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

Abstract

Abstract: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.

Introducing Catastrophe-QSAR. Application on Modeling Molecular Mechanisms of Pyridinone Derivative-Type HIV Non-Nucleoside Reverse Transcriptase Inhibitors

“…An unambiguous algorithm : The Spectral-SAR minimum path principle [31,55–57] is here generalized to include relevant combination of statistical information (e.g., the correlation factor R , Student’s t -test, Fischer’s F -test) to provide an equal footing multi-dimensional Euler distance [see Equations (8–16)], thus avoiding the previously identified discrepancy in judging the mid-range performance in terms of correlation or other statistical factors [56]. …”

Role of computer-aided drug design in modern drug discovery

“…More recent 3D-QSAR strategies include Topomer CoMFA (Cramer 2003), spectral structure activity relationship (S-SAR) (Putz and Lacrama 2007), adaptation of the fields for molecular comparison (AFMoC) (Gohlke and Klebe 2002), and comparative residue interaction analysis (CoRIA) (Datar et al 2006). Despite its notable successes in the drug discovery field, 3D-QSAR still has numerous shortcomings that can be solved by more advanced multidimensional QSAR strategies in the form of 4D, 5D, and 6D-QSAR.…”

Köln-Timişoara Molecular Activity Combined Models toward Interspecies Toxicity Assessment

“…However, unlike other important studies addressing this problem [15–17], the present Spectral-SAR [7] assumes the prediction error vector as being orthogonal to all others: $\langle Y_{\text{italicPRED}}|\text{italicprediction}\hspace{0.17em}\text{italicerror}\rangle =0$since it is not known a priori any correlation is made. Moreover, Equations (1a), (1b), and (1c) imply that the prediction error vector has to be orthogonal on all known descriptors (states) of predicted activity: $\langle X_{i=\overline{0,M}}|\text{italicprediction}\hspace{0.17em}\text{italicerror}\rangle =0$assuring therefore the reliability of the present ket states approach.…”

“…According with a well known algebraic theorem, the system (4) has no trivial solution if and only if the associated extended determinant vanishes; this way the Spectral-SAR determinant features the form [7]: $\left|\begin{array}{lllllll}left|Y_{\mathit{\text{PRED}}}\rangle \hfill & {\omega }_0\hfill & {\omega }_1\hfill & \dots \hfill & {\omega }_k\hfill & \dots \hfill & {\omega }_M\hfill \\ left|X_0\rangle \hfill & 1\hfill & 0\hfill & \dots \hfill & 0\hfill & \dots \hfill & 0\hfill \\ left|X_1\rangle \hfill & r_0^1\hfill & 1\hfill & \dots \hfill & 0\hfill & \dots \hfill & 0\hfill \\ left\dots \hfill & \dots \hfill & \dots \hfill & \dots \hfill & \dots \hfill & \dots \hfill & \dots \hfill \\ left|X_k\rangle \hfill & r_0^k\hfill & r_1^k\hfill & \dots \hfill & 1\hfill & \dots \hfill & 0\hfill \\ left\dots \hfill & \dots \hfill & \dots \hfill & \dots \hfill & \dots \hfill & \dots \hfill & \dots \hfill \\ left|X_M\rangle \hfill & r_0^M\hfill & r_1^M\hfill & \dots \hfill & r_k^M\hfill & \dots \hfill & 1\hfill \end{array}\right|=0$…”

“…However, besides the effectiveness of the S-SAR methodology in reproducing the old-fashioned multi-linear QSAR analysis [7,21], one of its advantages concerns on the possibility of introducing the so called ( vectorial ) norms (see Appendix A1) associated with either experimental (measured or observed) or predicted (computed) activities: $\left|\left||Y_{\text{italicOBS}/\text{italicPPED}}\rangle \right|\right|=\sqrt{\langle Y_{\text{italicOBS}/\text{italicPRED}}|Y_{\text{italicOBS}/\text{italicPRED}}\rangle }=\sqrt{\sum _{i=1}^N{y}_{i-\mathit{\text{OBS}}/\mathit{\text{PRED}}}^2}$…”