Ion-activated attractive patches as a mechanism for controlled protein interactions

The ion-activated attractive patchy particle model and its application to the liquid-vapor phase transitions

Patchy particles are an intriguing subject of study and indeed a model system in the field of soft matter physics. In recent years, patchy particle models have been applied to describe a wide variety of systems, including colloidal crystals, macromolecular interactions, liquid crystals, and nanoparticle assemblies. Given the importance of the topic, rationalizing and capturing the basic features of these models is crucial to their correct application in specific systems. In this study, we extend the ion-activated attractive patchy particles model previously employed to elucidate the phase behavior of protein solutions in the presence of trivalent salts. Our extension incorporates the effect of repulsion between unoccupied and occupied binding sites, depicted as patches. Furthermore, we examine the influence of model parameters on the liquid-vapor coexistence region within the phase diagram, employing numerical methods. A deeper understanding of this model will facilitate a better comprehension of the effects observed in experiments.

From adsorption to crystallization of proteins: Evidence for interface-assisted nucleation

Protein crystallization is among the key processes in biomolecular research, but the underlying mechanisms are still elusive. Here, we address the role of inevitable interfaces for the nucleation process. Quartz crystal microbalance with dissipation monitoring (QCM-D) with simultaneously optical microscopy, confocal microscopy, and grazing-incidence small angle X-rays scattering (GISAXS) were employed to investigate the temporal behavior from the initial stage of protein adsorption to crystallization. Here we studied the crystallization of the Human Serum Albumin (HSA), the most abundant blood protein, in the presence of a charged surface and a trivalent salt. We found evidence for interface-assisted nucleation of crystals. The kinetic stages involved are initial adsorption followed by enhanced adsorption after longer times, subsequent nucleation, and finally crystal growth. The results highlight the importance of interfaces for protein phase behavior and in particular for nucleation.

Effective interactions and phase behavior of protein solutions in the presence of hexamine cobalt(III) chloride

It is well established that deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) exhibit a reentrant condensation (RC) phase behavior in the presence of the trivalent hexamine cobalt(III) cations (Hac) which can be important for their packing and folding. A similar behavior can be observed for negatively charged globular proteins in the presence of trivalent metal cations, such as Y3+ or La3+. This phase behavior is mainly driven by charge inversion upon an increasing salt concentration for a fixed protein concentration (cp). However, as Hac exhibits structural differences compared to other multivalent metal cations, with six ammonia ligands (NH3) covalently bonded to the central cobalt atom, it is not clear that Hac can induce a similar phase behavior for proteins. In this work, we systematically investigate whether negatively charged globular proteins β-lactoglobulin (BLG), bovine serum albumin (BSA), human serum albumin (HSA) and ovalbumin (OVA) feature Hac-induced RC. Effective protein-protein interactions were investigated by small-angle X-ray scattering. The reduced second virial coefficient (B2/B2HS) was obtained as a function of salt concentration. The virial coefficient analysis performed confirms the reentrant interaction (RI) behavior for BLG without actually inducing RC, given the insufficient strengths of the interactions for the latter to occur. In contrast, the strength of attraction for BSA, HSA and OVA are too weak to show RC. Model free analysis of the inverse intensity [Formula: see text] also supports this finding. Looking at different q-range by employing static (SLS) and dynamic light scattering experiments, the presence of RI behavior can be confirmed. The results are further discussed in view of metal cation binding sites in nucleic acids (DNA and RNA), where Hac induced RC phase behavior.

Bridging attraction of condensed bovine serum albumin solution in the presence of trivalent ions: A SANS study

The bridging attraction of condensed bovine serum albumin (BSA) solution (D2O) in the presence of yttrium chloride (YCl3) was studied by small angle neutron scattering (SANS). With increasing the concentration of YCl3 (cY) from 3 to 15 mM and from 15 to 100 mM, the intensity in low-q region increases and then decreases. Combining the tri-axial ellipsoid (TaE) geometry and the multi-component sticky hard sphere (SHS) potential, a SHS-TaE model was established to quantitatively determine the size and distribution of particles. In this way, the structural mechanism of the aggregation-redissolution process in protein solution was demonstrated and discussed. As cY increases from 3 to 100 mM, the SHS radius rL decreases from ca. 2.97 to 2.50 nm, suggesting that the relatively well dispersed BSAs may form aggregates with various polydispersities. The axis a increases from 1.88 to 2.30 nm, while b and c decrease from 3.53 to 3.23 nm and from 4.12 to 3.55 nm, respectively. (RgTaE decreases from ca. 2.57 to 2.38 nm). Moreover, the scattering length density (SLD) of BSA decreases from 3.67 to 1.56 × 10-6 Å-2. All these results consistently indicate a strengthened attraction and the BSA molecules might shrink and tune out to be more like of oblate ellipsoid with increasing the amount of YCl3.

Protein Association in Solution: Statistical Mechanical Modeling

Protein molecules associate in solution, often in clusters beyond pairwise, leading to liquid phase separations and high viscosities. It is often impractical to study these multi-protein systems by atomistic computer simulations, particularly in multi-component solvents. Instead, their forces and states can be studied by liquid state statistical mechanics. However, past such approaches, such as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, were limited to modeling proteins as spheres, and contained no microscopic structure-property relations. Recently, this limitation has been partly overcome by bringing the powerful Wertheim theory of associating molecules to bear on protein association equilibria. Here, we review these developments.

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.

Protein solutions close to liquid-liquid phase separation exhibit a universal osmotic equation of state and dynamical behavior

Liquid-liquid phase separation (LLPS) of protein solutions is governed by highly complex protein-protein interactions. Nevertheless, it has been suggested that based on the extended law of corresponding states (ELCS), as proposed for colloids with short-range attractions, one can rationalize not only the thermodynamics, but also the structure and dynamics of such systems. This claim is systematically and comprehensively tested here by static and dynamic light scattering experiments. Spinodal lines, the isothermal osmotic compressibility κ_T and the relaxation rate of concentration fluctuations Γ are determined for protein solutions in the vicinity of LLPS. All these quantities are found to exhibit a corresponding-states behavior. This means that, for different solution conditions, these quantities are essentially the same if considered at similar reduced temperature or second virial coefficient. For moderately concentrated solutions, the volume fraction ϕ dependence of κ_T and Γ can be consistently described by Baxter's model of adhesive hard spheres. The off-critical, asymptotic T behavior of κ_T and Γ close to LLPS is consistent with the scaling laws predicted by mean-field theory. Thus, the present work aims at a comprehensive experimental test of the applicability of the ELCS to structural and dynamical properties of concentrated protein solutions.

