3D-MEDNEs: An Alternative “In Silico” Technique forChemical Research in Toxicology. 1. Prediction of

Chemically Induced Agranulocytosis

Humberto Gonzalez Dıaz,*,† Yovani Marrero,‡ Ivan Hernandez,†Iyusmila Bastida,† Esvieta Tenorio,† Oslay Nasco,† Eugenio Uriarte,§

Nilo Castanedo,† Miguel A. Cabrera,† Edisleidy Aguila,† Osmani Marrero,†Armando Morales,† and Maikel Perez†

Chemical Bio-actives Center, Central University of “Las Villas” 54830, Cuba, Department ofPharmacy, Central University of “Las Villas” 54830, Cuba, and Department of Organic Chemistry,

Faculty of Pharmacy, University of Santiago de Compostela 15782, Spain

Received October 9, 2002

A novel approach to molecular negentropy from the point of view of Markov models isintroduced. Stochastic negentropies (MEDNEs) are used to develop a linear discriminantanalysis. The discriminant analysis produced a set of two discriminant functions, which gaverise to a very good separation of 93.38% of 151 chemicals (training series) into two groups.The total predictability (86.67%, i.e., 52 compounds out of 60) was tested by means of an externalvalidation set. Randic’s orthogonalization procedures allowed interpretation of the model whileavoiding collinearity descriptors. On the other hand, factor analysis was used to suggest therelation of MEDNEs with other molecular descriptors and properties into a property space.Three principal factors (related to three orthogonal MEDNEs) can be used to explain ∼90% ofthe variance of different molecular parameters of halobenzenes including bulk, energetic,dipolar, molecular surface-related, and hydrophobic parameters. Finally, preliminary experi-mental results coincide with a theoretical prediction when agranulocytosis induction by G-1,a novel microcidal that presents Z/E isomerism, is not detected.

Introduction

Alternative techniques can help to reduce the numberof animals required in medical and scientific research,thus precluding the suffering of any animals that wouldotherwise be used and, whenever possible, replacinganimals by other techniques. This approach is termedthe “three R’s” rule: reduction, refinement, and replace-ment (1, 2). In this sense, QSA(T)R methods (quantitativestructure-activity (or toxicity) relationships) appear tobe promising approaches (3-7).

In this context, one important application of QSTRmodels is the detection of unreported negative and/ortoxicological effects for drugs that are either marketedor under clinical development. Among the clinically sig-nificant side effects is so-called blood dyscracias: mildleukocytosis, leukopenia, eosinophilia, and, more specif-ically, agranulocytosis, which may occur with antipsy-chotic, antiviral, antithyroid, anticancer, and other medi-cations (8). Chemically induced agranulocytosis is quitemarked in antibacterial drug use (9).

However, our knowledge of QSTRs is very limited interms of blood dyscracias both for general and forantibacterial drugs. The problem with this techniquebecomes more challenging and rewarding when consider-ing the existence of three-dimensional (3D) isomers indrugs (10). Current research in the Chemical Bio-active

Center has been focused on the microcidal potential of2-furylethylenes. In particular, G-1 [E-1-bromo-1-nitro-2-(5-bromo-fur-2-yl)ethylene] has shown a pronounceddouble effect (antifungicidal/antibacterial) (11). It wastherefore of major interest for us to develop a generalmodel for predicting the risk of agranulocytosis inductionfor a given molecular structure, with the major emphasison the case of 2-furylethylenes. These compounds maypresent Z/E isomerism, and so, our QSTR study couldnot be based on classical topological indices (12).

On the other hand, quantum mechanics-based descrip-tors are 3D specific but their use is also time-consuming(13). Moreover, comparative molecular field analysis-likemethods are specific only for homologous series’ ofcompounds (14). These two techniques were thereforenot considered for application in QSTR-based drug-screening programs that pretend to find drug hits fromlarge and heterogeneous series of compounds. A veryinteresting development has recently been describedin the use of 3D molecular similarity indices (15). In-deed, our efforts in this case were directed toward theuse of 3D topological indices because these kinds ofindices are timely and appear to be extremely versatile(16-18).

