Absence of equilibrium cluster phase in concentrated lysozyme solutions

Diffusion and Viscosity in Mixed Protein Solutions

The viscosity and diffusion properties of crowded protein systems were investigated with molecular dynamics simulations of SH3 mixtures with different crowders, and results were compared with experimental data. The simulations accurately reproduced experimental trends across a wide range of protein concentrations, including highly crowded environments up to 300 g/L. Notably, viscosity increased with crowding but varied little between different crowder types, while diffusion rates were significantly reduced depending on protein-protein interaction strength. Analysis using the Stokes-Einstein relation indicated that the reduction in diffusion exceeded what was expected from viscosity changes alone, with the additional slow-down attributable to transient cluster formation driven by weakly attractive interactions. Contact kinetics analysis further revealed that longer-lived interactions contributed more significantly to reduced diffusion rates than short-lived interactions. This study also highlights the accuracy of current computational methodologies for capturing the dynamics of proteins in highly concentrated solutions and provides insights into the molecular mechanisms affecting protein mobility in crowded environments.

Calculating Structure Factors of Protein Solutions by Atomistic Modeling of Protein-Protein Interactions

We present a method, FMAPS(q), for calculating the structure factor, S ( q ) , of a protein solution, by extending our fast Fourier transform-based modeling of atomistic protein-protein interactions (FMAP) approach. The interaction energy consists of steric, nonpolar attractive, and electrostatic terms that are additive among all pairs of atoms between two protein molecules. In the present version, we invoke the free-rotation approximation, such that the structure factor is given by the Fourier transform of the protein center-center distribution function g C ( R ) . At low protein concentrations, g C ( R ) can be approximated as e - β W ( R ) , where W ( R ) is the potential of mean force along the center-center distance R . We calculate W ( R ) using FMAPB2, a member of the FMAP class of methods that is specialized for the second virial coefficient [Qin and Zhou, J Phys Chem B 123 (2019) 8203-8215]. For higher protein concentrations, we obtain S ( q ) by a modified random-phase approximation, which is a perturbation around the steric-only energy function. Without adjusting any parameters, the calculated structure factors for lysozyme and bovine serum albumin at various ionic strengths, temperatures, and protein concentrations are all in reasonable agreement with those measured by small-angle X-ray or neutron scattering. This initial success motivates further developments, including removing approximations and parameterizing the interaction energy function.

Induced Circular Dichroism Analysis of Thermally Induced Conformational Changes on Protein Binding Sites Under a Crowding Environment

Protein-ligand interactions in crowded cellular environments play a crucial role in biological functions. The crowded environment can perturb the overall protein structure and local conformation, thereby influencing the binding pathway of protein-ligand reactions within the cellular milieu. Therefore, a detailed understanding of the local conformation is crucial for elucidating the intricacies of protein-ligand interactions in crowded cellular environments. In this study, we investigated the feasibility of induced circular dichroism (ICD) using 8-anilinonaphthalene-1-sulfonic acid (ANS) for local conformational analysis at the binding site in a crowding environment. Bovine serum albumin (BSA) concentration-dependent measurements were performed to assess the feasibility of ANS-ICD for analyzing protein interior binding sites. The results showed distinct changes in the ANS-ICD spectra of BSA solutions, indicating their potential for analyzing the internal conformation of proteins. Moreover, temperature-dependent measurements were performed in dilute and crowding environments, revealing distinct denaturation pathways of BSA binding sites. Principal component analysis of ANS-ICD spectral changes revealed lower temperature pre-denaturation in the crowded solution than that in the diluted solution, suggesting destabilization of binding sites owing to self-crowding repulsive interactions. The established ANS-ICD method can provide valuable conformational insights into protein-ligand interactions in crowded cellular environments.

Nanocrystallites Modulate Intermolecular Interactions in Cryoprotected Protein Solutions

Studying protein interactions at low temperatures has important implications for optimizing cryostorage processes of biological tissue, food, and protein-based drugs. One of the major issues is related to the formation of ice nanocrystals, which can occur even in the presence of cryoprotectants and can lead to protein denaturation. The presence of ice nanocrystals in protein solutions poses several challenges since, contrary to microscopic ice crystals, they can be difficult to resolve and can complicate the interpretation of experimental data. Here, using a combination of small- and wide-angle X-ray scattering (SAXS and WAXS), we investigate the structural evolution of concentrated lysozyme solutions in a cryoprotected glycerol-water mixture from room temperature (T = 300 K) down to cryogenic temperatures (T = 195 K). Upon cooling, we observe a transition near the melting temperature of the solution (T ≈ 245 K), which manifests both in the temperature dependence of the scattering intensity peak position reflecting protein-protein length scales (SAXS) and the interatomic distances within the solvent (WAXS). Upon thermal cycling, a hysteresis is observed in the scattering intensity, which is attributed to the formation of nanocrystallites in the order of 10 nm. The experimental data are well described by the two-Yukawa model, which indicates temperature-dependent changes in the short-range attraction of the protein-protein interaction potential. Our results demonstrate that the nanocrystal growth yields effectively stronger protein-protein attraction and influences the protein pair distribution function beyond the first coordination shell.

