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

Slow and fluctuating dynamics in high concentration BSA protein solutions

We present a study on globular bovine serum albumin (BSA) protein solutions using particle tracking microrheology and dynamic light scattering over a wide concentration range (1-55 g/dl). We measured the expected drastic increase in viscosity and relaxation times with concentration, highlighting the slowing down of the dynamics associated with collective molecular motions as concentration increases. A novel aspect of our study emerged at very high concentrations, where the slow relaxation times exhibit only a mild increase with concentration, resembling the behavior observed in very soft colloids. Upon quenching the temperature to induce very slow dynamics, we observe fluctuating dynamics, suggesting a mild aging regime characterized by micro-rearrangements of BSA proteins. We use protein concentration (mass per volume) as the control parameter due to the precision of Bradford assay measurements, facilitating straightforward comparisons with other studies. Our work offers new insights into the phase behavior of BSA solutions across a wide concentration range, with implications for understanding protein solution dynamics at high concentrations.

Dynamical arrest for globular proteins with patchy attractions

Attempts to use colloid science concepts to better understand the dynamic properties of concentrated or crowded protein solutions are challenging due to the fact that globular proteins generally have heterogeneous surfaces that result in anisotropic or patchy contributions to their interaction potential. This is particularly difficult when targeting non-equilibrium transitions such as glass and gel formation in concentrated protein solutions. Here we report a systematic study of the reduced zero shear viscosity ηr of the globular protein γB-crystallin, an eye lens protein that plays a vital role in vision-related phenomena such as cataract formation or presbyopia, and compare the results to the existing structural and dynamic data. Combining two different tracer particle-based microrheology methods allows us to precisely locate the line of kinetic arrest within the phase diagram and characterize the functional form of the concentration and temperature dependence of ηr. We show that while our results qualitatively confirm the existing view that this protein can be reasonably well described using a coarse-grained picture of a patchy colloid with short range attractions, there are a number of novel findings that cannot easily be understood with the existing simple colloid models. We demonstrate in particular the complete failure of an extended law of corresponding states for a description of the temperature dependence of the arrest line, and discuss the role that transient clusters play in this context.

Competition between cross-linking and force-induced local conformational changes determines the structure and mechanics of labile protein networks

Folded protein hydrogels are emerging as promising new materials for medicine and healthcare applications. Folded globular proteins can be modelled as colloids which exhibit site specific cross-linking for controlled network formation. However, folded proteins have inherent mechanical stability and unfolded in response to an applied force. It is not yet understood how colloidal network theory maps onto folded protein hydrogels and whether it models the impact of protein unfolding on network properties. To address this, we study a hybrid system which contains folded proteins (patchy colloids) and unfolded proteins (biopolymers). We use a model protein, bovine serum albumin (BSA), to explore network architecture and mechanics in folded protein hydrogels. We alter both the photo-chemical cross-linking reaction rate and the mechanical properties of the protein building block, via illumination intensity and redox removal of robust intra-protein covalent bonds, respectively. This dual approach, in conjunction with rheological and structural techniques, allows us to show that while reaction rate can 'fine-tune' the mechanical and structural properties of protein hydrogels, it is the force-lability of the protein which has the greatest impact on network architecture and rigidity. To understand these results, we consider a colloidal model which successfully describes the behaviour of the folded protein hydrogels but cannot account for the behaviour observed in force-labile hydrogels containing unfolded protein. Alternative models are needed which combine the properties of colloids (folded proteins) and biopolymers (unfolded proteins) in cross-linked networks. This work provides important insights into the accessible design space of folded protein hydrogels without the need for complex and costly protein engineering, aiding the development of protein-based biomaterials.

Liquid-liquid phase separation driven by charge heterogeneity

Despite the intrinsic charge heterogeneity of proteins plays a crucial role in the liquid-liquid phase separation (LLPS) of a broad variety of protein systems, our understanding of the effects of their electrostatic anisotropy is still in its early stages. We approach this issue by means of a coarse-grained model based on a robust mean-field description that extends the DLVO theory to non-uniformly charged particles. We numerically investigate the effect of surface charge patchiness and net particle charge on varying these features independently and with the use of a few parameters only. The effect of charge anisotropy on the LLPS critical point is rationalized via a thermodynamic-independent parameter based on orientationally averaged pair properties, that estimates the particle connectivity and controls the propensity of the liquid phase to condensate. We show that, even though directional attraction alone is able to lower the particle bonding valence-thus shifting the critical point towards lower temperatures and densities-directional repulsion significantly and systematically diminishes the particle functionality, thus further reducing the critical parameters. This electrostatically-driven shift can be understood in terms of the additional morphological constraints introduced by the directional repulsion, that hinder the condensation of dense aggregates.

Continuity of Short-Time Dynamics Crossing the Liquid-Liquid Phase Separation in Charge-Tuned Protein Solutions

Liquid-liquid phase separation (LLPS) constitutes a crucial phenomenon in biological self-organization, not only intervening in the formation of membraneless organelles but also triggering pathological protein aggregation, which is a hallmark in neurodegenerative diseases. Employing incoherent quasi-elastic neutron spectroscopy (QENS), we examine the short-time self-diffusion of a model protein undergoing LLPS as a function of phase splitting and temperature to access information on the nanosecond hydrodynamic response to the cluster formation both within and outside the LLPS regime. We investigate the samples as they dissociate into microdroplets of a dense protein phase dispersed in a dilute phase as well as the separated dense and dilute phases obtained from centrifugation. By interpreting the QENS results in terms of the local concentrations in the two phases determined by UV-vis spectroscopy, we hypothesize that the short-time transient protein cluster size distribution is conserved at the transition point while the local volume fractions separate.

