Experimental determination of the temperature–concentration diagram of flexible polymer solutions by neutron scattering

Ensemble structure of the N-terminal domain (1-267) of FUS in a biomolecular condensate

Solutions of some proteins phase separate into a condensed state of high protein concentration and a dispersed state of low concentration. Such behavior is observed in living cells for a number of RNA-binding proteins that feature intrinsically disordered domains. It is relevant for cell function via the formation of membraneless organelles and transcriptional condensates. On a basic level, the process can be studied in vitro on protein domains that are necessary and sufficient for liquid-liquid phase separation (LLPS). We have performed distance distribution measurements by electron paramagnetic resonance for 13 sections in an N-terminal domain (NTD) construct of the protein fused in sarcoma (FUS), consisting of the QGSY-rich domain and the RGG1 domain, in the denatured, dispersed, and condensed state. Using 10 distance distribution restraints for ensemble modeling and three such restraints for model validation, we have found that FUS NTD behaves as a random-coil polymer under good-solvent conditions in both the dispersed and condensed state. Conformation distribution in the biomolecular condensate is virtually indistinguishable from the one in an unrestrained ensemble, with the latter one being based on only residue-specific Ramachandran angle distributions. Over its whole length, FUS NTD is slightly more compact in the condensed than in the dispersed state, which is in line with the theory for random coils in good solvent proposed by de Gennes, Daoud, and Jannink. The estimated concentration in the condensate exceeds the overlap concentration resulting from this theory. The QGSY-rich domain is slightly more extended, slightly more hydrated, and has slightly higher propensity for LLPS than the RGG1 domain. Our results support previous suggestions that LLPS of FUS is driven by multiple transient nonspecific hydrogen bonding and π-sp2 interactions.

Electrostatic Repulsion Slows Relaxations of Polyelectrolytes in Semidilute Solutions

We investigate the structure and dynamics of unentangled semidilute solutions of sodium polystyrenesulfonate (NaPSS) using small-angle neutron scattering (SANS) and neutron spin-echo (NSE) spectroscopy. The effects of electrostatic interactions and chain structure are examined as a function of ionic strength and polymer concentration, respectively. The SANS profiles exhibit a characteristic structural peak, signature of polyelectrolyte solutions, that can be fit with a combination of a semiflexible chain with excluded volume interactions form factor and a polymer reference interaction site model (PRISM) structure factor. We confirm that electrostatic interactions vary with ionic strength across solutions with similar geometries. The segmental relaxations from NSE deviate from theoretical predictions from Zimm and exhibit two scaling behaviors, with the crossover between the two regimes taking place around the characteristic structural peak. The chain dynamics are suppressed across the length scale of the correlation blob, and inversely related to the structure factor. These observations suggest that the highly correlated nature of polyelectrolytes presents an additional energy barrier that leads to de Gennes narrowing behavior.

A study combining magic-angle spinning NMR and small-angle X-ray scattering on the interaction in the mixture of poly(benzyl methacrylate) and ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide

Despite being an LCST system, the NMR results indicate that the number of ionic liquid ions interacting with the solute polymer increases even at temperatures approaching the separation line.

Screening lengths and osmotic compressibility of flexible polyelectrolytes in excess salt solutions

We report results of small angle neutron scattering measurements made on sodium polystyrene sulfonate in aqueous salt solutions. The correlation length (ξ) and osmotic compressibility are measured as a function of polymer (c) and added salt (cS) concentrations, and the results are compared with scaling predictions and the random-phase approximation (RPA). In Dobrynin et al.'s scaling model the osmotic pressure consists of a counter-ion contribution and a polymer contribution. The polymer contribution is found to be two orders of magnitude smaller than expected from the scaling model, in agreement with earlier observations made on neutral polymers in good solvent condition. RPA allows the determination of single-chain dimensions in semidilute solutions at high polymer and added salt concentrations, but fails for cS≤ 2 M. The χ parameter can be modelled as the sum of an intrinsic contribution (χ0) and an electrostatic term: χ∼χ0 + K'/√cS, where χ0 > 0.5 is consistent with the hydrophobic nature of the backbone of NaPSS. The dependence of χelec∼ 1/√cS disagrees with the random-phase approximation (χelec∼ 1/cs), but agrees with the light scattering results in dilute solution and Dobrynin et al.'s scaling treatment of electrostatic excluded volume.

