A computational approach to pharmacological targets

The aim of the work was to improve the current computational methods for determining the 3-dimensional protein structure from RDC. The pur- pose was to formulate an e±cient automated method providing faster and exact solutions for the structural features of proteins, which are pharma- cological targets, contributing to rational drug design. Residual Dipolar Coupling (RDC) is an e±cient method of solution NMR spectroscopy o®ering global orientation constraints. We developed a new algorithm for determining the protein backbone structure by pro- cessing systematically the constraints of RDC illustrated on ubiquitin. Firstly, the orientation of one bond vector in consecutive peptide planes is computed from the RDC equations of two media then we solve for the (A; A) of two independent backbone halves ?ltering the optimum confor- mation. Next, the orientation of the Z axis of a global frame relative to secondary structures is determined from two media then the relative orientation of secondary structures is obtained from a rotation matrix mapping one molecular frame to the other. Next, a system of 9 polyno- mial equations, derived from exactly 3 distance constraints, determines the relative position of two oriented secondary structures; thus, the exact 3-dimensional backbone structure is computed. The novelty of our approach relative to numerical approximating or stochastic non-deterministic methods typically used in NMR is that we apply straightforward algebraic techniques, implemented on the computer algebra package MAPLE, providing always the true structure. We use the least number of experimental data while the runtimes take an order of seconds on a common PC. The results are expected to be applied mainly to receptors connected with G proteins and to subsequent design of ligands for these receptors