Electrostatically Mediated Protein-Protein Interactions for Monoclonal Antibodies: A Combined Experimental and Coarse-Grained Molecular Modeling Approach

Quantifying Protein Shape to Elucidate Its Influence on Solution Viscosity in High-Concentration Electrolyte Solutions

Therapeutic proteins with a high concentration and low viscosity are highly desirable for subcutaneous and certain local injections. The shape of a protein is known to influence solution viscosity; however, the precise quantification of protein shape and its relative impact compared to other factors like charge-charge interactions remains unclear. In this study, we utilized seven model proteins of varying shapes and experimentally determined their shape factors (v) based on Einstein's viscosity theory, which correlate strongly with the ratios of the proteins' surface area to the 2/3 power of their respective volumes, based on protein crystal structures resolved experimentally or predicted by AlphaFold. This finding confirms the feasibility of computationally estimating protein shape factors from amino acid sequences alone. Furthermore, our results demonstrated that, in high-concentration electrolyte solutions, a more spherical protein shape increases the protein's critical concentration (C*), the transition concentration beyond which protein viscosity increases exponentially relative to concentration increases. In summary, our work elucidates protein shape as a key determinant of solution viscosity through quantitative analysis and comparison with other contributing factors. This provides insights into molecular engineering strategies to optimize the molecular design of therapeutic proteins, thus optimizing their viscosity.

Electrostatically Mediated Attractive Self-Interactions and Reversible Self-Association of Fc-Fusion Proteins

Attractive self-interactions and reversible self-association are implicated in many problematic solution behaviors for therapeutic proteins, such as irreversible aggregation, elevated viscosity, phase separation, and opalescence. Protein self-interactions and reversible oligomerization of two Fc-fusion proteins (monovalent and bivalent) and the corresponding fusion partner protein were characterized experimentally with static and dynamic light scattering as a function of pH (5 and 6.5) and ionic strength (10 mM to at least 300 mM). The fusion partner protein and monovalent Fc-fusion each displayed net attractive electrostatic self-interactions at pH 6.5 and net repulsive electrostatic self-interactions at pH 5. Solutions of the bivalent Fc-fusion contained higher molecular weight species that prevented quantification of typical interaction parameters (B22 and kD). All three of the proteins displayed reversible self-association at pH 6.5, where oligomers dissociated with increased ionic strength. Coarse-grained molecular simulations were used to model the self-interactions measured experimentally, assess net self-interactions for the bivalent Fc-fusion, and probe the specific electrostatic interactions between charged amino acids that were involved in attractive electrostatic self-interactions. Mayer-weighted pairwise electrostatic energies from the simulations suggested that attractive electrostatic self-interactions at pH 6.5 for the two Fc-fusion proteins were due to cross-domain interactions between the fusion partner domain(s) and the Fc domain.

Computational Screening for mAb Colloidal Stability with Coarse-Grained, Molecular-Scale Simulations

Monoclonal antibodies (mAbs) are an important modality of protein therapeutics with broad applications for numerous diseases. However, colloidal instabilities occurring at high protein concentrations can limit the ability to develop stable, high-concentration liquid dosage forms that are required for patient-centric, device-mediated products. Therefore, it is advantageous to identify colloidally stable mAbs early in the discovery process to ensure that they are selected for development. Experimental screening for colloidal stability can be time- and resource-consuming and is most feasible at the later stages of drug development due to material requirements. Alternatively, computational approaches have emerging potential to provide efficient screening and focus developmental efforts on mAbs with the greatest developability potential, while providing mechanistic relationships for colloidal instability. In this work, coarse-grained, molecular-scale models were fine-tuned to screen for colloidal stability at amino-acid resolution. This model parameterization provides a framework to screen for mAb self-interactions and extrapolate to bulk solution behavior. This approach was applied to a wide array of mAbs under multiple buffer conditions, demonstrating the utility of the presented computational approach to augment early candidate screening and later formulation strategies for protein therapeutics.

