Anders Madsen

Structure of the cross-|[beta]| spine of amyloid-like fibrils

Numerous soluble proteins convert to insoluble amyloid-like fibrils that have common properties. Amyloid fibrils are associated with fatal diseases such as Alzheimers, and amyloid-like fibrils can be formed in vitro. For the yeast protein Sup35, conversion to amyloid-like fibrils is associated with a transmissible infection akin to that caused by mammalian prions. A seven-residue peptide segment from Sup35 forms amyloid-like fibrils and closely related microcrystals, from which we have determined the atomic structure of the cross-β spine. It is a double β-sheet, with each sheet formed from parallel segments stacked in register. Side chains protruding from the two sheets form a dry, tightly self-complementing steric zipper, bonding the sheets. Within each sheet, every segment is bound to its two neighbouring segments through stacks of both backbone and side-chain hydrogen bonds. The structure illuminates the stability of amyloid fibrils, their self-seeding characteristic and their tendency to form polymorphic structures.

Beyond simple exponential correlation functions and equilibrium dynamics in x-ray photon correlation spectroscopy

We discuss the complex dynamics in condensed matter studied with x-ray photon correlation spectroscopy (XPCS) in which non-exponential correlation functions and dispersion relations deviating from the simple diffusion law are observed. Results are presented for two systems whose dynamics are characterized by compressed, faster-than-exponential correlation functions associated with hyper-diffusive motion. In the first case, the microscopic response of an aerogel following sectioning is investigated. In the second, the out-of-equilibrium dynamics in a dense colloidal gel recovering from shear is analyzed. In both cases, the dynamics, which can be associated with relaxation of internal stress, exhibits ageing. Included in the analyses are calculations of two-time correlation functions and the variance of the instantaneous degree of correlation, yielding the dynamical susceptibility.

Heterogeneous and anisotropic dynamics of a 2D gel.

We report x-ray photon correlation spectroscopy (XPCS) results on bidimensional (2D) gels formed by a Langmuir monolayer of gold nanoparticles. The system allows an experimental determination of the fourth order time correlation function, which is compared to the usual second order correlation function and to the mechanical response measured on macroscopic scale. The observed dynamics is anisotropic, heterogeneous and superdiffusive on the nanoscale. Different time scales, associated with fast heterogeneous dynamics inside 2D cages and slower motion of larger parts of the film, can be identified from the correlation functions. The XPCS results are discussed in view of other experimental results and models of three-dimensional gel dynamics.

A novel event correlation scheme for X‐ray photon correlation spectroscopy

X-ray photon correlation spectroscopy (XPCS) was employed to measure the time-dependent intermediate scattering function in an organic molecular glass former. Slow translational dynamics were probed in the glassy state and the correlation functions were calculated from two-dimensional speckle patterns recorded by a CCD detector. The image frames were analysed using a droplet algorithm together with an event correlation scheme. This method provides results analogous to standard intensity correlation algorithms but is much faster, hence addressing the recurrent problem of insufficient computing power for online analysis in XPCS. The event correlator has a wide range of potential future applications at synchrotrons and free-electron laser sources.

Low-frequency elastic behavior of a supercooled liquid

By X-ray photon correlation spectroscopy we quantify the influence of elasticity and viscosity on the capillary wave (CW) surface dynamics of a supercooled liquid. To fit the data a novel model combining Maxwell-Debye and Voigt-Kelvin viscoelasticity is derived yielding a saturation of relaxation rates at high q as well as an offset in the CW dispersion relation. Diffuse X-ray scattering confirms the result and data taken on the surface of supercooled polypropylene glycol (PPG-4000) evidence a low-frequency elastic plateau of the storage modulus. A possible connection between the observed solid-like response and the supercooled state is discussed.

Dynamics and rheology under continuous shear flow studied by x-ray photon correlation spectroscopy

X-ray photon correlation spectroscopy (XPCS) has emerged as a unique technique allowing the measurement of dynamics of materials on mesoscopic lengthscales. One of the most common problems associated with the use of bright x-ray beams is beam-induced radiation damage, and this is likely to become an even more limiting factor at future synchrotron and free-electron laser sources. Flowing the sample during data acquisition is one of the simplest methods allowing the radiation damage to be limited. In addition to distributing the dose over many different scatterers, the method also enables new functionalities such as time-resolved studies. Here, we further develop a recently proposed experimental technique that combines XPCS and continuously flowing samples. More specifically, we use a model colloidal suspension to show how the macroscopic advective response to flow and the microscopic dissipative dynamics (diffusion) can be quantified from the x-ray data. Our results show very good quantitative agreement with a Poisseuille-flow hydrodynamical model combined with Brownian mechanics. The method has many potential applications, e.g. in the study of dynamics of glasses and gels under continuous shear/flow, protein aggregation processes and the interplay between dynamics and rheology in complex fluids.