Ion-bridges and lipids drive aggregation of same-charge nanoparticles on lipid membranes

The control of the aggregation of biomedical nanoparticles (NP) in physiological conditions is crucial as clustering may change completely the way they interact with the biological environment. Here we show that Au nanoparticles, functionalized by an anionic, amphiphilic shell, spontaneously aggregate in fluid zwitterionic lipid bilayers. We use molecular dynamics and enhanced sampling techniques to disentangle the short-range and long-range driving forces of aggregation. At short inter-particle distances, ion-mediated, charge-charge interactions (ion bridging) stabilize the formation of large NP aggregates, as confirmed by cryo-electron microscopy. Lipid depletion and membrane curvature are the main membrane deformations driving long-range NP-NP attraction. Ion bridging, lipid depletion, and membrane curvature stem from the configurational flexibility of the nanoparticle shell. Our simulations show, more in general, that the aggregation of same-charge membrane inclusions can be expected as a result of intrinsically nanoscale effects taking place at the NP-NP and NP-bilayer soft interfaces.

Exploring Nucleation Pathways in Distinct Physicochemical Environments Unveiling Novel Options to Modulate and Optimize Protein Crystallization

The scientific discussion about classical and nonclassical nucleation theories has lasted for two decades so far. Recently, multiple nucleation pathways and the occurrence and role of metastable intermediates in crystallization processes have attracted increasing attention, following the discovery of functional phase separation, which is now under investigation in different fields of cellular life sciences, providing interesting and novel aspects for conventional crystallization experiments. In this context, more systematic investigations need to be carried out to extend the current knowledge about nucleation processes. In terms of the data we present, a well-studied model protein, glucose isomerase (GI), was employed first to investigate systematically the early stages of the crystallization process, covering condensing and prenucleation ordering of protein molecules in diverse scenarios, including varying ionic and crowding agent conditions, as well as the application of a pulsed electric field (pEF). The main method used to characterize the early events of nucleation was synchronized polarized and depolarized dynamic light scattering (DLS/DDLS), which is capable of collecting the polarized and depolarized component of scattered light from a sample suspension in parallel, thus monitoring the time-resolved evolution of the condensation and geometrical ordering of proteins at the early stages of nucleation. A diffusion interaction parameter, KD, of GI under varying salt conditions was evaluated to discuss how the proportion of specific and non-specific protein–protein interactions affects the nucleation process. The effect of mesoscopic ordered clusters (MOCs) on protein crystallization was explored further by adding different ratios of MOCs induced by a pEF to fresh GI droplets in solution with different PEG concentrations. To emphasize and complement the data and results obtained with GI, a recombinant pyridoxal 5-phosphate (vitamin B6) synthase (Pdx) complex of Staphylococcus aureus assembled from twelve monomers of Pdx1 and twelve monomers of Pdx2 was employed to validate the ability of the pEF influencing the nucleation of complex macromolecules and the effect of MOCs on adjusting the crystallization pathway. In summary, our data revealed multiple nucleation pathways by tuning the proportion of specific and non-specific protein interactions, or by utilizing a pEF which turned out to be efficient to accelerate the nucleation process. Finally, a novel and reproducible experimental strategy, which can adjust and facilitate a crystallization process by pEF-induced MOCs, was summarized and reported for the first time.

Accelerated simulation method for charge regulation effects

The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, charge regulation (CR), in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient CR Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the large-scale Atomic/Molecular Massively Parallel Simulator molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of CR on the nature of the polyelectrolyte coil-globule transition and on the effective interaction between oppositely charged nanoparticles.

Role of entropy in determining the phase behavior of protein solutions induced by multivalent ions

Recent experiments have reported lower critical solution temperature (LCST) phase behavior of aqueous solutions of proteins induced by multivalent ions, where the solution phase separates upon heating. This phenomenon is linked to complex hydration effects that result in a net entropy gain upon phase separation. To decipher the underlying molecular mechanism, we use all-atom molecular dynamics simulations along with the two-phase thermodynamic method for entropy calculation. Based on simulations of a single BSA protein in various salt solutions (NaCl, CaCl₂, MgCl₂, and YCl₃) at temperatures (T) ranging 283-323 K, we find that the cation-protein binding affinity increases with T, reflecting its thermodynamic driving force to be entropic in origin. We show that in the cation binding process, many tightly bound water molecules from the solvation shells of a cation and the protein are released to the bulk, resulting in entropy gain. To rationalize the LCST behavior, we calculate the ζ-potential that shows charge inversion of the protein for solutions containing multivalent ions. The ζ-potential increases with T. Performing simulations of two BSA proteins, we demonstrate that the protein-protein binding is mediated by multiple cation bridges and involves similar dehydration effects that cause a large entropy gain which more than compensates for rotational and translational entropy losses of the proteins. Thus, the LCST behavior is entropy-driven, but the associated solvation effects are markedly different from hydrophobic hydration. Our findings have direct implications for tuning the phase behavior of biological and soft-matter systems, e.g., protein condensation and crystallization.

