3D pharmacophore mapping using 4D QSAR analysis for the cytotoxicity of lamellarins against human hormone-dependent T47D breast cancer cells.

4D quantitative structure-activity relationship (QSAR) and 3D pharmacophore models were built and investigated for cytotoxicity using a training set of 25 lamellarins against human hormone dependent T47D breast cancer cells. Receptor-independent (RI) 4D QSAR models were first constructed from the exploration of eight possible receptor-binding alignments for the entire training set. Since the training set is small (25 compounds), the generality of the 4D QSAR paradigm was then exploited to devise a strategy to maximize the extraction of binding information from the training set and to also permit virtual screening of diverse lamellarin chemistry. 4D QSAR models were sought for only six of the most potent lamellarins of the training set as well as another subset composed of lamellarins with constrained ranges in molecular weight and lipophilicity. This overall modeling strategy has permitted maximizing 3D pharmacophore information from this small set of structurally complex lamellarins that can be used to drive future analog synthesis and the selection of alternate scaffolds. Overall, it was found that the formation of an intermolecular hydrogen bond and the hydrophobic interactions for substituents on the E ring most modulate the cytotoxicity against T47D breast cancer cells. Hydrophobic substitutions on the F-ring can also enhance cytotoxic potency. A complementary high-throughput virtual screen to the 3D pharmacophore models, a 4D fingerprint QSAR model, was constructed using absolute molecular similarity. This 4D fingerprint virtual high-throughput screen permits a larger range of chemistry diversity to be assayed than with the 4D QSAR models. The optimized 4D QSAR 3D pharmacophore model has a leave-one-out cross-correlation value of xv-r2 = 0.947, while the optimized 4D fingerprint virtual screening model has a value of xv-r2 = 0.719. This work reveals that it is possible to develop significant QSAR, 3D pharmacophore, and virtual screening models for a small set of lamellarins showing cytotoxic behavior in breast cancer screens that can guide future drug development based upon lamellarin chemistry.

Membrane-interaction quantitative structure--activity relationship (MI-QSAR) analyses of skin penetration enhancers.

Membrane-interaction quantitative structure-activity relationship (MI-QSAR) models for two skin penetration enhancer data sets of 61 and 42 compounds were constructed and compared to QSAR models constructed for the same two data sets using only classic intramolecular QSAR descriptors. These two data sets involve skin penetration enhancement of hydrocortisone and hydrocortisone acetate, and the enhancers are generally similar in structure to lipids and surfactants. A new MI-QSAR descriptor, the difference in the integrated cylindrical distribution functions over the phospholipid monolayer model, in and out of the presence of the skin penetration enhancer, DeltaSigma h(r), was developed. This descriptor is dominant in the optimized MI-QSAR models of both training sets studied and greatly reduces the size and complexity of the MI-QSAR models as compared to those QSAR models developed using the classic intramolecular descriptors. The MI-QSAR models indicate that good penetration enhancers make bigger "holes" in the monolayer and are less aqueous-soluble, so as to preferentially enter the monolayer, than are poor penetration enhancers. The skin penetration enhancer thus alters the structure and organization of the monolayer. This space and time alteration in the structure and dynamics of the membrane monolayer is captured by DeltaSigma h(r) and is simplistically referred to as "holes" in the monolayer. The MI-QSAR models explain 70-80% of the variance in skin penetration enhancement across each of the two training sets and are stable predictive models using accepted diagnostic measures of robustness and predictivity.

Treating chemical diversity in QSAR analysis: modeling diverse HIV-1 integrase inhibitors using 4D fingerprints.

A set of 213 compounds across 12 structurally diverse classes of HIV-1 integrase inhibitors was used to develop and evaluate a combined clustering and QSAR modeling methodology to construct significant, reliable, and robust models for structurally diverse data sets. The trial-descriptor pool for both clustering- and QSAR-model building consisted of 4D fingerprints and classic QSAR descriptors. Clustering was carried out using a combination of the partitioning around medoids method and divisive hierarchical clustering. QSAR models were constructed for members of each cluster by linear-regression fitting and model optimization using the genetic function approximation. The 12 structurally diverse classes of integrase inhbitors were partitioned into five clusters from which corresponding QSAR models, overwhelmingly composed of 4D fingerprint descriptors, were constructed. Analysis of the five QSAR models suggests that three models correspond to structurally diverse inhibitors that likely bind at a common site on integrase characterized by a common inhibitor hydrogen-bond donor, but involving somewhat different alignments and/or poses for the inhibitors of each of the three clusters. The particular alignments for the inhibitors of each of the three QSAR models involve specific distributions of nonpolar groups over the inhibitors. The two other clusters, one for coumarins and the other for depsides and depsidones, lead to QSAR models with less-defined pharmacophores, likely representing an inhibitor binding to a site(s) different from that of the other nine classes of inhibitors. Overall, the clustering and QSAR methodology employed in this study suggests that it can meaningfully partition structurally diverse compounds expressing a common endpoint in such a manner that leads to statistically significant and pharmacologically insightful composite QSAR models.

