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A Conceptual DFT Approach Towards Developing New QSTR Models

Quantitative-structure-toxicity-relationship (QSTR) models are developed for predicting the toxicity (pIGC50) of 252 aliphatic compounds on Tetrahymena pyriformis. The single parameter models with a simple molecular descriptor, the number of atoms in the molecule, provide unbelievable results. Better QSTR models with two parameters result when global electrophilicity is used as the second descriptor. In order to tackle both charge- and frontier-controlled reactions the importance of the local electro (nucleo) philicities and atomic charges is also analyzed. Best possible three parameter QSTR models are prescribed.


Introduction
Ever since the power of Quantitative-structure-activity-relationship (QSAR) based techniques has been highlighted, several descriptors have been proposed from time to time in developing QSAR models [1][2][3][4][5][6][7][8] for understanding various aspects of pharmacological sciences including drug design and the possible ecotoxicological characteristics of the drug molecules. Specific quantitative structure toxicity relationship (QSTR) models have also been developed. In these studies the toxicity of various chemicals have been understood via corresponding molecular structures. An extensive research has been carried out [9][10][11][12][13][14][15][16] in understanding the toxicological effects of several aliphatic compounds on ciliated protozoa called Tetrahymena pyriformis. Both European Union and U.S. Environmental Protection Agency require reliable toxicity data set for various classes of living systems like primary producers, invertebrates and vertebrates.
This information is used for QSAR/QSTR as well as regulatory purposes. The ciliated protozoa, Tetrahymena pyriformis has been considered to be ideal for the associated laboratory research. In this ciliate species, diverse endpoints can be used to originate the cytotoxic effects and xenobiotics. Experimental determination of toxicological and biochemical endpoints is a difficult task. Hence, QSAR/QSTR modeling of the toxicity of aliphatic compounds on the T. pyriformis is of vital importance in investigation of its toxicity in terms of its inhibitory growth concentration (IGC). A multitude of QSTR models exist which analyze the associated toxicity behavior. Quantum chemical descriptors 17-20 have also been used for this purpose and they have been proved to be versatile and reliable.
Toxicity analyses of a diverse class of systems have been carried out using conceptual density functional theory (DFT) based reactivity/selectivity descriptors.
Possibility of electron transfer between a toxic molecule and a biosystem has been considered to be one of the major reasons of toxic behavior of these molecules.
Accordingly the related descriptors like electron affinity, ionization potential, planarity, electrophilicity etc. have been turned out to be useful QSTR descriptors. Experimental toxicity values of a wide variety of polyaromatic hydrocarbons like polychlorinated dibenzofurans (PCDFs), polychlorinated biphenyls (PCBs), polychlorinated dibenzo-pdioxins (PCDDs) and chlorophenols (CP), several aliphatic and aromatic toxic molecules have been shown to correlate very well [20][21][22][23][24][25][26][27][28][29][30] with the corresponding toxicity values estimated using various conceptual DFT descriptors especially global and local electrophilicities. [31][32][33] Several researchers [9][10][11][12][13][14][15][16] have studied the toxicological behavior of various compounds on Tetrahymena pyriformis. They have highlighted the importance of the studies as well as the possibility of constructing a large number of QSTR models with a varied range of success and the difficulty in computation. A state-of-the art QSTR model has been developed by Schultz et al. 13 Toxicity of a large number of aliphatic compounds on Tetrahymena pyriformis has been studied 13 through QSTR models developed 13 in terms of logP and the lowest unoccupied molecular orbital energy (E LUMO ) whereas the effect of several aromatic compounds on the same system has been analyzed 14 in terms of log P, E LUMO and maximum acceptor superdelocalizability (A max ). In both cases the models are found to be robust. We have shown 20,25 that global and local electrophilicities are useful descriptors of toxicity prediction. In the present work we propose to develop QSTR models for toxicity of several aliphatic compounds on Tetrahymena pyriformis, using a simple descriptor, viz. the number of atoms present in the molecule, which can be obtained without even touching a computer. Section 2 provides the theoretical background whereas the computational details are provided in section 3. Results and discussion are provided in section 4 and finally, section 5 contains some concluding remarks.

Theoretical Background
We consider the number of atoms in a molecule to be a valid descriptor of its toxic nature. For a given group of molecules the number of electrons (N) is expected to scale as the number of atoms present (N a ). Molecules with larger N a values are supposed to have larger molecular weights implying larger log P values. That in turn will provide larger toxicity values. For simplicity we consider the number of carbon atoms (N C ) as the variable and for the set of molecules with a constant N C we may choose the number of non-hydrogenic atoms (N NH ) as the descriptor. Related descriptors have been used in the past. 34 In order to have a complete analysis we also check the nature of the model where electrophilicity ) (ω is used as an additional descriptor, which has been shown 20,25 to be a reliable descriptor of biological activity 19 and toxicity. 20,25 The electrophilicity is defined as 31,32 η μ ω are the electronic chemical potential and hardness respectively. I and A being the ionization potential and electron affinity respectively. It has also been shown 20,25 that apart from global electrophilic power the local electro (nucleo) philicity is important in understanding the possible charge transfer between a toxin and a receptor. The philicity at an atom k of the molecule is defined as 33 .
where { } k f α are the condensed-to-atom-k Fukui functions calculated in terms of the electronic population q k and α = +, -and 0 refers to nucleophilic, electrophilic and radical attacks respectively. The condensed Fukui functions are given by 35 Since the Fukui function based descriptors are ideally suited for soft-soft-frontiercontrolled reactions and the atomic charges (Q k ) in a molecule are known to be appropriate local descriptors in analyzing essentially charged-controlled reactions between a hard nucleophile and a hard electrophile [36][37][38] we also consider the latter in our analysis.

