Abstract
A novel quantitative structure-activity (property) relationship model, namelySpectral-SAR, is presented in an exclusive algebraic way replacing the old-fashionedmulti-regression one. The actual S-SAR method interprets structural descriptors as vectorsin a generic data space that is further mapped into a full orthogonal space by means of theGram-Schmidt algorithm. Then, by coordinated transformation between the data andorthogonal spaces, the S-SAR equation is given under simple determinant form for anychemical-biological interactions under study. While proving to give the same analyticalequation and correlation results with standard multivariate statistics, the actual S-SARframe allows the introduction of the spectral norm as a valid substitute for the correlationfactor, while also having the advantage to design the various related SAR models throughthe introduced “minimal spectral path” rule. An application is given performing a completeS-SAR analysis upon the Tetrahymena pyriformis ciliate species employing its reportedeco-toxicity activities among relevant classes of xenobiotics. By representing the spectralnorm of the endpoint models against the concerned structural coordinates, the obtainedS-SAR endpoints hierarchy scheme opens the perspective to further design the eco-toxicological test batteries with organisms from different species.
Highlights
In Chemistry, the first systematic correlations come from Lavoisier's law of conservation of mass and energy, followed by the Dalton conception of structural matter
Aiming to solve part of the many challenges posed by quantitative structure-activity relationships (QSARs) and its applications, with a view to generating a mechanistic-causal vision of the data recorded, the current paper introduces both a new analytical structure-activity relationships (SARs) modelling algorithm and its associated minimum spectral action principle, following the activity norm of the models generated
Despite the fact that many QSAR approaches make use of algorithms that separate or transform initial non-orthogonal data into an orthogonal space, in search of a better correlation, many of them provide no significant improvement over the standard QSAR least square recipe
Summary
In Chemistry, the first systematic correlations come from Lavoisier's law of conservation of mass and energy, followed by the Dalton conception of structural matter. Even combined with PLS (partial least squares) cross-validation technique to produce higher predictive QSAR models, the main drawback still remains since they furnish scarce possibility to interpret the obtained models [44,46] Another way of interpreting orthogonality was given through producing an orthogonal space by transforming the original basis set of descriptors in an orthogonal one by searching of inter-regression equations between them [47], followed, eventually, by their reciprocal subtractions [48]. The third attempt of interpreting the orthogonal problem is considering the scalar product as the main vehicle in releasing the QSAR solution in a completely algebraic way furnishing the so called Spectral-SAR (S-SAR) technique in Figure 1 for reasons revealed bellow It is based on the employment of the generalized Euclidian scalar product rule among the vectors associated to the descriptors’ data in a way that produce, thought the Gram-Schmidt algorithm and coordinate transformation, precisely the same results as the statistical multi linear regression techniques do. The present S-SAR analysis leaves room for other similar studies when it is joined with other classical, 3-dimensional and decisional QSAR techniques of Figure 1 so contributing to unite the chemical-biological interactions in a veritable QSAR science
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