QSAR analyses of skin penetration enhancers.

QSAR models for four skin penetration enhancer data sets of 61, 44, 42, and 17 compounds were constructed using classic QSAR descriptors and 4D-fingerprints. Three data sets involved skin penetration enhancement of hydrocortisone and hydrocortisone acetate. The other data set involved skin penetration enhancement of fluorouracil. The measure of penetration enhancement is the ratio of the net permeation of the penetrant with and without a common fixed concentration of enhancer. Significant QSAR models could be built using multidimensional linear regression fitting and genetic function model optimization for all four data sets when both classic and 4D-fingerprint descriptors were used in the trial descriptor pool. Reasonable QSAR models could be built when only 4D-fingerprint descriptors were employed, and no significant QSAR models could be built using only classic descriptors for two of the four data sets. Comparison analyses of the descriptor terms, and their respective regression coefficients, across the pairs of the best QSAR models of the four skin penetration enhancer data sets did not reveal any significant extent of similar terms. Overall, the QSAR models for the penetration-enhancer systems appear meaningfully different from one another, suggesting that there are distinct mechanisms of skin penetration enhancement that depend on the chemistry of both the enhancer and the penetrant.

Prediction and mechanistic interpretation of human oral drug absorption using MI-QSAR analysis.

Membrane-interaction [MI]-QSAR analysis, which includes descriptors explicitly derived from simulations of solutes [drugs] interacting with phospholipid membrane models, was used to construct QSAR models for human oral intestinal drug absorption. A data set of 188 compounds, which are mainly drugs, was divided into a parent training set of 164 compounds and a test set of 24 compounds. Stable, but not highly fit [R2 = 0.68] MI-QSAR models could be built for all 188 compounds. However, the relatively large number [47] of drugs having 100% absorption, as well as all zwitterionic compounds [11], had to be eliminated from the training set in order to construct a linear five-term oral absorption diffusion model for 106 compounds which was both stable [R2 = 0.82, Q2 = 0.79] and predictive given the test set compounds were predicted with nearly the same average accuracy as the compounds of the training set. Intermolecular membrane-solute descriptors are essential to building good oral absorption models, and these intermolecular descriptors are displaced in model optimizations and intramolecular solute descriptors found in published oral absorption QSAR models. A general form for all of the oral intestinal absorption MI-QSAR models has three classes of descriptors indicative of three thermodynamic processes: (1) solubility and partitioning, (2) membrane-solute interactions, and (3) flexibility of the solute and/or membrane. The intestinal oral absorption MI-QSAR models were compared to MI-QSAR models previously developed for Caco-2 cell permeation and for blood-brain barrier penetration. The MI-QSAR models for all three of these ADME endpoints share several common descriptors, and suggest a common mechanism of transport across all three barriers. A further analysis of these three types of MI-QSAR models has been done to identify descriptor-term differences across these three models, and the corresponding differences in thermodynamic transport behavior of the three barriers.

A study of the relationship between cornea permeability and eye irritation using membrane-interaction QSAR analysis.

A methodology termed membrane-interaction QSAR (MI-QSAR) analysis has been used to develop QSAR models to predict drug permeability coefficients across cornea and its component layers (epithelium, stroma, and endothelium). From a training set of 25 structurally diverse drugs, significant QSAR models are constructed and compared for the permeability of the cornea, epithelium, and stroma plus endothelium. Cornea permeability is found to depend on the measured distribution coefficient of the drug, the cohesive energy of the drug, the total potential energy of the drug-membrane "complex," and three other energy refinement descriptor terms. The endothelium may be a more important barrier in cornea permeation than the stroma. Moreover, an investigation of the correlation between cornea permeation and eye irritation is presented as an example of a cross study on different ADMET properties using MI-QSAR analysis. Thirteen structurally diverse drugs, whose molar-adjusted eye irritation scores (MES) have been measured using the Draize rabbit-eye test, were chosen as an eye irritation comparison set. A poor correlation (R(2) = 0.0232) between the MES measures and the predicted cornea permeability coefficients for the drugs in the eye irritation set suggests there is no significant relationship between eye irritation potency and the cornea permeability.

