Anisotropic twicing for single particle reconstruction using autocorrelation analysis
This addresses a bottleneck in structural biology for researchers using X-ray free electron lasers and cryo-EM, though it is an incremental improvement over existing molecular replacement techniques.
The paper tackles the missing orthogonal matrices problem in single particle reconstruction by generalizing the twicing method to matrix estimation, enabling 3D homology modeling in cryo-EM directly from experimental data without iterative refinement or class averaging.
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.