Predicting Protein Interactions of Concentrated Globular Protein Solutions Using Colloidal Models

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.

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.

Modelling network formation in folded protein hydrogels by cluster aggregation kinetics

Globular folded protein-based hydrogels are becoming increasingly attractive due to their specific biological functionality, as well as their responsiveness to stimuli. By modelling folded proteins as colloids, there are rich opportunities to explore network formation mechanisms in protein hydrogels that negate the need for computationally expensive simulations which capture the full complexity of proteins. Here we present a kinetic lattice-based model which simulates the formation of irreversibly chemically crosslinked, folded protein-based hydrogels. We identify the critical point of gel percolation, explore the range of network regimes covering diffusion-limited to reaction-limited cluster aggregation (DLCA and RLCA, respectively) network formation mechanisms and predict the final network structure, fractal dimensions and final gel porosity. We reveal a crossover between DLCA and RLCA mechanisms as a function of protein volume fraction and show how the final network structure is governed by the structure at the percolation point, regardless of the broad variation of non-percolating cluster masses observed across all systems. An analysis of the pore size distribution in the final network structures reveals that, approaching RLCA, gels have larger maximal pores than the DLCA counterparts for both volume fractions studied. This general kinetic model and the analysis tools generate predictions of network structure and concurrent porosity over a broad range of experimentally controllable parameters that are consistent with current expectations and understanding of experimental results.

Investigating the Orientation of an Interfacially Adsorbed Monoclonal Antibody and Its Fragments Using Neutron Reflection

Interfacial adsorption is a molecular process occurring during the production, purification, transport, and storage of antibodies, with a direct impact on their structural stability and subsequent implications on their bioactivities. While the average conformational orientation of an adsorbed protein can be readily determined, its associated structures are more complex to characterize. Neutron reflection has been used in this work to investigate the conformational orientations of the monoclonal antibody COE-3 and its Fab and Fc fragments at the oil/water and air/water interfaces. Rigid body rotation modeling was found to be suitable for globular and relatively rigid proteins such as the Fab and Fc fragments but less so for relatively flexible proteins such as full COE-3. Fab and Fc fragments adopted a 'flat-on' orientation at the air/water interface, minimizing the thickness of the protein layer, but they adopted a substantially tilted orientation at the oil/water interface with increased layer thickness. In contrast, COE-3 was found to adsorb in tilted orientations at both interfaces, with one fragment protruding into the solution. This work demonstrates that rigid-body modeling can provide additional insights into protein layers at various interfaces relevant to bioprocess engineering.

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.

Effects of Monovalent Salt on Protein-Protein Interactions of Dilute and Concentrated Monoclonal Antibody Formulations

In this study, we used sodium chloride (NaCl) to extensively modulate non-specific protein-protein interactions (PPI) of a humanized anti-streptavidin monoclonal antibody class 2 molecule (ASA-IgG2). The changes in PPI with varying NaCl (C_NaCl) and monoclonal antibody (mAb) concentration (C_mAb) were assessed using the diffusion interaction parameter k_D and second virial coefficient B₂₂ measured from solutions with low to moderate C_mAb. The effective structure factor S(q)_eff measured from concentrated mAb solutions using small-angle X-ray and neutron scattering (SAXS/SANS) was also used to characterize the PPI. Our results found that the nature of net PPI changed not only with C_NaCl, but also with increasing C_mAb. As a result, parameters measured from dilute and concentrated mAb samples could lead to different predictions on the stability of mAb formulations. We also compared experimentally determined viscosity results with those predicted from interaction parameters, including k_D and S(q)_eff. The lack of a clear correlation between interaction parameters and measured viscosity values indicates that the relationship between viscosity and PPI is concentration-dependent. Collectively, the behavior of flexible mAb molecules in concentrated solutions may not be correctly predicted using models where proteins are considered to be uniform colloid particles defined by parameters derived from low C_mAb.

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.

