Chemical carcinogenesis became an experimental science in 1918, when Yamagiwa and Lchihawa reproduced coal tar carcinogenicity in rabbit skin [1]. In 1930, Yoshida reported hepato-carcinogenicity of a pure aminoazo dye in rats [2], while in 1938, Hueper et al. induced urinary bladder cancer in dogs using 2-naphthylamine [3]. In the following decades, the carcinogenicity of a number of polycyclic hydrocarbons, and the strong dependence of their activities on structural features, was demonstrated [4].

Thereafter, Miller and Miller suggested that chemical carcinogens are converted in vivo to reactive electrophilic derivates that combine with nucleophilic groups such as nucleic acids and proteins. These conclusions were based on observations that changes in genetic information were caused by reaction with alkylating electrophiles and were the initial event in chemical carcinogenesis. In this framework, then, chemical carcinogens are simply strong electrophilic reactants [5,6].

The benchmark in vitro model of chemical carcinogenicity is a series of genetically-engineered Salmonella typhimurium bacterial strains created by Bruce Ames [7]. John Ashby contributed to the identification and compilation of a list of structural alerts (SAs), which are chemically reactive functional groups that induce mutations and cancer [8]. All of the four basic sets of SAs (generically identified as Ashby SAs, Bailey SAs, Kazius SAs and the Ames test) give similar results for Salmonella mutagenicity and rodent carcinogenicity [9].

Ames (1984) showed that a high percentage of known human carcinogens can be detected as mutagens (around 83%) [7]. Oxygen radicals are the most important class of mutagens contributing to aging and cancer, but they are not detected as mutagens by the standard Salmonella strains used in such assays. Hydroperoxides generated by lipid peroxidation may damage DNA through the generation of hydroxyl radicals, which are also the main agents in radiation damage to DNA.

“Mutagenicity” refers to a substance’s capacity to cause genetic mutations; it is of great public concern because it is closely related to carcinogenicity and, potentially, reproductive toxicity. Mutagenicity can be assessed experimentally with the Ames Salmonella test, which has an estimated reproducibility of 85%. This intrinsic limitation of the in vitro test, along with the need for faster and less expensive predictive alternatives, has led to interest in other assessment methods, such as in silico structure-activity (toxicity) relationship [QSA(T)R] models [10].

In one example, because nitro compounds were observed to induce mutations in the S. typhimurium TA98 strain, QSTR techniques were employed to develop models of nitroarene mutagenicity using a set of 197 nitro-aromatic and heteroaromatic molecules. These models employed QSAR techniques with 2D and 3D descriptors such as electron distribution, spatial disposition, molecular volume, hydrophobicity, steric features, solubility and ionization constants [11].

A recent study by Perez-Garrido et al. (2010) investigating the relationships between various bond types and mutagenicity suggested a correlation between mutagenicity and hydrophobicity and molecular volume. This led to a series of proposed structural alerts for mutagenicity. The reactivity of carbonyl groups in electrophilic addition processes was found to be influenced by the size and electronic effects of the substituents; molecular size was found to increase with the number of hydrogens attached to sp³ carbons, leading to a reduction in mutagenicity; and the presence of a terminal double bond was also correlated with mutagenicity. The models created have a concordance of 86% and correctly classify 95% of mutagenic substances [12].

Investigation of the biological property of carcinogenicity using computational and network interaction studies may help to explain the increasing incidence of cancer. A successful predictive model must be generally valid for compounds with diverse molecular structures, obtain similar results for substances with similar physico-chemical properties and correctly model the relationship between sensitivity and specificity [13].

Recently, CAESAR, a project developing models of chemical properties that affect human health, included prediction of carcinogenicity in its set of goals [14,15]. Recent logical-chemoinformatics studies, using methods such as Counter Propagation Artificial Neural Networks (CP ANN), found that high levels of sensitivity (75%) and specificity (69%) were related to electrotopological states and molecular connectivity [16].

These models provide predictions of biological activity and information about the structures, toxicities and solubilities of all compounds analyzed. Since the European Parliament adopted a legislative proposal for the REACH (registration, evaluation and authorization of chemicals) chemical management system in 2006, in vivo testing has diminished in importance because the similar information can be obtained in silico through quantitative structure-activity relationships (QSARs) [17]. Carcinogens can be separated into two classes based on their mechanisms of action: genotoxic carcinogens directly damage DNA (thus producing mutagenesis as the first step of chemical carcinogenesis) [9,13], while epigenetic carcinogens do not bind covalently to DNA.

