic rate constants evaluated in the absence of sorbitol multiplied by a constant factor α2, which was determined by fitting to the experimental data. Moreover, the fractal dimension was measured by SLS and λ was estimated as λ ≈ 1 − 1/df. The parameters used for the simulations are summarized in Table 2. In particular, we obtained α2 = 0.6 and α2 = 0.35 at 250 and 500 mM sorbitol, respectively. As shown in Figure 5 the model simulations describe very well the set of experimental data, thus confirming that sorbitol delays in a concentration dependent manner all the elementary steps that contribute to the global aggregation process to the same extent.

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DISCUSSION We investigated the impact of NaCl and sorbitol on the aggregation kinetics of two monoclonal antibodies under thermal stress. The two cosolutes were selected for their relevance in drug formulation and for their opposite effects on protein stability: while salt addition accelerates the kinetics of protein aggregation, the presence of polyol sugar delays the aggregation process. For each mAb and for each condition investigated, we are able to describe the monomer depletion, the dimer and trimer formation as well as the increase in the aggregate molecular weight by using a kinetic model based on Smoluchowski’s population balance equations modified to account for nucleation events. By applying kinetic analysis, we are in a position to discriminate the impact of the two cosolutes on the elementary steps that contribute to the global protein aggregation rate. Our results are summarized in Figure 6, which presents a schematic drawing of the kinetic mechanisms of the two antibodies under investigation and highlights the impact of NaCl and sorbitol on the elementary events. The impact of NaCl and sorbitol on the aggregation kinetics of mAb-1 is further illustrated with the energy diagram shown in Figure 7a, where the global aggregation pathway is schematically represented as a unimolecular unfolding event followed by a bimolecular collision step leading to aggregates formation. By applying kinetic analysis, we showed that, in the investigated range of cosolute concentrations, NaCl promotes aggregate growth without impacting protein unfolding, while sorbitol delays protein unfolding without affecting aggregate growth. We can therefore conclude that NaCl reduces the activation energy of aggregation without impacting the activation energy of protein unfolding, while sorbitol increases the activation energy of protein unfolding without impacting the activation energy of aggregation. The decrease in the energy barrier that colliding particles must overcome before aggregating in the presence of NaCl can be partly attributed to the reduction of electrostatic repulsion induced by salt addition. Since it has been shown in a previous study that the contribution of electrostatics to the colloidal stability is small,34 it is also likely that the presence of salt modifies the aggregation kinetics of mAb-1 by impacting other intermolecular forces, such as hydration forces. Moreover, it is worth highlighting that the impact of salt on mAb aggregation kinetics was studied in the millimolar range. At higher salt concentrations, additional effects such as specific ion binding may occur, possibly affecting the kinetics of protein unfolding. On the other hand, the finding that sorbitol increases

Figure 6. Scheme of the aggregation mechanism of (a) mAb-1 and (b) mAb-2 highlighting the impact of NaCl and sorbitol on the elementary steps. In the case of mAb-1, NaCl accelerates the aggregation process without impacting the unfolding step, while sorbitol inhibits protein unfolding without affecting the aggregation process. In the case of mAb-2, all the elementary steps are accelerated by NaCl and inhibited by sorbitol to the same extent.

the energy barrier of protein unfolding can be related to the preferential exclusion of sugars at the protein surface. Sugars and polyol sugars have been shown to impart thermodynamic stability (i.e., increase the Gibbs free energy difference between folded and unfolded state) to protein solutions due to unfavorable protein−solvent interactions that favor compact protein conformations with respect to more open unfolded structures. Timasheff and Arakawa indeed provided evidence that the stabilization action of sugars on the protein structure is driven by the stronger exclusion of sugar molecules from the unfolded protein than from the native protein.24,38,39 In this work, we show that the preferential exclusion of sorbitol from the protein surface induces also a kinetic stabilization since sorbitol is found to be capable of delaying protein unfolding. The impact of cosolutes on the elementary events involved in the aggregation process was also quantified in terms of characteristic times, as shown in Figure 7b. As protein unfolding is a monomolecular event described by a first order kinetic, its characteristic time was simply computed as τUnf = 1/kU. Dimerization, instead, arises from a bimolecular collision event 11927



