Coarse-Grained Modeling of Antibodies from Small-Angle Scattering Profiles

Combining Scattering Experiments and Colloid Theory to Characterize Charge Effects in Concentrated Antibody Solutions

Charges and their contribution to protein-protein interactions are essential for the key structural and dynamic properties of monoclonal antibody (mAb) solutions. In fact, they influence the apparent molecular weight, the static structure factor, the collective diffusion coefficient, or the relative viscosity, and their concentration dependence. Further, charges play an important role in the colloidal stability of mAbs. There exist standard experimental tools to characterize mAb net charges, such as the measurement of the electrophoretic mobility, the second virial coefficient, or the diffusion interaction parameter. However, the resulting values are difficult to directly relate to the actual overall net charge of the antibody and to theoretical predictions based on its known molecular structure. Here, we report the results of a systematic investigation of the solution properties of a charged IgG1 mAb as a function of concentration and ionic strength using a combination of electrophoretic measurements, static and dynamic light scattering, small-angle X-ray scattering, and tracer particle-based microrheology. We analyze and interpret the experimental results using established colloid theory and coarse-grained computer simulations. We discuss the potential and limits of colloidal models for the description of the interaction effects of charged mAbs, in particular pointing out the importance of incorporating shape and charge anisotropy when attempting to predict structural and dynamic solution properties at high concentrations.

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

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

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

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

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.

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.

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.

Molecular Flexibility of Antibodies Preserved Even in the Dense Phase after Macroscopic Phase Separation

Antibody therapies are typically based on high-concentration formulations that need to be administered subcutaneously. These conditions induce several challenges, inter alia a viscosity suitable for injection, sufficient solution stability, and preservation of molecular function. To obtain systematic insights into the molecular factors, we study the dynamics on the molecular level under strongly varying solution conditions. In particular, we use solutions of antibodies with poly(ethylene glycol), in which simple cooling from room temperature to freezing temperatures induces a transition from a well-dispersed solution into a phase-separated and macroscopically arrested system. Using quasi-elastic neutron scattering during in situ cooling ramps and in prethermalized measurements, we observe a strong decrease in antibody diffusion, while internal flexibility persists to a significant degree, thus ensuring the movement necessary for the preservation of molecular function. These results are relevant for a more dynamic understanding of antibodies in high-concentration formulations, which affects the formation of transient clusters governing the solution viscosity.

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

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

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.

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.

Monoclonal Antibody Aggregation near Silicone Oil-Water Interfaces

In this work, we study the hydrodynamic behavior of monoclonal antibodies in the presence of silicone oil-water interfaces. We model the antibody molecules using a coarse-grained 24-bead model, where two beads are used to represent each antibody domain. We consider the spatial variation of the antibody polarity in our model as each bead represents a set of hydrophilic or hydrophobic amino acids. We use the dissipative particle dynamics scheme to represent the coarse-grained force field which governs the motion of the beads. In addition, interprotein interactions are modeled using an electrostatic force field. The model parameters are determined by comparing the structure factor against experimental structure factor data ranging from a low concentration regime (10 mg/mL) to a high concentration regime (150 mg/mL). Next, we conduct simulations for a suspension of antibody molecules in the presence of silicone oil-water interfaces. Protein loss from the bulk solution is noticed as the molecules adsorb at the interface. We observe dynamic cluster formation in the solution bulk and at the interface, as the antibody molecules self-associate along their trajectories. We quantify the aggregation using a density clustering algorithm and investigate the effect of the antibody concentration on the diffusivity of the antibody solution, aggregation propensity, and protein loss from the bulk. Our study shows that numerical simulations can be an important tool for understanding the molecular mechanisms driving protein aggregation near hydrophobic interfaces.