In this sense, our research group has introduced thenovel computer-aided drug design scheme MARCH-INSIDE (Markovian chemicals in silico design). Thisapproach is based on the theory of Markov chains (MCH)(19) and involves modeling the intramolecular move-ments of electrons with time after a specific fluctuationof their stationary distribution. The method essentially

† Chemical Bio-actives Center, Central University of “Las Villas”.‡ Department of Pharmacy, Central University of “Las Villas”.§ Department of Organic Chemistry, University of Santiago de

Compostela.

1318 Chem. Res. Toxicol. 2003, 16, 1318-1327

10.1021/tx0256432 CCC: $25.00 © 2003 American Chemical SocietyPublished on Web 09/11/2003

codifies electronic structural information. This point ofview was successfully applied to the experimental dis-covery of new fluckicidal drugs (20). The method is veryflexible and makes possible the study of small moleculesas well as macromolecules such as proteins (21). Interest-ingly, MARCH-INSIDE molecular descriptors can begeneralized to allow the codification of 3D features (22).Another important point is the calculation of negentro-pies for the intramolecular movement of electrons. Anumber of successful indices, such as molecular negent-ropy, have previously been defined based on the conceptof Shannon’s entropy from the point of view of informa-tion theory (23-26). In this context, the present paperdeals with the formulation of novel 3D molecular descrip-tors in terms of a Shannon’s entropy-like approach usingMCH for QSTR studies.

Initially, it was necessary to define the novel moleculardescriptors. A QSTR was then performed discriminatingbetween agranulocytosis-causing chemicals and nontoxicones. Second, the QSTR was validated by means of anexternal prediction series. Finally, the theoretical predic-tion of the harmless characteristics of G-1 in relation tochemically induced agranulocytosis was shown to agreewith preliminary experimental assays.

Experimental Section

Three-Dimensional Markovian Electron Delocaliza-tion Negentropies (MEDNEs). Katritzky and Douglas haverecently published a summary of QSTR results (27) and thereader is referred to that article for an overview of this field.Our attention in this paper will be focused on describing theparticular aspects of the present approach.

The approach described here may be considered as a stochas-tic interpretation of the concept of molecular negentropy, asintroduced by Kier for biological studies (25). The method isbased on a simple model for the intramolecular movement ofelectrons from the point of view of MCH. Let us consider ahypothetical situation in which a set of atoms is free in spaceat an arbitrary initial time (t0). Alternatively, a more realisticsituation can be imagined in which, after perturbation by someexternal factor, electrons reach a distribution that differs fromthat in the stationary state. One external factor that may beconsidered, for instance, is the perturbation of molecularelectron “clouds” during the early stages of drug target docking.It certainly appears logical to accept that the return of electronsto their stationary position will depend on the specific molecularstructure of each drug and, thus, may be related to biologicaleffects. If we accept this situation, it would be of interest todevelop a simple stochastic model for the return of electrons tothe original position with time.

It can also be supposed that after any of these two initialsituations, electrons begin to distribute around atom cores indiscrete intervals of time tk. Thus, by using MCH (19-22,28) it is possible to calculate the probabilities with whichelectrons move around these atom cores in subsequent timeintervals until they reach a stationary electron density dis-tribution (see Figure 1). As depicted in Figure 1, such a modelwould deal with the calculation of the probabilities (kpij) withwhich electrons move from an arbitrary atom i at time t0 (inblack) to other atoms j (in white) along discrete time periods tk

(k ) 1, 2, 3...) and throughout the chemical-bonding system.Such a model is stochastic per se (probabilistic electron distribu-tion in time) but in fact considers molecular connectivity(electron distribution in space throughout the chemical-bondingsystem).