Enabling Efficient Design of Biological Formulations Through Advanced Characterization

The present review summarizes the use of differential scanning calorimetry (DSC) and scattering techniques in the context of protein formulation design and characterization. The scattering techniques include wide angle X-ray diffractometry (XRD), small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS). While DSC is valuable for understanding thermal behavior of the excipients, XRD provides critical information about physical state of solutes during freezing, annealing and in the final lyophile. However, as these techniques lack the sensitivity to detect biomolecule-related transitions, complementary characterization techniques such as small-angle scattering can provide valuable insights.

Visualizing how inclusion of higher reciprocal space in SWAXS data analysis improves shape restoration of biomolecules: case of lysozyme

Query remains whether use of increased resolution data from X-ray scattering aids in better understanding of the dynamic shape of the biomolecule in solution? To address this, we acquired Small/Wide angle X-ray scattering (SWAXS) data in the q range of 0.008 - 1.72 Å^-1 from dilute solutions of lysozyme (0.9 to 5 mg/ml). Samples lacked any interparticulate effect and datasets showed Bragg peaks at q∼0.325, 0.65 and 1.4 Å^-1, as reported before by other authors. Considering an averaged profile, we estimated shape parameters and distance distribution profiles of interatomic vectors by gradually increasing input q_max value. Interestingly, use of higher resolution led to emergence of new peaks amongst smaller vectors. Deconvolution of these peaks provided positions of smaller peaks which correlated well with an earlier theoretical work. These peaks arise from secondary structures or due to non-uniform internal motions within the larger shape of this protein. Dummy residue modeling considering uniform density yielded model(s) with holes or cavities when considering higher q values implying limitations of this method. Employing normal mode calculations, we searched for better fitting model of lysozyme using differentially ranged SWAXS data and a crystal structure of lysozyme as starting structure. Comparison of refined models with structures from crystallography and NMR data showed that use of data till mid q region resulted in adjustments near the center of mass of starting structure, and inclusion of higher resolution induced pan-structure adjustments. We conclude that high resolution SWAXS data analysis provides additional dimension towards understanding biomolecular structural dynamics.Communicated by Ramaswamy H. Sarma.

Multi-length scale structural investigation of lysozyme self-assembly

Reactive amyloid oligomers are responsible for cytotoxicity in amyloid pathologies and because of their unstable nature characterizing their behavior is a challenge. The physics governing the self-assembly of proteins in crowded conditions is extremely complex and its comprehension, despite its paramount relevance to understanding molecular mechanisms inside cells and optimizing pharmaceutical processes, remains inconclusive. Here, we focus on the amyloid oligomerization process in self-crowded lysozyme aqueous solutions in acidic conditions. We reveal that the amyloid oligomers form at high protein concentration and low pH. Through multi-length scale spectroscopic investigations, we find that amyloid oligomers can further interconnect with each other by weak and non-specific interactions forming an extended network that leads to the percolation of the whole system. Our multi-length scale structural analysis follows the thermal history of amyloid oligomers from different perspectives and highlights the impact of hierarchical self-assembly of biological macromolecules on functional properties.

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Use of multi-length scale spectroscopies to characterize unstable amyloid oligomers

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Lysozyme form thermo-labile amyloid oligomers in self-crowded conditions

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Amyloid oligomers interact and form an extended hydrogel network

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Amyloid oligomers are responsible for the existence of the hydrogel matrix

Competing effects of rotational diffusivity and activity on finite-sized clusters

Colloidal particles interacting via short-range attraction and long-range repulsion are known to stabilize finite-sized clusters under equilibrium conditions. In this work, the effect of self-propulsion speed (activity) and rotational diffusivity (D_r) on the phase behavior of such particles is investigated using Brownian dynamics simulations. The system exhibits rich phase behavior consisting of clusters of different kinds. The cluster size varies non-monotonically with activity: increasing first and decreasing at higher activity, thus driving cluster-to-fluid phase transition. Rotational diffusivity also facilitates the formation of clusters. Larger clusters could be stabilized at lowD_rvalues while at highD_rvalues, clusters are stable even at higher activities. The analysis of the static structure factor of the system confirms that rotational diffusivity delays the cluster-to-fluid transition driven by activity.

Impact of lyoprotectors on protein-protein separation in the solid state: Neutron- and X-ray-scattering investigation

BACKGROUND

Polyhydroxycompounds (PHC) are used as lyoprotectors to minimize aggregation of pharmaceutical proteins during freeze-drying and storage.

METHODS

Lysozyme/PHC mixtures with 1:1 and 1:3 (w/w) ratios are freeze-dried from either H₂O or D₂O solutions. Disaccharides (sucrose and trehalose), monosaccharide (glucose), and sugar alcohol (sorbitol) are used in the study. Small-angle neutron and X-ray scattering (SANS and SAXS) are applied to study protein-protein interaction in the freeze-dried samples.

