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.

On the role of softness in ionic microgel interactions.

Thermoresponsive microgels are a popular model system to study phase transitions in soft matter, because temperature directly controls their volume fraction. Ionic microgels are additionally pH-responsive and possess a rich phase diagram. Although effective interaction potentials between microgel particles have been proposed, these have never been fully tested, leading to a gap in our understanding of the link between single-particle and collective properties. To help resolve this gap, four sets of ionic microgels with varying crosslinker density were synthesised and characterised using light scattering techniques and confocal microscopy. The resultant structural and dynamical information was used to investigate how particle softness affects the phase behaviour of ionic microgels and to validate the proposed interaction potential. We find that the architecture of the microgel plays a marked role in its phase behaviour. Rather than the ionic charges, it is the dangling ends which drive phase transitions and interactions at low concentration. Comparison to theory underlines the need for a refined theoretical model which takes into consideration these close-contact interactions.

ArGSLab: a tool for analyzing experimental or simulated particle networks.

Microscopy and particle-based simulations are both powerful techniques to study aggregated particulate matter such as colloidal gels. The data provided by these techniques often contains information on a wide array of length scales, but structural analysis methods typically focus on the local particle arrangement, even though the data also contains information about the particle network on the mesoscopic length scale. In this paper, we present a MATLAB software package for quantifying mesoscopic network structures in colloidal samples. ArGSLab (Arrested and Gelated Structures Laboratory) extracts a network backbone from the input data, which is in turn transformed into a set of nodes and links for graph theory-based analysis. The routines can process both image stacks from microscopy as well as explicit coordinate data, and thus allows quantitative comparison between simulations and experiments. ArGSLab furthermore enables the accurate analysis of microscopy data where, e.g., an extended point spread function prohibits the resolution of individual particles. We demonstrate the resulting output for example datasets from both microscopy and simulation of colloidal gels, in order to showcase the capability of ArGSLab to quantitatively analyze data from various sources. The freely available software package can be used either with a provided graphical user interface or directly as a MATLAB script.

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.

Using Patchy Particles to Prevent Local Rearrangements in Models of Non-equilibrium Colloidal Gels.

Simple models based on isotropic interparticle attractions often fail to capture experimentally observed structures of colloidal gels formed through spinodal decomposition and subsequent arrest: the resulting gels are typically denser and less branched than their experimental counterparts. Here, we simulate gels formed from soft particles with directional attractions ("patchy particles"), designed to inhibit lateral particle rearrangement after aggregation. We directly compare simulated structures with experimental colloidal gels made using soft attractive microgel particles, by employing a "skeletonization" method that reconstructs the three-dimensional backbone from experiment or simulation. We show that including directional attractions with sufficient valency leads to strongly branched structures compared to isotropic models. Furthermore, combining isotropic and directional attractions provides additional control over aggregation kinetics and gel structure. Our results show that the inhibition of lateral particle rearrangements strongly affects the gel topology and is an important effect to consider in computational models of colloidal gels.

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.

Controlling the morphology of microgels by ionic stimuli.

Stimuli-responsive microgels have attracted much interest for their use as vehicles for drug delivery or as the building blocks of adaptive materials. Ionic microgel particles, including popular poly(NIPAM-co-acrylic acid), show strong mechanical responsiveness to many external stimuli, including changes in ionic strength or acidity. In this work, we demonstrate that combining multiple ionic stimuli can enable detailed control over the morphology of microgels. To this extent, we analyze the particle morphology in various surroundings with light-scattering techniques. First, we find strong indications of an inverted density profile in the core of the particles. Secondly, we show that the swelling of this hydrogel core and the corona of dangling polymer ends can be targeted separately by a combination of deionization and deprotonation steps. Hence, this work represents an advance in tailoring particle morphologies after synthesis in a predictable fashion.

A microgel-Pickering emulsion route to colloidal molecules with temperature-tunable interaction sites.

