Solution of the Conformation and Alignment Tensors for the Binding of Trimethoprim and Its Analogs to Dihydrofolate Reductase:  3D-Quantitative Structure−Activity Relationship Study Using Molecular Shape Analysis, 3-Way Partial Least-Squares Regression, and 3-Way Factor Analysis

Molecular recognition is the basis of rational drug design, and for this reason it has been extensively studied. However, the process by which a ligand recognizes and binds to its receptor is complex and not well understood. For the case in which the geometries (conformation and alignment) of the ligand and receptor are known from X-ray crystal structure data, the problem is simplified. The receptor-bound conformation and alignment of the ligand is assumed, and those of additional ligands are inferred. For the general case in which the geometries of the ligand(s) and receptor are unknown, no general treatment or solution is available and receptor−ligand geometries must be obtained indirectly from structure−activity studies or synthesis and evaluation of rigid analogs. A general treatment for solving for the receptor-bound geometry of a series of ligands is presented here. Using molecular shape analysis, for ligand description, tensor analysis of N-way arrays by partial least-squares (PLS) regression, and 3-way factor analysis, the receptor-bound geometries of trimethoprim and a series of trimethoprim-like dihydrofolate reductase inhibitors are correctly predicted.