a new topological descriptors based model for predicting ...csps/jpps7(2)/y.ponce/caco-2.pdfon the...

J Pharm Pharmaceut Sci (www.ualberta.ca/~csps) 7(2):186-199, 2004

Corresponding Author: Yovani Marrero Ponce, Department of Phar-macy, Faculty of Chemical-Pharmacy, Central University of Las Villas,Santa Clara 54830, Villa Clara, Cuba. [email protected]

A new topological descriptors based model for predicting intestinal epithelial transport of drugs in caco-2 cell culture.

Yovani Marrero Ponce, Miguel A. Cabrera Pérez, Vicente Romero Zaldivar, Humberto González Díaz, Francisco TorrensDepartment of Pharmacy, Faculty of Chemical-Pharmacy. Central University of Las Villas, Santa Clara, Villa Clara, Cuba; Department of Drug Design, Chemical Bioactive Center. Central University of Las Villas, Santa Clara, Villa Clara, Cuba; Faculty of Informatics. University of Cienfuegos, Cienfuegos, Cuba; Institut Universitari de Ciència Molecular, Universitat de València, Burjassot (València), Spain

Received 20 February 2004, Revised 26 March 2004, Accepted 14 April 2004, Published 29 June 2004

Abstract Purpose: Quantitative Structure–Permeabil-ity Relationships (QSPerR) of the intestinal permeabil-ity across the (Caco-2) cells monolayer could beobtained by the application of new molecular descrip-tors. Method: A novel topologic-molecular approachto computer molecular design (TOMOCOMD-CARDD) has been used to estimate the intestinal-epi-thelial transport of drug in Caco-2 cell culture.Results: The Permeability Coefficients in Caco-2 cells(P) for 33 structurally diverse drugs were welldescribed using quadratic indices of the molecularpseudograph’s atom adjacency matrix as moleculardescriptors. A quantitative model that discriminatesthe high-absorption compounds from those with mod-erate-poor absorption was obtained for the trainingdata set, showing a global classification of 87.87%. Inaddition, two QSPerR models, through a multiple lin-ear regression, were obtained to predict the P [apical tobasolateral (AP→BL) and basolateral to apical(BL→AP)]. A leave-n-out and leave-one-out cross-valida-tion procedure revealed that the discriminant andregression models respectively, had a good predictabil-ity. Furthermore, others 18 drugs were selected as atest set in order to assess the predictive power of themodels and the accuracy of the final prediction wassimilar to achieve for the data set. Besides, the use ofboth regression models, in a combinative way, is possi-ble to predict the Permeability Directional Ratio(PDR, BL→AP/AP→BL) value. The found models wereused in virtual screening of drug intestinal permeabil-ity and a relationship between calculated P and per-centage of human intestinal absorption for severalcompounds was established. Furthermore, this approx-imation permits us to obtain a good explanation of theexperiment based on the molecular structural features.

Conclusions: These results suggest that the proposedmethod is able to predict the P values and it proved tobe a good tool for studying the oral absorption of drugcandidates during the drug development process.

INTRODUCTION

The estimation of human oral absorption of new drugcandidates in the early stage of the drug discovery pro-cess is a useful tool in the lead-compound selection (1-2). Several in vitro approaches, based on cell cultures,have been used in this area over the last few years.Among the cell culture models, the Caco-2 cell line isthe most widely employed and it has been investigatedlike a potential in vitro model for drug absorption andmetabolism studies (3-4). In this sense, considering thesimilarity of Caco-2 cell with the small intestineenterocytes and their capacity to express carrier-medi-ated transport systems and typical small intestinalenzymes (3-4), the permeability coefficient acrossCaco-2 cell monolayer (P) is increasingly used to esti-mate the oral absorption of new chemical entities (5-7).

Nevertheless, the permeability of compounds that aretransported via carrier-mediated absorption is lowerthan that obtained through the human small intestine.In addition, these carcinoma colon cells have poor per-meability for hydrophilic compounds, which can passthrough this barrier by paracellular route (through theintercellular space) (8). Furthermore, due to cancerousorigin of this cell line, they over-express the P-glyco-protein with the consequently lower permeability’s inthe absorptive direction (9). Finally, the long cultureperiod with the consequent high-research cost and thedifficulty to extrapolate these in vitro results with thein vivo situation are considered as main practical limi-tations.

