| In the design of ligands which may be flexible, and may assume many receptor alignments, finding the "active" conformation and the correct alignment is a significant, unsolved problem. If the three-dimensional structure of the receptor and a bound ligand are not known, the active conformation and alignment can be deduced from studies such as structure-activity relationships (SARs) and synthesis of rigid analogs.; The CoMFA and Molecular Shape Analysis (MSA), methodologies are 3D-QSAR approaches which consider conformation and alignment. MSA considers plausible "active" conformations and alignments. Methods of QSAR are then applied to derive models. A general approach would be to relax the conformation and alignment constraint and generate data for each compound in all combinations of thermodynamically reasonable conformation/alignment sets. This has been done on a series of dihydrofolate reductase (DHFR) inhibitors, 2,4-diaminopyrimidine analogs of trimethoprim, for which the bound conformation is known, and the result is a 3-way array of descriptor data which can be correlated with biological activity. This generalized formalism of 3D-QSAR analysis for flexible molecules using tensor representation, directly obtains the optimum 3D-QSAR in terms of conformation (shape) and alignment, by utilizing either MLR, 3-way partials least squares regression or 3-way factor analysis.; An approach to introducing time-dependence (dynamics) into MSA-3D-QSARs, was also implemented. The time-dependent spatial occupancy profiles of a set of DHFR, inhibitors and a set flexible prostaglandin, PGF{dollar}sb2alpha{dollar} analogs, were determined with the goal of constructing 3D-QSARs using time-dependent intramolecular descriptors. Space is divided into a grid of specified dimensions, and the molecules are then aligned along a set of user specified orientation vectors. The frequency of occupancy of each grid cell by each atom of each molecule is then monitored over time, based upon a molecular dynamics simulation. Time-dependent occupancy descriptors of each cell are computed. Each cell occupancy descriptor can then be mapped to activity by utilizing a genetic algorithm employing partial least squares is utilized to yield the optimum 3D-QSAR. The usefulness of this method stems from the fact that it includes the inherent flexibility of a molecule, and hence, changes in molecular shape over time, in deriving a MSA-3D-QSAR. |
