The influence of excipients on the viscosity of monoclonal antibody solutions

Abstract

The aggregation propensity of monoclonal antibodies can be modified by adding different cosolutes into the solution. A simple coarse-grained model in the combination with the thermodynamic perturbation theory was used to predict cluster distribution and viscosity of the solutions of IgG4 monoclonal anibody in the presence of L-Arginine Hydrochloride. The data were analysed using binding polynomial to describe the binding of cosolute (Arginine) to the antibody molecule. The results show that by binding to the antibody molecule the cosolute occupies some of the binding sites of the antibody, and in this way reduces the amount of binding sites available to other antibody molecules. The aggregation propensity of the antibody molecules is therefore reduced.

1. Introduction

In the last decades monoclonal antibodies (mAbs) became one of the fastest-growing biological therapeutics in pharmaceutical industry. Their implication ranges from treating cancers, autoimmunity diseases and metabolic disorders to emerging infectious diseases. The reasons behind their broad range of applicability are high binding affinity and specificity, long circulation half-life in blood stream, non-toxic nature and easy manufacturing [1,2]. Unlike most of more traditional drugs biological therapeutics are stored and delivered to patients as liquids [3]. Since mAbs to be effective for therapeutical use, they need to be administered to a patient in a relatively large dose, in terms of the mass or protein per unit mass of the patient body weight, and the maximum volume that can be delivered per dose in such cases is approximately 1 mL, this requires the mAb concentrations that are on the order of 100 mg/mL [4]. While proteins are inherently prone to form certain types of aggregates over time, even at much lower concentrations, these much higher protein concentrations pose further issues via a range of different aggregated states. While the aggregates may pose a problem from the perspective of product quality, an important challenge for such formulations is aggregation related high viscosity that causes difficulties in manufacturing, as well as administrating these therapeutics [4,5]. With the goal of improving the quality of the therapeutics a lot of effort has therefore been put into the researching the driving forces of aggregates formation as well as the methods for predicting the high concentration viscosity behavior of the mAbs formulations.

While it is known that the mAb-mAb aggregation is driven by protein–protein interactions [6], various experimental studies showed that these can be modified by changing pH of the formulation [7,8], adjusting ionic strength [7,5,9,10], and/or adding cosolutes such as carbohydrates [11–13], hydrophobic ions [14,15], and amino acids and their derivatives. [8,15–24] While all these studies show that the cosolutes influence the aggregation process of mAb molecules, and with it the viscosity of mAb solutions [25] the mechanism of their activity is still not fully explained.

Since determining protein–protein interactions experimentally can be extremely costly in terms of time and protein material, computer simulations could represent a great help in that direction. Unfortunately, all-atom simulations for large proteins, such as antibodies, at concentrations where aggregation becomes important are still beyond reach. Therefore, the coarse-grained models with different level of coarse-graining of mAb molecules are a popular tool to study mAb solutions via computer simulations to interpret and predict experimental data for mAb solutions [26–31]. They are commonly built from fused hard spheres or sticks and interaction between molecules is described through hard sphere, van der Waals, electrostatic, and/or patchy attractive interaction sites on the surface of the molecule [32,33]. The parameters of models are either based on the experimental observations described above or fit to describe certain experimentally observed property. The main advantage of the coarse-grained models compared to the all-atom ones still remains their use in computer simulations for fast scanning of model parameters as for their influence on the aggregation propensity and viscosity, for identifying the aggregates that are the most relevant for the viscosity increase, and enabling an insight into their formation mechanism (that could be hindered by the addition of appropriate excipients). Even though the coarse-grained models can be efficiently studied by computer simulations, the simulations still require considerable CPU time [26], and the results are subject to statistical errors that can in certain cases prevent subtle differences in the solution behavior to be observed.

Couple of years ago we have developed a coarse-grained model for different shaped proteins [34–36], that overcomes these difficulties. Namely, the model can be used in the statistical-thermodynamic theories that are free of statistical errors and are at the same time reliable in predicting the thermodynamic, as well as certain dynamic properties of the solutions, such as viscosity. In this model the proteins are modeled as one or several fused hard spheres decorated with the short-ranged attractive interaction sitess on their surfaces. The model can then be treated with the associative Wertheim thermodynamic perturbation theory [37] to obtain the free energy, and related thermodynamic properties, as well as cluster size distribution. The latter can be, in the combination with relations from polymer physics converted to the solution viscosity [36,6]. The model and the theory have been successfully used to analyse the viscosity data of mAb solutions at different conditions, and in the presence of different cosolutes [36,6]. We used this model here to analyse the obtained cluster size distribution data as a consequence of binding of a cosolute to the antibody molecule.

