Hybrid-Genetic Algorithm based Descriptor Optimization and QSAR Models for Predicting the Biological Activity of Tipranavir Analogs for HIV Protease Inhibition

Abstract

The prediction of biological activity of a chemical compound from its structural features plays an important role in drug design. In this paper, we discuss the quantitative structure activity relationship (QSAR) prediction models developed on a dataset of 170 HIV protease enzyme inhibitors. Various chemical descriptors that encode hydrophobic, topological, geometrical and electronic properties are calculated to represent the structures of the molecules in the dataset. We use the hybrid-GA (genetic algorithm) optimization technique for descriptor space reduction. The linear multiple regression analysis (MLR), correlation-based feature selection (CFS), non-linear decision tree (DT), and artificial neural network (ANN) approaches are used as fitness functions. The selected descriptors represent the overall descriptor space and account well for the binding nature of the considered dataset. These selected features are also human interpretable and can be used to explain the interactions between a drug molecule and its receptor protein (HIV protease). The selected descriptors are then used for developing the QSAR prediction models by using the MLR, DT and ANN approaches. These models are discussed, analyzed and compared to validate and test their performance for this dataset. All the three approaches yield the QSAR models with good prediction performance. The models developed by DT and ANN are comparable and have better prediction than the MLR model. For ANN model, weight analysis is carried out to analyze the role of various descriptors in activity prediction. All the prediction models point towards the involvement of hydrophobic interactions. These models can be useful for predicting the biological activity of new untested HIV protease inhibitors and virtual screening for identifying new lead compounds.

I. INTRODUCTION

HIV protease (HIV-PR) is one of the major viral targets for the development of new chemotherapeutics. Currently, many HIV-PR inhibitor drugs are used in combination with other drugs [1-4]. However, the use of current drugs regimens is compounded by several issues such as - adherence, tolerability, long-term toxicity, and drug- and cross-resistance. Besides, the mutations also enable HIV to resist currently available treatments [5]. Therefore, there is a continuing need for the development of new chemotherapeutics with improved antiviral potency and favorable pharmacokinetic profile. One way of designing the effective inhibitors is modeling the biological activity to propose new candidate molecules. This can be partially fulfilled by understanding the existing structure-activity relationship (SAR) data to develop QSAR prediction models.

The process of relating the molecular structure of a chemical compound to its biological activity, ADME (absorption, distribution, metabolism, and excretion) properties, or to its chemical reactivity is important in drug design [6-9]. With increase in the amount and complexity of available chemical and biological data, the development of new computational models is becoming increasingly important, for understanding and predicting the interactions between drug molecules and their receptor proteins. The quantitative structure activity relationship (QSAR) models have shown great promise for handling this massive amount of structural and biological data. These models relate the descriptors (also known as parameters or features) of a small molecule or compound, computed based on its physicochemical properties, to its biological activity [10-12]. QSAR is a well known approach for identifying the lead compounds from existing database of compounds with the known biological activity [12-14]. The QSAR models are developed using linear regression techniques (e.g., multiple linear regression (MLR) [15], partial least squares (PLS)) [16] or non-linear machine learning techniques (e.g., artificial neural network (ANN) [17-19], support vector machine (SVM) [20] or decision trees (DT)) [21].

A large number of descriptors are usually computed for a small set of molecules. However, a good descriptor set should contain the descriptors that are highly correlated with the target, yet uncorrelated with each other. Optimization of descriptor set and selecting an appropriate statistical or machine learning technique plays a major role in developing the robust QSAR prediction models. The feature optimization techniques are used to remove the irrelevant and correlated descriptors. The genetic algorithm (GA), which belongs to the class of evolutionary algorithms, has been widely used for feature optimization in QSAR models [22-23]. Solutions generated by GA have less probability of being affected by local minima due to the use of inheritance, mutation, selection, and crossover [24]. Since GA does not carry out the fitness evaluation of the population, different types of fitness functions are used for this purpose, including the MLR [15], partial least square (PLS) [25], correlation-based feature selection (CFS) [26-28], DT [21] and ANN [17-19]. The selected descriptors are then used as input variables for developing QSAR model(s). Similarly, the clustering techniques (e.g., K-means clustering, K-nearest neighborhood) are used for removing the outlier compounds or descriptors [29]. This reduces the dimensionality of data and allows learning algorithms to operate faster and more effectively. In some cases, the classification accuracy can be improved, while in others, the result is a more compact prediction model with easy interpretation.

QSAR Models for HIV Studies

Many MLR based QSAR models have been used to model the activity of inhibitors of HIV proteins, including models developed by our coauthor R. Garg et al. [30-31]. Boiani et al. used a DT method to develop QSAR models for N-Oxide containing heterocycles compounds for anti-Trypanosoma cruzi activity [32]. Daszykowski et al. demonstrated the application of CART (Classification and Regression Trees) for the analysis of biological activity of non-nucleoside reverse transcriptase inhibitors (NNRTIs) for HIV reverse transcriptase [33].

Similarly, the ANN QSAR models have also been widely used to predict HIV drug resistance [17-18], to elicit structural information about viral enzymes [34], and to predict the activity of potential drugs [35-36]. Wang and Larder [17] used a three-layer ANN to predict Lopinavir resistance. Draghici et al. [18] studied the HIV protease resistance to drugs (e.g., Indinavir and Saquinavir) by considering the structural features of the HIV protease drug inhibitor complex as descriptors. Yang and Thomson [34] developed bio-basis function ANNs to predict the protease cleavage sites in proteins. Douali et al. [35] developed the QSAR models for HEPT derivatives by both the linear regression and ANN techniques. From the models obtained using linear regression techniques, they estimated the contribution of each descriptor to the model, and confirmed the hydrophobic requirements for HIV inhibition. Hecht et al. [37] applied the pre-clustering and evolved neural networks to develop prediction models for high-throughput screening of anti-HIV compounds.

