Dynamic structure factor of undulating vesicles: finite-size and spherical geometry effects with application to neutron spin echo experiments.

We consider the dynamic structure factor (DSF) of quasi-spherical vesicles and present a generalization of an expression that was originally formulated by Zilman and Granek (ZG) for scattering from isotropically oriented quasi-flat membrane plaquettes. The expression is obtained in the form of a multi-dimensional integral over the undulating membrane surface. The new expression reduces to the original stretched exponential form in the limit of sufficiently large vesicles, i.e., in the micron range or larger. For much smaller unilamellar vesicles, deviations from the asymptotic, stretched exponential equation are noticeable even if one assumes that the Seifert-Langer leaflet density mode is completely relaxed and membrane viscosity is neglected. To avoid the need for an exhaustive numerical integration while fitting to neutron spin echo (NSE) data, we provide a useful approximation for polydisperse systems that tests well against the numerical integration of the complete expression. To validate the new expression, we performed NSE experiments on variable-size vesicles made of a POPC/POPS lipid mixture and demonstrate an advantage over the original stretched exponential form or other manipulations of the original ZG expression that have been deployed over the years to fit the NSE data. In particular, values of the membrane bending rigidity extracted from the NSE data using the new approximations were insensitive to the vesicle radii and scattering wavenumber and compared very well with expected values of the effective bending modulus ([Formula: see text]) calculated from results in the literature. Moreover, the generalized scattering theory presented here for an undulating quasi-spherical shell can be easily extended to other models for the membrane undulation dynamics beyond the Helfrich Hamiltonian and thereby provides the foundation for the study of the nanoscale dynamics in more complex and biologically relevant model membrane systems.

The Internal Structure of the Velvet Worm Projectile Slime: A Small-Angle Scattering Study.

For prey capture and defense, velvet worms eject an adhesive slime which has been established as a model system for recyclable complex liquids. Triggered by mechanical agitation, the liquid bio-adhesive rapidly transitions into solid fibers. In order to understand this mechanoresponsive behavior, here, the nanostructural organization of slime components are studied using small-angle scattering with neutrons and X-rays. The scattering intensities are successfully described with a three-component model accounting for proteins of two dominant molecular weight fractions and nanoscale globules. In contrast to the previous assumption that high molecular weight proteins-the presumed building blocks of the fiber core-are contained in the nanoglobules, it is found that the majority of slime proteins exist freely in solution. Only less than 10% of the slime proteins are contained in the nanoglobules, necessitating a reassessment of their function in fiber formation. Comparing scattering data of slime re-hydrated with light and heavy water reveals that the majority of lipids in slime are contained in the nanoglobules with homogeneous distribution. Vibrating mechanical impact under exclusion of air neither leads to formation of fibers nor alters the bulk structure of slime significantly, suggesting that interfacial phenomena and directional shearing are required for fiber formation.

The membrane regulator squalane increases membrane rigidity under high hydrostatic pressure in archaeal membrane mimics.

Apolar lipids within the membranes of archaea are thought to play a role in membrane regulation. In this work we explore the effect of the apolar lipid squalane on the dynamics of a model archaeal-like membrane, under pressure, using neutron spin echo spectroscopy. To the best of our knowledge, this is the first report on membrane dynamics at high pressure using NSE spectroscopy. Increasing pressure leads to an increase in membrane rigidity, in agreement with other techniques. The presence of squalane in the membrane results in a stiffer membrane supporting its role as a membrane regulator.

Ca2+ and Ag+ orient low-molecular weight amphiphile self-assembly into "nano-fishnet" fibrillar hydrogels with unusual ß-sheet-like raft domains.

Low-molecular weight gelators (LMWGs) are small molecules (Mw < ∼1 kDa), which form self-assembled fibrillar network (SAFiN) hydrogels in water when triggered by an external stimulus. A great majority of SAFiN gels involve an entangled network of self-assembled fibers, in analogy to a polymer in a good solvent. In some rare cases, a combination of attractive van der Waals and repulsive electrostatic forces drives the formation of bundles with a suprafibrillar hexagonal order. In this work, an unexpected micelle-to-fiber transition is triggered by Ca2+ or Ag+ ions added to a micellar solution of a novel glycolipid surfactant, whereas salt-induced fibrillation is not common for surfactants. The resulting SAFiN, which forms a hydrogel above 0.5 wt%, has a "nano-fishnet" structure, characterized by a fibrous network of both entangled fibers and ß-sheet-like rafts, generally observed for silk fibroin, actin hydrogels or mineral imogolite nanotubes, but not known for SAFiNs. The ß-sheet-like raft domains are characterized by a combination of cryo-TEM and SAXS and seem to contribute to the stability of glycolipid gels. Furthermore, glycolipid is obtained by fermentation from natural resources (glucose, rapeseed oil), thus showing that naturally engineered compounds can have unprecedented properties, when compared to the wide range of chemically derived amphiphiles.

