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.

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.

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.

The Onset of Molecule-Spanning Dynamics in Heat Shock Protein Hsp90.

Protein dynamics have been investigated on a wide range of time scales. Nano- and picosecond dynamics have been assigned to local fluctuations, while slower dynamics have been attributed to larger conformational changes. However, it is largely unknown how fast (local) fluctuations can lead to slow global (allosteric) changes. Here, fast molecule-spanning dynamics on the 100 to 200 ns time scale in the heat shock protein 90 (Hsp90) are shown. Global real-space movements are assigned to dynamic modes on this time scale, which is possible by a combination of single-molecule fluorescence, quasi-elastic neutron scattering and all-atom molecular dynamics (MD) simulations. The time scale of these dynamic modes depends on the conformational state of the Hsp90 dimer. In addition, the dynamic modes are affected to various degrees by Sba1, a co-chaperone of Hsp90, depending on the location within Hsp90, which is in very good agreement with MD simulations. Altogether, this data is best described by fast molecule-spanning dynamics, which precede larger conformational changes in Hsp90 and might be the molecular basis for allostery. This integrative approach provides comprehensive insights into molecule-spanning dynamics on the nanosecond time scale for a multi-domain protein.

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.

Interchain Hydrodynamic Interaction and Internal Friction of Polyelectrolytes.

Polyelectrolytes (PE) are polymeric macromolecules in aqueous solutions characterized by their chain topology and intrinsic charge in a neutralizing fluid. Structure and dynamics are related to several characteristic screening length scales determined by electrostatic, excluded volume, and hydrodynamic interactions. We examine PE dynamics in dilute to semidilute conditions using dynamic light scattering, neutron spinecho spectroscopy, and pulse field gradient NMR spectroscopy. We connect macroscopic diffusion to segmental chain dynamics, revealing a decoupling of local chain dynamics from interchain interactions. Collective diffusion is described within a colloidal picture, including electrostatic and hydrodynamic interactions. Chain dynamics is characterized by the classical Zimm model of a neutral chain retarded by internal friction. We observe that hydrodynamic interactions are not fully screened between chains and that the internal friction within the chain increases with an increase in ion condensation on the chain.

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.

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.

Chain Confinement and Anomalous Diffusion in the Cross over Regime between Rouse and Reptation.

By neutron spin echo (NSE) and pulsed field gradient (PFG) NMR, we study the dynamics of a polyethylene-oxide melt (PEO) with a molecular weight in the transition regime between Rouse and reptation dynamics. We analyze the data with a Rouse mode analysis allowing for reduced long wavelength Rouse modes amplitudes. For short times, subdiffusive center-of-mass mean square displacement ⟨rcom2(t)⟩ was allowed. This approach captures the NSE data well and provides accurate information on the topological constraints in a chain length regime, where the tube model is inapplicable. As predicted by reptation for the polymer ⟨rcom2(t)⟩, we experimentally found the subdiffusive regime with an exponent close to µ=12, which, however, crosses over to Fickian diffusion not at the Rouse time, but at a later time, when the ⟨rcom2(t)⟩ has covered a distance related to the tube diameter.

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.

Membrane stiffening in Chitosan mediated multilamellar vesicles of alkyl ether carboxylates.

HYPOTHESIS: Membrane undulations are known to strongly affect the stability of uni- and multilamellar vesicles formed by surfactants or phospholipids. Herein, based on the same arguments, we hypothesise that the properties of polyelectrolyte mediated surfactant multilamellar vesicles, in particular the multiplicity - i.e. the number of layers forming the vesicle - depend on the dynamics of the membrane. EXPERIMENTS: Small-angle neutron scattering (SANS) and neutron spin-echo (NSE) were used to probe the structure and the dynamics of the multilayered vesicles formed in mixtures of the biopolymer chitosan and oppositely charged alkyl ether carboxylates. The neutron scattering data are complemented by static and dynamic light scattering experiments. Experiments were performed in polyelectrolyte excess conditions, and at a pH close to the pKa of the surfactant. FINDINGS: The structural investigation shows very clearly that multilayered surfactant/polyelectrolyte vesicles are formed in the investigated mixtures. Only 3 to 5 layers form, on average, one vesicle, as similarly found in mixtures of chitosan and phospholipid vesicles. NSE shows that the surfactant membrane becomes stiffer upon complexation with chitosan, and that the fluctuation of the layers is strongly coupled in time and space. Such strong coupling and the increase in overall stiffness is associated with a high entropic cost. Accordingly, the combined SANS and NSE study points out that the low multiplicity found in multilayered vesicles involving the rigid polysaccharide chitosan arises from the strongly coupled dynamics of the membrane layers.