A (Q)SAR model, according to Organization of Economic Cooperation and Development (OECD) guidelines, has the following characteristics: a defined endpoint, an unambiguous algorithm, a defined domain of applicability, statistical performance and predictive power, and a mechanistic interpretation [18,19]. In this sense, a valid model will be the simplest and most mechanistically transparent. Good statistical performance is not sufficient for selection of a model; it should be compatible with existing knowledge in the fields of QSAR, chemistry and biology [9]. In construction of the model, if the compounds considered are not sufficiently similar in chemical-biological space or do not have a predefined activity ordering (e.g., a Gaussian distribution), the model will have poor predictive value for smaller datasets. Construction of a QSAR requires experimental data, molecular representation and fitting algorithms. Different QSAR implementations have varying requirements due to resource constraints and legal considerations; any model must therefore be evaluated in the context of its intended use [9].

The present work makes two contributions for advanced residual-QSAR modeling of genotoxic carcinogenesis [20]. First, to gain mechanistic insight into mutagenesis, the influence of explicit reactivity and electrophilic parameters on the derived QSAR models of carcinogenesis was investigated. Second, the residual QSAR method is extended by considering molecular fragment information in structural alerts, which aids in elucidating the electrophilic theory of chemical carcinogenesis.

It was recently shown [20] that direct and residual correlations should be combined; that is, for a given parameter set and an observed endpoint set, ( { X i } i = 1 , M ¯ , A ), the direct QSAR can be written as (1) A M = a 0 + ∑ i = 1 M b 0 i X iand residual analysis gives (2) ARA M = a 1 + b 1 ( A − A M )

Here the superscript “M” refers to either the full molecule or the structural parameters for each molecule under study. Equations (1) and (2), with the assumption that the obtained residual-QSAR matches the observed activity, (3) A = ARA Mprovide the “asymptotic residual QSAR”, (4) ARA M = 1 1 − b 1 [ a 1 − b 1 a 0 − b 1 ∑ i = 1 M b 0 i X i ]

Because Equation (4) is modulated by the parameters b₁ → 1, it is invariantly obtained throughout this procedure regardless of the structural parameters or form of the direct QSAR. While such behavior is common in cancer modeling, it presents conceptual limitations in assessing the model of interest.

The present approach avoids such drawbacks by making use of the properties of the structural alerts. It specifically employs the physico-chemical properties of these alerts to build associated QSARs and residual QSAR counterparts to build a multi-regression model of the molecular mechanism.

The present alert-QSAR algorithm is shown qualitatively in Figure 1. This algorithm provides activity predictions either by considering the full molecular structures or the substructures of the structural alerts.

The algorithm assumes a structure–activity multi-linear correlation problem using the structural alert (SA) parameters and observed endpoint set: ( { X i SA } i = 1 , M ¯ , A ). The associated alert-QSARs corresponding to specific regressions over subsets of the structural parameters may be computed, for instance, for (1 = m₁ < … < m_i < m_{i + 1} < … < m_{j – 1} < m_j < … < m_M = M): (5) A ( m i , m j ) SA = a 0 ( m i , m j ) SA + ∑ k = m i m j b 0 k SA X k SA

The residuals associated with Equation (5) are (6) RA ( m i , m j ) SA = A − A ( m i , m j ) SA

Equations (5) and (6) give the formed residual-alert-QSAR equation (7) ARA { ( m i , m j ) } SA = a 1 { ( m i , m j ) } SA + ∑ m i = 1 m j m j − 1 ∑ = m i + 1 m k ≤ M b 1 ( m i , m j ) SA RA ( m i , m j ) SA

Combining this expression with the activity matching condition of Equation (3), here rewritten in actual terms, (8) A = ARA { ( m i , m j ) } SAyields the structural alert residual correlation. (9) ARA { ( m i , m j ) } SA = 1 1 − ∑ m i = 1 m j m j − 1 ∑ = m i + 1 m k ≤ M b 1 ( m i , m j ) SA [ a 1 { ( m i , m j ) } SA − ∑ m i = 1 m j m j − 1 ∑ = m i + 1 m k ≤ M b 1 ( m i , m j ) SA ( a 0 ( m i , m j ) SA + ∑ k = m i m j b 0 k SA X k SA ) ]