Colloid-like solution behavior of computationally designed coiled coil bundlemers

The use of isotropic potential models of simple colloids for describing complex protein-protein interactions is a topic of ongoing debate in the biophysical community. This contention stems from the unavailability of synthetic protein-like model particles that are amenable to systematic experimental characterization. In this article, we test the utility of colloidal theory to capture the solution structure, interactions and dynamics of novel globular protein-mimicking, computationally designed peptide assemblies called bundlemers that are programmable model systems at the intersection of colloids and proteins. Small-angle neutron scattering (SANS) measurements of semi-dilute bundlemer solutions in low and high ionic strength solution indicate that bundlemers interact locally via repulsive interactions that can be described by a screened repulsive potential. We also present neutron spin echo (NSE) spectroscopy results that show high-Q freely-diffusive dynamics of bundlemers. Importantly, formation of clusters due to short-range attractive, inter-bundlemer interactions is observed in SANS even at dilute bundlemer concentrations, which is indicative of the complexity of the bundlemer charged surface. The similarities and differences between bundlemers and simple colloidal as well as complex protein-protein interactions is discussed in detail.

Interactions in protein solutions close to liquid-liquid phase separation: ethanol reduces attractions via changes of the dielectric solution properties

Ethanol is a common protein crystallization agent, precipitant, and denaturant, but also alters the dielectric properties of solutions. While ethanol-induced unfolding is largely ascribed to its hydrophobic parts, its effect on protein phase separation and inter-protein interactions remains poorly understood. Here, the effects of ethanol and NaCl on the phase behavior and interactions of protein solutions are studied in terms of the metastable liquid-liquid phase separation (LLPS) and the second virial coefficient B₂ using lysozyme solutions. Determination of the phase diagrams shows that the cloud-point temperatures are reduced and raised by the addition of ethanol and salt, respectively. The observed trends can be explained using the extended law of corresponding states as changes of B₂. The results for B₂ agree quantitatively with those of static light scattering and small-angle X-ray scattering experiments. Furthermore, B₂ values calculated based on inter-protein interactions described by the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential and considering the dielectric solution properties and electrostatic screening due to the ethanol and salt content quantitatively agree with the experimentally observed B₂ values.

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.

Bulk phase behaviour vs interface adsorption: Effects of anions and isotopes on β-lactoglobulin (BLG) interactions

HYPOTHESIS

Protein adsorption is highly relevant in numerous applications ranging from food processing to medical implants. In this context, it is important to gain a deeper understanding of protein-protein and protein-surface interactions. Thus, the focus of this investigation is on the interplay of bulk properties and surface properties on protein adsorption. It was hypothesised that the type of solvent and ions in solution should significantly influence the protein's bulk and interface behaviour, which has been observed in literature and previous work for other net negatively charged, globular proteins such as bovine serum albumin (BSA).

EXPERIMENTS

The phase behaviour of β-lactoglobulin (BLG) with lanthanum chloride (LaCl₃) and iodide (LaI₃) in normal water H₂O(l) and heavy water (D₂O(l)) was established via optical microscopy and ultraviolet-visible spectroscopy. The formation of an adsorption layer and its properties such as thickness, density, structure, and hydration was investigated via neutron reflectivity, quartz-crystal microbalance with dissipation, and infra-red measurements.

FINDINGS

β-lactoglobulin does not show significant anion-induced or isotope-induced effects - neither in bulk nor at the solid-liquid interface, which deviates strongly from the behaviour of bovine serum albumin. We also provide a comprehensive discussion and comparison of protein-specific bulk and interface behaviour between bovine serum albumin and β-lactoglobulin dependent on anion, cation, solvent, and substrate properties. These findings pave the way for understanding the transition from adsorption to crystallisation.

Transfer of a Rational Crystal Contact Engineering Strategy between Diverse Alcohol Dehydrogenases

Protein crystallization can serve as a purification step in biotechnological processes but is often limited by the non-crystallizability of proteins. Enabling or improving crystallization is mostly achieved by high-throughput screening of crystallization conditions and, more recently, by rational crystal contact engineering. Two selected rational crystal contact mutations, Q126K and T102E, were transferred from the alcohol dehydrogenases of Lactobacillus brevis (LbADH) to Lactobacillus kefir (LkADH). Proteins were expressed in E. coli and batch protein crystallization was performed in stirred crystallizers. Highly similar crystal packing of LkADH wild type compared to LbADH, which is necessary for the transfer of crystal contact engineering strategies, was achieved by aligning purification tag and crystallization conditions, as shown by X-ray diffraction. After comparing the crystal sizes after crystallization of LkADH mutants with the wild type, the mean protein crystal size of LkADH mutants was reduced by 40–70% in length with a concomitant increase in the total amount of crystals (higher number of nucleation events). Applying this measure to the LkADH variants studied results in an order of crystallizability T102E > Q126K > LkADH wild type, which corresponds to the results with LbADH mutants and shows, for the first time, the successful transfer of crystal contact engineering strategies.

Charge Regulation Effects in Nanoparticle Self-Assembly

Nanoparticles in solution acquire charge through the dissociation or association of surface groups. Thus, a proper description of their electrostatic interactions requires the use of charge-regulating boundary conditions rather than the commonly employed constant-charge approximation. We implement a hybrid Monte Carlo/molecular dynamics scheme that dynamically adjusts the charges of individual surface groups of objects while evolving their trajectories. Charge regulation effects are shown to qualitatively change self-assembled structures due to global charge redistribution, stabilizing asymmetric constructs. We delineate under which conditions the conventional constant-charge approximation may be employed and clarify the interplay between charge regulation and dielectric polarization.

Impact of Arginine-Phosphate Interactions on the Reentrant Condensation of Disordered Proteins

Re-entrant condensation results in the formation of a condensed protein regime between two critical ion concentrations. The process is driven by neutralization and inversion of the protein charge by oppositely charged ions. Re-entrant condensation of cationic proteins by the polyvalent anions, pyrophosphate and tripolyphosphate, has previously been observed, but not for citrate, which has similar charge and size compared to the polyphosphates. Therefore, besides electrostatic interactions, other specific interactions between the polyphosphate ions and proteins must contribute. Here, we show that additional attractive interactions between arginine and tripolyphosphate determine the re-entrant condensation and decondensation boundaries of the cationic, intrinsically disordered saliva protein, histatin 5. Furthermore, we show by small-angle X-ray scattering (SAXS) that polyvalent anions cause compaction of histatin 5, as would be expected based solely on electrostatic interactions. Hence, we conclude that arginine-phosphate-specific interactions not only regulate solution properties but also influence the conformational ensemble of histatin 5, which is shown to vary with the number of arginine residues. Together, the results presented here provide further insight into an organizational mechanism that can be used to tune protein interactions in solution of both naturally occurring and synthetic proteins.