Molecular Dynamics Simulation of an Iron(III) Binding Site on the Fc Domain of IgG1 Relevant for Visible Light-Induced Protein Fragmentation

Molecular dynamics simulations were employed to investigate the interaction between Fe(III) and an iron-binding site composed of THR259, ASP252, and GLU261 on the Fc domain of an IgG1. The goal was to provide microscopic mechanistic information for the photochemical, iron-dependent site-specific oxidative fragmentation of IgG1 at THR259 reported in our previous paper. The distance between Fe(III) and residues of interest as well as the binding pocket size was examined for both protonated and deprotonated THR259. The Fe(III) binding free energy (ΔG) was estimated by using an umbrella sampling approach. The pKa shift of the THR259 hydroxyl group caused by the presence of nearby Fe(III) was estimated based on a thermodynamic cycle. The simulation results show that Fe(III) resides inside the proposed binding pocket and profoundly changes the pocket configuration. The ΔG values indicate that the pocket possesses a strong binding affinity for Fe(III). Furthermore, Fe(III) profoundly lowers the pKa value of the THR259 hydroxyl group by 5.4 pKa units.

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.

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.

Development of in silico models to predict viscosity and mouse clearance using a comprehensive analytical data set collected on 83 scaffold-consistent monoclonal antibodies

Biologic drug discovery pipelines are designed to deliver protein therapeutics that have exquisite functional potency and selectivity while also manifesting biophysical characteristics suitable for manufacturing, storage, and convenient administration to patients. The ability to use computational methods to predict biophysical properties from protein sequence, potentially in combination with high throughput assays, could decrease timelines and increase the success rates for therapeutic developability engineering by eliminating lengthy and expensive cycles of recombinant protein production and testing. To support development of high-quality predictive models for antibody developability, we designed a sequence-diverse panel of 83 effector functionless IgG1 antibodies displaying a range of biophysical properties, produced and formulated each protein under standard platform conditions, and collected a comprehensive package of analytical data, including in vitro assays and in vivo mouse pharmacokinetics. We used this robust training data set to build machine learning classifier models that can predict complex protein behavior from these data and features derived from predicted and/or experimental structures. Our models predict with 87% accuracy whether viscosity at 150 mg/mL is above or below a threshold of 15 centipoise (cP) and with 75% accuracy whether the area under the plasma drug concentration-time curve (AUC0-672 h) in normal mouse is above or below a threshold of 3.9 × 106 h x ng/mL.

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.

Electrostatically Driven Protein-Protein Interactions: Quantitative Prediction of Second Osmotic Virial Coefficients to Aid Antibody Design

Electrostatically driven attractions between proteins can result in issues for therapeutic protein formulations such as solubility limits, aggregation, and high solution viscosity. Previous work showed that a model monoclonal antibody displayed large and potentially problematic electrostatically driven attractions at typical pH (5-8) and ionic strength conditions (∼10-100 mM). Molecular simulations of a hybrid coarse-grained model (1bC/D, one bead per charged site and per domain) were used to predict potential point mutations to identify key charge changes (charge-to-neutral or charge-swap) that could greatly reduce the net attractive protein-protein self-interactions. A series of variants were tested experimentally with static and dynamic light scattering to quantify interactions and compared to model predictions at low and intermediate ionic strength. Differential scanning calorimetry and circular dichroism confirmed minimal impact on structural or thermal stability of the variants. The model provided quantitative/semiquantitative predictions of protein self-interactions compared to experimental results as well as showed which amino acid pairings or groups had the most impact.

Self-Interactions of Two Monoclonal Antibodies: Small-Angle X-ray Scattering, Light Scattering, and Coarse-Grained Modeling

Using light scattering (LS), small-angle X-ray scattering (SAXS), and coarse-grained Monte Carlo (MC) simulations, we studied the self-interactions of two monoclonal antibodies (mAbs), PPI03 and PPI13. With LS measurements, we obtained the osmotic second virial coefficient, B₂₂, and the molecular weight, M_w, of the two mAbs, while with SAXS measurements, we studied the mAbs' self-interaction behavior in the high protein concentration regime up to 125 g/L. Through SAXS-derived coarse-grained representations of the mAbs, we performed MC simulations with either a one-protein or a two-protein model to predict B₂₂. By comparing simulation and experimental results, we validated our models and obtained insights into the mAbs' self-interaction properties, highlighting the role of both ion binding and charged patches on the mAb surfaces. Our models provide useful information about mAbs' self-interaction properties and can assist the screening of conditions driving to colloidal stability.