4D-fingerprints, universal QSAR and QSPR descriptors.

An elusive goal in the field of chemoinformatics and molecular modeling has been the generation of a set of descriptors that, once calculated for a molecule, may be used in a wide variety of applications. Since such universal descriptors are generated free from external constraints, they are inherently independent of the data set in which they are employed. The realization of a set of universal descriptors would significantly streamline such chemoinformatics tasks as virtual high-throughout screening (VHTS) and toxicity profiling. The current study reports the derivation and validation of a potential set of universal descriptors, referred to as the 4D-fingerprints. The 4D-fingerprints are derived from the 4D-molecular similarity analysis. To evaluate the applicability of the 4D-fingerprints as universal descriptors, they are used to generate descriptive QSAR models for 5 independent training sets. Each of the training sets has been analyzed previously by several varying QSAR methods, and the results of the models generated using the 4D-fingerprints are compared to the results of the previous QSAR analyses. It was found that the models generated using the 4D-fingerprints are comparable in quality, based on statistical measures of fit and test set prediction, to the previously reported models for the other QSAR methods. This finding is particularly significant considering the 4D-fingerprints are generated independent of external constraints such as alignment, while the QSAR methods used for comparison all require an alignment analysis.

Construction, molecular modeling, and simulation of Mycobacterium tuberculosis cell walls.

The mycobacterial cell wall is extraordinarily thick and tight consisting mainly of (1). long chain fatty acids, the mycolic acids, and (2). a unique polysaccharide, arabinogalactan (AG). These two chemical constituents are covalently linked through ester bonds. Minnikin (The Biology of the Mycobacteria; Academic: London, 1982) proposed that the mycobacterial cell wall is composed of an asymmetric lipid bilayer. The inner leaflet of the cell wall contains mycolic acids covalently linked to AG. This inner leaflet is believed to have the lowest permeability to organic compounds of the overall cell wall. Conformational search and molecular dynamics simulation were used to explore the conformational profile of AG and the conformations and structural organization of the mycolic acid-AG complex, and overall, an inner leaflet molecular model of the cell wall was constructed. The terminal arabinose residues of AG that serve as linkers between AG and mycolic acids were found to exist in four major chemical configurations. The mycolate hydrocarbon chains were determined to be tightly packed and perpendicular to the "plane" formed by the oxygen atoms of the 5-hydroxyl groups of the terminal arabinose residues. For Mycobacterium tuberculosis, the average packing distance between mycolic acids is estimated to be approximately 7.3 A. Thus, Minnikin's model is supported by this computational study. Overall, this modeling and simulation approach provides a way to probe the mechanism of low permeability of the cell wall and the intrinsic drug resistance of M. tuberculosis. In addition, monolayer models were built for both dipalmitoylphosphatidylethanolamine and dimyristoylphosphatidylcholine, two common phospholipids in bacterial and animal membranes, respectively. Structural comparisons of these cell wall phospholipid membrane models were made to the M. tuberculosis cell wall model.

Molecular modeling and simulation of Mycobacterium tuberculosis cell wall permeability.

The low permeability of the mycobacterial cell wall is thought to contribute to the intrinsic drug resistance of mycobacteria. In this study, the permeability of the Mycobacterium tuberculosis cell wall is studied by computer simulation. Thirteen known drugs with diverse chemical structures were modeled as solutes undergoing transport across a model for the M. tuberculosis cell wall. The properties of the solute-membrane complexes were investigated by means of molecular dynamics simulation, especially the diffusion coefficients of the solute molecules inside the cell wall. The molecular shape of the solute was found to be an important factor for permeation through the M. tuberculosis cell wall. Predominant lateral diffusion within, as opposed to transverse diffusion across, the membrane/cell wall system was observed for some solutes. The extent of lateral diffusion relative to transverse diffusion of a solute within a biological cell membrane may be an important finding with respect to absorption distribution, metabolism, elimination, and toxicity properties of drug candidates. Molecular similarity measures among the solutes were computed, and the results suggest that compounds having high molecular similarity will display similar transport behavior in a common membrane/cell wall environment. In addition, the diffusion coefficients of the solute molecules across the M. tuberculosis cell wall model were compared to those across the monolayers of dipalmitoylphosphatidylethanolamine and dimyristoylphosphatidylcholine, are two common phospholipids in bacterial and animal membranes. The differences among these three groups of diffusion coefficients were observed and analyzed.