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In order to accelerate the growing of Caco-2 cell mono-layer a rapid culture system has been used (Paccelerate)(10).

On the other hand, the theoretical approach appears tobe a good alternative to prediction of human absorp-tion for new drug candidates obtained by combinato-rial chemistry methodologies (11-13), avoidingsignificant failure in late stage of the drug-discoveryprocess (14). In the last few years, graph-theoreticalmethods have become one of the most important toolsfor quantifying molecular structure. These theoreticalstrategies have emerged as a promising solution to theefficient search of new lead compounds (15) and it hasbeen very useful to elucidate quantitative structure-property (QSPR) and quantitative structure-activity(QSAR) relationships. Trying to demonstrate theimportance and relevance of the theoretical methods inthe determination of the drugs absorption, the mainobjectives of the present work were, to find a quantita-tive model that discriminates, within the data set, thehigh-absorption compounds from those with moder-ate-poor absorption; and to develop quantitative rela-tionships between the structure, expressed by thequadratic indices of the molecular pseudograph’s atomadjacency matrix (16-18), and the P in both membranedirections, using a multiple linear regression method.Finally, to use both obtained models on virtual screen-ing of drug intestinal permeability.

THEORETICAL APPROACH

The general principles of the quadratic indices of the“molecular pseudograph`s atom adjacent matrix” forsmall-to-medium sized organic compounds have beenexplained in some detail elsewhere (17, 18). However,an overview of this approach will be given.

The molecular vector (X) is constructed in order to cal-culate the molecular quadratic indices for a moleculewhere the components of this vector are numeric val-ues, which represent a certain atomic property.

These properties characterize each kind atom withinthe molecule. Such properties can be the electronega-tivity, density, atomic radii, and so on.

If a molecule consists of n atoms (vector of ℜ n), thenthe kth total quadratic indices, qk(x) are calculated as a

quadratic form (q:ℜ n→ℜ ) in canonical basis asshown in Eq. 1,

(1)

where, kaij = kaji (symmetric square matrix), n is thenumber of atoms of the molecule and X1,…,Xn are thecoordinates of the molecular vector (X) in a system ofbasis vectors of the ℜ n. One can choose the basis vec-tors the coordinates of the same vector will be differ-ent. The values of the coordinates depend thus in anessential way on the choice of the basis. The so-calledcanonical ('natural') bases, ej denote the n-tuple having1 in the jth position and 0's elsewhere. In the canonicalbases, the coordinates of any vector X coincide withthe components of this vector. For that reason, thosecoordinates can be considered as weights (atom-labels)of the vertices of the pseudograph.

The coefficients kaij are the elements of the kth power ofthe matrix M (G) of the molecular pseudograph (G).Here, M (G) = M = [aij], denote the matrix of qk(x)with respect to the natural basis. In this matrix n is thenumber of vertices (atoms) of G and the elements aij aredefined as follows:

(2)

where, E(G) represents the set of edges of G. Pij is thenumber of edges between vertices vi y vj and Lii is thenumber of loops in vi.

Given that aij = Pij, the elements aij of this matrix repre-sent the number of bonds between an atom i and other j.The matrix Mk provides the number of walks of length kthat links the vertices vi and vj. For this reason, each edgein M1 represents 2 electrons belonging to the covalentbond between atoms (vertices) vi and vj; e.g. the inputs ofM1 are equal to 1, 2 or 3 when appears simple, double ortriple bonds between vertices vi and vj, respectively. Onthe other hand, molecules containing aromatic rings withmore than one canonical structure are represented like apseudograph. It happens for substituted aromatic com-pounds such as pyridine, naphthalene, quinoline, and soon, where the presence PI(π) electrons is accounted bymeans of loops in each atom of the aromatic ring. Con-versely, aromatic rings having only one canonical struc-

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ture, such as furan, thiophene and pyrrol are representedlike a multigraph.

On the other hand, the defining equation (1) for qk(x)may be written as the single matrix equation:

(3)

or in the more compact form,

(4)

where [X] is a column vector (a nx1 matrix) of thecoordinates of X in the canonical base of ℜ n, [X]t thetranspose of [X] (a 1xn matrix) and Mk the kth power ofthe matrix M of the molecular pseudograph G (mathe-matical quadratic form's matrix). In Table 1, the calcu-lation of six quadratic indices for acetylsalicylic acid isexemplified.