Biophysical Principles Emerging from Experiments on Protein-Protein Association and Aggregation

Protein-protein association and aggregation are fundamental processes that play critical roles in various biological phenomena, from cellular signaling to disease progression. Understanding the underlying biophysical principles governing these processes is crucial for elucidating their mechanisms and developing strategies for therapeutic intervention. In this review, we provide an overview of recent experimental studies focused on protein-protein association and aggregation. We explore the key biophysical factors that influence these processes, including protein structure, conformational dynamics, and intermolecular interactions. We discuss the effects of environmental conditions such as temperature, pH and related buffer-specific effects, and ionic strength and related ion-specific effects on protein aggregation. The effects of polymer crowders and sugars are also addressed. We list the techniques used to study aggregation. We analyze emerging trends and challenges in the field, including the development of computational models and the integration of multidisciplinary approaches for a comprehensive understanding of protein-protein association and aggregation.

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.

Inelastic neutron scattering and spectroscopy methods to characterize dynamics in colloidal and soft matter systems

Colloidal systems and soft materials are well suited to neutron scattering, and the community has readily adopted elastic scattering techniques to investigate their structure. Due to their unique properties, neutrons may also be used to characterize the dynamics of soft materials over a wide range of length and time scales in situ. Both static structures and an understanding of how molecules move about their equilibrium positions is essential if we are to deliver on the promise of rationally designing soft materials. In this review we introduce the basics of neutron spectroscopy and explore the ways in which inelastic neutron scattering can be used to study colloidal and soft materials. Illustrative examples are chosen that highlight the phenomena suitable for investigation using this suite of techniques.

Triblock Proteins with Weakly Dimerizing Terminal Blocks and an Intrinsically Disordered Region for Rational Design of Condensate Properties

Condensates are molecular assemblies that are formed through liquid-liquid phase separation and play important roles in many biological processes. The rational design of condensate formation and their properties is central to applications, such as biosynthetic materials, synthetic biology, and for understanding cell biology. Protein engineering is used to make a triblock structure with varying terminal blocks of folded proteins on both sides of an intrinsically disordered mid-region. Dissociation constants are determined in the range of micromolar to millimolar for a set of proteins suitable for use as terminal blocks. Varying the weak dimerization of terminal blocks leads to an adjustable tendency for condensate formation while keeping the intrinsically disordered region constant. The dissociation constants of the terminal domains correlate directly with the tendency to undergo liquid-liquid phase separation. Differences in physical properties, such as diffusion rate are not directly correlated with the strength of dimerization but can be understood from the properties and interplay of the constituent blocks. The work demonstrates the importance of weak interactions in condensate formation and shows a principle for protein design that will help in fabricating functional condensates in a predictable and rational way.

Effects of flexibility in coarse-grained models for bovine serum albumin and immunoglobulin G

We construct a coarse-grained, structure-based, low-resolution, 6-bead flexible model of bovine serum albumin (BSA, PDB: 4F5S), which is a popular example of a globular protein in biophysical research. The model is obtained via direct Boltzmann inversion using all-atom simulations of a single molecule, and its particular form is selected from a large pool of 6-bead coarse-grained models using two suitable metrics that quantify the agreement in the distribution of collective coordinates between all-atom and coarse-grained Brownian dynamics simulations of solutions in the dilute limit. For immunoglobulin G (IgG), a similar structure-based 12-bead model has been introduced in the literature [Chaudhri et al., J. Phys. Chem. B 116, 8045 (2012)] and is employed here to compare findings for the compact BSA molecule and the more anisotropic IgG molecule. We define several modified coarse-grained models of BSA and IgG, which differ in their internal constraints and thus account for a variation of flexibility. We study denser solutions of the coarse-grained models with purely repulsive molecules (achievable by suitable salt conditions) and address the effect of packing and flexibility on dynamic and static behavior. Translational and rotational self-diffusivity is enhanced for more elastic models. Finally, we discuss a number of effective sphere sizes for the BSA molecule, which can be defined from its static and dynamic properties. Here, it is found that the effective sphere diameters lie between 4.9 and 6.1 nm, corresponding to a relative spread of about ±10% around a mean of 5.5 nm.

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.

Protein Condensation, Cellular Organization, and Spatiotemporal Regulation of Cytoplasmic Properties

The cytoplasm is an aqueous, highly crowded solution of active macromolecules. Its properties influence the behavior of proteins, including their folding, motion, and interactions. In particular, proteins in the cytoplasm can interact to form phase-separated assemblies, so-called biomolecular condensates. The interplay between cytoplasmic properties and protein condensation is critical in a number of functional contexts and is the subject of this review. The authors first describe how cytoplasmic properties can affect protein behavior, in particular condensate formation, and then describe the functional implications of this interplay in three cellular contexts, which exemplify how protein self-organization can be adapted to support certain physiological phenotypes. The authors then describe the formation of RNA-protein condensates in highly polarized cells such as neurons, where condensates play a critical role in the regulation of local protein synthesis, and describe how different stressors trigger extensive reorganization of the cytoplasm, both through signaling pathways and through direct stress-induced changes in cytoplasmic properties. Finally, the authors describe changes in protein behavior and cytoplasmic properties that may occur in extremophiles, in particular organisms that have adapted to inhabit environments of extreme temperature, and discuss the implications and functional importance of these changes.

