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.

Using Cluster Theory to Calculate the Experimental Structure Factors of Antibody Solutions.

Monoclonal antibody solutions are set to become a major therapeutic tool in the years to come, capable of targeting various diseases by clever design of their antigen binding site. However, the formulation of stable solutions suitable for patient self-administration typically presents challenges, as a result of the increase in viscosity that often occurs at high concentrations. Here, we establish a link between the microscopic molecular details and the resulting properties of an antibody solution through the characterization of clusters, which arise in the presence of self-associating antibodies. In particular, we find that experimental small-angle X-ray scattering data can be interpreted by means of analytical models previously exploited for the study of polymeric and colloidal objects, based on the presence of such clusters. The latter are determined by theoretical calculations and supported by computer simulations of a coarse-grained minimal model, in which antibodies are treated as Y-shaped colloidal molecules and attractive domains are designed as patches. Using the theoretically predicted cluster size distributions, we are able to describe the experimental structure factors over a wide range of concentration and salt conditions. We thus provide microscopic evidence for the well-established fact that the concentration-dependent increase in viscosity is originated by the presence of clusters. Our findings bring new insights on the self-assembly of monoclonal antibodies, which can be exploited for guiding the formulation of stable and effective antibody solutions.

Probing Cage Relaxation in Concentrated Protein Solutions by X-Ray Photon Correlation Spectroscopy.

Diffusion of proteins on length scales of their size is crucial for understanding the machinery of living cells. X-ray photon correlation spectroscopy (XPCS) is currently the only way to access long-time collective diffusion on these length scales, but radiation damage so far limits the use in biological systems. We apply a new approach to use XPCS to measure cage relaxation in crowded α-crystallin solutions. This allows us to correct for radiation effects, obtain missing information on long time diffusion, and support the fundamental analogy between protein and colloid dynamical arrest.

Crowding in the Eye Lens: Modeling the Multisubunit Protein ß-Crystallin with a Colloidal Approach.

We present a multiscale characterization of aqueous solutions of the bovine eye lens protein ßH crystallin from dilute conditions up to dynamical arrest, combining dynamic light scattering, small-angle x-ray scattering, tracer-based microrheology, and neutron spin echo spectroscopy. We obtain a comprehensive explanation of the observed experimental signatures from a model of polydisperse hard spheres with additional weak attraction. In particular, the model predictions quantitatively describe the multiscale dynamical results from microscopic nanometer cage diffusion over mesoscopic micrometer gradient diffusion up to macroscopic viscosity. Based on a comparative discussion with results from other crystallin proteins, we suggest an interesting common pathway for dynamical arrest in all crystallin proteins, with potential implications for the understanding of crowding effects in the eye lens.

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.

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.

Optical Microrheology of Protein Solutions Using Tailored Nanoparticles.

This work represents a critical re-examination of the application of dynamic light scattering (DLS)-based tracer particle microrheology to measure the zero shear viscosity of aqueous solutions of different proteins up to very high concentrations. It is demonstrated that a combination of surface-functionalized tracer particles, the use of the so-called 3D-DLS technique, and carefully chosen parameters for the scattering experiments is essential for a reliable and artifact-free determination of the viscosity of highly diverse protein solutions, while keeping the amount of protein to a minimum. The major challenges that arise in such microrheology experiments with protein solutions are discussed and used as guiding principles for the synthesis of all-purpose tracer particles with optimal size and an efficient surface functionalization, and the choice of the appropriate amount of tracers in the sample. Potential problems arising from depletion attractions between the tracer particles induced by the proteins are addressed, and compelling evidences for the absence of such effects are presented. The validity of the approach is corroborated by the perfect agreement between the zero shear viscosity obtained from 3D-DLS-based microrheology and literature data from classical rheological measurements for two vastly different protein-solvent systems up to concentrations close to the arrest transition.

Hard sphere-like glass transition in eye lens α-crystallin solutions.

We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens α-crystallin solutions, using small-angle X-ray scattering, static and dynamic light scattering, viscometry, molecular dynamics simulations, and mode-coupling theory. We find that a polydisperse Percus-Yevick hard-sphere liquid-structure model accurately reproduces both static light scattering data and small-angle X-ray scattering liquid structure data from α-crystallin solutions over an extended range of protein concentrations up to 290 mg/mL or 49% vol fraction and up to ca. 330 mg/mL for static light scattering. The measured dynamic light scattering and viscosity properties are also consistent with those of hard-sphere colloids and show power laws characteristic of an approach toward a glass transition at α-crystallin volume fractions near 58%. Dynamic light scattering at a volume fraction beyond the glass transition indicates formation of an arrested state. We further perform event-driven molecular dynamics simulations of polydisperse hard-sphere systems and use mode-coupling theory to compare the measured dynamic power laws with those of hard-sphere models. The static and dynamic data, simulations, and analysis show that aqueous eye lens α-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The α-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis.