Table 1: Definition and calculation of six (k = 0-5) totalquadratic indices of the molecular pseudograph’s atomadjacency matrix of the molecule of acetylsalicylic acid.

In addition to a total quadratic indices computed forthe whole-molecule a local-fragment (atom and atom-type) formalism can be developed. These descriptorsare termed local quadratic indices of the “molecular

pseudograph´s atom adjacency matrix”, qkL(x). TheqkL(x) are graph-theoretical invariant for a given frag-ment FR (connected subgraph) within a specificpseudograph G. The definition of these descriptors isas follows:

(5)

where m is the number of atoms of the fragment ofinterest and kaijL is the element of the file “i” and col-umn “j” of the matrix Mk

L= Mk(G, FR) [qkL(x) = qk(x,FR)]. This matrix is extracted from the Mk matrix andcontains the information referred to the vertices of thespecific molecular fragments (FR) and of the molecularenvironment. The matrix Mk

L= [kaijL] with elementskaijL is defined as follows:

(6)

with the kaij being the elements of the kth power of M.These local analogues can also be expressed in matrixform by the expression:

(7)

Note that for every partitioning of a molecule into Zmolecular fragment there will be Z local molecularfragment matrices. That is to say, if a molecule is parti-tioned into Z molecular fragments, the matrix Mk canbe partitioned into Z local matrices Mk

L, L = 1,... Z andthe kth power of matrix M is exactly the sum of the kth

power of the local (‘molecular fragment’) Z matrices,

(8)

or in the same way as Mk = [kaij] where,

(9)

and the total quadratic indices is the sum in the qua-dratic indices of the Z molecular fragments,

(10)

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Any local quadratic index has a particular meaning,especially for the first values of k, where the informa-tion about the structure of the fragment FR is con-tained.

High values of k are in relation with the environmentinformation of the fragment FR considered inside themolecular pseudograph (G).

Atom and atom-type quadratic indices are specific caseof local quadratic indices (for FR = atom or atom-type).In this sense, the kth atom-type quadratic indices arecalculated by summing the kth atom quadratic indicesof all atoms of the same atom type in the molecule.

In the atom-type quadratic indices formalism, eachatom in the molecule is classified into an atom-type(fragment), such as heteroatoms, heteroatoms H-bond-ing acceptor (O, N and S), halogens, aliphatic carbonchain, aromatic atoms (aromatic rings), an so on. Forall data sets, including those with a common molecularscaffold as well as those with very diverse structure, thekth atom-type quadratic indices provide much usefulinformation.

In any case, whether a complete series of indices is con-sidered, a specific characterization of the chemicalstructure is obtained (whole structure or fragment),which is not repeated in any other molecule. The gen-eralization of the matrices and descriptors to “superioranalogues” is necessary for the evaluation of situationswhere only one descriptor is unable to bring a goodstructural characterization (19). These local indices canalso be used together with total indices as variables ofQSAR and QSPerR models for properties or activitiesthat depend more on a region or a fragment than onthe whole molecule.

METHODS

TOMOCOMD-CARDD Approach

TOMOCOMD is an interactive program for moleculardesign and bioinformatics research (16-18). The pro-gram is composed by four subprograms, each one ofthem dealing with drawing structures (drawing mode)and calculating 2D and 3D molecular descriptors (cal-culation mode). The modules are named CARDD(Computed-Aided ‘Rational’ Drug Design), CAMPS(Computed-Aided Modelling in Protein Science),

CANAR (Computed-Aided Nucleic Acid Research)and CABPD (Computed-Aided Bio-Polymers Dock-ing). In this paper, we outline salient features con-cerned with only one of these subprograms: CARDD.This subprogram was developed based on a user-friendly philosophy without prior knowledge of pro-gramming skills.

