| Part 1: We have developed a web server that implements the two complementary methods to quantify the depth of ligand and/or ligand binding site (LBS) in a protein-ligand complex. The two methods are the 'secant plane' (SP) and the 'tangent sphere' (TS) methods. In the SP and TS methods, the protein molecular centroid (global centroid, GC), and the LBS centroid (local centroid, LC) are first determined. The SP is defined as the plane passing through the LBS centroid and normal to the line passing through the LC and the protein molecular centroid. The "exterior side" of the SP is the side opposite GC. The TS is defined as the sphere with center at GC and tangent to the SP at LC. The percentage of protein atoms (a.) inside the TS (TSi) and (b.) on the exterior side of the SP (SPi), are two complementary measures of ligand or LBS depth. The SPi is directly proportional to LBS depth while the TSi is inversely proportional to LBS depth. We tested the SP and TS methods using a test set of 67 well characterized protein-ligand structures (Laskowski, et al. 1996), as well as the theoretical case of an artificial protein in the form of a cubic lattice grid of points in the overall shape of a sphere and in which LBS of any depth can be specified. Results from both the SP and TS methods agree very well with reported data (Laskowski, et al. 1996), and results from the theoretical case further confirm that both methods are suitable measures of ligand burial or LBS depth. There are two modes by which one can utilize our web server. In the first mode we term the 'ligand mode', the user inputs the PDB structure coordinates of the protein as well as those of its ligand (one ligand at a time if there is more than one). The second mode, the 'LBS mode', is the same as the first except that the ligand coordinates are assumed to be unavailable; hence the user inputs what s/he believes to be the coordinates of the LBS amino acid residues. In both cases, the web server outputs the SP and TS indices. LBS depth is an important parameter as it is usually directly related to the amount of conformational change a protein undergoes upon ligand binding, and ability to quantify it could allow meaningful comparison of protein flexibility and dynamics. The URL of our web server is http://tortellini.bioinformatics.rit.edu/sxc6274/thesis1.php.;Part 2: Based on overall 3D structure, proteins may be grouped into two broad, general categories, namely, globular proteins or 'spheroproteins', and elongated or 'fibrous proteins'. The former comprises the significant majority. This work concerns the second general category of protein structures, namely, the fibrous or rod-shaped class of proteins (sometimes also referred to as "filamentous proteins"). Unlike an 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, (rho, theta, z), with the z-axis as the main axis and one 'tip' of the protein at the origin. A 'tip' is defined as one of two extreme points in the protein 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 alpha (in degrees) between vectors 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 T 1 T2 so it will coincide with the positive z-axis. We use a matrix form of Rodrigue's formula to perform the actual rotation. Finally we apply the Cartesian to cylindrical coordinate transformation equations to the system. The URL of our web server is http://tortellini.bioinformatics.rit.edu/sxc6274/thesis2.php (Abstract shortened by UMI.). |
