SparseAlign: A Grid-Free Algorithm for Automatic Marker Localization and Deformation Estimation in Cryo-Electron Tomography

Abstract

Tilt-series alignment is crucial to obtaining highresolution reconstructions in cryo-electron tomography. Beaminduced local deformation of the sample is hard to estimate from the low-contrast sample alone, and often requires fiducial gold bead markers. The state-of-the-art approach for deformation estimation uses (semi-)manually labelled marker locations in projection data to fit the parameters of a polynomial deformation model. Manually-labelled marker locations are difficult to obtain when data are noisy or markers overlap in projection data. We propose an alternative mathematical approach for simultaneous marker localization and deformation estimation by extending a grid-free algorithm first proposed in the context of superresolution single-molecule localization microscopy. Our approach does not require labelled marker locations; instead, we use an image-based loss where we compare the forward projection of markers with the observed data. We equip this marker localization scheme with an additional deformation estimation component and solve for a reduced number of deformation parameters. Using extensive numerical studies on marker-only samples, we show that our approach automatically finds markers and reliably estimates sample deformation without labelled marker data. We further demonstrate the applicability of our approach for a broad range of model mismatch scenarios, including experimental electron tomography data of gold markers on ice.

Computational methods for in situ structural studies with cryogenic electron tomography

“…In cryo-electron tomography, the beam-induced motion is usually attributed to multiple factors, including electron beam interaction with the specimen, stage vibration, sample deformation, intense ionization in materials, and measurement error ( Naydenova et al., 2020 ; Thorne, 2020 ). The local sample motion induced by the electron beam can be observed as a “doming” motion ( Ganguly et al., 2022 ), where the sample suffers an upward deformation perpendicular to the sample plane. The intermolecular correlation shifts and the measurement error of the projections should be considered.…”

“…The dose-fraction frames are aligned and corrected in Fourier space. Instead of manually or semi-manually labeling marker locations, SparseAlign ( Ganguly et al., 2022 ) is a mathematical method for marker localization and deformation estimation simultaneously. The SparseAlign solves a few deformation parameters based on an image-based loss between the forward projection of markers and the observed projections.…”