Crowding and confinement act in concert to slow DNA diffusion within cell-sized droplets

Dynamics of biological macromolecules, such as DNA, in crowded and confined environments are critical to understanding cellular processes such as transcription, infection, and replication. However, the combined effects of cellular confinement and crowding on macromolecular dynamics remain poorly understood. Here, we use differential dynamic microscopy to investigate the diffusion of large DNA molecules confined in cell-sized droplets and crowded by dextran polymers. We show that confined and crowded DNA molecules exhibit universal anomalous subdiffusion with scaling that is insensitive to the degree of confinement and crowding. However, effective DNA diffusion coefficients Deff decrease up to 2 orders of magnitude as droplet size decreases—an effect that is enhanced by increased crowding. We mathematically model the coupling of crowding and confinement by combining polymer scaling theories with confinement-induced depletion effects. The generality and tunability of our system and models render them applicable to elucidating wide-ranging crowded and confined systems.

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DNA diffusion measured in cell-sized droplets with differential dynamic microscopy

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Combination of crowding and confinement leads to subdiffusion and slowing

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Diffusion coefficients of DNA decrease strongly with decreasing droplet size

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Polymer scaling theories and depletion effects predict observed dynamics

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.

Variation of Structural and Dynamical Flexibility of Myelin Basic Protein in Response to Guanidinium Chloride

Myelin basic protein (MBP) is intrinsically disordered in solution and is considered as a conformationally flexible biomacromolecule. Here, we present a study on perturbation of MBP structure and dynamics by the denaturant guanidinium chloride (GndCl) using small-angle scattering and neutron spin-echo spectroscopy (NSE). A concentration of 0.2 M GndCl causes charge screening in MBP resulting in a compact, but still disordered protein conformation, while GndCl concentrations above 1 M lead to structural expansion and swelling of MBP. NSE data of MBP were analyzed using the Zimm model with internal friction (ZIF) and normal mode (NM) analysis. A significant contribution of internal friction was found in compact states of MBP that approaches a non-vanishing internal friction relaxation time of approximately 40 ns at high GndCl concentrations. NM analysis demonstrates that the relaxation rates of internal modes of MBP remain unaffected by GndCl, while structural expansion due to GndCl results in increased amplitudes of internal motions. Within the model of the Brownian oscillator our observations can be rationalized by a loss of friction within the protein due to structural expansion. Our study highlights the intimate coupling of structural and dynamical plasticity of MBP, and its fundamental difference to the behavior of ideal polymers in solution.

Dynamical Behavior of Disordered Regions in Disease-Related Proteins Revealed by Quasielastic Neutron Scattering

Background and Objectives: Intrinsically disordered proteins (IDPs) and proteins containing intrinsically disordered regions (IDRs) are known to be involved in various human diseases. Since the IDPs/IDRs are fluctuating between many structural substrates, the dynamical behavior of the disease-related IDPs/IDRs needs to be characterized to elucidate the mechanisms of the pathogenesis of the diseases. As protein motions have a hierarchy ranging from local side-chain motions, through segmental motions of loops or disordered regions, to diffusive motions of entire molecules, segmental motions, as well as local motions, need to be characterized. Materials and Methods: Combined analysis of quasielastic neutron scattering (QENS) spectra with the structural data provides information on both the segmental motions and the local motions of the IDPs/IDRs. Here, this method is applied to re-analyze the QENS spectra of the troponin core domain (Tn-CD), various mutants of which cause the pathogenesis of familial cardiomyopathy (FCM), and α-synuclein (αSyn), amyloid fibril formation of which is closely related to the pathogenesis of Parkinson's disease, collected in the previous studies. The dynamical behavior of wild-type Tn-CD, FCM-related mutant Tn-CD, and αSyn in the different propensity states for fibril formation is characterized. Results: In the Tn-CD, the behavior of the segmental motions is shown to be different between the wild type and the mutant. This difference is likely to arise from changes in the intramolecular interactions, which are suggested to be related to the functional aberration of the mutant Tn-CD. In αSyn, concerted enhancement of the segmental motions and the local motions is observed with an increased propensity for fibril formation, suggesting the importance of these motions in fibril formation. Conclusions: Characterization of the segmental motions as well as the local motions is thus useful for discussing how the changes in dynamical behavior caused by the disease-related mutations and/or environmental changes could be related to the functional and/or behavioral aberrations of these proteins.