Ideal Agent System with Triplet States: Model Parameter Identification of Agent-Field Interaction.

On the capital market, price movements of stock corporations can be observed independent of overall market developments as a result of company-specific news, which suggests the occurrence of a sudden risk event. In recent years, numerous concepts from statistical physics have been transferred to econometrics to model these effects and other issues, e.g., in socioeconomics. Like other studies, we extend the approaches based on the "buy" and "sell" positions of agents (investors' stance) with a third "hold" position. We develop the corresponding theory within the framework of the microcanonical and canonical ensembles for an ideal agent system and apply it to a capital market example. We thereby design a procedure to estimate the required model parameters from time series on the capital market. The aim is the appropriate modeling and the one-step-ahead assessment of the effect of a sudden risk event. From a one-step-ahead performance comparison with selected benchmark approaches, we infer that the model is well-specified and the model parameters are well determined.

Strikingly Different Roles of SARS-CoV-2 Fusion Peptides Uncovered by Neutron Scattering.

Coronavirus disease-2019 (COVID-19), a potentially lethal respiratory illness caused by the coronavirus SARS-CoV-2, emerged in the end of 2019 and has since spread aggressively across the globe. A thorough understanding of the molecular mechanisms of cellular infection by coronaviruses is therefore of utmost importance. A critical stage in infection is the fusion between viral and host membranes. Here, we present a detailed investigation of the role of selected SARS-CoV-2 Spike fusion peptides, and the influence of calcium and cholesterol, in this fusion process. Structural information from specular neutron reflectometry and small angle neutron scattering, complemented by dynamics information from quasi-elastic and spin-echo neutron spectroscopy, revealed strikingly different functions encoded in the Spike fusion domain. Calcium drives the N-terminal of the Spike fusion domain to fully cross the host plasma membrane. Removing calcium, however, reorients the peptide back to the lipid leaflet closest to the virus, leading to significant changes in lipid fluidity and rigidity. In conjunction with other regions of the fusion domain, which are also positioned to bridge and dehydrate viral and host membranes, the molecular events leading to cell entry by SARS-CoV-2 are proposed.

Stimuli-responsive polyelectrolyte surfactant complexes for the reversible control of solution viscosity.

Interactions of polyelectrolytes with oppositely charged surfactants can give rise to a large variety of self-assembled structures. Some of these systems cause a drastic increase in solution viscosity, which is related to the surfactant forming aggregates interconnecting several polyelectrolyte chains. For these aggregates to form, the surfactant needs to be sufficiently hydrophobic. Here, we present a system consisting of the anionic surfactant sodium monododecyl phosphate and the cationic cellulose-based polyelectrolyte JR 400. The hydrophobicity of the surfactant can be controlled by the solution's pH. At pH > 12, the surfactant headgroup bears two charges. As a consequence, the solution viscosity decreases drastically by up to two orders of magnitude, while it can be as high as 10 Pa s at lower pH. In this paper, we investigate the changes of the mesoscopic structure of the system which lead to such drastic changes in viscosity using small angle neutron scattering and neutron spin-echo spectroscopy. Such systems are potentially interesting as they allow for a modular design where stimuli responsiveness is introduced by relatively small amounts of surfactant reusing the same simple polyelectrolyte.

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

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

Adsorption Kinetics of Oppositely Charged Hard and Soft Nanoparticles with Phospholipid Membranes.

Nanoparticles (NPs) have great potential for biological applications as typically they exhibit strongly size-dependent properties. Specifically, the interaction of NPs with phospholipid membranes is significantly relevant to nanomedicine and the related field of nanotoxicology. Therefore, the investigation of interactions of NPs with model membranes is not only fundamentally important but also practically valuable to understand interactions of NPs with more complex cell membranes. Here, we report on the interaction of anionic vesicles of different charge densities and cationic SiO2 NPs, either covered by a bare surface functionalized with amino moieties (-NH2) or covered by poly[2-(dimethylamino) ethyl methacrylate]. We studied the kinetics of binding of NPs to the vesicle surface by time-resolved scattering experiments. A key result of the study is that binding is favored in the presence of electrostatic attraction, but the polymer layer decreases the binding rate drastically.

