Spherical Harmonics based Subtomogram Alignment
In cryoelectron tomography alignment and averaging of subtomograms, each depicting the same macromolecule, improves the resolution compared to the individual subtomogram. Major challenges of subtomogram alignment are noise enhancement due to overfitting, the bias of an initial reference in the iterative alignment process, and the computational cost of processing increasingly large amounts of data. Here, we propose an efficient and accurate alignment algorithm via a generalized convolution theorem, which allows computation of a constrained correlation function using spherical harmonics. This formulation increases computational speed of rotational matching dramatically compared to rotation search in Cartesian space without sacrificing accuracy in contrast to other spherical harmonic based approaches. Using this sampling method, a reference-free alignment procedure is proposed to tackle reference bias and overfitting, which also includes contrast transfer function correction by Wiener filtering. Application of the method to simulated data allowed us to obtain resolutions near the ground truth. For two experimental datasets, ribosomes from yeast lysate and purified 20S proteasomes, we achieved reconstructions of approximately 20A and 16A, respectively. The software is ready-to-use and made public to the community.
The published software consists of a low-level core, which is programmed in C++, and a python libraries. The low-level library is used for tranformation of volumes into spherical harmonics and generalized convolution. It is open source and intended for developers who want to tinker with volumetric alignment or other applications where these functions are beneficial. The library can be obtained here: Download on Bitbucket.
The python libary takes care of the actual volume alignment done by a quasi-expectation maximization algorithm. It is part of the PyTom package, which can be downloaded here: Download on Sourceforge.
Usage of SPH alignment is documented in the PyTom documentation:
Please download the package for the most recent version of the documentation if required.