Reexamining protein-protein and protein-solvent interactions from Kirkwood-Buff analysis of light scattering in multi-component solutions

Flow Activation Energy of High-Concentration Monoclonal Antibody Solutions and Protein-Protein Interactions Influenced by NaCl and Sucrose

The solution viscosity and protein-protein interactions (PPIs) as a function of temperature (4-40 °C) were measured at a series of protein concentrations for a monoclonal antibody (mAb) with different formulation conditions, which include NaCl and sucrose. The flow activation energy (Eη) was extracted from the temperature dependence of solution viscosity using the Arrhenius equation. PPIs were quantified via the protein diffusion interaction parameter (kD) measured by dynamic light scattering, together with the osmotic second virial coefficient and the structure factor obtained through small-angle X-ray scattering. Both viscosity and PPIs were found to vary with the formulation conditions. Adding NaCl introduces an attractive interaction but leads to a significant reduction in the viscosity. However, adding sucrose enhances an overall repulsive effect and leads to a slight decrease in viscosity. Thus, the averaged (attractive or repulsive) PPI information is not a good indicator of viscosity at high protein concentrations for the mAb studied here. Instead, a correlation based on the temperature dependence of viscosity (i.e., Eη) and the temperature sensitivity in PPIs was observed for this specific mAb. When kD is more sensitive to the temperature variation, it corresponds to a larger value of Eη and thus a higher viscosity in concentrated protein solutions. When kD is less sensitive to temperature change, it corresponds to a smaller value of Eη and thus a lower viscosity at high protein concentrations. Rather than the absolute value of PPIs at a given temperature, our results show that the temperature sensitivity of PPIs may be a more useful metric for predicting issues with high viscosity of concentrated solutions. In addition, we also demonstrate that caution is required in choosing a proper protein concentration range to extract kD. In some excipient conditions studied here, the appropriate protein concentration range needs to be less than 4 mg/mL, remarkably lower than the typical concentration range used in the literature.

Impact of Glycosylation on Protein-Protein Self-Interactions of Monoclonal Antibodies

Protein self-interactions measured via second osmotic virial coefficients (B22) and dynamic light scattering interaction parameter values (kD) are often used as metrics for assessing the favorability of protein candidates and different formulations during monoclonal antibody (MAb) product development. Model predictions of B22 or kD typically do not account for glycans, though glycosylation can potentially impact experimental MAb self-interactions. To the best of our knowledge, the impact of MAb glycosylation on the experimentally measured B22 and kD values has not yet been reported. B22 and kD values of two fully deglycosylated MAbs and their native (i.e., fully glycosylated) counterparts were measured by light scattering over a range of pH and ionic strength conditions. Significant differences between B22 and kD of the native and deglycosylated forms were observed at a range of low to high ionic strengths used to modulate the effect of electrostatic contributions. Differences were most pronounced at low ionic strength, indicating that electrostatic interactions are a contributing factor. Though B22 and kD values were statistically equivalent at high ionic strengths where electrostatics were fully screened, we observed protein-dependent qualitative differences, which indicate that steric interactions may also play a role in the observed B22 and kD differences. A domain-level coarse-grained molecular model accounting for charge differences was considered to potentially provide additional insight but was not fully predictive of the behavior across all of the solution conditions investigated. This highlights that both the level of modeling and lack of inclusion of glycans may limit existing models in making quantitatively accurate predictions of self-interactions.

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.

The origins of nonideality exhibited by monoclonal antibodies and Fab fragments in human serum

The development of therapeutic antibodies remains challenging, time-consuming, and expensive. A key contributing factor is a lack of understanding of how proteins are affected by complex biological environments such as serum and plasma. Nonideality due to attractive or repulsive interactions with cosolutes can alter the stability, aggregation propensity, and binding interactions of proteins in solution. Fluorescence correlation spectroscopy (FCS) can be used to measure apparent second virial coefficient (B2,app ) values for therapeutic and model monoclonal antibodies (mAbs) that capture the nature and strength of interactions with cosolutes directly in undiluted serum and similar complex biological media. Here, we use FCS-derived B2,app measurements to identify the components of human serum responsible for nonideal interactions with mAbs and Fab fragments. Most mAbs exhibit neutral or slightly attractive interactions with intact serum. Generally, mAbs display repulsive interactions with albumin and mildly attractive interactions with IgGs in the context of whole serum. Crucially, however, these attractive interactions are much stronger with pooled IgGs isolated from other serum components, indicating that the effects of serum nonideality can only be understood by studying the intact medium (rather than isolated components). Moreover, Fab fragments universally exhibited more attractive interactions than their parental mAbs, potentially rendering them more susceptible to nonideality-driven perturbations. FCS-based B2,app measurements have the potential to advance our understanding of how physiological environments impact protein-based therapeutics in general. Furthermore, incorporating such assays into preclinical biologics development may help de-risk molecules and make for a faster and more efficient development process.

