柱坐标系下杆状蛋白质三维结构的表示
Representing Rod-Shaped Protein 3D Structures in Cylindrical Coordinates
摘要：
基于整体3D结构，蛋白质可分为两大类，即球状蛋白（球蛋白）和细长或杆状蛋白（RSP）。前者包括绝大多数蛋白质。这项工作涉及第二类。与球蛋白不同，RSP在其最长维度上具有明显的轴。为了利用这种对称元素，我们决定使用圆柱坐标（rho，theta，z）表示RSP，z轴作为主轴，蛋白质的一个尖端位于原点。“尖端”是蛋白质中沿着蛋白质轴沿其最长维度的两个极端点之一。我们首先使用蛋白质图形软件识别RSP的两个尖端T1和T2，然后分别确定它们的（笛卡尔）坐标（h，k，l）和（m，n，o）。选择T1作为原点的尖端，我们通过从所有结构坐标中减去（h，k，l）来翻译蛋白质。然后，我们通过计算向量T1-T2和OP的标量积来找到向量T1-T2和正z轴之间的角度α，其中P是沿正z轴的任意点。我们通常使用（0，0，p），其中p是合适的正数。然后我们计算两个向量的叉积，以确定我们应该旋转向量T1-T2的轴，使其与正z轴重合。我们使用Rodrigues公式的矩阵形式来进行旋转。然后，我们应用笛卡尔柱面坐标变换方程的系统。我们将上述变换应用于15个RSP：1 QCE，2 JJ 7，2KPE，3 K2 A，3LHP，2LOE，2L 3 H，2L 1 P，1 KSG，1 KSJ，1 KSH，2KOL，2KZG，2KPF和3 MQC。我们还创建了一个Web服务器，可以获取RSP的PDB坐标文件并输出其圆柱坐标。我们的网站服务器的URL将在适当的时候公布。
英文摘要：
Based on overall 3D structure, proteins may be grouped into two broad categories, namely, globular proteins (spheroproteins), and elongated or rod-shaped proteins (RSP). The former comprises a significant majority of proteins. This work concerns the second category. Unlike a spheroprotein, an RSP possesses a conspicuous axis along its longest dimension. To take advantage of this symmetry element, we decided to represent RSPs using cylindrical coordinates, (rho, theta, z), with the z-axis as the main axis, and one tip of the protein at the origin. A "tip" is one of two extreme points in the protein lying along the protein axis along its longest dimension. We first identify the two tips, T1 and T2, of the RSP using a protein graphics software, then determine their (Cartesian) coordinates, (h, k, l) and (m, n, o), respectively. Arbitrarily selecting T1 as the tip at the origin, we translate the protein by subtracting (h, k, l) from all structural coordinates. We then find the angle alpha between vector T1-T2 and the positive z-axis by computing the scalar product of vectors T1- T2 and OP where P is an arbitrary point along the positive z-axis. We typically use (0, 0, p) where p is a suitable positive number. Then we compute the cross product of the two vectors to determine the axis about which we should rotate vector T1-T2 to make it coincide with the positive z-axis. We use a matrix form of Rodrigues' formula to do the rotation. We then apply the Cartesian to cylindrical coordinate transformation equations to the system. We have applied the above transformation to 15 RSPs: 1QCE, 2JJ7, 2KPE, 3K2A, 3LHP, 2LOE, 2L3H, 2L1P, 1KSG, 1KSJ, 1KSH, 2KOL, 2KZG, 2KPF and 3MQC. We have also created a web server that can take the PDB coordinate file of an RSP and output its cylindrical coordinates. The URL of our web server will be announced publicly in due course.
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