Introducing Spectral Structure Activity Relationship (S-SAR) Analysis. Application to Ecotoxicology

A novel quantitative structure-activity (property) relationship model, namely Spectral-SAR, is presented in an exclusive algebraic way replacing the old-fashioned multi-regression one. The actual S-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 S-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 S-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 S-SAR analysis upon the Tetrahymena pyriformis ciliate species employing its reported eco-toxicity activities among relevant classes of xenobiotics. By representing the spectral norm of the endpoint models against the concerned structural coordinates, the obtained S-SAR endpoints hierarchy scheme opens the perspective to further design the ecotoxicological test batteries with organisms from different species.