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,kDor the second virial osmotic coefficient,B22. In two studies comparing large datasets obtained for multiple mAbs in the same formulation, one was negativekDofB22, 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 attractivenesskDofB22High 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 usekDofB22is 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,Sq=0at zeroqhydrodynamic function,Hq=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,kH. The Huggins coefficient is derived from the linear dependence of the concentration on the viscosity of the dilute solution.of[31], [32],ofcruz=ofspC=of/of0-1C=[of]+kH[of]2CWhereofcruzis the reduced viscosity,ofspis the specific viscosity,of0is the viscosity of the solvent, and [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.kHfor 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,kH[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 calculatekHas a function of temperature using a modified Arrhenius equation. However, no attempt was made to bindkHto the properties of proteins or PPIs. Of great importance to this study, presented by Yadav et al. [14]kHResults for a pool of four mAbs at pH 6.5 15 mM NaCl. The interaction parameter,kDthe zeta potential and viscosity at high concentration were also measured. Although the zeta potential was not correlated withkH, a correlation was observed where greaterkHvalues ​​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 andkHfor 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 ofkHunderstanding the factors that control the viscosity of the concentrated solution may be partly related to challenges in experimental measurementkH. There may be inaccuracies in the calculation.kHto 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). [of] IkHvalues ​​at pH 5 and pH 7). precise measurements ofkHwould 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 ​​ofkHclosely 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 betweenkHthat high-concentration viscosity and rationalize why the correlation of viscosity with protein-protein interaction parameters,kDofB22, are much weaker.

extract section


All buffer components used in this study are analytical grade. Sodium acetate (NaAce), histidine (His), TRIS and sodium phosphate are used as buffering agents. Sodium chloride (NaCl) and sodium thiocyanate (NaSCN) are used to adjust the ionic strength. The phosphate buffer used in the SEC-MALS-VISC experiments was prepared as a 38 mM Na solution.2HPO4NaH 12 mM2AT4150 mM NaCl. For all other buffers, the appropriate weight of buffer salt calculated for pH and ionic strength was given in the text.

(Video) Interactions, clustering, and rheology of highly concentrated antibody solutions

Development of the Multi-Injection Differential Viscometry Method for Measuring Intrinsic Viscosity and the Huggins Coefficient

The use of differential viscometers to determine the intrinsic viscosity of polymers and proteins is an established technique [57], [43]. The sample is separated by size exclusion chromatography, the specific viscosity at the sample peak is measured with a differential viscometer, and the concentration at the peak is measured by UV or refractive index detection. At diluted protein concentrations of 0.1 to 0.5 mg ml−1eluted from an SEC column, it is just the intrinsic viscosity

Protocol validation for measuring [of] &kHby MIDV

Multiple Injection Differential Viscometry (MIDV) was developed and qualified using BSA samples and the PPI03 antibody. The intrinsic viscosity and Huggins coefficient of the samples were validated against measurements made by microfluidic rheometry. The results and uncertainties of the fitting parameters are listed in Table 1. The fitting graphs for Eq. 1 for viscosity data measured by microfluidic rheometry with 95% confidence intervals shown in FIG. and b. Also these numbers


An important question to consider is whykHcorrelate better with the viscosity of the concentrated solution thankDIB22which are direct targets of protein-protein interactions. We expect that there are several reasons, depending in part on whether the comparison is made on different mAbs or for the same mAb but under different solution conditions.

For PPI03, the lack of correlation between the viscosity of the concentrated solution andB22emerges more clearly when we look at the circumstances


Understanding the relationship between PPI and the viscosity of high-concentration protein solutions is essential for designing good quality protein formulations. Until now, this field has been limited by prohibitive protein requirements for viscosity measurements and by conflicting results in correlating dilute solution thermodynamic parameters.kDIB22, to the behavior of the solution with high concentrations.

We present a technique for determining the Huggins coefficient and the intrinsic viscosity of

Author statement on contribution CRediT

Aisling Roche:Conceptualization, methodology, software, research, formal analysis, writing - original design.Lawrence sir:Methodology, writing – review and edition.Nicole Sibanda:Research, formal analysis.Dierk Roessner:Fuentes.Papas Frita Wolfgang:Resources, Writing - proofreading and editing, Supervision.Steven P. Trainoff:Conceptualization, Methodology, Writing - revision and edition.Robin Curtis:Conceptualization, Supervision, Writing - revision and edition.