Role of Domain-Domain Interactions on the Self-Association and Physical Stability of Monoclonal Antibodies: Effect of pH and Salt

Monoclonal antibodies (mAbs) make up a major class of biotherapeutics with a wide range of clinical applications. Their physical stability can be affected by various environmental factors. For instance, an acidic pH can be encountered during different stages of the mAb manufacturing process, including purification and storage. Therefore, understanding the behavior of flexible mAb molecules in acidic solution environments will benefit the development of stable mAb products. This study used small-angle X-ray scattering (SAXS) and complementary biophysical characterization techniques to investigate the conformational flexibility and protein-protein interactions (PPI) of a model mAb molecule under near-neutral and acidic conditions. The study also characterized the interactions between Fab and Fc fragments under the same buffer conditions to identify domain-domain interactions. The results suggest that solution pH significantly influences mAb flexibility and thus could help mAbs remain physically stable by maximizing local electrostatic repulsions when mAbs become crowded in solution. Under acidic buffer conditions, both Fab and Fc contribute to the repulsive PPI observed among the full mAb at a low ionic strength. However, as ionic strength increases, hydrophobic interactions lead to the self-association of Fc fragments and, subsequently, could affect the aggregation state of the mAb.

Eliminating finite-size effects on the calculation of x-ray scattering from molecular dynamics simulations

Structural studies using x-ray scattering methods for investigating molecules in solution are shifting focus toward describing the role and effects of the surrounding solvent. However, forward models based on molecular dynamics (MD) simulations to simulate structure factors and x-ray scattering from interatomic distributions such as radial distribution functions (RDFs) face limitations imposed by simulations, particularly at low values of the scattering vector q. In this work, we show how the value of the structure factor at q = 0 calculated from RDFs sampled from finite MD simulations is effectively dependent on the size of the simulation cell. To eliminate this error, we derive a new scheme to renormalize the sampled RDFs based on a model of the excluded volume of the particle-pairs they were sampled from, to emulate sampling from an infinite system. We compare this new correction method to two previous RDF-correction methods, developed for Kirkwood-Buff theory applications. We present a quantitative test to assess the reliability of the simulated low-q scattering signal and show that our RDF-correction successfully recovers the correct q = 0 limit for neat water. We investigate the effect of MD-sampling time on the RDF-corrections, before advancing to a molecular example system, comprised of a transition metal complex solvated in a series of water cells with varying densities. We show that our correction recovers the correct q = 0 behavior for all densities. Furthermore, we employ a simple continuum scattering model to dissect the total scattering signal from the solvent-solvent structural correlations in a solute-solvent model system to find two distinct contributions: a non-local density-contribution from the finite, fixed cell size in NVT simulations, and a local contribution from the solvent shell. We show how the second contribution can be approximated without also including the finite-size contribution. Finally, we provide a "best-practices"-checklist for experimentalists planning to incorporate explicit solvation MD simulations in future work, offering guidance for improving the accuracy and reliability of structural studies using x-ray scattering methods in solution.

Experimental support for reclassification of the light scattering second virial coefficient from macromolecular solutions as a hydrodynamic parameter

This investigation examines the source of the disparity between experimental values of the light scattering second virial coefficient [Formula: see text] (mL.mol/g2) for proteins and those predicted on the statistical mechanical basis of excluded volume. A much better theoretical description of published results for lysozyme is obtained by considering the experimental parameters to monitor the difference between the thermodynamic excluded volume term and its hydrodynamic counterpart. This involves a combination of parameters quantifying concentration dependence of the translational diffusion coefficient obtained from dynamic light scattering measurements. That finding is shown to account for observations of a strong correlation between [Formula: see text] (mL/g), where M2 is the molar mass (molecular weight) of the macromolecule and the diffusion concentration parameter [Formula: see text] (mL/g). On the grounds that [Formula: see text] is regarded as a hydrodynamic parameter, the same status should be accorded the light scattering second virial coefficient rather than its current incorrect thermodynamic designation as [Formula: see text] (mL.mol/g2), or just B, the osmotic second virial coefficient for protein self-interaction.

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.