Theoretical predictions of structures in dispersions containing charged colloidal particles and non-adsorbing polymers.

We develop a theoretical model to describe structural effects on a specific system of charged colloidal polystyrene particles, upon the addition of non-adsorbing PEG polymers. This system has previously been investigated experimentally, by scattering methods, so we are able to quantitatively compare predicted structure factors with corresponding experimental data. Our aim is to construct a model that is coarse-grained enough to be computationally manageable, yet detailed enough to capture the important physics. To this end, we utilize classical polymer density functional theory, wherein all possible polymer configurations are accounted for, subject to a mean-field Boltzmann weight. We make efforts to counteract drawbacks with this mean-field approach, resulting in structural predictions that agree very well with computationally more demanding simulations. Electrostatic interactions are handled at the fully non-linear Poisson-Boltzmann level, and we demonstrate that a linearization leads to less accurate predictions. The particle charge is an experimentally unknown parameter. We define the surface charge such that the experimental and theoretical gel point at equal polymer concentration coincide. Assuming a fixed surface charge for a certain salt concentration, we find very good agreements between measured and predicted structure factors across a wide range of polymer concentrations. We also present predictions for other structural quantities, such as radial distribution functions, and cluster size distributions. Finally, we demonstrate that our model predicts the occurrence of equilibrium clusters at high polymer concentrations, but low particle volume fractions and salt levels.

A multi-scale numerical approach to study monoclonal antibodies in solution.

Developing efficient and robust computational models is essential to improve our understanding of protein solution behavior. This becomes particularly important to tackle the high-concentration regime. In this context, the main challenge is to put forward coarse-grained descriptions able to reduce the level of detail, while retaining key features and relevant information. In this work, we develop an efficient strategy that can be used to investigate and gain insight into monoclonal antibody solutions under different conditions. We use a multi-scale numerical approach, which connects information obtained at all-atom and amino-acid levels to bead models. The latter has the advantage of reproducing the properties of interest while being computationally much faster. Indeed, these models allow us to perform many-protein simulations with a large number of molecules. We can, thus, explore conditions not easily accessible with more detailed descriptions, perform effective comparisons with experimental data up to very high protein concentrations, and efficiently investigate protein-protein interactions and their role in phase behavior and protein self-assembly. Here, a particular emphasis is given to the effects of charges at different ionic strengths.

Testing mixing rules for structural and dynamical quantities in multi-component crowded protein solutions.

Crowding effects significantly influence the phase behavior and the structural and dynamic properties of the concentrated protein mixtures present in the cytoplasm of cells or in the blood serum. This poses enormous difficulties for our theoretical understanding and our ability to predict the behavior of these systems. While the use of course grained colloid-inspired models allows us to reproduce the key physical solution properties of concentrated monodisperse solutions of individual proteins, we lack corresponding theories for complex polydisperse mixtures. Here, we test the applicability of simple mixing rules in order to predict solution properties of protein mixtures. We use binary mixtures of the well-characterized bovine eye lens proteins α and γB crystallin as model systems. Combining microrheology with static and dynamic scattering techniques and observations of the phase diagram for liquid-liquid phase separation, we show that reasonably accurate descriptions are possible for macroscopic and mesoscopic signatures, while information on the length scale of the individual protein size requires more information on cross-component interaction.

Sterically stabilized colloids with tunable repulsions.

When studying tunable electrostatic repulsions in aqueous suspensions of charged colloids, irreversible colloid aggregation or gelation may occur at high salt concentrations. For many commonly used synthetic colloids, such as polystyrene and silica particles, the reason for coagulation is the presence of unbalanced, strongly attractive, and short-ranged van der Waals (VDW) forces. Here, we present an aqueous polystyrene model colloid that is sterically stabilized against VDW attractions. We show that the synthesis procedure, based on a neutral initiator couple and a nonionic surfactant, introduces surface charges that can be further increased by the addition of charged comonomer methacrylic acid. Thus, the interactions between the polystyrene spheres can be conveniently tuned from hard-sphere-like to charge-stabilized with long-ranged electrostatic repulsions described by a Yukawa-type pair potential. The particle size, grafting density, core-shell structure, and surface charge are characterized by light and neutron scattering. Using X-ray and neutron scattering in combination with an accurate analytic integral equation scheme for the colloidal static structure factor, we deduce effective particle charges for colloid volume fractions ≥0.1 and salt concentrations in the range of 1.5 to 50 mM.