Quantifying the Separation of Positive and Negative Areas in Electrostatic Potential for Predicting Feasibility of Ammonium Sulfate for Protein Crystallization

Ammonium sulfate (AS) and poly(ethylene glycol) (PEG) are the most popular precipitants in protein crystallization. Some proteins are preferably crystallized by AS, while some are by PEG. The electrostatic potential is related to the preference of the precipitant agents. The iso-surfaces of the electrostatic potentials for the AS-crystallized proteins display a common shape and a distinct separation between the positive and negative areas. In contrast, the PEG-crystallized proteins show unclear positive and negative separation. In this work, we propose schemes to quantitatively evaluate the separation for predicting which precipitant is favorable for crystal growth between AS or PEG. Three methods were attempted to quantify the amplitude of the separation, separation distance, dipole moment, and shape regularity. The positive and negative areas are approximated to the spherical potentials caused by point charges. The first method is a measurement of the distance between the positive and negative point charges. The second one is an assessment including the quantity of electric charge into the distance. The last one is an approach monitoring the clarity of the positive and negative separation. The average value for 25 kinds of AS-preferring proteins was higher than that for the PEG-preferring ones in all three methods. Therefore, every method can distinguish the proteins preferring AS for crystal growth from those preferring PEG. These methods require an iso-surface of the electrostatic potential depicted at a certain contouring value. The shape of the iso-surface depends on the contouring value. The dependency on contour was examined by depicting the iso-surfaces of electrostatic potential with three values at ±0.8, ±0.5, and ±0.2 kT/e. While reducing the contouring value leads to the increase in separation distance and the decrease in shape regularity, dipole moment is independent of the alteration of contouring value. While the AS-preferring proteins are distinguishable from the PEG-preferring ones in any contouring values, the iso-surface at ±0.5 kT/e seems adequate for regular use. The dipole moment assessment is feasible for the choice of potent precipitants for crystal growth in experiments.

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.

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.

Charge-driven condensation of RNA and proteins suggests broad role of phase separation in cytoplasmic environments

Phase separation processes are increasingly being recognized as important organizing mechanisms of biological macromolecules in cellular environments. Well-established drivers of phase separation are multi-valency and intrinsic disorder. Here, we show that globular macromolecules may condense simply based on electrostatic complementarity. More specifically, phase separation of mixtures between RNA and positively charged proteins is described from a combination of multiscale computer simulations with microscopy and spectroscopy experiments. Phase diagrams were mapped out as a function of molecular concentrations in experiment and as a function of molecular size and temperature via simulations. The resulting condensates were found to retain at least some degree of internal dynamics varying as a function of the molecular composition. The results suggest a more general principle for phase separation that is based primarily on electrostatic complementarity without invoking polymer properties as in most previous studies. Simulation results furthermore suggest that such phase separation may occur widely in heterogenous cellular environment between nucleic acid and protein components.

Temperature Dependence of Protein Solution Viscosity and Protein-Protein Interactions: Insights into the Origins of High-Viscosity Protein Solutions

Protein solution viscosity (η) as a function of temperature was measured at a series of protein concentrations under a range of formulation conditions for two monoclonal antibodies (MAbs) and a globular protein (aCgn). Based on theoretical arguments, a strong temperature dependence for protein-protein interactions (PPI) indicates highly anisotropic, short-ranged attractions that could lead to higher solution viscosities. The semi-empirical Ross-Minton model was used to determine the apparent intrinsic viscosity, shape, and "crowding" factors for each protein as a function of temperature and formulation conditions. The apparent intrinsic viscosity was independent of temperature for aCgn, while a slight decrease with increasing temperature was observed for the MAbs. The temperature dependence of solution viscosity was analyzed using the Andrade-Eyring equation to determine the effective activation energy of viscous flow (E_a,η). While E_a,η values were different for each protein, they were independent of formulation conditions for a given protein. PPI were quantified via the osmotic second virial coefficient (B₂₂) and the protein diffusion interaction parameter (k_D) as a function of temperature under the same formulation conditions as the viscosity measurements. Net interactions ranged from strongly attractive to repulsive by changing formulation pH and ionic strength for each protein. Overall, larger activation energies for PPI corresponded to larger activation energies for η, and those were predictive of the highest η values at higher protein concentrations.

