# Investigation of Antileishmanial Activities of Acridines Derivatives against Promastigotes and Amastigotes Form of Parasites Using Quantitative Structure Activity Relationship Analysis

Authors: Samir Chtita; Mounir Ghamali; Rachid Hmamouchi; Bouhya Elidrissi; Mohamed Bourass; Majdouline Larif; Mohammed Bouachrine; Tahar Lakhlifi
Journal: Advances in Physical Chemistry
 (2016)

---

## Abstract

In a search of newer and potent antileishmanial (against promastigotes and amastigotes form of parasites) drug, a series of 60 variously substituted acridines derivatives were subjected to a quantitative structure activity relationship (QSAR) analysis for studying, interpreting, and predicting activities and designing new compounds by using multiple linear regression and artificial neural network (ANN) methods. The used descriptors were computed with Gaussian 03, ACD/ChemSketch, Marvin Sketch, and ChemOffice programs. The QSAR models developed were validated according to the principles set up by the Organisation for Economic Co-operation and Development (OECD). The principal component analysis (PCA) has been used to select descriptors that show a high correlation with activities. The univariate partitioning (UP) method was used to divide the dataset into training and test sets. The multiple linear regression (MLR) method showed a correlation coefficient of 0.850 and 0.814 for antileishmanial activities against promastigotes and amastigotes forms of parasites, respectively. Internal and external validations were used to determine the statistical quality of QSAR of the two MLR models. The artificial neural network (ANN) method, considering the relevant descriptors obtained from the MLR, showed a correlation coefficient of 0.933 and 0.918 with 7-3-1 and 6-3-1 ANN models architecture for antileishmanial activities against promastigotes and amastigotes forms of parasites, respectively. The applicability domain of MLR models was investigated using simple and leverage approaches to detect outliers and outsides compounds. The effects of different descriptors in the activities were described and used to study and design new compounds with higher activities compared to the existing ones.


---

## Body

## 1. Introduction

For hundreds of years, Leishmaniasis, a disease caused by a number of species of protozoan parasites belonging to the genusLeishmania, is recognized as an important public health problem throughout the world [1–3]. Currently, the leishmaniases are considered to be endemic in 88 countries and, according to World Health Organization (WHO) [4], twelve million people are infected, with about two to three million new cases each year, and 350 million people are under risk of infection; it is a major public health problem particularly in Latin America, Africa, and Asia [5–9]. To date, no vaccine against any clinical form of Leishmaniasis has been commercialized and treatment relies only on chemotherapy, which has been based on the use of pentavalent antimonial drugs. Other medications, such as pentamidine and amphotericin B, have been used as alternative drugs for resistant parasites. With the emergence of some resistant strains, the toxicity of current drugs, severe side effects, and high cost and/or restricted therapeutic spectrum, a need for development of new and safer drugs is warranted [2, 3, 10]. A great number of natural and synthetic compounds have been tested in the past years in antileishmanial assays. Their structures are diverse and often contain nitrogen heterocycles such as quinolines, pyrimidines, acridines, phenothiazines, and indoles [11–13].Many experiments have been performed with the compounds bearing the heterocyclic ring structures to explore their effectiveness against Leishmania. These studies suggested their similar pharmacophoric feature of the heterocyclic scaffold as a potential target for drug discovery of antileishmanial drugs [14].Leishmania parasites exist in two forms, one is promastigotes and the other is amastigotes. The promastigotes are flagellated and found in sand fly, while the amastigotes are ovoid and nonflagellated form ofLeishmania [15]. Antileishmanial activity is performed against promastigotes and then amastigotes forms of parasites. Heterocyclic system may also be formed by fusion with other rings, either carbocyclic or heterocyclic.Since their discovery in the 1880s, acridines family have demonstrated a broad spectrum of pharmacological properties [16]. First employed as antibacterial agents during the beginning of the twentieth century [17]. They have been rapidly revealing interesting antiproliferative activities against both protozoa and tumor cells [18, 19]. Consequently, they have been extensively used in antiparasitic chemotherapy and a wide range of new acridines derivatives have been synthesized and successfully assessed for their antileishmanial activities [20, 21].In order to open a new way in antileishmanial drug research, a series of sixty acridines derivatives were synthesized [22–24] and studied for their antileishmanial (against promastigotes and amastigotes form of parasites) activities. The aim of this study was to develop a QSAR model able to correlate the structural features of the acridines derivatives with their biological activities.In general, the QSAR methods are based on the assumption that the activity of a certain chemical compound related to its structure through a certain mathematical algorithm. This relationship can be used in the prediction, interpretation, and assessment of new compounds with desired activities reducing and rationalizing time, efforts, and cost of synthesis and new product development.The basic assumption to drive a QSAR model is presented due to a mathematical function of the chemical properties which is related to the effect (activity). Therefore, the effect is like the function “f” of the chemical properties “x”: y=f(x). To find this algorithm, we use a number of chemical compounds with known values of the studied effect (y). For each chemical compound, we calculate a series of parameters (called chemical descriptors). Then, we find an algorithm that provides a quite accurate value, similar to the real experimental value. The final step is to check if the obtained algorithm is able to predict the activity values for other chemicals not used to build up the model (external validation).Indeed, it is very important to generate a model which worked not only for the chemical substances used within the training set but also for other similar chemicals. Consequently, the challenge is to define the correct statistical properties of the model.


## 2. Materials and Methods

The current QSAR study investigates prediction and interpretation of the studied compounds and was also used for designing new proposed compounds by using linear and nonlinear methods. It consists of four stages: selection of dataset and generation of molecular descriptors, descriptive analysis, statistical analysis (prediction and evaluation), and suggestion of novel compounds.A flow chart for the development of the QSAR model along with the various validation methods used in this work is demonstrated in Figure1.Figure 1
Flow chart of the methodology used in this work.


### 2.1. Selection of Dataset and Generation of Molecular Descriptors

#### 2.1.1. Selection of Dataset

In this stage, the datasets of the antileishmanial activities (against promastigotes and amastigotes forms of parasites) of various acridine derivatives (4-monosubstituted acridines, 3,6-disubstituted acridines, 4,5-disubstituted acridines, and 7-monosubstituted 9-chloro and 9-amino-2-methoxy acridines) were collected from previous works [22–24]. The molecular structures of the studied molecules with their antileishmanial activities are presented in Table 1. All experimental IC50 antileishmanial activity values (μM) were converted to the negative logarithm of IC50  pIC50=-log10⁡IC50.Table 1
Chemical structure and antileishmanial activities of studied compounds (see Figure8).
Number R1 R2 R3 R4 R5 R6 R7 p I C 50 b PROc AMAd 1 H NHCOCH3 H H H NHCOCH3 H −2.533 −0.653 2 H NHCOC2H5 H H H NHCOC2H5 H −2.204 −0.886 3 H NHCOC3H7 H H H NHCOC3H7 H −1.669 −1.107 4 H NHCOph H H H NHCOPh H −0.634 −0.041 5 H NHCO-p-PhCl H H H NHCO-p-PhCl H — 0.699 6 H NHCO-p-PhF H H H NHCO-p-PhF H −0.230 1.523 7 H NHCO-p-PhOMe H H H NHCO-p-PhOMe H −0.681 −0.041 8 H NHCO-m,p-Ph(OMe)2 H H H NHCO-m,p-Ph(OMe)2 H −1.207 0.097 9 H NHCOMe H H H NHCOph H −2.270 Toxa 10 H NHCOMe H H H NHCO-p-PhCl H −1.061 −0.462 11 H NHCOMe H H H NHCO-p-PhF H −2.123 0.174 12 H NHCOMe H H H NHCO-p-PhOMe H −1.939 Toxa 13 H NHCOMe H H H NHCO-m,p-Ph(OMe)2 H — −0.114 14 H H CH3 NH2 OMe H H 0.301 0.398 15 H H CH2OH NH2 OMe H H −0.732 −0.613 16 H H CH2Br NH2 OMe H H −0.556 −0.663 17 H H (CH2)2OCOOMe NH2 OMe H H −0.380 −0.114 18 H H (CH2)2OCO(CH2)2CH3 NH2 OMe H H −0.491 −0.398 19 H H (CH2)2OCOCH2CH(CH3)2 NH2 OMe H H −0.342 Toxa 20 H H (CH2)2OCOPh NH2 OMe H H 0.398 0.699 21 H H (CH2)2OCOPhF NH2 OMe H H −0.114 0.222 23 H H (CH2)2OCOPhOMe NH2 OMe H H −0.279 Toxa 24 H H CH3 Cl OMe H H −0.041 −0.362 25 H H CH2OH Cl OMe H H −2.262 −0.959 26 H H CH2Br Cl OMe H H −1.703 −1.170 27 H H (CH2)2OCOOMe Cl OMe H H −2.178 −1.877 28 H H (CH2)2OCO(CH2)2CH3 Cl OMe H H −1.707 −1.628 29 H H (CH2)2OCOCH2CH(CH3)2 Cl OMe H H −1.446 −1.561 30 H H (CH2)2OCOPh Cl OMe H H −2.135 Toxa 31 H H (CH2)2OCOPhF Cl OMe H H −2.295 −1.645 32 H H (CH2)2OCOPhCl Cl OMe H H −2.194 −2.191 33 H H (CH2)2OCOPhOMe Cl OMe H H −2.098 −2.088 34 CH2NH2 H H H H H H −0.230 −0.531 35 CH2OH H H H H H H Toxa −1.515 36 CH2NHCO(CH2)3Cl H H H H H H −1.655 −1.427 37 CH2OCO(CH2)3Cl H H H H H H −2.200 −2.185 38 CH2NHCOCH=CH2 H H H H H H −2.245 −0.833 39 CH2OCOCH=CH2 H H H H H H −1.464 — 40 CH2NHCOPh H H H H H H −1.654 −1.121 41 CH2OCOPh H H H H H H −1.885 Toxa 42 CH2NHCO-p-PhF H H H H H H −1.815 — 43 CH2OCO-p-PhF H H H H H H −1.741 Toxa 44 CH2NHCO-p-PhCl H H H H H H Toxa −1.004 45 CH2OCO-p-PhCl H H H H H H −1.790 −1.433 46 CH2NHCO-p-PhOMe H H H H H H −1.513 −0.973 47 CH2OCO-p-PhOMe H H H H H H −1.471 −0.869 48 CH2NHCO-p-PhNMe2 H H H H H H −1.539 −0.672 49 CH2OCO-p-PhNMe2 H H H H H H −1.819 Toxa 50 CH2NH2 H H H H H CH2NH2 −0.820 −0.531 51 CH2OH H H H H H CH2OH Toxa 0.222 52 CH2NHCO(CH2)3Cl H H H H H CH2NHCO(CH2)3Cl −0.663 −0.813 54 CH2NHCOCH=CH2 H H H H H CH2NHCOCHCH2 −1.061 Toxa 56 CH2NHCOPh H H H H H CH2NHCOPh −0.556 −1.236 57 CH2OCOPh H H H H H CH2OCOPh Toxa −0.716 58 CH2NHCO-p-PhF H H H H H CH2NHCO-p-PhF −0.756 −0.255 60 CH2NHCO-p-PhCl H H H H H CH2NHCO-p-PhCl — −1.562 62 CH2NHCO-p-PhOMe H H H H H CH2NHCO-p-PhOMe −1.797 Toxa 63 CH2OCO-p-PhOMe H H H H H CH2OCO-p-PhOMe Toxa −1.825 64 CH2NHCO-p-PhNMe2 H H H H H CH2NHCO-p-PhNMe2 −0.940 −0.724 65 CH2OCO-p-PhNMe2 H H H H H CH2OCO-p-PhNMe2 Toxa −1.667 aToxic: toxicity observed on human macrophages at concentrations that did not display antileishmanial activity; -p-: para; -m-: meta; bpIC50 = −log (IC50); cpIC50 AMA: antileishmanial activity against amastigotes parasite form; dpIC50 PRO: antileishmanial activity against promastigotes parasite form.