Zinc determines dynamical properties and aggregation kinetics of human insulin

Protein aggregation is a widespread process leading to deleterious consequences in the organism, with amyloid aggregates being important not only in biology but also for drug design and biomaterial production. Insulin is a protein largely used in diabetes treatment, and its amyloid aggregation is at the basis of the so-called insulin-derived amyloidosis. Here, we uncover the major role of zinc in both insulin dynamics and aggregation kinetics at low pH, in which the formation of different amyloid superstructures (fibrils and spherulites) can be thermally induced. Amyloid aggregation is accompanied by zinc release and the suppression of water-sustained insulin dynamics, as shown by particle-induced x-ray emission and x-ray absorption spectroscopy and by neutron spectroscopy, respectively. Our study shows that zinc binding stabilizes the native form of insulin by facilitating hydration of this hydrophobic protein and suggests that introducing new binding sites for zinc can improve insulin stability and tune its aggregation propensity.

Solvent effect for an effective attraction between like-charged macroions immersed in an electrolyte solution: The intensification mechanism of the effective attraction caused by the translational motion of solvent particles

The effective interaction between macroanions immersed in an electrolyte solution was calculated using an integral equation theory of liquids to study the solvent granularity effect on the effective attraction mediated by cations. Explicit and implicit solvent models were examined. The effective attraction for the explicit solvent model was found to be stronger than that for the implicit solvent model. This solvent effect was remarkably enhanced only when the effective attraction between macroanions was strong; this means that the solvent effect is not a usual excluded volume effect. The intensification mechanism of the attraction by the solvent granularity is analyzed in the present study, and an indirect mechanism is proposed.

Bulk Phase Behavior vs Interface Adsorption: Specific Multivalent Cation and Anion Effects on BSA Interactions

Proteins are ubiquitous and play a critical role in many areas from living organisms to protein microchips. In humans, serum albumin has a prominent role in the foreign body response since it is the first protein which will interact with, e.g., an implant or stent. In this study, we focused on the influence of salts (i.e., different cations (Y³⁺, La³⁺) and anions (Cl^-, I^-) on bovine serum albumin (BSA) in terms of its bulk behavior as well as the role of charges for protein adsorption at the solid-liquid interface in order to understand and control the underlying molecular mechanisms and interactions. This is part of our group's effort to gain a deeper understanding of protein-protein and protein-surface interactions in the presence of multivalent ions. In the bulk, we established two new phase diagrams and found not only multivalent cation-triggered phase transitions, but also a dependence of the protein behavior on the type of anion. The attractive interactions between proteins were observed to increase from Cl^- < NO₃^- < I^-, resulting in iodide preventing re-entrant condensation and promoting liquid-liquid phase separation in bulk. Using ellipsometry and a quartz-crystal microbalance with dissipation (QCM-D), we obtained insight into the growth of the protein adsorption layer. Importantly, we found that phase transitions at the substrate can be triggered by certain interface properties, whether they exist in the bulk solution or not. Through the use of a hydrophilic, negatively charged surface (native silica), the direct binding of anions to the interface was prevented. Interestingly, this led to re-entrant adsorption even in the absence of re-entrant condensation in bulk. However, the overall amount of adsorbed protein was enhanced through stronger attractive protein-protein interactions in the presence of iodide salts. These findings illustrate how carefully chosen surface properties and salts can directly steer the binding of anions and cations, which guide protein behavior, thus paving the way for specific/triggered protein-protein, protein-salt, and protein-surface interactions.

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.

Protein Surface Printer for Exploring Protein Domains

The surface of proteins is vital in determining protein functions. Herein, a program, Protein Surface Printer (PSP), is built that performs multiple functions in quantifying protein surface domains. Two proteins, PETase and cytochrome P450, are used to validate that the program supports atomistic simulations with different combinations of programs and force fields. A case study is conducted on the structural analysis of the spike proteins of SARS-CoV-2 and SARS-CoV and the human cell receptor ACE2. Although the surface domains of both spike proteins are highly similar, their receptor-binding domains (RBDs) and the O-linked glycan domains are structurally different. The O-linked glycan domain of SARS-CoV-2 is highly positively charged, which may promote binding to negatively charged human cells.

Aggregation, liquid-liquid phase separation, and percolation behaviour of a model antibody fluid constrained by hard-sphere obstacles

This study is concerned with the behaviour of proteins within confinement created by hard-sphere obstacles. An individual antibody molecule is depicted as an assembly of seven hard spheres, organized to resemble a Y-shaped (on average) antibody (7-bead model) protein. For comparison with other studies we, in one case, model the protein as a hard sphere decorated by three short-range attractive sites. The antibody has two Fab and one Fc domains located in the corners of the letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pair interactions are possible. The confinement is formed by the randomly distributed hard-sphere obstacles fixed in space. Aside from size exclusion, the obstacles do not interact with antibodies, but they affect the protein-protein correlation. We used a combination of the scaled-particle theory, Wertheim's thermodynamic perturbation theory and the Flory-Stockmayer theory to calculate: (i) the second virial coefficient of the protein fluid, (ii) the percolation threshold, (iii) cluster size distributions, and (iv) the liquid-liquid phase separation as a function of the strength of the various pair interactions of the protein and the model parameters, such as protein concentration and the packing fraction of obstacles. The conclusion is that hard-sphere obstacles strongly decrease the critical density and also, but to a much lesser extent, the critical temperature. Also, the confinement enhances clustering, making the percolating region broader. The effect depends on the model parameters, such as the packing fraction of obstacles η0, the inter-site interaction strength εIJ, and the ratio between the size of the obstacle σ0 and the size of one bead of the model antibody σhs; the value of this ratio is varied here from 2 to 5. Interestingly, at low to moderate packing fractions of obstacles, the second virial coefficient first slightly decreases (destabilization), and the slope depends on the observation temperature, but then at higher values of η0 it increases. The calculated values of the second virial coefficient also depend on the size of the obstacles.