The QSAR models, developed using MLR [35], [38] or partial least squares (PLS) [25] techniques, are easy to interpret and can provide useful insight into drug-receptor interactions. On the other hand, the QSAR models developed using non-linear techniques (e.g., ANN) have better predictive power but do not provide straightforward interpretation [17-18] [34]. The decision tree based QSAR models fall in between the linear and non-linear models in terms of their predictive and interpretation abilities. They are more transparent, easy to understand and convert to a set of prediction rules [21][32-33]. Therefore, we have used all three above-mentioned approaches in order to develop robust QSAR prediction models for the HIV protease inhibitor dataset, which have good predictive power as well as interpretability.

In this paper, we discuss the QSAR prediction models developed on a cycloalkylpyranone dataset of HIV protease enzyme inhibitors from which Tipranavir, a U. S. FDA approved HIV protease inhibitor drug was developed [5]. This dataset was developed in-house and curated for quality assurance. For descriptor optimization, we use four variations of hybrid-GA techniques, in which GA is used for searching the descriptor subspace whereas the MLR, CFS, DT and ANN are used for fitness evaluation. The QSAR prediction models are developed using three approaches – MLR, ANN and DT. We use the weight analysis to interpret the importance of descriptors in ANN models. The major objectives of this study are: (i) to study and analyze the reduced descriptor sets obtained by the hybrid-GA feature optimization techniques, (ii) to develop robust QSAR models for biological activity prediction of HIV protease inhibitors, and (iii) to compare the performance of QSAR models developed by using three different classes of techniques, in terms of their predictive power as well as interpretability.

Remainder of the paper is organized as follows: The dataset construction, descriptor computation and selection, QSAR prediction model development and validation are discussed in Section II. Results of descriptor selection and QSAR prediction model development, including the interpretation of selected descriptors and analysis of developed models, are discussed in Section III. Conclusion is given in Section IV.

II. METHODS

The methodology adopted for this research is illustrated in Figure 1 and discussed below.

Fig. 1.

Flow chart depicting the proposed methodology.

II A. Dataset Construction

The dataset used for this study consists of SAR biological activity (K_i) data of 170 cycloalkyl pyranone analogs. Tipranavir, one of the cycloalkyl pyranone artifacts is a U. S. FDA approved HIV protease inhibitor drug to treat HIV infection and AIDS [5]. Cycloalkylpyranones are the non-peptidic lead structures obtained by the chemical modification of coumarin. The benzene ring of coumarin was replaced by conformationally-flexible cycloalkyl rings of various sizes. The detailed description of the structural modifications of the data set is illustrated in a roadmap of structural modification (Figure 2). Here the biological activity (K_i) is the inhibition constant for a drug, which represents the concentration of competing ligand in a competition assay that would occupy 50% of the receptors if no radio-ligand were present.

Fig. 2.

Structural modifications of cycloalkylpyranone scaffold

The data was taken from the published literature and the dataset is made available in supplementary information. The similar compounds published in separate tables or in series of articles were combined, and the repeated data was omitted. We also removed the compounds which are enantiomers and racemic mixtures. The compounds in the dataset have structural variations in their side chains, aromatic groups and heterocyclic rings.

Descriptor calculation

All the compounds were optimized and minimum energy conformations were generated for each compound using MOE (Molecular Operating Environment) software [39]. The 233 descriptors were calculated for each compound using the descriptor generation module of MOE software [39]. These descriptors include both 2D and 3D descriptors and represent various topological (such as topological indices, structural keys, E-state indices, connectivity and shape indices), physicochemical (such as partition coefficient, molecular weight and molar refractivity), and electrostatic (such as partial charges, topological polar surface area and van der Wall surface area) properties as depicted in Figure 3. Three additional descriptors, namely ClogP (calculated octanol/water partition coefficient), CMR (calculated molar refractivity) and MgVol (McGowan volume), were also calculated using the CSQAR software [40]. These CQSAR descriptors have been found important in many HIV protease QSAR prediction models [25-26].

Fig. 3.

Pie chart depicting distribution of various categories of 233 MOE [39] descriptors.

Pre-screening

In the first step, the compounds and descriptors with missing (or null) values were removed from the dataset. Next, we employed the identity test using Matlab [41] and removed 15 descriptors, which had 90% or more zero values. Finally, the 93 descriptors were removed by the pairwise correlation analysis using the Matlab, in which the descriptors with more than 90% correlation in their values were identified and one of the correlated descriptors was removed. This pre-screening gave us a quality-assured dataset of 155 compounds, each with 128 descriptor values which are used for further analysis as discussed below.

II B. Descriptor Set Optimization

As discussed in Section I, identifying a small subset of descriptors, which represent the total set of descriptors, is important for developing a good QSAR prediction model. We have used the hybrid-GA optimization technique, where GA is used for searching the descriptor subspace, whereas the MLR, CFS, DT or ANN is used for fitness evaluation. GA is governed by biological evolution rules and can investigate several possible solutions simultaneously, each of which explores different regions in the descriptor space. Fitness of each solution is evaluated by one of the above mentioned techniques. The MLR and DT are the linear fitness functions whereas ANN is a non-linear function. The use of ANN can handle the optimization of non-linear descriptor space more efficiently [19]. The major steps employed in the hybrid-GA scheme are illustrated in Figure 4.