RESULTS

Protein interaction peak in the freeze-dried mixtures has been detected by both SANS (D₂O-based samples only) and SAXS (both D₂O- and H₂O-based). In the 1:1 mixtures, protein separation distances are similar (center-of-mass distance of approx. 31 Å) between all lyoprotectors studied. Mixtures with a higher content of the disaccharides (1:3 ratio) have a higher separation distance of approx 40 Å. The higher separation could reduce protein-protein contacts and therefore be associated with less favourable aggregation conditions. In the 1:3 mixtures with glucose and sorbitol, complex SANS and SAXS/WAXS patterns are observed. The pattern for the glucose sample indicate two populations of lysozyme molecules, while the origin of multiple SAXS peaks in the lysozyme/sorbitol 1:3 mixture is uncertain.

CONCLUSIONS

Protein-protein separation distance is determined predominantly by the lyoprotector/protein weight ratio.

GENERAL SIGNIFICANCE

Use of SANS and SAXS improves understanding of mechanisms of protein stabilization by sugars in freeze-dried formulations, and provide a tool to verify hypothesis on relationship between protein/protein separation and aggregation propensity in the dried state.

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.

Protein-polymer mixtures in the colloid limit: Aggregation, sedimentation, and crystallization

While proteins have been treated as particles with a spherically symmetric interaction, of course in reality, the situation is rather more complex. A simple step toward higher complexity is to treat the proteins as non-spherical particles and that is the approach we pursue here. We investigate the phase behavior of the enhanced green fluorescent protein (eGFP) under the addition of a non-adsorbing polymer, polyethylene glycol. From small angle x-ray scattering, we infer that the eGFP undergoes dimerization and we treat the dimers as spherocylinders with aspect ratio L/D - 1 = 1.05. Despite the complex nature of the proteins, we find that the phase behavior is similar to that of hard spherocylinders with an ideal polymer depletant, exhibiting aggregation and, in a small region of the phase diagram, crystallization. By comparing our measurements of the onset of aggregation with predictions for hard colloids and ideal polymers [S. V. Savenko and M. Dijkstra, J. Chem. Phys. 124, 234902 (2006) and Lo Verso et al., Phys. Rev. E 73, 061407 (2006)], we find good agreement, which suggests that the behavior of the eGFP is consistent with that of hard spherocylinders and ideal polymers.

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.

Post-Translational Modifications of G Protein-Coupled Receptors Control Cellular Signaling Dynamics in Space and Time

G protein-coupled receptors (GPCRs) are a large family comprising >800 signaling receptors that regulate numerous cellular and physiologic responses. GPCRs have been implicated in numerous diseases and represent the largest class of drug targets. Although advances in GPCR structure and pharmacology have improved drug discovery, the regulation of GPCR function by diverse post-translational modifications (PTMs) has received minimal attention. Over 200 PTMs are known to exist in mammalian cells, yet only a few have been reported for GPCRs. Early studies revealed phosphorylation as a major regulator of GPCR signaling, whereas later reports implicated a function for ubiquitination, glycosylation, and palmitoylation in GPCR biology. Although our knowledge of GPCR phosphorylation is extensive, our knowledge of the modifying enzymes, regulation, and function of other GPCR PTMs is limited. In this review we provide a comprehensive overview of GPCR post-translational modifications with a greater focus on new discoveries. We discuss the subcellular location and regulatory mechanisms that control post-translational modifications of GPCRs. The functional implications of newly discovered GPCR PTMs on receptor folding, biosynthesis, endocytic trafficking, dimerization, compartmentalized signaling, and biased signaling are also provided. Methods to detect and study GPCR PTMs as well as PTM crosstalk are further highlighted. Finally, we conclude with a discussion of the implications of GPCR PTMs in human disease and their importance for drug discovery. SIGNIFICANCE STATEMENT: Post-translational modification of G protein-coupled receptors (GPCRs) controls all aspects of receptor function; however, the detection and study of diverse types of GPCR modifications are limited. A thorough understanding of the role and mechanisms by which diverse post-translational modifications regulate GPCR signaling and trafficking is essential for understanding dysregulated mechanisms in disease and for improving and refining drug development for GPCRs.

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.

Hydration-Induced Structural Changes in the Solid State of Protein: A SAXS/WAXS Study on Lysozyme

The stability of biologically produced pharmaceuticals is the limiting factor to various applications, which can be improved by formulation in solid-state forms, mostly via lyophilization. Knowledge about the protein structure at the molecular level in the solid state and its transition upon rehydration is however scarce, and yet it most likely affects the physical and chemical stability of the biological drug. In this work, synchrotron small- and wide-angle X-ray scattering (SWAXS) are used to characterize the structure of a model protein, lysozyme, in the solid state and its structural transition upon rehydration to the liquid state. The results show that the protein undergoes distortion upon drying to adopt structures that can continuously fill the space to remove the protein–air interface that may be formed upon dehydration. Above a hydration threshold of 35 wt %, the native structure of the protein is recovered. The evolution of SWAXS peaks as a function of water content in a broad range of concentrations is discussed in relation to the structural changes in the protein. The findings presented here can be used for the design and optimization of solid-state formulations of proteins with improved stability.