Uncommon Structures of Oppositely Charged Hyaluronan/Surfactant Assemblies under Physiological Conditions.

Self-assembled aggregates formed by semidilute polyanion hyaluronan (hyaluronic acid, HA) and an oppositely charged surfactant tetradecyltrimethylammonium bromide (TTAB) in an aqueous phosphate-buffered saline (PBS) solution have been studied via light scattering (LS), small-angle neutron scattering (SANS), and cryogenic transmission electron microscopy (cryo-TEM). The addition of 0-20 mM TTAB to a 27.7 mM (monomer, 1 wt %) HA solution (597 kDa) in PBS buffer leads to soluble complexes until phase separation occurs near charge equilibrium (>20 mM TTAB). While the viscosity remains rather constant, already small amounts of added TTAB lead to the formation of large globular superstructures, which are built in a hierarchical fashion from a locally threadlike structural arrangement of TTA micelles along the stiff HA chains, within the little changed HA network. These globular domains have radii of 60-100 nm and contain 500-700 TTA micelles, which means that they are very "fluffy" and composed of about 99% water. They do not grow in size or number upon further TTAB addition, but, instead, the additional TTA micelles form further threadlike complexes outside of the big globular domains. Such a type of polyelectrolyte-surfactant complexes (PESCs) has not been described before and has to be attributed to the particular properties of HA, which are high stiffness and relatively weak interactions with oppositely charged micelles due to having the charged carboxylic group close to the polysaccharide backbone. These findings demonstrate that the HA network structure in solution basically remains unaffected by complexation with an oppositely charged surfactant, explaining the unchanged rheological behavior and the formation of a unique PESC local "coacervate" structure within the HA hydrogel network.

Disentangling of complex polymer dynamics under soft nanoscopic confinement.

We discuss the complex interplay between host and guest dynamics for a polymer in soft confinement by a droplet-phase microemulsion. Intermediate scattering functions obtained by neutron spin echo spectroscopy are first analysed by means of an effective diffusion coefficient. From its dependence on the absolute of the scattering vector q we concluded a sophisticated model for the systems dynamics taking both polymer and microemulsion contributions into account. Global fitting of this model to the intermediate scattering functions at all measured q-values and all investigated confinement sizes eventually allows for a precise disentangling of the pure polymer dynamics in confinement from the overlaying microemulsion dynamics. Validity of our approach is further supported by numerical random walk calculations.

Direct Observation of Dynamic Tube Dilation in Entangled Polymer Blends: A Combination of Neutron Scattering and Dielectric Techniques.

We report a microscopic observation of the time-dependent dynamic tube dilation process on isofrictional bidisperse melts. By applying neutron spin echo (NSE) and dielectric techniques on blends of long polyisoprene (PI) chains with short PI additives with different topology, we access the dynamics of the tube dilation process on a molecular scale. The time-dependent tube dilation is directly revealed by NSE as an additional time dependence of the dynamic structure factor in the local reptation regime. We identify the characteristic time of tube dilation as the terminal time of the additive.

Influence of PEGylation on Domain Dynamics of Phosphoglycerate Kinase: PEG Acts Like Entropic Spring for the Protein.

Protein-polymer conjugation is a widely used technique to develop protein therapeutics with improved pharmacokinetic properties as prolonged half-life, higher stability, water solubility, lower immunogenicity, and antigenicity. Combining biochemical methods, small angle scattering (SAXS/SANS), and neutron spin-echo spectroscopy, here we examine the impact of PEGylation (i.e., the covalent conjugation with poly(ethylene glycol) or PEG) on structure and internal domain dynamics of phosphoglycerate kinase (PGK) to elucidate the reason for reduced activity that is connected to PEGylation. PGK is a protein with a hinge motion between the two main domains that is directly related to function. We find that secondary structure and ligand access to the binding sites are not affected. The ligand induced cleft closing is unchanged. We observe an additional internal motion between covalent bonded PEG and the protein compatible with Brownian motion of PGK in a harmonic potential. Entropic interaction with the full PEG chain leads to a force constant of about 8 pN/nm independent of PEG chain length. This additional force preserves protein structure and has negligible effects on the functional domain dynamics of the protein. PEGylation seems to reduce activity just by acting as a local crowder for the ligands. The newly identified interaction mechanism might open possibilities to improve rational design of protein-polymer conjugates.

