Controlling the viscosities of antibody solutions through control of their binding sites

Biophysical Principles Emerging from Experiments on Protein-Protein Association and Aggregation

Protein-protein association and aggregation are fundamental processes that play critical roles in various biological phenomena, from cellular signaling to disease progression. Understanding the underlying biophysical principles governing these processes is crucial for elucidating their mechanisms and developing strategies for therapeutic intervention. In this review, we provide an overview of recent experimental studies focused on protein-protein association and aggregation. We explore the key biophysical factors that influence these processes, including protein structure, conformational dynamics, and intermolecular interactions. We discuss the effects of environmental conditions such as temperature, pH and related buffer-specific effects, and ionic strength and related ion-specific effects on protein aggregation. The effects of polymer crowders and sugars are also addressed. We list the techniques used to study aggregation. We analyze emerging trends and challenges in the field, including the development of computational models and the integration of multidisciplinary approaches for a comprehensive understanding of protein-protein association and aggregation.

Stability of Protein Pharmaceuticals: Recent Advances

There have been significant advances in the formulation and stabilization of proteins in the liquid state over the past years since our previous review. Our mechanistic understanding of protein-excipient interactions has increased, allowing one to develop formulations in a more rational fashion. The field has moved towards more complex and challenging formulations, such as high concentration formulations to allow for subcutaneous administration and co-formulation. While much of the published work has focused on mAbs, the principles appear to apply to any therapeutic protein, although mAbs clearly have some distinctive features. In this review, we first discuss chemical degradation reactions. This is followed by a section on physical instability issues. Then, more specific topics are addressed: instability induced by interactions with interfaces, predictive methods for physical stability and interplay between chemical and physical instability. The final parts are devoted to discussions how all the above impacts (co-)formulation strategies, in particular for high protein concentration solutions.'

Computational Procedure for Predicting Excipient Effects on Protein-Protein Affinities

Protein-protein interactions lie at the center of many biological processes and are a challenge in formulating biological drugs, such as antibodies. A key to mitigating protein association is to use small-molecule additives, i.e., excipients that can weaken protein-protein interactions. Here, we develop a computationally efficient model for predicting the viscosity-reducing effect of different excipient molecules by combining atomic-resolution MD simulations, binding polynomials, and a thermodynamic perturbation theory. In a proof of principle, this method successfully ranks the order of four types of excipients known to reduce the viscosity of solutions of a particular monoclonal antibody. This approach appears useful for predicting the effects of excipients on protein association and phase separation, as well as the effects of buffers on protein solutions.

Antibody association in solution: cluster distributions and mechanisms

Understanding factors that affect the clustering and association of antibodies molecules in solution is critical to their development as therapeutics. For 19 different monoclonal antibody (mAb) solutions, we measured the viscosities, the second virial coefficients, the Kirkwood-Buff integrals, and the cluster distributions of the antibody molecules as functions of protein concentration. Solutions were modeled using the statistical-physics Wertheim liquid-solution theory, representing antibodies as Y-shaped molecular structures of seven beads each. We found that high-viscosity solutions result from more antibody molecules per cluster. Multi-body properties such as viscosity are well predicted experimentally by the 2-body Kirkwood-Buff quantity, G22, but not by the second virial coefficient, B22, and well-predicted theoretically from the Wertheim protein-protein sticking energy. Weakly interacting antibodies are rate-limited by nucleation; strongly interacting ones by propagation. This approach gives a way to relate micro to macro properties of solutions of associating proteins.

A computational procedure for predicting excipient effects on protein-protein affinities

Protein-protein interactions lie at the center of much biology and are a challenge in formulating biological drugs such as antibodies. A key to mitigating protein association is to use small molecule additives, i.e. excipients that can weaken protein-protein interactions. Here, we develop a computationally efficient model for predicting the viscosity-reducing effect of different excipient molecules by combining atomic-resolution MD simulations, binding polynomials and a thermodynamic perturbation theory. In a proof of principle, this method successfully rank orders four types of excipients known to reduce the viscosity of solutions of a particular monoclonal antibody. This approach appears useful for predicting effects of excipients on protein association and phase separation, as well as the effects of buffers on protein solutions.

