Aqueous Solubility

A rapidly advancing area of modern pharmaceutical research is the prediction of the aqueous solubility of complex drug-sized compounds from their molecular structures. The ability to design novel entities with sufficient aqueous solubility can bring many benefits to both pre-clinical research and clinical development. For example, accurate activity measurements can be obtained only if the substance is sufficiently soluble—above the detection limits of the assay. Otherwise, a potentially good SAR can be obscured by apparent poor activity due to insufficient solubility rather than inadequate potency. Finding a ligand with adequate solubility is also a key factor that determines the success of macromolecular structure determination. In X-ray crystallography, the formation of crystals appears to be very sensitive to the solubility of ligands. Most biostructural NMR experiments require ligands dissolved at a relatively high concentration in a buffer. At a more downstream level in drug development, the solubility of a drug candidate has perhaps the most profound effect on absorption. Although pro-drug strategies or special methods in pharmaceutical formulation can help to increase oral absorption, the solubility largely dictates the route of drug administration and, quite often, the fate of the drug candidates.

The aqueous solubility of a substance is often expressed as log units of molar solubility (mol/L), or logS. It is suggested that solubility is determined by three major thermodynamic components that describe the solubilization process.⁴ The first is the crystal packing energy, which measures the strength of a solid lattice. The second is the cavitation energy, which accounts for the loss of hydrogen bonds between the structured water upon the formation of a cavity to host the solute. The third is the solvation energy, which gauges the interaction energy between the solute and the water molecules. To account for these effects, a number of experimental and theoretical descriptors have been introduced to solubility models in the past year. Some of them include melting points,^12–14 cohesive interaction indices,¹⁵ solvatochromic parameters,^16,17 shape, electronic and topological descriptors,^18–23 and mobile order parameters.²⁴ Most of this work has been summarized in an excellent review by Lipinski et al,⁴ and will not be discussed here. In this Section, we will focus on some of the most recent developments involving the use of neural networks to correlate a set of physicochemical or topological descriptors with experimental solubility.

The earliest neural network-based solubility model in the literature was reported by Bodor and coworkers.¹⁸ Fifty-six molecular descriptors, which mostly accounted for geometric (e.g., surface, volume, and ovality), electronic (e.g., dipole moment, partial charges on various atom-types) and structural (e.g., alkenes, aliphatic amines, number of N-H bonds) properties, were generated from the AMPAC optimized structures of 311 compounds. Empirically, Bodor et al determined that 17 out of the 56 descriptors seemed most relevant for solubility and the resulting 17–18–1 neural network yielded a standard deviation of error of 0.23, which was superior to the corresponding regression model (0.30), based on identical descriptors. In spite of such success, we think that there are two major deficiencies in this neural network model. First, the use of 18 nodes in the hidden layer may be excessive for this application, given that there are only ∼300 training examples. Second, some of the 17 input descriptors are, in our opinion, redundant. For example, the inclusion of functional transforms of a descriptor (e.g., Q_N² and Q_N⁴ are functions of Q_N) might be unnecessary because a neural network should be able to handle such mapping implicitly. To overcome such limitations PCA and smaller networks could be applied.

The research group of Jurs at Pennsylvania State University has investigated many QSPR/QSAR models for a wide range of physical or biological properties based on molecular structures.^{21–23,25–31} Recently, they published two solubility studies using their in-house ADAPT (Automated Data Analysis and Pattern Recognition Toolkit) routine and neural network modeling.^22,23 Briefly, each molecule was entered into the ADAPT system as a sketch and the three-dimensional structure was optimized using MOPAC with the PM3 Hamiltonian. In addition to topological indices, many geometric and electronic descriptors, including solvent-accessible surface area and volume, moments of inertia, shadow area projections, gravitational indices, and charged partial surface area (CPSA) were computed. To reduce the descriptor set they applied a genetic algorithm and simulated annealing techniques to select a subset of descriptors that yielded optimal predictivity of a 'validation' set (here, a small set of test molecules that was typically 10% of the training set). In the first study,²² application of the ADAPT procedure to 123 organic compounds led to the selection of nine descriptors for solubility correlation. The rms errors of the regression and the 9–3–1 neural network models were 0.277 and 0.217 log units, respectively. In the next study,²³ the same methodology was applied to a much larger data set containing 332 compounds, whose solubility spanned a range of over 14 log units. The best model reported in this study was a 9–6–1 neural network yielding a rms error of 0.39 log units for the training compounds. It is noteworthy that there was no correspondence between any of the current descriptors to the set that was selected by their previous model. A possible explanation is that the ADAPT descriptors may be highly inter-correlated and therefore the majority of the descriptors are interchangeable in the model with no apparent loss in predictivity.

Perhaps the most comprehensive neural network studies of solubility were performed by Huuskonen et al.^32–34 In their first study,³² system-specific ANN models were developed to predict solubility for three different drug classes, which comprised 28 steroids, 31 barbituric acid derivatives, and 24 heterocyclic reverse transciptase (RT) inhibitors. The experimental logS of these compounds ranged from −5 to −2. For each class of compounds, the initial list of descriptors contained ∼30 molecular connectivity indices, shape indices, and E-state indices. Five representative subgroups of descriptors were established, based on the clustering of their pairwise Pearson correlation coefficients. A set of five parameters were then selected, one from each subgroup, as inputs to a 5–3–1 ANN for correlation analysis. Several five-descriptor combinations were tried, and those that gave the best fit of training data were further investigated. To minimize overtraining, an early stopping strategy was applied, so that the training of the neural network stopped when the leave-one-out cross-validation statistics began to deteriorate. The final models yielded q² values of 0.80, 0.86, and 0.72 for the steroids, barbiturates, and RT inhibitors classes, respectively. Overall, the standard error of predictions was approximately 0.3 to 0.4 log units. Since each ANN was optimized with respect to a specific compound class, it was not surprising that application of solubility models derived from a particular class to other classes of compounds yields unsatisfactory results. It was more surprising, however, that the effort to unravel an universal solubility model applicable to all three classes of compounds also proved unsuccessful (Note: They could, in theory, obtain reasonable predictivity for the combined set if an indicator variable was introduced to specify each compound class. However, this would obviously defeat the purpose of a generally applicable model). One possible explanation is that the combined data set (83 compounds in total) contained compounds segregated in distinct chemical spaces and it would be difficult to find a set of common descriptors that could accurately account for the behavior of each group of compounds.