Dynamic cluster formation determines viscosity and diffusion in dense protein solutions

We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in explicit solvent. Our systems contain up to 540 fully flexible proteins with 3.6 million atoms. In concentrated protein solutions (100 mg/mL and higher), the proteins ubiquitin and lysozyme, as well as the protein domains third IgG-binding domain of protein G and villin headpiece, diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. A dynamic cluster model nearly quantitatively explains the increase in viscosity and the decrease in protein diffusivity with protein volume fraction, which both exceed the predictions from widely used colloid models. The Stokes-Einstein relations for translational and rotational diffusion remain valid, but the effective hydrodynamic radius grows linearly with protein volume fraction. This increase follows the observed increase in cluster size and explains the more dramatic slowdown of protein rotation compared with translation. Baxter's sticky-sphere model of colloidal suspensions captures the concentration dependence of cluster size, viscosity, and rotational and translational diffusion. The consistency between simulations and experiments for a diverse set of soluble globular proteins indicates that the cluster model applies broadly to concentrated protein solutions, with equilibrium dissociation constants for nonspecific protein-protein binding in the Kd ≈ 10-mM regime.

Spectroscopic Analysis of Protein-Crowded Environments Using the Charge-Transfer Fluorescence Probe 8-Anilino-1-Naphthalenesulfonic Acid

The molecular behaviors of proteins under crowding conditions are crucial for understanding the protein actions in intracellular environments. Under a crowded environment, the distance between protein molecules is almost the same size as the molecular level, thus, both the excluded volume effect and short ranged soft chemical interaction on protein surface could induce the complicated influence on the protein behavior cooperatively. Recently, various kinds of analytical approaches from macroscopic to microscopic aspects have been made to evaluate the crowding effect. The method, however, has not been established to evaluate the surface specific interactions on protein surface. In this study, the analytical method to evaluate the crowding effect has been suggested by using a charge-transfer fluorescence probe, ANS. By employing the unique property of ANS attaching to charged residues on the surface of lysozyme, the crowding effect was focused, while the case was compared as a reference, in which ANS is confined in hydrophobic pockets of BSA. Consequently, the surface specific changes of fluorescence spectra were readily observed under the crowded environment, whereas the fluorescence spectra of ANS in protein inside did not change. This result suggests the fluorescence spectra of ANS binding to protein surface have the capability to estimate the crowding effect of proteins.

Colloidal systems with a short-range attraction and long-range repulsion: Phase diagrams, structures, and dynamics

Colloidal systems with both a short-range attraction and long-range repulsion (SALR) have rich phases compared with the traditional hard sphere systems or sticky hard sphere systems. The competition between the short-range attraction and long-range repulsion results in the frustrated phase separation, which leads to the formation of intermediate range order (IRO) structures and introduces new phases to both equilibrium and nonequilibrium phase diagrams, such as clustered fluid, cluster percolated fluid, Wigner glass, and cluster glass. One hallmark feature of many SALR systems is the appearance of the IRO peak in the interparticle structure factor, which is associated with different types of IRO structures. The relationship between the IRO peak and the clustered fluid state has been careful investigated. Not surprisingly, the morphology of clusters in solutions can be affected and controlled by the SALR potential. And the effect of the SALR potential on the dynamic properties is also reviewed here. Even though much progress has been made in understanding SALR systems, many future works are still needed to have quantitative comparisons between experiments and simulations/theories and understand the differences from different experimental systems. Owing to the large parameter space available for SALR systems, many exciting features of SALR systems are not fully explored yet. Because proteins in low-salinity solutions have SALR interactions, the understanding of SALR systems can greatly help understand protein behavior in concentrated solutions or crowded conditions.

Mechanism of silica-lysozyme composite formation unravelled by in situ fast SAXS

A quantitative understanding of aggregation mechanisms leading to the formation of composites of inorganic nanoparticles (NPs) and proteins in aqueous media is of paramount interest for colloid chemistry. In particular, the interactions between silica (SiO2) NPs and lysozyme (LZM) have attracted attention, because LZM is well-known to adsorb strongly to silica NPs, while at the same time preserving its enzymatic activity. The inherent nature of the aggregation processes leading to NP-LZM composites involves structural changes at length scales from few to at least hundreds of nanometres but also time scales much smaller than one second. To unravel these we used in situ synchrotron-based small-angle X-ray scattering (SAXS) and followed the subtle interparticle interactions in solution at a time resolution of 50 ms/frame (20 fps). We show that if the size of silica NPs (ca. 5 nm diameter) is matched by the dimensions of LZM, the evolving scattering patterns contain a unique structure-factor contribution originating from the presence of LZM. We developed a scattering model and applied it to analyse this structure function, which allowed us to extract structural information on the deformation of lysozyme molecules during aggregation, as well as to derive the mechanisms of composite formation.

Soft-Matter Approaches for Controlling Food Protein Interactions and Assembly

Animal- and plant-based proteins are present in a wide variety of raw and processed foods. They play an important role in determining the final structure of food matrices. Food proteins are diverse in terms of their biological origin, molecular structure, and supramolecular assembly. This diversity has led to segmented experimental studies that typically focus on one or two proteins but hinder a more general understanding of food protein structuring as a whole. In this review, we propose a unified view of how soft-matter physics can be used to control food protein assembly. We discuss physical models from polymer and colloidal science that best describe and predict the phase behavior of proteins. We explore the occurrence of phase transitions along two axes: increasing protein concentration and increasing molecular attraction. This review provides new perspectives on the link between the interactions, phase transitions, and assembly of proteins that can help in designing new food products and innovative food processing operations.