The calculation of total and local quadratic indices forany organic molecule (or any drug-like compounds)was implemented in the TOMOCOMD-CARDD soft-ware (16). The main steps for the application of thismethod in QSAR/QSPerR can be briefly resumed asfollows:

1. Draw the molecular pseudographs for each mole-cule of the data set, using the software-drawingmode. This procedure is carried out by a selectionof the active atom symbol belonging to differentgroups of the periodic table,

2. Use appropriated atom weights in order to differ-entiate the molecular atoms. In this work, weused as atomic property the Mulliken electronega-tivity (20) for each kind of atom,

3. Compute the total and local quadratic indices ofthe molecular pseudograph’s atom adjacencymatrix. They can be carried out in the softwarecalculation mode, which you can select the atomicproperties and the family descriptor previously tocalculate the molecular indices. This software gen-erate a table in which the rows correspond to thecompounds and columns correspond to the totaland local quadratic indices or any others familymolecular descriptors implemented in this pro-gram,

4. Find a QSPerR/QSAR equation by using statisti-cal techniques, such as multilinear regression anal-ysis (MRA), Neural Networks (NN), LinearDiscrimination Analysis (LDA), and so on. Thatis to say, we can find a quantitative relationbetween P values and the quadratic indices hav-ing, for instance, the following appearance,

(11)

where *qk(x) [or qkL(x)] is the kth total [or local] qua-

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dratic indices, and the ak’s are the coefficients obtainedby the linear regression analysis.

5. Test the robustness and predictive power of theQSPerR/QSAR equation by using internal andexternal cross-validation techniques,

6. Develop a structural interpretation of obtainedQSPerR/QSAR model using quadratic indices asmolecular descriptors.

The descriptors used in order to achieve the theoreticalmodels were the following:

(1) qk(x) and qkH(x) are the kth total quadratic indices cal-

culated using the kth power of the matrices [Mk (G)] ofthe molecular pseudograph (G) considering and notconsidering hydrogen atoms respectively.

(2) EqkL(x) [or EqkLH(x)], AqkL(x) [or AqkL

H(x)] and Hqkk(x) arethe kth local quadratic indices calculated using a kth

power of the local matrices [MkL(G, Fi)] of the molecu-

lar pseudograph (G) not considering (or considering)hydrogen atoms for heteroatoms (S, N, O), aromaticsystems and hydrogen-bonding heteroatoms (S, N, O),respectively.

Permeability Data

The experimental data set, used in the present study,was composed by 33 structurally diverse drugs, whichwere experimentally studied by Liang et al (21).

These authors used a traditionally and accelerate Caco-2 cell permeability model and the experimental valuesof P (AP→BL) and P (BL→AP) are depicted in Tables2 y 3, respectively. The P values of the test set of 18drugs were taken from a study developed by Yazda-nian and co-workers (6). The compounds used byLiang et al. were taken from reference 6. Both studieswere carried out under the same experimental condi-tions. The selected data set for ‘in silico’ permeabilitystudies included model compounds with absorption byparacellular and transcellular diffusion, carrier-medi-ated absorption as well as substrates for carrier-medi-ated secretion via P-glycoprotein. These compoundshad a molecular weight between 60 and 515 amu andtheir molecular charge was variable at pH 7.4 (6).

Table 2: Experimental (traditional or accelerated model)and calculated values of the Caco-2 cell permeabilitycoefficients (AP→BL) of 33 compounds as well asresiduals of the regression and cross-validation.

aFrom Ref. (21). bCalculated with the Eq. (13). cResidual, defined as Ptraditional (obsd) - Ptraditional (calc). dResidual of the cross-validation.

Table 3: Experimental (by either traditional oraccelerated model) and calculated values of the Caco-2cell permeability coefficients (BL→AP) of 17 compoundsas well as residuals of the regression and cross-validation.

*Outlier. aFrom Ref. (21). bCalculated with the Eq. (14). cResid-ual, defined as Ptraditional. (obsd) - Ptraditional (calc). dResidual of the cross-validation.

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Statistical Analysis

All statistical analyses were developed with the STA-TISTICA 5.5 (22). The classification analysis was doneusing the Linear Discriminant Analysis (LDA). Thequality of the model was determined examining thestatistics parameter of multivariable comparison of theregression and by the cross-validation procedure (leave-n-out). The classification trees module was used tocarry out leave-n-out cross validation procedures.

The linear multiple regression analysis (LMR) wasdeveloped to obtain the quantitative models betweenchemical structure and P values determined by tradi-tional and accelerated methods.

The statistics quality of these models was evaluatedtaking into consideration the statistics graphics, the sta-tistics parameters of multivariable comparison of theregression and the cross-validation procedure (leave-one-out).