Multiphasic effect of vinyl pyrrolidone polymers on amyloidogenesis, from macromolecular crowding to inhibition

Deposition of misfolded amyloid polypeptides, associated with cell death, is the hallmark of many degenerative diseases (e.g. type II diabetes mellitus and Alzheimer's disease). In vivo, cellular and extracellular spaces are occupied by a high volume fraction of macromolecules. The resulting macromolecular crowding energetically affects reactions. Amyloidogenesis can either be promoted by macromolecular crowding through the excluded volume effect or inhibited due to a viscosity increase reducing kinetics. Macromolecular crowding can be mimicked in vitro by the addition of non-specific polymers, e.g. Ficoll, dextran and polyvinyl pyrrolidone (PVP), the latter being rarely used to study amyloid systems. We investigated the effect of PVP on amyloidogenesis of full-length human islet amyloid polypeptide (involved in type II diabetes) using fibrillisation and surface activity assays, ELISA, immunoblot and microscale thermophoresis. We demonstrate that high molecular mass PVP360 promotes amyloidogenesis due to volume exclusion and increase in effective amyloidogenic monomer concentration, like other crowders, but without the confounding effects of viscosity and surface activity. Interestingly, we also show that low molecular mass PVP10 has unique inhibitory properties as inhibition of fibril elongation occurs mainly in the bulk solution and is due to PVP10 directly and strongly interacting with amyloid species rather than the increase in viscosity typically associated with macromolecular crowding. In vivo, amyloidogenesis might be affected by the properties and proximity of endogenous macromolecular crowders, which could contribute to changes in associated pathogenesis. More generally, the PVP10 molecular backbone could be used to design small compounds as potential inhibitors of toxic species formation.

Conformational Transitions of Polymer Chains in Solutions Characterized by Fluorescence Resonance Energy Transfer

The critical overlap concentration C* is an important concept in polymer solutions and is defined as the boundary between dilute and semidilute regimes. In this study, the chain conformational changes of polystyrene (PS) with both high (M_n = 200,000 Da) and low (M_n = 13,000 Da) molecular weights in cis-decalin were compared by intrachain fluorescence resonance energy transfer (FRET). The random labeling of donor and acceptor chromophores strategy was employed for long PS chains, whereas chain-end labeling was used for short PS chains. By monitoring the spectroscopic intensity ratio between acceptor and donor, the concentration dependence on chain conformation from dilute to semidilute solutions was determined. Both long and short chains exhibit a conformational transition concentration, above which the polymer chains begin to collapse with concentration significantly. Interestingly, for randomly labeled polymer long chains, such concentration is consistent with C* determined from the viscosity result, below which only slight conformational change of polymer chain takes place. However, for the chain-end labeled short chain, the conformational transition concentration takes place earlier than C*, below which no significant polymer conformation change is observed.

Functionalized Nanochannels from Self-Assembled and Photomodified Poly(Styrene-b-Butadiene-b-Styrene)