#### 2.1.2. Molecular Descriptors Generation

A wide variety of molecular descriptors was calculated using Gaussian 03, ACD/ChemSketch, Marvin Sketch, and ChemOffice programs [25–28] to predict the correlation between these descriptors for the studied molecules with their antileishmanial activities and to develop linear (multiple linear regression (MLR)) and nonlinear (artificial neural network (ANN)) models. Tables 3 and 4 show the selected descriptors (using the PCA method; see more in descriptive analysis results) to be used in this study.


### 2.2. Descriptive Analysis

In this stage, the principal component analysis (PCA) was used to determine the nonlinearity and nonmulticollinearity among variables (descriptors) and to select descriptors that correlate with the activity. After that, the univariate partitioning (UP) method was used to form dissimilar clusters of compounds, to which the query compounds would be compared for determining the degree of similarity and dividing the dataset into training and test sets.


### 2.3. Statistical Analysis (Models Development and Evaluation)

In this stage, linear and nonlinear QSAR models were developed and evaluated to predict the activities of the test compounds. The study we conducted consists of the multiple linear regression (MLR) available in the XLSTAT software and the artificial neural network (ANN) available in the Matlab software.In order to propose models and to evaluate quantitatively the physicochemical effects of the substituents on the activities of molecules, we submitted the data matrix constituted obviously from the used variables (descriptors) corresponding to the dataset molecules to a descendant MLR analysis and to an ANN. We use the coefficientsR, R2, R2adj, MSE, and P value to select the best regression performance [29], where R is the correlation coefficient; R2 is the coefficient of determination; R2adj is the coefficient adjusted for degrees of freedom. Mean squared error (MSE) is the standard error of the coefficient of each descriptor and of the global model, which gives an indication of the valid inclusion of a descriptor in a QSAR model. P value is the probability (P) of Fisher statistics (F), which gives an indication of the probability that a QSAR is a chance correlation.In order to assess the significance of the models and accurate prediction ability for new compounds:(i)
we use an internal validation procedure (leave-one-out cross validation), whereby one compound is removed and the rebuilt model with the remaining molecules is used to predict the response of the eliminated compound. This one is then returned and a second is removed, and the cycle is repeated, and so on, until all compounds have been removed one by one, and an overall correlation coefficientRcv is computed;(ii)
after the model is built, an external prediction is necessary. In this one, the obtained model was used to predict the activities of a test set comprising compounds that are similar to those not used in the training set. This is usually performed by splitting a dataset into a training set and a test set, typically in a 1/5 ratio. Further, before performing the external validation of a model, it is very important to check for the presence of systematic error that violates the basic assumptions of the least squares regression model. If high systematic error (bias) is present in the model, then such model should be discarded and performing any external validation test is of no use on such biased model. Xternal Validation Plus is a tool that checks the presence of systematic errors in the model and further computes all the required external validation parameters, while judging the performance of actual prediction quality of a QSAR model based on recently proposed MAE-based criteria [30];(iii)
a model is valid only within its training domain and new molecules must be considered as belonging to the domain before the model is applied (OECD Principle 3 [31]). Without applicability domain (AD), each model can predict the activity of any compound, even with a completely different structure from those included in the study. Therefore, the AD is a tool to find out compounds that are outside the applicability domain of the built QSAR model and it detects outliers present in the training set compounds. There are several methods for defining the applicability domain (AD) of QSAR models [32], but the most common one is determining the leverage values hi  hi=xiTXTX-1xii=1,2,…,n for each compound, where xi is the descriptor row-vector of query compound, X is nxk-1 matrix of k model descriptor values for n training set compounds, and the superscript T refers to the transpose of matrix/vector [32, 33]. In this study, we use Williams plot; in this plot, the applicability domain is established inside a squared area within standard deviation ±x (in this study x=3; “three-sigma rule” [34]) and a leverage threshold h∗(h∗=3∗(k+1)/n) [35], where n is the number of training set compounds; k is the number of model descriptors. The leverage (h) greater than the warning leverage (h∗) suggested that the compound was very influential on the model [36]. The results of the leverage approach were compared with that of the simple approach introduced by Roy et al. [37].


#### 2.3.1. Multiple Linear Regression (MLR)

The descendent multiple linear regression (MLR) analysis, based on the elimination of aberrant descriptors (one by one) until a valid model (including the critical probability:P value < 0.05 for all descriptors and the model complete), was employed to find a linear model of the activity of interest, which takes the following form:(1)Y=a0+∑i=1naixi,where Y is the studied activity, which is the dependent variable. a0 is the intercept of the equation. xi are the molecular descriptors. ai are the coefficients of those descriptors.This method is one of the most popular methods of QSAR/QSPR thanks to its simplicity in operation, reproducibility, and ability to allow easy interpretation of the features used. The important advantage of the linear regression analysis is that it is highly transparent; therefore, the algorithm is available and predictions can be made easily [38]. It has served also to select the descriptors used as the input parameters in the artificial neural network (ANN).


#### 2.3.2. Artificial Neural Networks (ANN)

The artificial neural networks (ANN) are used in order to increase the probability of characterizing the compounds and to generate a predictive QSAR model between the set of molecular descriptors obtained from the MLR models and the observed activities values. The ANN model is done on the MATLAB R2009b software. It consists of three layers of neurons, called input layer, hidden layer, and output layer (Figure2). The input layer formed by a number of neurons equal to the number of descriptors obtained in the multiple linear regression models and the output layer represents the calculated activity values. For determination of the number of hidden neurons in the hidden layer, where all calculations of parameter optimization of neural networks are made, a parameter ρ has been proposed. The parameter ρ plays a major role in determining the best artificial neural network architecture [39, 40]; ρ is defined as follows:(2)ρ=number of data points in the training setsum of the number of connections in the ANN.In order to avoid overfitting or underfitting, it is recommended that the value of ρ should be between 1.00 and 3.00; if ρ<1, the network simply memorizes the data, whereas if ρ>3, the network is not able to generalize [41].Figure 2
The architecture used in our study of the artificial neural network.


### 2.4. Software Packages Used in Our QSAR Development Study

There are various free and commercial software available for QSAR development. These include specialized software for drawing chemical structures, generating 3D structures, calculating chemical descriptors, and developing QSAR models. The software packages used in our works are represented in Table2.Table 2
Software packages used in this work.
Drawing chemical structures Marvin Sketch, ACD/ChemSketch, and ChemBioDraw Generating 3D structures Gauss View 3.0 and ChemBio3D Calculating chemical descriptors Gaussian 03, Marvin Sketch 6.2, ChemSketch, and ChemBio3D Developing QSAR models XLSTAT 2009 and Matlab 7.9.0 (version 2011)Table 3
The absolute values of correlation coefficients with descriptors and activities.
Descriptors r Promastigotes Henry’s law constant (KH) 0.130 Ideal gas thermal capacity (IGTC) 0.108 Number of H-Bond acceptors (NHA) 0.299 Number of H-Bond donors (NHD) 0.250 Balaban index (J) 0.133 Shape coefficient (I) 0.135 Total valence connectivity (TVC) 0.292 N% 0.238 H% 0.260 Gibbs free energy (G) 0.119 Dipole moment (μ) 0.213 Electronegativity (χ) 0.599 Electrophilicity index (ω) 0.630 Molecular topological index (MTI) 0.116 Polar surface area (PSA) 0.282 Total connectivity (TC) 0.269 Wiener index (W) 0.124 EHOMO 0.554 ELUMO 0.632 EGap 0.227 Amastigotes Total energy,E 0.160 EHOMO 0.286 Electronegativity (χ) 0.316 Polar surface area (PSA) 0.391 O% 0.105 Index of refraction (n) 0.548 Density (d) 0.242 Critical pressure (CP) 0.176 Gibbs free energy (G) 0.195 Henry’s law constant (KH) 0.387 Number of H-Bond acceptors (NHA) 0.198 Number of H-Bond donors (NHD) 0.587 Number of rotatable bonds (NRB) 0.139 Sum of valence degrees (SVD) 0.146 Dipole moment (μ) 0.224 ELUMO 0.338 Electrophilicity index (ω) 0.335 N% 0.436 C% 0.155 Surface tension (γ) 0.553 Boiling point (TB) 0.254 Critical temperature (CT) 0.276 Heat of formation (H°) 0.152 log⁡P 0.248 Melting point (T) 0.314 Partition coefficient (PC) 0.163 Shape coefficient (I) 0.176 Winner index (W) 0.103Table 4
Descriptors selected by the principal component analysis (PCA) and software packages used in the calculation of descriptors.
Software Descriptors Gaussian 03 Highest occupied molecular orbital energyEHOMO (eV); lowest unoccupied molecular orbital energy ELUMO (eV); hardness η (eV) = (ELUMO-EHOMO)/2; electronegativity χ (eV) = -(ELUMO+EHOMO)/2; electrophilicity index ω (eV) = χ2/2η; total energy E (eV); dipole moment μ (Debye); energy gap between EHOMO and ELUMO values EGap (eV)  ChemOffice Heat of formationH° (kJ mol−1); Gibbs free energy G (kJ mol−1); ideal gas thermal capacity (IGTC) (J mol−1 K−1); melting point T (Kelvin); critical temperature (CT) (Kelvin); boiling point (TB) (Kelvin); critical pressure (CP) (Bar); Henry’s law constant KH; total valence connectivity (TVC); partition coefficient (PC); molecular topological index (MTI); number of rotatable bonds (NRB); shape coefficient I; sum of valence degrees (SVD); total connectivity (TC)  ChemSketch Percent ratios of nitrogen, hydrogen, oxygen, and carbon atoms (N%; H%; O%; and C%); surface tensionγ (dyne/cm); index of refraction (n); density (d)  Marvin Sketch log ⁡ P; Winner index (W); number of H-Bond acceptors (NHA); number of H-Bond donors (NHD); Balaban index (J); polar surface area (PSA) (A°)2


