ABSTRACT
A novel quantitative structure-activity (property) relationship model, namely SPECTRAL-SAR (Special Computing Trace of Algebraic SAR), is presented in an exclusive algebraic way replacing the old-fashioned multi-regression one. The actual SPECTRAL-SAR method interprets structural descriptors as vectors in a generic data space that is further mapped into a full orthogonal space by means of the Gram-Schmidt algorithm. Then, by coordinated transformation between the data and orthogonal spaces, the SPECTRAL-SAR equation is given under simple determinant form for any chemical-biological interactions under study. While proving to give the same analytical equation and correlation results with standard multivariate statistics, the actual SPECTRAL-SAR frame allows the introduction of the spectral norm as a valid substitute for the correlation factor, while also having the advantage to design the various related SAR models through the introduced “minimal spectral path” rule. An application is given performing a complete SPECTRAL-SAR analysis upon the Tetrahymena pyriformis ciliate species employing its reported ecotoxicity activities among relevant classes of xenobiotics. By representing the spectral norm of the endpoint models against the concerned structural coordinates, the obtained SPECTRALSAR endpoints hierarchy scheme opens the perspective to further design the ecotoxicological test batteries with organisms from different species.