Nucleation of protein crystals - a nanoscopic perspective

Macromolecular phase transitions bear great medical, scientific and industrial relevance, yet the molecular picture of their earliest beginnings is still far from complete. For decades, progress has been hampered by the challenges associated with studying stochastic nucleation phenomena occurring on nanoscopic length scales. In the last 5 years, however, the field has advanced with great strides due to the recent buildout of experimental techniques that allow us to observe details of the nucleation process on the nanoscale. In this review, we present a historical overview and state-of-the-art analysis of protein crystal nucleation from an experimentalist's perspective. After a short introduction of key concepts from classical nucleation theory, we discuss the advancements that have led to the development of alternative models of protein nucleation. We summarize the experimental proof in favour of these various models, but we also focus on some of their shortcomings and experimental blind spots. In our penultimate section we highlight recent works that have provided direct nanoscopic insight into the nucleation of protein crystals. We end with concluding paragraphs discussing outstanding questions and possible strategies to advance the field further in the future.

Physical principles of intracellular organization via active and passive phase transitions

Exciting recent developments suggest that phase transitions represent an important and ubiquitous mechanism underlying intracellular organization. We describe key experimental findings in this area of study, as well as the application of classical theoretical approaches for quantitatively understanding these data. We also discuss the way in which equilibrium thermodynamic driving forces may interface with the fundamentally out-of-equilibrium nature of living cells. In particular, time and/or space-dependent concentration profiles may modulate the phase behavior of biomolecules in living cells. We suggest future directions for both theoretical and experimental work that will shed light on the way in which biological activity modulates the assembly, properties, and function of viscoelastic states of living matter.

Binding of Lysozyme to Spherical Poly(styrenesulfonate) Gels

Polyelectrolyte gels are useful as carriers of proteins and other biomacromolecules in, e.g., drug delivery. The rational design of such systems requires knowledge about how the binding and release are affected by electrostatic and hydrophobic interactions between the components. To this end we have investigated the uptake of lysozyme by weakly crosslinked spherical poly(styrenesulfonate) (PSS) microgels and macrogels by means of micromanipulator assisted light microscopy and small angle X-ray scattering (SAXS) in an aqueous environment. The results show that the binding process is an order of magnitude slower than for cytochrome c and for lysozyme binding to sodium polyacrylate gels under the same conditions. This is attributed to the formation of very dense protein-rich shells in the outer layers of the microgels with low permeability to the protein. The shells in macrogels contain 60 wt % water and nearly charge stoichiometric amounts of lysozyme and PSS in the form of dense complexes of radius 8 nm comprising 30⁻60 lysozyme molecules. With support from kinetic modelling results we propose that the rate of protein binding and the relaxation rate of the microgel are controlled by the protein mass transport through the shell, which is strongly affected by hydrophobic and electrostatic interactions. The mechanism explains, in turn, an observed dependence of the diffusion rate on the apparent degree of crosslinking of the networks.

Nonclassical nucleation pathways in protein crystallization

Classical nucleation theory (CNT), which was established about 90 years ago, has been very successful in many research fields, and continues to be the most commonly used theory in describing the nucleation process. For a fluid-to-solid phase transition, CNT states that the solute molecules in a supersaturated solution reversibly form small clusters. Once the cluster size reaches a critical value, it becomes thermodynamically stable and favored for further growth. One of the most important assumptions of CNT is that the nucleation process is described by one reaction coordinate and all order parameters proceed simultaneously. Recent studies in experiments, computer simulations and theory have revealed nonclassical features in the early stage of nucleation. In particular, the decoupling of order parameters involved during a fluid-to-solid transition leads to the so-called two-step nucleation mechanism, in which a metastable intermediate phase (MIP) exists between the initial supersaturated solution and the final crystals. Depending on the exact free energy landscapes, the MIPs can be a high density liquid phase, mesoscopic clusters, or a pre-ordered state. In this review, we focus on the studies of nonclassical pathways in protein crystallization and discuss the applications of the various scenarios of two-step nucleation theory. In particular, we focus on protein solutions in the presence of multivalent salts, which serve as a model protein system to study the nucleation pathways. We wish to point out the unique features of proteins as model systems for further studies.

Nanoscale Dynamics of Protein Assembly Networks in Supersaturated Solutions

Proteins in solution are conventionally considered macromolecules. Dynamic microscopic structures in supersaturated protein solutions have received increasing attention in the study of protein crystallisation and the formation of misfolded aggregates. Here, we present a method for observing rotational dynamic structures that can detect the interaction of nanoscale lysozyme protein networks via diffracted X-ray tracking (DXT). Our DXT analysis demonstrated that the rearrangement behaviours of lysozyme networks or clusters, which are driven by local density and concentration fluctuations, generate force fields on the femtonewton to attonewton (fN – aN) scale. This quantitative parameter was previously observed in our experiments on supersaturated inorganic solutions. This commonality provides a way to clarify the solution structures of a variety of supersaturated solutions as well as to control nucleation and crystallisation in supersaturated solutions.