Prediction of Antibody Viscosity from Dilute Solution Measurements

The high antibody doses required to achieve a therapeutic effect often necessitate high-concentration products that can lead to challenging viscosity issues in production and delivery. Predicting antibody viscosity in early development can play a pivotal role in reducing late-stage development costs. In recent years, numerous efforts have been made to predict antibody viscosity through dilute solution measurements. A key finding is that the entanglement of long, flexible complexes contributes to the sharp rise in antibody viscosity at the required dosing. This entanglement model establishes a connection between the two-body binding affinity and the many-body viscosity. Exploiting this insight, this study connects dilute solution measurements of self-association to high-concentration viscosity profiles to quantify the relationship between these regimes. The resulting model has exhibited success in predicting viscosity at high concentrations (around 150 mg/mL) from dilute solution measurements, with only a few outliers remaining. Our physics-based approach provides an understanding of fundamental physics, interpretable connections to experimental data, the potential to extrapolate beyond training conditions, and the capacity to effectively explain the physical mechanics behind these outliers. Conducting hypothesis-driven experiments that specifically target the viscosity and relaxation mechanisms of outlier molecules may allow us to unravel the intricacies of their behavior and, in turn, enhance the performance of our model.

Protein Association in Solution: Statistical Mechanical Modeling

Protein molecules associate in solution, often in clusters beyond pairwise, leading to liquid phase separations and high viscosities. It is often impractical to study these multi-protein systems by atomistic computer simulations, particularly in multi-component solvents. Instead, their forces and states can be studied by liquid state statistical mechanics. However, past such approaches, such as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, were limited to modeling proteins as spheres, and contained no microscopic structure-property relations. Recently, this limitation has been partly overcome by bringing the powerful Wertheim theory of associating molecules to bear on protein association equilibria. Here, we review these developments.

Characterizing Protein-Protein Interactions and Viscosity of a Monoclonal Antibody from Low to High Concentration Using Small-Angle X-ray Scattering and Molecular Dynamics Simulations

Understanding protein-protein interactions and formation of reversible oligomers (clusters) in concentrated monoclonal antibody (mAb) solutions is necessary for designing stable, low viscosity (η) concentrated formulations for processing and subcutaneous injection. Here we characterize the strength (K) of short-range anisotropic attractions (SRA) for 75-200 mg/mL mAb2 solutions at different pH and cosolute conditions by analyzing structure factors (Seff(q)) from small-angle X-ray scattering (SAXS) using coarse-grained molecular dynamics simulations. Best fit simulations additionally provide cluster size distributions, fractal dimensions, cluster occluded volume, and mAb coordination numbers. These equilibrium properties are utilized in a model to account for increases in viscosity caused by occluded volume in the clusters (packing effects) and dissipation of stress across lubricated fractal clusters. Seff(q) is highly sensitive to K at 75 mg/mL where mAbs can mutually align to form SRA contacts but becomes less sensitive at 200 mg/mL as steric repulsion due to packing becomes dominant. In contrast, η at 200 mg/mL is highly sensitive to SRA and the average cluster size from SAXS/simulation, which is observed to track the cluster relaxation time from shear thinning. By analyzing the distribution of sub-bead hot spots on the 3D mAb surface, we identify a strongly attractive hydrophobic patch in the complementarity determining region (CDR) at pH 4.5 that contributes to the high K and consequently large cluster sizes and high η. Adding NaCl screens electrostatic interactions and increases the impact of hydrophobic attraction on cluster size and raises η, whereas nonspecific binding of Arg attenuates all SRA, reducing η. The hydrophobic patch is absent at higher pH values, leading to smaller K, smaller clusters, and lower η. This work constitutes a first attempt to use SAXS and CG modeling to link both structural and rheological properties of concentrated mAb solutions to the energetics of specific hydrophobic patches on mAb surfaces. As such, our work opens an avenue for future research, including the possibility of designing coarse-grained models with physically meaningful interacting hot spots.

Subclass Effects on Self-Association and Viscosity of Monoclonal Antibodies at High Concentrations

The effects of a subclass of monoclonal antibodies (mAbs) on protein-protein interactions, formation of reversible oligomers (clusters), and viscosity (η) are not well understood at high concentrations. Herein, we quantify a short-range anisotropic attraction between the complementarity-determining region (CDR) and CH3 domains (K_CDR-CH3) for vedolizumab IgG1, IgG2, or IgG4 subclasses by fitting small-angle X-ray scattering (SAXS) structure factor S_eff(q) data with an extensive library of 12-bead coarse-grained (CG) molecular dynamics simulations. The K_CDR-CH3 bead attraction strength was isolated from the strength of long-range electrostatic repulsion for the full mAb, which was determined from the theoretical net charge and a scaling parameter ψ to account for solvent accessibility and ion pairing. At low ionic strength (IS), the strongest short-range attraction (K_CDR-CH3) and consequently the largest clusters and highest η were observed with IgG1, the subclass with the most positively charged CH3 domain. Furthermore, the trend in K_CDR-CH3 with the subclass followed the electrostatic interaction energy between the CDR and CH3 regions calculated with the BioLuminate software using the 3D mAb structure and molecular interaction potentials. Whereas the equilibrium cluster size distributions and fractal dimensions were determined from fits of SAXS with the MD simulations, the degree of cluster rigidity under flow was estimated from the experimental η with a phenomenological model. For the systems with the largest clusters, especially IgG1, the inefficient packing of mAbs in the clusters played the largest role in increasing η, whereas for other systems, the relative contribution from stress produced by the clusters was more significant. The ability to relate η to short-range attraction from SAXS measurements at high concentrations and to theoretical characterization of electrostatic patches on the 3D surface is not only of fundamental interest but also of practical value for mAb discovery, processing, formulation, and subcutaneous delivery.