An Intercompany Perspective on Practical Experiences of Predicting, Optimizing and Analyzing High Concentration Biologic Therapeutic Formulations

Developing high-dose biologic drugs for subcutaneous injection often requires high-concentration formulations and optimizing viscosity, solubility, and stability while overcoming analytical, manufacturing, and administration challenges. To understand industry approaches for developing high-concentration formulations, the Formulation Workstream of the BioPhorum Development Group, an industry-wide consortium, conducted an inter-company collaborative exercise which included several surveys. This collaboration provided an industry perspective, experience, and insight into the practicalities for developing high-concentration biologics. To understand solubility and viscosity, companies desire predictive tools, but experience indicates that these are not reliable and experimental strategies are best. Similarly, most companies prefer accelerated and stress stability studies to in-silico or biophysical-based prediction methods to assess aggregation. In addition, optimization of primary container-closure and devices are pursued to mitigate challenges associated with high viscosity of the formulation. Formulation strategies including excipient selection and application of studies at low concentration to high-concentration formulations are reported. Finally, analytical approaches to high concentration formulations are presented. The survey suggests that although prediction of viscosity, solubility, and long-term stability is desirable, the outcome can be inconsistent and molecule dependent. Significant experimental studies are required to confirm robust product definition as modeling at low protein concentrations will not necessarily extrapolate to high concentration formulations.

Anomalous Concentration Dependence of Surface Tension and Concentration-Concentration Correlation Functions of Binary Non-Electrolyte Solutions

The concentration dependence of the surface tension of several binary mixtures of non-electrolytes has been measured at 298.15 K. The mixtures have been chosen since they presented a so-called "W-shape" concentration dependence of the excess constant pressure heat capacity and high values of the concentration-concentration correlation function. This behavior was interpreted in terms of the existence of anomalously high concentration fluctuations that resemble those existing in the proximities of critical points. However, no liquid-liquid phase separation has been found in any of these mixtures over a wide temperature range. In this work, we have extended these studies to the liquid-air interfacial properties. The results show that the concentration dependence of the surface tension shows a plateau and the mixing surface tension presents a "W-shape" behavior. To the best of our knowledge, this is the first time that this behavior is reported. The weak anomalies of the surface tension near a liquid-liquid critical point suggest that the results obtained cannot be considered far-from-critical effects. The usual approach of substituting the activity by the concentration in the Gibbs equation for the relative surface concentration has been found to lead to large errors and the mixtures to have a fuzzy and thick liquid/vapor interface.

Phase separation and dynamical arrest of protein solutions dominated by short-range attractions

The interplay of liquid-liquid phase separation (LLPS) and dynamical arrest can lead to the formation of gels and glasses, which is relevant for such diverse fields as condensed matter physics, materials science, food engineering, and the pharmaceutical industry. In this context, protein solutions exhibit remarkable equilibrium and non-equilibrium behaviors. In the regime where attractive and repulsive forces compete, it has been demonstrated, for example, that the location of the dynamical arrest line seems to be independent of ionic strength, so that the arrest lines at different ionic screening lengths overlap, in contrast to the LLPS coexistence curves, which strongly depend on the salt concentration. In this work, we show that the same phenomenology can also be observed when the electrostatic repulsions are largely screened, and the range and strength of the attractions are varied. In particular, using lysozyme in brine as a model system, the metastable gas-liquid binodal and the dynamical arrest line as well as the second virial coefficient have been determined for various solution conditions by cloud-point measurements, optical microscopy, centrifugation experiments, and light scattering. With the aim of understanding this new experimental phenomenology, we apply the non-equilibrium self-consistent generalized Langevin equation theory to a simple model system with only excluded volume plus short-range attractions, to study the dependence of the predicted arrest lines on the range of the attractive interaction. The theoretical predictions find a good qualitative agreement with experiments when the range of the attraction is not too small compared with the size of the protein.

Predicting Experimental B22 Values and the Effects of Histidine Charge States for Monoclonal Antibodies Using Coarse-Grained Molecular Simulations

Static light scattering (SLS) was used to characterize five monoclonal antibodies (MAbs) as a function of total ionic strength (TIS) at pH values between 5.5 and 7.0. Second osmotic virial coefficient (B₂₂) values were determined experimentally for each MAb as a function of TIS using low protein concentration SLS data. Coarse-grained molecular simulations were performed to predict the B₂₂ values for each MAb at a given pH and TIS. To include the effect of charge fluctuations of titratable residues in the B₂₂ calculations, a statistical approach was introduced in the Monte Carlo algorithm based on the protonation probability based on a given pH value and the Henderson-Hasselbalch equation. The charged residues were allowed to fluctuate individually, based on the sampled microstates and the influence of electrostatic interactions on net protein-protein interactions during the simulations. Compared to static charge simulations, the new approach provided improved results compared to experimental B₂₂ values at pH conditions near the pK_a of titratable residues.

