Towards an improved prediction of the viscosity of concentrated antibody solution using the Huggins coefficient (2023)

Monoclonal antibodies are regularly formulated at high protein concentrations to meet drug potency requirements within the constraints of 1 ml injection volume for subcutaneous administration [1], [2]. Highly concentrated protein formulations can generate unacceptably high viscosities above 30 cP, leading to production problems, increased injection force and pain during patient administration [1], [3], [4]. Next-generation biologics, such as bispecific antibodies and Fc fusion proteins, are also likely to have viscosities in the problematic range [5], [6].

The viscosity of the concentrated solution of protein solutions is difficult to predict. Protein viscosity data have been shown to fit colloidal models, such as the Krieger–Dougherty and Ross–Minton–Mooney models, when the parameters are free to vary, but the resulting parameters are often inconsistent with the measurements. based theoretical calculations. properties. Fitting the viscosity data for BSA solutions at high concentrations using the Krieger–Dougherty model resulted in unrealistic maximum volume fraction values ​​and intrinsic viscosities much higher than those measured in dilute solution [7] , [8] . Effective intrinsic viscosity values ​​obtained from the Ross-Minton-Mooney model fits to mAb viscosity data [9], [10], [11] are typically greater than 10 mLg⁻¹However, mAb solutions typically have an intrinsic viscosity between 6 and 7 mL.⁻¹measured in dilute solution [12], [13], [14], [15]. Therefore, quantitative prediction of the viscosity of protein solutions using colloidal models is impractical, as parametrizing the models with independent measurements of dilute solutions requires considerable effort, but rarely captures the behavior of concentrated solutions.

One of the reasons that hard sphere colloid rheology models do not accurately predict the viscosity of concentrated protein solutions is that the models do not explicitly account for the effects of protein–protein interactions (PPIs). An alternative approach to predicting the viscosity of the concentrated solution is to look for correlations with parameters of the dilute solution that reflect PPI, such as the diffusion coefficient interaction parameter,k_Dor the second virial osmotic coefficient,B₂₂. In two studies comparing large datasets obtained for multiple mAbs in the same formulation, one was negativek_DofB₂₂, indicating attractive PPI, was correlated with high sample viscosities [16], [17]. With varying pH and ionic strength, a maximum in mAb viscosity is sometimes observed at pH conditions closest to the protein's isoelectric point at low ionic strength, corresponding to the solution with the strongest protein-protein attractions [18] , [19] . The direct correlation between net PPI and high concentration viscosity is not valid for other studies. Correlation between attractivenessk_DofB₂₂High concentration values ​​and viscosities were weak, protein specific or not observed in several studies [19], [14], [20], [18], [10], [20].

One of the biggest shortcomings of the usek_DofB₂₂is that the parameters refer to an average protein-protein interaction, which does not reflect the orientational correlations between a pair of interacting proteins. As such, the measurements are not sensitive to the anisotropic interactions that occur between many mAbs due to electrostatic attractions arising from surface charge heterogeneity and the presence of non-polar surface planes [21], [22], [23], [24 ], [25]. At low protein concentrations, anisotropic interactions stabilize reversible oligomers, which associate further at high protein concentrations to form transient networks or clusters [26], [22], [10], [9], [27], [28]. Bond properties are important determinants of viscosity. For some mAbs, viscosity scales linearly with pool size [ 26 ], while other mAbs show non-monotonic relationships between viscosity and pool size [ 10 ]. Contrasting behavior has been rationalized in terms of cluster shapes and their effective volumes, which are determined by the valence of the mAb-mAb interactions [10], [27], [9], [22], [28]. Linear viscosity profiles with respect to group size are expected when the groups are more open, which occurs in low-valence interactions. On the other hand, higher valence interactions lead to more compact clusters that contribute less to the solution viscosity compared to linear clusters of the same size.