Multivalent ions and biomolecules: Attempting a comprehensive perspective

Ions are ubiquitous in nature. They play a key role for many biological processes on the molecular scale, from molecular interactions, to mechanical properties, to folding, to self-organisation and assembly, to reaction equilibria, to signalling, to energy and material transport, to recognition etc. Going beyond monovalent ions to multivalent ions, the effects of the ions are frequently not only stronger (due to the obviously higher charge), but qualitatively different. A typical example is the process of binding of multivalent ions, such as Ca2+ , to a macromolecule and the consequences of this ion binding such as compaction, collapse, potential charge inversion and precipitation of the macromolecule. Here we review these effects and phenomena induced by multivalent ions for biological (macro)molecules, from the "atomistic/molecular" local picture of (potentially specific) interactions to the more global picture of phase behaviour including, e. g., crystallisation, phase separation, oligomerisation etc. Rather than attempting an encyclopedic list of systems, we rather aim for an embracing discussion using typical case studies. We try to cover predominantly three main classes: proteins, nucleic acids, and amphiphilic molecules including interface effects. We do not cover in detail, but make some comparisons to, ion channels, colloidal systems, and synthetic polymers. While there are obvious differences in the behaviour of, and the relevance of multivalent ions for, the three main classes of systems, we also point out analogies. Our attempt of a comprehensive discussion is guided by the idea that there are not only important differences and specific phenomena with regard to the effects of multivalent ions on the main systems, but also important similarities. We hope to bridge physico-chemical mechanisms, concepts of soft matter, and biological observations and connect the different communities further.

Enhanced protein adsorption upon bulk phase separation

In all areas related to protein adsorption, from medicine to biotechnology to heterogeneous nucleation, the question about its dominant forces and control arises. In this study, we used ellipsometry and quartz-crystal microbalance with dissipation (QCM-D), as well as density-functional theory (DFT) to obtain insight into the mechanism behind a wetting transition of a protein solution. We established that using multivalent ions in a net negatively charged globular protein solution (BSA) can either cause simple adsorption on a negatively charged interface, or a (diverging) wetting layer when approaching liquid-liquid phase separation (LLPS) by changing protein concentration (cp) or temperature (T). We observed that the water to protein ratio in the wetting layer is substantially larger compared to simple adsorption. In the corresponding theoretical model, we treated the proteins as limited-valence (patchy) particles and identified a wetting transition for this complex system. This wetting is driven by a bulk instability introduced by metastable LLPS exposed to an ion-activated attractive substrate.

Unification of lower and upper critical solution temperature phase behavior of globular protein solutions in the presence of multivalent cations

In globular protein systems, upper critical solution temperature (UCST) behavior is common, but lower critical solution temperature (LCST) phase transitions are rare. In addition, the temperature sensitivity of such systems is usually difficult to tune. Here we demonstrate that the charge state of globular proteins in aqueous solutions can alter their temperature-dependent phase behavior. We show a universal way to tune the effective protein interactions and induce both UCST and LCST-type transitions in the system using trivalent salts. We provide a phase diagram identifying LCST and UCST regimes as a function of protein and salt concentrations. We further propose a model based on an entropy-driven cation binding mechanism to explain the experimental observations.

Calculation of salt-dependent free energy of binding of β-lactoglobulin homodimer formation and mechanism of dimer formation using molecular dynamics simulation and three-dimensional reference interaction site model (3D-RISM): diffuse salt ions and non-polar interactions between the monomers favor the dimer formation

There are several important phenomena in chemistry, biology, and physics where molecules (or parts of a molecule) having charges of the same sign come closer together and become stable. DNA condensation, RNA folding, colloid-colloid interactions are some of the examples of this kind. In the current work, we have investigated how β-lactoglobulin, a protein found in milk, in spite of carrying +13 charge, favors the homodimer formation in the presence of salt. We have focussed on calculating the protein-protein binding free energy in the presence of salt and identifying the thermodynamic and microscopic mechanism of the process. Estimation of binding free energy of this salt-dependent process is done by combining molecular dynamics simulation with statistical mechanical theory of three-dimensional reference interaction site model (3D-RISM). Binding free energy is evaluated from the chemical potential of the solutes as opposed to potential of mean force calculation, which gives only a constrained free energy. Our calculated values semi-quantitatively match with the experimental results. By examining the different components of binding free energy, we have found that the role of salt ions (especially of Cl^-) is to shift the equilibrium towards the dimer. Non-polar (Lennard-Jones) interactions between the monomers is also favorable to the binding free energy. However, water slightly disfavors the dimer formation. For the microscopic mechanism, heterogeneous of both Na⁺ and Cl^- near the charged residues at the binding interface and change of this charge distribution on dimer formation contribute to the stability. A fine-tuning of enthalpic and entropic effects of salt ions is found to operate at different salt concentrations. Both thermodynamic and microscopic mechanism of dimer formation gives detailed insight into the complex electrostatics of charged protein-protein binding.

Model for Counterion Binding and Charge Reversal on Protein Surfaces

The structural stability and solubility of proteins in liquid therapeutic formulations is important, especially since new generations of therapeutics are designed for efficacy before consideration of stability. We introduce an electrostatic binding model to measure the net charge of proteins with bound ions in solution. The electrostatic potential on a protein surface is used to separately group together acidic and basic amino acids into patches, which are then iteratively bound with oppositely charged counterions. This model is aimed toward formulation chemists for initial screening of a range of conditions prior to lab-work. Computed results compare well with experimental zeta potential measurements from the literature covering a range of solution conditions. Importantly, the binding model reproduces the charge reversal phenomenon that is observed with polyvalent ion binding to proteins and its dependence on ion charge and concentration. Intriguingly, protein sequence can be used to give similarly good agreement with experiment as protein structure, interpreted as resulting from the close proximity of charged side chains on a protein surface. Further, application of the model to human proteins suggests that polyanion binding and overcharging, including charge reversal for cationic proteins, is a general feature. These results add to evidence that addition of polyanions to protein formulations could be a general mechanism for modulating solution stability.