Light and neutron scattering study of PEG-oleate and its use in emulsion polymerization.

Steric stabilization of colloids forms a robust mechanism to obtain colloids that are stable in a variety of environments, and that can be used to study the phase behavior of hard or soft spheres. We report the synthesis of sterically stabilized colloids in an aqueous environment using readily dissolvable surfactants, with an unsaturated hydrophobic tail. We synthesized a new surfactant by esterification of a poly(ethylene glycol) (PEG) chain of 4.1 kg/mol with oleic acid, called PEG4OA. The micellization of PEG4OA was characterized by light and neutron scattering, which yielded values for the aggregation number and the overall size that are in excellent agreement with a comparable surfactant with a saturated octadecane chain, Brij 700. We successfully used PEG4OA in the emulsion polymerization of polystyrene colloids. In comparison with the smaller surfactant Tween 80, PEG4OA yielded smaller colloids with radii around 50 nm, and the addition of 1-dodecanethiol reduced the formation of aggregates during the synthesis. A contrast variation study with small angle neutron scattering (SANS) showed that a dense PEG layer was grafted to the colloid surface.

Accurate Correction of the "Bulk Response" in Surface Plasmon Resonance Sensing Provides New Insights on Interactions Involving Lysozyme and Poly(ethylene glycol).

Surface plasmon resonance is a very well-established surface sensitive technique for label-free analysis of biomolecular interactions, generating thousands of publications each year. An inconvenient effect that complicates interpretation of SPR results is the "bulk response" from molecules in solution, which generate signals without really binding to the surface. Here we present a physical model for determining the bulk response contribution and verify its accuracy. Our method does not require a reference channel or a separate surface region. We show that proper subtraction of the bulk response reveals an interaction between poly(ethylene glycol) brushes and the protein lysozyme at physiological conditions. Importantly, we also show that the bulk response correction method implemented in commercial instruments is not generally accurate. Using our method, the equilibrium affinity between polymer and protein is determined to be KD = 200 µM. One reason for the weak affinity is that the interaction is relatively short-lived (1/koff < 30 s). Furthermore, we show that the bulk response correction also reveals the dynamics of self-interactions between lysozyme molecules on surfaces. Besides providing new insights on important biomolecular interactions, our method can be widely applied to improve the accuracy of SPR data generated by instruments worldwide.

The pH induced sol-gel transition in skim milk revisited. A detailed study using time-resolved light and x-ray scattering experiments.

We present a detailed study of the evolution of the size, structure and stability of casein micelles upon acidification of skim milk typically applied in yogurt-making processes using a combination of time-resolved light and small-angle X-ray scattering experiments. While most of the available light scattering studies on casein acidification have been restricted to transparent and therefore highly diluted samples, we now profit from a newly developed multiangle 3D light scattering instrument, which allows for time-resolved measurements in highly turbid samples. Our experiments clearly demonstrate the presence of two parallel pH-dependent processes, micellar reassembly and aggregation. Using a systematic investigation of the effect of casein concentration, acidification rate, and ionic strength, we are able to decouple these two processes and obtain detailed information about the pH-induced restructuration of the casein micelle structure that occurs prior to destabilization. Moreover, our experiments also unambiguously demonstrate that these micellar reassembly processes are highly concentration dependent, and that typical light scattering studies conducted under highly diluted conditions are resulting in findings that may not be relevant for the situation encountered in industrial processes at higher concentrations. Experiments conducted with covalently cross-linked micelles, where the pH-induced reassembly has been suppressed, further confirm our findings.

Self-diffusion of nonspherical particles fundamentally conflicts with effective sphere models.

Modeling diffusion of nonspherical particles presents an unsolved and considerable challenge, despite its importance for the understanding of crowding effects in biology, food technology and formulation science. A common approach in experiment and simulation is to map nonspherical objects on effective spheres to subsequently use the established predictions for spheres to approximate phenomena for nonspherical particles. Using numerical evaluation of the hydrodynamic mobility tensor, we show that this so-called effective sphere model fundamentally fails to represent the self-diffusion in solutions of ellipsoids as well as rod-like assemblies of spherical beads. The effective sphere model drastically overestimates the slowing down of self-diffusion down to volume fractions below 0.01. Furthermore, even the linear term relevant at lower volume fraction is inaccurate, linked to a fundamental misconception of effective sphere models. To overcome the severe problems related with the use of effective sphere models, we suggest a protocol to predict the short-time self-diffusion of rod-like systems, based on simulations with hydrodynamic interactions that become feasible even for more complex molecules as the essential observable shows a negligible system-size effect.

