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A modulated icosahedral shell with an inclusion is a concise description ofmany viruses, including recently-discovered large double-stranded DNA ones.Many X-ray scattering patterns of such viruses show major polygonal fringes,which can be reproduced in image reconstruction with a homogeneous icosahedralshell. A key question regarding a low-resolution reconstruction is how tointroduce further changes to the 3D profile in an efficient way with only a fewparameters. Here, we derive and compile different analytical models of such anobject with consideration of practical optical setups and typical structures ofsuch viruses. The benefits of such models include 1) inherent filtering andsuppressing different numerical errors of a discrete grid, 2) providing aconcise and meaningful set of descriptors for feature extraction inhigh-throughput classification/sorting and higher-resolution cumulativereconstructions, 3) disentangling (physical) resolution from (numerical)discretization step and having a vector graphics format for visualization orfurther analysis at arbitrary scales, 4) eliminating the phase-retrieval stepand enforcing transparent, relevant, and controlled type/level of a-prioriinformation in a real-space formulation, and 5) evaluating the reflections andsurface resonances of an icosahedral object, and hence corrections for thecommon scattering model.

Analytical models of icosahedral shells for 3D optical imaging of viruses