The correlation of viscosity with dilute solution parameters fails because the parameters do not solely determine the microstructure of concentrated solutions. However, the properties measured at high protein concentration do not show a strong correlation with viscosity either. There are no generalized correlations between the parameters for high concentration, zeroqfactor structure,S_q=0at zeroqhydrodynamic function,H_q=0, and high concentration viscosity was found when several mAb systems were compared in formulations varying in pH, ionic strength, and excipient composition [9] , [29] . On the other hand, a recent study has shown that viscosity can be predicted from osmotic compressibility measurements and interdiffusion coefficients up to high protein concentrations [30]. In that study, thermodynamic measurements were used to parameterize a patchy colloid model, which in turn was used to estimate pool size and volume as a function of protein concentration. Mooney's equation was used to calculate the viscosity by treating the clumps as polydisperse spheres. More research is needed to see if the approach can capture the behavior of other mAbs that show different patterns of cluster formation.

The search for a parameter that can be measured with a minimum of protein material and that reliably correlates with solution viscosity at high protein concentrations under physiological formulation conditions is ongoing. A dilute solution parameter that has the potential to correlate well with the viscosity of solution of high protein concentration is the Huggins coefficient,k_H. The Huggins coefficient is derived from the linear dependence of the concentration on the viscosity of the dilute solution.$\mathrm{of}$[31], [32],${\mathrm{of}}_{\mathrm{cruz}}=\frac{{\mathrm{of}}_{\mathrm{sp}}}{C}=\frac{\mathrm{of}/{\mathrm{of}}_0-1}{C}=[\mathrm{of}]+k_H{[\mathrm{of}]}^{2}C$Where$\mathrm{of}$_cruzis the reduced viscosity,$\mathrm{of}$_spis the specific viscosity,${\mathrm{of}}_0$is the viscosity of the solvent, and [$\mathrm{of}$] is the intrinsic viscosity.

The Huggin coefficient provides a good starting point for understanding the relationship between PPI and viscosity, as there are theories about relationships.$k_{\mathrm{H}}$for simplified models of colloidal interaction potential [31], [33], [34]. However, only a few measurements have been reported in the literature. Some of the first studies to determine protein intrinsic viscosity reported the slope of the equation. 1,k_H[$\mathrm{of}$]²[35], [36], [37], but did not elaborate on the physical meaning of the parameter. Monkos [38], [13], [39], [40] provided useful data sets on the viscosity of unbuffered solutions of various albumins and immunoglobulins and also derived a model to calculatek_Has a function of temperature using a modified Arrhenius equation. However, no attempt was made to bind$k_{\mathrm{H}}$to the properties of proteins or PPIs. Of great importance to this study, presented by Yadav et al. [14]k_HResults for a pool of four mAbs at pH 6.5 15 mM NaCl. The interaction parameter,k_Dthe zeta potential and viscosity at high concentration were also measured. Although the zeta potential was not correlated withk_H, a correlation was observed where greaterk_Hvalues ​​were found for solutions with attractive PPI and higher viscosities at high protein concentrations. Recently, Pathak and colleagues [41] found that colloidal models could not capture the relationship between protein-protein interactions and$k_{\mathrm{H}}$for a range of 3 mAb, which was attributed to the inability to account for solvation effects. In that work, intrinsic viscosity measurements indicated a significant variation in protein conformation and structure with changing solution conditions, which could be another reason why colloidal models could not describe the behavior of the compounds. mAb.

The limited use of$k_{\mathrm{H}}$understanding the factors that control the viscosity of the concentrated solution may be partly related to challenges in experimental measurementk_H. There may be inaccuracies in the calculation.k_Hto apply the linear model to curved data and of the compound uncertainty of the instruments used to measure concentration and viscosity [42], [13], [43]. When applied to viscosity data collected for proteins, the linearized form of the Huggins equation can generate negative values ​​that are difficult to interpret [44] and published values ​​can vary widely (see Supplementary Information for a BSA table). [$\mathrm{of}$] Ik_Hvalues ​​at pH 5 and pH 7). precise measurements of$k_{\mathrm{H}}$would allow us to investigate whether colloidal models are applicable to describe the viscosity of protein solutions.

Therefore, in this study, a new method has been developed and used to measure the intrinsic viscosity and Huggins ratio of BSA and two mAbs, PPI03 and PPI19. We show that the measured values ​​of$k_{\mathrm{H}}$closely matches the predictions of the colloidal sticky hard sphere models for BSA and for PPI03, whereas models that account for anisotropic shape and interactions are more applicable to PPI19. We see a very strong correlation betweenk_Hthat high-concentration viscosity and rationalize why the correlation of viscosity with protein-protein interaction parameters,k_DofB₂₂, are much weaker.