Equilibrium cluster formation in concentrated protein solutions and colloids.

Controlling interparticle interactions, aggregation and cluster formation is of central importance in a number of areas, ranging from cluster formation in various disease processes to protein crystallography and the production of photonic crystals. Recent developments in the description of the interaction of colloidal particles with short-range attractive potentials have led to interesting findings including metastable liquid-liquid phase separation and the formation of dynamically arrested states (such as the existence of attractive and repulsive glasses, and transient gels). The emerging glass paradigm has been successfully applied to complex soft-matter systems, such as colloid-polymer systems and concentrated protein solutions. However, intriguing problems like the frequent occurrence of cluster phases remain. Here we report small-angle scattering and confocal microscopy investigations of two model systems: protein solutions and colloid-polymer mixtures. We demonstrate that in both systems, a combination of short-range attraction and long-range repulsion results in the formation of small equilibrium clusters. We discuss the relevance of this finding for nucleation processes during protein crystallization, protein or DNA self-assembly and the previously observed formation of cluster and gel phases in colloidal suspensions.

Eye lens crystallin proteins inhibit the autocatalytic amyloid amplification nature of mature α-synuclein fibrils.

Parkinson´s disease is characterized by the accumulation of proteinaceous aggregates in Lewy bodies and Lewy Neurites. The main component found in such aggregates is α-synuclein. Here, we investigate how bovine eye lens crystallin proteins influence the aggregation kinetics of α-synuclein at mildly acidic pH (5.5) where the underlying aggregation mechanism of this protein is dominated by secondary nucleation of monomers on fibril surface providing an autocatalytic amyloid amplification process. Bovine α-, ßH- and γB-crystallins were found to display chaperone-like activity inhibiting α-synuclein aggregation. This effect was shown to be time-dependent, with early additions of α-crystallin capable of retarding and even inhibiting aggregation during the time frame of the experiment. The inhibitory nature of crystallins was further investigated using trap and seed kinetic experiments. We propose crystallins interact with mature α-synuclein fibrils, possibly binding along the surfaces and at fibril free ends, inhibiting both elongation and monomer-dependent secondary nucleation processes in a mechanism that may be generic to some chaperones that prevent the onset of protein misfolding related pathologies.

Synthesis and application of PEGylated tracer particles for measuring protein solution viscosities using Dynamic Light Scattering-based microrheology.

The measurement of flow properties, such as the zero shear viscosity, of protein solutions is of paramount importance for many applications such as pharmaceutical formulations, where the syringeability of physiologically effective doses is a key property. However, the determination of these properties with classical rheological methods is often challenging due to e.g. detrimental surface effects or simply the lack of sufficient material. A possible alternative is Dynamic Light Scattering-based microrheology, where the Brownian motion of tracer particles embedded in the protein solution is monitored to access the zero shear viscosity of the sample. The prime advantages of this method compared to classical rheology are the absence of disturbing surface effects and the up to two orders of magnitude smaller protein quantities needed for an entire concentration series. This Protocol provides a detailed description of the synthesis of sterically stabilized tracer particles with surface and overall particle properties specifically designed to investigate the viscosity of protein solutions up to concentrations close to the arrest transition. These particles are tailored to avoid protein-particle as well as particle-particle aggregation at various sample conditions and thus allow for an artifact-free application of Dynamic Light Scattering-based tracer microrheology to determine the flow behaviour of biological samples. The Protocol concludes with step by step instructions for the characterization of protein solutions using a combination of the tracer particles and an advanced dynamic light scattering technique yielding the concentration-dependent zero shear viscosity.

Experimental Evidence for a Cluster Glass Transition in Concentrated Lysozyme Solutions.

Lysozyme is known to form equilibrium clusters at pH ≈ 7.8 and at low ionic strength as a result of a mixed potential. While this cluster formation and the related dynamic and static structure factors have been extensively investigated, its consequences on the macroscopic dynamic behavior expressed by the zero shear viscosity η0 remain controversial. Here we present results from a systematic investigation of η0 using two complementary passive microrheology techniques, dynamic light scattering based tracer microrheology, and multiple particle tracking using confocal microscopy. The combination of these techniques with a simple but effective evaporation approach allows for reaching concentrations close to and above the arrest transition in a controlled and gentle way. We find a strong increase of η0 with increasing volume fraction ϕ with an apparent divergence at ϕ ≈ 0.35, and unambiguously demonstrate that this is due to the existence of an arrest transition where a cluster glass forms. These findings demonstrate the power of tracer microrheology to investigate complex fluids, where weak temporary bonds and limited sample volumes make measurements with classical rheology challenging.