Dynamics of small unilamellar vesicles.

In this paper, we investigate the dynamics of small unilamellar vesicles with the aid of neutron spin-echo spectroscopy. The purpose of this investigation is twofold. On the one hand, we investigate the influence of solubilised cosurfactant on the dynamics of the vesicle's surfactant bilayer. On the other hand, the small unilamellar vesicles used here have a size between larger vesicles, with dynamics being well described by the Zilman-Granek model and smaller microemulsion droplets which can be described by the Milner-Safran model. Therefore, we want to elucidate the question, which model is more suitable for the description of the membrane dynamics of small vesicles, where the finite curvature of the bilayer is felt by the contained amphiphilic molecules. This question is of substantial relevance for our understanding of membranes and how their dynamics is affected by curvature, a problem that is also of key importance in a number of biological questions. Our results indicate the even down to vesicle radii of 20 nm the Zilman-Granek model appears to be the more suitable one.

Micellar Self-Assembly of Recombinant Resilin-/Elastin-Like Block Copolypeptides.

Reported here is the synthesis of perfectly sequence defined, monodisperse diblock copolypeptides of hydrophilic elastin-like and hydrophobic resilin-like polypeptide blocks and characterization of their self-assembly as a function of structural parameters by light scattering, cryo-TEM, and small-angle neutron scattering. A subset of these diblock copolypeptides exhibit lower critical solution temperature and upper critical solution temperature phase behavior and self-assemble into spherical or cylindrical micelles. Their morphologies are dictated by their chain length, degree of hydrophilicity, and hydrophilic weight fraction of the ELP block. We find that (1) independent of the length of the corona-forming ELP block there is a minimum threshold in the length of the RLP block below which self-assembly does not occur, but that once that threshold is crossed, (2) the RLP block length is a unique molecular parameter to independently tune self-assembly and (3) increasing the hydrophobicity of the corona-forming ELP drives a transition from spherical to cylindrical morphology. Unlike the self-assembly of purely ELP-based block copolymers, the self-assembly of RLP-ELPs can be understood by simple principles of polymer physics relating hydrophilic weight fraction and polymer-polymer and polymer-solvent interactions to micellar morphology, which is important as it provides a route for the de novo design of desired nanoscale morphologies from first principles.

Phase Behavior and Self-Assembly of Perfectly Sequence-Defined and Monodisperse Multiblock Copolypeptides.

This paper investigates how the properties of multiblock copolypeptides can be tuned by their block architecture, defined by the size and distribution of blocks along the polymer chain. These parameters were explored by the precise, genetically encoded synthesis of recombinant elastin-like polypeptides (ELPs). A family of ELPs was synthesized in which the composition and length were conserved while the block length and distribution were varied, thus creating 11 ELPs with unique block architectures. To our knowledge, these polymers are unprecedented in their intricately and precisely varied architectures. ELPs exhibit lower critical solution temperature (LCST) behavior and micellar self-assembly, both of which impart easily measured physicochemical properties to the copolymers, providing insight into polymer hydrophobicity and self-assembly into higher order structures, as a function of solution temperature. Even subtle variation in block architecture changed the LCST phase behavior and morphology of these ELPs, measured by their temperature-triggered phase transition and nanoscale self-assembly. Size and morphology of polypeptide micelles could be tuned solely by controlling the block architecture, thus demonstrating that when sequence can be precisely controlled, nanoscale self-assembly of polypeptides can be modulated by block architecture.

Kinetics of Oil Exchange in Nanoemulsions Prepared with the Phase Inversion Concentration Method.

