This Small Business Innovation Research project will produce a general algorithm, and corresponding software package, based upon tensor representation of multidimensional data blocks, to express relationships between dependent properties and independent molecular feature measures. The solutions to these data riet problems are three-dimensional quantitative structure-property relationships, 3D-QSPRs. While this proposal focuses on three-dimensional relationships, the formalism can easily be extended to higher dimensions. The molecular features are partitioned into the intrinsic molecular shape tensor, the molecular field tensor, a non-shape/field feature tensor, and an experimental feature tensor. The intrinsic molecular shape tensor contains information on the shape of a molecule within the contact surface while the molecular field tensor contains information outside of the contact surface. Molecular features not directly related to molecular shape are placed in the non-shape/field tensor. Experimental measures not being used as dependent variables can be considered as independent molecular features in the experimental tensor. The 3D-QSPR is realized by constructing the transformation tensor which optimizes the statistical significance between the dependent and independent variables. Factor analysis, partial least squares regression and multidimensional linear regression analyses will be explored individually, and in combination, to determine the transformation tensors. The proposed formalism has beran applied (in a limited fashion) to a raet of flexible M2/M3 muscarinic inhibitors leading to a 3D-QSA (Property=Activity) R in which an active conformation has been identified, and to a set of benzylpyrimidine inhibitors of dihydrofolate reductase where the enzyme bound conformation and alignment have been correctly identified. Other data sets to further explore the utility of the proposed formalism are presented. The proposed algorithm has far-reaching implications in the field of computer-aided molecular design. It is the only method proposed to date, which once developed, will provide the researcher with general, analytical functions which quantitatively relate structure to properties of members of sets of flexible molecules which can assume multiple alignments. The proposed 3D-QSPR algorithm product is likely to be purchased by all sites currently used CoMFA in order to facilitate treatment of conformational flexibility and multiple alignments. In addition, the general features to compute molecular shape propertles (molecular shape analysis) make the package a stand-alone 3D-QSPR product. More than installations have been targeted as likely within 18 months of version 1.0 product release.