Characterization of skin penetration processes of organic molecules using molecular similarity and QSAR analysis.

Molecular similarity and QSAR analyses have been used to develop compact, robust, and definitive models for skin penetration by organic compounds. The QSAR models have been sought to provide an interpretation and characterization of plausible molecular mechanisms of skin penetration. A training set of 40 structurally diverse compounds were selected to be representative of a parent set of 152 compounds in terms of both structural diversity and range in measured skin penetration. The subset of 40 compounds was used in a series of QSAR analyses in the search for the most significant, compact, and straightforward skin penetration QSAR models. Molecular dynamics simulations were employed to determine a set of MI (membrane-interaction) descriptors for each test compound (solute) interacting with a model DMPC monolayer membrane model. The MI-QSAR models may capture features of cellular membrane lateral transverse transport involved in the overall skin penetration process by organic compounds. An additional set of intramolecular solute descriptors, the non-MI-QSAR descriptors, were computed and added to the trial pool of descriptors for building QSAR models. All QSAR models were constructed using multidimensional linear regression fitting and a genetic algorithm optimization function. QSAR models were constructed using only non-MI-QSAR descriptors and using a combination of both these descriptor sets. It was found that a combination of non-MI-QSAR and MI-QSAR descriptors yielded the optimum models, not only with respect to the statistical measures of fit but also regarding model predictivity.

A simple clustering technique to improve QSAR model selection and predictivity: application to a receptor independent 4D-QSAR analysis of cyclic urea derived inhibitors of HIV-1 protease.

A training set of 50 tetrahydropyrimidine-2-one based inhibitors of HIV-1 protease, for which the -log K(i) values were measured, was used to construct receptor independent 4D-QSAR models. A novel clustering technique was employed to facilitate and improve model selection as well as test set predictions. Following the manifold model theory, five unique models were chosen by the clustering algorithm (q(2) = 0.81-0.84). The models were used to map the atom type morphology of the inhibitor binding site of HIV-1 protease as well as to predict the potencies (-log K(i)) of 10 test set compounds. The rank-difference correlation coefficient was used to evaluate the quality of the test set predictions, which was improved from 0.39 to 0.68 when the clustering technique was applied. The set of five models, collectively, identify the important binding characteristics of the HIV protease receptor site. This study demonstrates that the selected simple clustering technique provides a discrete algorithm for model selection, as well as improving the quality of test set, or unknown, compound prediction as determined by the rank-difference correlation coefficient.

Quantitative structure-based design: formalism and application of receptor-dependent RD-4D-QSAR analysis to a set of glucose analogue inhibitors of glycogen phosphorylase.

A method for performing quantitative structure-based design has been developed by extending the current receptor-independent RI-4D-QSAR methodology to include receptor geometry. The resultant receptor-dependent RD-4D-QSAR approach employs a novel receptor-pruning technique to permit effective processing of ligands with the lining of the binding site wrapped about them. Data reduction, QSAR model construction, and identification of possible pharmacophore sites are achieved by a three-step statistical analysis consisting of genetic algorithm optimization followed by backward elimination multidimensional regression and ending with another genetic algorithm optimization. The RD-4D-QSAR method is applied to a series of glucose inhibitors of glycogen phosphorylase b, GPb. The statistical quality of the best RI- and RD-4D-QSAR models are about the same. However, the predictivity of the RD- model is quite superior to that of the RI-4D-QSAR model for a test set. The superior predictive performance of the RD- model is due to its dependence on receptor geometry. There is a unique induced-fit between each inhibitor and the GPb binding site. This induced-fit results in the side chain of Asn-284 serving as both a hydrogen bond acceptor and donor site depending upon inhibitor structure. The RD-4D-QSAR model strongly suggests that quantitative structure-based design cannot be successful unless the receptor is allowed to be completely flexible.

Receptor-independent 4D-QSAR analysis of a set of norstatine derived inhibitors of HIV-1 protease.

