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.
本文提出了一种基于对偶四元数配准的蛋白质局部螺旋结构参数拟合（DQRFit）方法。该方法首先提取蛋白质结构数据中各残基的 C、N 原子坐标，然后用滑动窗口分别构造各段的待配准数据和参考数据。接着以配准前后数据点的距离平方和最小为寻优目标，利用对偶四元数配准算法求解出最优的旋转矩阵和平移向量并计算出该段二级结构的螺旋参数：每周残基数（ τ）、螺旋半径（ ρ）和螺距（ p）。本文通过对偶四元数配准可实现 τ、 ρ、 p 三个螺旋参数的同时拟合，并且滑动窗口宽度可调以适应不同的误差等级。与传统螺旋拟合方法相比，具有计算复杂度低、抗干扰性好、拟合精度高的优点。将本文算法应用于蛋白质 α 螺旋结构检测，结果表明检测精度与蛋白质二级结构词典（DSSP）相当，而明显优于其它几种传统方法。本文研究结果或可在今后的蛋白质结构分类和功能预测、药物设计、蛋白质结构可视化等领域具有重大意义。.
Keywords: dual quaternions; helix parameters fitting; registration; secondary protein structure; α helix detection.