Toward a Suite of Coarse-Grained Models for Molecular Simulation of Monoclonal Antibodies and Therapeutic Proteins

A series of coarse-grained models for molecular simulation of proteins are considered, with emphasis on the application of predicting protein-protein self-interactions for monoclonal antibodies (MAbs). As an illustrative example and for quantitative comparison, the models are used to predict osmotic virial coefficients over a broad range of attractive and repulsive self-interactions and solution conditions for a series of MAbs where the second osmotic virial coefficient has been experimentally determined in prior work. The models are compared based on how well they can predict experimental behavior, their computational burdens, and scalability. An intermediate-resolution model is also introduced that can capture specific electrostatic interactions with improved efficiency and similar or improved accuracy when compared to the previously published models. Guidance is included for the selection of coarse-grained models more generally for capturing a balance of electrostatic, steric, and short-ranged nonelectrostatic interactions for proteins from low to high concentrations.

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.

Molecular forces governing protein-protein interaction: Structure-function relationship of complexes protein in the food industry

The application of protein-protein interaction (PPI) has been widely used in various industries, such as food, nutraceutical, and pharmaceutical. A deeper understanding of PPI is needed, and the molecular forces governing proteins and their interaction must be explained. The design of new structures with improved functional properties, e.g., solubility, emulsion, and gelation, has been fueled by the development of structural and colloidal building blocks. In this review, the molecular forces of protein structures are discussed, followed by the relationship between molecular force and structure, ways of a bind of proteins together in solution or at the interface, and functional properties. A more detailed look is thus taken at the relationship between the various influencing factors on molecular forces involved in PPI. These factors include protein properties, such as types, concentration, and mixing ratio, and solvent conditions, such as ionic strength and pH. This review also summarizes methods tha1t are capable of identifying molecular forces in protein and PPI, as well as characterizing protein structure.

Product-Specific Impact of Viscosity Modulating Formulation Excipients During Ultra-High Concentration Biotherapeutics Drug Product Development

Developing ultra-high concentration biotherapeutics drug products can be challenging due to increased viscosity, processing, and stability issues. Excipients used to alleviate these concerns are traditionally evaluated at lower protein concentrations. This study investigates whether classically known modulators of stability and viscosity at low (<50 mg/mL) to high (>50 - 150 mg/mL) protein concentrations are beneficial in ultra-high (>150 mg/mL) concentration protein formulations and drug products. This study evaluates the effect of arginine monohydrochloride, proline, and lysine monohydrochloride on viscosity and concentratability at different high and ultra-high protein concentrations using a monoclonal antibody, mAbN, formulation as a candidate protein system. The effect of excipients on the viscosity and concentratability (rate and extent) was different at high versus ultra-high protein concentrations. These results highlight that classical excipients in literature known to modulate protein interactions at low protein concentrations and reduce viscosity at high protein concentrations may need to be evaluated at target protein concentrations in a product-specific manner while developing ultra-high concentration biologics drug products.

Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation

Computational studies play an increasingly important role in chemistry and biophysics, mainly thanks to improvements in hardware and algorithms. In drug discovery and development, computational studies can reduce the costs and risks of bringing a new medicine to market. Computational simulations are mainly used to optimize promising new compounds by estimating their binding affinity to proteins. This is challenging due to the complexity of the simulated system. To assess the present and future value of simulation for drug discovery, we review key applications of advanced methods for sampling complex free-energy landscapes at near nonergodicity conditions and for estimating the rate coefficients of very slow processes of pharmacological interest. We outline the statistical mechanics and computational background behind this research, including methods such as steered molecular dynamics and metadynamics. We review recent applications to pharmacology and drug discovery and discuss possible guidelines for the practitioner. Recent trends in machine learning are also briefly discussed. Thanks to the rapid development of methods for characterizing and quantifying rare events, simulation's role in drug discovery is likely to expand, making it a valuable complement to experimental and clinical approaches.

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.

