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The lateral mobility of lipids in phospholipid membranes has attracted numerous experimental and theoretical studies, inspired by the model of Singer and Nicholson (1972. Science, 175:720-731) and the theoretical description by Saffman and Delbrück (1975. Proc. Natl. Acad. Sci. USA. 72:3111-3113). Fluorescence recovery after photobleaching (FRAP) is used as the standard experimental technique for the study of lateral mobility, yielding an ensemble-averaged diffusion constant. Single-particle tracking (SPT) and the recently developed single-molecule imaging techniques now give access to data on individual displacements of molecules, which can be used for characterization of the mobility in a membrane. Here we present a new type of analysis for tracking data by making use of the probability distribution of square displacements. The potential of this new type of analysis is shown for single-molecule imaging, which was employed to follow the motion of individual fluorescence-labeled lipids in two systems: a fluid-supported phospholipid membrane and a solid polymerstabilized phospholipid monolayer. In the fluid membrane, a high-mobility component characterized by a diffusion constant of 4.4 microns2/s and a low-mobility component characterized by a diffusion constant of 0.07 micron2/s were identified. It is proposed that the latter characterizes the so-called immobile fraction often found in FRAP experiments. In the polymer-stabilized system, diffusion restricted to corrals of 140 nm was directly visualized. Both examples show the potentials of such detailed analysis in combination with single-molecule techniques: with minimal interference with the native structure, inhomogeneities of membrane mobility can be resolved with a spatial resolution of 100 nm, well below the diffraction limit.

In recent years observations at the level of individual atoms and molecules became possible by micros

The concepts and technical realisation of the high-resolution soft X-ray beamline ADRESS operating in the energy range from 300 to 1600 eV and intended for resonant inelastic X-ray scattering (RIXS) and angle-resolved photoelectron spectroscopy (ARPES) are described. The photon source is an undulator of novel fixed-gap design where longitudinal movement of permanent magnetic arrays controls not only the light polarization (including circular and 0-180 rotatable linear polarizations) but also the energy without changing the gap. The beamline optics is based on the well established scheme of planegrating monochromator operating in collimated light. The ultimate resolving power E/ÁE is above 33000 at 1 keV photon energy. The choice of blazed versus lamellar gratings and optimization of their profile parameters is described. Owing to glancing angles on the mirrors as well as optimized groove densities and profiles of the gratings, the beamline is capable of delivering high photon flux up to 1 Â 10 13 photons s À1 (0.01% BW) À1 at 1 keV. Ellipsoidal refocusing optics used for the RIXS endstation demagnifies the vertical spot size down to 4 mm, which allows slitless operation and thus maximal transmission of the highresolution RIXS spectrometer delivering E/ÁE > 11000 at 1 keV photon energy. Apart from the beamline optics, an overview of the control system is given, the diagnostics and software tools are described, and strategies used for the optical alignment are discussed. An introduction to the concepts and instrumental realisation of the ARPES and RIXS endstations is given.

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