Fig. 4.

Schematic representation of hybrid GA algorithm.

The first step in the hybrid GA is to create a population of N individuals (feature subsets). Each individual encodes the same number of randomly chosen descriptors, and the fitness of each individual in this generation is determined. The compounds in the dataset were divided into a training (66%) and test set (34%). The test set is not used during training but serves to test the predictive ability of final models. Here, the root mean squared error (RMSE) is taken as the fitness measure. Next, a fraction of children of the next generation is produced by crossover and the rest by mutation from the parents on the basis of their scaled fitness scores. The new offspring contains characteristics from one or both parents, and is evaluated for fitness. The cycle continues for a predetermined number of generations, or until the results do not change continuously for a specified number of generations [24].

The GA-MLR, GA-DT and GA-CFS techniques are implemented using WEKA program [42], and the GA-ANN is implemented in MATLAB. The values of various hybrid-GA parameters and measures are discussed in Section III.A. Since the MLR, DT and ANN are also used for developing the QSAR models, they are discussed in the next section, whereas the GA-CFS is discussed below.

GA-CFS

As shown in Figure 5, the correlation-based feature selection (CFS) algorithm evaluates each feature subset by considering the individual predictive ability of each feature along with the degree of redundancy between them, and returns a numeric measure that guides the search [26-27]. The CFS fitness function takes into account the usefulness of individual features for predicting the activity along with the level of inter-correlation to give the goodness of feature subsets. It has wide range of applications for feature selection including QSAR [28-29].

Fig. 5.

Schematic representation of GA-CFS algorithm.

CFS is a simple filter algorithm that ranks feature subsets according to a correlation based heuristic evaluation function (see Equation (1)). The bias of the evaluation function is toward subsets that contain features that are highly correlated with the class and yet uncorrelated with each other.

$$M_s=\frac{k\overline{r_{\mathit{cf}}}}{\sqrt{k+k(k-1)\overline{r_{\mathit{ff}}}}}$$ (1)

Here M_s is the heuristic “merit” of a feature subset S (fitness function) containing k features, $\overline{r_{\mathit{cf}}}$ is the average feature-activity correlation (f∈S), and $\overline{r_{\mathit{ff}}}$ is the average feature-feature inter-correlation [27].

The numerator of (1) provides an indication of how predictive of the class a set of features are. The denominator provides an indication of the redundancy among the features. Equation (1) forms the core of CFS and imposes a ranking on feature subsets in the search space of all possible feature subsets. To measure the feature-class correlations ( $\overline{r_{\mathit{cf}}}$) and feature-feature intercorrelations ( $\overline{r_{\mathit{ff}}}$), we adopt the symmetrical uncertainty (U), which uses a modified information gain (InfoGain) measure (see Equations (2a), (2b) and (3)) [22]. The symmetrical uncertainty is defined for features X and Y as follows:

$$U=2.0\times \left[\frac{\mathit{InfoGain}}{H(Y)+H(X)}\right]$$ (2a)

where H(Y) is entropy of Y given as,

$$H\left(Y\right)=-\sum _{y\in Y}p\left(y\right)\log \left(p\left(y\right)\right)$$ (2b)

and

$$\mathit{InfoGain}=\mathrm{H}(\mathrm{Y})-\mathrm{H}(\mathrm{Y}/\mathrm{X})=-\sum _{y\in Y}p(y)\log (p(y))+\sum _{x\in X}p(x)\sum _{y\in Y}p(y/x)\log (p(y/x))$$ (3)

II C. QSAR Prediction Models

The descriptors obtained after feature optimization are used to develop prediction models. We have used three different approaches to develop QSAR prediction models – linear MLR, non-linear DT, and ANN as discussed below. These belong to different classes and would help us in developing the robust QSAR prediction models for this dataset.

Multiple Linear Regression (MLR)

The MLR models serve as the basis for a number of multivariate methods. They establish a quantitative relationship between a group of predictor variables (X) and a response Y as shown in Equation (4). This relationship is useful for understanding which predictors have the greatest effect and the direction of the effect [11].

$$Y=X\beta +\in$$ (4)

Here Y is an n × 1 vector of observations, X is an n × p matrix of regressors, β is a p × 1 vector of parameters, and ∈ is an n × 1 vector of normally distributed noise. The aim of this regression method is to estimate the β̄ = (β_l,…, β_p), by using $\mathit{Min}\sum _1^n{(Y_i-\beta {\mathrm{X}}_{i1}-\dots -\beta {\mathrm{X}}_{\mathit{ip}})}^2$.

Although MLR is computationally simple and the prediction models give strong mechanistic interpretation, it is criticized for its lack of robustness in handling the nonlinear data. It also has certain other limitations, especially when the number of variables is large, or when the degree of correlation between the variables (or samples) is large. We implemented MLR scheme in Weka [42]. Various parameters and measures used for evaluating the fitness of the MLR models are discussed at the end of this section (see ‘Over fitting and Model Validation’).

Decision Trees (DT)

The DTs are widely used machine learning methods used in pharmaceutical industry for predicting the quantitative structure-activity relationships. They are known for their predictive ability and are easy to interpret. DT approximates the discrete-valued functions, is robust to noisy data and capable of learning disjunctive expressions [21].

