The application of new HARD-descriptor available from the CORAL software to building up NOAEL models

The HARD-index is a line of eleven symbols, which r epresents the presence, or absence of eight chemical elements (nitrogen, oxygen, sulfur, phosph rus, fluorine, chlorine, bromine, and iodine) and different kinds of chemical bonds (double bond, triple bond, and stereo chemical bond). Optimal molecular descriptors calculated with the M onte Carlo technique (maximization of correlation coefficient between the descriptor and e point) gives satisfactory predictive models for no observed adverse effect levels (NOAEL). The mode ls are built up in accordance with OECD principles.


Introduction
According to REACH (REACH, 2007), the NOAEL (no observed adverse effect levels) is a reliable criterion for risk assessment various chemicals. Regulators are continually facing the task of assessing health hazards and environmental effects of various chemicals. In fact, the number of substances, which should be taken into account is enormous. For instance, the database of Environmental Risk assessment (ERA) contains more than 100,000 chemical compounds on the European Inventory of Existing Chemicals (EINECS List) (Zvinavashe et al., 2009). Under such circumstances, computational models are very useful tools which can contribute to the hazard assessment of many compounds while reducing de novo animal testing (Kleandrova et al., 2014a,b;Luan et al., 2014). Computational toxicology, an applied science, utilizes the latest advances in mathematics, biology, chemistry, and computer technologies. Integrating all of these sciences into a biologically based computational model enables the researcher to numerically investigate the impact of exposure to environmental chemicals on living systems (Gadaleta et al., 2016;Dearden, 2016;Roy et al., 2015a;Roy and Ambure, 2016;Benfenati, 2007). In addition, the World Health Organization (WHO, 2000) have established an acceptable daily intake (ADI) for an actual risk assessment.
Traditionally, such safe levels in human risk assessment are derived from results of sub-chronic to chronic in vivo toxicological studies in test species (mostly rat, mouse, dog and rabbit) such as Noobserved adverse effect level (NOAEL) or Lowest observed adverse effect level (LOAEL) or more recently a benchmark dose limit (BMDL) on which most often a 100-fold uncertainty factor. In food safety, such safe levels are denominated Acceptable daily intake (ADI) or tolerable daily intake (TDI) for regulated compounds (such as pesticides, food and feed additives) and Tolerable Daily Intake for contaminants of anthropogenic or natural origins (e.g dioxins, brominated flame retardants, marine biotins, mycotoxins, alkaloids) (Dorne, 2010;Pizzo and Benfenati, 2016;Diaza et al., 2015;Marzo et al., 2016;Veselinović et al., 2016;Toropova et al., 2015;Toropov et al., 2015).
The NOAEL is an important indicator of danger in utilization of a substance after repeated use and is requested for regulatory purposes (Pizzo and Benfenati, 2016;Diaza et al., 2015;Marzo et al., The NOAEL is defined as dose level at which no adverse effects has been observed in a repeated dose toxicity study and is used to derive the threshold below which a risk for human health is not likely. In this process several assessment factors are applied to consider differences in human susceptibility as well as interspecies differences. In vivo studies are, however, no more permitted by the cosmetics directive, and in general have to be avoided, when feasible, also within other regulations (e.g. REACH). So far, alternative methods predicting the NOAELs are currently not available and several initiatives are ongoing to solve this issue.
This endpoint is measured with animal experiments, which are no more permitted by the cosmetics directive, and in general it should be avoided, when feasible, also within other regulations.
However, so far, the alternative methods for this endpoint have not proved the possibility to replace it, and several initiatives are ongoing to solve this issue. Among the alternative methods, there are a few works modelling this endpoint with quantitative structure -activity relationships (QSARs) methods (Toropov et al., 2015;Goto 2013;Dobchev et al., 2013;Pizzo and Benfenati, 2016). These models represent interesting efforts to predict a complex endpoint. The difficulties for the specific toxicological property are related to the fact that the number of substances with high quality NOAEL values is quite limited. Further, several mechanisms lead to the NOAEL e.g. different apical findings in different organs. Beside the biological diversity, NOAELs inherit some uncertainty e.g. due to differences in the experimental protocol (such as time of treatment, scope of examination, dose selection and dose spacing) as well as interspecies differences. It is to be noted, that NOAEL can be interrelated with biochemical processes which influence genetical phenomena (Mukerji et al., 2016).
The aim of this work is the development and the evaluation of QSAR models for NOAEL (Park and Cho, 2011;Rupp et al., 2010;Alexeeff et al., 2002;Bitsch et al., 2006) by means of the CORAL software based on the Monte Carlo technique.

Data
The data set are made using the data on the NOAEL taken from the Fraunhofer RepDose® database and the EFSA's Chemical Hazards Database (Bitsch et al., 2006;EFSA 2013EFSA , 2014.
OpenFoodTox provides open source data for the substance characterization, the links to EFSA' s output, background regulations, and a summary of hazard identification and hazard characterization for more than 400 substances from over 1650 Scientific Opinions, Statements and Conclusions through the work of its scientific Panels, Units and Scientific Committee. The database is available as an opensource tool under: https://dwh.efsa.europa.eu/bi/asp/Main.aspx?rwtrep=400.

