Effective Interactions and Colloidal Stability of Bovine γ-Globulin in Solution

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.

Biophysical Determinants for the Viscosity of Concentrated Monoclonal Antibody Solutions

Monoclonal antibodies (mAbs) are particularly relevant for therapeutics due to their high specificity and versatility, and mAb-based drugs are hence used to treat numerous diseases. The increased patient compliance of self-administration motivates the formulation of products for subcutaneous (SC) administration. The associated challenge is to formulate highly concentrated antibody solutions to achieve a significant therapeutic effect, while limiting their viscosity and preserving their physicochemical stability. Protein-protein interactions (PPIs) are in fact the root cause of several potential problems concerning the stability, manufacturability, and delivery of a drug product. The understanding of macroscopic viscosity requires an in-depth knowledge on protein diffusion, PPIs, and self-association/aggregation. Here, we study the self-diffusion of different mAbs of the IgG1 subtype in aqueous solution as a function of the concentration and temperature by quasi-elastic neutron scattering (QENS). QENS allows us to probe the short-time self-diffusion of the molecules and therefore to determine the hydrodynamic mAb cluster size and to gain information on the internal mAb dynamics. Small-angle neutron scattering (SANS) is jointly employed to probe structural details and to understand the nature and intensity of PPIs. Complementary information is provided by molecular dynamics (MD) simulations and viscometry, thus obtaining a comprehensive picture of mAb diffusion.

Examining polymer-protein biophysical interactions with small-angle x-ray scattering and quartz crystal microbalance with dissipation

Polymer-protein hybrids can be deployed to improve protein solubility and stability in denaturing environments. While previous work used robotics and active machine learning to inform new designs, further biophysical information is required to ascertain structure-function behavior. Here, we show the value of tandem small-angle x-ray scattering (SAXS) and quartz crystal microbalance with dissipation (QCMD) experiments to reveal detailed polymer-protein interactions with horseradish peroxidase (HRP) as a test case. Of particular interest was the process of polymer-protein complex formation under thermal stress whereby SAXS monitors formation in solution while QCMD follows these dynamics at an interface. The radius of gyration (Rg ) of the protein as measured by SAXS does not change significantly in the presence of polymer under denaturing conditions, but thickness and dissipation changes were observed in QCMD data. SAXS data with and without thermal stress were utilized to create bead models of the potential complexes and denatured enzyme, and each model fit provided insight into the degree of interactions. Additionally, QCMD data demonstrated that HRP deforms by spreading upon surface adsorption at low concentration as shown by longer adsorption times and smaller frequency shifts. In contrast, thermally stressed and highly inactive HRP had faster adsorption kinetics. The combination of SAXS and QCMD serves as a framework for biophysical characterization of interactions between proteins and polymers which could be useful in designing polymer-protein hybrids.

Synergistic Effects of Multiple Excipients on Controlling Viscosity of Concentrated Protein Dispersions

Viscosity control is essential for the manufacturing and delivery of concentrated therapeutic proteins. Limited availability of the precious protein-based drugs hinders the characterization and screening of the formulation conditions with new types or different combinations of excipients. In this work, a droplet-based microfluidic device with incorporated multiple particle tracking microrheology (MPT) is developed to quantify the effects of two excipients, arginine hydrochloride (ArgHCl) and caffeine, on the viscosity of concentrated bovine gamma globulin (BGG) dispersions at two different values of pH. The effectiveness of both ArgHCl and caffeine show dependence on the BGG concentration and solution pH. The data set with high compositional resolution provides useful information to guide formulation with multiple viscosity-reducing excipients and quantification appropriate to start elucidating the connection to protein-protein interaction mechanisms. Overall, this work has demonstrated that the developed microfluidic approach has the potential to effectively assess the impact of multiple excipients on the viscosity and provide data for computational methods to predict viscosity for high concentration protein formulations.