Declaration of competitive interest

The authors declare the following financial interests/personal relationships that may be considered potential competing interests: Steven P. Trainoff is a principal scientist and full-time employee of Wyatt Technology Corporation, the manufacturer of the ViscoStar instrument used for this work. Dierk Roessner is the CEO and full-time employee of Wyatt Technology Europe GmbH, the European headquarters of Wyatt Technology Corporation.

expression of gratitude

Aisling Roche and Lorenzo Gentiluomo were supported by the EU's Horizon 2020 Research and Innovation Program under Marie Skłodowska-Curie Grant Agreement No. 675074. Nicole Sibanda was supported by an EPSRC DTP grant (Ref. No. 2389795) with a financial contribution from AstraZeneca ( With immune). The authors thank Alfredo Lanzaro, Daniel Corbett, Maryam Shah, Jai Pathak, Vanessa Schneider, Arthur Porfetye, Roger Scherrer and all staff at Wyatt Europe, Pernille Harris and the ESRs and

Selected articles (6)

  • Research article

    Application of a high-throughput, automated workflow for the development of therapeutic protein formulations

    Journal of Pharmaceutical Sciences, bind 110, nummer 3, 2021, s. 1130-1141

    (Video) Rheology of Highly Concentrated Antibody Solutions

    Rapid and efficient formulation development is critical to successfully bringing protein therapies to a competitive marketplace on increasingly aggressive timelines. The conventional use of high-throughput techniques for formulation development is limited to lower protein concentrations, which are not applicable to the late-stage development of high-concentration therapies. In this paper, we present a high-throughput (HT) workflow that enables detection at representative concentrations by integrating a microbuffer exchange system with automated analytical instruments. The operational recommendations associated with the use of such HT systems as well as the efficiencies achieved (reduction of handling time and execution time by more than 70% and 30% respectively), which allow the practical characterization of a wide design space of formulation, have been discussed . To demonstrate the fit-for-purpose of the workflow, the formulation properties and stability profiles (SEC and CEX) of samples generated by the HT workflow were compared to those treated by ultrafiltration/diafiltration, and the results were found to be in agreement. This approach was subsequently applied to two case studies, one focused on a formulation evaluation studying the effects of pH and excipient on viscosity and stability, and the other focused on the selection of an appropriate viscosity mimetic solution for a protein product.

  • Research article

    High shear rheology and anisotropy in concentrated solutions of monoclonal antibodies

    Journal of Pharmaceutical Sciences, bind 102, nummer 8, 2013, pp. 2538-2549

    The high-shear rheology of three concentrated solutions of immunoglobulin G1 monoclonal antibodies (mAb1, mAb2, and mAb3) differing only in their complementarity-determining regions was characterized by rotational and capillary rheometry. The most viscous solutions (mAb1 and mAb3) exhibited non-Newtonian behavior at high shear rates and showed shear thinning and noticeable normal stress differences (NSD) over the shear rate range.C=10 to 104S−1. Subsequently, the rheograms were recoveredCincreases and decreases, indicating reversible self-associations during displacement. On the contrary, the mAb2 solutions showed a Newtonian behavior untilC=6×104S−1. The critical shear stressTC, corresponding to the onset of viscosity reductionof, is a measure of the strength of the mAb equilibrium group and increases rapidly with concentration for high viscosity mAb solutions above 100 mg/ml. In addition, the lowering of the temperature increased from 20°C to 5°Cofat its lowest pointC, but shear thinning was enhanced and onset occurred at a lower levelCC. Using an Arrhenius modelof= an experience (miIN/kT), the activation energy for viscous flowmiINwas found to decrease for mAb1 solnsCincreased from 10 to 104S−1, indicating disruption or rearrangement of the mAb pool during shear. For mAb2, this is on the other handmiINremained constant inCrange. Finally, the mAb1 and mAb3 solutions showed significant NSD with theirsnorte1>0 linear scale withCi serie 103in 104S−1, while his |norte2/norte1| was less than 0.25 in this region. These suggest anisotropy and deformation of the microstructure of their solution towards the extensional quadrant of the high-altitude flow.C. In contrast, the NSDs of mAb2 were close to zero, indicating that the microstructure of the solution under shear is nearly isotropic. © 2013 Wiley Periodicals, Inc. and American Pharmacists Association J Pharm Sci 102:2538–2549, 2013

    (Video) Viscosity and Stability of a Highly Concentrated Monoclonal Antibody

  • Research article

    Influence of excipients on the viscosity of monoclonal antibody solutions

    Journal of Molecular Liquids, bind 366, 2022, artikel 120349

    The aggregation tendency of the monoclonal antibodies can be modified by adding different excipients to the solution. A simple coarse-grained model in combination with thermodynamic perturbation theory was used to predict the cluster distribution and viscosity of IgG4 monoclonal antibody solutions in the presence of L-arginine hydrochloride. Data were analyzed using a binding polynomial to describe the binding of cosolute (arginine) to the antibody molecule. The results show that upon binding to the antibody molecule, cosolute occupies some of the antibody binding sites, which reduces the number of available binding sites for other antibody molecules. In this way, the tendency of the antibody molecules to aggregate is reduced.