In their next study,³³ Huuskonen et al collated experimental solubilities of 211 drugs and related analogs from literature. This set of compounds spanned approximately six log units (from −5.6 to 0.6), which was almost twice the range of their previous study. Thirty-one molecular descriptors, which included 21 E-state indices, 7 molecular connectivity indices, number of hydrogen donors, number of hydrogen acceptors, and an aromaticity indicator, were used initially in model building. The final number of descriptors was later pruned to a subset of 23 by probing the contribution of each individual parameter. The final ANN model had a 23–5–1 configuration, and yielded r² = 0.90, and s = 0.46 for the 160-member training set, and r² = 0.86, s = 0.53 for the remaining 51 test compounds. Besides these descriptive statistical parameters, the authors also published the individual predictions for these compounds. Because all 24 RT inhibitors from the previous study were part of the data set, this allowed us to investigate the relative merit of a system-specific solubility model versus a generally applicable model. Of the 24 compounds, 20 were selected for the training set, and 4 were used as test compounds. Figure 2(a) shows the predicted versus observed aqueous solubilities for the RT inhibitor in their previous system-specific model, and Figure 2(b) is the corresponding plot for the predicted solubilities from the general purpose model. It is clear that, although the predictions of most RT inhibitors were within the correct solubility range (logS ∼ _2 to _5), a comparison of individual predictions for this class of compounds reveals very weak correlation (r² = 0.16; s = 0.73). This result contrasted sharply with the very good predictivity (r² = 0.73; s = 0.41) when the RT inhibitors had been considered on their own.³² This supports the notion that a system-specific solubility predictor is more accurate than a general one, though the former obviously has only limited scope. Thus, one must choose an appropriate prediction tool depending on the nature of the intended application. For instance, if the emphasis is on a single class of compounds we should consider the construction of a specialist model (provided there are sufficient experimental data for the series) or recalibrate the general model by seeding its training set with compounds of interest.

Figure 2

Predicted versus experimental solubility for the 24 RT inhibitors using (a) a system-specific solubility model and (b) a general model.

In his most recent study,³⁴ Huuskonen attempted to improve the accuracy and generality of his aqueous solubility model by considering a large, diverse collection of ∼1,300 compounds. The logS values for these compounds ranged from _11.6 to +1.6, which essentially covers the range of solubilities that can be reliably measured. The full data set was partitioned to a randomly chosen training set of 884 compounds and a test set of 413. Starting from 55 molecular connectivity, structural, and E-state descriptors, he applied a MLR stepwise backward elimination strategy to reduce the set to 30 descriptors. For the training data, this equation yielded r² = 0.89, s = 0.67, and r²_cv = 0.88, s_cv = 0.71. The statistical parameters for the 413 test set were essentially identical to that of leave-one-out cross-validation, thereby indicating the generally robust nature of this model. He applied ANN modeling to the same set of parameters in order to determine whether the prediction could be further improved via nonlinear dependencies. Using a 30–12–1 ANN, he obtained r² = 0.94, s = 0.47 for the training set, and r² = 0.92, s = 0.60 for the test set, which were both significantly better than the MLR model. The general applicability of the MLR and ANN models was further verified by application to a set of 21 compounds suggested by Yalkowsky,³⁵ which has since become a benchmark for novel methods. The r² and s values for the MLR model are 0.83 and 0.88, and for the ANN, 0.91 and 0.63, in good agreement with their respective cross-validated and external test statistics. Both results were, however, significantly better than those derived from their previous model constructed using 160 training compounds (r² = 0.68, s = 1.25). This indicated that a large and structurally diverse set of compounds were required to train a model capable of giving reasonable solubility predictions for structures relevant to pharmaceutical and environment interest, such as the set of compounds under consideration in this study.

logP

The n-octanol/water partition coefficient of a chemical is the ratio of its concentration in n-octanol to that in aqueous medium at equilibrium. The logarithm of this coefficient, logP, is perhaps the best-known descriptor in classical QSAR studies. The reason for the usefulness of this property is related to its correlation with the hydrophobicity of organic substances, which plays a key role in the modulation of many key ADME processes. Specifically, drug-membrane interactions, drug transport, biotransformation, distribution, accumulation, protein and receptor binding are all related to drug hydrophobicity.³⁶ The significance of logP is also captured by the Rule-of-5,⁴ which states that a molecule will likely be poorly absorbed if its logP value exceeds five. Other researchers also established links between logP and blood-brain barrier (BBB) penetration, a critical component in the realization of activity on the central nervous system (CNS).^10,37–42 For CNS-active compounds, usually a logP around 4–5 is required.

One of the earliest attempts to derive logP values from computational means was the f-constant method proposed by Rekker.⁴³ Later, Leo and Hansch made a significant advance to this fragment-based approach that ultimately led to the successful development of the widely popular ClogP program.⁴⁴ In summary, they assumed an additive nature of hydrophobicity values from different molecular fragments, whose parameter values were calibrated by statistical analysis of a large experimental database. To estimate the logP value of a novel molecule, the chemical structure is first decomposed into smaller fragments that can be recognized by the program. The logP value of the molecule is simply the incremental sum of parameter values from the composite fragments, and in some cases, additional correction factors. The main advantage of a fragment-based method is that it tends to be very accurate. However, this approach suffers from two major problems. The first is that the molecular decomposition process is often very tricky. The second, and the more serious, concerns missing parameter values when a given structure cannot be decomposed to structures for which fragment values are available. Thus, it becomes more fashionable to treat the molecule in its entirety, and to correlate its logP value with descriptors that are easy to calculate. Most published reports follow this scheme and are based on the use of MLR or ANN on some combination of electronic and steric properties. For example, molecular descriptors such as atomic charges, hydrogen bond effects, molecular volumes or surface areas have been considered in this role.

Schaper and Samitier proposed a logP method based on an ANN to determine the lipophilicity of unionized organic substances by recognition of structural features.⁴⁵ Molecules were encoded by a connection table, where indicator variables were used to denote the presence or absence of specific atoms or bonds in different molecular positions. Eight different atom types (C, N, O, S, F, Cl, Br, and I) and four different bond types (single, double, triple, and resonant) were represented in their implementation. For compounds with up to 10 non-hydrogen atoms, a full description of the molecule required 260 variables (10 × 8 indicator variables for atoms and 45 × 4 for bonds). After preliminary analysis of their data set, which was comprised of 268 training and 50 test compounds, 147 non-zero descriptors were retained. They experimented with three different hidden layer configurations (2, 3, and 4 hidden nodes) and suggested that an ANN with three hidden layer neurons was the optimal choice based on the prediction accuracy of the test set. The 147–3–1 NN yielded a Pearson correlation coefficient (r_trn) of 0.98 and a standard deviation (s_trn) of 0.25 between observed and calculated logP values for the training compounds. It is interesting to note that, despite the use of a large number of adjustable parameters (448), this particular NN showed little evidence of overfitting: the test set correlation coefficient (r_tst) is 0.88 and standard deviation (s_tst) = 0.66. The authors suggested that with a decrease in the rho (r) ratio (either an increase in data objects or a reduction in non-critical indicator variables), the predictivity of this type of NN system would further increase. The major shortcoming of this approach is that the molecular representation is based on connection matrix/indicator variables. Their study was limited to compounds containing no more than 10 non-hydrogen atoms. With a connection matrix, the number of input descriptors to the ANN increases quadratically with the maximum number of allowed atoms (N_MaxAtom) in the data set. For example, using the current scheme of 8 atom-types and 4 bond-types, the total number of descriptors is calculated by:

If we were to apply this method to drug-size molecules, which contain on average of 20–25 non-hydrogen atoms, then the ANN would need to deal with approximately 1,000 indicator variables. Introduction of new atom-types, such as phosphorus, would add further complexity to the molecular description. This begs the question: are all these descriptors necessary to produce a sound logP model? The answer is, most probably, no. We speculate that because molecular connectivity descriptors have no physical meaning a large number of them is required to depict or correlate physicochemical properties. If physically meaningful descriptors are used, then one may obtain a more direct relationship from fewer predictors.

In a recent study, Breindl, Beck, and Clark applied semi-empirical methods to obtain a small set of quantum chemical descriptors to correlate the logP values for 105 organic molecules.⁴⁶ They used the CONCORD program to convert 2D connectivity into standard 3D structures,⁴⁷ whose geometries were further refined by energy minimization using SYBYL.⁴⁸ The structures were then optimized using VAMP,⁴⁹ a semi-empirical program. The input descriptors, which included both electrostatic and shape properties of the molecules, were derived from AM1 and PM3 calculations. Using MLR analysis, they derived a 10-term equation that reported a r_trn value of 0.94 and r_cv of 0.87. The choice of descriptors for this MLR model was further analyzed using ANN. With a 12–4–1 back-propagation network, they improved the fitting of the training set to r_trn = 0.96 and r_cv = 0.93 and, furthermore, the neural network also seemed to perform consistently well on 18 test set molecules. Finally, this approach was validated with a larger data set of 1085 compounds, for which 980 molecules were used as the training set and 105 were held back for testing. The best performance was obtained with a 16–25–1 network, which yields a r_trn = 0.97 for training and a r_cv of 0.93 with the AM1 parameters, and a slightly worse (r_trn = 0.94 and r_cv = 0.91, s_trn = 0.45) result for the PM3 set. Again, the validity of the neural network result was confirmed by accurate test set predictions, which yielded impressive statistical parameters of r_tst = 0.95 and s_tst = 0.53 for the AM1 result and, again, slightly worse values for the PM3 set (r_tst = 0.91; s_tst = 0.67). The deficiency of the PM3 set was further analyzed, and it was concluded that there was a systematic problem with the estimation of logP values for those compounds with large alkyl chains. They reasoned that the large error was due to the uncertainty of appropriate conformations from gas phase geometries under their setup. By systematically varying the values of one input descriptor while keeping others fixed, they concluded that the logP values were predominately influenced by three descriptors, namely polarizability, balance u, and charge OSUM. Furthermore, a direct linear dependence between logP and polarizability was observed. On the other hand, the effects for the balance parameter and OSUM were shown to be highly non-linear with respect to logP. Overall, it seems that reliable logP models can be sought using a few quantum chemical parameters, although the time-consuming nature of the calculation makes it less attractive for analysis of large virtual libraries.

To address some of the limitations of the older QSPR approaches, Huuskonen and coworkers proposed the use of atom-type electrotropological state (E-state) indices for logP correlation.³⁶ The E-state indices were first introduced by Kier and Hall,^50,51 and have been validated in many QSAR and QSPR applications. They capture both the electronic and topological characteristics surrounding an atomic center as well as its neighboring environment. In the implementation of E-state descriptors by Huuskonen et al, several new atom-types corresponding to contributions from amino, hydroxyl, and carbonyl groups in different bonding environments were introduced. This level of detail seems particularly relevant for the purpose of hydrophobicity modeling. For instance, it is known that an aromatic amino group is generally less basic than its aliphatic counterpart, which makes the former less likely to ionize and presumably more hydrophobic. The use of the extended parameter set was justified by a significant improvement in cross-validated statistics of the 1,754 training set. An MLR model using 34 basic E-state descriptors yielded a q² value of 0.81 and an RMS_cv of 0.64; whereas with 41 extended parameters, the corresponding values were 0.85 and 0.55. Huuskonen et al also applied an ANN to be able to model higher-order nonlinearity between the input descriptors and logP. The final model, which had a 39–5–1 architecture, gave a q² value of 0.90 and an RMS_cv 0.46 for leave-one-out cross-validation. Further validation on three independent test sets yielded a similar RMS error (0.41), thereby confirming the consistency of the predictions. The logP predictions of this new method were compared to those derived from commercial programs. It was found that this method was as reliable or better than the established methods for even the most complex structures.

In our opinion, the approach of Huuskonen and coworkers represents a method of choice for fast logP estimation, particularly for applications where both speed and accuracy are critical. Because the algorithm does not depend on the identification of suitable basis fragments, the method is generally applicable. Unlike methods that utilize quantum chemical descriptors, the calculation is genuinely high-throughput because E-state indices can be computed directly from SMILES line notation without costly structure optimization. Furthermore, this hydrophobicity model, which was developed using ∼40 descriptors, can account for most, if not all, molecules of pharmaceutical interest. In contrast, a connectivity table representation may require on the order of thousands of input values, which also increases the risk of chance correlation. The major limitation of the Huuskonen hydrophobicity method is the difficulty of chemical interpretation. This is in part due to the topological nature of the molecular description and in part the use of nonlinear neural networks for property correlation. Particularly, it is hard to isolate the individual contributions of the constituent functional groups to the overall hydrophobicity; or conversely, to design modifications that will lead to a desirable property profile (i.e., the inverse QSPR problem). Another important issue that has not been addressed concerns the treatment of ionizable compounds, which may adopt distinct protonation states under different solvent environments (e.g., water and 1-octanol). Currently, this phenomenon is either ignored or assumed to be handled implicitly. Together with the inverse QSPR problem, the correct handling of such molecules will be the major question that needs to be answered by the next generation logP prediction systems.