## 2.1. Selection of Dataset and Generation of Molecular Descriptors

### 2.1.1. Selection of Dataset

In this stage, the datasets of the antileishmanial activities (against promastigotes and amastigotes forms of parasites) of various acridine derivatives (4-monosubstituted acridines, 3,6-disubstituted acridines, 4,5-disubstituted acridines, and 7-monosubstituted 9-chloro and 9-amino-2-methoxy acridines) were collected from previous works [22–24]. The molecular structures of the studied molecules with their antileishmanial activities are presented in Table 1. All experimental IC50 antileishmanial activity values (μM) were converted to the negative logarithm of IC50  pIC50=-log10⁡IC50.Table 1
Chemical structure and antileishmanial activities of studied compounds (see Figure8).
Number R1 R2 R3 R4 R5 R6 R7 p I C 50 b PROc AMAd 1 H NHCOCH3 H H H NHCOCH3 H −2.533 −0.653 2 H NHCOC2H5 H H H NHCOC2H5 H −2.204 −0.886 3 H NHCOC3H7 H H H NHCOC3H7 H −1.669 −1.107 4 H NHCOph H H H NHCOPh H −0.634 −0.041 5 H NHCO-p-PhCl H H H NHCO-p-PhCl H — 0.699 6 H NHCO-p-PhF H H H NHCO-p-PhF H −0.230 1.523 7 H NHCO-p-PhOMe H H H NHCO-p-PhOMe H −0.681 −0.041 8 H NHCO-m,p-Ph(OMe)2 H H H NHCO-m,p-Ph(OMe)2 H −1.207 0.097 9 H NHCOMe H H H NHCOph H −2.270 Toxa 10 H NHCOMe H H H NHCO-p-PhCl H −1.061 −0.462 11 H NHCOMe H H H NHCO-p-PhF H −2.123 0.174 12 H NHCOMe H H H NHCO-p-PhOMe H −1.939 Toxa 13 H NHCOMe H H H NHCO-m,p-Ph(OMe)2 H — −0.114 14 H H CH3 NH2 OMe H H 0.301 0.398 15 H H CH2OH NH2 OMe H H −0.732 −0.613 16 H H CH2Br NH2 OMe H H −0.556 −0.663 17 H H (CH2)2OCOOMe NH2 OMe H H −0.380 −0.114 18 H H (CH2)2OCO(CH2)2CH3 NH2 OMe H H −0.491 −0.398 19 H H (CH2)2OCOCH2CH(CH3)2 NH2 OMe H H −0.342 Toxa 20 H H (CH2)2OCOPh NH2 OMe H H 0.398 0.699 21 H H (CH2)2OCOPhF NH2 OMe H H −0.114 0.222 23 H H (CH2)2OCOPhOMe NH2 OMe H H −0.279 Toxa 24 H H CH3 Cl OMe H H −0.041 −0.362 25 H H CH2OH Cl OMe H H −2.262 −0.959 26 H H CH2Br Cl OMe H H −1.703 −1.170 27 H H (CH2)2OCOOMe Cl OMe H H −2.178 −1.877 28 H H (CH2)2OCO(CH2)2CH3 Cl OMe H H −1.707 −1.628 29 H H (CH2)2OCOCH2CH(CH3)2 Cl OMe H H −1.446 −1.561 30 H H (CH2)2OCOPh Cl OMe H H −2.135 Toxa 31 H H (CH2)2OCOPhF Cl OMe H H −2.295 −1.645 32 H H (CH2)2OCOPhCl Cl OMe H H −2.194 −2.191 33 H H (CH2)2OCOPhOMe Cl OMe H H −2.098 −2.088 34 CH2NH2 H H H H H H −0.230 −0.531 35 CH2OH H H H H H H Toxa −1.515 36 CH2NHCO(CH2)3Cl H H H H H H −1.655 −1.427 37 CH2OCO(CH2)3Cl H H H H H H −2.200 −2.185 38 CH2NHCOCH=CH2 H H H H H H −2.245 −0.833 39 CH2OCOCH=CH2 H H H H H H −1.464 — 40 CH2NHCOPh H H H H H H −1.654 −1.121 41 CH2OCOPh H H H H H H −1.885 Toxa 42 CH2NHCO-p-PhF H H H H H H −1.815 — 43 CH2OCO-p-PhF H H H H H H −1.741 Toxa 44 CH2NHCO-p-PhCl H H H H H H Toxa −1.004 45 CH2OCO-p-PhCl H H H H H H −1.790 −1.433 46 CH2NHCO-p-PhOMe H H H H H H −1.513 −0.973 47 CH2OCO-p-PhOMe H H H H H H −1.471 −0.869 48 CH2NHCO-p-PhNMe2 H H H H H H −1.539 −0.672 49 CH2OCO-p-PhNMe2 H H H H H H −1.819 Toxa 50 CH2NH2 H H H H H CH2NH2 −0.820 −0.531 51 CH2OH H H H H H CH2OH Toxa 0.222 52 CH2NHCO(CH2)3Cl H H H H H CH2NHCO(CH2)3Cl −0.663 −0.813 54 CH2NHCOCH=CH2 H H H H H CH2NHCOCHCH2 −1.061 Toxa 56 CH2NHCOPh H H H H H CH2NHCOPh −0.556 −1.236 57 CH2OCOPh H H H H H CH2OCOPh Toxa −0.716 58 CH2NHCO-p-PhF H H H H H CH2NHCO-p-PhF −0.756 −0.255 60 CH2NHCO-p-PhCl H H H H H CH2NHCO-p-PhCl — −1.562 62 CH2NHCO-p-PhOMe H H H H H CH2NHCO-p-PhOMe −1.797 Toxa 63 CH2OCO-p-PhOMe H H H H H CH2OCO-p-PhOMe Toxa −1.825 64 CH2NHCO-p-PhNMe2 H H H H H CH2NHCO-p-PhNMe2 −0.940 −0.724 65 CH2OCO-p-PhNMe2 H H H H H CH2OCO-p-PhNMe2 Toxa −1.667 aToxic: toxicity observed on human macrophages at concentrations that did not display antileishmanial activity; -p-: para; -m-: meta; bpIC50 = −log (IC50); cpIC50 AMA: antileishmanial activity against amastigotes parasite form; dpIC50 PRO: antileishmanial activity against promastigotes parasite form.


### 2.1.2. Molecular Descriptors Generation

A wide variety of molecular descriptors was calculated using Gaussian 03, ACD/ChemSketch, Marvin Sketch, and ChemOffice programs [25–28] to predict the correlation between these descriptors for the studied molecules with their antileishmanial activities and to develop linear (multiple linear regression (MLR)) and nonlinear (artificial neural network (ANN)) models. Tables 3 and 4 show the selected descriptors (using the PCA method; see more in descriptive analysis results) to be used in this study.


## 2.1.1. Selection of Dataset

In this stage, the datasets of the antileishmanial activities (against promastigotes and amastigotes forms of parasites) of various acridine derivatives (4-monosubstituted acridines, 3,6-disubstituted acridines, 4,5-disubstituted acridines, and 7-monosubstituted 9-chloro and 9-amino-2-methoxy acridines) were collected from previous works [22–24]. The molecular structures of the studied molecules with their antileishmanial activities are presented in Table 1. All experimental IC50 antileishmanial activity values (μM) were converted to the negative logarithm of IC50  pIC50=-log10⁡IC50.Table 1
Chemical structure and antileishmanial activities of studied compounds (see Figure8).
Number R1 R2 R3 R4 R5 R6 R7 p I C 50 b PROc AMAd 1 H NHCOCH3 H H H NHCOCH3 H −2.533 −0.653 2 H NHCOC2H5 H H H NHCOC2H5 H −2.204 −0.886 3 H NHCOC3H7 H H H NHCOC3H7 H −1.669 −1.107 4 H NHCOph H H H NHCOPh H −0.634 −0.041 5 H NHCO-p-PhCl H H H NHCO-p-PhCl H — 0.699 6 H NHCO-p-PhF H H H NHCO-p-PhF H −0.230 1.523 7 H NHCO-p-PhOMe H H H NHCO-p-PhOMe H −0.681 −0.041 8 H NHCO-m,p-Ph(OMe)2 H H H NHCO-m,p-Ph(OMe)2 H −1.207 0.097 9 H NHCOMe H H H NHCOph H −2.270 Toxa 10 H NHCOMe H H H NHCO-p-PhCl H −1.061 −0.462 11 H NHCOMe H H H NHCO-p-PhF H −2.123 0.174 12 H NHCOMe H H H NHCO-p-PhOMe H −1.939 Toxa 13 H NHCOMe H H H NHCO-m,p-Ph(OMe)2 H — −0.114 14 H H CH3 NH2 OMe H H 0.301 0.398 15 H H CH2OH NH2 OMe H H −0.732 −0.613 16 H H CH2Br NH2 OMe H H −0.556 −0.663 17 H H (CH2)2OCOOMe NH2 OMe H H −0.380 −0.114 18 H H (CH2)2OCO(CH2)2CH3 NH2 OMe H H −0.491 −0.398 19 H H (CH2)2OCOCH2CH(CH3)2 NH2 OMe H H −0.342 Toxa 20 H H (CH2)2OCOPh NH2 OMe H H 0.398 0.699 21 H H (CH2)2OCOPhF NH2 OMe H H −0.114 0.222 23 H H (CH2)2OCOPhOMe NH2 OMe H H −0.279 Toxa 24 H H CH3 Cl OMe H H −0.041 −0.362 25 H H CH2OH Cl OMe H H −2.262 −0.959 26 H H CH2Br Cl OMe H H −1.703 −1.170 27 H H (CH2)2OCOOMe Cl OMe H H −2.178 −1.877 28 H H (CH2)2OCO(CH2)2CH3 Cl OMe H H −1.707 −1.628 29 H H (CH2)2OCOCH2CH(CH3)2 Cl OMe H H −1.446 −1.561 30 H H (CH2)2OCOPh Cl OMe H H −2.135 Toxa 31 H H (CH2)2OCOPhF Cl OMe H H −2.295 −1.645 32 H H (CH2)2OCOPhCl Cl OMe H H −2.194 −2.191 33 H H (CH2)2OCOPhOMe Cl OMe H H −2.098 −2.088 34 CH2NH2 H H H H H H −0.230 −0.531 35 CH2OH H H H H H H Toxa −1.515 36 CH2NHCO(CH2)3Cl H H H H H H −1.655 −1.427 37 CH2OCO(CH2)3Cl H H H H H H −2.200 −2.185 38 CH2NHCOCH=CH2 H H H H H H −2.245 −0.833 39 CH2OCOCH=CH2 H H H H H H −1.464 — 40 CH2NHCOPh H H H H H H −1.654 −1.121 41 CH2OCOPh H H H H H H −1.885 Toxa 42 CH2NHCO-p-PhF H H H H H H −1.815 — 43 CH2OCO-p-PhF H H H H H H −1.741 Toxa 44 CH2NHCO-p-PhCl H H H H H H Toxa −1.004 45 CH2OCO-p-PhCl H H H H H H −1.790 −1.433 46 CH2NHCO-p-PhOMe H H H H H H −1.513 −0.973 47 CH2OCO-p-PhOMe H H H H H H −1.471 −0.869 48 CH2NHCO-p-PhNMe2 H H H H H H −1.539 −0.672 49 CH2OCO-p-PhNMe2 H H H H H H −1.819 Toxa 50 CH2NH2 H H H H H CH2NH2 −0.820 −0.531 51 CH2OH H H H H H CH2OH Toxa 0.222 52 CH2NHCO(CH2)3Cl H H H H H CH2NHCO(CH2)3Cl −0.663 −0.813 54 CH2NHCOCH=CH2 H H H H H CH2NHCOCHCH2 −1.061 Toxa 56 CH2NHCOPh H H H H H CH2NHCOPh −0.556 −1.236 57 CH2OCOPh H H H H H CH2OCOPh Toxa −0.716 58 CH2NHCO-p-PhF H H H H H CH2NHCO-p-PhF −0.756 −0.255 60 CH2NHCO-p-PhCl H H H H H CH2NHCO-p-PhCl — −1.562 62 CH2NHCO-p-PhOMe H H H H H CH2NHCO-p-PhOMe −1.797 Toxa 63 CH2OCO-p-PhOMe H H H H H CH2OCO-p-PhOMe Toxa −1.825 64 CH2NHCO-p-PhNMe2 H H H H H CH2NHCO-p-PhNMe2 −0.940 −0.724 65 CH2OCO-p-PhNMe2 H H H H H CH2OCO-p-PhNMe2 Toxa −1.667 aToxic: toxicity observed on human macrophages at concentrations that did not display antileishmanial activity; -p-: para; -m-: meta; bpIC50 = −log (IC50); cpIC50 AMA: antileishmanial activity against amastigotes parasite form; dpIC50 PRO: antileishmanial activity against promastigotes parasite form.