Sorting of proteins with shape and curvature anisotropy on a lipid bilayer tube

Curvature induced sorting of lipid membrane bound proteins has been widely studied through experiments that induce curvature variation in a giant unilamellar lipid-bilayer vesicle with adsorbed proteins by pulling thin cylindrical tethers. In the theoretical space, this has been supplemented with models that capture curvature dependent interaction between membrane and idealized protein particles, through free energy contributions. Many membrane proteins such as the BAR domain proteins are known to have extremely anisotropic shapes and soft interacting potentials, whereas the idealizations of protein particles explored in models have only assumed them as hard disk-like particles with curvature anisotropy. Here, we present a model of sorting of the proteins while including the effects of softness in their interaction potentials, shape anisotropy in the protein structure, and curvature anisotropy in the interactions with the membrane. This is based on a clean separation of free energy contributions from non-ideal fluid behavior of soft anisotropic particles and curvature interactions between proteins and membranes. We probe the behavior of the sorting function under limiting conditions and show that it converges to the previously derived models. In addition to this, we present a comparison of the variation in sorting ratio due to the observed variation in the shape parameter values in known membrane proteins. Finally, using published experimental data for membrane proteins, we perform fitting and derive model parameters. We observe that shape anisotropy adversely affects the sorting of proteins to a high curvature region, whereas curvature anisotropy and softer interaction between proteins favor sorting.

Diffusion and sedimentation in colloidal suspensions using multiparticle collision dynamics with a discrete particle model

We study self-diffusion and sedimentation in colloidal suspensions of nearly hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to experimental data and Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne-Prager-Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the solvent at short times. However, the long-time self-diffusion coefficient in MD+MPCD is comparable to that in experiments, and the sedimentation coefficient in MD+MPCD is in good agreement with that in experiments and BD+RPY, suggesting that MD+MPCD gives a reasonable description of hydrodynamic interactions in colloidal suspensions. The discrete-particle MD+MPCD approach is convenient and readily extended to more complex shapes, and we determine the long-time self-diffusion coefficient in suspensions of nearly hard cubes to demonstrate its generality.

Temperature and salt controlled tuning of protein clusters

The formation of molecular assemblies in protein solutions is of strong interest both from a fundamental viewpoint and for biomedical applications. While ordered and desired protein assemblies are indispensable for some biological functions, undesired protein condensation can induce serious diseases. As a common cofactor, the presence of salt ions is essential for some biological processes involving proteins, and in aqueous suspensions of proteins can also give rise to complex phase diagrams including homogeneous solutions, large aggregates, and dissolution regimes. Here, we systematically study the cluster formation approaching the phase separation in aqueous solutions of the globular protein BSA as a function of temperature (T), the protein concentration (c_p) and the concentrations of the trivalent salts YCl₃ and LaCl₃ (c_s). As an important complement to structural, i.e. time-averaged, techniques we employ a dynamical technique that can detect clusters even when they are transient on the order of a few nanoseconds. By employing incoherent neutron spectroscopy, we unambiguously determine the short-time self-diffusion of the protein clusters depending on c_p, c_s and T. We determine the cluster size in terms of effective hydrodynamic radii as manifested by the cluster center-of-mass diffusion coefficients D. For both salts, we find a simple functional form D(c_p, c_s, T) in the parameter range explored. The calculated inter-particle attraction strength, determined from the microscopic and short-time diffusive properties of the samples, increases with salt concentration and temperature in the regime investigated and can be linked to the macroscopic behavior of the samples.

Hydrodynamics of immiscible binary fluids with viscosity contrast: a multiparticle collision dynamics approach

We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids A and B of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.

Real space analysis of colloidal gels: triumphs, challenges and future directions

Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such as an increase in strength prior to catastrophic failure. Remarkably, such complex phenomena are faithfully captured by an extremely simple model-'sticky spheres'. Here we review progress in our understanding of colloidal gels made through the use of real space analysis and particle resolved studies. We consider the challenges of obtaining a suitable experimental system where the refractive index and density of the colloidal particles is matched to that of the solvent. We review work to obtain a particle-level mechanism for rigidity in gels and the evolution of our understanding of time-dependent behaviour, from early-time aggregation to ageing, before considering the response of colloidal gels to deformation and then move on to more complex systems of anisotropic particles and mixtures. Finally we note some more exotic materials with similar properties.

The Role of pH and Ionic Strength in the Attraction-Repulsion Balance of Fibrinogen Interactions

Fibrinogen (Fg) self-assembly is sensitive to the physicochemical properties of an environment like pH and ionic strength. These parameters tune the direction and strength of noncovalent physical driving forces determining protein intermolecular interactions. The attraction-repulsion balance in intermolecular interactions of the multidomain protein Fg at pH values 3.5, 7.4, and 9.5 and varying ionic strengths of the water medium has been analyzed by the complex diffusive approach, proposed by us previously. The concentration dependence of protein collective diffusion was analyzed within the phenomenological approach, based on the frictional formalism of nonequilibrium thermodynamics proposed by H. Vink. The analysis of protein diffusion data has shown the fundamental difference in the physical nature and direction of interaction forces between protein molecules at different conditions. The paired interaction potential of protein molecules was characterized in terms of second virial coefficients and Hamaker constants within the Deryaguin-Landau-Verwey-Overbeek theory and the "porous" colloid particle model. Our results indicated the maximum Hamaker constant and dominance of the van der Waals attraction between Fg molecules at pH 7.4. The increase in pH up to 9.5 results in the zero values of the second virial coefficient and Hamaker constant, corresponding to the full reciprocal compensation for electrostatic repulsion and van der Waals attraction. In the acidic medium (pH 3.5), the strong electrostatic repulsion substantially exceeds the van der Waals attraction. A high ionic strength is characterized by a significant decrease of all intermolecular interactions, which is expressed in almost zero values of virial coefficients and the Hamaker constant. Thus, it is experimentally shown that the physiological conditions of the Fg environment (pH 7.4 and slight ionic strength) provide a high probability for peak physical attraction between fibrinogen molecules, which is used in nature to facilitate blood clotting.