Human Intestinal Absorption

The major hurdle in the development of a robust absorption model—and other models—is very often the lack of reliable experimental data. Experimental percent human intestinal absorption (%HIA) data have generally large variability and are usually skewed to either very low or very high values, with only few compounds in the intermediate range. Jurs and coworkers collated a data set of 86 compounds with measured %HIA from the literature.³¹ The data were divided to three groups: a training set of 67 compounds, a validation set of 9 compounds; and an external prediction set of 10 compounds. Using their in-house ADAPT program, 162 real-value descriptors were generated that encoded the topological, electronic and geometric characteristics for every structure. In addition, 566 binary descriptors were added to the set to indicate the presence of certain substructural fragments. Two approaches were applied to prune this initial set of 728 descriptors to a smaller pool of 127. First, descriptors that had variance less than a user-defined minimum threshold were removed to limit the extent of single-example peculiarities in the data set. Second, a correlation analysis was performed to discard potentially redundant descriptors. Application of a GA-NN type hybrid system to this data set yielded a six-descriptor QSAR model. The mean absolute error was 6.7 %HIA units for the training set, 15.4 %HIA units for the validation set, and 11 %HIA units for the external prediction set. The six descriptors that were selected by the GA could elucidate the mechanism of intestinal absorption via passive transport, which is controlled by diffusion through lipid and aqueous media. Three descriptors are related to hydrogen bonding capability, which reflects the lipophilic and lipophobic characteristics of the molecule. The fourth descriptor is the number of single bonds, which can be regarded as a measure of structural flexibility. The other two descriptors represent geometric properties providing information about the molecular size. This set of descriptors, in our opinion, shares a certain similarity to the ones that define the Pfizer rule. However, it is fair to point out the great popularity of the Pfizer rule amongst medicinal chemists is, in the words of Lipinski et al,⁴ “because the calculated parameters are very readily visualized structurally and are presented in a pattern recognition format”. On the contrary, the use of more complex 3D descriptors and neural network modeling may enhance prediction accuracy, although it is probably at the expense of a diminished practical acceptance.

Overall, the result of this initial attempt to predict absorption models is encouraging and more work in this area is assured. Because in vivo data are generally more variable and expensive, there will be strong emphasis on correlating oral absorption and in vitro permeability obtained from model systems such as Caco-2 or immobilized artificial membranes. In addition, future absorption models may have a molecular recognition component, which will handle compounds that are substrates for biological transporters.

Drug Metabolism

Drug metabolism refers to the enzymatic biotransformations which drug molecules are subject to the body. This is an important defensive mechanism of our bodies against potential toxins, which are generally lipophilic and are converted to more soluble derivatives that can be excreted more readily. Most drug metabolism processes occur in the liver, where degradation of drugs is catalyzed by a class of enzymes called hepatic microsomal enzymes. This constitutes the first-pass effect, which can limit a drug's systemic oral bioavailability. In the past, relatively few researchers paid special attention to drug clearance until a lead molecule had advanced nearly to the stage of clinical candidate selection. More recently this attitude has changed as the requirement for pharmacokinetic data for the purposes of correct dose calibration has been recognized. Thus, there is considerable interest in the development of in vitro or in vivo physiological models to predict hepatic metabolic clearance during the lead optimization stage.

Lavé and coworkers at Roche made an attempt to correlate human pharmacokinetic data from in vitro and in vivo metabolic data.⁵³ They collated experimental data for 22 literature and in-house compounds that were structurally diverse. The in vitro metabolic data were derived from the metabolic stability of the substances in hepatocytes isolated from rats, dogs, and humans, and the in vivo pharmacokinetic data were measured after intravenous administration for the same species. All in vitro data, as well as the in vivo data for rats and dogs, were used in combination to predict the human in vivo data. Their statistical analysis included multiple linear regression (MLR), principal component regression (PCR), partial least squares (PLS) regression, and artificial neural networks (ANN). The results of their study are summarized in Table 3. The major conclusion from this study is that the strongest predictors of human in vivo data were human and rat hepatocyte data; the in vivo clearance data from either rats or dogs did not significantly contribute to any statistical model. One possible explanation is that the results from in vivo experiments are generally more variable and are therefore more noisy when they were used as predictors. It is also clear that all statistical methods (MLR, PCR, PLS and ANN) appeared to work satisfactorily for this data set; in fact, from a statistical view point the results are practically identical. It is interesting to note that the non-linear mapping capability of a neural network was not required in this case, probably because of the already strong linear correlation between the human in vivo data and the human hepatocyte data (r = 0.88) and to the rat hepatocyte data (r = 0.81). Overall, despite the limitation of modest data set size, the results of this study provide further support for early in vitro screening of drug candidates because satisfactory human pharmacokinetic data can be predicted through mathematical modeling of these less expensive parameters. It is also fair to point out that the accuracy of their model does come with a price, that is one must first synthesize a compound and determine the appropriate biological parameters before a prediction can be made.

Table 3

Accuracy of the statistical models for human in vivo clearance prediction.

To overcome this problem, some researchers prefer to focus on theoretical descriptors that can be computed from molecular structure. Recently, Quiñones et al tried to correlate drug half-life values based on physicochemical or topological descriptors, which were derived from a series of 30 structurally diverse antihistamines.⁵⁴ These descriptors were used as input values to an ANN and were trained against the experimental half-life of a drug, which is the time it takes for one-half of a standard dose to be eliminated from the body. Initially, they tried to formulate a model that made use of seven physicochemical descriptors: logP, pKa, molecular weight, molar refractivity, molar volume, parachor, and polarizability. However, it did not lead to a statistically significant model. They then investigated the possibility of using the CODES descriptors, which capture the atomic character as well as its neighboring chemical environment for each individual atom. In their study, they picked four CODES descriptors that corresponded to a common chemical substructure present in all 30 antihistamines. Two neural network configurations, one with five hidden nodes and another with six, were tested. The results from cross-validated predictions of their model were very encouraging, and they were mostly consistent with the range of experimental half-life values (Fig. 3). A test set of five other antihistamines was used to evaluate the two ANN models. Again, there was good agreement between the experimental and calculated half-life values, indicating the general robustness of their models, at least within the domain of biogenic amines.

Figure 3

Calculated half-life values from a neural network versus experimental values. The cross-validated predictions for the 30 training compounds are shown as open circles; the predictions for the 5 test set compounds are shown in filled squares. The experimental (more...)

