Structure of Single Particles from Randomly Oriented Ensembles Using an X-Ray Free Electron Laser BJSTR

Theory

Before proceeding further we would like to discuss angular pair correlations that play a central part of our theory. Suppose A. are the scattered amplitudes from protein j of a set that is illuminated. The total intensity expected to be measured in a coherent instrument like an XFEL is thus

Reconstruction of a Single Particle from Multiple Particle Diffraction Patterns

The importance of scattering by multiple particles is because there is still a considerable gap between the focal spot size aimed for by the XFEL instrument manufacturers and the sizes of typical proteins. Suppose one uses a concentration of 0.6 moles/ m3 as in SAXS. The design specification of the world’s first X-ray free electron laser (XFEL), the Linac Coherent Light Source (LCLS), is for a focal spot size is about 0.1 micron square, and since the minimum size of a liquid droplet claimed is about 0.3 microns [17], the volume illuminated will be about 3x10–21m3, or else about 1.8x10–21 moles. But Avogadro’s number is about 6x10 molecules/mole. Thus the minimum number of molecules illuminated will be about would be about 400.

Experimental Determination of the Time-Resolved Structure of Proteins

Armed with these facts about angular correlations, and their remarkable ability to study structure from disordered ensembles, we return now to the main problem addressed in this paper, namely the recovery of time-resolved information about proteins from XFEL diffraction patterns. Paradoxically, it is easier to extract useful information from more complex particles in a time-resolved experiment of the form of Figure 3, although the advantages suggested above of not needing to focus on a single particle remain. In this arrangement the particles are incident on an XFEL in a liquid jet. A short time before the incidence of the X-ray beam on the liquid jet it is illuminated by light from an optical laser which puts suitable molecules into a light-induced excited state. A schematic diagram of the apparatus is shown in Figure 4. Although this experiment describes excitation by light, other similar experiments may be considered in which one studies the set of molecules immediately after they has been mixed with a substrate, for example. As we have already seen.

Conclusion

The significance of this work is that if these simulations are realized in practice, we now have, for the first time, a method of finding the structures of particles such as molecules from diffraction patterns of copies of many of the molecules even if they are not of identical orientations as in a crystal. In the last application we have shown that even time-resolved structure may be determined of molecules that are in random orientations, thus opening to experimentally observing realistic chemical reactions. It should be pointed out that many of the effects we have ignored, such as scattering by solvent, are fairly unimportant for the time-resolved problem since here we look at differences in the correlations between the photo excited and ground state molecules, where such factors tend to subtract out. Indeed in the time-resolved problem we study only features of the diffraction patterns that are different due to the photoexcitation. Of course solvent is perhaps 100 times as prevalent as solute and could give rise to Poisson noise that does not cancel between the photo excited and ground state structures so some care has to be exercised.

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BJSTR

BJSTR

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Biomedical Journal of Scientific & Technical Research (BJSTR) is a multidisciplinary, scholarly Open Access publisher focused on Genetic, Biomedical