Specific Ion Effects of Trivalent Cations on the Structure and Charging State of β-Lactoglobulin Adsorption Layers

The properties of proteins at interfaces are important to many processes as well as in soft matter materials such as aqueous foam. Particularly, the protein interfacial behavior is strongly linked to different factors like the solution pH or the presence of electrolytes. Here, the nature of the electrolyte ions can significantly modify the interfacial properties of proteins. Therefore, molecular level studies on interfacial structures and charging states are needed. In this work, we addressed the effects of Y³⁺ and Nd³⁺ cations on the adsorption of the whey protein β-lactoglobulin (BLG) at air-water interfaces as the function of electrolyte concentration. Both cations caused very similar but dramatic changes at the interface and in the bulk solution. Here, measurements of the electrophoretic mobility and with vibrational sum-frequency generation (SFG) spectroscopy were applied and consistently showed a reversal of the BLG net charge at remarkably low ion concentrations of 30 (bulk) and 40 (interface) μM of Y³⁺ or Nd³⁺ for a BLG concentration of 15 μM. SFG spectra of carboxylate stretching vibrations from Asp or Glu residues of interfacial BLG showed significant changes in the resonance frequency, which we associate to specific and efficient binding of Y³⁺ or Nd³⁺ ions to the proteins carboxylate groups. Characteristic reentrant condensation for BLG moieties with bound trivalent ions was found in a broad concentration range around the point of zero net charge. The highest colloidal stability of BLG was found for ion concentrations <20 μM and >50 μM. Investigations on macroscopic foams from BLG solutions revealed the existence of structure-property relations between the interfacial charging state and the foam stability. In fact, a minimum in foam stability at 20 μM ion concentration was found when the interfacial net charge was negligible. At this concentration, we propose that the persistent BLG molecules and weakly charged BLG aggregates drive foam stability, while outside the bulk reentrant zone the electrostatic disjoining pressure inside foam lamellae dominates foam stability. Our results provide new information on the charge reversal at the liquid-gas interface of protein/ion dispersions. Therefore, we see our findings as an important step in the clarification of reentrant condensation effects at interfaces and their relevance to foam stability.

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.

A Colloid Approach to Self-Assembling Antibodies

Concentrated solutions of monoclonal antibodies have attracted considerable attention due to their importance in pharmaceutical formulations; yet, their tendency to aggregate and the resulting high viscosity pose considerable problems. Here we tackle this problem by a soft condensed matter physics approach, which combines a variety of experimental measurements with a patchy colloid model, amenable of analytical solution. We thus report results of structural antibodies and dynamic properties obtained through scattering methods and microrheological experiments. We model the data using a colloid-inspired approach, explicitly taking into account both the anisotropic shape of the molecule and its charge distribution. Our simple patchy model is able to disentangle self-assembly and intermolecular interactions and to quantitatively describe the concentration-dependence of the osmotic compressibility, collective diffusion coefficient, and zero shear viscosity. Our results offer new insights on the key problem of antibody formulations, providing a theoretical and experimental framework for a quantitative assessment of the effects of additional excipients or chemical modifications and a prediction of the resulting viscosity.

Evolution of Interactions in the Protein Solution As Induced by Mono and Multivalent Ions

The evolution of interactions in the bovine serum albumin (BSA) protein solution on addition of mono and multivalent (di, tri and tetra) counterions has been studied using small-angle neutron scattering (SANS), dynamic light scattering (DLS) and ζ-potential measurements. It is found that in the presence of mono and divalent counterions, protein behavior can be well explained by DLVO theory, combining the contributions of screened Coulomb repulsion with the van der Waals attraction. The addition of mono or divalent salts in protein solution reduces the repulsive barrier and hence the overall interaction becomes attractive, but the system remains in one-phase for the entire concentration range of the salts, added in the system. However, contrary to DLVO theory, the protein solution undergoes a reentrant phase transition from one-phase to a two-phase system and then back to the one-phase system in the presence of tri and tetravalent counterions. The results show that tri and tetravalent (unlike mono and divalent) counterions induce short-range attraction between the protein molecules, leading to the transformation from one-phase to two-phase system. The two-phase is characterized by the fractal structure of protein aggregates. The excess condensation of these higher-valent counterions in the double layer around the BSA causes the reversal of charge of the protein molecules resulting into reentrant of the one-phase, at higher salt concentrations. The complete phase behavior with mono and multivalent ions has been explained in terms of the interplay of electrostatic repulsion and ion-induced short-range attraction between the protein molecules.

Phase-Separation Kinetics in Protein-Salt Mixtures with Compositionally Tuned Interactions

Liquid-liquid phase separation (LLPS) in protein systems is relevant for many phenomena, from protein condensation diseases to subcellular organization to possible pathways toward protein crystallization. Understanding and controlling LLPS in proteins is therefore highly relevant for various areas of (biological) soft matter research. Solutions of the protein bovine serum albumin (BSA) have been shown to have a lower critical solution temperature-LLPS (LCST-LLPS) induceable by multivalent salts. Importantly, the nature of the multivalent cation used influences the LCST-LLPS in such systems. Here, we present a systematic ultrasmall-angle X-ray scattering investigation of the kinetics of LCST-LLPS of BSA in the presence of different mixtures of HoCl₃ and LaCl₃, resulting in different effective interprotein attraction strengths. We monitor the characteristic length scales ξ( t, T_fin) after inducing LLPS by subjecting the respective systems to temperature jumps in their liquid-liquid coexistence regions. With increasing interprotein attraction and increasing T_fin, we observe an increasing deviation from the growth law of ξ ∼ t^1/3 and an increased trend toward arrest. We thus establish a multidimensional method to tune phase transitions in our systems. Our findings help shed light on general questions regarding LLPS and the tunability of its kinetics in both proteins and colloidal systems.

