Book of Abstracts: Albany 2011
June 14-18 2011
©Adenine Press (2010)
Using Cylindrical Coordinates to Represent Rod-Shaped and Other Fibrous Protein 3D Structures: Potential Advantages and Applications
Based on overall 3D structure, proteins may be grouped into two broad, general categories, namely, globular proteins or ‘spheroproteins’, and elongated or ‘fibrous proteins’, and the former comprises the significant majority. Our research group is trying to use alternative representations for proteins structures, and has made progress on representing spheroproteins using spherical coordinates (ρ,φ,θ) (1). This work concerns the second general category of protein structures, namely, the fibrous or rod-shaped class of proteins. Unlike a spheroprotein, a rod-shaped protein (RSP) possesses a visibly conspicuous axis along its longest dimension. To take advantage of this potential symmetry element, we decided to represent RSPs using cylindrical coordinates, (ρ,θ,z), with the z-axis as the main axis and one ‘tip’ of the protein at the origin, with ‘tip’ being defined as one of two points lying along the protein axis and defining its longest dimension. To do this, we first visually identify the two tips T1 and T2 of the protein using appropriate graphics software, then determine their Cartesian coordinates, (h,k,l) and (m,n,o), respectively. Arbitrarily selecting T1 as the tip to coincide with the origin, we translate the protein by subtracting (h,k,l) from all structural coordinates. We then find the angle α (in degrees) between vectors T1T2 and the positive z-axis by computing the scalar product of vectors T1T2 and OP where P is an arbitrary point along the positive z-axis, which is typically (0,0,p), where p is the approximate length of the rod-shaped protein under investigation. Then we compute the cross product of the two vectors to determine the axis about which we should rotate vector T1T2 so it coincides with the positive z-axis. We then use a matrix form of Rodrigues’ formula to perform the actual rotation. Finally we apply the Cartesian to cylindrical coordinate transformation equations to the system. Thus far, we have applied the above transformation to 15 rod-shaped proteins, prominent among which are 1DXX, 2KOL, 2KZG, 3LHP and 3MQC. We have also created a database/webserver that can take in the PDB coordinate file of a rod-shaped protein and output its cylindrical coordinates based on the transformation steps described above. We shall implement this process in both all-atom and reduced protein representations (2). The URL will be http:// tortellini. bioinformatics. rit. edu/ sxc6274/ thesis2.php and it will be made freely available to the community very soon.
Biological Sciences Dept.