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Based on overall 3D structure, proteins may be grouped into two broadcategories, namely, globular proteins (spheroproteins), and elongated orrod-shaped proteins (RSP). The former comprises a significant majority ofproteins. This work concerns the second category. Unlike a spheroprotein, anRSP possesses a conspicuous axis along its longest dimension. To take advantageof this symmetry element, we decided to represent RSPs using cylindricalcoordinates, (rho, theta, z), with the z-axis as the main axis, and one tip ofthe protein at the origin. A "tip" is one of two extreme points in the proteinlying along the protein axis along its longest dimension. We first identify thetwo tips, T1 and T2, of the RSP using a protein graphics software, thendetermine their (Cartesian) coordinates, (h, k, l) and (m, n, o), respectively.Arbitrarily selecting T1 as the tip at the origin, we translate the protein bysubtracting (h, k, l) from all structural coordinates. We then find the anglealpha between vector T1-T2 and the positive z-axis by computing the scalarproduct of vectors T1- T2 and OP where P is an arbitrary point along thepositive z-axis. We typically use (0, 0, p) where p is a suitable positivenumber. Then we compute the cross product of the two vectors to determine theaxis about which we should rotate vector T1-T2 to make it coincide with thepositive z-axis. We use a matrix form of Rodrigues' formula to do the rotation.We then apply the Cartesian to cylindrical coordinate transformation equationsto 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 and3MQC. We have also created a web server that can take the PDB coordinate fileof an RSP and output its cylindrical coordinates. The URL of our web serverwill be announced publicly in due course.

Representing Rod-Shaped Protein 3D Structures in Cylindrical Coordinates