Controlling Phase Separation of Lysozyme with Polyvalent Anions

The ability of polyvalent anions to influence protein-protein interactions and protein net charge was investigated through solubility and turbidity experiments, determination of osmotic second virial coefficients ( B₂₂), and ζ-potential values for lysozyme solutions.  B₂₂ values showed that all anions reduce protein-protein repulsion between positively charged lysozyme molecules, and those anions with higher net valencies are more effective. The polyvalent anions pyrophosphate and tripolyphosphate were observed to induce protein reentrant condensation, which has been previously observed with negatively charged proteins in the presence of trivalent cations. Reentrant condensation is a phenomenon in which low concentrations of polyvalent ions induce protein precipitation, but further increasing polyvalent ion concentration causes the protein precipitate to resolubilize. Interestingly, citrate does not induce lysozyme reentrant condensation despite having a similar charge, size, and shape to pyrophosphate. We observe qualitative differences in protein behavior when compared against negatively charged proteins in solutions of trivalent cations. The polyphosphate ions induce a much stronger protein-protein attraction, which correlates with the occurrence of a liquid-gel transition that replaces the liquid-liquid transition observed with trivalent cations. The results indicate that solutions of polyphosphate ions provide a model system for exploring the link between the protein-phase diagram and model interaction potentials and also highlight the importance that ion-specific effects can have on protein solubility.

Patchy Particle Models to Understand Protein Phase Behavior

In this chapter we describe numerical procedures to evaluate the phase behavior of coarse-grained models for globular proteins. Specifically we focus on models based on hard spheres complemented with "patchy-like" anisotropic interactions that mimic the attractive regions on the surface of the proteins. We introduce the basic elements of grand canonical Monte Carlo simulations for these types of models in which rotational and translational moves need to be accounted for. We describe the techniques for the estimation of the fluid-fluid critical point, coexistence curve, and fluid-crystal boundaries. We also discuss an efficient method for the evaluation of the fluid-fluid phase diagram: the successive umbrella sampling technique. Finally we briefly describe how to exploit the same tools for the calculation of the phase behavior of protein binary mixtures.

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.

Reentrant Phase Behavior in Protein Solutions Induced by Multivalent Salts: Strong Effect of Anions Cl- Versus NO3

In this work, the effects of the two anions Cl^- and NO₃^- on the phase behavior of bovine serum albumin (BSA) in solution with trivalent salts are compared systematically. In the presence of trivalent metal salts, negatively charged proteins such as BSA in solution undergo a reentrant condensation (RC) phase behavior, which has been established for several proteins with chlorides of trivalent salts. Here, we show that replacing Cl^- by NO₃^- leads to a marked change in the phase behavior. The effect is investigated for the two different cations Y³⁺ and La³⁺. The salts are thus YCl₃, Y(NO₃)₃, LaCl₃, and La(NO₃)₃. The experimental phase behavior shows that while the chloride salts induce both liquid-liquid phase separation (LLPS) and RC, the nitrate salts also induce LLPS, but RC becomes partial with La(NO₃)₃ and disappears with Y(NO₃)₃. The observed phase behavior is rationalized by effective protein-protein interactions which are characterized using small-angle X-ray scattering. The results based on the reduced second virial coefficients B₂/ B₂^HS and 1/ I( q → 0) demonstrate that the NO₃^- salts induce a stronger attraction than the Cl^- salts. Overall, the effective attraction, the width of the condensed regime in the RC phase diagram, and the nature of LLPS follow the order LaCl₃ < YCl₃ < La(NO₃)₃ < Y(NO₃)₃. Despite the decisive role of cations in RC phase behavior, isothermal titration calorimetry measurements indicate that replacing anions does not significantly influence the cation binding to proteins. The experimental results observed are discussed based on an "enhanced Hofmeister effect" including electrostatic and hydrophobic interactions between protein-cation complexes.

Tuning phase transitions of aqueous protein solutions by multivalent cations

In the presence of trivalent cations, negatively charged globular proteins show a rich phase behaviour including reentrant condensation, crystallisation, clustering and lower critical solution temperature metastable liquid-liquid phase separation (LCST-LLPS). Here, we present a systematic study on how different multivalent cations can be employed to tune the interactions and the associated phase behaviour of proteins. We focus our investigations on the protein bovine serum albumin (BSA) in the presence of HoCl3, LaCl3 and YCl3. Using UV-Vis spectroscopy and small-angle X-ray scattering (SAXS), we find that the interprotein attraction induced by Ho3+ is very strong, while the one induced by La3+ is comparatively weak when comparing the data to BSA-Y3+ systems based on our previous work. Using zeta potential and isothermal titration calorimetry (ITC) measurements, we establish different binding affinities of cations to BSA with Ho3+ having the highest one. We propose that a combination of different cation features such as radius, polarisability and in particular hydration effects determine the protein-protein interaction induced by these cations. Our findings imply that subtle differences in cation properties can be a sensitive tool to fine-tune protein-protein interactions and phase behaviour in solution.

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.

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.

Effective potential between negatively charged patches on acidic proteins immersed in various electrolyte solutions

Effective interactions between O-sized anions in various electrolyte solutions were calculated by using the integral equation theory with some simple models. The results indicated that only multivalent cations mediated a strong effective attraction between O-sized anions at a certain concentration. The effective interaction turned from repulsive to attractive as the electrolyte concentration increased, and the effective attraction decreased when more electrolyte was added. Moreover, the effective interactions between O-sized anions in the electrolyte solution did not present a long repulsive tail, although the effective attraction caused by the divalent cations appeared. By contrast, the effective attraction mediated by monovalent cations and the reentrant behavior did not appear and the effective interaction was basically repulsive. These behaviors agree with the experimental results for reentrant condensation of acidic proteins in various electrolyte solutions. The calculated results suggest that the dissociated carboxylic acidic groups on the proteins form attractive patches between proteins under certain concentration conditions.