Equation (9) improves upon Equation (4) by using structural alert information instead of molecular information, avoiding singularities in the denominator, i.e., (10) 1 ≠ ∑ m i = 1 m j m j − 1 ∑ = m i + 1 m k ≤ M b 1 ( m i , m j ) SA

This gives a residual-alert QSAR, a self-consistent correlation equation for the observed activity based on structural alert-predicted activities and residuals thereof. The method is next illustrated by reanalyzing previous toxicological carcinogenic series and studies [20].

This study targeted carcinogenic activity in rats (Rattus norvegicus), as measured by TD₅₀ values (in mg/kg body wt/day) derived from the Carcinogenic Potency Database (CPD) [16]. Activity is expressed here as a function of the TD₅₀ values, A = Log(1/TD₅₀). The working series of molecules, were chosen to have a high diversity molecular structure and fulfilling the Topliss-Costello rule [21] according to which their cardinal should be at least 5-times larger the number of structural descriptors used. They are separately shown in Tables 1 and 2, as calibration/trial/trainin sets using Gaussian screening and as test set using quasi-Gaussian distribution screening (Figure 2), respectively. The parameters recommended by Hansch [22] (hydrophobicity, polarizability and total energy) and special reactivity indices (electronegativity and chemical hardness), all computed using the semiempirical PM3 method, were used for both full molecules and structural alerts for the molecules found in Tables 1 and 2.

However, as noted by Hansch, “there is no substitute for extensive experience…in physical organic chemistry and QSAR” [22]. Highly diverse molecular groups were employed in assessing the observed genotoxic carcinogenesis/mutagenicity. Several particular choices or “degrees of freedom” can be considered in to bring the analysis in line with the traditional QSAR dogma of “congeneric molecules”.

Physicochemical parameters: meaningful physicochemical parameters as hydrophobicity, polarizability, total energy, electronegativity, and chemical hardness should be considered in order to better interpret the derived models in terms of molecular mechanisms.

The direct and residual-QSARs as applied to the full molecules and structural alerts shown in Tables 1 and 2 were applied as follows:

Step I: Structural alert QSARs for the trial compounds of Table 1 gave the structural alert activities A^SA shown in Table 3. Full molecular QSARs for the trial molecules of Table 1 are reported in Table 4 as “M” computed/predicted models. Combined QSAR predictions based on the molecular descriptors from Table 1 and the structural alert activities of Table 3 are reported in Table 4 as “M∧SA”; these results showcase how consideration of the structural alerts allows systematic improvement of the predictions over the molecular indicators. Note that the structural alert parameters may be combined with the molecular ones only at the level of full molecules; in this way, full molecular parameters are combined with predicted activity at the molecular level as provided by structural alerts modeling.

Step II: Residual QSARs for the structural alert models derived in Step I are computed, considering the predicted activities in Table 3; the results are presented in Table 5. Considerable correlation was found, indicating the indirect influence of structural alerts on mutagenicity and carcinogenesis.

Step III: Structural residual alert QSARs were obtained by selecting models from Step II that reproduce the structural alerts’ parameter correlations (10) as given in Equation (9). The residual-alert methodology may lead to new equations besides those presented in Table 3. The results are displayed in Table 6, with correlation performances reported for the trial molecules of Table 1 and the test compounds of Table 2.

Step IV: Euclidean paths for residual-alert QSARs for the trial molecules of Table 1 and the test compounds of Table 2 were constructed from the models of Step III. The models were arranged so that each model emerges from the previous one on the basis of their common descriptors; the results are reported in Table 7 by employing the Euclidean path between two successive QSAR models (computed endpoints), (11) [ QSAR [ a ] , QSAR [ b ] ] = ( R [ a ] − R [ b ] ′ ) 2