Resolving molecular diffusion and aggregation of antibody proteins with megahertz X-ray free-electron laser pulses

X-ray free-electron lasers (XFELs) with megahertz repetition rate can provide novel insights into structural dynamics of biological macromolecule solutions. However, very high dose rates can lead to beam-induced dynamics and structural changes due to radiation damage. Here, we probe the dynamics of dense antibody protein (Ig-PEG) solutions using megahertz X-ray photon correlation spectroscopy (MHz-XPCS) at the European XFEL. By varying the total dose and dose rate, we identify a regime for measuring the motion of proteins in their first coordination shell, quantify XFEL-induced effects such as driven motion, and map out the extent of agglomeration dynamics. The results indicate that for average dose rates below 1.06 kGy μs^-1 in a time window up to 10 μs, it is possible to capture the protein dynamics before the onset of beam induced aggregation. We refer to this approach as correlation before aggregation and demonstrate that MHz-XPCS bridges an important spatio-temporal gap in measurement techniques for biological samples.

Short-Time Transport Properties of Bidisperse Suspensions of Immunoglobulins and Serum Albumins Consistent with a Colloid Physics Picture

The crowded environment of biological systems such as the interior of living cells is occupied by macromolecules with a broad size distribution. This situation of polydispersity might influence the dependence of the diffusive dynamics of a given tracer macromolecule in a monodisperse solution on its hydrodynamic size and on the volume fraction. The resulting size dependence of diffusive transport crucially influences the function of a living cell. Here, we investigate a simplified model system consisting of two constituents in aqueous solution, namely, of the proteins bovine serum albumin (BSA) and bovine polyclonal gamma-globulin (Ig), systematically depending on the total volume fraction and ratio of these constituents. From high-resolution quasi-elastic neutron spectroscopy, the separate apparent short-time diffusion coefficients for BSA and Ig in the mixture are extracted, which show substantial deviations from the diffusion coefficients measured in monodisperse solutions at the same total volume fraction. These deviations can be modeled quantitatively using results from the short-time rotational and translational diffusion in a two-component hard sphere system with two distinct, effective hydrodynamic radii. Thus, we find that a simple colloid picture well describes short-time diffusion in binary mixtures as a function of the mixing ratio and the total volume fraction. Notably, the self-diffusion of the smaller protein BSA in the mixture is faster than the diffusion in a pure BSA solution, whereas the self-diffusion of Ig in the mixture is slower than in the pure Ig solution.

Suppression of Liquid‐Liquid Phase Separation and Aggregation of Antibodies by Modest Pressure Application

The high colloidal stability of antibody (immunoglobulin) solutions is important for pharmaceutical applications. Inert cosolutes, excipients, are generally used in therapeutic protein formulations to minimize physical instabilities, such as liquid–liquid phase separation (LLPS), aggregation and precipitation, which are often encountered during manufacturing and storage. Despite their widespread use, a detailed understanding of how excipients modulate the specific protein‐protein interactions responsible for these instabilities is still lacking. In this work, we demonstrate the high sensitivity to pressure of globulin condensates as a suitable means to suppress LLPS and subsequent aggregation of concentrated antibody solutions. The addition of excipients has only a minor effect. The high pressure sensitivity observed is due to the fact that these flexible Y‐shaped molecules create a considerable amount of void volume in the condensed phase, leading to an overall decrease in the volume of the system upon dissociation of the droplet phase by pressure already at a few tens of to hundred bar. Moreover, we show that immunoglobulin molecules themselves are highly resistant to unfolding under pressure, and can even sustain pressures up to about 6 kbar without conformational changes. This implies that immunoglobulins are resistant to the pressure treatment of foods, such as milk, in high‐pressure food‐processing technologies, thereby preserving their immunological activity.

Nanoparticle-Protein Interaction: Demystifying the Correlation between Protein Corona and Aggregation Phenomena

Protein corona formation and nanoparticles' aggregation have been heavily discussed over the past years since the lack of fine-mapping of these two combined effects has hindered the targeted delivery evolution and the personalized nanomedicine development. We present a multitechnique approach that combines dynamic light and small-angle X-ray scattering techniques with cryotransmission electron microscopy in a given fashion that efficiently distinguishes protein corona from aggregates formation. This methodology was tested using ∼25 nm model silica nanoparticles incubated with either model proteins or biologically relevant proteomes (such as fetal bovine serum and human plasma) in low and high ionic strength buffers to precisely tune particle-to-protein interactions. In this work, we were able to differentiate protein corona, small aggregates formation, and massive aggregation, as well as obtain fractal information on the aggregates reliably and straightforwardly. The strategy presented here can be expanded to other particle-to-protein mixtures and might be employed as a quality control platform for samples that undergo biological tests.