The selection of a Markov model is not arbitrary. It is well-known from quantum physics that if electrons are labeled atan initial time, one cannot use these labels to distinguish

between them at subsequent times. This physical fact has beenhistorically called the principle of indistinguishability of identi-cal particles (29). Our MCH model will obey this principlebecause in MCH the occurrence of one event (in this caseelectron movement) does not depend on the history of theprocess. In other words, the type of model described here willnot depend a priori on electron labeling.

The present procedure considers as states of the MCH theexternal electron layers of any atom core in the molecule, i.e.,the valence shell (30, 31). The method uses the matrix 1Π(ωk,Iøk), which has the elements 1pij. This matrix is built as asquared table of order n, where n represents the number ofatoms in the molecule. The numbers 1pij are the transitionprobabilities with which electrons move from atom i to j in theinterval t1 ) 1 (considering t0 ) 0):

where Iøk is Pauling’s electronegativity of atom j, which isbonded to the atom i (30). The elements of the new matrix(1pij) are defined to codify information about the electron-withdrawing strength of atoms, i.e., the power to withdrawelectrons from their neighbors in the molecule while con-sidering 3D structural features. The 3D dummy variable ωk

can take different values in order to codify specific stereochem-ical information such as chirality, Z/E isomerism, and so on(10). It is remarkable that 1pij is proportional to Iøj, theelectronegativity of the atom that attracts the electrons. Con-versely, the pij values are inversely related to the electronega-tivity of the atoms that “compete” with j to withdraw electronsfrom i.

The selection of the Pauling scale (Iøj) or any other linearlyrelated scale (IIøj ) a ‚ Iøj) such as Kier-Hall electronegativity(32) does not make any difference in this method. In fact, thepresent approach is invariant to the choice of electronegativityscale (22). It is also remarkable that in the approach describedhere, it is possible but not necessary to use electronegativityscales to distinguish between hybrid states of atoms in bonds(32). It can clearly be seen from Figure 2 that electrons will havea higher probability of returning to the sp carbon (0.313) thanto the sp2 carbon (0.200) despite the use of the same electro-negativity.

As mentioned above, the present approach codifies 3D infor-mation by the introduction of a local exponential factor ωk (22):

Figure 1. Diagrammatic representation of the stochasticelectron distribution kinetic in a simple Markovian model formolecule formation.

1p(ω)ij )Iøj ‚ eωj

∑k)1

δ+1Iøk ‚ eωk

(1)

Prediction of Chemically Induced Agranulocytosis Chem. Res. Toxicol., Vol. 16, No. 10, 2003 1319

The 3D factor exp(ωk) therefore takes values in the followingorder exp(1) > exp (0) > exp(-1) for atoms that have specific3D environments. The chemical idea here is not that theattraction of electrons by an atom depends on their 3D environ-ment but on their chirality. Experience shows that chirality doesnot change the electronegativities of atoms in the molecule inan isotropic environment in an observable way. The 1pij valuesare the conditional probabilities with which electrons move fromatom i to atom j, given a priori that these atoms have specific3D environments in the following order of preference: R ) E )a > nonchiral ) no Z/E isomerism involved ) no a/e substitution> S ) Z ) e. This kind of interpretation is mainly probabilisticand must not be the source of any misunderstanding whatsoever(22). A very interesting point is that the present 3D descriptorreduces to simple MARCH-INSIDE ones for molecules withoutspecific 3D characteristics because exp(0) ) 1 (22).

The interpretation described above can be illustrated graph-ically using a hypothetical case of a chiral system (Figure 3).We will consider a specific atom class with three differentlabels: R (white), nonchiral (shaded), or S (black). As the atomshave the same electronegativity, we can state that in situations(a)-(f), electrons in atom 1 are attracted with the same strengthby the cores 2, 3, and 4. We can then ask the question: whatare the probabilities with which atoms 2, 3, and 4 are with-drawing electrons from atom 1? The answer is that the prob-abilities are identical. However, if the question concerns whichelectrons in atom 1 have a higher probability of moving to anatom with configuration R and lower probability to move to anatom with S configuration, a different answer is forthcoming.In this case, there is no doubt that these probabilities must bearranged in the following order: (a), (b) ... to (f), with situation(a) having the highest probability. Similar questions could beanswered by employing 3D MARCH-INSIDE calculations, bear-

ing in mind the attraction of electrons by atoms at topologicaldistances greater than 1 [as in (g), (h), and (i)]. The explanationoutlined above is easily extended to include other cases such asa/e substitutions and Z/E or π-isomer differentiation.