Cluster Percolation Causes Shear Thinning Behavior in Concentrated Solutions of Monoclonal Antibodies

High-concentration (>100 g/L) solutions of monoclonal antibodies (mAbs) are typically characterized by anomalously large solution viscosity and shear thinning behavior for strain rates ≥10³ s^-1. Here, the link between protein-protein interactions (PPIs) and the rheology of concentrated solutions of COE-03 and COE-19 mAbs is studied by means of static and dynamic light scattering and microfluidic rheometry. By comparing the experimental data with predictions based on the Baxter sticky hard-sphere model, we surprisingly find a connection between the observed shear thinning and the predicted percolation threshold. The longest shear relaxation time of mAbs was much larger than that of model sticky hard spheres within the same region of the phase diagram, which is attributed to the anisotropy of the mAb PPIs. Our results suggest that not only the strength but also the patchiness of short-range attractive PPIs should be explicitly accounted for by theoretical approaches aimed at predicting the shear rate-dependent viscosity of dense mAb solutions.

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.

Towards molecular movies with X-ray photon correlation spectroscopy

In this perspective article we highlight research opportunities and challenges in probing structural dynamics of molecular systems using X-ray Photon Correlation Spectroscopy (XPCS). The development of new X-ray sources, such as 4th generation storage rings and X-ray free-electron lasers (XFELs), provides promising new insights into molecular motion. Employing XPCS at these sources allows to capture a very broad range of timescales and lengthscales, spanning from femtoseconds to minutes and atomic scales to the mesoscale. Here, we discuss the scientific questions that can be addressed with these novel tools for two prominent examples: the dynamics of proteins in biomolecular condensates and the dynamics of supercooled water. Finally, we provide practical tips for designing and estimating feasibility of XPCS experiments as well as on detecting and mitigating radiation damage.

Membrane Surface Modulates Slow Diffusion in Small Crowded Droplets

Membranes are ubiquitous structures in cells. The effects of membranes on various functional molecules have been reported, but their behaviors under macromolecular crowding and cell-sized confinement have not fully been understood. In this study, we model an intracellular environment by crowding micrometer-sized droplets and investigate the effects of membrane properties on molecular diffusion. The molecular diffusion inside small droplets covered with a lipid layer of phosphatidylcholine (PC) becomes slower compared with that of the corresponding bulk solutions under a crowding condition of polysaccharide dextran but not of its monomer unit, glucose. The addition of a poly(ethylene glycol) conjugated lipid (PEGylated lipid) to the PC membrane significantly alters the degree of slow diffusion observed inside small droplets of concentrated dextran. Interestingly, the change is not monotonic against dextran concentration; that is, the PEGylated membrane increases and decreases the degree of slow diffusion with increasing dextran concentration. We explain the nonmonotonic alternation from the increase in effective dextran concentration and the hindered temporal adsorption of dextran to the membrane. Because diffusion alteration by adding PEGylated lipid is observed for condensed small droplets of linear polymer PEG and hydrophilic protein bovine serum albumin, the phenomenon is general for other polymer systems as well. Furthermore, our findings may facilitate the understanding of intracellular molecular behaviors based on membrane effects as well as the development of numerous applications using polymer droplets.

Salicylic acid regulates PIN2 auxin transporter hyperclustering and root gravitropic growth via Remorin-dependent lipid nanodomain organisation in Arabidopsis thaliana

To adapt to the diverse array of biotic and abiotic cues, plants have evolved sophisticated mechanisms to sense changes in environmental conditions and modulate their growth. Growth-promoting hormones and defence signalling fine tune plant development antagonistically. During host-pathogen interactions, this defence-growth trade-off is mediated by the counteractive effects of the defence hormone salicylic acid (SA) and the growth hormone auxin. Here we revealed an underlying mechanism of SA regulating auxin signalling by constraining the plasma membrane dynamics of PIN2 auxin efflux transporter in Arabidopsis thaliana roots. The lateral diffusion of PIN2 proteins is constrained by SA signalling, during which PIN2 proteins are condensed into hyperclusters depending on REM1.2-mediated nanodomain compartmentalisation. Furthermore, membrane nanodomain compartmentalisation by SA or Remorin (REM) assembly significantly suppressed clathrin-mediated endocytosis. Consequently, SA-induced heterogeneous surface condensation disrupted asymmetric auxin distribution and the resultant gravitropic response. Our results demonstrated a defence-growth trade-off mechanism by which SA signalling crosstalked with auxin transport by concentrating membrane-resident PIN2 into heterogeneous compartments.