Multispectroscopic studies on the molecular interactions between bovine gamma-globulin and borohydride-capped silver nanoparticles

Interactions between bovine gamma-globulin (BGG) and borohydride-capped silver nanoparticles (BAgNPs) were studied using dynamic light scattering and spectroscopic techniques like UV-Vis, fluorescence and circular dichroism. The results were compared with earlier reported^[1] interactions between γ-globulin and citrate-coated AgNPs (CAgNPs). BAgNPs were synthesized and characterized. Irrespective of the coating on AgNPs, nanoparticles had formed ground state complexes with the protein. CAgNPs as well as BAgNPS had caused static quenching of tryptophan (Trp) fluorescence of the protein. The change in the capping agent from citrate to borohydride weakened the binding of nanoparticles with the protein. But the same change in capping agent had increased the- fluorescence quenching efficiency of AgNPs. Hydrogen bonding and van der Waals interactions were involved in BGG-BAgNPs complex similar to the CAgNPs complex with γ-globulin. Polarity of the Trp microenvironment in BGG was not altered by BAgNPs contrary to CAgNPs as supported by synchronous and three-dimensional fluorescence. Resonance light scattering experiment also suggested nano-bio conjugation. Far-UV and near-UV CD spectra respectively pointed towards changes in the secondary and tertiary structure of BGG by BAgNPs, which was not observed in case of CAgNPs.

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.

Interactions in protein solutions close to liquid-liquid phase separation: ethanol reduces attractions via changes of the dielectric solution properties

Ethanol is a common protein crystallization agent, precipitant, and denaturant, but also alters the dielectric properties of solutions. While ethanol-induced unfolding is largely ascribed to its hydrophobic parts, its effect on protein phase separation and inter-protein interactions remains poorly understood. Here, the effects of ethanol and NaCl on the phase behavior and interactions of protein solutions are studied in terms of the metastable liquid-liquid phase separation (LLPS) and the second virial coefficient B₂ using lysozyme solutions. Determination of the phase diagrams shows that the cloud-point temperatures are reduced and raised by the addition of ethanol and salt, respectively. The observed trends can be explained using the extended law of corresponding states as changes of B₂. The results for B₂ agree quantitatively with those of static light scattering and small-angle X-ray scattering experiments. Furthermore, B₂ values calculated based on inter-protein interactions described by the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential and considering the dielectric solution properties and electrostatic screening due to the ethanol and salt content quantitatively agree with the experimentally observed B₂ values.

Protein corona meets freeze-drying: overcoming the challenges of colloidal stability, toxicity, and opsonin adsorption

Freeze-drying of nanoparticle suspensions is capable of generating stable nanoformulations with improved storage times and easier transportation. Nonetheless, nanoparticle aggregation is likely induced during freeze-drying, which reduces its redispersibility upon reconstitution and leads to undesirable effects such as non-specific toxicity and impaired efficacy. In this work, bovine serum albumin (BSA) is described as a suitable protectant for silica nanoparticles (SNPs), which result in solid structures with excellent redispersibility and negligible signs of aggregation even when longer storage times are considered. We experimentally demonstrated that massive system aggregation can be prevented when a saturated BSA corona around the nanoparticle is formed before the lyophilization process. Furthermore, the BSA corona is able to suppress non-specific interactions between these nanoparticles and biological systems, as evidenced by the lack of residual cytotoxicity, hemolytic activity and opsonin adsorption. Hence, BSA can be seriously considered for industry as an additive for nanoparticle freeze-drying since it generates solid and redispersible nanoformulations with improved biocompatibility.