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Data were selected from sub-chronic studies on rat and with way of exposure oral. Form EFSA database all studies with experimental duration between 77 and 98 days were selected for a total of 166 compounds of which 96 with multiple value (the lowest value was selected for developing the model). Among these 166 data a cluster of aliphatic chain of aldehydes, carboxylic acids and alcohols was found, this cluster include 39 compounds with the same experimental value, so to prevent a bias in the model development only 13 of these compounds randomly chosen among the three chemical classes was selected. Were then selected 137 compounds from EFSA database whit experimental value for NOAEL. From Fraunhofer database (Bitsch et al., 2006) all studies with reliability "A" and "B" and with experimental duration between 85 and 99 days was selected for a total of 362 compounds of which 44 with multiple value (also here the lowest value was selected for developing the model). The two data set was merged and between the two data set there was 15 compounds in common, the lowest value was selected (5 lowest values were from EFSA and 10 from RepDose data set). The final data set obtained is composed by 475 compounds, 119 from EFSA database and 356 from RepDose database.

Optimal descriptor
The so-called the hybrid optimal descriptor (Veselinovic et al., 2016;Toropova et al., 2015;Toropov et al., 2015) is utilized in this work. The hybrid descriptor takes into account molecular features extracted from simplified molecular input-line entry system (SMILES) and from hydrogensuppressed graph (HSG). In fact, SMILES and HSG are different (similar but non-identical) representations of the molecular structure (Toropova et al., 2015).
The paradigm used in this work can be expressed as the following: In Eq. 1, the SMILES is provider of (i) SMILES-atoms i.e. one or two characters, which cannot be examined separately (e.g. 'Cl', 'Br', etc.); (ii) pairs of SMILES-atoms (Table 1) (Table 1): The N total , N carbon , and N nonCarbon are the total number of neighbors, the number of neighbors which are carbon atoms, and the number of compounds which are not carbon, respectively.
[ Table 1 around here] Table 2 contains the general scheme of the construction of BOND, HALO, NOSP, and HARD.
[ Table 2 around here] Thus, the models suggested in this work are calculated with descriptor of optimal correlation weights (DCW) using the following two different equations (Toropova et al., 2015;Toropov et al., 2015): The correlation weights are calculated with the Monte Carlo optimization aimed to maximize the correlation coefficient between optimal descriptor and NOAEL. The optimization should be stopped In order to get more robust and representative statistical parameters, based on the presence of different chemicals in the sub-sets above discussed, we randomly split the overall set of compounds three times, with different compositions of the chemicals in the sub-sets.  Table 3 contains the statistical quality of models related to three different splits into the training, invisible training, calibration and validation sets.

Results and Discussion
The comparison of the models obtained with the new integrated descriptor HARD with model calculated with separated BOND, NOSP, and HALO shows that for the given total set of 487 compounds, the HARD improves the predictive potential of the models (Table 3).
The correlation coefficient metrics for external validation may be misleading (Roy and Ambure, 2016, Afantitis et al., 2008). In this work the average correlation coefficient value is calculated with three different models based on the three different splits of available data into the training, invisible training, calibration, and external validation sets is used as the measure of the predictive potential of the suggested approach.
where P T (F k ) and P C (F k ) are probabilities of attribute F k in the training and the calibration set, respectively; N T (F k ) and N C (F k ) are prevalence (frequency) of attribute F k in the training set and the calibration set, respectively. The d(F k ) =1, if N C (F k ) = 0. This situation represents the case with an unbalanced distributions of F k in the two sets and obviously this is the worst situation. Ideally, the value should be close to 0.
The defect of SMILES and HSG d(SMILES) can be estimated via defects of F k which presence in the SMILES and HSG: The defect of a split into the training, invisible training, calibration, and validation sets can be estimated with the sum of defects of SMILES from the training and calibration sets: Computational experiments have shown, that described models have preferable predictive The number of outliers according to inequality 15 are 4, 2, and 4 for splits 1, 2, and 3 respectively.
The split defects calculated with Eq. 14 (which related to the sum of all the contributions of defects) are 76.3, 64.3, and 85.2 for splits 1, 2, and 3 respectively. The second split is the best and third split is the worst according to criterion calculated with Eq.14. In this way it is possible to identify more perspective split among different splits, which are not equally useful for modeling purposes. Table 6 contains the comparison of the statistical quality of the models studied in this work with models suggested in the literature. The comparison confirms that the suggested approach gives satisfactory models, which are able to have practical applications. Our model is based on a larger set of compounds, and the higher performance obtained in particular on the data in the external validation set are quite encouraging.

Conclusions
The HARD index, which is an integrated attribute of SMILES, improves the predictive potential of QSAR models calculated with the Monte Carlo technique described in this work. The new approach has been tested on a set of compounds with values towards NOAEL, which is quite a complex toxicological property. The statistical quality of the suggested models are comparable or even better than the statistical quality of models reported in the literature. The special probabilistic criteria for the definition of domain of applicability are suggested (Eqs. 12-15). Mechanistic interpretation of the CORAL models in terms of promoters of increase or decrease for NOAEL value is used (Table 4). Thus, the CORAL software is building up predictive models for NOAEL according to OECD principles (OECD, 2007).

Molecular graph
Cl 1 C 2 C 3 S 4 C 5 C 6 Cl 7 Cl 1 0   Table 3 The statistical characteristics of QSAR models for three splits of data into the training, invisible training, calibration, and validation sets. The n is the number of compounds in a set; the r 2 is correlation coefficient between experimental and calculated NOAEL; the q 2 is the leave-one-out cross-validated r 2 ; the s is root-mean squared error; the F is the Fischer F-ratio **) The best prediction indicated by bold ***) Y-randomization test (Afantitis et al., 2008) M A N U S C R I P T Table 4 Correlation weights of promoters of increase or decrease for NOAEL according to three runs of the optimization procedure for split 1.

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A C C E P T E D ACCEPTED MANUSCRIPT  In this work (split 1) *) This is a "total" training set, which is structured into a group of (i) training set (n=159), (ii) invisible training set (n=156), and (iii) calibration set (n=81). .

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