A training set of 27 norstatine derived inhibitors of HIV-1 protease, based on the 3(S)-amino-2(S)-hydroxyl-4-phenylbutanoic acid core (AHPBA), for which the -log IC(50) values were measured, was used to construct 4D-QSAR models. Five unique RI-4D-QSAR models, from two different alignments, were identified (q(2) = 0.86-0.95). These five models were used to map the atom type morphology of the lining of the inhibitor binding site at the HIV protease receptor site as well as predict the inhibition potencies of seven test set compounds for model validation. The five models, overall, predict the -log IC(50) activity values for the test set compounds in a manner consistent with their q(2) values. The models also correctly identify the hydrophobic nature of the HIV protease receptor site, and inferences are made as to further structural modifications to improve the potency of the AHPBA inhibitors of HIV protease. The finding of five unique, and nearly statistically equivalent, RI-4D-QSAR models for the training set demonstrates that there can be more than one way to fit structure-activity data even within a given QSAR methodology. This set of unique, equally good individual models is referred to as the manifold model.

3D-pharmacophores of flavonoid binding at the benzodiazepine GABA(A) receptor site using 4D-QSAR analysis.

4D-QSAR analysis was applied to a training set of 38 flavonoids where affinity constants, Ki, to the GABA(A) benzodiazepine receptor site, BzR, were determined. It was found that the -logKi values of the compounds are highly dependent on the size and electrostatics character of the substituents at the R(3') and R(6) positions of the flavonoid scaffold. Polar negative groups correctly embedded in the R(3') and/or R(6) substituents are predicted to increase -logKi values. A planar conformation of the flavonoid scaffold was found not to be a requirement for the flavonoids to be active. A test set of four compounds was used to evaluate the predictivity of the 4D-QSAR models.

Predicting blood-brain barrier partitioning of organic molecules using membrane-interaction QSAR analysis.

PURPOSE: Membrane-interaction quantitative structure-activity relationship (OSAR) analysis (MI-QSAR) has been used to develop predictive models of blood-brain barrier partitioning of organic compounds by, in part, simulating the interaction of an organic compound with the phospholipid-rich regions of cellular membranes. METHOD: A training set of 56 structurally diverse compounds whose blood-brain barrier partition coefficients were measured was used to construct MI-QSAR models. Molecular dynamics simulations were used to determine the explicit interaction of each test compound (solute) with a model DMPC monolayer membrane model. An additional set of intramolecular solute descriptors were computed and considered in the trial pool of descriptors for building MI-QSAR models. The QSAR models were optimized using multidimensional linear regression fitting and a genetic algorithm. A test set of seven compounds was evaluated using the MI-QSAR models as part of a validation process. RESULTS: Significant MI-QSAR models (R2 = 0.845, Q2 = 0.795) of the blood-brain partitioning process were constructed. Blood-brain barrier partitioning is found to depend upon the polar surface area. the octanol/water partition coefficient, and the conformational flexibility of the compounds as well as the strength of their binding" to the model biologic membrane. The blood-brain barrier partitioning measures of the test set compounds were predicted with the same accuracy as the compounds of the training set. CONCLUSION: The MI-QSAR models indicate that the blood-brain barrier partitioning process can be reliably described for structurally diverse molecules provided interactions of the molecule with the phospholipids-rich regions of cellular membranes are explicitly considered.

4D-QSAR analysis of a set of propofol analogues: mapping binding sites for an anesthetic phenol on the GABA(A) receptor.

A training set of 27 propofol (2,6-diisopropylphenol) analogues was used to construct four-dimensional (4D) quantitative structure-activity relationship (QSAR) models for three screens of biological activity: loss of righting reflex (LORR) in tadpoles, enhancement of agonist activity at the gamma-aminobutyric acid type A (GABA(A)) receptor, and direct (agonist-independent) activation of the receptor. The three resulting 4D-QSAR models are almost identical in form, and all suggest three key ligand-receptor interaction sites. The formation of an intermolecular hydrogen bond involving the proton of the ligand -OH group is the most important binding interaction. A hydrophobic pocket binding interaction involving the six-substituent is the second most significant binding site, and a similar hydrophobic pocket binding interaction near the two-substituent is the third postulated binding site from the 4D-QSAR models. A test set of eight compounds was used to evaluate the tadpole LORR 4D-QSAR model. Those compounds highly congeneric to the training set compounds were accurately predicted. However, compounds exploring substituent sites and/or electronic structures different from the training set were less well-predicted. Overall, the results show a striking similarity between the models of the sites responsible for anesthesia and those mediating effects of the training set of propofol analogues on the GABA(A) receptor; it follows that the GABA(A) receptor is therefore the likely site of propofol's anesthetic action.

Prediction of skin irritation from organic chemicals using membrane-interaction QSAR analysis.

