The achievable resolution for X-ray imaging of cells and other soft biological material
Authors: Nave Colin 
Published: March 2020

X-ray imaging of soft materials is often difficult because of the low contrast of the components. This particularly applies to frozen hydrated biological cells where the feature of interest can have a similar density to the surroundings. As a consequence, a high dose is often required to achieve the desired resolution. However, the maximum dose that a specimen can tolerate is limited by radiation damage. Results from 3D coherent diffraction imaging (CDI) of frozen hydrated specimens have given resolutions of ∼80 nm compared with the expected resolution of 10 nm predicted from theoretical considerations for identifying a protein embedded in water. Possible explanations for this include the inapplicability of the dose-fractionation theorem, the difficulty of phase determination, an overall object-size dependence on the required fluence and dose, a low contrast within the biological cell, insufficient exposure, and a variety of practical difficulties such as scattering from surrounding material. A recent article [Villaneuva-Perez et al. (2018), Optica, 5, 450–457] concluded that imaging by Compton scattering gave a large dose advantage compared with CDI because of the object-size dependence for CDI. An object-size dependence would severely limit the applicability of CDI and perhaps related coherence-based methods for structural studies. This article specifically includes the overall object size in the analysis of the fluence and dose requirements for coherent imaging in order to investigate whether there is a dependence on object size. The applicability of the dose-fractionation theorem is also discussed. The analysis is extended to absorption-based imaging and imaging by incoherent scattering (Compton) and fluorescence. This article includes analysis of the dose required for imaging specific low-contrast cellular organelles as well as for protein against water. This article concludes that for both absorption-based and coherent diffraction imaging, the dose-fractionation theorem applies and the required dose is independent of the overall size of the object. For incoherent-imaging methods such as Compton scattering, the required dose depends on the X-ray path length through the specimen. For all three types of imaging, the dependence of fluence and dose on a resolution d goes as 1/d
4 when imaging uniform-density voxels. The independence of CDI on object size means that there is no advantage for Compton scattering over coherent-based imaging methods. The most optimistic estimate of achievable resolution is 3 nm for imaging protein molecules in water/ice using lensless imaging methods in the water window. However, the attainable resolution depends on a variety of assumptions including the model for radiation damage as a function of resolution, the efficiency of any phase-retrieval process, the actual contrast of the feature of interest within the cell and the definition of resolution itself. There is insufficient observational information available regarding the most appropriate model for radiation damage in frozen hydrated biological material. It is advocated that, in order to compare theory with experiment, standard methods of reporting results covering parameters such as the feature examined (e.g. which cellular organelle), resolution, contrast, depth of the material (for 2D), estimate of noise and dose should be adopted.