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

TL;DR

This paper develops analytical models of icosahedral viral shells to improve 3D optical imaging, enabling efficient feature extraction, resolution control, and correction of scattering effects in virus reconstruction.

Contribution

It introduces new analytical models considering optical setups and virus structures, enhancing 3D imaging and analysis of icosahedral shells with fewer parameters and better physical interpretation.

Findings

Models improve feature extraction for high-throughput classification

Eliminate phase-retrieval step in 3D reconstruction

Enable correction of scattering effects and surface resonances

Abstract

A modulated icosahedral shell with an inclusion is a concise description of many 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 icosahedral shell. A key question regarding a low-resolution reconstruction is how to introduce further changes to the 3D profile in an efficient way with only a few parameters. Here, we derive and compile different analytical models of such an object with consideration of practical optical setups and typical structures of such viruses. The benefits of such models include 1) inherent filtering and suppressing different numerical errors of a discrete grid, 2) providing a concise and meaningful set of descriptors for feature extraction in high-throughput classification/sorting and higher-resolution cumulative reconstructions, 3) disentangling (physical) resolution from (numerical) discretization step and having a vector graphics format for visualization or further analysis at arbitrary scales, 4) eliminating the phase-retrieval step and enforcing transparent, relevant, and controlled type/level of a-priori information in a real-space formulation, and 5) evaluating the reflections and surface resonances of an icosahedral object, and hence corrections for the common scattering model.