This paper proposes a method based on quaternion for characterization α helix of proteins. The method defines the parameter called Quaternion Helix Axis Spherical Distance (QHASD) on the basis of mapping protein Cα frames′ helical axis onto a unit sphere, and uses QHASD to characterize the α helix of the protein secondary structure. Application of this method has been verified based on the PDBselect database, with an α helix characterization accuracy of 91.7%. This method possesses significant advantages of high detection accuracy, low computation and clear geometric significance.
Diffusion tensor imaging (DTI) is a rapid development technology in recent years of magnetic resonance imaging. The diffusion tensor interpolation is a very important procedure in DTI image processing. The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy, but the method does not revise the size of tensors. The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation. Firstly, we decomposed diffusion tensors with the direction of tensors being represented by quaternion. Then we revised the size and direction of the tensor respectively according to different situations. Finally, we acquired the tensor of interpolation point by calculating the weighted average. We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data. The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy (FA) and the determinant of tensors, but also preserve the tensor anisotropy at the same time. In conclusion, the improved method provides a kind of important interpolation method for diffusion tensor image processing.
A fitting method of calculating local helix parameters of proteins based on dual quaternions registration fitting (DQRFit) is proposed in this paper. First, the C and N atom coordinates of each residue in the protein structure data are extracted. Then the unregistered data and reference data are constructed using the sliding windows. The square sum of the distance of the data points before and after registration is regarded as an optimization goal. We calculate the optimal rotation matrix and the translation vector using the dual quaternion registration algorithm, and get the helix parameters of the secondary structure which contain the number of residues per turn(τ), helix radius(ρ)and helix pitch(p). Furthermore, we can achieve the fitting of three-helix parameters of τ, ρ, p simultaneously with the dual quaternion registration, and can adjust the sliding windows to adapt to different error levels. Compared with the traditional helix fitting method, DQRFit has some advantages such as low computational complexity, strong anti-interference, and high fitting accuracy. It is proven that the precision of proposed DQRFit for α helix detection is comparable to that of the dictionary of secondary structure of proteins (DSSP), and is better than that of other traditional methods. This is of great significance for the protein structure classification and functional prediction, drug design, protein structure visualization and other fields in the future.