Membrane-interaction (MI) quantitative structure activity relationship (QSAR) analysis was carried out for a training set of 22 hydroxy organic compounds for which the Draize skin irritation scores, PII, had been determined. Significant MI-QSAR models were constructed in which skin irritation potency is predicted to increase with (1) increasing effective concentration of the compound available for uptake into phospholipid-rich regions of a cellular membrane, (2) increasing binding of the compound to the phospholipid-rich regions of a cellular membrane, and (3) the chemical reactivity of the compound as reflected by the highest occupied molecular orbital (HOMO) and/or lowest unoccupied molecular orbital (LUMO) of the molecule. Overall, the MI-QSAR models constructed for skin irritation are very similar, with respect to the types of descriptors, to those found for eye irritation. In turn, the skin irritation MI-QSAR models suggest a similar molecular mechanism of action to that postulated for eye irritation from MI-QSAR analysis. Significant and predictive QSAR models cannot be constructed unless test compound-membrane interaction descriptors are computed and used to build the QSAR models.

Predicting Caco-2 cell permeation coefficients of organic molecules using membrane-interaction QSAR analysis.

A methodology termed membrane-interaction QSAR (MI-QSAR) analysis has been developed in order to predict the behavior of organic compounds interacting with the phospholipid-rich regions of biological membranes. One important application of MI-QSAR analysis is to estimate ADME properties including the transport of organic solutes through biological membranes as a computational approach to forecasting drug intestinal absorption. A training set of 30 structurally diverse drugs, whose permeability coefficients across the cellular membranes of Caco-2 cells were measured, was used to construct significant MI-QSAR models of Caco-2 cell permeation. Cellular permeation is found to depend primarily upon aqueous solvation free energy (solubility) of the drug, the extent of drug interaction with a model phospholipid (DMPC) monolayer, and the conformational flexibility of the solute within the model membrane. A test set of eight drugs was used to evaluate the predictivity of the MI-QSAR models. The permeation coefficients of the test set compounds were predicted with the same accuracy as the compounds of the training set.

4D-QSAR analysis of a set of ecdysteroids and a comparison to CoMFA modeling.

The ecdysteroid-responsive Drosophila melanogaster B(II) cell line is a prototypical homologous inducible gene expression system. A training set of 71 ecdysteroids, for which the -log(EC(50)) potencies in the ecdysteroid-responsive B(II) cell line were measured, was used to construct 4D-QSAR models. Four nearly equivalent optimum 4D-QSAR models, for two modestly different alignments, were identified (Q(2) = 0.76-0.80). These four models, together with two CoMFA models, were used in consensus modeling to arrive at a three-dimensional pharmacophore. The C-2 and C-22 hydroxyls are identified as hydrogen-bond acceptor sites which enhance activity. A hydrophobic site near C-12 is consistent with increasing activity. The side-chain substituents at C-17 are predicted to adopt semiextended "active" conformations which could fit into a cylinder-shaped binding pocket lined largely with nonpolar residues for enhanced activity. A test set of 20 ecdysteroids was used to evaluate the QSAR models. Two 4D-QSAR models for one alignment were identified to be superior to the others based on having the smallest average residuals of prediction for the prediction set (0.69 and 1.13 -log[EC(50)] units). The correlation coefficients of the optimum 4D-QSAR models (R(2) = 0.87 and 0.88) are nearly the same as those of the best CoMFA model (R(2) = 0.92) determined for the same training set. However, the cross-validation correlation coefficient of the CoMFA model is less significant (Q(2) = 0.59) than those of the 4D-QSAR models (Q(2) = 0.80 and 0.80).

Estimation of molecular similarity based on 4D-QSAR analysis: formalism and validation.

The 4D-QSAR paradigm has been used to develop a formalism to estimate molecular similarity measures as a function of conformation, alignment, and atom type. It is possible to estimate the molecular similarity of pairs of molecules based upon the entire ensemble of conformational states each molecule can adopt at a given temperature, normally room temperature. Molecular similarity can be measured in terms of the types of atoms composing each molecule leading to multiple measures of molecular similarity. Multiple measures of molecular similarity can also arise from using different alignment rules to perform relative molecular similarity, RMS, analysis. An alignment independent method of determining molecular similarity measures, referred to as absolute molecular similarity, AMS, analysis has been developed. Various sets and libraries of compounds, including the amino acids, are analyzed using 4D-QSAR molecular similarity analysis to demonstrate the features of the formalism. Exploration of molecular similarity as a function of chirality, identification of common embedded 3D pharmacophores in compounds, and elucidation of 3D-isosteric compounds from structurally diverse libraries are carried out in the application studies.