RESULTS AND DISCUSSION

Developing the Discrimination Function

Linear discriminant analysis (LDA) was employedwith the aim of developing a function that discrimi-nates between high and moderate-poor absorbed com-pounds. For this purpose, this data set was split intotwo subsets according to the quantitative value of P(AP→BL) (23): the first group was composed by 18compounds (high-absorption group; P (AP→BL) ≥10x10-6cm/s) and the second one by 15 compoundswith moderate-poor absorption (P (AP→BL) < 10x10-

6cm/s). The range selection for permeability coefficientin Caco-2 cells is a bottleneck whether a correlationwith the human absorption is searched. Several classifi-cation methods have been described in the literature,(6, 24-26) where the inter-laboratory and experimentalvariability is considered. Nevertheless, if all theapproaches reported in the literature are analyzed, itcan be stated that a value of P greater than 10x10-6cm/swill classify good-absorption compounds (70-100%).Taking into consideration the reported selectionapproaches, a second group with moderate-poorabsorption (<10x10-6cm/s) was selected, although inthis range a high variability is appreciated when thehuman oral absorption is predicted from the P values(6, 24-26).

From a practical perspective the established boundary,assure that classified compounds have a good absorp-tion profile. The best classification model found, by aforward-stepwise variable selection procedure,together with the statistical parameters, is shownbelow:

(12)

where, N is the number of compounds, λ is Wilks´coefficient, F is the Fisher ratio, D2 is the squaredMahalanobis distance and p-value is the significancelevel. The Wilks´ λ parameter for overall discrimina-tion can take values in the range of 0 (perfect discrimina-tion) to 1 (no discrimination). The Mahalanobis distanceindicates the separation between the respective groups.This model classified correctly 80.00% of compoundswith moderate-poor absorption properties and a 94.44%of compounds with high absorption. The global classifi-cation for the data set was 87.87%. Only four com-pounds were classified bad, one of them with highabsorption was classified as a moderate-poor absorptiondrug (3.03%, false negative compound) and threebelonging to the moderate-poor absorption group wereclassified as high-absorption drugs (9.09%, false posi-tive compounds).

From a practical point of view and in the developmentof the classifier model, the prediction of false negativesis considered more important because they are com-pounds that will be rejected for their poor predictedintestinal absorptions and therefore they will never beevaluated experimentally, and their true absorptionwould never be discovered. On the contrary, the falsepositive compounds eventually will be detected.

In Table 4 are shown the results of classification and aposteriori probabilities for the 33 compounds of thedata set. The predictability of the model obtained byLDA was assessed through a leave-one-out (LOO)cross-validation procedure. In this methodology, themodel was built after removing one compound and theresulting model was used to predict the property of theone removed. This was repeated to obtain a predictionfor every compound. Using this approach, the modelclassified correctly 80.00% and 94.44% of compoundsfrom the training set that belong to the moderate-poorand high-absorption group, respectively.

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The global classification of the cross-validation was87.87%.

Table 4: Results of Compounds Classification for theData and External Prediction Set (AP→BL).

aObserved classification: H (high-absorption group) and M-P (moderate-poor absorption group). bProbability calculated. cProbability calculated LOO cross-validation. dProbability cal-culated for the test set. *Misclassified Compounds for the test set.

For a more exhaustive testing of the predictive powerof the found model a leave-n-out (LnO) cross valida-tion procedures was carried out using the classificationtree module (22). The selected conditions for the vali-dation procedure were discriminant-based linear com-bination as split method, prune on misclassificationerror as stopping rule and the same prior probabilitiesthan in Eq. 12. Once the selected conditions areapplied in the classification trees’ module, Eq. 12 isobtained and a LnO procedure can be developed vary-ing the folding parameter of the cross validation. Thismodel shown a 91.3, 91.5, 93.8, 91.8, 92.0 and 92.2% ofgood global classification when n varied from 2 to 7respectively in the LnO cross validation procedures.The model was stabilized around 92.5% when n was >7 (see Figure 1).In addition, to assess the predictivepower of the model an external prediction set of 18drugs was used, where the percentage of good globalclassification was 88.88%. If we considered the data setand the test set together (full set) the percentage ofgood classification was 88.23%. At the bottom of Table

4 appear the obtained results for the external predic-tion set. As it can be seen, in both series, the predict-ability and robustness of the theoretical model wasdemonstrated.

