Signal-to-noise ratio issues in protein crystallography
The "bottom line" criteria of data quality in PX - Rsym, Rmerge and I/s<I> - are well understood functions of intensity values summed from diffraction camera image frame sets. However, the relationship between the incident beam at the crystal, the crystal size and resulting diffraction pattern characteristics are often [intentionally] neglected in performance comparisons between crystallography systems. Here we seek to present the major experimental factors that must be considered in any meaningful comparison of signal/noise ratio between different diffraction schemes.
Beam size and crystal size
It is often assumed that the optimum configuration for PX is a beam larger than the longest dimension of the crystal, and that beams significantly larger than the crystal produce no disadvantage. The reality is that our crystals are invariably frozen within a liquor meniscus supported within a larger cryoloop, and situated inside a dense gas coldstream. This results in incoherent scatter of similar magnitude per unit cross-sectional area as is produced by the specimen crystal itself. For this reason, the ideal geometry (neglecting camera issues - see below) for optimum diffraction signal to scatter noise is a beam equal to the smallest dimension of the crystal. On that basis, consider the following (simplified) comparison:
Signal/scatter cross-sections for 0.3mm-beam vs. 0.1mm beam
... suggesting that if the crystal is smaller than the lesser beam size, the relative signal/noise ratio is simply given by the ratio of the beam cross-sections being compared. However in practice there are several factors which further increase the relative SNR:
Relative Beam Intensity: In principle, the incoherent scatter varies directly with incident flux for a given configuration, so signal/scatter should be constant as flux varies. However where the two cases compared above involve beams of different intensity, the relative SNR is complicated by detector response factors. For example, doubling the intensity of a beam while halving the exposure time results in better data when using image-plate cameras due to reduced image-decay during exposure and lower background radiation accumulation, or reduced dark-current accumulation with CCD cameras. Thus increasing the intensity of the smaller-diameter beam in the above comparison will result in proportionately better relative SNR than the figure based on geometry alone, but the degree of improvement is instrumentally determined.
Diffraction spot size: The process of diffraction data integration requires the summing of pixel values over a fixed detector area corresponding to the size of a diffraction spot at the high-resolution edges of the pattern, and a value of background adjacent to each spot. The calculation of spot intensity involves subtracting an equal number of pixels of background level from the sum for the diffraction spot. Thus a better spot signal/noise ratio is achieved by spots occupying fewer pixels for a given total recorded X-ray flux, and is is one of the major advantages of the small-diameter, low divergence beams avalable at good synchrotron PX beamlines. For this reason a small-diameter beam of greater intensity - even with less total flux - than a large-diameter beam will still produce better signal/noise ratios in diffraction data, even where the crystal is larger than either beam.
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