The paper is organized as follows: After this brief introduction, the model and theoretical methods used are described in section 2. Results and discussion are given in section 3 and conclusions in 4.

2. Model and Method

Within this work we used a simple coarse-grained mAb model in combination with thermodynamic perturbation theory (TPT) to obtain the mAb cluster distribution, and viscosity as a function of mAb concentration in aqueous solutions (pH = 5.5) in the presence of L-Arginine hydrochloride (250 mM). The experimental data were taken from [38], and apply to IgG4 monoclonal antibody (M_w = 156900 g/mol).

We used the 7-bead mAb coarse-grained model where each mAb molecule is described as 7 fused hard spheres with diameter of σ = 3 nm to form a Y-shaped particle (Fig. 1). The so-formed molecules interact with each other through two interaction sites of the same interactions strength (e), positioned at the end spheres of two arms (the detailed description of the model is given in [36]). The solvent and cosolvent are not treated explicitely but can only influence the strength of the interaction site.

Fig. 1.

The model mAb molecule. 7 hard spheres with equal diameter are fused together through infinitely large attraction between pairs of interaction sites (colored white). The interaction sites through which different mAb molecules interact with each other are colored black. u(x) shows the interaction potential between two such interaction sites at a distance x from each other. ε denotes the depth, and ω the range of the attractive square-well potential between them.

Within the Wertheim’s thermodynamic perturbation theory (TPT1) [37,36] the Helmholtz free energy F of the model solution is decomposed in the ideal F_id, hard-sphere F_hs, and association term F_ass [36]:

$$\frac{\beta F_{id}}{V}=\sum _{i=7}^7\rho \left[ln\left({\Lambda }^3\rho \right)-1\right]$$ (1)

$$\frac{\beta F_{hs}}{V}=\frac{4\eta -3{\eta }^2}{{(1-\eta )}^2}{\rho }_t$$ (2)

$$\frac{\beta F_{ass}}{V}=\rho \left\{\left(2ln\left(x_A\right)-x_A+1\right)-6\left[ln\left(\rho {\sigma }^3{g}_{hs}^{py}\right)-1\right]\right\}$$ (3)

where Λ is the de Broglie thermal wavelength, ρ_t = 7ρ η = πρ_tσ³/6, and $g_{hs}^{py}=(1+\eta /2)/{(1-\eta )}^2$ is the Percus–Yevick expression for the contact value of the hard-sphere radial distribution function. X_A is the fraction of the particles, which do not bond via the biding site, and equals to:

$$x_A={\left(1+2\rho \Delta x_A\right)}^{-1}$$ (4)

where Δ equals to:

$$\Delta =4\pi g_{hs}^{py}(\sigma ){\int }_{\sigma }^{\sigma +\omega }<f(r)>r^{2}dr$$ (5)

and < f(r) > is the orientation average of the Mayer function for the square-well site-site interaction [37]:

$$<f(r)>=\frac{exp(\beta \epsilon )-1}{6{\sigma }^{2}r}{(\omega +\sigma -r)}^2(2\omega -\sigma +r)$$ (6)

ω was taken as in previous works to be 0.18 nm.

After the equations are solved, the n-size cluster fraction distribution, H(n) can be calculated as (n indicates the number of molecules contained in a cluster):

$$H(n)=x_A{\left(1-x_A\right)}^{n-1}$$ (7)

and mass fraction distribution, P(n) is then obtained as P(n) = nx_AH(n) [36].

In polymer physics an approximate relation can be deduced that translates the normalized mass fraction distribution of clusters of size n, P(n), to relative viscosity, η/η₀,

$$\frac{\eta }{{\eta }_0}=\sum _n\gamma P(n)c{n}^d$$ (8)

where γ is the mass concentration of the solution. The parameters c and d were taken as in [36] to be c = 0.01205 mL/mg, and d = 0.3762.

Taking the viscosity data from [38] we have adjusted the interaction parameter of our model, ε to obtain the best possible agreement with the experimental data in the whole concentration range. The value of ε was found to be 4400 k_B (k_B is the Boltzmann constant). The agreement between experimental viscosity data [38] and our model is shown in Fig. 2.

Fig. 2.

The relative viscosity of IgG4 solutions in the presence of 250 mM L-arginine hydrochloride. Experimental data taken from [38] are shown as symbols, and prediction of our model is shown with lines.