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-of-the-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.

Crowding-Controlled Cluster Size in Concentrated Aqueous Protein Solutions: Structure, Self- and Collective Diffusion

We investigate the concentration-controlled formation of clusters in β-lactoglobulin (BLG) protein solutions combining structural and dynamical scattering techniques. The static structure factor from small-angle X-ray scattering as well as de-Gennes narrowing in the nanosecond diffusion function D(q) from neutron spin echo spectroscopy support a picture of cluster formation. Using neutron backscattering spectroscopy, a monotonous increase of the average hydrodynamic cluster radius is monitored over a broad protein concentration range, corresponding to oligomeric structures of BLG ranging from the native dimers up to roughly four dimers. The results suggest that BLG forms compact clusters that are static on the observation time scale of several nanoseconds. The presented analysis provides a general framework to access the structure and dynamics of macromolecular assemblies in solution.

Intermediate scattering function for macromolecules in solutions probed by neutron spin echo

The neutron-spin-echo method (NSE) is a powerful technique for studying internal dynamics of macromolecules in solutions because it can simultaneously probe length and time scales comparable to intramolecular density fluctuations of macromolecules. Recently, there has been increased, strong interest in studying protein internal motions using NSE. The coherent intermediate scattering function (ISF) measured by NSE depends on internal, rotational, and translational motions of macromolecules in solutions. It is thus critical, but highly nontrivial, to separate the internal motion from other motions in order to properly understand protein internal dynamics. Even though many experiments are performed at relatively high concentrations, current theories of calculating the ISF of concentrated protein solutions are either inaccurate or flawed by incorrect assumptions for realistic protein systems with anisotropic shapes. Here, a theoretical framework is developed to establish the quantitative relationship of different motions included in the ISF. This theory based on the dynamic decoupling approximation is applicable to a wide range of protein concentrations, including dilute cases. It is also, in general, useful for studying many other types of macromolecule systems studied by NSE.

Aggregation of cyclic polypeptoids bearing zwitterionic end-groups with attractive dipole–dipole and solvophobic interactions: a study by small-angle neutron scattering and molecular dynamics simulation

The aggregation behavior of cyclic polypeptoids has been studied using experiments and simulations.

Morphology dictated heterogeneous dynamics in two-dimensional aggregates

Particulate aggregates occur in a variety of non-equilibrium steady-state morphologies ranging from finite-size compact crystalline structures to non-compact string-like conformations. This diversity is due to the competition between pair-wise short range attraction and long range repulsion between particles. We identify different microscopic mechanisms in action by following the simulated particle trajectories for different morphologies in two dimensions at a fixed density and temperature. In particular, we show that the compact clusters are governed by symmetric caging of particles by their nearest neighbors while sidewise asymmetric binding of particles leads to non-compact aggregates. The measured timescales for these two mechanisms are found to be distinctly different providing phenomenological evidence of a relation between microstructure and dynamics of particulate aggregates. Supporting these findings, the time dependent diffusivity is observed to differ across the morphological hierarchy, while the average long-time dynamics is, in general, sub-diffusive at 'low' temperatures. Finally, one generic relation between diffusivity and structural randomness, applicable to simple equilibrium systems, is validated for complex aggregate forming systems through further analysis of the same system at different temperatures.

Effects of confinement on pattern formation in two dimensional systems with competing interactions

Template-assisted pattern formation in monolayers of particles with competing short-range attraction and long-range repulsion interactions (SALR) is studied by Monte Carlo simulations in a simple generic model [N. G. Almarza et al., J. Chem. Phys., 2014, 140, 164708]. We focus on densities corresponding to formation of parallel stripes of particles and on monolayers laterally confined between straight parallel walls. We analyze both the morphology of the developed structures and the thermodynamic functions for broad ranges of temperature T and the separation L2 between the walls. At low temperature stripes parallel to the boundaries appear, with some corrugation when the distance between the walls does not match the bulk periodicity of the striped structure. The stripes integrity, however, is rarely broken for any L2. This structural order is lost at T = TK(L2) depending on L2 according to a Kelvin-like equation. Above the Kelvin temperature TK(L2) many topological defects such as breaking or branching of the stripes appear, but a certain anisotropy in the orientation of the stripes persists. Finally, at high temperature and away from the walls, the system behaves as an isotropic fluid of elongated clusters of various lengths and with various numbers of branches. For L2 optimal for the stripe pattern the heat capacity as a function of temperature takes the maximum at T = TK(L2).

Softness and non-spherical shape define the phase behavior and the structural properties of lysozyme in aqueous solutions

In this study, Boltzmann inversion is applied in conjunction with molecular dynamics simulations to derive inter-molecular potential for protein lysozyme in aqueous solution directly from experimental static structure factor. The potential has a soft repulsion at short distances and an attraction well at intermediate distances that give rise to the liquid-liquid phase separation. Moreover, Gibbs ensemble Monte Carlo simulations demonstrate that a non-spherical description of lysozyme is better suited to correctly reproduce the experimentally observed properties of such a phase separation. Our findings shed new light on the common problem in molecular and cell biology: "How to model proteins in their natural aqueous environments?"