Figure 1: Result obtained to assess the predictive powerof the discrimination model (Eq. 12) using LnO Cross-Validation procedure. The model (Eq. 12) was stabilizedaround 92.5% when n was > 7.

From the full data set, only 6 compounds were classi-fied badly. Two drugs (salicylic acid and phenytoin)were classified as false negative and four as false posi-tive compounds (bremazocine, uracil, acebutolol andAcetylsalicylic acid). The high percentage of misclassi-fied compounds belongs to the moderate-poor absorp-tion group. In this set, they were included compoundswith P values lower than 10x10-6. This is a logic resultdue to the fact that in this group there are some com-pounds with high variability in relation to the humanabsorption values and it is not always possible anextrapolation between human absorption and the Pvalues (P < 10); for example a drug like acebutolol (P= 0.51) has a 90% of human absorption (27). In addi-tion, others compounds such as acetylsalicylic acid (P= 9.09) and bremazocine (P = 8.02) have P values closeto the selected limit value (10x10-6) and in the first casethe low percentage of classification (57.06%) can beexplained when the human absorption value is consid-ered (100%) (6).

The Regression Models

With the aim of predicting the P values, we developtwo quantitative models that relate the quadratic indi-ces of the molecules with the P (AP→BL) and P(BL→AP). The best linear regression models for P wereobtained by a forward stepwise procedure; the equa-tion and the statistical parameters are shown below:

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(13)

(14)

where, R is the multiple regression coefficient, s thestandard deviation of the regression, sCV are the stan-dard deviation of the LOO cross-validation procedure;F is the Fisher ratio at the 95% confidence level and p-value is the significance level.

In Tables 2 and 3, the values of experimental and calcu-lated permeability coefficients for the data set aregiven, and in the Figures 2 and 3, the existing linearrelationships between them are depicted. In the devel-opment of the quantitative model for description of P(BL→AP) of the data set, one compound was detectedas statistical outliers (Caffeine). Outliers’ detection wascarried out by using the following standard statisticaltests: residual, standardized residuals, studentized resid-ual and Cooks’ distance (28).

Figure 2: Correlation between experimental andcalculated P (AP→BL) values of 33 compounds of the dataset.

Figure 3: Correlation between experimental andcalculated P (BL→AP) values of 16 compounds of the dataset. Caffeine was detected as statistical outlier. For thisreason, this compound was excluded of the statisticalanalysis.

Several researchers have explored QSPerR involvingCaco-2 cell permeability. In these studies, some typesof molecular descriptors have been introduced, wheresize and hydrogen-bonding descriptors (13), polar sur-face area (PSA) (8, 29, 30), Molsurf-derived descriptors(31), MO-calculation (11) and using membrane-interac-tion analysis (32) are included. These QSPerR modelshave predicted the P values with a reasonable accuracy,although the numbers of compounds in the data setshave been limited. For example, Fujiwara et al. consid-ered quadratic and interactive terms (11) in the equa-tions and the correlation coefficients were 0.74 and0.76, respectively. In the same paper, these authorsincreased the correlation coefficient up to 0.790 using aneural network. In addition, van de Waterbeemd et al.obtained an R-value for P between 0.513 and 0.884(13). In other paper, Ren and Lien (33) developed aQSAR analysis where an adequate regression coeffi-cient value, for the same data set of 51 compounds usedin this study, was obtained (0.79). Finally, in a recentlystudy developed by Kulkarni et al. (32), about predic-tion of P values, 6 predictive models were obtainedusing Multidimensional Linear Regression (MLR) andthe R values were between 0.86 and 0.92; but in thiscase only 74% from the original data set (6) was cho-sen.

Interpretation of QSPerR Models

Up to now, it is known that the absorption is influ-enced by a different kind of interactions. Several stud-ies have demonstrated that the permeabilitycoefficient, measured by a transport through Caco-2monolayer cell cultures, is correlated with lipophilicity(6, 12, 13, 33), while others emphasize on the role ofhydrogen-bonding capacity or charge (7, 8, 12, 13). Aparadigm of structure-permeability relationship hasbeen expressed as (13):

(15)

As it can be observed, in the discriminant and theregression models, the included variables are very closeto the factors that influence on the P values. These fac-tors are related with the structural features of mole-cules. For example in Eq. 12, the variables Hq2L(x),Hq4L(x) and Hq7L(x) are connected with the hydrogenatoms as donors, while the Eq1L