Slow dynamics in an azopolymer molecular layer studied by x-ray photon correlation spectroscopy.

We report the results of x-ray photon correlation spectroscopy (XPCS) experiments on multilayers of a photosensitive azo-polymer which can be softened by photoisomerization. Time correlation functions have been measured at different temperatures and momentum transfers (q) and under different illumination conditions (dark, UV or visible). The correlation functions are well described by the Kohlrausch-Williams-Watts (KWW) form with relaxation times that are proportional to q(-1). The characteristic relaxation times follow the same Vogel-Fulcher-Tammann law describing the bulk viscosity of this polymer. The out-of-equilibrium relaxation dynamics following a UV photoperturbation are accelerated, which is in agreement with a fluidification effect previously measured by rheology. The transient dynamics are characterized by two times correlation function, and dynamical heterogeneity is evidenced by calculating the variance χ of the degree of correlation as a function of ageing time. A clear peak in χ appears at a well defined time τ(C) which scales with q(-1) and with the ageing time, in a similar fashion as previously reported in colloidal suspensions [O. Dauchot, Phys. Rev. Lett. 95, 265701 (2005)]. From an accurate analysis of the correlation functions we could demonstrate a temperature and light dependent cross-over from compressed KWW to simple exponential behavior.

Setup for in situ surface investigations of the liquid/glass transition with (coherent) x rays

A dedicated setup comprising an efficient cryogenic device for the in situ preparation of large surface areas of prototypical organic glass formers in a wide temperature range (170–340 K) is presented. This setup provides the necessary temperature and vibrational stability for surface x-ray and neutron scattering experiments, including the extremely sensitive technique of x-ray photon correlation spectroscopy (XPCS). XPCS is an emerging method which is made possible by the high coherent photon flux produced by third-generation synchrotrons. We demonstrate that microscopic motion at the surface can be studied in a direct way in the liquid and supercooled state using XPCS. In addition, we have used a charge-coupled-device detector to record two-dimensional images of static speckle patterns forming on surfaces in the glassy state.

Evolution of dynamics and structure during formation of a cross-linked polymer gel

By in situ X-ray photon correlation spectroscopy and small-angle X-ray scattering we quantify the evolution of dynamics and structure during the formation of a cross-linked polymer gel. A fast, non-ergodic relaxation stemming from localized motions of polymer clusters indicates a stiffening network on the nano-scale as a signature of the gelation. A second, much slower relaxation that restores ergodicity is due to the dynamics of the gel network. As the gelation proceeds the reinforcement of the cross-linked network is accompanied by a slowing-down of this second relaxation that also changes line shape during the reaction. Spatial anisotropy develops in the network dynamics but without any signs of dynamical heterogeneity. This distinguishes the observed dynamics from that of typical jammed systems where dynamical heterogeneity is a hallmark.

Dynamics in dense hard-sphere colloidal suspensions

The dynamic behavior of a hard-sphere colloidal suspension was studied by x-ray photon correlation spectroscopy and small-angle x-ray scattering over a wide range of particle volume fractions. The short-time mobility of the particles was found to be smaller than that of free particles even at relatively low concentrations, showing the importance of indirect hydrodynamic interactions. Hydrodynamic functions were derived from the data, and for moderate particle volume fractions (Φ≤ 0.40) there is good agreement with earlier many-body theory calculations by Beenakker and Mazur [Physica A 120, 349 (1984)]. Important discrepancies appear at higher concentrations, above Φ≈ 0.40, where the hydrodynamic effects are overestimated by the Beenakker-Mazur theory, but predicted accurately by an accelerated Stokesian dynamics algorithm developed by Banchio and Brady [J. Chem. Phys. 118, 10323 (2003)]. For the relaxation rates, good agreement was also found between the experimental data and a scaling form predicted by the mode coupling theory. In the high concentration range, with the fluid suspensions approaching the glass transition, the long-time diffusion coefficient was compared with the short-time collective diffusion coefficient to verify a scaling relation previously proposed by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)]. We discuss our results in view of previous experimental attempts to validate this scaling law [L. Lurio et al., Phys. Rev. Lett. 84, 785 (2000)].