Conformational Changes and Drivers of Monoclonal Antibody Liquid-Liquid Phase Separation

Liquid-liquid phase separation is a phenomenon within biology whereby proteins can separate into dense and more dilute phases with distinct properties. Three antibodies that undergo liquid-liquid phase separation were characterized in the protein-rich and protein-poor phases. In comparison to the protein-poor phase, the protein-rich phase demonstrates more blue-shift tryptophan emissions and red-shifted amide I absorbances. Large changes involving conformational isomerization around disulfide bonds were observed using Raman spectroscopy. Amide I and protein fluorescence differences between the phases persisted to temperatures above the critical temperature but ceased at the temperature at which aggregation occurred. In addition, large changes occurred in the structural organization of water molecules within the protein-rich phase for all three antibodies. It is hypothesized that as the proteins have the same chemical potential in both phases, the protein viscosity is higher in the protein-rich phase resulting in slowed diffusion dependent protein aggregation in this phase. For all three antibodies we performed accelerated stability studies and found that the protein-rich phase aggregated at the same rate or slower than the protein-poor phase.

Characterizing Experimental Monoclonal Antibody Interactions and Clustering Using a Coarse-Grained Simulation Library and a Viscosity Model

Attractive protein-protein interactions in concentrated monoclonal antibody (mAb) solutions may lead to the formation of clusters that increase viscosity. Here, we propose an analytical model that relates mAb solution viscosity to clustering by accounting for the contributions of suboptimal mAb packing within a cluster and cluster fractal dimension. The influence of short-range, anisotropic attractions and long-range Coulombic repulsion on cluster properties is investigated by analyzing the cluster-size distributions, cluster fractal dimensions, radial distribution functions, and static structure factors from a library of coarse-grained molecular dynamics simulations. The library spans a vast range of mAb charges and attractive interactions in solutions of varying ionic strength. We present a framework for combining the viscosity model and simulation library to successfully characterize the attraction, repulsion, and clustering of an experimental mAb in three different pH and cosolute conditions by fitting the measured viscosity or structure factor from small-angle X-ray scattering. At low ionic strength, the cluster-size distribution is impacted by strong charges, and both the viscosity and net charge or structure factor and net charge must be considered to deconvolute the effects of short-range attraction and long-range repulsion.

Behaviour of the model antibody fluid constrained by rigid spherical obstacles: Effects of the obstacle-antibody attraction

This study investigates the behaviour of a fluid of monoclonal antibodies (mAbs) when trapped in a confinement represented by rigid spherical obstacles that attract antibodies. The antibody molecule is depicted as an assembly of seven hard spheres (7-bead model), organized to resemble a Y-shaped object. The model antibody has two Fab and one Fc domains located in the corners of letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pairs of interactions are effective. The confinement is formed by the randomly distributed hard-spheres fixed in space. The spherical obstacles, besides the size exclusion, interact with beads of the antibody molecules via the Yukawa attractive potential. We applied the combination of the scaled particle theory, replica Ornstein-Zernike equations, Wertheim's thermodynamic perturbation approach and the Flory-Stockmayer theory to calculate: (i) the phase diagram of the liquid-liquid phase separation and the percolation threshold, (ii) the cluster size distributions, and (iii) the second virial coefficient of the protein fluid distributed among the obstacles. All these quantities were calculated as functions of the strength of the attraction between the monoclonal antibodies, and the monoclonal antibodies and obstacles. The conclusion is that while the hard-sphere obstacles decrease the critical density and the critical temperature of the mAbs fluid, the effect of the protein-obstacle attraction is more complex. Adding an attractive potential to the obstacle-mAbs interaction first increases the wideness of the T*-ρ envelope. However, with the further increase of the obstacle-mAbs attraction intensity, we observe reversal of the effect, the T*-ρ curves become narrower. At some point, depending on the obstacle-mAbs interaction, the situation is observed where two different temperatures have the same fluid density (re-entry point). In all the cases shown here the critical point decreases below the value for the neat fluid, but the behaviour with respect to an increase of the strength of the obstacle-mAbs attraction is not monotonic. Yet another interesting phenomenon, known in the literature as an approach toward the "empty liquid" state, is observed. The stability of the "protein droplets", formed by the liquid-liquid phase separation, depends on their local environment and temperature.