Potential and limits of a colloid approach to protein solutions

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

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

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

A Colloid Approach to Self-Assembling Antibodies

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

Web-based display of protein surface and pH-dependent properties for assessing the developability of biotherapeutics

Protein instability leads to reversible self-association and irreversible aggregation which is a major concern for developing new biopharmaceutical leads. Protein solution behaviour is dictated by the physicochemical properties of the protein and the solution. Optimising protein solutions through experimental screens and targeted protein engineering can be a difficult and time consuming process. Here, we describe development of the protein-sol web server, which was previously restricted to protein solubility prediction from amino acid sequence. Tools are presented for calculating and mapping patches of hydrophobicity and charge on the protein surface. In addition, predictions of folded state stability and net charge are displayed as a heatmap for a range of pH and ionic strength conditions. Tools are evaluated in the context of antibodies, their fragments and interactions. Surprisingly, antibody-antigen interfaces are, on average, at least as polar as Fab surfaces. This benchmarking process provides the user with thresholds with which to assess non-polar surface patches, and possible solubility implications, in proteins of interest. Stability heatmaps compare favourably with experimental data for CH2 and CH3 domains. Display and quantification of surface polarity and pH/ionic strength dependence will be useful generally for investigation of protein biophysics.

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.

Self-Interaction of Human Serum Albumin: A Formulation Perspective

In the present study, small-angle X-ray scattering (SAXS) and static light scattering (SLS) have been used to study the solution properties and self-interaction of recombinant human serum albumin (rHSA) molecules in three pharmaceutically relevant buffer systems. Measurements are carried out up to high protein concentrations and as a function of ionic strength by adding sodium chloride to probe the role of electrostatic interactions. The effective structure factors (S _eff) as a function of the scattering vector magnitude q have been extracted from the scattering profiles and fit to the solution of the Ornstein-Zernike equation using a screened Yukawa potential to describe the double-layer force. Although only a limited q range is used, accurate fits required including an electrostatic repulsion element in the model at low ionic strength, while only a hard sphere model with a tunable diameter is necessary for fitting to high-ionic-strength data. The fit values of net charge agree with available data from potentiometric titrations. Osmotic compressibility data obtained by extrapolating the SAXS profiles or directly from SLS measurements has been fit to a 10-term virial expansion for hard spheres and an equation of state for hard biaxial ellipsoids. We show that modeling rHSA as an ellipsoid, rather than a sphere, provides a much more accurate fit for the thermodynamic data over the entire concentration range. Osmotic virial coefficient data, derived at low protein concentration, can be used to parameterize the model for predicting the behavior up to concentrations as high as 450 g/L. The findings are especially important for the biopharmaceutical sector, which require approaches for predicting concentrated protein solution behavior using minimal sample consumption.

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.

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.

Structure and Relaxation in Solutions of Monoclonal Antibodies

Reversible self-association of therapeutic antibodies is a key factor in high protein solution viscosities. In the present work, a coarse-grained computational model accounting for electrostatic, dispersion, and long-ranged hydrodynamic interactions of two model monoclonal antibodies is applied to understand the nature of self-association, predicting the solution microstructure and resulting transport properties of the solution. For the proteins investigated, the structure factor across a range of solution conditions shows quantitative agreement with neutron-scattering experiments. We observe a homogeneous, dynamical association of the antibodies with no evidence of phase separation. Calculations of self-diffusivity and viscosity from coarse-grained dynamic simulations show the appropriate trends with concentration but, respectively, over- and under-predict the experimentally measured values. By adding constraints to the self-associated clusters that rigidify them under flow, prediction of the transport properties is significantly improved with respect to experimental measurements. We hypothesize that these rigidity constraints are associated with missing degrees of freedom in the coarse-grained model resulting from patchy and heterogeneous interactions among coarse-grained domains. These results demonstrate how structural anisotropy and anisotropy of interactions generated by features at the 2-5 nm length scale in antibodies are sufficient to recover the dynamics and rheological properties of these important macromolecular solutions.

Characterization of Monoclonal Antibody-Protein Antigen Complexes Using Small-Angle Scattering and Molecular Modeling

The determination of monoclonal antibody interactions with protein antigens in solution can lead to important insights guiding physical characterization and molecular engineering of therapeutic targets. We used small-angle scattering (SAS) combined with size-exclusion multi-angle light scattering high-performance liquid chromatography to obtain monodisperse samples with defined stoichiometry to study an anti-streptavidin monoclonal antibody interacting with tetrameric streptavidin. Ensembles of structures with both monodentate and bidentate antibody-antigen complexes were generated using molecular docking protocols and molecular simulations. By comparing theoretical SAS profiles to the experimental data it was determined that the primary component(s) were compact monodentate and/or bidentate complexes. SAS profiles of extended monodentate complexes were not consistent with the experimental data. These results highlight the capability for determining the shape of monoclonal antibody-antigen complexes in solution using SAS data and physics-based molecular modeling.