A Rapid, Small-Volume Approach to Evaluate Protein Aggregation at Air-Water Interfaces

Non-native protein aggregation is a common concern for biopharmaceuticals. A given protein may aggregate through a variety of mechanisms that depend on solution and physico-chemical stress conditions. A thorough evaluation of aggregation behavior for a protein under all conditions of interest is necessary to ensure drug safety and efficacy. This work introduces a rapid, small-volume approach to evaluate protein aggregation propensity upon exposure to air-water interfaces (AWI). A microtensiometer apparatus is used to aerate a small volume of a protein solution with microbubbles for short periods of time (≤10 s). Sub-visible particles that form are captured and analyzed using backgrounded membrane imaging. This allows one to capture all particles in the solution while being sample sparing. The surface-mediated aggregation of two model monoclonal antibodies (MAbs) and a globular protein (aCgn) was tested as a function of pH and temperature. Temperature had a negligible effect under the rapid interface turnover time scales with this technique. Electrostatic protein-protein interactions, mediated by pH changes, were more influential for particle formation via AWI. Nonionic surfactants substantially reduced particle formation for all MAb solutions, but not aCgn. The results are contrasted with expectations when exposing samples to much larger air-water interfacial stress.

Mesoscale Modeling of Nucleosome-Binding Antibody PL2-6: Mono- versus Bivalent Chromatin Complexes

Interactions of chromatin with bivalent immunoglobin nucleosome-binding antibodies and their monovalent (papain-derived) antigen-binding fragment analogs are useful probes for examining chromatin conformational states. To help interpret antibody-chromatin interactions and explore how antibodies might compete for interactions with chromatin components, we incorporate coarse-grained PL2-6 antibody modeling into our mesoscale chromatin model. We analyze interactions and fiber structures for the antibody-chromatin complexes in open and condensed chromatin, with and without H1 linker histone (LH). Despite minimal and transient interactions at physiological salt, we capture significant differences in antibody-chromatin complex configurations in open fibers, with more intense interactions between the bivalent antibody and chromatin compared to monovalent antigen-binding fragments. For these open chromatin fiber morphologies, antibody binding to histone tails is increased and compaction is greater for bivalent compared to monovalent and antibody-free systems. Differences between monovalent and bivalent binding result from antibody competition with internal chromatin fiber components (nucleosome core and linker DNA) for histone tail (H3, H4, H2A, H2B) interactions. This antibody competition for tail contacts reduces tail-core and tail-linker interactions and increases tail-antibody interactions. Such internal structural changes in open fibers resemble mechanisms of LH condensation, driven by charge screening and entropy changes. For condensed fibers at physiological salt, the three systems are much more similar overall, but some subtle tail interaction differences can be noted. Adding LH results in less-dramatic changes for all systems, except that the bivalent complex at physiological salt shows cooperative effects between LH and the antibodies in condensing chromatin fibers. Such dynamic interactions that depend on the internal structure and complex-stabilizing interactions within the chromatin fiber have implications for gene regulation and other chromatin complexes such as with LH, remodeling proteins, and small molecular chaperones that bind and modulate chromatin structure.

Calculation of salt-dependent free energy of binding of β-lactoglobulin homodimer formation and mechanism of dimer formation using molecular dynamics simulation and three-dimensional reference interaction site model (3D-RISM): diffuse salt ions and non-polar interactions between the monomers favor the dimer formation

There are several important phenomena in chemistry, biology, and physics where molecules (or parts of a molecule) having charges of the same sign come closer together and become stable. DNA condensation, RNA folding, colloid-colloid interactions are some of the examples of this kind. In the current work, we have investigated how β-lactoglobulin, a protein found in milk, in spite of carrying +13 charge, favors the homodimer formation in the presence of salt. We have focussed on calculating the protein-protein binding free energy in the presence of salt and identifying the thermodynamic and microscopic mechanism of the process. Estimation of binding free energy of this salt-dependent process is done by combining molecular dynamics simulation with statistical mechanical theory of three-dimensional reference interaction site model (3D-RISM). Binding free energy is evaluated from the chemical potential of the solutes as opposed to potential of mean force calculation, which gives only a constrained free energy. Our calculated values semi-quantitatively match with the experimental results. By examining the different components of binding free energy, we have found that the role of salt ions (especially of Cl^-) is to shift the equilibrium towards the dimer. Non-polar (Lennard-Jones) interactions between the monomers is also favorable to the binding free energy. However, water slightly disfavors the dimer formation. For the microscopic mechanism, heterogeneous of both Na⁺ and Cl^- near the charged residues at the binding interface and change of this charge distribution on dimer formation contribute to the stability. A fine-tuning of enthalpic and entropic effects of salt ions is found to operate at different salt concentrations. Both thermodynamic and microscopic mechanism of dimer formation gives detailed insight into the complex electrostatics of charged protein-protein binding.