BioMThermDB 1.0: Thermophysical Database of Proteins in Solutions

We present here a freely available web-based database, called BioMThermDB 1.0, of thermophysical and dynamic properties of various proteins and their aqueous solutions. It contains the hydrodynamic radius, electrophoretic mobility, zeta potential, self-diffusion coefficient, solution viscosity, and cloud-point temperature, as well as the conditions for those determinations and details of the experimental method. It can facilitate the meta-analysis and visualization of data, can enable comparisons, and may be useful for comparing theoretical model predictions with experiments.

The influence of excipients on the viscosity of monoclonal antibody solutions

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.

Computational models for studying physical instabilities in high concentration biotherapeutic formulations

Computational prediction of the behavior of concentrated protein solutions is particularly advantageous in early development stages of biotherapeutics when material availability is limited and a large set of formulation conditions needs to be explored. This review provides an overview of the different computational paradigms that have been successfully used in modeling undesirable physical behaviors of protein solutions with a particular emphasis on high-concentration drug formulations. This includes models ranging from all-atom simulations, coarse-grained representations to macro-scale mathematical descriptions used to study physical instability phenomena of protein solutions such as aggregation, elevated viscosity, and phase separation. These models are compared and summarized in the context of the physical processes and their underlying assumptions and limitations. A detailed analysis is also given for identifying protein interaction processes that are explicitly or implicitly considered in the different modeling approaches and particularly their relations to various formulation parameters. Lastly, many of the shortcomings of existing computational models are discussed, providing perspectives and possible directions toward an efficient computational framework for designing effective protein formulations.

New Model to Predict the Concentration-Dependent Viscosity of Monoclonal Antibody Solutions

Concentrated monoclonal antibody solutions exhibit high solution viscosity, which is experimentally measured to be ∼1-2 orders of magnitude higher than the viscosity of water. However, physical processes responsible for the high antibody viscosity are not fully understood. We show that fluid occlusion due to the trapped solvent molecules within the boundaries formed by the aggregated antibodies is responsible for the elevated solution viscosity. We develop a theory to predict the viscosity of monoclonal antibodies based on the geometry of the antibody molecule and the aggregate morphology. We validate our theory with experiments and highlight useful insights obtained from the viscosity equation which could help in controlling the drug viscosity at the molecular design stage itself.

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

The viscosity of a monoclonal antibody solution must be monitored and controlled as it can adversely affect product processing, packaging and administration. Engineering low viscosity mAb formulations is challenging as prohibitive amounts of material are required for concentrated solution analysis, and it is difficult to predict viscosity from parameters obtained through low-volume, high-throughput measurements such as the interaction parameter, k_D, and the second osmotic virial coefficient, B₂₂. As a measure encompassing the effect of intermolecular interactions on dilute solution viscosity, the Huggins coefficient, k_h, is a promising candidate as a parameter measureable at low concentrations, but indicative of concentrated solution viscosity. In this study, a differential viscometry technique is developed to measure the intrinsic viscosity, [η], and the Huggins coefficient, k_h, of protein solutions. To understand the effect of colloidal protein-protein interactions on the viscosity of concentrated protein formulations, the viscometric parameters are compared to k_D and B₂₂ of two mAbs, tuning the contributions of repulsive and attractive forces to the net protein-protein interaction by adjusting solution pH and ionic strength. We find a strong correlation between the concentrated protein solution viscosity and the k_h but this was not observed for the k_D or the b₂₂, which have been previously used as indicators of high concentration viscosity. Trends observed in [η] and k_h values as a function of pH and ionic strength are rationalised in terms of protein-protein interactions.

The Protein Folding Problem: The Role of Theory

The protein folding problem was first articulated as question of how order arose from disorder in proteins: How did the various native structures of proteins arise from interatomic driving forces encoded within their amino acid sequences, and how did they fold so fast? These matters have now been largely resolved by theory and statistical mechanics combined with experiments. There are general principles. Chain randomness is overcome by solvation-based codes. And in the needle-in-a-haystack metaphor, native states are found efficiently because protein haystacks (conformational ensembles) are funnel-shaped. Order-disorder theory has now grown to encompass a large swath of protein physical science across biology.