Structural characteristics of circulating immune complexes in calves with bronchopneumonia: Impact on the quiescent leukocytes

Calf bronchopneumonia is accompanied by increased level of circulating immune complexes (CIC), and we analysed size, and protein and lipid constituents of these CIC with an attempt to elucidate the connection between the CIC structural properties and their capacity to modulate leukocyte function. CIC of heathy calves (CIC_H) and calves with naturally occurring bronchopneumonia (CIC_D) were isolated by PEG precipitation and analysed by electrophoresis and chromatography. The predominant CIC proteins were IgG, albumin, and transferrin. Affinity isolated serum and CIC IgG coprecipitated several proteins, but only 75 and 80 kDa proteins bound CIC IgG, exclusively. 60 and 65 kDa proteins co-precipitated with CIC_D IgG, unlike CIC_H IgG. In both CIC_H and CIC_D, oleic acid-containing phospholipids predominated. In CIC_D, the content of oleic and vaccenic acid was higher than in CIC_H, while myristic, palmitic, stearic, linoleic and arachidonic acid showed lower content. Dynamic light scattering displayed difference in particle size distribution between CIC_H and CIC_D; 1280 nm large particles were present only in CIC_D. The effect of CIC_H and CIC_D on mononuclear cells (MNC) and granulocytes was analysed in vitro. CIC_H and CIC_D, with slight difference in intensity, stimulate MNC apoptosis, promote cell cycle arrest of unstimulated MNC, and cell cycle progression of PHA stimulated MNC. Both CIC reduced granulocyte apoptosis after 24 h while after 48 h this effect was detected for CIC_D only. These results indicate that structural differences of CIC_H and CIC_D might interfere with the CIC functional capacity, which we consider important for evaluation of CIC immunoregulatory function.

Interplay between Glass Formation and Liquid-Liquid Phase Separation Revealed by the Scattering Invariant

The interplay of the glass transition with liquid-liquid phase separation (LLPS) is a subject of intense debate. We use the scattering invariant Q to probe how approaching the glass transition affects the shape of LLPS boundaries in the temperature/volume fraction plane. Two protein systems featuring kinetic arrest with a lower and an upper critical solution temperature phase behavior, respectively, are studied varying the quench depth. Using Q we noninvasively identify system-dependent differences for the effect of glass formation on the LLPS boundary. The glassy dense phase appears to enter the coexistence region for the albumin-YCl₃ system, whereas it follows the equilibrium binodal for the γ-globulin-PEG system.

Unification of lower and upper critical solution temperature phase behavior of globular protein solutions in the presence of multivalent cations

In globular protein systems, upper critical solution temperature (UCST) behavior is common, but lower critical solution temperature (LCST) phase transitions are rare. In addition, the temperature sensitivity of such systems is usually difficult to tune. Here we demonstrate that the charge state of globular proteins in aqueous solutions can alter their temperature-dependent phase behavior. We show a universal way to tune the effective protein interactions and induce both UCST and LCST-type transitions in the system using trivalent salts. We provide a phase diagram identifying LCST and UCST regimes as a function of protein and salt concentrations. We further propose a model based on an entropy-driven cation binding mechanism to explain the experimental observations.

Atomistic Modeling of Scattering Curves for Human IgG1/4 Reveals New Structure-Function Insights

Small angle x-ray and neutron scattering are techniques that give solution structures for large macromolecules. The creation of physically realistic atomistic models from known high-resolution structures to determine joint x-ray and neutron scattering best-fit structures offers a, to our knowledge, new method that significantly enhances the utility of scattering. To validate this approach, we determined scattering curves for two human antibody subclasses, immunoglobulin G (IgG) 1 and IgG4, on five different x-ray and neutron instruments to show that these were reproducible, then we modeled these by Monte Carlo simulations. The two antibodies have different hinge lengths that connect their antigen-binding Fab and effector-binding Fc regions. Starting from 231,492 and 190,437 acceptable conformations for IgG1 and IgG4, respectively, joint x-ray and neutron scattering curve fits gave low goodness-of-fit R factors for 28 IgG1 and 2748 IgG4 structures that satisfied the disulphide connectivity in their hinges. These joint best-fit structures showed that the best-fit IgG1 models had a greater separation between the centers of their Fab regions than those for IgG4, in agreement with their hinge lengths of 15 and 12 residues, respectively. The resulting asymmetric IgG1 solution structures resembled its crystal structure. Both symmetric and asymmetric solution structures were determined for IgG4. Docking simulations with our best-fit IgG4 structures showed greater steric clashes with its receptor to explain its weaker FcγRI receptor binding compared to our best-fit IgG1 structures with fewer clashes and stronger receptor binding. Compared to earlier approaches for fitting molecular antibody structures by solution scattering, we conclude that this joint fit approach based on x-ray and neutron scattering data, combined with Monte Carlo simulations, significantly improved our understanding of antibody solution structures. The atomistic nature of the output extended our understanding of known functional differences in Fc receptor binding between IgG1 and IgG4.