A simple Pickering emulsion route has been developed for the assembly of temperature-responsive poly(N-isopropylacrylamide) (PNIPAM) microgel particles into colloidal molecules comprising a small number of discrete microgel interaction sites on a central oil emulsion droplet. Here, the surface activity of the microgels serves to drive their assembly through adsorption to growing polydimethylsiloxane (PDMS) emulsion oil droplets of high monodispersity, prepared in situ via ammonia-catalysed hydrolysis and condensation of dimethyldiethoxysilane (DMDES). A dialysis step is employed in order to limit further growth once the target assembly size has been reached, thus yielding narrowly size-distributed, colloidal molecule-like microgel-Pickering emulsion oil droplets with well-defined microgel interaction sites. The temperature-responsiveness of the PNIPAM interaction sites will allow for the directional interactions to be tuned in a facile manner with temperature, all the way from soft repulsive to short-range attractive as the their volume phase transition temperature (VPTT) is crossed. Finally, the microgel-Pickering emulsion approach is extended to a mixture of PNIPAM and poly(N-isopropylmethacrylamide) (PNIPMAM) microgels that differ with respect to their VPTT, this in order to prepare patchy colloidal molecules where the directional interactions will be more readily resolved.

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.

Preparation of colloidal molecules with temperature-tunable interactions from oppositely charged microgel spheres.

The self-assembly of small colloidal clusters, so-called colloidal molecules, into crystalline materials has proven extremely challenging, the outcome often being glassy, amorphous states where positions and orientations are locked. In this paper, a new type of colloidal molecule is therefore prepared, assembled from poly(N-isopropylacrylamide) (PNIPAM)-based microgels that due to their well documented softness and temperature-response allow for greater defect tolerance compared to hard spheres and for convenient in situ tuning of size, volume fraction and inter-particle interactions with temperature. The microgels (B) are assembled by electrostatic adsorption onto oppositely charged, smaller-sized microgels (A), where the relative size of the two determines the valency (n) of the resulting core-satellite ABn-type colloidal molecules. Following assembly, a microfluidic deterministic lateral displacement (DLD) device is used to effectively isolate AB4-type colloidal molecules of tetrahedral geometry that possess a repulsive-to-attractive transition on crossing the microgels' volume phase transition temperature (VPTT). These soft, temperature-responsive colloidal molecules constitute highly promising building blocks for the preparation of new materials with emergent properties, and their optical wavelength-size makes them especially interesting for optical applications.

Soft particles in an electric field - a zero average contrast study.

We report on the structural properties of ionic microgel particles subjected to alternating electric fields, using small-angle neutron scattering. The experiments were performed under so-called zero average contrast conditions, which cancel the structure factor contribution to the scattered intensity, allowing us to obtain direct information on the single particle size and structure as particles align in field-induced strings. Our results reveal only a marginal compression of the particles as they align in strings, and indicate considerable particle overlap at higher field strengths. These findings provide further insight into the origins of the previously reported unusual path dependent field-induced crystal-crystal transition found for these systems (P. S. Mohanty et al., Phys. Rev. X, 2015, 5, 011030).

Anomalous Dynamics of Magnetic Anisotropic Colloids Studied by XPCS.

The influence of an applied magnetic field on the collective dynamics of novel anisotropic colloidal particles whose shape resembles peanuts is reported. Being made up of hematite cores and silica shells, these micrometer-sized particles align in a direction perpendicular to the applied external magnetic field, and assemble into chains along the field direction. The anisotropic dynamics of these particles is investigated using multispeckle ultrasmall-angle X-ray photon correlation spectroscopy (USA-XPCS). The results indicate that along the direction of the magnetic field, the particle dynamics strongly depends on the length scale probed. Here, the relaxation of the intermediate scattering function follows a compressed exponential behavior at large distances, while it appears diffusive at distances comparable or smaller than the particle size. Perpendicular to the applied field (and along the direction of gravity), the experimental data can be quantitatively reproduced by a combination of an advective term originating from sedimentation and a purely diffusive one that describes the thermal diffusion of the assembled chains and individual particles.

Deswelling behaviour of ionic microgel particles from low to ultra-high densities.

The swelling of ionic microgel particles is investigated at a wide range of concentrations using a combination of light, X-ray and neutron scattering techniques. We employ a zero-average contrast approach for small-angle neutron scattering experiments, which enables a direct determination of the form factor at high concentrations. The observed particle size initially decreases strongly with the particle concentration in the dilute regime but approaches a constant value at intermediate concentrations. This is followed by a further deswelling at high concentrations above particle overlap. Theory and experiments point at a pivotal contribution of dangling polymer ends to the strong variation in size of ionic microgels, which presents itself mainly through the hydrodynamics properties of the system.