## 2.1.2. Molecular Descriptors Generation

A wide variety of molecular descriptors was calculated using Gaussian 03, ACD/ChemSketch, Marvin Sketch, and ChemOffice programs [25–28] to predict the correlation between these descriptors for the studied molecules with their antileishmanial activities and to develop linear (multiple linear regression (MLR)) and nonlinear (artificial neural network (ANN)) models. Tables 3 and 4 show the selected descriptors (using the PCA method; see more in descriptive analysis results) to be used in this study.


## 2.2. Descriptive Analysis

In this stage, the principal component analysis (PCA) was used to determine the nonlinearity and nonmulticollinearity among variables (descriptors) and to select descriptors that correlate with the activity. After that, the univariate partitioning (UP) method was used to form dissimilar clusters of compounds, to which the query compounds would be compared for determining the degree of similarity and dividing the dataset into training and test sets.


## 2.3. Statistical Analysis (Models Development and Evaluation)

In this stage, linear and nonlinear QSAR models were developed and evaluated to predict the activities of the test compounds. The study we conducted consists of the multiple linear regression (MLR) available in the XLSTAT software and the artificial neural network (ANN) available in the Matlab software.In order to propose models and to evaluate quantitatively the physicochemical effects of the substituents on the activities of molecules, we submitted the data matrix constituted obviously from the used variables (descriptors) corresponding to the dataset molecules to a descendant MLR analysis and to an ANN. We use the coefficientsR, R2, R2adj, MSE, and P value to select the best regression performance [29], where R is the correlation coefficient; R2 is the coefficient of determination; R2adj is the coefficient adjusted for degrees of freedom. Mean squared error (MSE) is the standard error of the coefficient of each descriptor and of the global model, which gives an indication of the valid inclusion of a descriptor in a QSAR model. P value is the probability (P) of Fisher statistics (F), which gives an indication of the probability that a QSAR is a chance correlation.In order to assess the significance of the models and accurate prediction ability for new compounds:(i)
we use an internal validation procedure (leave-one-out cross validation), whereby one compound is removed and the rebuilt model with the remaining molecules is used to predict the response of the eliminated compound. This one is then returned and a second is removed, and the cycle is repeated, and so on, until all compounds have been removed one by one, and an overall correlation coefficientRcv is computed;(ii)
after the model is built, an external prediction is necessary. In this one, the obtained model was used to predict the activities of a test set comprising compounds that are similar to those not used in the training set. This is usually performed by splitting a dataset into a training set and a test set, typically in a 1/5 ratio. Further, before performing the external validation of a model, it is very important to check for the presence of systematic error that violates the basic assumptions of the least squares regression model. If high systematic error (bias) is present in the model, then such model should be discarded and performing any external validation test is of no use on such biased model. Xternal Validation Plus is a tool that checks the presence of systematic errors in the model and further computes all the required external validation parameters, while judging the performance of actual prediction quality of a QSAR model based on recently proposed MAE-based criteria [30];(iii)
a model is valid only within its training domain and new molecules must be considered as belonging to the domain before the model is applied (OECD Principle 3 [31]). Without applicability domain (AD), each model can predict the activity of any compound, even with a completely different structure from those included in the study. Therefore, the AD is a tool to find out compounds that are outside the applicability domain of the built QSAR model and it detects outliers present in the training set compounds. There are several methods for defining the applicability domain (AD) of QSAR models [32], but the most common one is determining the leverage values hi  hi=xiTXTX-1xii=1,2,…,n for each compound, where xi is the descriptor row-vector of query compound, X is nxk-1 matrix of k model descriptor values for n training set compounds, and the superscript T refers to the transpose of matrix/vector [32, 33]. In this study, we use Williams plot; in this plot, the applicability domain is established inside a squared area within standard deviation ±x (in this study x=3; “three-sigma rule” [34]) and a leverage threshold h∗(h∗=3∗(k+1)/n) [35], where n is the number of training set compounds; k is the number of model descriptors. The leverage (h) greater than the warning leverage (h∗) suggested that the compound was very influential on the model [36]. The results of the leverage approach were compared with that of the simple approach introduced by Roy et al. [37].


### 2.3.1. Multiple Linear Regression (MLR)

The descendent multiple linear regression (MLR) analysis, based on the elimination of aberrant descriptors (one by one) until a valid model (including the critical probability:P value < 0.05 for all descriptors and the model complete), was employed to find a linear model of the activity of interest, which takes the following form:(1)Y=a0+∑i=1naixi,where Y is the studied activity, which is the dependent variable. a0 is the intercept of the equation. xi are the molecular descriptors. ai are the coefficients of those descriptors.This method is one of the most popular methods of QSAR/QSPR thanks to its simplicity in operation, reproducibility, and ability to allow easy interpretation of the features used. The important advantage of the linear regression analysis is that it is highly transparent; therefore, the algorithm is available and predictions can be made easily [38]. It has served also to select the descriptors used as the input parameters in the artificial neural network (ANN).


### 2.3.2. Artificial Neural Networks (ANN)

The artificial neural networks (ANN) are used in order to increase the probability of characterizing the compounds and to generate a predictive QSAR model between the set of molecular descriptors obtained from the MLR models and the observed activities values. The ANN model is done on the MATLAB R2009b software. It consists of three layers of neurons, called input layer, hidden layer, and output layer (Figure2). The input layer formed by a number of neurons equal to the number of descriptors obtained in the multiple linear regression models and the output layer represents the calculated activity values. For determination of the number of hidden neurons in the hidden layer, where all calculations of parameter optimization of neural networks are made, a parameter ρ has been proposed. The parameter ρ plays a major role in determining the best artificial neural network architecture [39, 40]; ρ is defined as follows:(2)ρ=number of data points in the training setsum of the number of connections in the ANN.In order to avoid overfitting or underfitting, it is recommended that the value of ρ should be between 1.00 and 3.00; if ρ<1, the network simply memorizes the data, whereas if ρ>3, the network is not able to generalize [41].Figure 2
The architecture used in our study of the artificial neural network.


## 2.3.1. Multiple Linear Regression (MLR)

The descendent multiple linear regression (MLR) analysis, based on the elimination of aberrant descriptors (one by one) until a valid model (including the critical probability:P value < 0.05 for all descriptors and the model complete), was employed to find a linear model of the activity of interest, which takes the following form:(1)Y=a0+∑i=1naixi,where Y is the studied activity, which is the dependent variable. a0 is the intercept of the equation. xi are the molecular descriptors. ai are the coefficients of those descriptors.This method is one of the most popular methods of QSAR/QSPR thanks to its simplicity in operation, reproducibility, and ability to allow easy interpretation of the features used. The important advantage of the linear regression analysis is that it is highly transparent; therefore, the algorithm is available and predictions can be made easily [38]. It has served also to select the descriptors used as the input parameters in the artificial neural network (ANN).


## 2.3.2. Artificial Neural Networks (ANN)

The artificial neural networks (ANN) are used in order to increase the probability of characterizing the compounds and to generate a predictive QSAR model between the set of molecular descriptors obtained from the MLR models and the observed activities values. The ANN model is done on the MATLAB R2009b software. It consists of three layers of neurons, called input layer, hidden layer, and output layer (Figure2). The input layer formed by a number of neurons equal to the number of descriptors obtained in the multiple linear regression models and the output layer represents the calculated activity values. For determination of the number of hidden neurons in the hidden layer, where all calculations of parameter optimization of neural networks are made, a parameter ρ has been proposed. The parameter ρ plays a major role in determining the best artificial neural network architecture [39, 40]; ρ is defined as follows:(2)ρ=number of data points in the training setsum of the number of connections in the ANN.In order to avoid overfitting or underfitting, it is recommended that the value of ρ should be between 1.00 and 3.00; if ρ<1, the network simply memorizes the data, whereas if ρ>3, the network is not able to generalize [41].Figure 2
The architecture used in our study of the artificial neural network.


## 2.4. Software Packages Used in Our QSAR Development Study

There are various free and commercial software available for QSAR development. These include specialized software for drawing chemical structures, generating 3D structures, calculating chemical descriptors, and developing QSAR models. The software packages used in our works are represented in Table2.Table 2
Software packages used in this work.
Drawing chemical structures Marvin Sketch, ACD/ChemSketch, and ChemBioDraw Generating 3D structures Gauss View 3.0 and ChemBio3D Calculating chemical descriptors Gaussian 03, Marvin Sketch 6.2, ChemSketch, and ChemBio3D Developing QSAR models XLSTAT 2009 and Matlab 7.9.0 (version 2011)Table 3
The absolute values of correlation coefficients with descriptors and activities.
Descriptors r Promastigotes Henry’s law constant (KH) 0.130 Ideal gas thermal capacity (IGTC) 0.108 Number of H-Bond acceptors (NHA) 0.299 Number of H-Bond donors (NHD) 0.250 Balaban index (J) 0.133 Shape coefficient (I) 0.135 Total valence connectivity (TVC) 0.292 N% 0.238 H% 0.260 Gibbs free energy (G) 0.119 Dipole moment (μ) 0.213 Electronegativity (χ) 0.599 Electrophilicity index (ω) 0.630 Molecular topological index (MTI) 0.116 Polar surface area (PSA) 0.282 Total connectivity (TC) 0.269 Wiener index (W) 0.124 EHOMO 0.554 ELUMO 0.632 EGap 0.227 Amastigotes Total energy,E 0.160 EHOMO 0.286 Electronegativity (χ) 0.316 Polar surface area (PSA) 0.391 O% 0.105 Index of refraction (n) 0.548 Density (d) 0.242 Critical pressure (CP) 0.176 Gibbs free energy (G) 0.195 Henry’s law constant (KH) 0.387 Number of H-Bond acceptors (NHA) 0.198 Number of H-Bond donors (NHD) 0.587 Number of rotatable bonds (NRB) 0.139 Sum of valence degrees (SVD) 0.146 Dipole moment (μ) 0.224 ELUMO 0.338 Electrophilicity index (ω) 0.335 N% 0.436 C% 0.155 Surface tension (γ) 0.553 Boiling point (TB) 0.254 Critical temperature (CT) 0.276 Heat of formation (H°) 0.152 log⁡P 0.248 Melting point (T) 0.314 Partition coefficient (PC) 0.163 Shape coefficient (I) 0.176 Winner index (W) 0.103Table 4
Descriptors selected by the principal component analysis (PCA) and software packages used in the calculation of descriptors.
Software Descriptors Gaussian 03 Highest occupied molecular orbital energyEHOMO (eV); lowest unoccupied molecular orbital energy ELUMO (eV); hardness η (eV) = (ELUMO-EHOMO)/2; electronegativity χ (eV) = -(ELUMO+EHOMO)/2; electrophilicity index ω (eV) = χ2/2η; total energy E (eV); dipole moment μ (Debye); energy gap between EHOMO and ELUMO values EGap (eV)  ChemOffice Heat of formationH° (kJ mol−1); Gibbs free energy G (kJ mol−1); ideal gas thermal capacity (IGTC) (J mol−1 K−1); melting point T (Kelvin); critical temperature (CT) (Kelvin); boiling point (TB) (Kelvin); critical pressure (CP) (Bar); Henry’s law constant KH; total valence connectivity (TVC); partition coefficient (PC); molecular topological index (MTI); number of rotatable bonds (NRB); shape coefficient I; sum of valence degrees (SVD); total connectivity (TC)  ChemSketch Percent ratios of nitrogen, hydrogen, oxygen, and carbon atoms (N%; H%; O%; and C%); surface tensionγ (dyne/cm); index of refraction (n); density (d)  Marvin Sketch log ⁡ P; Winner index (W); number of H-Bond acceptors (NHA); number of H-Bond donors (NHD); Balaban index (J); polar surface area (PSA) (A°)2


## 3. Results and Discussions

### 3.1. Principal Component Analysis (PCA)

PCA is a useful statistical technique for summarizing all the information encoded in the structures of the compounds. It is very helpful for understanding the distribution of the compounds. This is an essentially descriptive statistical method, which aims to extract the maximum of information contained in the dataset compounds [42, 43]. In this work, the PCA is used to overview the examined compounds for similarities and dissimilarities and to select descriptors that show a high correlation with the response activity; this one gives extra weight because it will be more effective at prediction [44]. Tables 3 and 4 present the descriptors with a correlation coefficient with the activity higher, in absolute value, than 0.1. The absence of any serious multicollinearity between the descriptors present in the model was confirmed by the correlation matrix.