Resolving Liquid-Liquid Phase Separation for a Peptide Fused Monoclonal Antibody by Formulation Optimization

Liquid-liquid phase separation (LLPS) of protein solutions has been usually related to strong protein-protein interactions (PPI) under certain conditions. For the first time, we observed the LLPS phenomenon for a novel protein modality, peptide-fused monoclonal antibody (pmAb). LLPS emerged within hours between pH 6.0 to 7.0 and disappeared when solution pH values decreased to pH 5.0 or lower. Negative values of interaction parameter (k_D) and close to zero values of zeta potential (ζ) were correlated to LLPS appearance. However, between pH 6.0 to 7.0, a strong electrostatic repulsion force was expected to potentially avoid LLPS based on the sequence predicted pI value, 8.35. Surprisingly, this is significantly away from experimentally determined pI, 6.25, which readily attributes the LLPS appearances of pmAb to the attenuated electrostatic repulsion force. Such discrepancy between experiment and prediction reminds the necessity of actual measurement for a complicated modality like pmAb. Furthermore, significant protein degradation took place upon thermal stress at pH 5.0 or lower. Therefore, the effects of pH and selected excipients on the thermal stability of pmAb were further assessed. A formulation consisting of arginine at pH 6.5 successfully prevented the appearance of LLPS and enhanced its thermal stability at 40 °C for pmAb. In conclusion, we have reported LLPS for a pmAb and successfully resolved the issue by optimizing formulation with aids from PPI characterization.

A single molecular descriptor to predict solution behavior of therapeutic antibodies

Despite the therapeutic success of monoclonal antibodies (mAbs), early identification of developable mAb drug candidates with optimal manufacturability, stability, and delivery attributes remains elusive. Poor solution behavior, which manifests as high solution viscosity or opalescence, profoundly affects the developability of mAb drugs. Using a diverse dataset of 59 mAbs, including 43 approved products, and an array of molecular descriptors spanning colloidal, conformational, charge-based, hydrodynamic, and hydrophobic properties, we show that poor solution behavior is prevalent (>30%) in mAbs and is singularly predicted (>90%) by the diffusion interaction parameter (k _D), a dilute-solution measure of colloidal self-interaction. No other descriptor, individually or in combination, was found to be as effective as k _D. We also show that well-behaved mAbs, a substantial subset of which bear high positive charge and pI, present no disadvantages with respect to pharmacokinetics in humans. Here, we provide a systematic framework with quantitative thresholds for selecting well-behaved therapeutic mAbs during drug discovery.

Identifying Key Residues That Drive Strong Electrostatic Attractions between Therapeutic Antibodies

Attractive electrostatic protein-protein interactions (PPI) necessarily involve identifying oppositely charged regions of the protein surface that interact favorably. This cannot be done reliably if one only considers a single protein in isolation unless there are obvious charge "patches" that result in extreme molecular dipoles. Prior work [ J. Pharm. Sci. 2019 , 108 , 120 - 132 ] identified three monoclonal antibodies (MAbs) that displayed experimental behavior ranging from net repulsive to strongly attractive electrostatic interactions. The present work provides a systematic computational approach for identifying the origin of diverse PPI, in terms of which sets of amino acids or individual amino acids are most influential, and determining if there are different patterns of pairwise amino acid interaction "maps" that result in different behaviors. The charge was eliminated computationally, one by one, for each charged residue in the wild-type sequences, which resulted in predicted changes in the second osmotic virial coefficient. The results highlight interaction "maps" that correspond to cases with qualitatively different net electrostatic PPI for the different MAbs and solution conditions, as well as key sets of residues that contribute to strongly attractive PPI. A more computationally efficient method is also proposed to identify key amino acids based on Mayer-weighted interaction energies.