Directed Self-Assembly of Polarizable Ellipsoids in an External Electric Field.

The interplay between shape anisotropy and directed long-range interactions enables the self-assembly of complex colloidal structures. As a recent highlight, ellipsoidal particles polarized in an external electric field were observed to associate into well-defined tubular structures. In this study, we systematically investigate such directed self-assembly using Monte Carlo simulations of a two-point-charge model of polarizable prolate ellipsoids. In spite of its simplicity and computational efficiency, we demonstrate that the model is capable of capturing the complex structures observed in experiments on ellipsoidal colloids at low volume fractions. We show that, at sufficiently high electric field strength, the anisotropy in shape and electrostatic interactions causes a transition from three-dimensional crystal structures observed at low aspect ratios to two-dimensional sheets and tubes at higher aspect ratios. Our work thus illustrates the rich self-assembly behavior accessible when exploiting the interplay between competing long- and short-range anisotropic interactions in colloidal systems.

Contrasting the dynamics of elastic and non-elastic deformations across an experimental colloidal Martensitic transition.

We present a framework to segregate the roles of elastic and non-elastic deformations in the examination of real-space experiments of solid-solid Martensitic transitions. The Martensitic transformation of a body-centred-tetragonal (BCT) to a body-centred-orthorhombic (BCO) crystal structure has been studied in a model system of micron-scale ionic microgel colloids (P. S. Mohanty, P. Bagheri, S. Nöjd, A. Yethiraj and P. Schurtenberger, Phys. Rev. X, 2015, 5, 011030). Non-affine fluctuations, i.e., displacement fluctuations that do not arise from purely elastic (affine) deformations, are detected in particle configurations acquired from the experiment. Tracking these fluctuations serves as a highly sensitive tool in signaling the onset of the Martensitic transition and precisely locating particle rearrangements occurring at length scales of a few particle diameters. Particle rearrangements associated with non-affine displacement modes become increasingly favorable during the transformation process. The nature of the displacement fluctuation modes that govern the transformation are shown to be different from those predominant in an equilibrium crystal. We show that BCO crystallites formed through shear may, remarkably, co-exist with those resulting from local rearrangements within the same sample.

Swelling of micro-hydrogels with a crosslinker gradient.

A heterogeneous distribution of crosslinker in micro-hydrogels (microgels) results in a non-uniform polymer density inside the particles. Identifying the morphology of the hydrogel backbone enables a bottom-up approach towards the structural and rheological properties of microgel systems. On a local level we use a Flory-Rehner inspired model that focuses on highly swollen networks, characterized by a Poisson's ratio of 1/4. Our ab initio calculations take account for the nonuniform distribution of crosslinker species during the synthesis of poly(N-isopropylacylamide) (PNIPAM) microgels, yet the method is also applicable to other microgel architectures. We recover a single-particle density profile that is in close agreement with SAXS data. Comparison with experimental data confirms that the surface of the cross-linked particle is decorated with dangling polymers ends of considerable size.

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.

Anisotropic magnetic particles in a magnetic field.

We characterize the structural properties of magnetic ellipsoidal hematite colloids with an aspect ratio ρ ≈ 2.3 using a combination of small-angle X-ray scattering and computer simulations. The evolution of the phase diagram with packing fraction ϕ and the strength of an applied magnetic field B is described, and the coupling between orientational order of magnetic ellipsoids and the bulk magnetic behavior of their suspension addressed. We establish quantitative structural criteria for the different phase and arrest transitions and map distinct isotropic, polarized non-nematic, and nematic phases over an extended range in the ϕ-B coordinates. We show that upon a rotational arrest of the ellipsoids around ϕ = 0.59, the bulk magnetic behavior of their suspension switches from superparamagnetic to ordered weakly ferromagnetic. If densely packed and arrested, these magnetic particles thus provide persisting remanent magnetization of the suspension. By exploring structural and magnetic properties together, we extend the often used colloid-atom analogy to the case of magnetic spins.