### 3.2. Univariate Partitioning (UP)

The aim of the UP was the recognition of groups of objects based on their similarity; this method is based on the criterion of partitioning proposed by Fisher [45]. In this study, the division of the dataset into training and test sets has been performed. In this one, from each obtained cluster, one compound for the training set was selected randomly to be used as test set compound. The partitioning results are given in Table 5.Table 5
The partitioning results of compounds into training and test sets.
Classes The test set compounds Promastigotes Amastigotes 3, 6, 10, 14, 17, 21, 37, 38, 42, 64 5, 6, 26, 27, 29, 36, 37, 44, 46, 50 1 1, 8,37, 40, 56 1, 10, 15, 16, 34, 48,50, 57, 64 2 2,14, 29, 34, 48 2, 25, 38,44, 47, 51, 52 3 3, 18, 19 3,26, 40, 56 4 4, 24, 25, 27, 30,42, 58 4, 7, 8, 11, 13, 17, 21,46 5 6, 26 5, 14, 20 6 7, 9, 12,21, 33, 39, 41, 47 6 7 10, 11, 16, 31, 32, 43, 45 18,29, 58 8 15,17, 23, 28, 36, 49, 52, 54 27, 63 9 20,38, 46, 62 24, 28, 31, 35,36, 45, 60, 65 10 50,64 32, 33,37


### 3.3. Multiple Linear Regression (MLR)

The QSAR analysis was performed using the values of the chemical descriptors selected by the PCA method and, on the other hand, the experimental values of the antileishmanial activities for 60 of the acridines derivatives (effect). Table  S1 in Supplementary Material available online athttp://dx.doi.org/10.1155/2016/5137289 shows the value of each molecular descriptor that is configured in established MLR models and the QSAR model built is represented by the following equations and the values of the statistical parameters.MLR Model for pIC 50 Promastigotes  (3) p I C 50 P R O = 3.030 - 8.214   10 - 02 N % + 0.239 μ - 1.264 ω - 0.233 N H A + 0.732 N H D + 3.311   10 - 05 M T I + 3.184   10 4 T V C .  Statistical Parameters. R2=0.723; R=0.850; R2adj=0.664; MSE=0.189;P value < 10−4.MLR Model for pIC 50 Amastigotes  (4) p I C 50 A M A = - 7.314 + 1.191 E H O M O + 2.543   10 - 02 C T - 0.350 K H - 1.632   10 - 02 T + 0.652 N H A + 1.262 N H D .  Statistical Parameters. R2=0.663; R=0.814; R2adj=0.598; MSE=0.208; P value < 10−4.(i)
For the two models,P value is lower than 0.0001; it means that we would be taking a lower than 0.01% risk in assuming that the null hypothesis (no effect of the explanatory variables) is wrong and that the regressions equations have statistical significance. Therefore, we can conclude with confidence that the selected variables do bring a significant amount of information.(ii)
Higher value ofR2 and R2adj and lower mean squared error (MSE) indicate that the two proposed models are predictive and reliable.(iii)
Our obtained models were validated internally by the leave-one-out cross validation technique; the cross validation coefficientR2cv for the two models was determined based on the predictive ability of the model. The value of R2cv is higher than 0.5 (R2cv=0.536 for the MLR pIC50 (PRO) model and R2cv=0.525 for the MLR pIC50 (AMA) model); indicating good predictability of the model.(iv)
True predictive power of these models is to test their ability to predict perfectlypIC50 of compounds from an external test set (compounds that were not used for the developed model); pIC50 of the remaining set of 10 compounds are deduced from the quantitative models proposed with the compounds used in training set by MLR. These models will be able to predict the activities of test set molecules in agreement with the experimentally determined value. The observed and calculated pIC50 values are given in Table 6. The predictive capacity of the models was judged, the higher value of R2test (R2test=0.660 for the MLR pIC50 (PRO) model and R2test=0.718 for the MLR pIC50 (AMA) model) indicates the improved predictability of the model.(v)
Xternal Validation Plus indicates the absence of systematic errors in the model and a moderate performance of prediction quality of a QSAR model based on proposed MAE-based criteria (Table  S2).(vi)
The values of calculated activities from (3) and (4) are given in Table  S1 and the correlations of calculated and observed activities values are illustrated in Figure 3.In the first model (pIC50 PRO), the descriptors influencing negatively the activities are the percent ratio of nitrogen (N%), the number of H-Bond acceptors (NHA), and the electrophilicity index (ω), and the parameters influencing positively the activities are the dipole moment (μ), the number of H-Bond donors (NHD), the molecular topological index (MTI), and the total valence connectivity (TVC).(i)
The number of H-Bond acceptors (NHA) has a negative sign in the model, which suggests that increased activity can be achieved by decreasing the number of heteroatoms (nitrogen or oxygen atoms), mostly the nitrogen ones for decreasing the ratio of nitrogen(N%) having also a negative sign in the model.(ii)
The electrophilicity indexω has a negative sign in the model, which suggests that increased activity can be achieved by decreasing the electrophilicity of the acridine derivatives (a high value of electrophilicity describes a good electrophile, while a small value of electrophilicity describes a good nucleophile).(iii)
The dipole momentμ has a positive sign in the model, which suggests that increased activity can be achieved by increasing the polarity of the acridine derivatives.(iv)
The number of H-Bond donors (NHD) has a positive sign in the model, which suggests that increased activity can be achieved by increasing of the heteroatom with one or more hydrogen atoms.(v)
The molecular topological index (MTI) coefficient (topological parameter) has a negative sign in the model, which suggests that increased activity can be achieved by increasing the flexibility of the substituent side chain.(vi)
The total valence connectivity (TVC) (topological parameter) has a positive sign in the model, which suggests that increased activity can be achieved by increasing in branching of the acridine derivatives, because the overall connectivity increases with both molecule size and complexity, as expressed in branching and cyclicity of molecular skeleton [46].In the second model (pIC50 AMA), the descriptors influencing negatively the activity are Henry’s law constant (KH) and the melting point (T), and the parameters influencing positively the activities are EHOMO energy, the critical temperature (CT), the number of H-Bond acceptors (NHA), and the number of H-Bond donors (NHD).(i)
Henry’s law constant (KH) has a negative sign in the model, which suggests that increased activity can be achieved by decreasing solubility; consequently, by decreasing the polarity, KH=c/p (c: solubility; p: pressure).(ii)
The melting point(T) has a negative sign in the model, which suggests that increased activity can be achieved by decreasing the polarity and the branching of molecule (increasing branching makes the molecule less compact. As the surface area of the molecule decreases, it will become more compact and thus easier to pack).(iii)
The highest occupied molecular orbital energyEHOMO (negative values) has a positive sign in the model, which suggests that the higher of EHOMO, the weaker donating electron ability, is showing the fact that the nucleophilic reaction occurs more easily and the activity of the compound is higher.(iv)
The critical temperature (CT) has a positive sign in the model, which suggests that increased activity can be achieved by increasing the critical temperature.(v)
The number of H-Bond acceptors (NHA) has a positive sign in the model, which suggests that increased activity can be achieved by increasing the number of heteroatoms (nitrogen or oxygen atoms).(vi)
The number of H-Bond donors (NHD) has a positive sign in the model, which suggests that increased activity can be achieved by increasing of the heteroatoms with one or more hydrogen atoms.Comparing the importance of each descriptor on pIC50 of acridines, we must know the standardized coefficient and the t-test values of them in the MLR equations. The bigger the absolute value of the t-test value is, the greater the influence of the descriptor is.Table 6
The values of chemical descriptors and the observed and predicted activities using the MLR models for the test set.
Test set (promastigotes) pIC50 PRO Number N% μ ω NHA NHD MTI TVC Obs. MLR 3 12.030 4.259 5.024 3 2 14075 3.891 10−07 −1.669 −2.047 6 9.270 5.640 4.654 5 2 28763 1.716 10−10 −0.230 −1.014 10 10.780 5.730 5.267 3 2 16459 4.902 10−08 −1.061 −1.832 14 11.760 2.698 3.062 3 1 4387 3.050 10−05 0.301 −0.012 17 8.580 4.969 3.431 4 1 10329 5.188 10−07 −0.380 −0.664 21 7.180 5.214 3.498 5 1 18600 1.334 10−08 −0.114 −0.551 37 4.460 6.939 4.779 2 0 8245 4.076 10−06 −2.200 −1.781 38 10.680 5.122 4.374 2 1 6388 5.083 10−06 −2.245 −1.512 42 8.480 5.260 4.457 3 1 12005 1.307 10−07 −1.815 −1.608 64 13.170 5.297 4.388 5 2 47653 1.201 10−10 −0.940 −0.455  Test set (amastigotes) pIC50 AMA Number E H O M O K H T NHA NHD CT Obs. MLR  5 −5.850 1064.61 1300.866 3 2 19.110 0.699 −0.787 6 −5.785 1005.95 1247.456 5 2 18.715 1.523 0.332 26 −5.665 583.700 926.651 2 0 7.815 −1.170 −1.456 27 −5.603 622.270 930.050 3 0 8.827 −1.877 −1.628 29 −5.640 618.850 938.380 3 0 9.007 −1.561 −1.467 36 −5.966 676.650 1037.977 2 1 12.201 −1.427 −0.774 37 −6.025 552.770 930.967 2 0 8.348 −2.185 −1.457 44 −5.919 749.400 1083.064 2 1 12.828 −1.004 −0.978 46 −5.790 752.980 1078.419 3 1 13.925 −0.973 −0.733 50 −5.461 625.750 913.563 3 2 13.449 −0.531 −1.028Figure 3
Correlations of observed and predicted activities (training set in black and test set in red) values calculated using MLR models.In (3), the t-test values are 1.773, −4.035, 7.408, 1.720, −3.361, −2.429, and −4.570 for N%, μ, ω, NHA, NHD, MTI, and TVC, respectively. Moreover, in (4), the t-test values are 3.196, 3.556, −3.764, −3.802, −3.838, and −6.012 for T, KH, CT, EHOMO, NHA, and NHD, respectively.This meant that thet-test values of ω, μ, NHD, and TVC are both larger than those of the other descriptors, which indicates that, in this model, the influence of these descriptors on activity is stronger than that of the others. It shows also the importance of electrophilicity index in the prediction of pIC50 PRO. Moreover, the t-test value of NHD is larger than that of the other descriptors, which indicates that the influence of this descriptor, in this model, on activity is stronger than that of the others.In the conclusion, these results illustrate that, to increase the antileishmanial activity against promastigotes parasites, we will decrease the electrophilicity and increase the branching, the polarity, and the number of hydrogen atoms attached in the heteroatom of the acridine derivatives. Moreover, to increase the antileishmanial activity against amastigotes parasites, we will decrease the solubility, the polarity, and the branching and increase the electrophilicity and the number of heteroatoms mostly attached in the hydrogen atoms and the critical temperature of the acridine derivatives.(i) Detection of Outliners: Applicability Domain (AD). The applicability domain (AD) of these models was evaluated by leverage analysis expressed as Williams plot (Figures 4 and 5), in which the standardized residuals (r) and the leverage threshold values (h∗=0.585 and 0.553 for pIC50 (PRO) and pIC50 (AMA), resp.) were plotted. Any new value of predicted pIC50 data must be considered reliable only for those compounds that fall within this AD on which the model was constructed.Figure 4
Williams plot of standardized residual versus leverage forpIC50 (PRO) MLR model (with h∗=0.585 and residual limits =±3).Figure 5
Williams plot of standardized residual versus leverage forpIC50 (AMA) MLR model (with h∗=0.553 and residual limits =±3).From these figures, it is obvious that there is no response outlier in training set and no response outside in test set. Only one chemical is identified as outside for MLR model forpIC50 PRO and two chemicals for MLR model for pIC50 AMA; these outsides compounds are given as follows.For pIC 50 PRO. Compound number64 in test set has higher leverage which is greater than h∗ value of 0.585 and all the compounds have a standard deviation into ±x interval (x=3).For pIC 50 AMA. Compounds numbers5 and6 in test set have a standard deviation value greater than the ±x interval (x=3).These results are confirmed using the simple approach (Tables  S3 and  S4), the chemical number 8 is identified as outlier and the chemical number64 is identified as outside for MLR model for pIC50 PRO, and any chemical is identified as outside or outlier for MLR model for pIC50 AMA.These erroneous predictions could probably be attributed to wrong experimental data or to the structure of these outsides; Cl, F, or NMe2 substitutes the tree compounds at the para position of the phenyl ring (Figure 6); maybe the selected descriptors do not pay much attention to these special substructures. The predictions of tree compounds are extrapolations of the model, but fortunately they are all “good leverage” chemicals.Figure 6
Chemical structures of the outsides compounds.