H(x) and Eq3LH(x) vari-

ables contain information about the number of hydro-

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gen acceptors and the charge of molecules. All of themare related with the total hydrogen bond capacity. Pnegatively depends on these descriptors. The values ofthese molecular indices increase with the rise of thenumbers of heteroatoms and the hydrogen bond toheteroatoms in the molecules. For this reason, we cansay that these molecular descriptors have a negativecontribution to P. These are a logical results becauseincreasing the number of heteroatoms and the hydro-gen bound to heteroatoms in the molecules decreasethe permeability across the biological membrane. Thiseffect is rather close to the molecular lipophilicitydecrease and the possibility of the molecule of ioniza-tion and to obtain a charge. The charge factor is relatedwith the negative charge of the biological membrane(34). This observation is supported by a study devel-oped by Ren et al., where the same full set used in thepresent study. First, a low regression coefficient (R =0.749) was evidenced when anionic, cationic and neu-tral compounds (the full set), were studied using thenet charge of molecules like a descriptor. When thesecompounds where divided into three subgroups,namely neutral, cationic and anionic compounds,much better correlation coefficients (R = 0.968, 0.915and 0.931, respectively) were obtained (33).

Other descriptor with a positive contribution to thediscriminant function is q0.q0(x). This variable containsinformation about the molecular weight and conse-quently of the size of molecules. For this reason,although, the number of heteroatoms is increased (neg-ative contribution to the permeability coefficient) thequadratic influence of molecular size (descriptor)should increase the permeability of molecules. In addi-tion, these properties (molecular weight, size), H-bonding and charge are components of lipophilicity(13). For each property there are limited ranges as it isestablished in the Rule- of- 5 (1), but anyone is indepen-dent (35).

Taking into consideration the above mentionedapproach it should be considered that successful drugcandidates will be characterized by an optimal range ofvalues for H-bonding, lipophilicity and size (36) andfor this reason, compounds with extreme positive val-ues of these properties could have a marked negativeeffect on permeability across the biological membrane(13).

As it can be seen, in the case of the linear regressionmodel there are some influences of the local and thetotal descriptor of different orders, in similar way tothe classification function. In the Eq.13, it appears thevariable Aq14L(x) that indicates the presence and size ofaromatic systems. In order to describe the P (AP→BL)and P (BL→AP) the descriptors selected by the regres-sion process, in both equations, were different. Thisfact suggests that the transport process is different intwo directions, explaining that some compounds arepotential substrate of cellular efflux pumps (21). Dur-ing the last few years, the Caco-2 cell model has beenused to evaluate whether new chemical entities havepossible cellular efflux pumps. For compounds that arecellular efflux pump substrates the P (BL→AP) valuewill be higher than P (AP→BL) (21) and for com-pounds that are not substrates the ratio between thistwo values should be near to 1. This ratio is called thePermeability Directional Ratio (PDR, BL→AP/AP→BL). For this reason through the use of bothregression models, in a combinative way, it is possibleto predict the PDR value. This theoretical approachappears like a new alternative to the study of cellularefflux pump.

Virtual Screening and Correlation with ‘in vivo’ Data

One of the most important aspects of any quantitativestructure-permeability model is its ability to predict thestudied P for any compound not included in the data (ortraining) set. Virtual screening has emerged as an inter-esting alternative to the handling and screening of largedatabases in order to find a reduced set of new potentialdrug candidates (37-39). In the present study, we simu-lated a virtual search of P (AP→BL) values by using thediscriminant function (Eq. 12) and regression equation(Eq. 13) obtained through the TOMOCOMD-CARDDapproach. In Table 5, the Caco-2 cell permeability datafor 134 structurally diverse compounds, obtained fromdifferent sources are summarized (32, 33, 40-50). Some-times they were obtained P experimental values fromtwo or more sources, existing significant variability inthese values. Several researchers have demonstratedinter-laboratory differences for Caco-2 cell permeabilitystudies (8, 51).

The evaluation results of these compounds are given inTable 5.

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Table 5: Result of the Virtual Screening for 134Structurally Diverse Compounds.