  • Research article

    Prediction of protein-protein interactions from concentrated antibody solutions using data from dilute solutions and coarse-grained molecular models

    Journal of Pharmaceutical Sciences, bind 107, nummer 5, 2018, pp. 1269-1281

    Protein-protein interactions for solutions of an IgG1 molecule were quantified using static light scattering (SLS) measurements from low to high protein concentrations (C2). SLS was used to determine the second virial osmotic coefficients (B22) at its lowest pointC2, and redundant Rayleigh profiles (Re.g/kin exchange forC2) and structure factors of q zero (Sq=0) as a function ofC2in higherC2to a variety of conditions (pH, sucrose concentration and total ionic strength [TIS]). Repulsive (attractive) interactions were observed at lowTIS(altTIS) for pH 5 and 6.5 with increasing repulsion when 5% w/w sucrose was also present. Previously developed and refined coarse-grained antibody models were used to fit model parameters.B22againstTISfacts. Parameters as a result of lowC2conditions were used as the sole input to multi-protein Monte Carlo simulations to obtain highC2 Re.g/kISq=0behavior up to 150 g/L. Experimental results at highC2The conditions were quantitatively predicted by simulations for coarse-grained models that treated antibody molecules as 6 or 12 (sub)domains that retained the basic shape of a monoclonal antibody. Finally, the preferential accumulation of sucrose around the protein surface was identified through high-precision density measurements, which consistently explains the SLS simulation and experimental results.

    (Video) Simple non-Newtonian Scaling Analysis for Protein Solutions
  • Research article

    DeepSCM: An Efficient Convolutional Neural Network Surrogate Model for Therapeutic Antibody Viscosity Detection

    Journal of Computational and Structural Biotechnology, bind 20, 2022, pp. 2143-2152

    Prediction of the viscosity of high-concentration antibodies is essential for developing subcutaneous delivery. Computer simulations offer promising tools to achieve this goal. An example of such a model is the space charge map (SCM) proposed by Agrawal and colleagues (mAbs.20158(1):43-48). SCM uses molecular dynamics simulations to calculate a score for detecting antibody viscosity at high concentrations. However, molecular dynamics simulations are computationally expensive and require structural information, a significant bottleneck in the application. In this work, high performance computing was performed to calculate SCM scores for 6596 non-redundant variable antibody regions. Based on this data set, a convolutional neural network surrogate model, DeepSCM, was developed, which only requires sequence information. The linear correlation coefficient of the DeepSCM and SCM scores reached 0.9 in the test set (N=1320). The DeepSCM model was applied to assess the viscosity of 38 therapeutic antibodies that correctly classified SCM and resulted in only one misclassification. The DeepSCM model will facilitate the detection of the viscosity of high concentration antibodies. The code and parameters are freely available at

  • Research article

    Observation of the formation of small clusters in concentrated solutions of monoclonal antibodies and its implications for solution viscosity

    Biophysical journal, volume 106, number 8, 2014, pp. 1763-1770

    Monoclonal antibodies (mAbs) are an important class of biopharmaceutical agents. It is believed that some concentrated mAb solutions show the formation of a solution phase consisting of reversible self-associated aggregates (or reversible clusters), which is believed to be responsible for their different dissolution properties. Here we report the direct observation of reversible clusters in concentrated mAb solutions using neutron spin echo. Specifically, a stable mAb solution is studied during a transition from dispersed monomers in dilute solution to clumped states under more concentrated conditions, where clusters of a preferred size are observed. Once mAb clumps are formed, their size, unlike that seen in typical globular protein solutions, has been found to remain nearly constant over a wide range of concentrations. Our results not only definitively establish a clear relationship between the undesired high viscosity of some mAb solutions and the formation of reversible clusters with extended open structures, but also directly observe mAb protein clusters with a limited size preference, corresponding to the . in the formation of micelles. that dominate the properties of concentrated mAb solutions.

    (Video) Predicting Injection Force for High Concentration Monoclonal Antibody Formulations

© 2021 Elsevier Inc. All rights reserved.


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