Membranes are prepared by self-assembly and casting of 5 and 13 wt% poly(styrene-b-butadiene-b-styrene) (PS-b-PB-b-PS) copolymers solutions in different solvents, followed by immersion in water or ethanol. By controlling the solution-casting gap, porous films of 50 and 1 µm thickness are obtained. A gradient of increasing pore size is generated as the distance from the surface increased. An ordered porous surface layer with continuous nanochannels can be observed. Its formation is investigated, by using time-resolved grazing incident small angle X-ray scattering, electron microscopy, and rheology, suggesting a strong effect of the air-solution interface on the morphology formation. The thin PS-b-PB-b-PS ordered films are modified, by promoting the photolytic addition of thioglycolic acid to the polybutadiene groups, adding chemical functionality and specific transport characteristics on the preformed nanochannels, without sacrificing the membrane morphology. Photomodification increases fivefold the water permeance to around 2 L m^-2 h^-1 bar^-1 , compared to that of the unmodified one. A rejection of 74% is measured for methyl orange in water. The membranes fabrication with tailored nanochannels and chemical functionalities can be demonstrated using relatively lower cost block copolymers. Casting on porous polyacrylonitrile supports makes the membranes even more scalable and competitive in large scale.

Surface interaction parameter measurement of solvated polymers via model end-tethered chains

We present a method for the direct measurement of the relative energy of interaction between a solvated polymer and a solid interface. By tethering linear chains covalently to the surface, we ensured the idealized and constant configuration of polymer molecules for measurement, modeling, and parameter estimation. For the case of amine-terminated polystyrene bound to a glycidoxypropyl silane film submerged in cyclohexane-d12, we estimated the χ parameter for the temperature range 10.7 °C to 52.0 °C, and found a downward sloping trend that crosses the χ = 0.5 threshold at 37 °C to 40 °C, in agreement with solution estimates for the same system. We simultaneously estimated the surface interaction parameter χ_s at each temperature, finding a decreasing affinity of the chains for the surface with increasing temperature, consistent with empirical observations. The theoretical model shows some limitations in a stronger solvent (toluene-d8) that prevent rigorous parameter estimation, but we demonstrate a qualitative change in χ and χ_s towards stronger solvency and weaker surface interaction with increasing temperature.

Hofmeister effect on thermo-responsive poly(propylene oxide): Role of polymer molecular weight and concentration

Although a vast amount of research has been dedicated to investigate the Hofmeister effect on the stability of polymer solutions, a clear understanding of the role of polymer properties in this phenomenon is still missing. Here, the Hofmeister effect of NaCl (destabilizing) and NaSCN (stabilizing) salts on aqueous solutions of poly(propylene oxide) (PPO) is studied. Four different molecular weights of PPO were investigated, to determine how the variation in the polymer coil size affects the Hofmeister effect. The investigation was further conducted for different PPO concentrations, in order to understand the effect of inter-chain interactions on the response to addition of salt. The temperature-driven phase separation of the solutions was monitored by differential scanning calorimetry, which provides the precise value of the phase separation temperature, as well as the enthalpy change accompanied with the transition. It was observed that increasing the molecular weight weakens the effect of the both salts, which is interpreted in terms of a scaling law between the molecular weight and the accessible surface area of the polymers. Increasing the PPO concentration further diminished the NaCl effect, but amplified the NaSCN effect. This difference is attributed to an electrostatic stabilization mechanism in the case of NaSCN.

Polymer fullerene solution phase behaviour and film formation pathways

We report the phase behaviour of polymer/fullerene/solvent ternary mixtures and its consequence for the morphology of the resulting composite thin films. We focus particularly on solutions of polystyrene (PS), C60 fullerene and toluene, which are examined by static and dynamic light scattering, and films obtained from various solution ages and thermal annealing conditions, using atomic force and light microscopy. Unexpectedly, the solution phase behaviour below the polymer overlap concentration, c*, is found to be described by a simple excluded volume argument (occupied by the polymer chains) and the neat C60/solvent miscibility. Scaling consistent with full exclusion is found when the miscibility of the fullerene in the solvent is much lower than that of the polymer, giving way to partial exclusion with more soluble fullerenes (phenyl-C61-butyric acid methyl ester, PCBM) and a less asymmetric solvent (chlorobenzene), employed in photovoltaic devices. Spun cast and drop cast films were prepared from PS/C60/toluene solutions across the phase diagram to yield an identical PS/C60 composition and film thickness, resulting in qualitatively different morphologies in agreement with our measured solution phase boundaries. Our findings are relevant to the solution processing of polymer/fullerene composites (including organic photovoltaic devices), which generally require effective solubilisation of fullerene derivatives and polymer pairs in this concentration range, and the design of well-defined thin film morphologies.

