ORIGINALARTICLE The Carbohydrate and Caloric Content of Concomitant Medications for Children with Epilepsy on the Ketogenic Diet Denis Lebel, Caroline Morin, Micheline Laberge, Nathalie Achim and Lionel Carmant ABSTRACT: Background: The ketogenic diet for children with refractory epilepsy requires a strict control of the amount of ingested carbohydrates. This can be altered by medicati
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No job nameJ. Chem. Inf. Comput. Sci. 2000, 40, 773-777
Estimation of Aqueous Solubility for a Diverse Set of Organic Compounds Based on
Division of Pharmaceutical Chemistry, Department of Pharmacy, POB 56, FIN-00014, An accurate and generally applicable method for estimating aqueous solubilities for a diverse set of 1297organic compounds based on multilinear regression and artificial neural network modeling was developed.
Molecular connectivity, shape, and atom-type electrotopological state (E-state) indices were used as structuralparameters. The data set was divided into a training set of 884 compounds and a randomly chosen test setof 413 compounds. The structural parameters in a 30-12-1 artificial neural network included 24 atom-type E-state indices and six other topological indices, and for the test set, a predictive r2 ) 0.92 and s )0.60 were achieved. With the same parameters the statistics in the multilinear regression were r2 ) 0.88 ands ) 0.71, respectively.
not be representative but compiled from structural analogues.
The use of a small and limited set of compounds in the The aqueous solubility of drug compounds is one of the training sets leads to models of closed systems, and their most important factors in determining its biological activity.
general applicability is questionable. This is clearly demon- In many cases drugs that show a good activity when strated by the fact that only three of above-mentioned administered parenterally maybe totally inactive when given methods6,7,17 have been applied to the test set designed by orally. In such cases poor oral activity is often due to the Yalkowsky.19 This test set contains 21 drug molecules and fact that a sufficient amount of drug to desired response is environmentally interesting compounds, like pesticides, with not reached in the site of action. Hence an insufficient aqueous solubility is likely to hamper bioavailability of the In our earlier studies we have shown that aqueous drugs. In recent years high-throughput screening, where solubilies,17 log S, and partition coefficients,20 log P, for drug collections of thousands of compounds are screened with compounds can be estimated with a reasonable accuracy on the intention of finding relevant biological activity, has the basis of parameters derived from molecular topology.
proven valuable in finding new lead compounds.1 It has been In this study we propose a method for estimating log S values noticed that the synthesis of combinatorial libraries tends to with the same parameters but for a much larger and diverse result in compounds with higher molecular weights and higher lipophilicity, and presumably lower aqueous solubility,than with conventional synthetic strategies. For this reason computational screens have been suggested and used to selectsublibraries with relevant physicochemical properties to the The applicability and accuracy of a log S estimation range of known values, such as lipophilicity and solubility, method are strongly affected by the size and quality of the of the orally active drugs.2-5 Hence there is a strong interest training set used. Experimental aqueous solubility values for in fast, reliable, and generally applicable structure-based the compounds used in this study were obtained from the methods for prediction of aqueous solubility of new drugs AQUASOL dATAbASE of the University of Arizona21 and before a promising drug candidate has even been synthesized.
SCR’s PHYSPROP Database.22 A set of 1297 organic Several approaches have been developed for the prediction compounds was extracted from these databases and was of aqueous solubility based on nonexperimental structural divided into a training set of 884 compounds and a randomly parameters. These can be divided in substructure (group chosen test set of 413 compounds. The aqueous solubility contribution) approaches6-8 and in approaches where pa- values in 20-25 °C expressed as log S, where S is solubility rameters are calculated directly from molecular structure,9-18 in mol/L, were used. The log S values of the training set such as topological indices, molecular volume, molecular ranged from -11.62 to +1.58 with a mean of -2.70 and surface area, etc. These methods employ multilinear regres- standard deviation of 2.01. For the testing set, the smallest sion or neural network modeling and varying ways of log S value was -10.41 and the largest +1.13. The mean structural parametrization. However, currently used methods and standard deviation were -2.77 and 2.07, respectively.
were developed from relatively small training sets (n ) 200-300). One problem with small training sets is that they might Three different types of topological indices introduced by Kier and Hall23-26 were used as structural parameters and 774 J. Chem. Inf. Comput. Sci., Vol. 40, No. 3, 2000
were calculated using the Molconn-Z (Hall Associated Table 1. Structural Parameters in the Multilinear Regression Model
Consulting, Quincy, MA) software with structure input for each analyzed compound using the SMILES line notation code. Simple and valence molecular connectivity indices up and 1-3 ν), shape indices (1-3κ, 1-3κR), flexibility index (φ), the number of hydrogen-bonding donors (HBD) and acceptors (HBA), and 39 atom-type electrotopological state (E-state) indices were calculated.
Cross-correlation analysis showed that pairwise correlations were r2 < 0.80; hence, all these 55 parameters contain useful (B) Atom-type Electrotopological State Indicesb information and could be used in regression analysis.
The multilinear regression (MLR) analysis was performed with SPSS software (v.8.0, SPSS Inc., Chicago, IL) running on a Pentium PC. The quality criteria on the fit in MLR analysis were squared correlation coefficient, r2, standard deviation, s, and Fischer significant value, F, when all parameters in the model were significant at the 95% The artificial neural network simulations were carried out using NeuDesk software (v 2.20, Neural Computational sciences, U.K.). A three-layered, fully connected neural network was trained by the standard back-propagation learning algorithm with a logistic f(x) ) 1/(1 + e-x) activation function for both hidden and output nodes. The same set of parameters as in the MLR equation was tested in artificial neural networks (ANNs) with one output neuron, Before the training was started, the input and output values were scaled between 0.1 and 0.9, and adjustable weights between neurons were given random values of between -0.5 and 0.5. The learning rate and momentum parameter were set at 0.1 and 0.9, respectively. The training end point was determined on the basis of the average training error (E), Indicator variable for compounds that contain only aliphatic C and H. b According to Kier and Hall.25 c The number of compounds for which is the mean-square error between the target and actual output. The optimal training end point was searched forovertraining the network. It has been accepted that the ratio, Stepwise and backward methods were employed in the , of the number of input parameters to the number of regression analysis, and the following equation containing weights should be greater than 2.0, although cross-validation 30 parameters was calculated for the training set allows for the use of smaller values.27,28 Hence networks with8, 10, 12, and 14 neurons in the hidden layer were studied.