DTs approach a classification or regression problem in divide-and-conquer fashion [21]. The decision trees, can classify both categorical and numerical data, but the output attribute must be categorical. There are no a priori assumptions about the nature of the data, but the multiple output attributes are not allowed. There are various classes of decision trees based on the process of construction, pruning methodology and their application [43]. The classification and regression trees (CART) [44] and random forests (RF) [45] are more widely used in drug design as well as QSAR. The model tree (i.e., M5 decision tree) is mainly used for developing models to predict the values [46]. Unlike other decision trees (e.g., CART), the M5 decision trees store multivariate linear models at their leaf nodes. So, they are analogous to piecewise linear functions, and hence are considered as nonlinear in nature.

M5 decision trees are constructed by first using a decision tree induction algorithm to build the initial tree, and then a multivariate linear regression model is constructed for each node of the tree. Each linear model is simplified by eliminating the parameters (by using a greedy search method) to minimize its estimated error. Then pruning of the tree is performed by examining each non-leaf node of the model tree to assign the linear model with lower estimated error to leaf nodes. Lastly smoothing process is applied to improve the prediction accuracy of the tree.

The advantage of the M5 tree over CART is that it is much smaller than CART, the decision is clear and the regression functions do not normally involve too many variables [47]. We have used the model tree program implemented in Weka [42]. Various parameters and measures used for evaluating the fitness of the DT models are discussed at the end of this section (see ‘Over fitting and Model Validation’).

Artificial Neural Network (ANN)

The ANN is used to identify correlated patterns between the input and target values and can subsequently predict outcomes from fresh inputs [17-19]. The ANNs generally consist of a number of interconnected processing elements or neurons. The descriptors obtained by feature selection are used to build the inputs of the ANN. Each input is associated with some weights (w) and biases (b) depending on the relative importance of the input.

We used a 3-layer ANN with back propagation for fitness evaluation of the population (in hybrid GA-ANN) as well as for the QSAR prediction model development. We investigated the performance of different learning schemes (e.g., Bayesian [48], scaled conjugate gradient [49], gradient descent [50], etc.), and observed that the Bayesian regularization (BR) learning showed the best performance for feature selection as well as biological activity prediction of this dataset.

We used the Bayesian learning algorithm by MacKay [51], and Foresee and Hagan [48], implemented in Matlab ANN toolbox [41]. The training function in Bayesian learning algorithm updates the weight and bias values according to Levenberg-Marquardt optimization procedure [52]. It minimizes a combination of sum of squared errors generated by the outputs (E_D) and sum of squares of weights that reflect the connections of network (E_w), and then determines the correct combination in order to produce a network that generalizes well. Thus the performance index modification (F) involves taking into account the sum of squares of the network weights (equation 5). Then optimization technique is used to minimize F.

$$F=\beta E_D+\alpha E_w$$ (5)

Here α and β are black box parameters and do not represent the momentum factor and learning rate.

The other network parameters, like number of hidden nodes and learning rate, were varied to build the best prediction model as discussed in more detail in Section III.B. The model validation parameters to evaluate the fitness of the model are discussed below.

Over fitting and Model Validation

To avoid over fitting, we used the 10-fold cross validation method to estimate the fitness of the model and compare all three types of QSAR models (i.e., MLR, DT and ANN based models). In 10-fold cross validation method, the data is partitioned into 10 sets of size n/10 each. Among them, nine sets are used for training and the remaining one set is used for testing. The procedure was repeated 10-times, and average accuracy was computed. Over fitting in ANN is also avoided by using the BR training algorithm [53]. The oversized networks which can cause over fitting can also be avoided by pruning away unnecessary neurons or starting with a low number of neurons and then gradually increasing as necessary while watching the generalization performance [54]. Reducing the number of inputs is also beneficial, which was done with the feature optimization as discussed earlier in this section. Various parameters used in our simulation are discussed in Section III.

For model validation, various measures such as correlation coefficient (R) (Equation (6a)), root mean squared error (RMSE) (Equation (6b)) and cross validated R-square (R²_cv) (Equation (6c)) were used. These measures are computed from the difference between the experimental values (Y_i) and the predicted value (Ŷ_i) for the i^th compound as discussed below.

The linear correlation coefficient (R), measures the strength and the direction of a linear relationship between (Y_i) and (Ŷ_i). Here n is the number of pairs of data.

$$\mathrm{R}=\frac{n\sum _{i=1}^n{Y}_i{\widehat{Y}}_i-\sum _{i=1}^n{Y}_i\sum _{i=1}^n{\widehat{Y}}_i}{\sqrt{\left[n\sum _{i=1}^n{Y}_i^2-{\left(\sum _{i=1}^n{Y}_i\right)}^2\right]}\left[n\sum _{i=1}^n{\widehat{Y}}_i^2-{\left(\sum _{i=1}^n{\widehat{Y}}_i\right)}^2\right]}$$ (6a)

The root mean squared error (RMSE) and cross validated R-square (R_cv²) values give the variance of predicted activity from the experimental activity. They are good measures to compare the fitness of the models and are defined below.

$$\mathrm{RMSE}=\sqrt{\frac{\sum _{i=1}^n{\left(Y_i-{\widehat{Y}}_i\right)}^2}{n}}$$ (6b)

$${\mathrm{R}}_{\mathrm{cv}}^2=\frac{\sum _{i=1}^n{\left(Y_i-\overline{Y}\right)}^2-\sum _{i=1}^n{\left(Y_i-{\widehat{Y}}_i\right)}^2}{\sum _{i=1}^n{\left(Y_i-\overline{Y}\right)}^2}$$ (6c)

where Ȳ is the mean value of the experimental dataset.