Cluster Percolation Causes Shear Thinning Behavior in Concentrated Solutions of Monoclonal Antibodies

High-concentration (>100 g/L) solutions of monoclonal antibodies (mAbs) are typically characterized by anomalously large solution viscosity and shear thinning behavior for strain rates ≥10³ s^-1. Here, the link between protein-protein interactions (PPIs) and the rheology of concentrated solutions of COE-03 and COE-19 mAbs is studied by means of static and dynamic light scattering and microfluidic rheometry. By comparing the experimental data with predictions based on the Baxter sticky hard-sphere model, we surprisingly find a connection between the observed shear thinning and the predicted percolation threshold. The longest shear relaxation time of mAbs was much larger than that of model sticky hard spheres within the same region of the phase diagram, which is attributed to the anisotropy of the mAb PPIs. Our results suggest that not only the strength but also the patchiness of short-range attractive PPIs should be explicitly accounted for by theoretical approaches aimed at predicting the shear rate-dependent viscosity of dense mAb solutions.

Comparison of Huggins Coefficients and Osmotic Second Virial Coefficients of Buffered Solutions of Monoclonal Antibodies

The Huggins coefficient kH is a well-known metric for quantifying the increase in solution viscosity arising from intermolecular interactions in relatively dilute macromolecular solutions, and there has been much interest in this solution property in connection with developing improved antibody therapeutics. While numerous kH measurements have been reported for select monoclonal antibodies (mAbs) solutions, there has been limited study of kH in terms of the fundamental molecular interactions that determine this property. In this paper, we compare measurements of the osmotic second virial coefficient B22, a common metric of intermolecular and interparticle interaction strength, to measurements of kH for model antibody solutions. This comparison is motivated by the seminal work of Russel for hard sphere particles having a short-range "sticky" interparticle interaction, and we also compare our data with known results for uncharged flexible polymers having variable excluded volume interactions because proteins are polypeptide chains. Our observations indicate that neither the adhesive hard sphere model, a common colloidal model of globular proteins, nor the familiar uncharged flexible polymer model, an excellent model of intrinsically disordered proteins, describes the dependence of kH of these antibodies on B22. Clearly, an improved understanding of protein and ion solvation by water as well as dipole-dipole and charge-dipole effects is required to understand the significance of kH from the standpoint of fundamental protein-protein interactions. Despite shortcomings in our theoretical understanding of kH for antibody solutions, this quantity provides a useful practical measure of the strength of interprotein interactions at elevated protein concentrations that is of direct significance for the development of antibody formulations that minimize the solution viscosity.

Dissecting the molecular basis of high viscosity of monospecific and bispecific IgG antibodies

Some antibodies exhibit elevated viscosity at high concentrations, making them poorly suited for therapeutic applications requiring administration by injection such as subcutaneous or ocular delivery. Here we studied an anti-IL-13/IL-17 bispecific IgG₄ antibody, which has anomalously high viscosity compared to its parent monospecific antibodies. The viscosity of the bispecific IgG₄ in solution was decreased by only ~30% in the presence of NaCl, suggesting electrostatic interactions are insufficient to fully explain the drivers of viscosity. Intriguingly, addition of arginine-HCl reduced the viscosity of the bispecific IgG₄ by ~50% to its parent IgG level. These data suggest that beyond electrostatics, additional types of interactions such as cation-π and/or π-π may contribute to high viscosity more significantly than previously understood. Molecular dynamics simulations of antibody fragments in the mixed solution of free arginine and explicit water were conducted to identify hotspots involved in self-interactions. Exposed surface aromatic amino acids displayed an increased number of contacts with arginine. Mutagenesis of the majority of aromatic residues pinpointed by molecular dynamics simulations effectively decreased the solution's viscosity when tested experimentally. This mutational method to reduce the viscosity of a bispecific antibody was extended to a monospecific anti-GCGR IgG₁ antibody with elevated viscosity. In all cases, point mutants were readily identified that both reduced viscosity and retained antigen-binding affinity. These studies demonstrate a new approach to mitigate high viscosity of some antibodies by mutagenesis of surface-exposed aromatic residues on complementarity-determining regions that may facilitate some clinical applications.

Toward Drug-Like Multispecific Antibodies by Design

The success of antibody therapeutics is strongly influenced by their multifunctional nature that couples antigen recognition mediated by their variable regions with effector functions and half-life extension mediated by a subset of their constant regions. Nevertheless, the monospecific IgG format is not optimal for many therapeutic applications, and this has led to the design of a vast number of unique multispecific antibody formats that enable targeting of multiple antigens or multiple epitopes on the same antigen. Despite the diversity of these formats, a common challenge in generating multispecific antibodies is that they display suboptimal physical and chemical properties relative to conventional IgGs and are more difficult to develop into therapeutics. Here we review advances in the design and engineering of multispecific antibodies with drug-like properties, including favorable stability, solubility, viscosity, specificity and pharmacokinetic properties. We also highlight emerging experimental and computational methods for improving the next generation of multispecific antibodies, as well as their constituent antibody fragments, with natural IgG-like properties. Finally, we identify several outstanding challenges that need to be addressed to increase the success of multispecific antibodies in the clinic.

