Fluctuation X-ray scattering: Mathematical solution

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  • Published: Aug 15, 2015
  • Author: David Bradley
  • Channels: X-ray Spectrometry
thumbnail image: Fluctuation X-ray scattering: Mathematical solution

Emerging X-ray technique

Illustration of a fluctuation scattering experiment, which collects X-ray diffraction snapshots of multiple identical proteins in solution. An ultrabright X-ray laser provides fast snapshots which avoids motion blur, ultimately resulting in a detailed view of biological nanostructures. (Image Credit: Peter Zwart, Berkeley Lab)

New mathematics could allow the emerging technique of fluctuation X-ray scattering (FXS) to provide orders of magnitude more detail on protein and virus structures, according to US scientists.

Understanding the structural details of macromolecules, proteins, and even viruses would hopefully lead to new developments in materials science and medicine, as new insights have in the past. To get in close, we have various techniques, including the well-known diffraction and spectroscopic methods. For solutions of such substances, which might offer a better "real world" picture than a crystal structure, we need increasingly powerful beams and solution scattering techniques as well as powerful software to interpret the data we retrieve. The emerging technique of fluctuation X-ray scattering (FXS) offers the promise of orders of magnitude more detail than conventional solution scattering but until now, we did not have the mathematical prowess to process the data efficiently and effectively.

Now, a team from Lawrence Berkeley National Laboratory (Berkeley Lab), writing in the Proceedings of the National Academy of Sciences (USA) at the beginning of August have developed a new mathematical theory and an algorithm to implement it in processing FXS data. Applied mathematicians Jeffrey Donatelli and James Sethian working with physical bioscientist Peter Zwart describe "multi-tiered iterative phasing" (M-TIP), which they suggest can be used "to solve the reconstruction problem from FXS data." Their code was able to quickly determine general structure from simulated data within minutes on a desktop computer rather than requiring the supercomputers often essential for big data processing of X-ray output. This approach could present a step change in biophysics allowing relatively easy access to a powerful tool in the life sciences and beyond.

Freeze the action

"These are exciting times," says Zwart. "Although fluctuation scattering was first proposed 38 years ago, its routine practical realization has only now become feasible with the advent of modern X-ray light sources. This novel reconstruction method plays a central role in mapping out the strengths of fluctuation scattering as a routine biophysical technique."

Faster and brighter light sources, of course allow researchers to "freeze the action" even in solution in a way that is not possible in small- and wide-angle x-ray scattering (SAXS/WAXS) experiments, wherein molecules have rotated during the long exposure time of the snapshot with a concomitant loss of information, just as a moving subject will be blurred if one uses too slow a camera shutter speed in photography. New US DOE (Department of Energy) free electron laser (FEL) facilities, such as the Linac Coherent Light Source (LCLS) at Stanford, are bringing these new powerful beams online. By using FXS, additional angular correlation information can be extracted providing more details.

In recovery

Standard diffraction techniques only require the user to recover the missing complex phases, but FXS studies need the three-dimensional intensity information to be recovered as well. The team's new "M-TIP" algorithm by turns projects a model to agree with the FXS data along with any prior known constraints about the solution, such as density upper and lower bounds, size, and/or symmetry, and can simultaneously determine the intensities, complex phases, and molecular structure, the team reports.

"In order to develop a robust and efficient FXS reconstruction algorithm, we had to solve a number of non-trivial mathematical problems," explains Donatelli. "Deriving the relation between structure and FXS data involves a substantial amount of harmonic analysis and linear algebra and we also needed to develop several new computational tools, such as a fast and reliable polar Fourier transform."

Of course, FXS itself is still a relatively novel technique and at the time of the study Donatelli, Sethian and Zwart had no public domain data with which to test their algorithm. As such, they have tested the method on simulated FXS data for various structure, including a model of a pentameric ligand-gated ion channel (pLGIC). They report that their algorithm was able to quickly produce an accurate, high-resolution reconstructions of these shapes from the corresponding FXS data.

"Ultimately, the goal is to provide the scientific community with a powerful new tool to determine the structure and dynamics of nano-sized particles in a routine, high- throughput fashion," explains Zwart. "The full deployment of FXS as a new tool in the arsenal of the structural biologist will take some time, but this is an important breakthrough."

"The next step in this research is to test and tune our algorithm on experimental data," Donatelli tols SpectroscopyNOW. "We also plan to incorporate the use of additional sources of experimental data and leverage statistical information obtained from homologous structures. Ultimately, we want to use this technique to help solve complex problems in the health and energy sciences."

Related Links

Proc Natl Acad Sci 2015, online: "Iterative phasing for fluctuation X-ray scattering"

Article by David Bradley

The views represented in this article are solely those of the author and do not necessarily represent those of John Wiley and Sons, Ltd.

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