References where were collected the P values. bPermeability coefficient: P (AP→BL) x10-6cm/s, obtained from literature. cPermeability coeffi-cient: P (AP→BL) x10-6cm/s, obtained using regression model (Eq. 13). dClassification and probability obtained using discriminant function (Eq. 12): H [high-absorption group (P (AP→BL) ≥ 10x10-6cm/s)] and M

[moderate-poor absorption group (P (AP→BL) < 10x10-6cm/s)]. fO-cyclopropane carboxylic acid ester.

As can be seen in this Table, most of the 134 evaluatedcompounds are adequately predicted, although itshould be considered that collected data are influencedby variations in cell culture conditions such as passagenumber, type of medium, day in culture, as well as theexperimental conditions used for their measurement. Itis obvious that from the results the quality of the pre-dictions corroborates the predictive power of the mod-els found and justified their use in the prediction of thisimportant property. Besides, this is not a fortuitousresult due to the data set used in this study includingabsorption model compounds such as drugs with para-cellular passive absorption (e.g. atenolol, furosemide,mannitol, terbutaline), transcellular passive absorption(e.g. antipyrine, ketoprofen, metoprolol, piroxicam),active transport processes (carrier-mediated up-take,e.g. Gly-Pro and L-phenylalanine) and carried mediatedsecretion via P-glycoprotein (e.g. talinolol, cimetidine,acebutolol, ranitidine, chlorothiazide).

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On the other hand, the ‘in silico’ estimated intestinalpermeability could be used as a predictor of the truefraction of the absorbed drug.

The theoretical relationship between the fraction ofdrug absorbed (Fa) and permeability has beendescribed by Amidon et al. (52):

(16)

When the absorbed dose fraction, from human studies,is compared with the predictive P, a good relationshipbetween the theoretical and observed values isobtained.

The following Table 6 a, b demonstrates this relationfor several compounds used in the study.

Table 6: a Caco-2 cell permeability coefficients calculateusing discriminant and regression models and percent GIabsorption in human from the different reports forcompounds with moderate-poor absorption.

Table 6: b Caco-2 cell permeability coefficients calculateusing discriminant and regression models and percent GIabsorption in human from the different reports forcompounds with high absorption

aReferences where were collected the P values. bPermeability coefficient: P (AP→BL) x10-6cm/s, obtained from literature. cPermeability coefficient: P (AP→BL) x10-6cm/s, obtained using regression model (Eq. 13). dClassification and probability obtained using discriminant function (Eq. 12): H [high-absorp-tion group (P (AP→BL) ≥ 10x10-6cm/s)] and M [moderate-poor absorption group (P (AP→BL) < 10x10-6cm/s)]. eHuman frac-tion absorbed.

CONCLUSIONS

The total and local quadratic indices appear to be apromising structural invariant. Using these molecularindices and statistical techniques, a function discrimi-nant that allows the correct classification of 87.87% ofthe compounds in the data set was developed. Usingmultiple regressions, two QSPerR models wereobtained for the description and determination of P(AP→BL) and P (BL→AP) transport across monolayerof intestinal epithelial (Caco-2) cell. A LnO and LOOcross-validation procedure revealed that the discrimi-nant and regression models respectively, had a fairlygood predictability. Furthermore, other 18 drugs wereselected as a test set (external prediction set) in order toassess the predictive power of the models. The P valuesof the test-set compounds were predicted with thesame accuracy as the compounds of the data set. Theuse of both regression models, in a combinative way, is

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possible to predict the Permeability Directional Ratio(PDR, BL→AP/ AP→BL) value. The obtained modelswere used in virtual screening for drug intestinal per-meability obtaining good relation with in vivo humanabsorption data. The ‘in silico’ methodology, used inthis study, shows how to provide an excellent alterna-tive to the experimental models for rank-ordering com-pounds by reducing time and cost. Moreover, thisapproximation permits us to obtain significant inter-pretation of the experiment result in terms of the struc-tural features of molecules. The application of thepresent method to the prediction of pharmacokineticproperties for several classes of organic compounds isnow in progress and will be the subject of a future pub-lication.

ACKNOWLEDGEMENTS

We sincerely thank Drs. Eric J. Lien, Mehran Yazda-nian, A. J. Hopfinger, Mitsuru Hashida and Han vande Waterbeemd for providing some manuscriptreprints from their works, which significantly contrib-ute to the development of this paper. In addition, theauthors thank the anonymous referees for theiruseful comments, which contributed to animproved presentation of these results.

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