Programmable Anisotropy and Percolation in Supramolecular Patchy Particle Gels

Patchy particle interactions are predicted to facilitate the controlled self-assembly and arrest of particles into phase-stable and morphologically tunable "equilibrium" gels, which avoids the arrested phase separation and subsequent aging that is typically observed in traditional particle gels with isotropic interactions. Despite these promising traits of patchy particle interactions, such tunable equilibrium gels have yet to be realized in the laboratory due to experimental limitations associated with synthesizing patchy particles in high yield. Here, we introduce a supramolecular metal-coordination platform consisting of metallic nanoparticles linked by telechelic polymer chains, which validates the predictions associated with patchy particle interactions and facilitates the design of equilibrium particle hydrogels through limited valency interactions. We demonstrate that the interaction valency and self-assembly of the particles can be effectively controlled by adjusting the relative concentration of polymeric linkers to nanoparticles, which enables the gelation of patchy particle hydrogels with programmable local anisotropy, morphology, and low mechanical percolation thresholds. Moreover, by crowding the local environment around the patchy particles with competing interactions, we introduce an independent method to control the self-assembly of the nanoparticles, thereby enabling the design of highly anisotropic particle hydrogels with substantially reduced percolation thresholds. We thus establish a canonical platform that facilitates multifaceted control of the self-assembly of the patchy nanoparticles en route to the design of patchy particle gels with tunable valencies, morphologies, and percolation thresholds. These advances lay important foundations for further fundamental studies of patchy particle systems and for designing tunable gel materials that address a wide range of engineering applications.

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

We present a multiscale characterization of aqueous solutions of the bovine eye lens protein β_H 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.

Tracer diffusion in crowded solutions of sticky polymers

Macromolecular diffusion in strongly confined geometries and crowded environments is still to a large extent an open subject in soft matter physics and biology. In this paper, we employ large-scale Langevin dynamics simulations to investigate how the diffusion of a tracer is influenced by the combined action of excluded-volume and weak attractive crowder-tracer interactions. We consider two species of tracers, standard hard-core particles described by the Weeks-Chandler-Andersen (WCA) repulsive potential and core-softened (CS) particles, which model, e.g., globular proteins, charged colloids, and nanoparticles covered by polymeric brushes. These systems are characterized by the presence of two length scales in the interaction and can show waterlike anomalies in their diffusion, stemming from the inherent competition between different length scales. Here we report a comprehensive study of both diffusion and structure of these two tracer species in an environment crowded by quenched configurations of polymers at increasing density. We analyze in detail how the tracer-polymer affinity and the system density affect transport as compared to the emergence of specific static spatial correlations. In particular, we find that, while hardly any differences emerge in the diffusion properties of WCA and CS particles, the propensity to develop structural order for large crowding is strongly frustrated for CS particles. Surprisingly, for large enough affinity for the crowding matrix, the diffusion coefficient of WCA tracers display a nonmonotonic trend as their density is increased when compared to the zero affinity scenario. This waterlike anomaly turns out to be even larger than what observed for CS particle and appears to be rooted in a similar competition between excluded-volume and affinity effects.

Packing and dynamics of a protein solution approaching the jammed state

The packing of proteins and their collective behavior in crowded media is crucial for the understanding of biological processes. Here we study the structural and dynamical evolution of solutions of the globular protein bovine serum albumin with increasing concentration via drying using small angle X-ray scattering and dynamic light scattering. We probe an evolving correlation peak on the scattering profile, corresponding to the inter-protein distance, ξ, which decreases following a power law of the protein volume fraction, φ. The rate of decrease in ξ becomes faster above a protein concentration of ∼200 mg ml-1 (φ = 0.15). The power law exponent changes from 0.33, which is typical of colloidal or protein solutions, to 0.41. During the entire drying process, we observe the development and the growth of two-step relaxation dynamics with increasing φ as revealed by dynamic light scattering. We find three different regimes of the dependence of ξ as a function of φ. In the dilute regime (φ < 0.22), protein molecules are far apart from each other compared to their size. In this case, the dynamics mainly corresponds to Brownian motion. At an intermediate concentration (0.22 < φ < 0.47), inter-protein distances become comparable to the size of protein molecules, leading to a preferential orientation of the ellipsoidal protein molecules along with a possible deformation. In this regime, the dynamics shows two distinct relaxation times. At a very high concentration (φ > 0.47), the system reaches a jammed state. Subsequently, the secondary relaxation time in this state becomes extremely slow. In this state, the protein molecules have approximately one hydration layer. This study contributes to the understanding of protein molecular packing in crowded environments and the phenomenon of density-driven jamming for soft matter systems.

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.

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.

Hydrodynamic correlations of viscoelastic fluids by multiparticle collision dynamics simulations

The emergent fluctuating hydrodynamics of a viscoelastic fluid modeled by the multiparticle collision dynamics (MPC) approach is studied. The fluid is composed of flexible, Gaussian phantom polymers that interact by local momentum-conserving stochastic MPCs. For comparison, the analytical solution of the linearized Navier-Stokes equation is calculated, where viscoelasticity is taken into account by a time-dependent shear relaxation modulus. The fluid properties are characterized by the transverse velocity autocorrelation function in Fourier space as well as in real space. Various polymer lengths are considered-from dumbbells to (near-)continuous polymers. Viscoelasticity affects the fluid properties and leads to strong correlations, which overall decay exponentially in Fourier space. In real space, the center-of-mass velocity autocorrelation function of individual polymers exhibits a long-time tail, independent of the polymer length, which decays as t^-3/2, similar to a Newtonian fluid, in the asymptotic limit t → ∞. Moreover, for long polymers, an additional power-law decay appears at time scales shorter than the longest polymer relaxation time with the same time dependence, but negative correlations, and the polymer length dependence L^-1/2. Good agreement is found between the analytical and simulation results.