Both approaches described above have their strengths and limitations. From a virtual screening perspective, the approach of Quiñones et al is more attractive since their model does not rely on any experimental parameters. However, the association between the four CODES descriptors and metabolism is unclear and the current model is relevant only to a specific class of compounds that share a common substructure. In this regard, it is our opinion that the set of structural descriptors used by Yoshida and Topliss⁵² are particularly informative because they represent some well-characterized metabolic liabilities. Nevertheless, drug metabolism is immensely complex and biotransformations are catalyzed by many enzymes—some of them may still be unknown to us. As different enzymes have different substrate specificity according to their structural requirement, it will be a challenging task to formulate a simple theoretical model that is generally applicable to many diverse chemical classes. On the other hand, the method proposed by Lavé is likely to be more general because their approach relies on experimental parameters and is thus less dependent on the metabolic pathways involved.⁵³ It is conceivable that we will see a process that is somewhat of a hybrid of the two in the future. A panel of lead compounds with similar structures could be synthesized and tested in vitro, which is generally less expensive and time-consuming than in vivo animal testing. These in vitro data will serve as calibration data for correlation with a set of relevant theoretical descriptors that are directly obtained from molecular structures. Because of the strong relationship between in vitro and in vivo data, the predictions from the resulting QSAR model could be used to predict human pharmacokinetic clearance for compounds that are within the scope of the original lead class. Further research to establish the relationship between in vitro assay from tissue cultures of major metabolic sites (e.g., liver, kidneys, lungs, gastrointestinal tract) and in vivo data appears to be justified.

CNS Activity

The nervous system of higher organisms is divided into a central system (CNS) that comprises the brain and spinal cord, and a peripheral system (PNS) that embodies the remaining nervous tissues in the body. The CNS coordinates the activities of our bodily functions, including the collection of information from the environment by means of receptors, the integration of such signals, the storage of information in terms of memory, and the generation of adaptive patterns of behavior. Many factors, such as infectious diseases, hormonal disorders and other neurological degenerative disorders, can disrupt the balance of this extremely complex system, leading to the manifestation of CNS-related diseases. These include depression, anxiety, sleep disorder, eating disorders, meningitis, Alzheimer's and Parkinson's diseases. The prevalence of such diseases in the modern world is reflected in part by the continuous growth of the market for CNS drugs, which is now the third highest selling therapeutic category behind cardiovascular and metabolic products, and is predicted to reach over $60 billion worldwide by 2002.⁵⁵ These drugs, which have the brain as the site of action, must cross the barrier between brain capillaries and brain tissue (the blood-brain barrier, or BBB). This barrier helps to protect the brain from sudden chemical changes and allows only a tiny fraction of a dose of most drugs to penetrate to cerebrospinal fluid and enter the brain.

Knowledge of the extent of drug penetration through the BBB is of significant importance in drug discovery, not only for new CNS drugs, but also for other peripherally acting drugs whose exposure to the brain should be limited in order to minimize the potential risk of CNS-related side-effects. It is believed that there are certain common physicochemical characteristics common to molecules that are capable of BBB penetration, whose extent is often quantified by logBB, the logarithm of the ratio of steady-state concentration of drug in brain to that in blood. Some of these attributes include size, lipophilicity, hydrogen-bonding propensity, charge, and conformation. It was about 20 years ago that Levin reported a study describing a strong relationship between rat brain penetration and molecular weight for drugs that have MW less than 400.³⁷ In a later study, Young et al observed that the logBB could be related to the difference between the experimental logP_{octanol/water} and logP_{cyclohexane/water} values for a set of histamine H2 antagonists.⁵⁶ This provided a rationale to improve blood-brain penetration of new designs by reduction of the overall hydrogen bonding propensity. The earliest correlative logBB study that involved theoretical descriptors was that of Kansy and van de Waterbeemd, who reported a two-descriptor MLR model using polar surface area (PSA) and molecular volume from a small set of compounds.³⁸ Although their model seemed to work well for the 20 compounds within the training set, it was evident that predictions for other compounds were rather unreliable, presumably due to erroneous extrapolation.⁵⁷ To overcome this problem, Abraham and coworkers examined a larger data set of 65 compounds and formulated QSAR models based on excess molar refraction, molecular volume, polarizability, and hydrogen-bonding parameters, as well as the experimental logP value.³⁹ Later, Lombardo et al performed semi-empirical calculations on a subset of 57 compounds selected from the Abraham training set, and derived a free energy solvation parameter that correlated well with the logBB values.⁵⁸ Norinder and coworkers developed PLS models of logBB using a set of MolSurf parameters, which provide information on physicochemical properties including lipophilicity, polarity, polarizability, and hydrogen bonding.⁴⁰ More recently, Luco applied the PLS method using topological and constitutive (e.g., element counts, sum of nitrogen atoms, and indicator variables of individual atoms or molecular fragments) descriptors to correlate logBB.⁵⁹ In the past two years, several research groups revisited the use of PSA and logP in attempts to create models that are easy to interpret and also generally applicable. These include Clark's MLR models,⁴² which are two-descriptor models based on PSA and logP values computed using different methods; the Österberg PLS model that considered logP and a simple count of hydrogen bond donor and acceptor atoms;⁶⁰ and the Feher MLR model,¹⁰ which utilized logP, polar surface area, and the number of solvent accessible hydrogen bond acceptors. Most recently, Keserü and Molnár reported a significant correlation between logBB and solvation free energy derived from generalized Born/surface area (GB/SA) continuum calculations. This established an efficient means to predict CNS penetration in terms of thermodynamic properties, whose utility had been limited previously due to high computational cost.⁶¹ The statistical parameters reported by the various studies discussed above are shown in Table 4. The following general comments can be made on these studies:

Table 4

Summary of representative linear logBB models that have appeared in the literature.

1. most models were developed from an analysis of a core set of ∼50 structures introduced by Young et al and Abraham et al;^56,39
2. the various linear models (either MLR or PLS) report r² values in the range of 0.7 to 0.9, and standard errors of ∼ 0.3 to 0.4 log units. The accuracy of the models is acceptable given that most data sets have logBB values that span over 3 log units;
3. the descriptors used can be categorized to the following classes: hydrophilic (PSA and its variant, hydrogen bond propensities), hydrophobic (either calculated or measured logP values), or solvation free energy (which arguably characterizes both the hydrophilic and hydrophobic properties of the molecule), or topological indices (which encode, perhaps indirectly, the above physicochemical properties);
4. with the exception of the study of Keserü and Molnár, few models have been validated extensively on a sufficiently large test set, probably due to scarcity of reliable data.

