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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Weak Shape Anisotropy Leads to a Nonmonotonic Contribution to Crowding, Impacting Protein Dynamics under Physiologically Relevant Conditions.

The effect of a nonspherical particle shape on the dynamics in crowded solutions presents a significant challenge for a comprehensive understanding of interaction and structural relaxation in biological and soft matter. We report that small deviations from a spherical shape induce a nonmonotonic contribution to the crowding effect on the short-time cage diffusion compared with spherical systems, using molecular dynamics simulations with mesoscale hydrodynamics of a multiparticle collision dynamics fluid in semidilute systems with volume fractions smaller than 0.35. We show that the nonmonotonic effect due to anisotropy is caused by the combination of a reduced relative mobility over the entire concentration range and a looser and less homogeneous cage packing of nonspherical particles. Our finding stresses that nonsphericity induces new complexity, which cannot be accounted for in effective sphere models, and is of great interest in applications such as formulations as well as for the fundamental understanding of soft matter in general and crowding effects in living cells in particular.

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.

Interpenetration of polymeric microgels at ultrahigh densities.

Soft particles such as polymeric microgels can form ultra-dense phases, where the average center-to-center distance a s can be smaller than the initial unperturbed particle diameter σ 0, due to their ability to interpenetrate and compress. However, despite of the effort devoted to microgels at ultrahigh densities, we know surprisingly little about their response to their environment at effective volume fractions ϕ eff above close packing (ϕ cp ), and the existing information is often contradictory. Here we report direct measurements of the size and shape of poly(N-isopropylacrylamide) microgels at concentrations below and above ϕ cp using the zero average contrast method in small-angle neutron scattering. We complement these experiments with measurements of the average interparticle distances using small-angle x-ray scattering, and a determination of the glass transition using dynamic light scattering. This allows us to unambiguously decouple interaction effects from density-dependent variations of the particle size and shape at all values of ϕ eff . We demonstrate that the microgels used in this study significantly interpenetrate and thus change their size and shape only marginally even for ϕ eff ≫ ϕ cp , a finding that may require changes in the interpretation of a number of previously published studies on the structural and dynamic properties of dense soft particle systems.

Characterization of cereal ß-glucan extracts from oat and barley and quantification of proteinaceous matter.

An extraction method for mixed-linkage ß-glucan from oat and barley was developed in order to minimize the effect of extraction on the ß-glucan structure. ß-Glucan were characterized in terms of molecular size and molar mass distributions using asymmetric flow field-flow fractionation (AF4) coupled to multiangle light scattering (MALS), differential refractive index (dRI) and fluorescence (FL) detection. The carbohydrate composition of the extracts was analysed using polysaccharide analysis by carbohydrate gel electrophoresis (PACE) and high-performance anion-exchange chromatography (HPAEC). Whether there were any proteinaceous moieties linked to ß-glucan was also examined. Purified extracts contained 65% and 53% ß-glucan for oats and barley, respectively. The main impurities were degradation products of starch. The extracts contained high molecular weight ß-glucan (105-108 g/mol) and large sizes (root-mean-square radii from 20 to 140 nm). No proteins covalently bound to ß-glucan were detected; therefore, any suggested functionality of proteins regarding the health benefits of ß-glucan can be discounted.

Dramatic influence of patchy attractions on short-time protein diffusion under crowded conditions.

In the dense and crowded environment of the cell cytoplasm, an individual protein feels the presence of and interacts with all surrounding proteins. While we expect this to strongly influence the short-time diffusion coefficient Ds of proteins on length scales comparable to the nearest-neighbor distance, this quantity is difficult to assess experimentally. We demonstrate that quantitative information about Ds can be obtained from quasi-elastic neutron scattering experiments using the neutron spin echo technique. We choose two well-characterized and highly stable eye lens proteins, bovine α-crystallin and γB-crystallin, and measure their diffusion at concentrations comparable to those present in the eye lens. While diffusion slows down with increasing concentration for both proteins, we find marked variations that are directly linked to subtle differences in their interaction potentials. A comparison with computer simulations shows that anisotropic and patchy interactions play an essential role in determining the local short-time dynamics. Hence, our study clearly demonstrates the enormous effect that weak attractions can have on the short-time diffusion of proteins at concentrations comparable to those in the cellular cytosol.

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.

Extended Law of Corresponding States Applied to Solvent Isotope Effect on a Globular Protein.

Investigating proteins with techniques such as NMR or neutron scattering frequently requires the partial or complete substitution of D2O for H2O as a solvent, often tacitly assuming that such a solvent substitution does not significantly alter the properties of the protein. Here, we report a systematic investigation of the solvent isotope effect on the phase diagram of the lens protein γB-crystallin in aqueous solution as a model system exhibiting liquid-liquid phase separation. We demonstrate that the observed strong variation of the critical temperature Tc can be described by the extended law of corresponding states for all H2O/D2O ratios, where scaling of the temperature by Tc or the reduced second virial coefficient accurately reproduces the binodal, spinodal, and osmotic compressibility. These findings highlight the impact of H2O/D2O substitution on γB-crystallin properties and warrant further investigations into the universality of this phenomenon and its underlying mechanisms.