III. RESULTS AND DISCUSSION

In this section, we discuss the performance of the feature optimization techniques and QSAR prediction models on HIVPR dataset. We also provide interpretation of the descriptors obtained from the feature optimization techniques and a comparative analysis of QSAR prediction models obtained from all the three approaches.

III A. Feature Optimization

We used the hybrid-GA techniques (GA-MLR, GA-CFS, GA-DT and GA-ANN) to optimize the 128 descriptors, obtained after pre-screening of 155 Tripinavir analogs as discussed in Section II.A.

The GA parameters, like number of generations and population size, were varied and their performance was analyzed. Using the WEKA software, we observed that increasing the number of generations and population size beyond 20 did not improve the results for GA-MLR, GA-CFS and GA-DT. Therefore, we chose only 20 generations and a population size of 20 for these three hybrid-GA schemes. The crossover probability of 0.5 and mutation probability of 0.033 was used. Default values used in WEKA were selected for the remaining GA parameters. Please note that MLR, CFS and DT did not require any parameter selection and the default values were chosen from WEKA.

In GA-ANN, we observed that increasing the number of generations from 20 to 100 improved the results. Since the improvement was moderate after 100 generations, we used only 100 generations. Similarly, we chose a population size of 40. The elite count was taken as 2 and crossover fraction was selected as 0.8. The rank function was used as the fitness scaling function in GA, which uses rank of each individual, rather than its score. Here, the rank of an individual is its position in the sorted scores and removes the effect of the spread of raw scores. The Gaussian function was used as the mutation function to make small random changes in the population, which provides genetic diversity and enables the GA to search a broader space. The stochastic uniform function was used for parent selection and stall fitness value was fixed as 0.001. When analyzing fitness of the population, we used a 3-layer back propagation ANN (BPNN), trained with 66% of the data while the remaining 34% data was used for testing the model. For the evaluation of fitness function, the BPNN with Bayesian regularization (BR) learning was used. The cross-validated RMSE was used as a fitness value for evaluating the population. Here, the learning rate and momentum factor values were chosen as 0.03 and 0.15, respectively.

Interpretation of the selected descriptors

We obtained nine descriptors using GA-MLR, seven descriptors using GA-CFS, 11 descriptors using GA-DT, and 13 descriptors using GA-ANN. These descriptors were found to represent the overall descriptor space (see Figure 6), and contribution of each category of descriptors was found to be relatively same before and after the feature optimization (Figures 3 and 6). The brief description and names of the descriptors obtained after using both methods are given in Table 1. The descriptors related to the adjacency & distance matrix, subdivided surface areas, partial charge, and atom & bond counts were found in all the descriptor sets. Here, the ‘adjacency and distance matrix’ and ‘subdivided surface area’ descriptors illustrate the importance of hydrophobicity, whereas others represent electrostatic/topological interactions for this dataset.

Fig. 6.

Pie charts depicting distribution of various categories of descriptors (including CQSAR descriptor ClogP) obtained after feature optimization by GA-MLR, GA-CFS, GA-DT and GA-ANN methods.

Table 1.

The descriptors obtained after feature optimization by GA-MLR, GA-CFS, GA-DT and GA-ANN methods

	Descriptor Type	GA-MLR	GA-CFS	GA-DT	GA-ANN
Hydrophobic	Adjacency and distance matrix descriptors	Opr_violation	BCUT_SLOGP_3	PetitjeanSC	BCUT_PEOE_1
			GCUT_SMR_0	Opr_violation	GCUT_PEOE_1
					balabanJ
	Subdivided surface areas			SlogP_VSA5	* ClogP
			SlogP_VSA0	SlogP_VSA8	SlogP_VSA1
		SlogP_VSA8	SlogP_VSA1	SlogP_VSA9	SlogP_VSA7
		SMR_VSA0	SMR_VSA3	SMR_VSA0	SlogP_VSA8
				SMR_VSA3	SMR_VSA3
Electrostatic	Partial charge descriptors	PEOE_VSA+2	PEOE_VSA-6	PEOE_VSA-4	PEOE_VSA+2
		Q_VSA_FHYD		Q_VSA_PNEG	Q_VSA_PPOS
	Conformation dependent charge	FASA_H			DCASA
	Pharmacophoric descriptors	a_don		vsa_acid	a_don
Others	Atom counts and bond counts	a_nN	a_nN	a_nN	b_rotN
	Physical Properties	PM3_dipole

Note: Opr_violation = The oprea rules violation count and lead-like assessment; BCUT and GCUT descriptors are evaluated from the atomic contribution to the given properties like partial charges (BCUT_PEOE_1, GCUT_PEOE_1), partition coefficient (BCUT_SLOGP_3) and molar refractivity (GCUT_SMR_0); PetitjeanSC = Petitjean graph Shape coefficient; balabanJ = Connectivity topological index; SlogP_VSA = Sum of the proximate accessible van der Waals surface area, vi, calculated for each atom over all the atoms, such that partition coefficient for atom i is in a specified range (a, b]; SMR_VSA = Sum of the proximate accessible van der Waals surface area vi, calculation for each atom over all the atoms i, such that molar refractivity for atom i is in a specified range (a, b]; ClogP = Partition coefficient (logP(o/w)); Partial charge descriptors (PEOE_VSA+2, PEOE_VSA-6, PEOE_VSA-4, Q_VSA_FHYD, Q_VSA_PNEG, Q_VSA_PPOS) are sum of the proximate accessible van der Waals surface area vi calculation for each atom over all the atoms i, such that partial charge of atom i is in a specified range; vsa_acid is the approximation to the sum of VDW surface areas of acidic atoms; FASA_H, DCASA are calculated from the water accessible surface areas of all the atoms; a_don is number of hydrogen bond donor atoms (not counting basic atoms but counting atoms that are both hydrogen bond donors and acceptors such as -OH); b_rotN is number of rotatable bonds; and a_nN is number of nitrogen atoms; PM3_diple is the dipole moment calculated using the PM3 Hamiltonian