Coupling and Decoupling of Rotational and Translational Diffusion of Proteins under Crowding Conditions

Molecular motion of biopolymers in vivo is known to be strongly influenced by the high concentration of organic matter inside cells, usually referred to as crowding conditions. To elucidate the effect of intermolecular interactions on Brownian motion of proteins, we performed (1)H pulsed-field gradient NMR and fluorescence correlation spectroscopy (FCS) experiments combined with small-angle X-ray scattering (SAXS) and viscosity measurements for three proteins, αB-crystalline (αBc), bovine serum albumin, and hen egg-white lysozyme (HEWL) in aqueous solution. Our results demonstrate that long-time translational diffusion quantitatively follows the expected increase of macro-viscosity upon increasing the protein concentration in all cases, while rotational diffusion as assessed by polarized FCS and previous multi-frequency (1)H NMR relaxometry experiments reveals protein-specific behavior spanning the full range between the limiting cases of full decoupling from (αBc) and full coupling to (HEWL) the macro-viscosity. SAXS was used to study the interactions between the proteins in solution, whereby it is shown that the three cases cover the range between a weakly interacting hard-sphere system (αBc) and screened Coulomb repulsion combined with short-range attraction (HEWL). Our results, as well as insights from the recent literature, suggest that the unusual rotational-translational coupling may be due to anisotropic interactions originating from hydrodynamic shape effects combined with high charge and possibly a patchy charge distribution.

Combination of acoustic levitation with small angle scattering techniques and synchrotron radiation circular dichroism. Application to the study of protein solutions

BACKGROUND

The acoustic levitation technique is a useful sample handling method for small solid and liquids samples, suspended in air by means of an ultrasonic field. This method was previously used at synchrotron sources for studying pharmaceutical liquids and protein solutions using x-ray diffraction and small angle x-ray scattering (SAXS).

METHODS

In this work we combined for the first time this containerless method with small angle neutron scattering (SANS) and synchrotron radiation circular dichroism (SRCD) to study the structural behavior of proteins in solutions during the water evaporation. SANS results are also compared with SAXS experiments.

RESULTS

The aggregation behavior of 45μl droplets of lysozyme protein diluted in water was followed during the continuous increase of the sample concentration by evaporating the solvent. The evaporation kinetics was followed at different drying stage by SANS and SAXS with a good data quality. In a prospective work using SRCD, we also studied the evolution of the secondary structure of the myoglobin protein in water solution in the same evaporation conditions.

CONCLUSIONS

Acoustic levitation was applied for the first time with SANS and the high performances of the used neutron instruments made it possible to monitor fast container-less reactions in situ. A preliminary work using SRCD shows the potentiality of its combination with acoustic levitation for studying the evolution of the protein structure with time.

GENERAL SIGNIFICANCE

This multi-techniques approach could give novel insights into crystallization and self-assembly phenomena of biological compound with promising potential applications in pharmaceutical, food and cosmetics industry. This article is part of a Special Issue entitled "Science for Life" Guest Editor: Dr. Austen Angell, Dr. Salvatore Magazù and Dr. Federica Migliardo.

Size-dependent interaction of silica nanoparticles with lysozyme and bovine serum albumin proteins

The interaction of three different sized (diameter 10, 18, and 28 nm) anionic silica nanoparticles with two model proteins-cationic lysozyme [molecular weight (MW) 14.7 kDa)] and anionic bovine serum albumin (BSA) (MW 66.4 kDa) has been studied by UV-vis spectroscopy, dynamic light scattering (DLS), and small-angle neutron scattering (SANS). The adsorption behavior of proteins on the nanoparticles, measured by UV-vis spectroscopy, is found to be very different for lysozyme and BSA. Lysozyme adsorbs strongly on the nanoparticles and shows exponential behavior as a function of lysozyme concentration irrespective of the nanoparticle size. The total amount of adsorbed lysozyme, as governed by the surface-to-volume ratio, increases on lowering the size of the nanoparticles for a fixed volume fraction of the nanoparticles. On the other hand, BSA does not show any adsorption for all the different sizes of the nanoparticles. Despite having different interactions, both proteins induce similar phase behavior where the nanoparticle-protein system transforms from one phase (clear) to two phase (turbid) as a function of protein concentration. The phase behavior is modified towards the lower concentrations for both proteins with increasing the nanoparticle size. DLS suggests that the phase behavior arises as a result of the nanoparticles' aggregation on the addition of proteins. The size-dependent modifications in the interaction potential, responsible for the phase behavior, have been determined by SANS data as modeled using the two-Yukawa potential accounting for the repulsive and attractive interactions in the systems. The protein-induced interaction between the nanoparticles is found to be short-range attraction for lysozyme and long-range attraction for BSA. The magnitude of attractive interaction irrespective of protein type is enhanced with increase in the size of the nanoparticles. The total (attractive+repulsive) potential leading to two-phase formation is found to be more attractive for larger sized nanoparticles. The nanoparticle aggregates are characterized by mass fractal.