Reentrant Phase Transitions and Non-Equilibrium Dynamics in Membraneless Organelles

Compartmentalization of biochemical components, interactions, and reactions is critical for the function of cells. While intracellular partitioning of molecules via membranes has been extensively studied, there has been an expanding focus in recent years on the critical cellular roles and biophysical mechanisms of action of membraneless organelles (MLOs) such as the nucleolus. In this context, a substantial body of recent work has demonstrated that liquid-liquid phase separation plays a key role in MLO formation. However, less is known about MLO dissociation, with phosphorylation being the primary mechanism demonstrated thus far. In this Perspective, we focus on another mechanism for MLO dissociation that has been described in recent work, namely a reentrant phase transition (RPT). This concept, which emerges from the polymer physics field, provides a mechanistic basis for both formation and dissolution of MLOs by monotonic tuning of RNA concentration, which is an outcome of cellular processes such as transcription. Furthermore, the RPT model also predicts the formation of dynamic substructures (vacuoles) of the kind that have been observed in cellular MLOs. We end with a discussion of future directions in terms of open questions and methods that can be used to answer them, including further exploration of RPTs in vitro, in cells, and in vivo using ensemble and single-molecule methods as well as theory and computation. We anticipate that continued studies will further illuminate the important roles of reentrant phase transitions and associated non-equilibrium dynamics in the spatial patterning of the biochemistry and biology of the cell.

Valence, loop formation and universality in self-assembling patchy particles

Patchy particles have emerged as an attractive model to mimic phase separation and self-assembly of globular proteins solutions, colloidal patchy particles, and molecular fluids where directional interactions are operative. In our previous work, we extensively explored the coupling of directional and isotropic interactions on both the phase separation and self-assembly in a system of patchy particles with five spots. Here, we extend this work to consider different patch valences and isotropic interaction strengths with an emphasis on self-assembly. Although the location of self-assembly transition lines in the temperature-density plane depend on a number of parameters, we find universal behavior of cluster size that is dependent only on the probability of a spot being bound, the patch valence, and the density. Using these principles, we quantify both the mass distribution and the shape for all clusters, as well as clusters containing loops. Following the logical implications of these results, combined with a simplified version of a mean-field theory that incorporates Flory-Stockmayer theory, we find a universal curve for the temperature dependence of cluster mass and a universal curve for the fraction of clusters that contain loops. As the curves are dependent on the particle valence, such results provide a method for parameterizing patchy particle models using experimental data.

Cluster Size and Quinary Structure Determine the Rheological Effects of Antibody Self-Association at High Concentrations

The question of how nonspecific reversible intermolecular protein interactions affect solution rheology at high concentrations is fundamentally rooted in the translation of nanometer-scale interactions into macroscopic properties. Well-defined solutions of purified monoclonal antibodies (mAbs) provide a useful system with which to investigate the manifold intricacies of weak protein interactions at high concentrations. Recently, characterization of self-associating IgG1 antibody (mAb2) solutions has established the direct role of protein clusters on concentrated mAb rheology. Expanding on our earlier work with three additional mAbs (mAb1, mAb3, and mAb4), the observed concentration-dependent static light scattering and rheological data present a substantially more complex relationship between protein interactions and solution viscosity at high concentrations. The four mAb systems exhibited divergent correlations between cluster formation (size) and concentrated solution viscosities dependent on mAb primary sequence and solution conditions. To address this challenge, well-established features of colloidal cluster phenomena could be applied as a framework for interpreting our observations. The initial stages of mAb cluster formation were investigated with small-angle X-ray scattering (SAXS) and ensemble-optimized fit methods, to uncover shifts in the dimer structure populations which are produced by changes in mAb interaction modes and association valence under the different solution conditions. Analysis of mAb average cluster number and effective hydrodynamic radii at high concentrations revealed cluster architectures can have a wide range of fractal dimensions. Collectively, the static light scattering, SAXS, and rheological characterization demonstrate that nonspecific and anisotropic attractive intermolecular interactions produce antibody clusters with different quinary structures to regulate the rheological properties of concentrated mAb solutions.

Multivalent-Ion-Activated Protein Adsorption Reflecting Bulk Reentrant Behavior

Protein adsorption at the solid-liquid interface is an important phenomenon that often can be observed as a first step in biological processes. Despite its inherent importance, still relatively little is known about the underlying microscopic mechanisms. Here, using multivalent ions, we demonstrate the control of the interactions and the corresponding adsorption of net-negatively charged proteins (bovine serum albumin) at a solid-liquid interface. This is demonstrated by ellipsometry and corroborated by neutron reflectivity and quartz-crystal microbalance experiments. We show that the reentrant condensation observed within the rich bulk phase behavior of the system featuring a nonmonotonic dependence of the second virial coefficient on salt concentration c_{s} is reflected in an intriguing way in the protein adsorption d(c_{s}) at the interface. Our findings are successfully described and understood by a model of ion-activated patchy interactions within the framework of the classical density functional theory. In addition to the general challenge of connecting bulk and interface behavior, our work has implications for, inter alia, nucleation at interfaces.

Arrested and temporarily arrested states in a protein-polymer mixture studied by USAXS and VSANS

We investigate the transition of the phase separation kinetics from a complete to an arrested liquid-liquid phase separation (LLPS) in mixtures of bovine γ-globulin with polyethylene glycol (PEG). The solutions feature LLPS with upper critical solution temperature phase behavior. At higher PEG concentrations or low temperatures, non-equilibrium, gel-like states are found. The kinetics is followed during off-critical quenches by ultra-small angle X-ray scattering (USAXS) and very-small angle neutron scattering (VSANS). For shallow quenches a kinetics consistent with classical spinodal decomposition is found, with the characteristic length (ξ) growing with time as ξ ∼ t^1/3. For deep quenches, ξ grows only very slowly with a growth exponent smaller than 0.05 during the observation time, indicating an arrested phase separation. For intermediate quench depths, a novel growth kinetics featuring a three-stage coarsening is observed, with an initial classical coarsening, a subsequent slowdown of the growth, and a later resumption of coarsening approaching again ξ ∼ t^1/3. Samples featuring the three-stage coarsening undergo a temporarily arrested state. We hypothesize that, while intermittent coarsening and collapse might contribute to the temporary nature of the arrested state, migration-coalescence of the minority liquid phase through the majority glassy phase may be the main mechanism underlying this kinetics, which is also consistent with earlier simulation results.

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.