The results from the linear models indicate that it is feasible to estimate candidate blood-brain penetration using computed physicochemical parameters from the molecular structure of a drug. The major drawback of the above models is that they were developed using limited data and therefore their general applicability may be questionable. A consequent solution to development therefore was to increase the diversity of the training set, with the advantage that a larger data set could also safeguard to some degree against model overfitting. This was the strategy followed by Ajay and coworkers at Vertex,⁴¹ who developed a Bayesian neural network (BNN) to predict drug BBB penetration using the knowledge acquired from a large (65,000) number of supposedly CNS-active and -inactive molecules. To construct this data set, they selected compounds from the CMC and the MDDR databases, based on therapeutic indication. In their initial classification, compounds that were within the following activity classes were defined as CNS active: anxiolytic, antipyschotic, neuronal injury inhibitor, neuroleptic, neurotropic, antidepressant, non-opioid analgesic, anticonvulsant, antimigraine, cerebral antiischemic, opioid analgesic, antiparkinsonian, sedative, hypnotic, central stimulant, antagonist to narcotics, centrally acting agent, nootropic agent, neurologic agent and epileptic. Other compounds that did not fall into the above categories were considered to be CNS inactive, an assumption that was later shown to be invalid. Based on this classification scheme, there were over 15,000 CNS active molecules and over 50,000 inactive ones. To minimize the risk of chance correlation, they elected to start with only a few molecular descriptors. The seven one-dimensional descriptors adopted in their earlier drug-likeness prediction system⁶ were also used in this work. These were molecular weight (MW), number of hydrogen bond donors (Don), number of hydrogen bond acceptors (Acc), number of rotatable bonds (Rot), ²κ_α (which indicates the degree of branching of a molecule), aromatic density (AR), and MlogP. The authors believed that this set of descriptors were related to the physical attributes that correlate with BBB penetration, thereby allowing the neural network to discriminate between CNS active and inactive compounds. Using a BNN with just the seven physicochemical descriptors, they achieved a prediction accuracy of 75% on active compounds and 65% on inactive ones. Further, they analyzed the false-positive entities among the supposedly inactive CMC compounds and discovered that a significant portion of the false positives actually had no information in the activity class (i.e., their inactivity labeling might be somewhat dubious). Interestingly, for the remaining false positives, the Vertex team discovered that most of the remaining compounds belonged to the following categories: tranquilizer, antivertigo, anorexic, narcotic antagonist, serotonin antagonist, anti-anxiety, sleep, enhancer, sigma opioid antagonist, antiemetic, antinauseant, antispasmodic, and anticholinergic. Thus, it is evident that there were significant omissions of therapeutic indication in the initial CNS activity definition; and furthermore, their BNN made sound generalizations that led to the correct identification of other known CNS agents. Additional validation of their method on a database of 275 compounds revealed that prediction accuracies of 93% and 72% were achieved for the CNS active and inactive compounds, respectively. The BNN method also ranked the relative importance of the seven descriptors in their CNS model, namely:

Acc > AR ∼ Don∼²_κα > MW ∼ MlogP > Rot

Ajay and coworkers concluded that CNS activity was negatively correlated with MW, ²κ_a, Rot, and Acc, and positively correlated with AR, Don, and MlogP, a result that was consistent with known attributes of CNS drugs. They found that the addition of 166 2D ISIS keys to the seven 1D descriptors yielded significant improvement, which confirmed their earlier drug-likeness prediction result.⁶ Using the combined 1D and 2D descriptors, the BNN yielded predictivity accuracy of 81% on the active compounds and 78% on the inactive.

The utility of this BNN as a filter to design a virtual library against CNS targets was subsequently demonstrated. As for any filter designed to handle large compound collections, the principal consideration was the throughput of the calculation. With their in-house implementation, they achieved a throughput of almost 1 million compounds on a single processor (195 MHz R10000) per day. The CNS activity filter was tested on a large virtual library, consisting of about 1 million molecules constructed with 100 drug-like scaffolds⁶³ combined with 300 most common side chains. Two types of filters were applied to prune this library. The first was substructure-based, to exclude compounds containing reactive functional groups; the second was property-based, to discard molecules with undesirable physicochemical properties, including high MW, high MlogP, and in the example case, low predicted CNS activity. From the remaining compounds, they identified several classes of molecules that have favorable BBB penetration properties and are also particularly amenable to combinatorial chemical library synthesis. As a result, such libraries are considered as privileged compound classes to address CNS targets.

Aquatic Toxicity

Aquatic toxicity is one of key toxicological indicators commonly used to assess the potential risk posed to human and environmental health by chemical substances. A number of marine and freshwater organisms, such as Pimephales promelas, Tetrahymena pyriformis, Daphnia magna, Daphnia pulex and Ceriodaphnia dubia, have become ecotoxicity systems of choice because of their fast growth rate under simple and inexpensive culture conditions. More significantly, the establishment of standard testing protocols for these species makes comparisons of inter-laboratory results meaningful. The most comprehensive resource for aquatic toxicity is the Aquatic Toxicity Information Retrieval (AQUIRE) Database maintained by the EPA, which contains data on ∼ 3,000 organisms and ∼ 6,000 environmental chemicals, extracted from over 7,000 publications. This abundant experimental data provides a foundation for some of the multivariate QSTR modeling work described here.

Basak and coworkers proposed a new approach called “hierarchical QSAR” for predicting the acute aquatic toxicity (LC₅₀) of a set of benzene derivatives.⁷² The data set, which included benzene and 68 substituted benzene derivatives containing chloro, bromo, nitro, methyl, methoxy, hydroxy, or amino substitutions. The toxicity test for these compounds were done against Pimephales promelas (fathead minnow), with pLC₅₀ values ranging from 3.04 to 6.37. Ninety-five descriptors belonging to four major categories were computed to characterize each molecule:

• 35 topostructural indices (TSI), which encode information on the molecular graph without any information on the chemical nature of the atoms or bonds;
• 51 topochemical indices (TCI), which were derived from the molecular graph weighted by relevant chemical or physical atom type properties;
• 3 geometric indices (3D), which carried three-dimensional information on the geometry of the molecule;
• 6 quantum chemical parameters (QCI), which were calculated using the MOPAC program (HOMO, LUMO, heat of formation, etc)