Use of Debye-Hückel-Henry charge measurements in early antibody development elucidates effects of non-specific association

The diffusion interaction parameter (kD) has been demonstrated to be a high-throughput technique for characterizing interactions between proteins in solution. kD reflects both attractive and repulsive interactions, including long-ranged electrostatic repulsions. Here, we plot the mutual diffusion coefficient (Dm) as a function of the experimentally determined Debye-Hückel-Henry surface charge (ZDHH) for seven human monoclonal antibodies (mAbs) in 15 mM histidine, pH 6. We find that graphs of Dm versus ZDHH intersect at ZDHH, ~ 2.6, independent of protein concentration. The same data plotted as kD vs. ZDHH shows a transition from net attractive to net repulsive interactions in the same region of the ZDHH intersection point. These data suggest that there is a minimum surface charge necessary on these mAbs needed to overcome attractive interactions.

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.

Measuring aggregates, self-association, and weak interactions in concentrated therapeutic antibody solutions

Monoclonal antibodies are a class of biotherapeutics used for an increasing variety of disorders, including cancer, autoimmune, neurodegenerative, and viral diseases. Besides their antigen specificity, therapeutic use also mandates control of their solution interactions and colloidal properties in order to achieve a stable, efficacious, non-immunogenic, and low viscosity antibody solution at concentrations in the range of 50–150 mg/mL. This requires characterization of their reversible self-association, aggregation, and weak attractive and repulsive interactions governing macromolecular distance distributions in solution. Simultaneous measurement of these properties, however, has been hampered by solution nonideality. Based on a recently introduced sedimentation velocity method for measuring macromolecular size distributions in a mean-field approximation for hydrodynamic interactions, we demonstrate simultaneous measurement of polydispersity and weak and strong solution interactions in a panel of antibodies with concentrations up to 45 mg/mL. By allowing approximately an order of magnitude higher concentrations than previously possible in sedimentation velocity size distribution analysis, this approach can substantially improve efficiency and sensitivity for characterizing polydispersity and interactions of therapeutic antibodies at or close to formulation conditions.

A coarse-grained xDLVO model for colloidal protein-protein interactions

Colloidal protein-protein interactions (PPIs) of attractive and repulsive nature modulate the solubility of proteins, their aggregation, precipitation and crystallization. Such interactions are very important for many biotechnological processes, but are complex and hard to control, therefore, difficult to be understood in terms of measurements alone. In diluted protein solutions, PPIs can be estimated from the osmotic second virial coefficient, B22, which has been calculated using different methods and levels of theory. The most popular approach is based on the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and its extended versions, i.e. xDLVO. Despite much efforts, these models are not fully quantitative and must be fitted to experiments, which limits their predictive value. Here, we report an extended xDLVO-CG model, which extends existing models by a coarse-grained representation of proteins and the inclusion of an additional ion-protein dispersion interaction term. We demonstrate for four proteins, i.e. lysozyme (LYZ), subtilisin (Subs), bovine serum albumin (BSA) and immunoglobulin (IgG1), that semi-quantitative agreement with experimental values without the need to fit to experimental B22 values. While most likely not the final step in the nearly hundred years of research in PPIs, xDLVO-CG is a step towards predictive PPIs calculations that are transferable to different proteins.

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.

Quantifying Protein-Protein Interactions in Molecular Simulations

Interactions among proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants K_d, and both binding and nonbinding interactions are quantified by second osmotic virial coefficients B₂. As a measure of nonspecific binding and stickiness, B₂ is receiving renewed attention in the context of so-called liquid–liquid phase separation in protein and nucleic acid solutions. We show that K_d is fully determined by B₂ and the fraction of the dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B₂. From molecular dynamics or Monte Carlo simulations using implicit solvents, we can determine B₂ from insertion and removal energies by applying Bennett’s acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvents, one can estimate B₂ from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. Our estimates for K_d and B₂ allow us to separate out the contributions of nonbinding interactions to B₂. Comparison of calculated and measured values of K_d and B₂ can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities, overall stickiness, and nonbinding interactions. The accuracy and efficiency of K_d and B₂ calculations make them well suited for high-throughput studies of large interactomes.

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.