2.1. Binding polynomial

In the next step we have adapted the idea of Cann [39] to interpret the role of cosolvent in the process of modifying the viscosity of the solutions. We assumed that the cosolvent binds to one or both of the interaction sites of the model antibody, and as such modifies the formation of mAb-mAb aggregates. mAb binds to another mAb with the equilibrium constant K_a, while a cosolute molecule (Arginine) binds to a mAb with equilibrium constant K_L. Examining the fraction distribution obtained from the theory (Fig. 3) the fractions of clusters larger than n = 4 are negligable, so we have only considered dimer, trimer, and tetramer formation within this work.

Fig. 3.

The fraction distribution obtained from the TPT theory.

The concentration of different species present in the solution are then the following ([M] and [X] are the molar concentrations of mAb monomers, and unbound cosolutes, respectively):

$$\left[MX\right]=K_L\left[M\left]\right[X\right]$$ (9)

$$\left[M{X}_2\right]=K_L^2[M]{[X]}^2$$ (10)

$$\left[M_2\right]=K_a{[M]}^2$$ (11)

$$\left[M_{2}X\right]=K_a{K}_L{[M]}^2[X]$$ (12)

$$\left[M_2{X}_2\right]=K_a^2{[M]}^3$$ (13)

$$\left[M_3\right]=K_a^2{[M]}^3$$ (14)

$$\left[M_{3}X\right]=K_a^2{K}_L{[M]}^3[X]$$ (15)

$$\left[M_3{X}_2\right]=K_a^2{K}_L^2{[M]}^3{[X]}^2$$ (16)

$$\left[M_4\right]=K_a^3{[M]}^4$$ (17)

$$\left[M_{4}X\right]=K_a^3{K}_L{[M]}^4[X]$$ (18)

$$\left[M_4{X}_2\right]=K_a^3{K}_L^2{[M]}^4{[X]}^2$$ (19)

Together with the mass action laws for mAb and cosolute the equations were solved by using Globally convergent Newton for non-linear set of equations to obtain the mass concentration of different species, and mass fraction distribution was calculated [40]. The equilibrium constants K_a and K_L were chosen in such a way to obtain the best agreement with the mass fraction distribution obtained from the theory (K_a = K_L = 0.025 L/mol).

3. Results and Discussion

First we present the results for the mass fraction distribution obtained from the TPT, compared to the results obtained using binding polynomial (Fig. 4).

Fig. 4.

The mass fraction distribution obtained from the TPT theory, P(n), (lines) compared to the results obtained through binding polynomials (symbols). Squares denote the masss fractions of monomers, circles denote dimers, and triangles trimers.

One can see that the agreement for mass fractions of monomers is excellent in the whole concentration range. The agreement for the mass fractions for dimers and trimers is slightly worse at mAb concentration higher than 150 mg/mL, but still reasonable.

Encouraged by these results we analyzed the fractions of different species to get an insight into the role of cosolute influencing the formation of mAb aggregates. The fractions of different monomer and dimer species present in the solution are shown in Fig. 5 (the fractions of species not present is less than 0.1 within the whole concentration range studied).

Fig. 5.

Fractions of different species present in the solution as predicted by the binding polynomial.

The results indicate that the fraction of all monomer species decrease with mAb concentration, while the fraction of dimer species increases with concentration, as expected (the same is true for trimer and tetramer species, not shown). The mAb molecules preferentially bind to another mAb molecule, while the species with two binding sites occupied by the cosolute are rare. However, the fraction of species with only one cosolute bound to the mAb aggregate increases together with the mAb concentration.

To test our assumption that the cosolute influences the mAb aggregate formation by occupying some binding sites being otherwise available for other mAb molecules we have used the binding polynomial to calculate the mass fractions of different aggregates in a case, where the binding constant for the cosolute is much larger than that of the mAb (K_L = 5 K_a); the results are shown in Fig. 6.

Fig. 6.

The mass fraction distribution obtained through binding polynomials for the case K_L = 5 K_a. Squares denote the masss fractions of monomers, circles denote dimers, and triangles trimers.

As predicted, one can see that strongly binding cosolute slows down the formation of mAb clusters in the solution.

4. Conclusions

In this work we present a simple analysis of cosolute function in influencing the viscosity of solutions of monoclonal antibodies. By using a binding polynomial approach we have shown that the role of cosolute could be explained by considering it as a competitive species for the binding sites of mAb molecules. Even though the calculations should be repeated for other types of cosolutes to generalize these finding, the results indicate that the stronger the binding of the cosolute to the mAb molecule, the slower is the mAb aggregation process. We plan to correlate the properties of the cosolute with the binding affinity in our future work.