Lipid Membrane Flexibility in Protic Ionic Liquids.

Here, we determine by neutron spin echo spectrometry (NSE) how the flexibility of egg lecithin vesicles depends on solvent composition in two protic ionic liquids (PILs) and their aqueous mixtures. In combination with small-angle neutron scattering (SANS), dynamic light scattering (DLS), and fluorescent probe microscopy, we show that the bending modulus is up to an order of magnitude lower than in water but with no change in bilayer thickness or nonpolar chain composition. This effect is attributed to the dynamic association and exchange of the IL cation between the membrane and bulk liquid, which has the same origin as the underlying amphiphilic nanostructure of the IL solvent itself. This provides a new mechanism by which to tune and control lipid membrane behavior.

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.

Alkanes as Membrane Regulators of the Response of Early Membranes to Extreme Temperatures.

One of the first steps in the origin of life was the formation of a membrane, a physical boundary that allowed the retention of molecules in concentrated solutions. The proto-membrane was likely formed by self-assembly of simple readily available amphiphiles, such as short-chain fatty acids and alcohols. In the commonly accepted scenario that life originated near hydrothermal systems, how these very simple membrane bilayers could be stable enough in time remains a debated issue. We used various complementary techniques such as dynamic light scattering, small angle neutron scattering, neutron spin-echo spectroscopy, and Fourier-transform infrared spectroscopy to explore the stability of a novel protomembrane system in which the insertion of alkanes in the midplane is proposed to shift membrane stability to higher temperatures, pH, and hydrostatic pressures. We show that, in absence of alkanes, protomembranes transition into lipid droplets when temperature increases; while in presence of alkanes, membranes persist for longer times in a concentration-dependent manner. Proto-membranes containing alkanes are stable at higher temperatures and for longer times, have a higher bending rigidity, and can revert more easily to their initial state upon temperature variations. Hence, the presence of membrane intercalating alkanes could explain how the first membranes could resist the harsh and changing environment of the hydrothermal systems. Furthermore, modulating the quantity of alkanes in the first membranes appears as a possible strategy to adapt the proto-membrane behavior according to temperature fluctuations, and it offers a first glimpse into the evolution of the first membranes.

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.

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.

Chain Dynamics of Ultrahigh Molecular Weight Polyethylene Composites with Graphene Oxide Nanosheets.

We investigate the melt chain dynamics of ultrahigh molecular weight polyethylene (UHMWPE) and its composites with graphene oxide (GO) nanosheets by means of neutron spin echo spectroscopy. For the GO concentrations explored, we observe hindered chain dynamics with respect to the pure UHMWPE. We propose a model where a fraction of the polymer is immobilized on top and at the bottom of GO sheets. This model enables us to provide a microscopic measurement of the adsorbed and free polymer fractions, as well as the thickness of the adsorbed layer. Our experiments provide experimental nanoscopic evidence of GO hindering entanglement formation in a polymer melt, a phenomenon that had been observed at the macroscale before via rheological measurements.

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.

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.

On the Mechanism of Shear-Thinning in Viscous Oppositely Charged Polyelectrolyte Surfactant Complexes (PESCs).

Semidilute mixtures of the cationically modified cellulose-based polyelectrolyte JR 400 and the anionic surfactant sodium dodecyl sulfate (SDS) form highly viscous solutions if a slight excess of charges from the polyelectrolyte is present. The reason for this is the formation of mixed rodlike aggregates in which the surfactant cross-links several polyelectrolyte chains. The same solutions also show shear-thinning behavior. In this paper, we use rheoSANS to investigate the structural evolution of the rodlike aggregates under steady shear and thereby elucidate the mechanism of shear-thinning in these viscous oppositely charged polyelectrolyte surfactant complexes.