Experimental determination of second virial coefficients by small-angle X-ray scattering: a problem revisited

This investigation examines the validity of employing single-solute theory to interpret SAXS measurements on buffered protein solutions-the current practice despite the necessity to regard the buffer components as additional non-scattering solutes rather than as part of the solvent. The present study of bovine serum albumin in phosphate-buffered saline supplemented with 20-100 g/L sucrose as small cosolute has certainly verified the prediction that the experimentally obtained second virial coefficient should contain protein-cosolute contributions. Nevertheless, the second virial coefficient determined for protein solutions supplemented with high cosolute concentrations on the basis of single-solute theory remains a valid means for identifying conditions conducive to protein crystallization, because the return of a slightly negative second virial coefficient based on single-solute theory [Formula: see text] still establishes the existence of slightly associative interactions between protein molecules, irrespective of the molecular source-protein self-interactions and/or protein-cosolute contributions.

Protein-protein interactions and water activity coefficients can be used to aid a first excipient choice in protein formulations

With respect to all biopharmaceuticals marketed to date, monoclonal antibodies represent the largest fraction with more than 48% market share (2012). However, the development of biopharmaceutical formulations is a challenging task, and time-consuming and cost-intensive high-throughput screenings are still state-of-the-art in formulation design. These screening techniques are almost exclusively based on heuristic decisions thus the benefit in terms of mechanistic understanding is often unclear. It requires novel, physical-sound methods to enhance/optimize future formulation development, ideally by understanding molecular interactions in these complex solutions. A suitable and evaluated measure-of-choice to characterize protein-protein interactions in aqueous protein solutions is the second osmotic virial coefficient B₂₂ which can be measured using static light scattering techniques. Furthermore B₂₂ can be modeled/predicted via the extended mxDLVO model for protein-protein interactions in the presence of single excipients and excipient-mixtures. Building up on this approach, giving an additional insight into water-water and water-excipient interactions, the thermodynamic equation-of-state ePC-SAFT is used to calculate water activity coefficients in the presence of excipient-mixtures. Immunoglobulin G (IgG) was chosen as a model protein to predict B₂₂-values for IgG in the presence of model excipient-mixtures (trehalose-NaCl, l-histidine-trehalose, l-histidine-NaCl). The combination of water activity coefficients and B₂₂ allows to quickly identify a first guess on suitable formulation conditions that then can be further evaluated with existing methods/knowledge.

Light Scattering to Quantify Protein-Protein Interactions at High Protein Concentrations

Static and dynamic (laser) light scattering (SLS and DLS, respectively) can be used to measure the so-called weak or colloidal protein-protein interactions in solution from low to high protein concentrations (c₂). This chapter describes a methodology to measure protein-protein self-interactions using SLS and DLS, with illustrative examples for monoclonal antibody solutions from low to high protein concentrations (c₂ ~ 1-10² g/L).

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.

A Reappraisal of Sedimentation Nonideality Coefficients for the Analysis of Weak Interactions of Therapeutic Proteins

The study of weak or colloidal interactions of therapeutic proteins in different formulations allows prediction and optimization of protein stability. Various biophysical techniques have been applied to determine the second osmotic virial coefficient B₂ as it reflects on the macromolecular distance distribution that governs solution behavior at high concentration. In the present work, we exploit a direct link predicted by hydrodynamic theory between B₂ and the nonideality of sedimentation, commonly measured in sedimentation velocity analytical ultracentrifugation through the nonideality coefficient of sedimentation, k_S. Using sedimentation equilibrium analytical ultracentrifugation for independent measurement of B₂, we have examined the dependence of k_S on B₂ for model proteins in different buffers. The data exhibit the expected linear relationship and highlight the impact of protein shape on the magnitude of the nonideality coefficient k_S. Recently, measurements of k_S have been considerably simplified allowing higher throughput and simultaneous polydispersity assessment at higher protein concentrations. Thus, sedimentation velocity may offer a useful approach to compare the impact of formulation conditions on weak interactions and simultaneously on higher-order structure of therapeutic proteins.

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.

Evaluating the Effects of Hinge Flexibility on the Solution Structure of Antibodies at Concentrated Conditions

Employing 2 different coarse-grained models, we evaluated the effect of intramolecular domain-domain distances and hinge flexibility on the general solution structure of monoclonal antibodies (mAbs), within the context of protein-protein steric repulsion. These models explicitly account for the hinge region, and represent antibodies at either domain or subdomain levels (i.e., 4-bead and 7-bead representations, respectively). Additionally, different levels of mAb flexibility are also considered. When evaluating mAbs as rigid structures, analysis of small-angle scattering profiles showed that changes in the relative internal distances between Fc and Fab domains significantly alter the local arrangement of neighboring molecules, as well as the molecular packing of the concentrated mAb solutions. Likewise, enabling hinge flexibility in either of the mAb models led to qualitatively similar results, where flexibility increases the spatial molecular arrangement at elevated concentrations. This occurs because fluctuations in mAb quaternary structure are modulated by the close proximity between molecules at elevated concentrations (>50 mg mL^-1), yielding an increased molecular packing and osmotic compressibility. However, our results also showed that the mechanism behind this synergy between flexibility and packing strongly depends on both the level of structural detail and the number of degrees-of-freedom considered in the coarse-grained model.