### 3.4. Artificial Neural Network (ANN)

In this study, we used a feed forward network with two layers, with a sigmoid transfer function in the hidden layer and a linear transfer function in the output layer (Figure2). The architecture of the artificial neural network used in this work was 7-3-1 and ρ=1.82 for pIC50 (PRO) and 6-3-1 and ρ=2 for pIC50 (AMA).The output layer represents the calculated activity values (predictedpIC50). The calculation result and the performance of established models are recorded in the output layer.To justify the predictive quality of models, total data are distributed randomly into three groups. The first group (70% of the total data) used to drive the system. The second group (15% of the total data) will be used to validate the network; and the remaining 15% that did not participate in the learning models will be used as an independent test of network generalization. The distribution of the total data into training, validation, and test sets is shown in Table7.Table 7
The coefficient of determination, the coe1fficient of correlation, and the MSE obtained by the model established by the ANN for the three phases: Training, validation, and test.
pIC50 PRO Model n = 51; MSE = 0.079; R2 = 0.870; R = 0.933 Training set [1; 3; 4; 5; 6; 7; 11; 12; 13; 14; 16; 19; 21; 25; 26; 27; 28; 30; 32; 34; 35; 36; 37; 38; 39; 40; 41; 43; 44; 46; 47; 48; 49; 50; 51] MSE = 0.044;R2 = 0.914; R = 0.956 Validation set [8; 17; 18; 22; 23; 24; 29; 31] MSE = 0.125;R2 = 0.922; R = 0.960 Test set [2; 9; 10; 15; 20; 33; 42; 45] MSE = 0.186;R2 = 0.725; R = 0.851  pIC50 AMA  Model n = 48; MSE = 0.104; R2 = 0.918; R = 0.843 Training set [2; 3; 4; 5; 6; 7; 10; 11; 13; 16; 18; 19; 20; 21; 23; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 41; 43; 44; 45; 46; 47] MSE = 0.060;R2 = 0.897; R = 0.947 Validation set [1; 8; 14; 15; 17; 24; 25] MSE = 0.198;R2 = 0.710; R = 0.843 Test set [9; 12; 22; 26; 40; 42; 48] MSE = 0.228;R2 = 0.791; R = 0.890The correlation between the experimental and calculated values using the artificial neural network models is highly significant, as illustrated in Figure7 and as indicated by better R and R2 and the small MSE values for all three phases: training, validation, and test (Table 7). The predicted activities calculated with the artificial neural network and the observed values are given in Table  S5.Figure 7
Correlations between observed and predicted activities values calculated using ANN models (training set in black, validation set in red, and test set in blue).Figure 8The results obtained by MLR and ANN are very sufficient to conclude the performance of the models. A comparison of the quality of the statistical terms of these models shows that the ANN has substantially better predictive capability. ANN was able to establish a more satisfactory relationship between the molecular descriptors and the activity of the studied compounds compared to MLR; but the most negative side of this method is the fact that it is poorly transparent, whereas transparency of MLR approach gives the most interpretable results and gives a good explanation of activities with descriptors. Consequently, we can design new compounds with improved values of activity compared to the studied compounds using the MLR models. Taking into account the above results, we added suitable substitutions and then we moved to calculate their activities using the proposed models equations ((3) and (4)). Therefore, the suggested models will reduce the time and cost of synthesis as well as the determination of the antileishmanial activities against promastigotes and amastigotes forms of parasites for the acridine derivatives.


### 3.5. Design New Compounds with Higher Antileishmanial Activities

According to the above discussions, the MLR models could be applied to other acridines derivatives according to Table1 and could add further knowledge in the improvement of new way in antileishmanial drug research. If we develop a new compound with better values than the existing ones, it may give rise to the development of more active compounds than those currently in use.In this way, we carried out structural modification starting from compounds having the highestpIC50 values as template (number14 and number 20). The structures of the designed compounds and their parameter values calculated by the same methods as well as pIC50 values theoretically predicted by the MLR models are listed in Table 8.Table 8
Values of descriptors, antileishmanial activity pIC50, and leverages (h) for the new designed compounds.
Designed compounds Number Descriptors values pIC50 (PRO) Number Descriptors values pIC50 (AMA) X 1 R1 = OH; R2 = CH3 N% = 12.490; μ = 2.232; ω = 3.099 NHA = 3; NHD = 2; MTI = 3651 TVC = 3.34 10−05 0.571 Y 1 R1 = OCH3; R2 = CF3  EHOMO = −5.235; CT = 885.365; KH = 9.302;  T = 581.430; NHA = 6; NHD = 1 1.395 Y 2 R1 = OH; R2 = CF3  EHOMO = −5.312; CT = 903.801; KH = 12.056;  T = 647.130; NHA = 6; NHD = 2 0.998 Y 3 R1 = OCH3; R2 = F EHOMO = −5.034; CT = 893.897; KH = 10.174;  T = 566.560; NHA = 4; NHD = 1 0.485 X 2 R1 = OH; R2 = OH N% = 12.380; μ = 1.080; ω = 3.131 NHA = 4; NHD = 3; MTI = 3497 TVC = 1.49 10−05 0.170 Y 4 R1 = R2 = OC2H5  EHOMO = −4.696; CT = 927.241; KH = 11.222;  T = 622.010; NHA = 4; NHD = 1 0.464 Y 5 R1 = R2 = OCH3  EHOMO = −4.731; CT = 916.967; KH = 11.469;  T = 599.470; NHA = 4; NHD = 1 0.442 Y 6 R1 = OCH3; R2 = OC(CH3)3  EHOMO = −4.872; CT = 928.656; KH = 11.099;  T = 635.700; NHA = 4; NHD = 1 0.109 Y 7 R1 = OCH3; R2 = CH2NH2  EHOMO = −4.801; CT = 934.561; KH = 14.185; T = 660.500; NHA = 4; NHD = 2 0.122  X 3 R1 = OH; R2 = meta-NH2 N% = 11.250; μ = 5.944; ω = 3.392 NHA = 5; NHD = 3; MTI = 17128 TVC = 2.23 10−08 0.838 Y 8 R1 = OCH3; R2 = para, meta -F: EHOMO = −5.081; CT = 1006.097; KH = 13.267; T = 762.370; NHA = 6; NHD = 1 0.308 X 4 R1 = OCH3; R2 = para-NH2 N% = 10.850; μ = 7.114; ω = 3.295 NHA = 5; NHD = 2; MTI = 19138 TVC = 2.04 10−08 0.607 Y 9 R1 = OCH3; R2 = para NH2: EHOMO = −4.966; CT = 1066.417;  KH = 16.853; T = 831.93; NHA = 5; NHD = 2 0.199 X 5 R1 = OCH3; R2 = meta-NH2 N% = 10.850; μ = 6.193; ω = 3.353 NHA = 5; NHD = 2; MTI = 18992 TVC = 2.04 10−08 0.309 Y 10 R1 = OCH3; R2 = meta NH2: EHOMO = −4.993; CT = 1066.417; KH = 16.853; T = 831.930; NHA = 5; NHD = 2 0.166 X 6 R1 = OH; R2 = H N% = 7.820; μ = 5.631; ω = 3.483 NHA = 4; NHD = 2; MTI = 15585 TVC = 4.47 10−08 0.381From the predicted activities, it has been observed that the designed compounds have higherpIC50 values than the existing compounds in the case of the 60 studied compounds (Table 1).The leverage values(h) for the new designed compounds are 0.268, 0.602, 0.775, 0.527, 0.386, and 0.369 for X1,X2,…,X6, respectively, and 0.649, 0.797, 0.201, 0.251, 0.235, 0.166, 0.176, 0.339, 0.169, and 0.166 for Y1,Y2,…,Y10, respectively (Table 8). Only compounds X2, X3, Y1, and Y2 are defined as outliers and consequently they are not be considered, because they have higher leverage which is greater than h∗ (0.585 for pIC50 (PRO) and 0.553 for pIC50 (AMA)); we suggest all other compounds as candidates that will be synthetized and evaluated as antileishmanial drugs.


## 3.1. Principal Component Analysis (PCA)

PCA is a useful statistical technique for summarizing all the information encoded in the structures of the compounds. It is very helpful for understanding the distribution of the compounds. This is an essentially descriptive statistical method, which aims to extract the maximum of information contained in the dataset compounds [42, 43]. In this work, the PCA is used to overview the examined compounds for similarities and dissimilarities and to select descriptors that show a high correlation with the response activity; this one gives extra weight because it will be more effective at prediction [44]. Tables 3 and 4 present the descriptors with a correlation coefficient with the activity higher, in absolute value, than 0.1. The absence of any serious multicollinearity between the descriptors present in the model was confirmed by the correlation matrix.