Dynamics of proteins in solution

The dynamics of proteins in solution includes a variety of processes, such as backbone and side-chain fluctuations, interdomain motions, as well as global rotational and translational (i.e. center of mass) diffusion. Since protein dynamics is related to protein function and essential transport processes, a detailed mechanistic understanding and monitoring of protein dynamics in solution is highly desirable. The hierarchical character of protein dynamics requires experimental tools addressing a broad range of time- and length scales. We discuss how different techniques contribute to a comprehensive picture of protein dynamics, and focus in particular on results from neutron spectroscopy. We outline the underlying principles and review available instrumentation as well as related analysis frameworks.

Normal stress difference-driven particle focusing in nanoparticle colloidal dispersion

Colloidal dispersion has elastic properties due to Brownian relaxation process. However, experimental evidence for the elastic properties, characterized with normal stress differences, is elusive in shearing colloidal dispersion, particularly at low Péclet numbers (Pe < 1). Here, we report that single micrometer-sized polystyrene (PS) beads, suspended in silica nanoparticle dispersion (8 nm radius; 22%, v/v), laterally migrate and form a tightly focused stream by the normal stress differences, generated in pressure-driven microtube flow at low Pe. The nanoparticle dispersion was expected to behave as a Newtonian fluid because of its ultrashort relaxation time (2 μs), but large shear strain experienced by the PS beads causes the notable non-Newtonian behavior. We demonstrate that the unique rheological properties of the nanoparticle dispersion generate the secondary flow in perpendicular to mainstream in a noncircular conduit, and the elastic properties of blood plasma-constituting protein solutions are elucidated by the colloidal dynamics of protein molecules.

Protein Short-Time Diffusion in a Naturally Crowded Environment

The interior of living cells is a dense and polydisperse suspension of macromolecules. Such a complex system challenges an understanding in terms of colloidal suspensions. As a fundamental test we employ neutron spectroscopy to measure the diffusion of tracer proteins (immunoglobulins) in a cell-like environment (cell lysate) with explicit control over crowding conditions. In combination with Stokesian dynamics simulation, we address protein diffusion on nanosecond time scales where hydrodynamic interactions dominate over negligible protein collisions. We successfully link the experimental results on these complex, flexible molecules with coarse-grained simulations providing a consistent understanding by colloid theories. Both experiments and simulations show that tracers in polydisperse solutions close to the effective particle radius R_eff = ⟨ R_i³⟩^1/3 diffuse approximately as if the suspension was monodisperse. The simulations further show that macromolecules of sizes R > R_eff ( R < R_eff) are slowed more (less) effectively even at nanosecond time scales, which is highly relevant for a quantitative understanding of cellular processes.

Reentrant Phase Behavior in Protein Solutions Induced by Multivalent Salts: Strong Effect of Anions Cl- Versus NO3

In this work, the effects of the two anions Cl^- and NO₃^- on the phase behavior of bovine serum albumin (BSA) in solution with trivalent salts are compared systematically. In the presence of trivalent metal salts, negatively charged proteins such as BSA in solution undergo a reentrant condensation (RC) phase behavior, which has been established for several proteins with chlorides of trivalent salts. Here, we show that replacing Cl^- by NO₃^- leads to a marked change in the phase behavior. The effect is investigated for the two different cations Y³⁺ and La³⁺. The salts are thus YCl₃, Y(NO₃)₃, LaCl₃, and La(NO₃)₃. The experimental phase behavior shows that while the chloride salts induce both liquid-liquid phase separation (LLPS) and RC, the nitrate salts also induce LLPS, but RC becomes partial with La(NO₃)₃ and disappears with Y(NO₃)₃. The observed phase behavior is rationalized by effective protein-protein interactions which are characterized using small-angle X-ray scattering. The results based on the reduced second virial coefficients B₂/ B₂^HS and 1/ I( q → 0) demonstrate that the NO₃^- salts induce a stronger attraction than the Cl^- salts. Overall, the effective attraction, the width of the condensed regime in the RC phase diagram, and the nature of LLPS follow the order LaCl₃ < YCl₃ < La(NO₃)₃ < Y(NO₃)₃. Despite the decisive role of cations in RC phase behavior, isothermal titration calorimetry measurements indicate that replacing anions does not significantly influence the cation binding to proteins. The experimental results observed are discussed based on an "enhanced Hofmeister effect" including electrostatic and hydrophobic interactions between protein-cation complexes.