Measuring macromolecular size distributions and interactions at high concentrations by sedimentation velocity

In concentrated macromolecular solutions, weak physical interactions control the solution behavior including particle size distribution, aggregation, liquid-liquid phase separation, or crystallization. This is central to many fields ranging from colloid chemistry to cell biology and pharmaceutical protein engineering. Unfortunately, it is very difficult to determine macromolecular assembly states and polydispersity at high concentrations in solution, since all motion is coupled through long-range hydrodynamic, electrostatic, steric, and other interactions, and scattering techniques report on the solution structure when average interparticle distances are comparable to macromolecular dimensions. Here we present a sedimentation velocity technique that, for the first time, can resolve macromolecular size distributions at high concentrations, by simultaneously accounting for average mutual hydrodynamic and thermodynamic interactions. It offers high resolution and sensitivity of protein solutions up to 50 mg/ml, extending studies of macromolecular solution state closer to the concentration range of therapeutic formulations, serum, or intracellular conditions.

Many aspects of concentrated macromolecular solutions, such as encountered in cytosol or in pharmaceutical formulations, are dependent on particle size distributions and weak intermolecular interactions. Here, the authors exploit hydrodynamic separation in the centrifugal field to measure both.

A methodology to calculate small-angle scattering profiles of macromolecular solutions from molecular simulations in the grand-canonical ensemble

The theoretical framework to evaluate small-angle scattering (SAS) profiles for multi-component macromolecular solutions is re-examined from the standpoint of molecular simulations in the grand-canonical ensemble, where the chemical potentials of all species in solution are fixed. This statistical mechanical ensemble resembles more closely scattering experiments, capturing concentration fluctuations that arise from the exchange of molecules between the scattering volume and the bulk solution. The resulting grand-canonical expression relates scattering intensities to the different intra- and intermolecular pair distribution functions, as well as to the distribution of molecular concentrations on the scattering volume. This formulation represents a generalized expression that encompasses most of the existing methods to evaluate SAS profiles from molecular simulations. The grand-canonical SAS methodology is probed for a series of different implicit-solvent, homogeneous systems at conditions ranging from dilute to concentrated. These systems consist of spherical colloids, dumbbell particles, and highly flexible polymer chains. Comparison of the resulting SAS curves against classical methodologies based on either theoretical approaches or canonical simulations (i.e., at a fixed number of molecules) shows equivalence between the different scattering intensities so long as interactions between molecules are net repulsive or weakly attractive. On the other hand, for strongly attractive interactions, grand-canonical SAS profiles deviate in the low- and intermediate-q range from those calculated in a canonical ensemble. Such differences are due to the distribution of molecules becoming asymmetric, which yields a higher contribution from configurations with molecular concentrations larger than the nominal value. Additionally, for flexible systems, explicit discrimination between intra- and inter-molecular SAS contributions permits the implementation of model-free, structural analysis such as Guinier's plots at high molecular concentrations, beyond what the traditional limits are for such analysis.

Biophysical characterization and molecular simulation of electrostatically driven self-association of a single-chain antibody

Colloidal protein-protein interactions (PPI) are often expected to impact key behaviors of proteins in solution, such as aggregation rates and mechanisms, aggregate structure, protein solubility, and solution viscosity. PPI of an anti-fluorescein single chain antibody variable fragment (scFv) were characterized experimentally at low to intermediate ionic strength using a combination of static light scattering and sedimentation equilibrium ultracentrifugation. Surprisingly, the results indicated that interactions were strongly net-attractive and electrostatics promoted self-association. Only repulsive interactions were expected based on prior work and calculations based a homology model of a related scFv crystal structure. However, the crystal structure lacks the charged, net-neutral linker sequence. PyRosetta was used to generate a set of scFv structures with different linker conformations, and coarse-grained Monte Carlo simulations were used to evaluate the effect of different linker configurations via second osmotic virial coefficient (B22 ) simulations. The results show that the configuration of the linker has a significant effect on the calculated B22 values, and can result in strong electrostatic attractions between oppositely charged residues on the protein surface. This is particularly relevant for development of non-natural antibody products, where charged linkers and other loop regions may be prevalent. The results also provide a preliminary computational framework to evaluate the effect of unstructured linkers on experimental protein-protein interaction parameters such as B22 .