Localised contacts lead to nanosecond hinge motions in dimeric bovine serum albumin

Domain motions in proteins are crucial for biological function. In the present manuscript, we present a neutron spin-echo spectroscopy (NSE) study of native bovine serum albumin (BSA) in solution. NSE allows to probe both global and internal dynamics of the BSA monomer and dimer equilibrium that is formed in solution. Using a model independent approach, we were able to identify an internal dynamic process in BSA that is visible in addition to global rigid-body diffusion of the BSA monomer and dimer mixture. The observed internal protein motion is characterised by a relaxation time of 43 ns. The overdamped Brownian oscillator was considered as an alternative analytical theory that was able to describe the internal process as first-order approximation. More detailed information on the physical nature of the internal protein motion was extracted from the q-dependent internal diffusion coefficients ΔDeff(q) that were detected by NSE in addition to global rigid-body translational and rotational diffusion. The ΔDeff(q) were interpreted using normal mode analysis based on the available crystal structures of the BSA monomer and dimer as structural test models. Normal mode analysis demonstrates that the observed internal dynamic process can be attributed to bending motion of the BSA dimer. The native BSA monomer does not show any internal dynamics on the time- and length-scales probed by NSE. An intermolecular disulphide bridge or a direct structural contact between the BSA monomers forms a localised link acting as a molecular hinge in the BSA dimer. The effect of that hinge on the observed motion of BSA in the used dimeric structural model is discussed in terms of normal modes in a molecular picture.

Whole-Cell Models and Simulations in Molecular Detail

Comprehensive data about the composition and structure of cellular components have enabled the construction of quantitative whole-cell models. While kinetic network-type models have been established, it is also becoming possible to build physical, molecular-level models of cellular environments. This review outlines challenges in constructing and simulating such models and discusses near- and long-term opportunities for developing physical whole-cell models that can connect molecular structure with biological function.

Temperature, Hydrostatic Pressure, and Osmolyte Effects on Liquid-Liquid Phase Separation in Protein Condensates: Physical Chemistry and Biological Implications

Liquid-liquid phase separation (LLPS) of proteins and other biomolecules play a critical role in the organization of extracellular materials and membrane-less compartmentalization of intra-organismal spaces through the formation of condensates. Structural properties of such mesoscopic droplet-like states were studied by spectroscopy, microscopy, and other biophysical techniques. The temperature dependence of biomolecular LLPS has been studied extensively, indicating that phase-separated condensed states of proteins can be stabilized or destabilized by increasing temperature. In contrast, the physical and biological significance of hydrostatic pressure on LLPS is less appreciated. Summarized here are recent investigations of protein LLPS under pressures up to the kbar-regime. Strikingly, for the cases studied thus far, LLPSs of both globular proteins and intrinsically disordered proteins/regions are typically more sensitive to pressure than the folding of proteins, suggesting that organisms inhabiting the deep sea and sub-seafloor sediments, under pressures up to 1 kbar and beyond, have to mitigate this pressure-sensitivity to avoid unwanted destabilization of their functional biomolecular condensates. Interestingly, we found that trimethylamine-N-oxide (TMAO), an osmolyte upregulated in deep-sea fish, can significantly stabilize protein droplets under pressure, pointing to another adaptive advantage for increased TMAO concentrations in deep-sea organisms besides the osmolyte's stabilizing effect against protein unfolding. As life on Earth might have originated in the deep sea, pressure-dependent LLPS is pertinent to questions regarding prebiotic proto-cells. Herein, we offer a conceptual framework for rationalizing the recent experimental findings and present an outline of the basic thermodynamics of temperature-, pressure-, and osmolyte-dependent LLPS as well as a molecular-level statistical mechanics picture in terms of solvent-mediated interactions and void volumes.

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

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

Surface heterogeneity affects percolation and gelation of colloids: dynamic simulations with random patchy spheres

Surface heterogeneity of colloidal particles has a significant impact on their structure in solution and their rheological properties. During particle synthesis, heterogeneous chemical functionalization, processes of self-assembly, or phase separation, can all lead to heterogeneous colloidal surfaces which impart anisotropic interactions to suspended particles. Additionally, an important class of colloids, biological macromolecules, exhibit similar localized, short-ranged, anisotropic interactions, which have a significant impact on their solution properties. Therefore, understanding the assembly and rheology of such colloids can provide insight into a wide variety of relevant physical systems. In this computational study, we investigate dispersions of particles having surface patches with randomized functionality as a model for heterogeneous colloids. We use Brownian dynamics simulations with hydrodynamic interactions to explore the differences between these random patchy particles and homogeneous (or isotropic) particles. The common basis used for comparing dispersions of particles with different surface functionality is equality of the second virial coefficient, so that dispersions of particles with different patterns of surface heterogeneity are similar thermodynamically at low particle concentrations. We show that at modest particle concentrations, significant deviations from the isotropic model are evident in the dispersion micro-structure, giving drastically different percolation transition points depending on the degree of surface heterogeneity. However, these deviations can be rationalized and a universal percolation criteria derived in terms of the osmotic pressure of the dispersion. Heterogeneous interactions also impose extra constraints on the relative translation and rotation between neighboring particles, which increase the viscosity and elastic modulus of aggregated dispersions and gels built from heterogeneous colloids and shifts the gel point measurably.