Nanoemulsions (NEs) are metastable emulsions with droplet sizes between 20 and 100 nm and with a wide range of applications, for example, in polymerization, in pharmaceutical and cosmetic formulations, and as drug delivery systems. Even though they are not in thermodynamic equilibrium, they can be metastable over relatively long times and have the advantage that they can be formed easily by low energy input methods. In particular, the phase inversion concentration (PIC) method allows the formation of NEs by the dilution of a suitable mixture of oil and surfactants with water. In this paper, we investigate the kinetics of the oil exchange process of NEs formed by the PIC method by looking at the exchange of different hydrophobic oils and by employing contrast variation stopped flow small-angle neutron scattering. These experiments demonstrate that this exchange becomes substantially slower by increasing the chain length of the alkane. This indicates a mechanism where monomer exchange is relevant, which would indicate also that for aging one would expect Ostwald ripening to be the determining factor. Such investigations can be carried out in a unique fashion by means of neutron scattering, and the results have important implications for the optimization of NE formulations.

Structure and dynamics of polyelectrolyte surfactant mixtures under conditions of surfactant excess.

Oppositely charged polyelectrolyte (PE) surfactant mixtures can self-assemble into a large variety of mesoscopic structures, so-called polyelectrolyte surfactant complexes (PESCs). These structures directly affect the macroscopic behavior of such solutions. In this study, we investigated mixtures of the cationically charged PE JR 400 and the anionic surfactant SDS with the help of different neutron scattering and fluorescence methods. While an excess of PE charges in semi-dilute solutions causes an increase of viscosity, it has been observed that an excess of surfactant charges reduces the viscosity while precipitation is observed at charge equilibrium. The increase in viscosity had been investigated before and was attributed to the formation of cross links between PE chains. In this publication we focus our attention on the reduction of viscosity which is observed with an excess of surfactant charges. It is found that the PE chains form relatively large and densely packed clusters near the phase boundary on the surfactant rich side, thereby occupying less space and reducing the viscosity. For even higher surfactant concentrations, individual surfactant decorated PE chains are observed and their viscosity is found to be similar to that of the pure PE.

On the mesoscopic origins of high viscosities in some polyelectrolyte-surfactant mixtures.

Oppositely charged polyelectrolyte (PE) surfactant mixtures allow the control of rheological parameters of a solution even at fairly low concentrations. For example, addition of 0.3 wt. % of anionic surfactant to a 1 wt. % solution of the polycation JR 400 increases the viscosity by 4 orders of magnitude. Recently, we could show that this increase is related to the formation of mixed, rod-like PE/surfactant aggregates which interconnect several polyelectrolyte chains [Hoffmann et al., Europhys. Lett. 104, 28001 (2013)]. In this paper, we refine our structural model of the aggregates to obtain a more consistent picture of their internal structure for different anionic surfactants. Combining small angle neutron scattering (SANS) and neutron spin-echo (NSE) allows us to determine the size of the aggregates. By comparing different contrasts, the internal structure of the aggregates can be elucidated and it is seen that the PE in the aggregates retains a relatively high freedom of movement. We proceeded to investigate the influence of the surfactant concentration and the surfactant type on structure and dynamics of the mixed aggregates. It is seen that the structural parameters of the aggregates depend very little on the surfactant concentration and headgroup. However, it is crucial to incorporate a sufficient amount of PE in the aggregates to increase the viscosity of the aggregates. By comparing viscous samples at 1 wt. % PE concentration with samples at a PE concentration of 0.3 wt. %, where no significant increase in viscosity is observed, we find that similar aggregates are formed already at this lower PE concentrations. However, the amount of PE incorporated in them is insufficient to interconnect several PE chains and therefore, they do not increase viscosity. So, our detailed investigation combining contrast variation SANS and NSE does not only allow to explain the viscosity behavior but also to deduced detailed information regarding the structures and the dynamics especially of the polyelectrolyte within the complexes.

Cooperative Dynamics of Highly Entangled Linear Polymers within the Entanglement Tube.

We present a quantitative comparison of the dynamic structure factors from unentangled and strongly entangled poly(butylene oxide) (PBO) melts. As expected, the low molecular weight PBO displays Rouse dynamics, however, with very significant subdiffusive center-of-mass diffusion. The spectra from high molecular weight entangled PBO can be very well described by the dynamic structure factor based on the concept of local reptation, including the Rouse dynamics within the tube and allowing for non-Gaussian corrections. Comparing quantitatively the spectra from both polymers leads to the surprising result that their spectra differ only by the contribution of classical Rouse diffusion for the low molecular weight melt. The subdiffusive component is common for both the low and high molecular weight PBO melts, indicating that in both melts the same interchain potential is active, thereby supporting the validity of the Generalized Langevin Equation approach.