Aggregation, liquid-liquid phase separation, and percolation behaviour of a model antibody fluid constrained by hard-sphere obstacles

This study is concerned with the behaviour of proteins within confinement created by hard-sphere obstacles. An individual antibody molecule is depicted as an assembly of seven hard spheres, organized to resemble a Y-shaped (on average) antibody (7-bead model) protein. For comparison with other studies we, in one case, model the protein as a hard sphere decorated by three short-range attractive sites. The antibody has two Fab and one Fc domains located in the corners of the letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pair interactions are possible. The confinement is formed by the randomly distributed hard-sphere obstacles fixed in space. Aside from size exclusion, the obstacles do not interact with antibodies, but they affect the protein-protein correlation. We used a combination of the scaled-particle theory, Wertheim's thermodynamic perturbation theory and the Flory-Stockmayer theory to calculate: (i) the second virial coefficient of the protein fluid, (ii) the percolation threshold, (iii) cluster size distributions, and (iv) the liquid-liquid phase separation as a function of the strength of the various pair interactions of the protein and the model parameters, such as protein concentration and the packing fraction of obstacles. The conclusion is that hard-sphere obstacles strongly decrease the critical density and also, but to a much lesser extent, the critical temperature. Also, the confinement enhances clustering, making the percolating region broader. The effect depends on the model parameters, such as the packing fraction of obstacles η0, the inter-site interaction strength εIJ, and the ratio between the size of the obstacle σ0 and the size of one bead of the model antibody σhs; the value of this ratio is varied here from 2 to 5. Interestingly, at low to moderate packing fractions of obstacles, the second virial coefficient first slightly decreases (destabilization), and the slope depends on the observation temperature, but then at higher values of η0 it increases. The calculated values of the second virial coefficient also depend on the size of the obstacles.

Multiscale Coarse-Grained Approach to Investigate Self-Association of Antibodies

Self-association of therapeutic monoclonal antibodies (mabs) are thought to modulate the undesirably high viscosity observed in their concentrated solutions. Computational prediction of such a self-association behavior is advantageous early during mab drug candidate selection when material availability is limited. Here, we present a coarse-grained (CG) simulation method that enables microsecond molecular dynamics simulations of full-length antibodies at high concentrations. The proposed approach differs from others in two ways: first, charges are assigned to CG beads in an effort to reproduce molecular multipole moments and charge asymmetry of full-length antibodies instead of only localized charges. This leads to great improvements in the agreement between CG and all-atom electrostatic fields. Second, the distinctive hydrophobic character of each antibody is incorporated through empirical adjustments to the short-range van der Waals terms dictated by cosolvent all-atom molecular dynamics simulations of antibody variable regions. CG simulations performed on a set of 15 different mabs reveal that diffusion coefficients in crowded environments are markedly impacted by intermolecular interactions. Diffusion coefficients computed from the simulations are in correlation with experimentally measured observables, including viscosities at a high concentration. Further, we show that the evaluation of electrostatic and hydrophobic characters of the mabs is useful in predicting the nonuniform effect of salt on the viscosity of mab solutions. This CG modeling approach is particularly applicable as a material-free screening tool for selecting antibody candidates with desirable viscosity properties.

Coarse-Grained Molecular Dynamics Simulations for Understanding the Impact of Short-Range Anisotropic Attractions on Structure and Viscosity of Concentrated Monoclonal Antibody Solutions

Understanding protein-protein interactions in concentrated therapeutic monoclonal antibody (mAb) solutions is desirable for improved drug discovery, processing, and administration. Here, we deduce both the net protein charge and the magnitude and geometry of short-ranged, anisotropic attractions of a mAb across multiple concentrations and cosolute conditions by comparing structure factors S(q) obtained from small-angle X-ray scattering experiments with those from molecular dynamics (MD) simulations. The simulations, which utilize coarse-grained 12-bead models exhibiting a uniform van der Waals attraction, uniform electrostatic repulsion, and short-range attractions between specific beads, are versatile enough to fit S(q) of a wide range of protein concentrations and ionic strength with the same charge on each bead and a single anisotropic short-range attraction strength. Cluster size distributions (CSDs) obtained from best fit simulations reveal that the experimental structure is consistent with small reversible oligomers in even low viscosity systems and help quantify the impact of these clusters on viscosity. The ability to systematically use experimental S(q) data together with MD simulations to discriminate between different possible protein-protein interactions, as well as to predict viscosities from protein CSDs, is beneficial for designing mAbs and developing formulation strategies that avoid high viscosities and aggregation at high concentration.