## 3.2. Univariate Partitioning (UP)

The aim of the UP was the recognition of groups of objects based on their similarity; this method is based on the criterion of partitioning proposed by Fisher [45]. In this study, the division of the dataset into training and test sets has been performed. In this one, from each obtained cluster, one compound for the training set was selected randomly to be used as test set compound. The partitioning results are given in Table 5.Table 5
The partitioning results of compounds into training and test sets.
Classes The test set compounds Promastigotes Amastigotes 3, 6, 10, 14, 17, 21, 37, 38, 42, 64 5, 6, 26, 27, 29, 36, 37, 44, 46, 50 1 1, 8,37, 40, 56 1, 10, 15, 16, 34, 48,50, 57, 64 2 2,14, 29, 34, 48 2, 25, 38,44, 47, 51, 52 3 3, 18, 19 3,26, 40, 56 4 4, 24, 25, 27, 30,42, 58 4, 7, 8, 11, 13, 17, 21,46 5 6, 26 5, 14, 20 6 7, 9, 12,21, 33, 39, 41, 47 6 7 10, 11, 16, 31, 32, 43, 45 18,29, 58 8 15,17, 23, 28, 36, 49, 52, 54 27, 63 9 20,38, 46, 62 24, 28, 31, 35,36, 45, 60, 65 10 50,64 32, 33,37


## 3.3. Multiple Linear Regression (MLR)

The QSAR analysis was performed using the values of the chemical descriptors selected by the PCA method and, on the other hand, the experimental values of the antileishmanial activities for 60 of the acridines derivatives (effect). Table  S1 in Supplementary Material available online athttp://dx.doi.org/10.1155/2016/5137289 shows the value of each molecular descriptor that is configured in established MLR models and the QSAR model built is represented by the following equations and the values of the statistical parameters.MLR Model for pIC 50 Promastigotes  (3) p I C 50 P R O = 3.030 - 8.214   10 - 02 N % + 0.239 μ - 1.264 ω - 0.233 N H A + 0.732 N H D + 3.311   10 - 05 M T I + 3.184   10 4 T V C .  Statistical Parameters. R2=0.723; R=0.850; R2adj=0.664; MSE=0.189;P value < 10−4.MLR Model for pIC 50 Amastigotes  (4) p I C 50 A M A = - 7.314 + 1.191 E H O M O + 2.543   10 - 02 C T - 0.350 K H - 1.632   10 - 02 T + 0.652 N H A + 1.262 N H D .  Statistical Parameters. R2=0.663; R=0.814; R2adj=0.598; MSE=0.208; P value < 10−4.(i)
For the two models,P value is lower than 0.0001; it means that we would be taking a lower than 0.01% risk in assuming that the null hypothesis (no effect of the explanatory variables) is wrong and that the regressions equations have statistical significance. Therefore, we can conclude with confidence that the selected variables do bring a significant amount of information.(ii)
Higher value ofR2 and R2adj and lower mean squared error (MSE) indicate that the two proposed models are predictive and reliable.(iii)
Our obtained models were validated internally by the leave-one-out cross validation technique; the cross validation coefficientR2cv for the two models was determined based on the predictive ability of the model. The value of R2cv is higher than 0.5 (R2cv=0.536 for the MLR pIC50 (PRO) model and R2cv=0.525 for the MLR pIC50 (AMA) model); indicating good predictability of the model.(iv)
True predictive power of these models is to test their ability to predict perfectlypIC50 of compounds from an external test set (compounds that were not used for the developed model); pIC50 of the remaining set of 10 compounds are deduced from the quantitative models proposed with the compounds used in training set by MLR. These models will be able to predict the activities of test set molecules in agreement with the experimentally determined value. The observed and calculated pIC50 values are given in Table 6. The predictive capacity of the models was judged, the higher value of R2test (R2test=0.660 for the MLR pIC50 (PRO) model and R2test=0.718 for the MLR pIC50 (AMA) model) indicates the improved predictability of the model.(v)
Xternal Validation Plus indicates the absence of systematic errors in the model and a moderate performance of prediction quality of a QSAR model based on proposed MAE-based criteria (Table  S2).(vi)
The values of calculated activities from (3) and (4) are given in Table  S1 and the correlations of calculated and observed activities values are illustrated in Figure 3.In the first model (pIC50 PRO), the descriptors influencing negatively the activities are the percent ratio of nitrogen (N%), the number of H-Bond acceptors (NHA), and the electrophilicity index (ω), and the parameters influencing positively the activities are the dipole moment (μ), the number of H-Bond donors (NHD), the molecular topological index (MTI), and the total valence connectivity (TVC).(i)
The number of H-Bond acceptors (NHA) has a negative sign in the model, which suggests that increased activity can be achieved by decreasing the number of heteroatoms (nitrogen or oxygen atoms), mostly the nitrogen ones for decreasing the ratio of nitrogen(N%) having also a negative sign in the model.(ii)
The electrophilicity indexω has a negative sign in the model, which suggests that increased activity can be achieved by decreasing the electrophilicity of the acridine derivatives (a high value of electrophilicity describes a good electrophile, while a small value of electrophilicity describes a good nucleophile).(iii)
The dipole momentμ has a positive sign in the model, which suggests that increased activity can be achieved by increasing the polarity of the acridine derivatives.(iv)
The number of H-Bond donors (NHD) has a positive sign in the model, which suggests that increased activity can be achieved by increasing of the heteroatom with one or more hydrogen atoms.(v)
The molecular topological index (MTI) coefficient (topological parameter) has a negative sign in the model, which suggests that increased activity can be achieved by increasing the flexibility of the substituent side chain.(vi)
The total valence connectivity (TVC) (topological parameter) has a positive sign in the model, which suggests that increased activity can be achieved by increasing in branching of the acridine derivatives, because the overall connectivity increases with both molecule size and complexity, as expressed in branching and cyclicity of molecular skeleton [46].In the second model (pIC50 AMA), the descriptors influencing negatively the activity are Henry’s law constant (KH) and the melting point (T), and the parameters influencing positively the activities are EHOMO energy, the critical temperature (CT), the number of H-Bond acceptors (NHA), and the number of H-Bond donors (NHD).(i)
Henry’s law constant (KH) has a negative sign in the model, which suggests that increased activity can be achieved by decreasing solubility; consequently, by decreasing the polarity, KH=c/p (c: solubility; p: pressure).(ii)
The melting point(T) has a negative sign in the model, which suggests that increased activity can be achieved by decreasing the polarity and the branching of molecule (increasing branching makes the molecule less compact. As the surface area of the molecule decreases, it will become more compact and thus easier to pack).(iii)
The highest occupied molecular orbital energyEHOMO (negative values) has a positive sign in the model, which suggests that the higher of EHOMO, the weaker donating electron ability, is showing the fact that the nucleophilic reaction occurs more easily and the activity of the compound is higher.(iv)
The critical temperature (CT) has a positive sign in the model, which suggests that increased activity can be achieved by increasing the critical temperature.(v)
The number of H-Bond acceptors (NHA) has a positive sign in the model, which suggests that increased activity can be achieved by increasing the number of heteroatoms (nitrogen or oxygen atoms).(vi)
The number of H-Bond donors (NHD) has a positive sign in the model, which suggests that increased activity can be achieved by increasing of the heteroatoms with one or more hydrogen atoms.Comparing the importance of each descriptor on pIC50 of acridines, we must know the standardized coefficient and the t-test values of them in the MLR equations. The bigger the absolute value of the t-test value is, the greater the influence of the descriptor is.Table 6
The values of chemical descriptors and the observed and predicted activities using the MLR models for the test set.
Test set (promastigotes) pIC50 PRO Number N% μ ω NHA NHD MTI TVC Obs. MLR 3 12.030 4.259 5.024 3 2 14075 3.891 10−07 −1.669 −2.047 6 9.270 5.640 4.654 5 2 28763 1.716 10−10 −0.230 −1.014 10 10.780 5.730 5.267 3 2 16459 4.902 10−08 −1.061 −1.832 14 11.760 2.698 3.062 3 1 4387 3.050 10−05 0.301 −0.012 17 8.580 4.969 3.431 4 1 10329 5.188 10−07 −0.380 −0.664 21 7.180 5.214 3.498 5 1 18600 1.334 10−08 −0.114 −0.551 37 4.460 6.939 4.779 2 0 8245 4.076 10−06 −2.200 −1.781 38 10.680 5.122 4.374 2 1 6388 5.083 10−06 −2.245 −1.512 42 8.480 5.260 4.457 3 1 12005 1.307 10−07 −1.815 −1.608 64 13.170 5.297 4.388 5 2 47653 1.201 10−10 −0.940 −0.455  Test set (amastigotes) pIC50 AMA Number E H O M O K H T NHA NHD CT Obs. MLR  5 −5.850 1064.61 1300.866 3 2 19.110 0.699 −0.787 6 −5.785 1005.95 1247.456 5 2 18.715 1.523 0.332 26 −5.665 583.700 926.651 2 0 7.815 −1.170 −1.456 27 −5.603 622.270 930.050 3 0 8.827 −1.877 −1.628 29 −5.640 618.850 938.380 3 0 9.007 −1.561 −1.467 36 −5.966 676.650 1037.977 2 1 12.201 −1.427 −0.774 37 −6.025 552.770 930.967 2 0 8.348 −2.185 −1.457 44 −5.919 749.400 1083.064 2 1 12.828 −1.004 −0.978 46 −5.790 752.980 1078.419 3 1 13.925 −0.973 −0.733 50 −5.461 625.750 913.563 3 2 13.449 −0.531 −1.028Figure 3
Correlations of observed and predicted activities (training set in black and test set in red) values calculated using MLR models.In (3), the t-test values are 1.773, −4.035, 7.408, 1.720, −3.361, −2.429, and −4.570 for N%, μ, ω, NHA, NHD, MTI, and TVC, respectively. Moreover, in (4), the t-test values are 3.196, 3.556, −3.764, −3.802, −3.838, and −6.012 for T, KH, CT, EHOMO, NHA, and NHD, respectively.This meant that thet-test values of ω, μ, NHD, and TVC are both larger than those of the other descriptors, which indicates that, in this model, the influence of these descriptors on activity is stronger than that of the others. It shows also the importance of electrophilicity index in the prediction of pIC50 PRO. Moreover, the t-test value of NHD is larger than that of the other descriptors, which indicates that the influence of this descriptor, in this model, on activity is stronger than that of the others.In the conclusion, these results illustrate that, to increase the antileishmanial activity against promastigotes parasites, we will decrease the electrophilicity and increase the branching, the polarity, and the number of hydrogen atoms attached in the heteroatom of the acridine derivatives. Moreover, to increase the antileishmanial activity against amastigotes parasites, we will decrease the solubility, the polarity, and the branching and increase the electrophilicity and the number of heteroatoms mostly attached in the hydrogen atoms and the critical temperature of the acridine derivatives.(i) Detection of Outliners: Applicability Domain (AD). The applicability domain (AD) of these models was evaluated by leverage analysis expressed as Williams plot (Figures 4 and 5), in which the standardized residuals (r) and the leverage threshold values (h∗=0.585 and 0.553 for pIC50 (PRO) and pIC50 (AMA), resp.) were plotted. Any new value of predicted pIC50 data must be considered reliable only for those compounds that fall within this AD on which the model was constructed.Figure 4
Williams plot of standardized residual versus leverage forpIC50 (PRO) MLR model (with h∗=0.585 and residual limits =±3).Figure 5
Williams plot of standardized residual versus leverage forpIC50 (AMA) MLR model (with h∗=0.553 and residual limits =±3).From these figures, it is obvious that there is no response outlier in training set and no response outside in test set. Only one chemical is identified as outside for MLR model forpIC50 PRO and two chemicals for MLR model for pIC50 AMA; these outsides compounds are given as follows.For pIC 50 PRO. Compound number64 in test set has higher leverage which is greater than h∗ value of 0.585 and all the compounds have a standard deviation into ±x interval (x=3).For pIC 50 AMA. Compounds numbers5 and6 in test set have a standard deviation value greater than the ±x interval (x=3).These results are confirmed using the simple approach (Tables  S3 and  S4), the chemical number 8 is identified as outlier and the chemical number64 is identified as outside for MLR model for pIC50 PRO, and any chemical is identified as outside or outlier for MLR model for pIC50 AMA.These erroneous predictions could probably be attributed to wrong experimental data or to the structure of these outsides; Cl, F, or NMe2 substitutes the tree compounds at the para position of the phenyl ring (Figure 6); maybe the selected descriptors do not pay much attention to these special substructures. The predictions of tree compounds are extrapolations of the model, but fortunately they are all “good leverage” chemicals.Figure 6
Chemical structures of the outsides compounds.


