On the interpretation of the first, sharp maximum in the X-ray scattering pattern of non-crystalline solids and liquids

1981 ◽  
Vol 44 (5) ◽  
pp. 557-567 ◽  
Author(s):  
S. Vepřek ◽  
H. U. Beyeler
2017 ◽  
Vol 50 (6) ◽  
pp. 1677-1690 ◽  
Author(s):  
Christopher D. Liman ◽  
Thomas A. Germer ◽  
Daniel F. Sunday ◽  
Dean M. DeLongchamp ◽  
R. Joseph Kline

There is a need to characterize nanoscale molecular orientation in soft materials, and polarized scattering is a powerful means to measure this property. However, few approaches have been demonstrated that quantitatively relate orientation to scattering. Here, a modeling framework to relate the molecular orientation of nanostructures to polarized resonant soft X-ray scattering measurements is developed. A variable-angle transmission measurement called critical-dimension X-ray scattering enables the characterization of the three-dimensional shape of periodic nanostructures. When this measurement is conducted at resonant soft X-ray energies with different polarizations to measure soft material nanostructures, the scattering contains convolved information about the nanostructure shape and the preferred molecular orientation as a function of position, which is extracted by fitting using inverse iterative algorithms. A computationally efficient Born approximation simulation of the scattering has been developed, with a full tensor treatment of the electric field that takes into account biaxial molecular orientation, and this approach is validated by comparing it with a rigorous coupled wave simulation. The ability of various sample models to generate unique best fit solutions is then analyzed by generating simulated scattering pattern sets and fitting them with an inverse iterative algorithm. The interaction of the measurement geometry and the change in orientation across a periodic repeat unit leads to distinct asymmetry in the scattering pattern which must be considered for an accurate fit of the scattering.


2015 ◽  
Vol 635 (10) ◽  
pp. 102008 ◽  
Author(s):  
Malik Muhammad Abdullah ◽  
Zoltan Jurek ◽  
Sang-Kil Son ◽  
Robin Santra

Author(s):  
Eva-Maria Mandelkow ◽  
Eckhard Mandelkow ◽  
Joan Bordas

When a solution of microtubule protein is changed from non-polymerising to polymerising conditions (e.g. by temperature jump or mixing with GTP) there is a series of structural transitions preceding microtubule growth. These have been detected by time-resolved X-ray scattering using synchrotron radiation, and they may be classified into pre-nucleation and nucleation events. X-ray patterns are good indicators for the average behavior of the particles in solution, but they are difficult to interpret unless additional information on their structure is available. We therefore studied the assembly process by electron microscopy under conditions approaching those of the X-ray experiment. There are two difficulties in the EM approach: One is that the particles important for assembly are usually small and not very regular and therefore tend to be overlooked. Secondly EM specimens require low concentrations which favor disassembly of the particles one wants to observe since there is a dynamic equilibrium between polymers and subunits.


Author(s):  
Eva-Maria Mandelkow ◽  
Ron Milligan

Microtubules form part of the cytoskeleton of eukaryotic cells. They are hollow libers of about 25 nm diameter made up of 13 protofilaments, each of which consists of a chain of heterodimers of α-and β-tubulin. Microtubules can be assembled in vitro at 37°C in the presence of GTP which is hydrolyzed during the reaction, and they are disassembled at 4°C. In contrast to most other polymers microtubules show the behavior of “dynamic instability”, i.e. they can switch between phases of growth and phases of shrinkage, even at an overall steady state [1]. In certain conditions an entire solution can be synchronized, leading to autonomous oscillations in the degree of assembly which can be observed by X-ray scattering (Fig. 1), light scattering, or electron microscopy [2-5]. In addition such solutions are capable of generating spontaneous spatial patterns [6].In an earlier study we have analyzed the structure of microtubules and their cold-induced disassembly by cryo-EM [7]. One result was that disassembly takes place by loss of protofilament fragments (tubulin oligomers) which fray apart at the microtubule ends. We also looked at microtubule oscillations by time-resolved X-ray scattering and proposed a reaction scheme [4] which involves a cyclic interconversion of tubulin, microtubules, and oligomers (Fig. 2). The present study was undertaken to answer two questions: (a) What is the nature of the oscillations as seen by time-resolved cryo-EM? (b) Do microtubules disassemble by fraying protofilament fragments during oscillations at 37°C?


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