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It is worth noticing that both cosolutes increase the ratio between the characteristic time of unfolding and the characteristic time of aggregation (Figure 7b). This important observation allows us to conclude that the monomer depletion remains ratelimited by protein unfolding upon addition of NaCl or sorbitol. While NaCl and sorbitol were shown to impact specific elementary steps in the aggregation mechanism of mAb-1, the addition of cosolutes in the case of mAb-2 was found to impact all the elementary steps (i.e., reversible oligomerization, irreversible oligomer rearrangement, and irreversible aggregate growth) to the same extent in the investigated range of cosolute concentrations. While all the elementary steps that contribute to the global aggregation process were found to be accelerated in equal measure upon NaCl addition, they were found to be all delayed to the same extent in the presence of sorbitol. The observed behaviors are specific to the proteins examined and do not identify the general properties of the respective classes IgG1 and IgG2. Indeed, due to the complex chemical structure of the antibodies, a large variety of aggregation behaviors has been observed even among members of the same class,40 and robust conclusions about the general properties of the different classes would require the analysis of a large number of molecules. In summary, we have shown how it is possible to combine experimental data with theoretical kinetic analysis to extract relevant information on the impact of cosolutes on the aggregation kinetics of proteins. This powerful approach, illustrated here with two model monoclonal antibodies, is sufficiently general to be applied to other protein systems.

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CONCLUSIONS We investigated the impact of NaCl and sorbitol on the aggregation kinetics 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 effect of cosolutes addition on the monomer depletion, as well as on the formation of dimer, trimer, and larger aggregates. For each mAb and for each investigated condition, it is possible to describe the experimental data by using kinetic models based on Smoluchowski’s population balance equations that were modified to account for nucleation events. By applying kinetic analysis, we are in a position to quantify the impact of cosolutes on the single elementary events that contribute to the global aggregation rate. In the case of the IgG1, it is found that NaCl accelerates the kinetics of aggregation by promoting all the single aggregation events, without impacting the kinetics of protein unfolding, which is rate-limiting the kinetics of monomer depletion. Conversely, sorbitol is found to delay the kinetics of aggregation by inhibiting specifically protein unfolding, without impacting the aggregation events. In the case of the IgG2, whose monomer consumption kinetics is ratelimited by dimer formation, both cosolutes are found to impact all the elementary steps to the same extent. This work illustrates the potential of combining experimental characterization with theoretical kinetic analysis to gain knowledge on the impact of cosolutes on the mechanisms of protein aggregation.

Figure 7. (a) Impact of NaCl and sorbitol on the aggregation pathway of mAb-1. (b) Impact of NaCl and sorbitol on the characteristic times of protein unfolding (τUnf) and dimer formation (τDim) of mAb-1. The characteristic times were computed as τUnf = 1/ku and τDim = 1/(k11M0), where kU is the unfolding rate constant, k11 is the rate constant of dimer formation (computed from W 11 ), and the reference protein concentration was chosen at M0 = 1 g/L. The dashed black line defines the border between a process which is unfolding rate limited and a process which is aggregation rate limited.

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and is described by a second order kinetics. Its characteristic time at a reference protein concentration M0 was thus computed as τDim = 1/(k11M0), where k11 is the aggregation rate constant of dimer formation (computed from W11). It can be seen that in the absence of cosolutes, the characteristic time of protein unfolding is on the order of 20 min, while the characteristic time of dimer formation is on the order of 1 min, consistent with the previous finding that mAb-1 aggregation is unfolding rate-limited.

ASSOCIATED CONTENT

* Supporting Information S

Kinetic mechanisms of mAb-1 and mAb-2 aggregation under thermal stress and parameter values used for the model simulations in the absence of cosolute. This material is available free of charge via the Internet at http://pubs.acs.org. 11928



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AUTHOR INFORMATION

Corresponding Author

*Phone: +41 44 632 30 34. E-mail: massimo.morbidelli@chem. ethz.ch. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

Financial support from the Fondation Claude et Giuliana and from 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 supplying materials and financial support.

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Role of Cosolutes in the Aggregation Kinetics of Monoclonal

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