Potential and limits of a colloid approach to protein solutions

Looking at globular proteins with the eyes of a colloid scientist has a long tradition, in fact a significant part of the early colloid literature was focused on protein solutions. However, it has also been recognized that proteins are much more complex than the typical hard sphere-like synthetic model colloids. Proteins are not perfect spheres, their interaction potentials are in general not isotropic, and using theories developed for such particles are thus clearly inadequate in many cases. In this perspective article, we now take a closer look at the field. In particular, we reflect on the fact that modern colloid science has been undergoing a tremendous development, where a multitude of novel systems have been developed in the lab and in silico. During the last decade we have seen a rapidly increasing number of reports on the synthesis of anisotropic, patchy and/or responsive synthetic colloids, that start to resemble their complex biological counterparts. This experimental development is also reflected in a corresponding theoretical and simulation effort. The experimental and theoretical toolbox of colloid science has thus rapidly expanded, and there is obviously an enormous potential for an application of these new concepts to protein solutions, which has already been realized and harvested in recent years. In this perspective article we make an attempt to critically discuss the exploitation of colloid science concepts to better understand protein solutions. We not only consider classical applications such as the attempt to understand and predict solution stability and phase behaviour, but also discuss new challenges related to the dynamics, flow behaviour and liquid-solid transitions found in concentrated or crowded protein solutions. It not only aims to provide an overview on the progress in experimental and theoretical (bio)colloid science, but also discusses current shortcomings in our ability to correctly reproduce and predict the structural and dynamic properties of protein solutions based on such a colloid approach.

Self-diffusion of a highly concentrated monoclonal antibody by fluorescence correlation spectroscopy: insight into protein-protein interactions and self-association

The dynamic behavior of monoclonal antibodies (mAbs) at high concentration provides insight into protein microstructure and protein-protein interactions (PPI) that influence solution viscosity and protein stability. At high concentration, interpretation of the collective-diffusion coefficient Dc, as determined by dynamic light scattering (DLS), is highly challenging given the complex hydrodynamics and PPI at close spacings. In contrast, self-diffusion of a tracer particle by Brownian motion is simpler to understand. Herein, we develop fluorescence correlation spectroscopy (FCS) for the measurement of the long-time self-diffusion of mAb2 over a wide range of concentrations and viscosities in multiple co-solute formulations with varying PPI. The normalized self-diffusion coefficient D0/Ds (equal to the microscopic relative viscosity ηeff/η0) was found to be smaller than η/η0. Smaller ratios of the microscopic to macroscopic viscosity (ηeff/η) are attributed to a combination of weaker PPI and less self-association. The interaction parameters extracted from fits of D0/Ds with a length scale dependent viscosity model agree with previous measurements of PPI by SLS and SAXS. Trends in the degree of self-association, estimated from ηeff/η with a microviscosity model, are consistent with oligomer sizes measured by SLS. Finally, measurements of collective diffusion and osmotic compressibility were combined with FCS data to demonstrate that the changes in self-diffusion between formulations are due primarily to changes in the protein-protein friction in these systems, and not to protein-solvent friction. Thus, FCS is a robust and accessible technique for measuring mAb self-diffusion, and, by extension, microviscosity, PPI and self-association that govern mAb solution dynamics.

A Colloid Approach to Self-Assembling Antibodies

Concentrated solutions of monoclonal antibodies have attracted considerable attention due to their importance in pharmaceutical formulations; yet, their tendency to aggregate and the resulting high viscosity pose considerable problems. Here we tackle this problem by a soft condensed matter physics approach, which combines a variety of experimental measurements with a patchy colloid model, amenable of analytical solution. We thus report results of structural antibodies and dynamic properties obtained through scattering methods and microrheological experiments. We model the data using a colloid-inspired approach, explicitly taking into account both the anisotropic shape of the molecule and its charge distribution. Our simple patchy model is able to disentangle self-assembly and intermolecular interactions and to quantitatively describe the concentration-dependence of the osmotic compressibility, collective diffusion coefficient, and zero shear viscosity. Our results offer new insights on the key problem of antibody formulations, providing a theoretical and experimental framework for a quantitative assessment of the effects of additional excipients or chemical modifications and a prediction of the resulting viscosity.

Cluster Formation and Entanglement in the Rheology of Antibody Solutions

Antibody solutions deviate from the dynamical and rheological response expected for globular proteins, especially as the volume fraction is increased. Experimental evidence shows that antibodies can reversibly bind to each other via F_ab and F_c domains and form larger structures (clusters) of several antibodies. Here, we present a microscopic equilibrium model to account for the distribution of cluster sizes. Antibody clusters are modeled as polymers that can grow via reversible bonds either between two F_ab domains or between F_ab and F_c domain. We propose that the dynamical and rheological behavior is determined by molecular entanglements of the clusters. This entanglement does not occur at low concentrations where antibody-antibody binding contributes to the viscosity by increasing the effective size of the particles. The model explains the observed shear-thinning behavior of antibody solutions.

