![]() To obtain consensus merged intensities, equivalent observations are then merged by weighted averaging assuming normally distributed errors. The observed intensities are then corrected by each scale parameter to yield scaled intensities. Traditionally, these artifacts are accounted for by estimating a series of scale parameters that are intended to explicitly model the physics of the sources of error 6, 11, 12, 13 (see the Supplementary Note for a description of crystallographic data reduction). For example, beam properties like intensity fluctuations 7 and polarization 8, crystal imperfections like mosaicity 9 and radiation damage 10, and absorption and scattering of X-rays by material around the crystal all modulate the measured diffraction intensities in a manner, which varies throughout the experiment. These scales depend non-linearly on the context of each observed reflection as illustrated in Fig. Even under well-controlled experimental conditions, redundant reflections are expressed on the X-ray detector with different scales (Fig. ![]() The full realization of the promise of these methods hinges on the ability to separate signals in X-ray diffraction that result from subtle structural changes from a multitude of systematic errors that can be specific to a crystal, X-ray source, detector, or sample environment 6. Estimates of the amplitudes and phases of these structure factors allow one to reconstruct the 3D electron density in the crystal by Fourier synthesis.īased on these principles, advances in X-ray diffraction now permit direct visualization of macromolecules in action 1 using short X-ray pulses generated at synchrotrons 2, 3 and X-ray Free-Electron Lasers (XFELs) 4, 5. Each structure factor reports on the electron density at a specific spatial frequency and direction, indexed by triplets of integers termed Miller indices. The resulting images contain discrete spots, known as reflections, with intensities proportional to the squared amplitudes of the Fourier components (structure factors) of the crystal’s electron density. In an X-ray diffraction experiment, the electrons of a molecular crystal scatter X-rays, yielding patterns of constructive interference recorded on an X-ray detector. X-ray crystallography has revolutionized our understanding of the molecular basis of life by providing atomic-resolution experimental access to the structure and dynamics of macromolecules and their assemblies. We find that this approach is applicable to the analysis of many types of diffraction experiments, while accurately and sensitively detecting subtle dynamics and anomalous scattering. We successfully apply this method to monochromatic and polychromatic single-crystal diffraction data, as well as serial femtosecond crystallography data. Here, we present a modern Bayesian solution to this problem, which uses deep learning and variational inference to simultaneously rescale and merge reflection observations. Systematic effects, however, lead to the measurement of equivalent reflections on different scales, corrupting observation of changes in electron density. To compute the electron density of a molecule, the intensity of each reflection must be estimated, and redundant observations reduced to consensus intensities. Diffraction data contain patterns of bright spots known as reflections. Key to this revolution is detection of often subtle conformational changes from diffraction data. Novel X-ray methods are transforming the study of the functional dynamics of biomolecules.
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