Anisotropic twicing for single particle reconstruction using autocorrelation analysis

TL;DR

This paper introduces Anisotropic Twicing, a novel estimator for matrix reconstruction in single particle analysis, enabling direct 3D modeling from experimental data without iterative refinement.

Contribution

It generalizes the twicing method to matrices in autocorrelation analysis, improving phase estimation in single particle reconstruction.

Findings

Anisotropic Twicing outperforms least squares and traditional twicing in simulations.

The method enables direct 3D cryo-EM modeling from experimental data.

First demonstration of direct 3D homology modeling without iterative refinement.

Abstract

The missing phase problem in X-ray crystallography is commonly solved using the technique of molecular replacement, which borrows phases from a previously solved homologous structure, and appends them to the measured Fourier magnitudes of the diffraction patterns of the unknown structure. More recently, molecular replacement has been proposed for solving the missing orthogonal matrices problem arising in Kam's autocorrelation analysis for single particle reconstruction using X-ray free electron lasers and cryo-EM. In classical molecular replacement, it is common to estimate the magnitudes of the unknown structure as twice the measured magnitudes minus the magnitudes of the homologous structure, a procedure known as `twicing'. Mathematically, this is equivalent to finding an unbiased estimator for a complex-valued scalar. We generalize this scheme for the case of estimating real or complex valued matrices arising in single particle autocorrelation analysis. We name this approach "Anisotropic Twicing" because unlike the scalar case, the unbiased estimator is not obtained by a simple magnitude isotropic correction. We compare the performance of the least squares, twicing and anisotropic twicing estimators on synthetic and experimental datasets. We demonstrate 3D homology modeling in cryo-EM directly from experimental data without iterative refinement or class averaging, for the first time.