Polymer and colloidal models describing structure-function relationships

Colloidal and polymer systems are not only abundant in food but also useful for gaining insights into structure-function relationships of food. Colloid and polymer systems are composed of mesoscopic scale particles dispersed in a liquid. Because of a relatively small potential barrier against aggregation between mesoscopic particles, a small change in temperature, pH, or chemical compositions can trigger aggregation and induce remarkable changes in structure and function of colloidal and polymer systems. An aggregated state is not normally an equilibrium state but a kinetically trapped state also called a jammed state. Various kinetic factors in food processing, such as the rate of changes in temperature, water content, and chemical compositions, must be taken into account to establish a complete state diagram of colloid- and polymer-based food systems.

Diffusion in polymer solutions studied by fluorescence correlation spectroscopy

We employed fluorescence correlation spectroscopy (FCS) to study the diffusion of molecular and macromolecular tracers in polystyrene solutions over a broad range of concentrations (c) and molecular weights (M(w,m)) of the matrix polymer. Molecular tracer diffusion scales only with the matrix concentration and superimposes on a single, nonpolymer specific, curve. On the contrary, the diffusion of macromolecular tracers in solutions of matrix polymers with M(w,m) sufficiently larger than the tracer molecular weight scales with c/c(p)*, where c(p)* is the tracer overlap concentration. We further demonstrate that FCS can address local and global dynamics simultaneously.

Testing the scaling behavior of microemulsion-polymer mixtures

The phase behavior and structural properties of "protein limit" mixtures of small (radius 20-30 A) water-in-oil microemulsion droplets (colloids) and large (radius 130-580 A) nonadsorbing polymer chains have been investigated. Accepted theoretical scaling relations for describing correlations have been applied and do not account fully for the observations; solvency effects may account for the deviations. The polymer/colloid size ratio has been varied from around 4 to 19 by using three different molecular weights of polyisoprene. Small-angle neutron scattering (SANS) has been used to determine partial structure factors (PSF) through contrast variation. The structure factors describing colloid-colloid interactions for the three polymers at fixed polymer concentration are shown to exhibit the same scaling behavior as the phase boundaries, provided that samples are sufficiently far from the demixing phase transition. The structure factors show a dramatic increase at low wavevectors on approaching the phase boundary, and behavior in this region does not obey expected scaling relations. By calculating effective polymer Flory-Huggins parameters, the effect of apparent solvent properties on adding microemulsion are shown to be less dramatic for the higher molecular weight polymers. This study extends previous work carried out on microemulsion-polymer mixtures.

Universal scaling, entanglements, and knots of model chain molecules

By identifying the maximally random jammed state of freely jointed chains of tangent hard spheres we are able to determine the distinct scaling regimes characterizing the dependence of chain dimensions and topology on volume fraction. Calculated distributions of (i) the contour length of the primitive paths and (ii) the number of entanglements per chain agree remarkably well with recent theoretical predictions in all scaling regimes. Furthermore, our simulations reveal a hitherto unsuspected connection between purely intramolecular (knots) and intermolecular (entanglements) topological constraints.

Effects of ammonium sulfate and sodium chloride concentration on PEG/protein liquid-liquid phase separation

When added to protein solutions, poly(ethylene glycol) (PEG) creates an effective attraction between protein molecules due to depletion forces. This effect has been widely used to crystallize proteins, and PEG is among the most successful crystallization agents in current use. However, PEG is almost always used in combination with a salt at either low or relatively high concentrations. Here the effects of sodium chloride and ammonium sulfate concentration on PEG 8000/ovalbumin liquid-liquid (L-L) phase separation are investigated. At low salt the L-L phase separation occurs at decreasing protein concentration with increasing salt concentration, presumably due to repulsive electrostatic interactions between proteins. At high salt concentration, the behavior depends on the nature of the salt. Sodium chloride has little effect on the L-L phase separation, but ammonium sulfate decreases the protein concentration at which the L-L phase separation occurs. This trend is attributed to the effects of critical fluctuations on depletion forces. The implications of these results for designing solution conditions optimal for protein crystallization are discussed.