^*Obtained using CQSAR [40] software, others from MOE [39] software

As shown in Figure 6, the ‘subdivided surface area’ descriptors (especially the van der Wall surface areas of atoms and the atomic contribution to SlogP) are dominating (22% in GA-MLR, 43% in GA-CFS, 45% GA-DT and 38% in GA-ANN). The next prominent category is the ‘adjacency and distance matrix’ descriptors (11% GA-MLR, 29% in GA-CFS, 18% in GA-DT and 23% in GA-ANN), which represent atomic contributions to the hydrophobicity and molar refractivity. In addition, ClogP (a CQSAR descriptor), which models the hydrophobic interaction, is also present as an important descriptor in the GA-ANN model. These classes of descriptors together represent contribution to hydrophobic interactions. The contribution of ‘partial charge’ descriptors contributing to electronic effects is also significant (22% GA-MLR, 14% in GA-CFS, 27% in GA-DT and 15% in GA-ANN). Except for GA-CFS, all other methods have identified surface area dependent descriptors (FASA_H, DCASA and vsa_acid) as vital descriptors. The ‘atom & bond count’ descriptors especially number of nitrogen atoms is chosen by most of the methods. The GA-MLR has predicted more variety of descriptors when compared to other feature optimization techniques.

It is well known that the HIV protease receptor site is hydrophobic in nature [34]. As a result, the inhibitors with hydrophobic groups and side chains can bind better to them. The same is reflected in the obtained descriptors as discussed above. Overall, 33% of GA-MLR, 72% of GA-CFS, 64% of the GA-DT and 61% of GA-ANN selected descriptors model hydrophobic nature of the inhibitors whereas rest of them model electrostatic/topological interactions.

It is noteworthy that these descriptors are human interpretable and are able to explain the interactions between ligands (Tipranavir analogs) and their receptor protein (HIV protease). Such features can thus be used to design and synthesize a new compound with potency and specificity.

III B. Prediction Model Development

The descriptors obtained using various feature optimization techniques (i.e., GA-MLR, GA-CFS, GA-DT and GA-ANN) were used to develop the prediction models. Three different approaches – linear MLR, non-linear DT and ANN – were used to develop these models. These models are discussed, analyzed and compared below in this section, to test their performance for this dataset. Table 2 shows the correlation coefficient (R) and root mean squared error (RMSE) values of the MLR, DT and ANN prediction models on the descriptor sets obtained using all the four feature optimization techniques. The values are reported for the training set as well as the 10-fold cross validation.

Table 2.

Correlation coefficient (R) and RMSE values obtained using various QSAR prediction models for full training set and 10-fold cross validation (CV) set

Method		Training Set		10-fold CV
		R	RMSE	R	RMSE
GA-MLR	MLR	0.880	0.516	0.857	0.566
	DT	0.901	0.475	0.844	0.585
	ANN	0.955	0.321	0.812	0.635
GA-CFS	MLR	0.845	0.582	0.823	0.618
	DT	0.910	0.453	0.846	0.582
	ANN	0.892	0.492	0.866	0.560
GA-DT	MLR	0.836	0.597	0.790	0.670
	DT	0.927	0.414	0.896	0.484
	ANN	0.960	0.310	0.826	0.608
GA-ANN	MLR	0.858	0.558	0.808	0.644
	DT	0.915	0.441	0.857	0.561
	ANN	0.974	0.250	0.886	0.527

For the full training set, the ANN prediction models achieved higher correlation coefficient (R) values than the MLR and DT prediction models for various feature optimization techniques, except the GA-CFS. For the 10-fold cross validation, superior prediction was achieved when the same fitness function of the hybrid GA technique was used to develop the prediction model. In case of GA-CFS descriptors, the ANN technique outperformed MLR and DT for 10-fold cross validation.

(i) MLR Prediction Models

Equations (7) and (8) below show the MLR models developed using the descriptors obtained by the GA-MLR and GA-CFS feature optimization methods, respectively. The plots of the experimental vs. predicted biological activity (log(1/K_i)) for the developed models are shown in Figure 7. These plots also show the values of correlation coefficient (R) by using the 10-fold cross validation, along with the standard deviation (SD), and cross validated R-square (R_cv²) values. It is observed from the plots that the MLR models developed using the GA-MLR descriptor set (Equation (7)) have slightly better prediction than the GA-CFS descriptor set (Equation (8)) as evident by their higher R = 0. 0.857 vs. 0.823, lower SD = 0.500 vs. 0.525 and higher R_cv² = 0.735 vs. 0.677 values. Similarly, the calculated RMSE value of the model obtained using GA-MLR descriptor set is lower than the model obtained using GA-CFS descriptor set (0.566 vs. 0.618) as shown in Table 2.

Fig. 7.