Step V: Optimum paths for residual-alert QSARs were derived from the results of Step IV by searching the minimum paths and the associated hierarchy according to the formal constraint [31–35] (12) δ [ QSAR [ 1 ] , … QSAR [ k ] … , QSAR [ m ] , ] = 0where QSAR^[1],...QSAR^[k],...,QSAR^[m] represent the endpoint residual-QSAR regression models computed with 1, …, k, …, m≤M structural parameters, respectively. These paths were computed for both trial and test compounds, and their average values (Table 7) for the residual-alert and direct-alert models (Table 6) are reported. The average column of Table 7 shows two sets of first (alpha), second (beta) and third (gamma) pathways in the ergodic pathways [36], i.e., those uniquely contained QSAR models across all possible combinations, namely:

those based on residual-alert QSARs: (13a) α : I a → II a 2 → I I I 2 χ SA , E tot SA … χ SA , LogP SA , E tot SA … χ SA , POL SA , LogP SA , E tot SA (13b) β : I d → II b 3 = II d 1 → III 5 η SA , E tot SA … η SA , POL SA , E tot SA … χ SA , η SA , POL SA , E tot SA (13c) γ : I e → II b 2 = II e 2 → III 3 POL SA , LogP SA … η SA , POL SA , LogP SA … η SA , POL SA , LogP SA , E tot SA

The remaining issue is to decide among these two pathways, while noting, for instance, the α- and v-residual-alert-QSARs are reproduced as β- and γ-direct-alert-QSARs, respectively. These and the resulting molecular mechanisms for the actual genotoxic effects on rats are clarified within the OECD-QSAR principles, as discussed below.

Generally, risk assessment comprises hazard identification (a qualitative risk assessment dealing with the inherent toxicity of a chemical substance), qualitative mutagenicity assessment (how likely an agent is to be a human mutagen), quantitative mutagenicity risk assessment (how much mutational damage is likely under particular exposure scenarios), dose-response assessment (relationship between the dose of a chemical and adverse effects) and exposure assessment (populations exposed to toxic chemicals).

Chemicals that have exhibited mutagenic activities in various test systems have been found in foods, tobacco, drugs, food additives, cosmetics, industrial compounds, pesticides and consumer products [37]. In this context, the OECD-QSAR principles can be used to guide any quantitative risk assessment of the carcinogenic potential under study through the provided QSAR models. They will be reviewed and illustrated using the present case study while emphasizing the specific advancements elucidated in this work.

The carcinogenesis process is divided into three operational stages: initiation, promotion and progression, with own unique mechanisms and QSAR characteristics that lead to an integrated approach with all the important elements to be considered. Consequently, the key to successful and meaningful QSAR formulation is the selection of appropriate molecular descriptors. It is critical to minimize the appearance of false negative results to increase regulatory acceptance of the developed models [9].

For carcinogenicity, it is important to address the mechanism of action and a negative (Q)SAR prediction for genotoxicity as well as negative results of an in vitro test with the conditions that mechanisms are sufficiently defined. QSAR models focus on the relationship between molecular structure and biological activity based on a comparison between the activities and structures of a series of chemicals. Nevertheless, until recently, the central dogma of QSAR asserted that the more local (specific, or a con-generic series) a model is in chemical-biological space, the higher the accuracy of its predictions [9]. As such, alongside the logical computational methods used for the QSAR modeling, i.e., genetic algorithms (optimization and search problems), artificial neural networks (non-parametric adaptive models), self organizing maps, support vector machines (classification and regression), partial least squares, decision forests, multiple linear regressions, k-mean clustering and TSAR [54], conceptual-QSAR has been developed to produce the meaningful physico-chemical models and paths to interpret ecotoxicological effects [31–36]. This approach ultimately ends in modeling of the carcinogenesis of highly diverse chemical structures [20], while considering the outliers’a analysis will lead with essential non-linear correlations [55].

The present work continues these efforts with the aim of clarifying the electrophilic mechanism of genotoxic carcinogenesis by modeling intermediate steps using structural alerts of the involved toxicants. We draw several main conclusions, as follows:

mutagenicity may be regarded as an electrophilic ligand-receptor interaction mechanism of covalent binding between the ligand molecule or SA and receptor;

The present study may be extended to assess the best molecular/structural alerts for residual-QSARs from a given pool of compounds. As well, it can be extended to include more statistical factors, such as standard error of estimation, Fisher and Student tests, to generalize the actual Euclidean measure to more elaborated statistical paths [56]. It may be also combined with 3D docking protocols to further validate the present residual-alert quantum-mechanical structural-reactivity analysis.