Unit quaternion description of spatial rotations in 3D electron cryo-microscopy

Electron cryo-microscopy (cryoEM) involves the estimation of spatial rotations, or saying orientations, of projection images or three-dimensional (3D) volumes. Euler angle system is widely used to describe spatial rotations in most cryoEM algorithms and software. In this review, we introduce unit quaternion as an alternate to Euler angles for describing spatial rotations, customize and develop corresponding tools for increasing demands of statistical analysis of spatial rotations in cryoEM. Some basic properties and definitions of quaternion are first recalled. Thereafter, distance and geodesic between rotations are introduced to aid comparisons and interpolations between rotations, which are prerequisites of statistics of rotations in 3D cryoEM. Furthermore, statistics of rotations are reviewed. Techniques potentially useful in cryoEM, such as calculations of the average rotation, generation of quasi-regular grids, sampling, inference with uniform distribution and angular central Gaussian (ACG) distribution, and estimation of rotation precision, are reviewed and developed. Finally, molecular symmetry presented in unit quaternion form is discussed. Unit quaternion system is shown as a convenient and comprehensive mathematical tool for cryoEM.

RNA 3D structure prediction by using a coarse-grained model and experimental data

RNAs form complex secondary and three-dimensional structures, and their biological functions highly rely on their structures and dynamics. Here we developed a general coarse-grained framework for RNA 3D structure prediction. A new, hybrid coarse-grained model that explicitly describes the electrostatics and hydrogen-bond interactions has been constructed based on experimental structural statistics. With the simulated annealing simulation protocol, several RNAs of less than 30-nt were folded to within 4.0 Å of the native structures. In addition, with limited restraints on Watson-Crick basepairing based on the data from NMR spectroscopy and small-angle X-ray scattering (SAXS) information, the current model was able to characterize the complex tertiary structures of large size RNAs, such as 5S ribosome and U2/U6 snRNA. We also demonstrated that the pseudoknot structure was better captured when the coordinating Mg(2+) cations and limited basepairing restraints were included. The accuracy of our model has been compared favorably with other RNA structure prediction methods presented in the previous study of RNA-Puzzles. Therefore the coarse-grained model presented here offers a unique approach for accurate prediction and modeling of RNA structures.

Coarse-grained model for simulation of RNA three-dimensional structures

The accurate prediction of an RNA's three-dimensional structure from its "primary structure" will have a tremendous influence on the experimental design and its interpretation and ultimately our understanding of the many functions of RNA. This paper presents a general coarse-grained (CG) potential for modeling RNA 3-D structures. Each nucleotide is represented by five pseudo atoms, two for the backbone (one for the phosphate and another for the sugar) and three for the base to represent base-stacking interactions. The CG potential has been parametrized from statistical analysis of 688 RNA experimental structures. Molecular dynamic simulations of 15 RNA molecules with the length of 12-27 nucleotides have been performed using the CG potential, with performance comparable to that from all-atom simulations. For ~75% of systems tested, simulated annealing led to native-like structures at least once out of multiple repeated runs. Furthermore, with weak distance restraints based on the knowledge of three to five canonical Watson-Crick pairs, all 15 RNAs tested are successfully folded to within 6.5 Å of native structures using the CG potential and simulated annealing. The results reveal that with a limited secondary structure model the current CG potential can reliably predict the 3-D structures for small RNA molecules. We also explored an all-atom force field to construct atomic structures from the CG simulations.

Systematic site-directed mutagenesis of human protein SRP54: interactions with signal recognition particle RNA and modes of signal peptide recognition

The amino acid residues of human protein SRP54 which are required for binding to SRP RNA were identified by generating 40 nonoverlapping tri-alanine alterations within its methionine-rich M-domain (SRP54M). The mutant polypeptides were expressed in Escherichia coli, and their ability to bind to human and Methanococcus jannaschii SRP RNA were determined in vitro. Residues at positions 379-387, 394-396, 400-405, and 409-411 of human SRP54 were within the predicted RNA binding site, and their alteration abolished the binding activities of the mutant polypeptides as expected. Changes at positions 418-423 had intermediate effects. Polypeptides containing mutations of 328-TLR-330 were inactive although these residues were far away from the presumed RNA binding site in the crystal structure of the free protein. Using the structures of the E. coli Ffh/4.5S core and of the human SRP54m dimer as templates, a molecular model of the complex between human SRP RNA helix 8 and a single SRP54M molecule was constructed in which Leucine 329 was positioned in closer proximity to the RNA binding domain. This representation was supported by studies of the SRP54m monomer/dimer ratio using gel filtration. The results were consistent with a change in the shape of the signal peptide binding groove upon binding of SRP54 to SRP RNA. We propose that the SRP RNA and a small region centered at a bulky nonpolar amino acid residue at position 329 of protein SRP54 play a critical role in the SRP-dependent binding and release of signal peptides.