The network architecture and the training end point giving the highest coefficient of determination, r2pred, and the loweststandard error s for the predictions of the test set were then n ) 884, r2 ) 0.89, s ) 0.67, F ) 227.31, used. To avoid chance effects, the predictions were repeated 10 times with different random starting weights in thenetwork, and the averaged log S values were calculated.
In this equation, n is the number of compounds used in thefit, F is the overall F-statistics for the addition of each successive term, r2cv is squared correlation coefficient of In this study the aqueous solubility values of a diverse set prediction in leave-one-out cross-validation, and ai and Si of 1297 organic compounds were compiled from two highly are the regression coefficients and the corresponding struc- evaluated databases. The data set was divided into a training tural parameters. The regression coefficients in the equation set of 884 compounds for developing the MLR and ANN are indicated in Table 1 with the t-scores of the significant models and a randomly chosen test set of 413 compounds parameters, and an example calculation of log S values by (test set 1) for evaluating the predictive ability of the models.
regression coefficients is given in Table 2. In the leave-one- Another test set of 21 compounds (test set 2) was also used out prediction of the MLR model, standard deviation of and allowed comparison of the predictions with earlier 0.71, is only 0.04 unit higher than for the fitting model, s ) 0.67. Such a small increase indicates a Myrdal et al.29 pointed out that the experimental solubility robustness of the model. Multilinear regression was also able values can differ by ∼1.0 log unit, especially for compounds to predict the log S values for 413 compounds in the test set with a very low log S value. Hence, for the training sets that with a coefficient of determination of r2 are compiled from relatively complex chemical structures, standard deviation of prediction s ) 0.71, which are in a standard deviation, s, will be not lower than ∼0.5 log unit.
good agreement with the results for the training set.
J. Chem. Inf. Comput. Sci., Vol. 40, No. 3, 2000 775
Table 2. E-State Indices Calculated for Benzocaine along with the
Atom-type E-State Indicesa and an Example of Calculating log S
Valueb by Regression Coefficients
Figure 1. Correlation of calculated log S vs observed log S values
for the training set by neural network.
a According to Hall and Kier.24 b log S ) -0.4381 + 0.1171 ν - 0.052φ - 0.475HBA - 0.438Ar - 1.96Alif - 0.174SsCH 0.205SssCH2 - 0.08SaaCH + 0.115SdssC - 0.078SaasC + 0.117Ss-NH + 0.048SdO + 0.160SssO - 1.35 ) -1.85 (estimated), -2.32 Table 3. Comparison of Predictive Ability of Multilinear
Regression and Neural Network Models Using the Same Set of
Figure 2. Correlation of predicted log S vs observed log S values
for the test set 1 by neural network.
training set, r2 ) 0.94, s ) 0.47, and n ) 884 and the test 0.92, s ) 0.60, and n ) 413, respectively.
Statistics for the estimated aqueous solubilities of the organic compounds in the training set and test sets are This study. b Our previous study.17 presented in Table 3. The calculated and experimentalaqueous solubilities of the training set and test sets are plotted It was possible that there were some nonlinear depend- in Figures 1-3. The list of all compounds and experimental encies between MLR optimized parameters and log S values.
and estimated log S values is available as Supporting Hence, an application of nonlinear methods of data analysis could provide a better modeling of data. The back-propaga- The general applicability for the prediction ability of tion artificial neural networks were used to detect the aqueous solubility was tested by the test set designed by presence of nonlinear dependencies in the analyzed data set Yalkowsky.19 This test set is compiled of 21 commonly used compounds of pharmaceutical and environmental interest.
The same set of the structural parameters as in the The results of the predictions for this test set are presented regression equation was used as inputs in neural network in Table 4. The present multilinear regression and neural modeling. Several assays were made to find the optimal network models gave standard deviations s ) 0.88 and 0.63.
training end point and network architecture. The best In our previous study17 the results by neural network were s performance of the network was achieved with 12 neurons ) 1.25 for all 21 compounds and s ) 0.55 for a subset of in the hidden layer with the value of F ) 2.30. The optimal 13 pharmaceuticals. Hence a significant improvement was training end point, E ) 0.032, required ≈2300 training achieved, and the predictions were better than those made epochs when an ANN architecture of 30-12-1 was used.
by Klopman6 and Ku¨hne.7 An interesting point of view is The neural network was able to estimate, with a reasonable that Ku¨hne used melting points in their group contribution degree of accuracy, most of the aqueous solubilities of the approach and got a better fit for the training set of 694 776 J. Chem. Inf. Comput. Sci., Vol. 40, No. 3, 2000
Table 4. Observed and Predicted Aqueous Solubilities for the Test Set 2
a Outliers in Klopman’s model. b Predicted values not given.
We thank William Howard from Syracuse Research Corporation for giving the PHYSOPROP database for ouruse and the Technology Development Center in Finland forfinancial support.
Supporting Information Available: Appendix I, giving
the names of the compounds used in this study with theircalculated and experimental aqueous solubility values (24pages). This material is available free of charge via theInternet at http://pubs.acs.org.
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