To reduce the number of model parameters, variables from the TSI and TCI categories were clustered based on their inter-correlation. The index that was most correlated with the cluster was automatically selected, along with other poorly correlated (r² < 0.7) indices that helped to explain data variance. The clustering procedure eliminated most of the descriptors from the two groups, and only five TSI and nine TCI descriptors were retained. All nine descriptors in 3D and QCI categories were kept because they were relatively few in number and in addition they seemed to be poorly correlated amongst themselves. As a result of this pre-processing, a group of 23 molecular descriptors were used for further statistical analysis. In the next step, the authors followed an incremental approach, hierarchical QSAR, to build a linear model based on the reduced descriptor set. First, an exhaustive enumeration of the five TSI descriptors yielded a four-parameter linear regression model with a cross-validated r² value (r_cv²) of 0.37. It was apparent that using the TSI parameters alone could not produce a satisfactory model. Next, they added the nine TCI descriptors to the four selected TSI features from the first model, and again performed an exhaustive search to examine all combinations of linear models. This led to an improved four-descriptor model, yielding r_cv² = 0.75. Repeating this procedure to include the 3D and QCI descriptors resulted in a four-descriptor and a seven-descriptor model that gave r_cv² values of 0.76 and 0.83, respectively. For comparison, they performed variable clustering on all 95 descriptors, and selected seven descriptors to build another linear model. It was noteworthy that this model gave essentially the same predictivity (r_cv² = 0.83) as the (different) selection based on the hierarchical procedure (see discussion below). Basak and coworkers also explored nonlinear models using neural networks. Due to high computational expense, instead of an exhaustive enumeration at every tier level, they decided to use all descriptors in each of the four categories at each hierarchy. The cross-validation results for the four models are shown in Table 5. The trend for improvement of predictive performance paralleled that of the regression model. Inclusion of the TCI descriptors appeared to yield the biggest improvement in r_cv². The neural network result also demonstrated that a smaller subset of descriptors can yield similar results as compared to the full 95-descriptor ANN model. Perhaps the most surprising result was that the linear regression model consistently outperformed ANN in this study, at least in terms of cross-validation statistics. We think that one possible reason was an overfitting of data by the neural network that hampered its ability to generalize on the training patterns. One of the ANN models reported by Basak et al had a configuration of 95–15–1. This means that over 1400 adjustable parameters were available to map a data set that was modest in size.⁶⁹ Consequently, the predictions were likely a result of memorization rather than generalization, leading to a deterioration of predictive performance. This example clearly demonstrates the usefulness of different models to address the same problem.

Table 5

Statistical results of the hierarchical QSAR models reported by Basak et al.

Based on the regression studies, the two seven-descriptor models yielded essentially identical statistics. This begs the question: what is the real merit of the hierarchical approach versus the traditional “kitchen sink” approach? From a computational point of view, the latter approach is probably simpler to execute. We believe that the biggest benefit of the hierarchical approach is to probe the dependence of activity prediction on a particular descriptor class. In their study, Basak et al demonstrated that the use of TCI descriptors would substantially increase the efficacy of both the neural network and the regression model, and this piece of information would not have been easily deciphered from the single cluster approach. However, to make this unequivocal, one should perform all combinations of cluster-based QSAR models. In addition, there is the issue of a possible order-dependence in the build-up of hierarchical layers. It is likely that if one starts with TCI as the first model, the final descriptor choice will differ from the reported set.

Recently, Niculescu et al published an in-depth study of the modeling of chemical toxicity to Tetrahymena pyriformis using molecular fragments and a probabilistic neural network (PNN).⁶⁵ They obtained the 48-hour ICG₅₀ sublethal toxicity data for T. pyriformis for 825 compounds from the TerraTox database.⁷³ This group of compounds covered a range of chemical classes, many of which have known mechanisms of toxic actions. They included narcotics, oxidative phosphorylation uncouplers, acetylcholinesterase inhibitors, respiratory inhibitors, and reactive electrophiles.⁷⁴ Instead of using physicochemical descriptors such as logP, Niculescu et al preferred functional group descriptors that represented certain molecular fragments. Each structural descriptor encoded the number of occurrences of specific molecular substructural/atomic features, and a total of 30 descriptors were used. They reasoned that there were two major advantages of this molecular presentation. First, substructural descriptors were considerably cheaper to calculate than most physicochemical or other 3D descriptors, and were also not subject to common errors in their generation (e.g., missing fragments or atom-types from logP calculations, or uncertainty of the 3D conformation). Second, they argued that the use of substructure-based descriptors would lead to a more general QSAR model. The authors suggested that one of the factors that contributed to their superior results relative to other toxicity prediction systems (such as ASTER, CNN, ECOSAR, OASIS, and TOPKAT) was that it did not rely on logP as an independent variable.

The 825-compound data set was partitioned to a larger set of 750 compounds which were used to derived quantitative models, and a smaller set of 75 compounds that were later used for model validation. They performed a five-way leave-group-out cross-validation experiment (i.e., 20% of data were left out at one time) on the larger data set, where 150 randomly selected compounds were left out in turn. Five sub-models, m₁ to m₅, were constructed using each data partition from the same input descriptors. They achieved very good performance for the five sets of training compounds (r² from 0.93 to 0.95) and also very respectable test performance (r² from 0.80 to 0.86). Further, the m₁-m₅ models, together with m₀ that was trained from the entire set of 750 compounds, were combined to produce a series of linear correction models. M₁ simply accounted for the unexplained variance of m₀ model. M₂ and M₃ were derived from geometric regression to force linear correction, and M₄ was a multivariate regression to fit all results:

Since all 750 compounds played a role in the building of M₁-M₄ models, their true predictivity could only be evaluated by the 75 compounds that had been left out in the initial partition. Figure 4 gives a summary of the data partition scheme. Judging from the results obtained for these external compounds, it is encouraging to see that all four models gave consistent predictions, with r² ranging from 0.88 to 0.89. They concluded that it was viable to utilize in silico prescreens to evaluate chemical toxicity towards a well-characterized endpoint.

Figure 4

Data partitioning scheme of Niculescu et al. The full data set is split into a 750-compound training set and a 75-compound external test set. Six sub-models are derived using full training set (m₀), and five leave-group-out cross-validation experiments (more...)

To demonstrate the generality of this approach to toxicity prediction, Niculescu et al applied this same technique to an analysis of the acute aquatic toxicity of 700 highly structurally diverse chemicals to Daphnia magna, another model organism with widespread use in ecotoxicological screening.⁷⁵ Using the same set of fragment descriptors as their previous work,⁶⁵ they obtained five sub-models (m₁-m₅), with reported r² values in the range 0.88 to 0.9 for the training compounds, and about 0.5 to 0.72 for the test objects. Again, they constructed four linearly corrected models M₁-M₄ that combined the characteristics of the individual sub-models. Consistent with the previous work, these corrected models yielded very similar predictivity, though the M₄ model, which was based on a linear combination of m₁-m₅, appeared to give the best overall result. Application of this model on 76 external compounds yielded a standard deviation error of 0.7 log units, which is very impressive, considering that the measured activity spanned approximately 9 orders of magnitude. In contrast, the ECOSAR system, the aquatic toxicity prediction program developed by the EPA, yielded a standard deviation error of 1.4 log units for these compounds. So it seems that, although ECOSAR has information of over 150 SARs for more than 50 chemical classes, the PNN models do cover a wider scope for general application.