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.

Whole-Cell Models and Simulations in Molecular Detail

Comprehensive data about the composition and structure of cellular components have enabled the construction of quantitative whole-cell models. While kinetic network-type models have been established, it is also becoming possible to build physical, molecular-level models of cellular environments. This review outlines challenges in constructing and simulating such models and discusses near- and long-term opportunities for developing physical whole-cell models that can connect molecular structure with biological function.

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.

Calculation of Second Virial Coefficients of Atomistic Proteins Using Fast Fourier Transform

The second virial coefficient, B₂, measures a protein solution's deviation from ideal behavior. It is widely used to predict or explain solubility, crystallization condition, aggregation propensity, and critical temperature for liquid-liquid phase separation. B₂ is determined by the interaction energy between two protein molecules and, specifically, by the integration of the Mayer f-function in the relative configurational space (translation and rotation) of the two molecules. Simple theoretical models, such as one attributed to Derjaguin, Landau, Verwey, and Overbeek (DLVO), can fit the dependence of B₂ on salt concentrations. However, model parameters derived often are physically unrealistic and hardly transferable from protein to protein. Previous B₂ calculations incorporating atomistic details were done with limited sampling in the configurational space, due to enormous computational cost. Our FMAP method, based on fast Fourier transform, can considerably accelerate such calculations, and here we adapt it to calculate B₂ values for proteins represented at the atomic level in implicit solvent. After tuning of a single parameter in the energy function, FMAPB2 predicts well the B₂ values for lysozyme and other proteins over wide ranges of solvent conditions (salt concentration, pH, and temperature). The method is available as a web server at http://pipe.rcc.fsu.edu/fmapb2 .

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.

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.

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 structural properties of fluids by thermodynamic extrapolation

We describe a methodology for extrapolating the structural properties of multicomponent fluids from one thermodynamic state to another. These properties generally include features of a system that may be computed from an individual configuration such as radial distribution functions, cluster size distributions, or a polymer's radius of gyration. This approach is based on the principle of using fluctuations in a system's extensive thermodynamic variables, such as energy, to construct an appropriate Taylor series expansion for these structural properties in terms of intensive conjugate variables, such as temperature. Thus, one may extrapolate these properties from one state to another when the series is truncated to some finite order. We demonstrate this extrapolation for simple and coarse-grained fluids in both the canonical and grand canonical ensembles, in terms of both temperatures and the chemical potentials of different components. The results show that this method is able to reasonably approximate structural properties of such fluids over a broad range of conditions. Consequently, this methodology may be employed to increase the computational efficiency of molecular simulations used to measure the structural properties of certain fluid systems, especially those used in high-throughput or data-driven investigations.

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.

Slow-Down in Diffusion in Crowded Protein Solutions Correlates with Transient Cluster Formation

For a long time, the effect of a crowded cellular environment on protein dynamics has been largely ignored. Recent experiments indicate that proteins diffuse more slowly in a living cell than in a diluted solution, and further studies suggest that the diffusion depends on the local surroundings. Here, detailed insight into how diffusion depends on protein-protein contacts is presented based on extensive all-atom molecular dynamics simulations of concentrated villin headpiece solutions. After force field adjustments in the form of increased protein-water interactions to reproduce experimental data, translational and rotational diffusion was analyzed in detail. Although internal protein dynamics remained largely unaltered, rotational diffusion was found to slow down more significantly than translational diffusion as the protein concentration increased. The decrease in diffusion is interpreted in terms of a transient formation of protein clusters. These clusters persist on sub-microsecond time scales and follow distributions that increasingly shift toward larger cluster size with increasing protein concentrations. Weighting diffusion coefficients estimated for different clusters extracted from the simulations with the distribution of clusters largely reproduces the overall observed diffusion rates, suggesting that transient cluster formation is a primary cause for a slow-down in diffusion upon crowding with other proteins.

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.