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.

Recent developments in small-angle X-ray scattering and hybrid method approaches for biomacromolecular solutions

Small-angle X-ray scattering (SAXS) has become a streamline method to characterize biological macromolecules, from small peptides to supramolecular complexes, in near-native solutions. Modern SAXS requires limited amounts of purified material, without the need for labelling, crystallization, or freezing. Dedicated beamlines at modern synchrotron sources yield high-quality data within or below several milliseconds of exposure time and are highly automated, allowing for rapid structural screening under different solutions and ambient conditions but also for time-resolved studies of biological processes. The advanced data analysis methods allow one to meaningfully interpret the scattering data from monodisperse systems, from transient complexes as well as flexible and heterogeneous systems in terms of structural models. Especially powerful are hybrid approaches utilizing SAXS with high-resolution structural techniques, but also with biochemical, biophysical, and computational methods. Here, we review the recent developments in the experimental SAXS practice and in analysis methods with a specific focus on the joint use of SAXS with complementary methods.

Metastability Gap in the Phase Diagram of Monoclonal IgG Antibody

Crystallization of IgG antibodies has important applications in the fields of structural biology, biotechnology, and biopharmaceutics. However, a rational approach to crystallize antibodies is still lacking. In this work, we report a method to estimate the solubility of antibodies at various temperatures. We experimentally determined the full phase diagram of an IgG antibody. Using the full diagram, we examined the metastability gaps, i.e., the distance between the crystal solubility line and the liquid-liquid coexistence curve, of IgG antibodies. By comparing our results to the partial phase diagrams of other IgGs reported in literature, we found that IgG antibodies have similar metastability gaps. Thereby, we present an equation with two phenomenological parameters to predict the approximate location of the solubility line of IgG antibodies with respect to their liquid-liquid coexistence curves. We have previously shown that the coexistence curve of an antibody solution can be readily determined by the polyethylene glycol-induced liquid-liquid phase separation method. Combining the polyethylene glycol-induced liquid-liquid phase separation measurements and the phenomenological equation in this article, we provide a general and practical means to predict the thermodynamic conditions for crystallizing IgG antibodies in the solution environments of interest.

Arrested and temporarily arrested states in a protein-polymer mixture studied by USAXS and VSANS

We investigate the transition of the phase separation kinetics from a complete to an arrested liquid-liquid phase separation (LLPS) in mixtures of bovine γ-globulin with polyethylene glycol (PEG). The solutions feature LLPS with upper critical solution temperature phase behavior. At higher PEG concentrations or low temperatures, non-equilibrium, gel-like states are found. The kinetics is followed during off-critical quenches by ultra-small angle X-ray scattering (USAXS) and very-small angle neutron scattering (VSANS). For shallow quenches a kinetics consistent with classical spinodal decomposition is found, with the characteristic length (ξ) growing with time as ξ ∼ t^1/3. For deep quenches, ξ grows only very slowly with a growth exponent smaller than 0.05 during the observation time, indicating an arrested phase separation. For intermediate quench depths, a novel growth kinetics featuring a three-stage coarsening is observed, with an initial classical coarsening, a subsequent slowdown of the growth, and a later resumption of coarsening approaching again ξ ∼ t^1/3. Samples featuring the three-stage coarsening undergo a temporarily arrested state. We hypothesize that, while intermittent coarsening and collapse might contribute to the temporary nature of the arrested state, migration-coalescence of the minority liquid phase through the majority glassy phase may be the main mechanism underlying this kinetics, which is also consistent with earlier simulation results.