Predicting Protein-Protein Interactions of Concentrated Antibody Solutions Using Dilute Solution Data and Coarse-Grained Molecular Models

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 second osmotic virial coefficients (B₂₂) at low c₂, and excess Rayleigh profiles (R^ex/K vs. c₂) and zero-q structure factors (S_q=0) as a function of c₂ at higher c₂ for a series of conditions (pH, sucrose concentration, and total ionic strength [TIS]). Repulsive (attractive) interactions were observed at low TIS (high TIS) for pH 5 and 6.5, with increasing repulsions when 5% w/w sucrose was also present. Previously developed and refined coarse-grained antibody models were used to fit model parameters from B₂₂ versus TIS data. The resulting parameters from low-c₂ conditions were used as the sole input to multiprotein Monte Carlo simulations to predict high-c₂R^ex/K and S_q=0 behavior up to 150 g/L. Experimental results at high-c₂ conditions were quantitatively predicted by the simulations for the coarse-grained models that treated antibody molecules as either 6 or 12 (sub) domains, which preserved the basic shape of a monoclonal antibody. Finally, preferential accumulation of sucrose around the protein surface was identified via high-precision density measurements, which self-consistently explained the simulation and experimental SLS results.

Protein Partial Molar Volumes in Multicomponent Solutions from the Perspective of Inverse Kirkwood-Buff Theory

Inverse Kirkwood-Buff (KB) solution theory can be used to relate macroscopic quantities with molecular scale interactions and correlation functions, in the form of KB integrals. Protein partial specific volumes ([Formula: see text]) from high-precision density measurements can be used to quantify solvent-solute and solute-solute KB integrals. Currently, general expressions for [Formula: see text] as a function of cosolute concentration (c₃) have been provided for only binary and ternary solutions. We derive a general multicomponent expression for [Formula: see text] in terms of the relevant KB integrals for the case of low (infinite dilution) protein concentration but arbitrary cosolute concentrations. To test the utility of treating a quaternary system with a pseudoternary approximation, α-Chymotrypsinogen (aCgn) solutions with a series of solutes (NaCl, sucrose, and trehalose) were compared as a function of solute concentration with and without buffer present. Comparison between those ternary and quaternary solutions shows equivalent results within experimental uncertainty and suggests the pseudoternary approximation may be reasonable. In the case of aCgn, doing so also revealed that the preferential interactions can depend on pH. Analysis of steric contributions also provides an example that illustrates how KB integrals allow one to interpret [Formula: see text] in terms of contributions from molecular volume, excluded volume, and hydration/solvation effects.

Effect of the surface charge distribution on the fluid phase behavior of charged colloids and proteins

A generic but simple model is presented to evaluate the effect of the heterogeneous surface charge distribution of proteins and zwitterionic nanoparticles on their thermodynamic phase behavior. By considering surface charges as continuous "patches," the rich set of surface patterns that is embedded in proteins and charged patchy particles can readily be described. This model is used to study the fluid phase separation of charged particles where the screening length is of the same order of magnitude as the particle size. In particular, two types of charged particles are studied: dipolar fluids and protein-like fluids. The former represents the simplest case of zwitterionic particles, whose charge distribution can be described by their dipole moment. The latter system corresponds to molecules/particles with complex surface charge arrangements such as those found in biomolecules. The results for both systems suggest a relation between the critical region, the strength of the interparticle interactions, and the arrangement of charged patches, where the critical temperature is strongly correlated to the magnitude of the dipole moment. Additionally, competition between attractive and repulsive charge-charge interactions seems to be related to the formation of fluctuating clusters in the dilute phase of dipolar fluids, as well as to the broadening of the binodal curve in protein-like fluids. Finally, a variety of self-assembled architectures are detected for dipolar fluids upon small changes to the charge distribution, providing the groundwork for studying the self-assembly of charged patchy particles.

Second Virial Coefficient As Determined from Protein Phase Behavior

We quantitatively link the macroscopic phase behavior of protein solutions to protein-protein interactions based on a coarse-grained colloidal approach. We exploit the extended law of corresponding states and apply the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory in order to infer the second virial coefficient b₂, an integral measure of the interaction potential, from the phase behavior, namely, cloud-point temperature (CPT) measurements under conditions favoring protein crystallization. This determination of b₂ yields values that quantitatively agree with the results of static light scattering (SLS) experiments. The strength of the attractions is quantified in terms of an effective Hamaker constant, which accounts for van der Waals attractions as well as non-DLVO forces, such as hydration and hydrophobic interactions. Our approach based on simple lab experiments to determine the CPT in combination with the DLVO theory is expected to facilitate further biophysical research on protein-protein interactions in complex solution environments.