Plot of experimental vs. predicted activity (log(1/K_I)) of 10-fold cross validated MLR prediction models based on the descriptors obtained using (a) GA-MLR, and (b) GA-CFS feature optimization methods.

$$\mathrm{Log}{(1/{\mathrm{K}}_{\mathrm{i}})}_{\mathrm{GA­MLR}}=0.7205\ast \mathrm{a}\_\mathrm{nN}+0.0157\ast \mathrm{PEOE}\_\mathrm{VSA}+2+9.2487\ast \mathrm{Q}\_\mathrm{VSA}\_\mathrm{FHYD}-0.1838\ast \mathrm{opr}\_\mathrm{violation}­0.6868\ast \mathrm{a}\_\mathrm{don}-0.0427\ast \mathrm{PM3}\_\mathrm{dipole}+0.0049\ast \mathrm{SlogP}\_\mathrm{VSA}8+0.0258\ast \mathrm{SMR}\_\mathrm{VSA}0-7.4414\ast \mathrm{FASA}\_\mathrm{H}+4.7546$$ (7)

$$\mathrm{Log}{(1/{\mathrm{K}}_{\mathrm{i}})}_{\mathrm{GA­CFS}}=1.6454\ast \mathrm{BCUT}\_\mathrm{SLOGP}\_3­66.9872\ast \mathrm{GCUT}\_\mathrm{SMR}\_0+0.3333\ast \mathrm{a}\_\mathrm{nN}+0.0147\ast \mathrm{PEOE}\_\mathrm{VSA}\_6­0.0171\ast \mathrm{SlogP}\_\mathrm{VSA}0+0.0133\ast \mathrm{SlogP}\_\mathrm{VSA}1+0.0297\ast \mathrm{SMR}\_\mathrm{VSA}3­34.6025$$ (8)

In the linear QSAR model developed on GA-MLR descriptors, negative coefficient of opr_violation and FASA_H (water accessible surface area) descriptors shows that these descriptors contribute negatively to the activity, whereas positive coefficients of other descriptors (partition coefficient based) show their positive contribution. GCUT_SMR_0 has large negative coefficient in Equation (8). In both the equations a_nN contributes significantly.

As discussed in Section III A, these descriptors are able to explain hydrophobic, electronic and topological interactions of the compounds in this dataset with HIV protease receptor. Similarly, Equation (8) is also able to explain interactions between ligands and receptor.

(ii) Decision Tree Prediction Models

As discussed in Section II C, the M5 decision trees implemented in Weka [41] were used to construct the pieces of linear equations (Linear Models (LM)) at the leaf nodes of decision tree. The six DT models using the GA-DT descriptors are shown in Figure 8.

Fig. 8.

Decision tree and the regression equations developed using the descriptors obtained using GA-DT feature optimization method.

Out of the 11 descriptors generated by the GA-DT feature selection technique, only five descriptors are involved in the decision making, which include SMR_VSA0, SlogP_VSA8, SlogP_VSA9 (hydrophobic), Q_VSA_PNEG (electronic) and a_nN (number of nitrogen atoms), at the root node atoms). All the linear models generated at the leaf nodes have a good similarity in their descriptors, but their coefficient values are different. It is noteworthy that the hydrophobic descriptors are involved in the decision making at each root node.

The plot of the experimental vs. predicted biological activity (log(1/K_i)) by the 10-fold CV method for the developed DT model is shown in Figure 9. As shown in Fig. 10, the R = 0.896 with standard deviation = 0.415 and R² = 0.804. The DT model developed using hybrid GA-DT descriptor set has slightly better prediction values than the models developed using other feature selection techniques.

Fig. 9.

Plot of experimental vs. predicted activity (log(1/Ki)) values of 10-fold cross validated DT model, based on the descriptors obtained using GA-DT feature optimization method.

Fig. 10.

Variation of correlation coefficient values of ANN prediction models with number of hidden neurons, for descriptors obtained using GA-ANN method.

(iii) ANN Prediction Models

Like in the GA-ANN feature optimization technique, a 3-layer back propagation ANN with Bayesian learning (BRNN) was used to develop the prediction model, and was fine tuned for the parameters like number of hidden nodes, learning rate and momentum factor [55]. Upon varying the learning rate and momentum factors from 0.01 to 0.5, we found that the higher learning rate values decreased the ANN performance in modeling the dataset activity, whereas variation in the momentum did not considerably influence the learning process. The learning rate and momentum factor were fixed at 0.03 and 0.3, respectively. As discussed earlier, the Bayesian learning is less likely to suffer from over-fitting as compared to other learning schemes. We used the 10-fold cross validation to study the accuracy of the predicted ANN model. To understand the model performance, the parameters like RMSE and R²_cv, defined in Section II C were used.

The probability of over-training the ANN is high when the number of layers and the hidden layer neurons is much larger than what is actually necessary to represent the structure of underlying learning problem. We used the network with one hidden layer and fine-tuned the number of hidden nodes. Figure 10 depicts the variation in the correlation coefficient (R) values with the number of hidden nodes. The R value increases with the number of hidden nodes for the training set indicating the overtraining. However four hidden nodes seem to be optimal for a good prediction on the test data. This is also in agreement with the number of hidden nodes for 2^nd order accuracy computed by a technique recently proposed by S. Trenn [55].

As shown in Figure 11 and Table 2, the final ANN model has good prediction accuracy as is evident from the ‘R’ values of 0.886 and 0.866 for the test set using GA-ANN and GA-CFS descriptors, respectively. The same is reflected in the lower SD value (0.441 and 0.460) and higher R²_cv value (0.786 and 0.750) from the plot and lower RMSE (Table 2). Furthermore, the model developed using the GA-ANN descriptors gives 0.02 extra fit as compared to the GA-CFS descriptor model, in terms of its ‘R’ value. Overall, the ANN prediction models have better prediction accuracy for our dataset than the other two (MLR and DT) models.

