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MPSA is a software package for deriving the three-dimensional (3D) structure of a biological complex (e.g. virus) from a collection of 2D projection images taken by electron cryo-microscopy (cryoEM). The approach for deriving a 3D structure is similar to that used by medical CT scans to synthesize a 3D volume (tomogram) of human organs for diagnosis. However, cryoEM has to take one extra step before performing 3D reconstruction for the following reasons. The raw images of CT-scan come from the same object, and their orientations are pre-determined by the instrument; on the contrary, the images of cryoEM are taken from multiple identical objects, randomly distributed and orientated in a thin layer of vitreous ice. It is vital to determine the relative orientations and the center positions of these cryoEM images before synthesizing 3D volume. The challenge of this nonlinear inverse problem of determining orientations and centers is further compounded by the weak signal-to-noise ratio of cryoEM images, increasing the alignment difficulty. To address this challenge we developed a state-of-the-art global optimization algorithm, multi-path simulated annealing (MPSA is named after this algorithm), to quickly and accurately align 2D images in Fourier space. Other than the 2D alignment algorithm, we also enhanced the 3D reconstruction algorithm by reducing interpolation error. To speed up the process of aligning tens of thousands of images, MPSA does parallel computing through Message Passing Interface (MPI) implemented in its C++ and python codes.

Utilizing the multi-path simulated annealing optimization algorithm, MPSA is able to simultaneously determine the center and orientation of a particle image, thus significantly improving the speed of structure convergence. Alignment parameters are determined based on individual particle images using a (cross) common-line method in Fourier space and no class averages are needed during the alignment. Once alignment parameters have been determined, the 3D electron density map is generated in Fourier space from the set of individual 2D single particle images. This process of 3D reconstruction is performed by inserting the 2D Fourier transform of each particle image into a 3D Fourier volume according to the central section theorem. After all of the single-particle images have been inserted into this volume, a 3D inverse Fourier transform is applied to generate a real-space 3D density volume/map. There are some advantages to processing images in Fourier space: (1) Easy to choose resolution range for the refinement, without manually filtering the data to the preferred resolution range, (2) Significantly reduced number of references (10 or less in Fourier space vs hundreds in real space), thus further reducing computational time, (3) The orientation accuracy is not limited by the angular step size of the references (common line approach), and (4) A more straightforward way of handling CTF correction algorithmically. However, it should be noted that interpolation error of non-integer Fourier transforms at high resolutions may be an issue. Accordingly, MPSA provides an oversample option that can minimize these errors for both 2D alignment and 3D reconstruction.

MPSA was initially designed to process cryoEM images of icosahedral virus particles. In order to explore structures of various virus infectious apparatus (e.g. tail or portal), MPSA provides an option to perform asymmetric reconstruction (without imposing icosahedral symmetry). Virus asymmetric reconstruction procedure takes the advantage of known icosahedral symmetrized orientation, and then determines which one of the 60 equivalent orientations is the true asymmetric orientation. Furthermore, MPSA can directly perform asymmetric reconstructions without considering the known symmetrized orientations to address macromolecular complexes without (or with low-) symmetry.

In addition to aligning conventional 2D images and synthesizing 3D volumes, MPSA provides additional utilities to manipulate 3D electron cryo-tomographic (cryoET) data of a polymorphic biological object (e.g. cell) and unconventional 2D images generated by the emerging imaging technologies (i.e. Zernike phase plate and direct detection device (DDD)).

MPSA can adaptively manage particle images. For 2D alignment, it allows the box and pixel sizes to be different from those of the reference images. It also allows the particle images themselves to have different box and pixel sizes. For 3D reconstruction, MPSA can take particle images with various sizes, and moreover, the output 3D map can have any user-specified volume and pixel sizes.

MPSA is implemented in C++ and Python and stems from the original framework of EMAN1. The core code is written in C++ and provides function libraries for processing 2D cryoEM images, reconstructing 3D density map/model, and handling data I/O. The majority of MPSA's executable programs are written in Python, however there are a few executable programs written in C/C++ and linux shell scripts. Boost Python is used to bridge the C++ and Python code. Both 2D alignment ( and 3D reconstruction (mp-3dbuilder) are parallelized using Message Passing Interface (MPI). As a result, both mpi libraries and python-mpi (provided in dependency libraries) are required. Quanternion is used for internal rotation of MPSA to avoid the non-uniformly sampling 3D space of Euler angles.

License: free software supported by NIH. No license limitation, but registration is required.

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