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.

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.

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.

Computing the 3D Radial Distribution Function from Particle Positions: An Advanced Analytic Approach

The radial distribution function, g( r), is ubiquitously used to analyze the internal structure of particulate systems. However, experimentally derived particle coordinates are always confined to a finite sample volume. This poses a particular challenge on computing g( r): Once the radial distance, r, extends beyond the sample boundaries in at least one dimension, substantial deviations from the true g( r) function can occur. State of the art algorithms for g( r) mitigate this issue for instance by using artificial periodic boundary conditions. However, ignoring the finite nature of the sample volume distorts g( r) significantly. Here, we present a simple, analytic algorithm for the computation of g( r) in finite samples. No additional assumptions about the sample are required. The key idea is to use an analytic solution for the intersection volume between a spherical shell and the sample volume. In addition, we discovered a natural upper bound for the radial distance that only depends on sample size and shape. This analytic approach will prove to be invaluable for the quantitative analysis of the increasing amount of experimentally derived tomography data.

Two time scales for self and collective diffusion near the critical point in a simple patchy model for proteins with floating bonds

Using dynamic Monte Carlo and Brownian dynamics, we investigate a floating bond model in which particles can bind through mobile bonds. The maximum number of bonds (here fixed to 4) can be tuned by appropriately choosing the repulsive, nonadditive interactions among bonds and particles. We compute the static and dynamic structure factor (intermediate scattering function) in the vicinity of the gas-liquid critical point. The static structure exhibits a weak tetrahedral network character. The intermediate scattering function shows a temporal decay deviating from a single exponential, which can be described by a double exponential decay where the two time scales differ approximately by one order of magnitude. This time scale separation is robust over a range of wave numbers. The analysis of clusters in real space indicates the formation of noncompact clusters and shows a considerable stretch in the instantaneous size distribution when approaching the critical point. The average time evolution of the largest subcluster of given initial clusters with 10 or more particles also shows a double exponential decay. The observation of two time scales in the intermediate scattering function at low packing fractions is consistent with similar findings in globular protein solutions with trivalent metal ions that act as bonds between proteins.

Spectroscopic methods for assessing the molecular origins of macroscopic solution properties of highly concentrated liquid protein solutions

In cases of subcutaneous injection of therapeutic monoclonal antibodies, high protein concentrations (>50 mg/ml) are often required. During the development of these high concentration liquid formulations (HCLF), challenges such as aggregation, gelation, opalescence, phase separation, and high solution viscosities are more prone compared to low concentrated protein formulations. These properties can impair manufacturing processes, as well as protein stability and shelf life. To avoid such unfavourable solution properties, a detailed understanding about the nature of these properties and their driving forces are required. However, the fundamental mechanisms that lead to macroscopic solution properties, as above mentioned, are complex and not fully understood, yet. Established analytical methods for assessing the colloidal stability, i.e. the ability of a native protein to remain dispersed in solution, are restricted to dilute conditions and provide parameters such as the second osmotic virial coefficient, B₂₂, and the diffusion interaction coefficient, k_D. These parameters are routinely applied for qualitative estimations and identifications of proteins with challenging solution behaviours, such as high viscosities and aggregation, although the assays are prepared for low protein concentration conditions, typically between 0.1 and 20 mg/ml ("ideal" solution conditions). Quantitative analysis of samples of high protein concentration is difficult and it is hard to obtain information about the driving forces of such solution properties and corresponding protein-protein self-interactions. An advantage of using specific spectroscopic methods is the potential of directly analysing highly concentrated protein solutions at different solution conditions. This allows for collecting/gaining valuable information about the fundamental mechanisms of solution properties of the high protein concentration regime. In addition, the derived parameters might be more predictive as compared to the parameters originating from assays which are optimized for the low protein concentration range. The provided information includes structural data, molecular dynamics at various timescales and protein-solvent interactions, which can be obtained at molecular resolution. Herein, we provide an overview about spectroscopic techniques for analysing the origins of macroscopic solution behaviours in general, with a specific focus on pharmaceutically relevant high protein concentration and formulation conditions.

Nanosecond Tracer Diffusion as a Probe of the Solution Structure and Molecular Mobility of Protein Assemblies: The Case of Ovalbumin

Protein diffusion is not only an important process ensuring biological function but can also be used as a probe to obtain information on structural properties of protein assemblies in liquid solutions. Here, we explore the oligomerization state of ovalbumin at high protein concentrations by means of its short-time self-diffusion. We employ high-resolution incoherent quasielastic neutron scattering to access the self-diffusion on nanosecond timescales, on which interparticle contacts are not altered. Our results indicate that ovalbumin in aqueous (D₂O) solutions occurs in increasingly large assemblies of its monomeric subunits with rising protein concentration. It changes from nearly monomeric toward dimeric and ultimately larger than tetrameric complexes. Simultaneously, we access information on the internal molecular mobility of ovalbumin on the nanometer length scale and compare it with results obtained for bovine serum albumin, immunoglobulin, and β-lactoglobulin.