Determination of Protein-Protein Interactions in a Mixture of Two Monoclonal Antibodies

The coformulation of monoclonal antibody (mAb) mixtures provides an attractive route to achieving therapeutic efficacy where the targeting of multiple epitopes is necessary. Controlling and predicting the behavior of such mixtures requires elucidating the molecular basis for the self- and cross-protein-protein interactions and how they depend on solution variables. While self-interactions are now beginning to be well understood, systematic studies of cross-interactions between mAbs in solution do not exist. Here, we have used static light scattering to measure the set of self- and cross-osmotic second virial coefficients in a solution containing a mixture of two mAbs, mAbA and mAbB, as a function of ionic strength and pH. mAbB exhibits strong association at a low ionic strength, which is attributed to an electrostatic attraction that is enhanced by the presence of a strong short-ranged attraction of nonelectrostatic origin. Under all solution conditions, the measured cross-interactions are intermediate self-interactions and follow similar patterns of behavior. There is a strong electrostatic attraction at higher pH values, reflecting the behavior of mAbB. Protein-protein interactions become more attractive with an increasing pH due to reducing the overall protein net charges, an effect that is attenuated with an increasing ionic strength due to the screening of electrostatic interactions. Under moderate ionic strength conditions, the reduced cross-virial coefficient, which reflects only the energetic contribution to protein-protein interactions, is given by a geometric average of the corresponding self-coefficients. We show the relationship can be rationalized using a patchy sphere model, where the interaction energy between sites i and j is given by the arithmetic mean of the i-i and j-j interactions. The geometric mean does not necessarily apply to all mAb mixtures and is expected to break down at a lower ionic strength due to the nonadditivity of electrostatic interactions.

Modeling Electrostatic Force in Protein-Protein Recognition

Electrostatic interactions are important for understanding molecular interactions, since they are long-range interactions and can guide binding partners to their correct binding positions. To investigate the role of electrostatic forces in molecular recognition, we calculated electrostatic forces between binding partners separated at various distances. The investigation was done on a large set of 275 protein complexes using recently developed DelPhiForce tool and in parallel, evaluating the total electrostatic force via electrostatic association energy. To accomplish the goal, we developed a method to find an appropriate direction to move one chain of protein complex away from its bound position and then calculate the corresponding electrostatic force as a function of separation distance. It is demonstrated that at large distances between the partners, the electrostatic force (magnitude and direction) is consistent among the protocols used and the main factors contributing to it are the net charge of the partners and their interfaces. However, at short distances, where partners form specific pair-wise interactions or de-solvation penalty becomes significant, the outcome depends on the precise balance of these factors. Based on the electrostatic force profile (force as a function of distance), we group the cases into four distinctive categories, among which the most intriguing is the case termed "soft landing." In this case, the electrostatic force at large distances is favorable assisting the partners to come together, while at short distance it opposes binding, and thus slows down the approach of the partners toward their physical binding.

Science and art of protein formulation development

Protein pharmaceuticals have become a significant class of marketed drug products and are expected to grow steadily over the next decade. Development of a commercial protein product is, however, a rather complex process. A critical step in this process is formulation development, enabling the final product configuration. A number of challenges still exist in the formulation development process. This review is intended to discuss these challenges, to illustrate the basic formulation development processes, and to compare the options and strategies in practical formulation development.

Predicting High-Concentration Interactions of Monoclonal Antibody Solutions: Comparison of Theoretical Approaches for Strongly Attractive Versus Repulsive Conditions

Nonspecific protein-protein interactions of a monoclonal antibody were quantified experimentally using light scattering from low to high protein concentrations (c₂) and compared with prior work for a different antibody that yielded qualitatively different behavior. The c₂ dependence of the excess Rayleigh ratio (R^ex) provided the osmotic second virial coefficient (B₂₂) at low c₂ and the static structure factor (S_q=0) at high c₂, as a function of solution pH, total ionic strength (TIS), and sucrose concentration. Net repulsive interactions were observed at pH 5, with weaker repulsions at higher TIS. Conversely, attractive electrostatic interactions were observed at pH 6.5, with weaker attractions at higher TIS. Refined coarse-grained models were used to fit model parameters using experimental B₂₂ versus TIS data. The parameters were used to predict high-c₂ R^ex values via Monte Carlo simulations and separately with Mayer-sampling calculations of higher-order virial coefficients. For both methods, predictions for repulsive to mildly attractive conditions were quantitatively accurate. However, only qualitatively accurate predictions were practical for strongly attractive conditions. An alternative, higher resolution model was used to show semiquantitatively and quantitatively accurate predictions of strong electrostatic attractions at low c₂ and low ionic strength.