Fig. 11.

Plot of experimental vs. predicted activity (log(1/Ki)) values using 10-fold cross validated ANN prediction model, based on the descriptors obtained using GA-ANN method.

ANN Weight Analysis

Although ANN provides better prediction models, they suffer from lack of interpretability and can’t be used for understanding the structure property (i.e., descriptor vs. activity) trends. We have used a method by Guha et al. [56] to determine the contribution of each descriptor in ANN model, by considering its final weights as briefly discussed below.

This approach considers the overall contribution of a hidden neuron to the output by using all the effective weights associated with it. The hidden neurons are ranked based on the weights, as they do not contribute to the output value equally. In general, the effective weight between the k^th input neuron and the output neuron, via the l^th hidden layer neuron, will be w_klw_l^H. Here, w_kl is the weight between the k^th input and l^th hidden neuron, and w_l^H is the weight between the l^th hidden neuron and the output.

The contribution of l^th hidden neuron is computed as,

$$C_l=\frac{1}{n_I}\sum _{l=1}^{n_I}{w}_{\mathit{kl}}{w}_l^H$$ (9)

Here, n_I represents the total number of input neurons. The relative contribution of each hidden neuron ‘l’ is computed in terms of its ‘squared contribution’ (SC) value as,

$$S{C}_l=\frac{C_l^2}{\sum _{l=1}^{n_H}{C}_l^2}$$ (10)

Here the SC_l values will sum to 1.0.

The SC value of each hidden neuron and its summed weights (effective weights) for each given descriptor are reported in Table 3. The SC value of 1^st hidden Node is 0.6414, which has the highest contribution. From the SC values, we observe that the total contribution of the 1^st and 3^rd hidden nodes is 98%. At the 1^st hidden Node, the descriptors SlogP_VSA8, a_don and ClogP have higher effective weights, whereas at the 3^rd hidden node which has 2^nd highest SC value, the SlogP_VSA7 and SlogP_VSA1 descriptors have higher contribution. Overall, the hydrophobic descriptors are found to be dominant, which is same as seen from the MLR and DT models. The weight of the SlogP_VSA1 descriptor has positive value at hidden nodes 1, 2 and 4, which is in agreement with the DT and MLR models. Next, the ClogP descriptor also has positive weight at hidden nodes 1, 2, and 3. The same is also observed for the DT models.

Table 3.

Sum of weights calculated for each hidden node (input-hidden) of ANN prediction model obtained for GA-ANN optimized descriptors

Descriptor	Hidden node number
	1	3	2	4
BCUT_PEOE_1	0.7787	-0.5586	-0.3139	-0.0475
GCUT_PEOE_1	0.0982	-0.5959	-0.1956	0.7651
b_rotN	0.5193	-0.3449	0.4358	-0.3112
balabanJ	0.4643	-0.3881	-1.1189	0.9853
PEOE_VSA+2	-0.4195	-0.5002	0.7517	0.1825
Q_VSA_PPOS	-0.2590	0.1427	-0.0828	0.1835
a_don	1.1124	-0.4039	-0.7429	-0.1935
SlogP_VSA1	0.5280	0.6645	-0.9109	0.2814
SlogP_VSA7	-0.1556	0.8763	0.0510	-0.5787
SlogP_VSA8	-1.2608	0.0349	1.2674	-0.0822
SMR_VSA3	0.3542	-0.0682	0.0179	-0.1583
DCASA	-0.2226	-0.4192	0.7029	0.1690
ClogP	0.9107	0.2462	0.4119	-1.6023
Summed Contribution (SC)	0.6414	0.3298	0.0288	0.0001

In summary, we developed and tested the QSAR prediction models, using (i) the full dataset as training as well as test set, and (ii) 10-fold cross validation test (described in Section II.C ‘Methodology’). The corresponding correlation coefficient (R) and RMSE values were reported in Table 2. We observed that the prediction models developed using GA-ANN descriptors are superior in terms of R and RMSE values when the full set is used for training as well as testing. The same is also true when 10-fold cross validation is used, except for the MLR prediction models which show better performance with the GA-CFS descriptor set.

IV. CONCLUSION

We applied four hybrid-GA descriptor selection techniques (GA-MLR, GA-DT, GA-CFS, GA-ANN) coupled with three statistical and machine-learning QSAR approaches (MLR, DT and ANN) for the prediction of biological activity of compounds on a quality-assured dataset of HIV protease inhibitors (Tipranavir analogs). This dataset was compiled in-house and has not been studied earlier using these methods.

All the four feature optimization approaches performed consistently, and the selected descriptors represented the whole descriptor space (Figures 3 and 6). Although the descriptors obtained using these approaches are different, they could account well for the binding nature of the considered dataset.

All the three QSAR techniques yielded the models with good prediction performance (Table 2). However, the ANN prediction models are slightly better than the MLR and DT models, whereas the MLR models have superior mechanistic interpretation. The weight analysis of the GA-ANN descriptors was carried out to interpret these models. Analysis of all three models provided useful insights about the role of various descriptors in predicting biological activity of compounds, including the involvement of hydrophobic interactions.

This study showed that the use of a hybrid GA-based descriptor selection technique in combination with a QSAR technique can provide robust prediction models with much better predictability as well as mechanistic interpretation. These models will further enhance our understanding of the hydrophobic and other interactions between HIV protease and its inhibitors.