Computational Details
Geometries of all the 252 aliphatic molecules (acceptors-171, donors-81) corresponding to the 13 groups are optimized at the Hatree-Fock level with 6-311G* basis set using the Gaussian 03 39 program. These molecules were tested before 20 Each statistical analysis is preceded by an analysis of the dataset. A graphical analysis of the residuals (residual plot, normal probability plot and regression plot) permits the user to confirm if the dataset is suitable for a multiple linear regression.

Results and Discussion
Experimental and calculated pIGC 50 values along with various descriptors are presented in Tables 1 and 2 for the electron acceptor and electron donor molecules respectively. Table 3  It may be noted that for a diverse class of chemical compounds N C and ω may still be considered to be useful descriptors. Corresponding plots are provided in Figure 2 (a, b).
The correlation improves further in case a couple of sets are removed as was done by Schultz et al. 13 For the shake of completeness we also include the plot of the experimental toxicity with log P for the same 252 molecules (Figure 2c). The correlation is comparable to that obtained in Figure 2a which is expected because of the inter correlation between log P and N C (Figure 2d). It may be noted that unlike log P, N C does not require any software (instrument) to compute it (determine it experimentally).
Now we try to develop the best possible three-parameter models (with the highest The fact that each of these 3-parameter models is statistically significant does not mean that they behave better then the corresponding 1-or 2-parameter models. In view of the behavior of these models one has to look at three parameters. First of all, as mentioned before, one has to compare the adjusted R² of the three-parameter model with those of the one-or two-parameter models. All of the three-parameter models concerning R² behave better than the corresponding one-or two-parameter models, except the model for the set of alpha-acetylenic alcohols, which behave worse than the two-parameter model. The remaining models can be used for predictive purposes, only if they do not fail on the Y-randomisation test. As can be seen on the graphs (e), this concerns only the threeparameter models of the aliphatic amines, the unsaturated alcohols, the monoesters and the carboxylic acids. The three parameter models for these sets are

Molecule set
The fact that the remaining models of the halogenated alcohols, the diols and the ketones do not provide good Y-randomisation test results might be originating from the small number of molecules (respectively 11, 10 and 15 ) for the number of descriptors used. 45 It is important to note that max ω + and max ω − respectively appear in the electron acceptor and donor sets, as expected. Except for the set of aliphatic amines the atom number is a valuable descriptor. The global electrophilicity is also a reliable descriptor in most cases.
In order to check the efficacy of the present QSTR models vis-à-vis other existing popular models we make a comparative analysis of our work with that reported by  Table 3, their one parameter models for nonpolar molecules (Table 1  Moreover, obtaining log P is much more difficult than counting N C ., b) For the two parameter models their coefficients for log P are always positive as in our case the coefficients for N C are also always positive. In their models the coefficients for E LUMO and the intercept are positive in some cases and negative in other cases as is the case with our coefficients of ω and the intercept., c) There is a good correlation 43 between log P and N C . It is expected that our works would be complimentary to their work., d) The problems they faced in modeling carboxylic acids, amino alcohols, α-halo-activated compounds etc. may be better tackled using these descriptors or a combination of them (log P (N C ), E LUMO , ω)., e) Importance of charge as the descriptor in modeling amines is now understood, f) Macroscopic descriptors like log P or N C would be useful for a broad spectrum of systems. However, electronic descriptors like ω would be useful when systems with similar electronic environment are analyzed. They would be specially useful when molecules will have nearly identical or identical log P (N C ) values. For molecules with similar electronic environment local (or group) electrophilicity would highlight the importance of the site (group) especially for the toxic behavior.

Concluding Remarks
The number of atoms in a molecule can provide important insights into its possible toxic behavior. It can be used as a molecular descriptor for predicting pIGC 50 values of various aliphatic compounds against the ciliate Tetrahymena pyriformis. The situation improves further when electrophilicity is used as an additional descriptor. Local electro (nucleo) philicity and atomic charges are also considered to take care of local softsoft and hard-hard interactions, which resulted in robust three parameter QSTR models.          A deceptively simple descriptor, viz. the number of carbon / non-hydrogenic atoms present in a molecule is prescribed for the development of useful quantitative-structuretoxicity-relationship (QSTR) models. Please see the text for details.