Protein-Protein Interactions of Highly Concentrated Monoclonal Antibody Solutions via Static Light Scattering and Influence on the Viscosity

The ability to design and formulate mAbs to minimize attractive interactions at high concentrations is important for protein processing, stability, and administration, particularly in subcutaneous delivery, where high viscosities are often challenging. The strength of protein-protein interactions (PPIs) of an IgG1 and IgG4 monoclonal antibody (mAb) from low to high concentration was determined by static light scattering (SLS) and used to understand viscosity data. The PPI were tuned using NaCl and five organic ionic co-solutes. The PPI strength was quantified by the normalized structure factor S(0)/ S(0)_HS and Kirkwood-Buff integral G₂₂/ G_22,HS (HS = hard sphere) determined from the SLS data and also by fits with (1) a spherical Yukawa potential and (2) an interacting hard sphere (IHS) model, which describes attraction in terms of hypothetical oligomers. The IHS model was better able to capture the scattering behavior of the more strongly interacting systems (mAb and/or co-solute) than the spherical Yukawa potential. For each descriptor of PPI, linear correlations were obtained between the viscosity at high concentration (200 mg/mL) and the interaction strengths evaluated both at low (20 mg/mL) and high concentrations (200 mg/mL) for a given mAb. However, the only parameter that provided a correlation across both mAbs was the oligomer mass ratio ( m_oligomer/ m_{monomer+dimer}) from the IHS model, indicating the importance of self-association (in addition to the direct influence of the attractive PPI) on the viscosity.

Patchy Particle Models to Understand Protein Phase Behavior

In this chapter we describe numerical procedures to evaluate the phase behavior of coarse-grained models for globular proteins. Specifically we focus on models based on hard spheres complemented with "patchy-like" anisotropic interactions that mimic the attractive regions on the surface of the proteins. We introduce the basic elements of grand canonical Monte Carlo simulations for these types of models in which rotational and translational moves need to be accounted for. We describe the techniques for the estimation of the fluid-fluid critical point, coexistence curve, and fluid-crystal boundaries. We also discuss an efficient method for the evaluation of the fluid-fluid phase diagram: the successive umbrella sampling technique. Finally we briefly describe how to exploit the same tools for the calculation of the phase behavior of protein binary mixtures.

Modeling the depletion effect caused by an addition of polymer to monoclonal antibody solutions

We present a theoretical study of colloidal stability of the model mixtures of monoclonal antibody molecules and non-adsorbing (no polymer-protein attraction) polymers. The antibodies are pictured as an assembly of seven hard spheres assuming a Y-like shape. Polymers present in the mixture are modeled as chain-like molecules having from 32 up to 128 monomers represented as hard spheres. We use Wertheim's thermodynamic perturbation theory to construct the two molecular species and to calculate measurable properties. The calculations are performed in the osmotic ensemble. In view that no direct attractive interaction is present in the model Hamiltonian, we only account for the entropic contribution to the phase equilibrium. We calculate chemical potentials and the equation of state for the model mixture to determine the liquid-liquid part of the phase diagram. We investigate how the critical antibody number density depends on the degree of polymerization and the bead size ratio of the polymer and protein components. The model mixture qualitatively correctly predicts some basic features of real systems. The effects of the model 'protein' geometry, that is the difference in results for the flexible Y-shaped protein versus the rigid spherical one, are also examined.

Theory for the Liquid-Liquid Phase Separation in Aqueous Antibody Solutions

This study presents the theory for liquid-liquid phase separation for systems of molecules modeling monoclonal antibodies. Individual molecule is depicted as an assembly of seven hard spheres, organized to mimic the Y-shaped antibody. We consider the antibody-antibody interactions either through Fab, Fab' (two Fab fragments may be different), or Fc domain. Interaction between these three domains of the molecule (hereafter denoted as A, B, and C, respectively) is modeled by a short-range square-well attraction. To obtain numerical results for the model under study, we adapt Wertheim's thermodynamic perturbation theory. We use this model to calculate the liquid-liquid phase separation curve and the second virial coefficient B2. Various interaction scenarios are examined to see how the strength of the site-site interactions and their range shape the coexistence curve. In the asymmetric case, where an attraction between two sites is favored and the interaction energies for the other sites kept constant, critical temperature first increases and than strongly decreases. Some more microscopic information, for example, the probability for the particular two sites to be connected, has been calculated. Analysis of the experimental liquid-liquid phase diagrams, obtained from literature, is presented. In addition, we calculate the second virial coefficient under conditions leading to the liquid-liquid phase separation and present this quantity on the graph B2 versus protein concentration.