Modulating non-native aggregation and electrostatic protein-protein interactions with computationally designed single-point mutations

Non-native protein aggregation is a ubiquitous challenge in the production, storage and administration of protein-based biotherapeutics. This study focuses on altering electrostatic protein-protein interactions as a strategy to modulate aggregation propensity in terms of temperature-dependent aggregation rates, using single-charge variants of human γ-D crystallin. Molecular models were combined to predict amino acid substitutions that would modulate protein-protein interactions with minimal effects on conformational stability. Experimental protein-protein interactions were quantified by the Kirkwood-Buff integrals (G22) from laser scattering, and G22 showed semi-quantitative agreement with model predictions. Experimental initial-rates for aggregation showed that increased (decreased) repulsive interactions led to significantly increased (decreased) aggregation resistance, even based solely on single-point mutations. However, in the case of a particular amino acid (E17), the aggregation mechanism was altered by substitution with R or K, and this greatly mitigated improvements in aggregation resistance. The results illustrate that predictions based on native protein-protein interactions can provide a useful design target for engineering aggregation resistance; however, this approach needs to be balanced with consideration of how mutations can impact aggregation mechanisms.

McMillan-Mayer theory of solutions revisited: simplifications and extensions

McMillan and Mayer (MM) proved two remarkable theorems in their paper on the equilibrium statistical mechanics of liquid solutions. They first showed that the grand canonical partition function for a solution can be reduced to one with an effectively solute-only form, by integrating out the solvent degrees of freedom. The total effective solute potential in the effective solute grand partition function can be decomposed into components which are potentials of mean force for isolated groups of one, two, three, etc., solute molecules. Second, from the first result, now assuming low solute concentration, MM derived an expansion for the osmotic pressure in powers of the solute concentration, in complete analogy with the virial expansion of gas pressure in powers of the density at low density. The molecular expressions found for the osmotic virial coefficients have exactly the same form as the corresponding gas virial coefficients, with potentials of mean force replacing vacuum potentials. In this paper, we restrict ourselves to binary liquid solutions with solute species A and solvent species B and do three things: (a) By working with a semi-grand canonical ensemble (grand with respect to solvent only) instead of the grand canonical ensemble used by MM, and avoiding graphical methods, we have greatly simplified the derivation of the first MM result, (b) by using a simple nongraphical method developed by van Kampen for gases, we have greatly simplified the derivation of the second MM result, i.e., the osmotic pressure virial expansion; as a by-product, we show the precise relation between MM theory and Widom potential distribution theory, and (c) we have extended MM theory by deriving virial expansions for other solution properties such as the enthalpy of mixing. The latter expansion is proving useful in analyzing ongoing isothermal titration calorimetry experiments with which we are involved. For the enthalpy virial expansion, we have also changed independent variables from semi-grand canonical, i.e., fixed {N(A), μ(B), V, T}, to those relevant to the experiment, i.e., fixed {N(A), N(B), p, T}, where μ denotes chemical potential, N the number of molecules, V the volume, p the pressure, and T the temperature.

Weak protein interactions and pH- and temperature-dependent aggregation of human Fc1

The Fc (fragment crystallizable) is a common structural region in immunoglobulin gamma (IgG) proteins, IgG-based multi-specific platforms, and Fc-fusion platform technologies. Changes in conformational stability, protein-protein interactions, and aggregation of NS0-produced human Fc1 were quantified experimentally as a function of pH (4 to 6) and temperature (30 to 77 °C), using a combination of differential scanning calorimetry, laser light scattering, size-exclusion chromatography, and capillary electrophoresis. The Fc1 was O-glycosylated at position 3 (threonine), and confirmed to correspond to the intact IgG1 by comparison with Fc1 produced by cleavage of the parent IgG1. Changing the pH caused large effects for thermal unfolding transitions, but it caused surprisingly smaller effects for electrostatic protein-protein interactions. The aggregation behavior was qualitatively similar across different solution conditions, with soluble dimers and larger oligomers formed in most cases. Aggregation rates spanned approximately 5 orders of magnitude and could be divided into 2 regimes: (i) Arrhenius, unfolding-limited aggregation at temperatures near or above the midpoint-unfolding temperature of the CH2 domain; (ii) a non-Arrhenius regime at lower temperatures, presumably as a result of the temperature dependence of the unfolding enthalpy for the CH2 domain. The non-Arrhenius regime was most pronounced for lower temperatures. Together with the weak protein-protein repulsions, these highlight challenges that are expected for maintaining long-term stability of biotechnology products that are based on human Fc constructs.