Studying solutions at high shear rates: a dedicated microfluidics setup

The development of a dedicated small-angle X-ray scattering setup for the investigation of complex fluids at different controlled shear conditions is reported. The setup utilizes a microfluidics chip with a narrowing channel. As a consequence, a shear gradient is generated within the channel and the effect of shear rate on structure and interactions is mapped spatially. In a first experiment small-angle X-ray scattering is utilized to investigate highly concentrated protein solutions up to a shear rate of 300000 s(-1). These data demonstrate that equilibrium clusters of lysozyme are destabilized at high shear rates.

Coupling of isotropic and directional interactions and its effect on phase separation and self-assembly

The interactions of molecules and particles in solution often involve an interplay between isotropic and highly directional interactions that lead to a mutual coupling of phase separation and self-assembly. This situation arises, for example, in proteins interacting through hydrophobic and charged patch regions on their surface and in nanoparticles with grafted polymer chains, such as DNA. As a minimal model of complex fluids exhibiting this interaction coupling, we investigate spherical particles having an isotropic interaction and a constellation of five attractive patches on the particle's surface. Monte Carlo simulations and mean-field calculations of the phase boundaries of this model depend strongly on the relative strength of the isotropic and patch potentials, where we surprisingly find that analytic mean-field predictions become increasingly accurate as the directional interactions become increasingly predominant. We quantitatively account for this effect by noting that the effective interaction range increases with increasing relative directional to isotropic interaction strength. We also identify thermodynamic transition lines associated with self-assembly, extract the entropy and energy of association, and characterize the resulting cluster properties obtained from simulations using percolation scaling theory and Flory-Stockmayer mean-field theory. We find that the fractal dimension and cluster size distribution are consistent with those of lattice animals, i.e., randomly branched polymers swollen by excluded volume interactions. We also identify a universal functional form for the average molecular weight and a nearly universal functional form for a scaling parameter characterizing the cluster size distribution. Since the formation of branched clusters at equilibrium is a common phenomenon in nature, we detail how our analysis can be used in experimental characterization of such associating fluids.

Protein self-assembly induces promiscuous nucleophilic biocatalysis in Morita–Baylis–Hillman (MBH) reaction

Self-assembled states of proteins render efficient promiscuous nucleophilic biocatalysis in MBH reaction in a green process.

Osmotic pressures of lysozyme solutions from gas-like to crystal states

Osmotic pressures of lysozyme solutions at concentrations up to 850 g L⁻¹ show three regimes and a clear influence of ionic strength.

The "long tail" of the protein tumbling correlation function: observation by (1)H NMR relaxometry in a wide frequency and concentration range

Inter-protein interactions in solution affect the auto-correlation function of Brownian tumbling not only in terms of a simple increase of the correlation time, they also lead to the appearance of a weak slow component ("long tail") of the correlation function due to a slowly changing local anisotropy of the microenvironment. The conventional protocol of correlation time estimation from the relaxation rate ratio R1/R2 assumes a single-component tumbling correlation function, and thus can provide incorrect results as soon as the "long tail" is of relevance. This effect, however, has been underestimated in many instances. In this work we present a detailed systematic study of the tumbling correlation function of two proteins, lysozyme and bovine serum albumin, at different concentrations and temperatures using proton field-cycling relaxometry combined with R1ρ and R2 measurements. Unlike high-field NMR relaxation methods, these techniques enable a detailed study of dynamics on a time scale longer than the normal protein tumbling correlation time and, thus, a reliable estimate of the parameters of the "long tail". In this work we analyze the concentration dependence of the intensity and correlation time of the slow component and perform simulations of high-field (15)N NMR relaxation data demonstrating the importance of taking the "long tail" in the analysis into account.

Lack of Dependence of the Sizes of the Mesoscopic Protein Clusters on Electrostatics

Protein-rich clusters of steady submicron size and narrow size distribution exist in protein solutions in apparent violation of the classical laws of phase equilibrium. Even though they contain a minor fraction of the total protein, evidence suggests that they may serve as essential precursors for the nucleation of ordered solids such as crystals, sickle-cell hemoglobin polymers, and amyloid fibrils. The cluster formation mechanism remains elusive. We use the highly basic protein lysozyme at nearly neutral and lower pH as a model and explore the response of the cluster population to the electrostatic forces, which govern numerous biophysical phenomena, including crystallization and fibrillization. We tune the strength of intermolecular electrostatic forces by varying the solution ionic strength I and pH and find that despite the weaker repulsion at higher I and pH, the cluster size remains constant. Cluster responses to the presence of urea and ethanol demonstrate that cluster formation is controlled by hydrophobic interactions between the peptide backbones, exposed to the solvent after partial protein unfolding that may lead to transient protein oligomers. These findings reveal that the mechanism of the mesoscopic clusters is fundamentally different from those underlying the two main classes of ordered protein solid phases, crystals and amyloid fibrils, and partial unfolding of the protein chain may play a significant role.