Carcinogenicity

Carcinogenicity is a toxicity endpoint that concerns the ability of a chemical to produce cancer in animals or humans. The extent of carcinogenicity of a substance is indicated qualitatively through the following categories: “Clear Evidence” or “Some Evidence” for positive results, “Equivocal Evidence” for uncertain finding, “No Evidence” in the absence of observable effects. Every year the National Toxicology Program publishes a list of carcinogens or potential carcinogens in the Annual Report on Carcinogens.

An approach for the prediction of the carcinogenic activity of polycyclic aromatic compounds using calculated semi-empirical parameters was described by Barone et al.⁷⁶ Central to this work was the use of electronic indices, which were first applied to a set of 26 non-methylated polycyclic aromatic hydrocarbons (PAH). They reasoned that the carcinogenicity of these compounds is related to the local density of state over the ring that contains the highest bond order and on the energy gap (ΔH) between HOMO and HOMO-1, the energy level right below HOMO. Six descriptors were considered:

• HOMO, the energy of highest occupied molecular orbital
• HOMO-1, the energy level right below HOMO
• DH, the difference between the energy of HOMO and HOMO-1
• CH, the HOMO contribution to the local density of state
• CH-1, the HOMO-1 contribution to the local density of state
• ηH, CH - CH-1

A simple rule, stating that if ηH > 0 eV and ΔH > 0.408 eV, then the molecule would likely be a carcinogen was formulated in this study. The use of electronic index methodology (EIM) was extended in a more recent study, where 81 non-methylated and methylated PAH were analyzed through the use of principal component analysis (PCA) and neural network methods.⁷⁷ For a set of 26 non-methylated compounds, PCA of the six thermodynamic parameters yielded two principal components that accounted for 42.6% and 35.2% of the total variance. For the 46 methylated compound, the first two principal components captured 81.5% and 15.9% of the variance, respectively. They characterized two clusters of active and a region of inactive compounds from a two-dimensional principal component score plot, for which only three carcinogenic molecules were incorrectly classified. The use of an ANN yielded the best result, both in separate non-methylated and methylated series or when in the combined set (Table 6). They concluded that the EIM, which explored energy separation between frontier molecular orbitals, offered a relevant set of descriptors that could be used for accurate modeling of carcinogenic activity of this class of compounds.

Table 6

Percentage of correct classification for the three different methodologies for 32 non-methylated and 46 methylated polycyclic aromatic hydrocarbons. The number of correct classifications in each instance is shown in parentheses.

In another study, Bahler et al constructed a rodent carcinogenicity model using a number of machine learning paradigms, including decision trees, neural networks, and Bayesian classifiers.⁷⁸ They analyzed a set of 904 rodent bioassay experiments, of which 468 were defined as either clear evidence or some evidence (referred as positive), 276 as no evidence (referred to as negative), and 160 equivocal cases that were eliminated from their analysis. They used 258 different attributes to characterize each of the subjects. Some of these attributes were theoretical descriptors, but the majority were observations from histopathological examination. These included 20 physicochemical parameters, 21 substructural alerts, 209 subchronic histopathology indicators, 4 attributes for maximally tolerated dose, sex and species exposed, route of administration and the Salmonella mutagenesis test result. A ten-way leave-group-out cross-validation was used to assess the predictivity of a neural network model. Using all attributes, the training accuracy converged to 90% whilst the test set reached about 80% before the performance deteriorated as the neural network began to overtrain. Later, they applied a feature selection routine, termed single hidden unit method,⁷⁹ to partition the descriptors into relevant and irrelevant features. They discovered that the removal of irrelevant features greatly improved the predictive accuracy for the test set (89%). In addition, the model successfully classified 392 of 452 (87%) of the positive cases, and 272 out of 292 (93%) of the negative cases. More significantly, they were able to extract knowledge embedded in the trained neural network and established a set of classification rules. It seemed that the conversion of a neural network system to such a rule-based system led to only minimal loss of prediction accuracy. For the same set of compounds, the rule-based system correctly identified 389 cases of true positives and 256 cases of true negatives, which corresponded to an overall accuracy of 87%. Because heuristic systems offer superior interpretability, while a neural network is generally more predictive, there is great optimism that the two methods can work synergistically in toxicological prediction.

In the past ten years we have witnessed significant development in computational toxicology.⁶⁷ In contrast to the experimental determination of physicochemical properties (e.g., logP, solubility), the toxicology endpoint has much greater variability, and is often assessed qualitatively (toxic/non-toxic, clear/some/equivocal/no evidence of carcinogenicity) rather than quantitatively. Due to this intrinsic uncertainty, as well as the fact that most, if not all, toxicity models are derived from limited data, we must address the predictions with appropriate caution. Further refinement in reliability estimation, such as the concept of optimum prediction space (i.e., the portion of chemical space within which the model is applicable) advocated in TOPKAT, should be a priority in future development. The major problem in toxicology modeling certainly is the lack of consistent data with uniform assay evaluation criteria. Not surprisingly, most of the larger data sets that have been compiled to date concern aquatic toxicity from simple model organisms, which are useful indicators for risk assessment in environmental safety. For the purpose of drug discovery, however, it would be desirable to have the predictions extrapolated from mammalian toxicity data, but traditional in vivo toxicity screening involves animal testing, which is costly and time-consuming, and is impractical for mass screening of a large library. With the advent of molecular biology, in particular innovative proteomics technology, one should soon be able to devise rapid in vitro toxicity methods that can gauge the effects of chemicals on human cellular proteins. An early fruit of such multidisciplinary research has appeared in the realm of toxicogenomics, offering hope for the prediction of the mechanisms of toxic action through DNA microarray analysis. Besides technological advances, another possible way to accelerate the compilation of toxicology data could be through a virtual laboratory,⁸⁰ where consortium members could exchange proprietary data in order to minimize unnecessary duplication of work. In regard to methodology development, the next major advance will probably come from the combined use of expert systems and correlative methods. We must emphasize that expert systems and neural network technologies should not be regarded as competitive, but rather as ideal complements. In particular, a neural network method can achieve an impressive predictive accuracy despite the fact that the method itself is naïve in the sense that it neither relies on any fundamental theory nor provides any clue in the formulation of its answer. While the ability of generalization is the key to the extraordinary power of neural networks, the lack of theory behind the predictions does, to a certain extent, impede its use. This is because scientists are generally less enthusiastic about reliance upon results which are conceived by a “black-box” approach that offers little or no qualitative explanation. Thus, it would be desirable to have an expert system—whether human or artificial—which could provide the logical reasoning complementary to the predictions made by the network. In this regard, the work by Bahler et al have given us a first glimpse of the cross-fertilization of artificial intelligence research in the form of future “expert-neural-network”.⁷⁸