Flexible chain molecules in the marginal and concentrated regimes: universal static scaling laws and cross-over predictions

We present predictions for the static scaling exponents and for the cross-over polymer volumetric fractions in the marginal and concentrated solution regimes. Corrections for finite chain length are made. Predictions are based on an analysis of correlated fluctuations in density and chain length, in a semigrand ensemble in which mers and solvent sites exchange identities. Cross-over volumetric fractions are found to be chain length independent to first order, although reciprocal-N corrections are also estimated. Predicted scaling exponents and cross-over regimes are compared with available data from extensive off-lattice Monte Carlo simulations [Karayiannis and Laso, Phys. Rev. Lett. 100, 050602 (2008)] on freely jointed, hard-sphere chains of average lengths from N=12-500 and at packing densities from dilute ones up to the maximally random jammed state.

Small-angle neutron scattering study of microemulsion-polymer mixtures in the protein limit

Contrast variation small-angle neutron scattering (SANS) has been employed to study complex fluids comprising model microemulsions and polymers. The systems are water-in-oil microemulsions with added non-adsorbing polymer, under good polymer solvency conditions and semidilute polymer concentrations. The polymer/colloid size ratio was q approximately 11, which is well within the "protein limit". Four scattering contrasts were produced by selective deuteration of the dispersed and continuous phases and also the surfactant. In this way, the separate partial structure factors (PSF) for colloid-colloid (c-c), polymer-polymer (p-p), and colloid-polymer (c-p) have been obtained. The c-c PSF has been compared with theoretical predictions, allowing determination of a polymer correlation length. This is compared with a similar correlation length obtained from the p-p PSF, which is shown to increase with colloid concentration. In this sense, adding microemulsion has a similar effect on the dissolved polymer as reducing the solvent quality, and an effective Flory-Huggins chi parameter has been calculated. The cross-term PSF shows a distinct anti-correlation. This is the first time such structure factors have been determined experimentally for colloid-polymer systems in the protein limit and these allow a more detailed understanding of the structural interactions in these systems.

Study of the Semidilute Solutions of Poly(N,N-dimethylacrylamide) by Fluorescence and Its Implications to the Kinetics of Coil-to-Globule Transitions

The large scale motions of poly(N,N-dimethylacrylamide) chains randomly labeled with pyrene (Py-PDMA) were monitored by steady-state and time-resolved fluorescence in semidilute solutions of naked PDMA in acetone and DMF for polymer concentrations ranging from 0 to 550 g/L. Although increasing the polymer concentration of the solution led to a decrease of the mobility of the chromophore attached onto the PDMA backbone, this reduction was rather modest when compared to the large increase of the macroscopic viscosity. This result indicated that locally, the monomer constituting the chains experienced freedom of movement despite the high solution viscosity. The restricted mobility of the chromophore was characterized by the number of monomers occupying the volume probed by the excited chromophore during its lifetime, referred to as a fluorescence "blob". The number of monomers constituting a fluorescence blob, N(F)(-)(blob), and the volume of a fluorescence blob, V(F)(-)(blob), were found to decrease as the polymer concentration of the solution increased, reflecting the decreased mobility experienced by the chromophore. In DMF, the radius of an F-blob was found to scale as N(nu)(F)(-)blob, where nu equaled 0.66 +/- 0.03, very close to the expected value of the Flory exponent of 0.6 for a polymer in a good solvent. The combined knowledge of how N(F)(-)(blob) varies with the fluorescence lifetime of the chromophore and the coil density of the polymer was used to propose a new means of studying coil-to-globule transitions with potential implications for predicting the rate of protein folding.