## 3.4. Artificial Neural Network (ANN)

In this study, we used a feed forward network with two layers, with a sigmoid transfer function in the hidden layer and a linear transfer function in the output layer (Figure2). The architecture of the artificial neural network used in this work was 7-3-1 and ρ=1.82 for pIC50 (PRO) and 6-3-1 and ρ=2 for pIC50 (AMA).The output layer represents the calculated activity values (predictedpIC50). The calculation result and the performance of established models are recorded in the output layer.To justify the predictive quality of models, total data are distributed randomly into three groups. The first group (70% of the total data) used to drive the system. The second group (15% of the total data) will be used to validate the network; and the remaining 15% that did not participate in the learning models will be used as an independent test of network generalization. The distribution of the total data into training, validation, and test sets is shown in Table7.Table 7
The coefficient of determination, the coe1fficient of correlation, and the MSE obtained by the model established by the ANN for the three phases: Training, validation, and test.
pIC50 PRO Model n = 51; MSE = 0.079; R2 = 0.870; R = 0.933 Training set [1; 3; 4; 5; 6; 7; 11; 12; 13; 14; 16; 19; 21; 25; 26; 27; 28; 30; 32; 34; 35; 36; 37; 38; 39; 40; 41; 43; 44; 46; 47; 48; 49; 50; 51] MSE = 0.044;R2 = 0.914; R = 0.956 Validation set [8; 17; 18; 22; 23; 24; 29; 31] MSE = 0.125;R2 = 0.922; R = 0.960 Test set [2; 9; 10; 15; 20; 33; 42; 45] MSE = 0.186;R2 = 0.725; R = 0.851  pIC50 AMA  Model n = 48; MSE = 0.104; R2 = 0.918; R = 0.843 Training set [2; 3; 4; 5; 6; 7; 10; 11; 13; 16; 18; 19; 20; 21; 23; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 41; 43; 44; 45; 46; 47] MSE = 0.060;R2 = 0.897; R = 0.947 Validation set [1; 8; 14; 15; 17; 24; 25] MSE = 0.198;R2 = 0.710; R = 0.843 Test set [9; 12; 22; 26; 40; 42; 48] MSE = 0.228;R2 = 0.791; R = 0.890The correlation between the experimental and calculated values using the artificial neural network models is highly significant, as illustrated in Figure7 and as indicated by better R and R2 and the small MSE values for all three phases: training, validation, and test (Table 7). The predicted activities calculated with the artificial neural network and the observed values are given in Table  S5.Figure 7
Correlations between observed and predicted activities values calculated using ANN models (training set in black, validation set in red, and test set in blue).Figure 8The results obtained by MLR and ANN are very sufficient to conclude the performance of the models. A comparison of the quality of the statistical terms of these models shows that the ANN has substantially better predictive capability. ANN was able to establish a more satisfactory relationship between the molecular descriptors and the activity of the studied compounds compared to MLR; but the most negative side of this method is the fact that it is poorly transparent, whereas transparency of MLR approach gives the most interpretable results and gives a good explanation of activities with descriptors. Consequently, we can design new compounds with improved values of activity compared to the studied compounds using the MLR models. Taking into account the above results, we added suitable substitutions and then we moved to calculate their activities using the proposed models equations ((3) and (4)). Therefore, the suggested models will reduce the time and cost of synthesis as well as the determination of the antileishmanial activities against promastigotes and amastigotes forms of parasites for the acridine derivatives.


## 3.5. Design New Compounds with Higher Antileishmanial Activities

According to the above discussions, the MLR models could be applied to other acridines derivatives according to Table1 and could add further knowledge in the improvement of new way in antileishmanial drug research. If we develop a new compound with better values than the existing ones, it may give rise to the development of more active compounds than those currently in use.In this way, we carried out structural modification starting from compounds having the highestpIC50 values as template (number14 and number 20). The structures of the designed compounds and their parameter values calculated by the same methods as well as pIC50 values theoretically predicted by the MLR models are listed in Table 8.Table 8
Values of descriptors, antileishmanial activity pIC50, and leverages (h) for the new designed compounds.
Designed compounds Number Descriptors values pIC50 (PRO) Number Descriptors values pIC50 (AMA) X 1 R1 = OH; R2 = CH3 N% = 12.490; μ = 2.232; ω = 3.099 NHA = 3; NHD = 2; MTI = 3651 TVC = 3.34 10−05 0.571 Y 1 R1 = OCH3; R2 = CF3  EHOMO = −5.235; CT = 885.365; KH = 9.302;  T = 581.430; NHA = 6; NHD = 1 1.395 Y 2 R1 = OH; R2 = CF3  EHOMO = −5.312; CT = 903.801; KH = 12.056;  T = 647.130; NHA = 6; NHD = 2 0.998 Y 3 R1 = OCH3; R2 = F EHOMO = −5.034; CT = 893.897; KH = 10.174;  T = 566.560; NHA = 4; NHD = 1 0.485 X 2 R1 = OH; R2 = OH N% = 12.380; μ = 1.080; ω = 3.131 NHA = 4; NHD = 3; MTI = 3497 TVC = 1.49 10−05 0.170 Y 4 R1 = R2 = OC2H5  EHOMO = −4.696; CT = 927.241; KH = 11.222;  T = 622.010; NHA = 4; NHD = 1 0.464 Y 5 R1 = R2 = OCH3  EHOMO = −4.731; CT = 916.967; KH = 11.469;  T = 599.470; NHA = 4; NHD = 1 0.442 Y 6 R1 = OCH3; R2 = OC(CH3)3  EHOMO = −4.872; CT = 928.656; KH = 11.099;  T = 635.700; NHA = 4; NHD = 1 0.109 Y 7 R1 = OCH3; R2 = CH2NH2  EHOMO = −4.801; CT = 934.561; KH = 14.185; T = 660.500; NHA = 4; NHD = 2 0.122  X 3 R1 = OH; R2 = meta-NH2 N% = 11.250; μ = 5.944; ω = 3.392 NHA = 5; NHD = 3; MTI = 17128 TVC = 2.23 10−08 0.838 Y 8 R1 = OCH3; R2 = para, meta -F: EHOMO = −5.081; CT = 1006.097; KH = 13.267; T = 762.370; NHA = 6; NHD = 1 0.308 X 4 R1 = OCH3; R2 = para-NH2 N% = 10.850; μ = 7.114; ω = 3.295 NHA = 5; NHD = 2; MTI = 19138 TVC = 2.04 10−08 0.607 Y 9 R1 = OCH3; R2 = para NH2: EHOMO = −4.966; CT = 1066.417;  KH = 16.853; T = 831.93; NHA = 5; NHD = 2 0.199 X 5 R1 = OCH3; R2 = meta-NH2 N% = 10.850; μ = 6.193; ω = 3.353 NHA = 5; NHD = 2; MTI = 18992 TVC = 2.04 10−08 0.309 Y 10 R1 = OCH3; R2 = meta NH2: EHOMO = −4.993; CT = 1066.417; KH = 16.853; T = 831.930; NHA = 5; NHD = 2 0.166 X 6 R1 = OH; R2 = H N% = 7.820; μ = 5.631; ω = 3.483 NHA = 4; NHD = 2; MTI = 15585 TVC = 4.47 10−08 0.381From the predicted activities, it has been observed that the designed compounds have higherpIC50 values than the existing compounds in the case of the 60 studied compounds (Table 1).The leverage values(h) for the new designed compounds are 0.268, 0.602, 0.775, 0.527, 0.386, and 0.369 for X1,X2,…,X6, respectively, and 0.649, 0.797, 0.201, 0.251, 0.235, 0.166, 0.176, 0.339, 0.169, and 0.166 for Y1,Y2,…,Y10, respectively (Table 8). Only compounds X2, X3, Y1, and Y2 are defined as outliers and consequently they are not be considered, because they have higher leverage which is greater than h∗ (0.585 for pIC50 (PRO) and 0.553 for pIC50 (AMA)); we suggest all other compounds as candidates that will be synthetized and evaluated as antileishmanial drugs.


## 4. Conclusion

Following the five principles of the Organisation for Economic Co-operation and Development (OECD) for the validation of QSAR models, two different modelling methods, multiple linear regression (MLR) and artificial neural network (ANN), were used in the construction of QSAR models for the antileishmanial activities against two forms of parasites (promastigotes and amastigotes) of acridines derivatives. The accuracy and predictability of the proposed models were proven by the comparison of key statistical terms of models. The good results obtained with the internal and external validations show that the proposed models in this paper are able to predict activities with a great performance and that the selected descriptors are pertinent. The applicability domain (AD) of the MLR model was defined. The resulting models have shown that we have established a relationship between some descriptors and the activities in satisfactory manners. The ANN results have substantially better predictive capability than the MLR, but the latter gives the most important interpretable results.The obtained results show that, to increase antileishmanial activity against promastigotes parasites, we will increase electrophilicity and decrease branching, polarity, and number of hydrogen atoms attached in the heteroatom of the acridine derivatives. Moreover, to increase antileishmanial activity against amastigotes parasites, we will increase solubility, polarity, and branching and decrease electrophilicity and number of heteroatoms mostly attached in the hydrogen atoms and critical temperature of acridine derivatives. Comparingt-test and standardized coefficient values of descriptors indicates that the influences of the electrophilicity index (ω) on pIC50 (PRO) and of the number of H-Bond donors (NHD) on pIC50 (AMA) are stronger than those of the others.The most important finding from this research is that we have designed and proposed new compounds with higher values of activities compared to existing ones by adding suitable substituents and calculating their activity using the regression equations. Consequently, the proposed models will reduce the time and cost of synthesis as well as the determination of the antileishmanial activities against promastigotes and amastigotes forms of parasites of acridine derivatives.



---

*Source: 5137289-2016-11-22.xml*