Exploring QSAR of non-nucleoside reverse transcriptase inhibitors by artificial neural networks: HEPT derivatives

.


Introduction
Acquired immunodeficiency syndrome (AIDS) is caused by the depletion of helper Tlymphocytes 1 through infection by the human immunodeficiency virus 2 type 1 (HIV-1) 3 and human immunodeficiency virus type 2 (HIV-2). 4Both of these retroviruses require a reverse transcriptase (RT) to convert viral RNA into proviral DNA 5,6 that can then be inserted into the host DNA.RT has become an important target for drug discovery because of its critical role in HIV production.RT inhibitors can be divided into two major categories; nucleoside analogues and non-nucleoside inhibitors.Nucleoside analogues 7 cause chain termination when they are incorporated within newly synthesized DNA.Non-nucleoside inhibitors block RT by binding to ARKAT USA, Inc.
General structure of HEPT derivatives.
The structures and anti-HIV-1 activities of these compounds were described previously. 27,28he anti-HIV activity of the compounds has been expressed by the compound's ability to protect MT-4 cells against the cytopathic effect of the virus.The concentration of the compound leading to 50% effect has been measured and expressed as EC 50 .The logarithm of the inverse of this parameter has been used as biological end points in the QSAR studies.
The chemical structure along with observed activity data of the compounds used in this study are shown in Table 1.

Neural Network
All the feed-forward NN used in this paper are three-layer networks with the first (input) layer having five neurones, representing the relevant descriptors obtained in MLR technique. 29lthough there are neither theoretical nor empirical rules to determinate the number of hidden layers or the number of neurone layers, one hidden layer seems to be sufficient in the most chemical application of ANN.The output layer represents the calculated activity values log (1/EC 50 ).Figure 2a show a typical architecture of such ANN.This is formed in three layers, called the input layer, hidden layer, and output layer.Each layer consists of one or more neurons, represented in this diagram by the small circles.The line between the neurons indicates the flow of information from one neuron to the next.The neurons of the input layer are passive while those of the hidden and output layers are active.The variables: X1 1 , X1 2 …, X1 5 (see text below) hold the data to be evaluated.Each value from the input layer is duplicated and sent to all of the hidden neurons (fully interconnected structure).As shown in Fig. 2b, the values entering the hidden neurons are multiplied by weights (the W i values).The weighted inputs are then added to produce a single number (shown in the diagram by the symbol Σ).Before leaving the neuron, this number is passed through a nonlinear mathematical function called sigmoid.This is an "S" shaped curve that limit the neuron's output between 0 and 1.

Computation
In a back-propagation ANN the input and output neurons are known since they represent respectively, in this study, the descriptors used and the anti-HIV-1 activity.Unfortunately, there are neither theoretical results available, nor satisfying empirical rules that would enable us to determine the number of hidden layers and of neurons contained in these layers.It seems that, for most applications of the ANN to chemistry, one hidden layer is sufficient. 30However, for the determination of the number of hidden neurons, some authors 31,32    MLR was performed on all compounds described in Table 1, a few suitable models were obtained and the pertinent descriptors appearing in the best one were selected to perform the ANN model (see Table 2).
To remain close to the experimental error (5%), we also take away the 8 molecules having higher than where d i is the value of descriptor i and is the mean of observed activity.The molecules that were removed are labelled with an asterisk in Table 1.Consequently, a new model was derived on 95 molecules.The [5-7-1] neural network architecture was developed with the optimum momentum 0.9 and with 10000 iterations.The seven hidden neurone were chosen to maintain ρ between 1 and 3 (1< ρ < 3).To verify this condition we have also performed a trial by taking five to thirteen neurons in the hidden layers.The best results for the training and tests are given in the is that corresponding to the optimum r and SEC parameters.A hidden layer of seven neurones was selected.
Table 2. Some of significant MLR models obtained for all compounds described in Table 1   With the above architecture, a correlation coefficient of 0.968 (n = 95) between calculated and observed log (1/EC 50 ) with a standard error of 0.413 was obtained.In comparison (see also figure 3), the model established with MLR gave a correlation coefficient of 0.916 and a standard error of 0.493.
ARKAT USA, Inc.Based on this result, a comparison of the quality of de MLR and ANN models shows that the ANN models have substantially better predictive capability because the ANN approach gives better results than MLR.The standard errors of calculation are lower and the correlation coefficients are higher with ANN than with regression analysis.This preliminary study enables us to conclude that all the NN architectures were able to establish a satisfactory relationship between the molecular descriptors and the anti-HIV-1 activity.

Assessment of the neural network validity and predictive ability
The ability of the network to learn the data and predict the biological activity was tested by the "leave-one-out" cross-validation. 33In this procedure one compound is removed from the 95 subsets data set.And the output of the removed compound was predicted for each subset.The cross-validation coefficient q 2 was then calculated according the following equation. 34ere PRESS is the predictive residual sum of squares.They yielded a q² = 0.8779 indicating a good predictive quality of the model, according to Wold. 35

Analysis of descriptor's contribution in ANN model
The contribution of descriptors i (i = 1-5) was estimated from the trained [5-7-1] configuration network.The descriptor under study was removed from the [5-7-1] trained ANN together with its corresponding weights.Then the network [4-7-1] calculated the output of each molecule as usual.The mean of the deviations absolute values ∆m i between the observed activity and the estimated one for all compounds was calculated.This process was reiterated for each descriptor.Finally, the contribution C i 36 of descriptor i is given by:  The comparison of the quality of the MLR and ANN models (Figure 5) shows that the latter have substantially better predictive capabilities.

Figure 2 .
Figure 2. Typical architecture of a three layer artificial neural network (a) and flow diagram of the active neurons used in the hidden and output layers (b).

yFigure 3 .
Figure 3. Observed versus calculated anti-HIV activities obtained with the ANN (a) and MLR (b) models.

Figure 4 .
Figure 4. Descriptor's contribution in the ANN model.

Figure 4
Figure 4 indicate that the relative importance of the descriptors varied in the following order: log P(R 3 ) > MW(R 3 ) > En > MR(R 4 ) > HBA(R 4 ).The comparison of the quality of the MLR and ANN models (Figure5) shows that the latter have substantially better predictive capabilities.

Figure 5 .
Figure 5. Observed (closed circles) and predicted (open circles) activity values with the ANN (a) and MLR (b)models.

Table 1 .
Chemical structure of HEPT derivatives and observed anti-HIV activities EC50) observed values were used as dependant variable in which EC50 represents the molar concentration of drug required to achieve 50% protection of MT-4 cells against effect of HIV-1.The molecules designated with an asterisk (*) were removed later based on their di value (see text below) to perform a new ANN model derived from the remains 95 subset data set.
have proposed a parameter ρ, which plays a major role in determining the best ANN architecture.ρ = (Number of data points in the training set / Sum of the number of connection in the NN).

Table 3 .
The best model ARKAT USA, Inc.

Table 3 .
Standard error of computation (SEC) and correlation coefficient obtained by NN trained with 95 data points