In addition, the stochastic nature of the present approachmakes it possible to quantify molecular structure in terms of anew kind of molecular negentropy (MEDNEs) (24-26). Equation1 represents the sum in the dominator over all of the atoms inthe molecule (n) rather than the sum up to δ + 1 only. Thisnew probability is called the 0 step absolute Markovian prob-ability of electron delocalization for atom j (Aπ0(j)). In fact, theseprobabilities for each atom are normalized, i.e., Aπ0(j) values obeythe normalization condition because their sum up to n is equalto 1 (19, 20-22, 28, 31).

By following the MCH theory formulation, the physicalmeaning of Aπ0(j) is very clear. Under the approximation thatelectronegativity describes the electron-withdrawing strengthof atoms in the molecule, π0(j) represents the probabilities withwhich a specific atom j attracts any electrons in the moleculeat t0. By analogy, Aπk(j) is the probability with which a specificatom j attracts any electrons in the molecule at any subsequenttime tk or after travelling through all different paths composedof k bonds or less. The calculation of this value is simple fromChapman-Kolmogorov equations (19):

where AΠk are 1 × n vectors whose elements Aπk(j) are theprobabilities found, AΠ0 is a 1 × n vector whose elements arethe Aπ0 (j) probabilities for the n atoms in the molecule, and kΠis the k-th natural power of the 1Π matrix. It is now very simpleto calculate the k-th step MEDNEs, which represents theentropy involved in the attraction of electrons at least k steps

Figure 2. Definition and calculation of 1Π matrix for a specificcase. The element symbol is used to denote the value of theelements electronegativity: F represents the electronegativityof fluorine ø(F).

wk )

{wk ) 1 when k has R (rectus), E (entgegen),or a (axial) notation according toCahn-Ingold-Prelog rules

wk ) 0 if k does not have a 3D specificenvironment

wk ) -1 when k has S (sinister), Z (zusammen),or e (equatorial) notation accordingto Cahn-Ingold-Prelog rules

(2)

Figure 3. Graphical representation of some hypotheticalsituations in order to facilitate the probabilistic interpretationof the Chiral MEDNEs approach.

Aπ0(j) )øj ‚ eωj

∑k)1

n

øk ‚ eωk

(3)

AΠk ) AΠ0 × (kΠ) (4)

1320 Chem. Res. Toxicol., Vol. 16, No. 10, 2003 Dıaz et al.

(bonds) away from any atom j in the molecule (Θk(j)). The sumof the Θk(j) values for all n atoms in the molecule gives the k-thMEDNEs used here as total molecular descriptors:

Boltzmann’s constant, kB, can be used, and this means thatour molecular descriptors are measured in kJ/K. Table 1illustrates the calculation of Θk for a pair of Z/E isomers, andthese calculations can easily be extended to R/S or axial/equatorial isomers.

Computer Software. The calculation of Θk for any organicor inorganic molecule was carried out using the softwareMARCH-INSIDE (33). This software has a graphical interfacethat makes it user friendly for medicinal chemists. The chemicalstructure is input directly using the molecular graphics in thesoftware draw mode. Clicking on an upper dynamic array, whichcontains the labels for the different groups of the Periodic table,enables selection of the active atom symbol. It is then possibleto select the calculation option and perform the calculation ofmolecular indices.

Statistical Analysis. As a continuation of the previoussections, we can attempt to develop a simple linear QSAR usingthe MEDNEs methodology. We selected linear discriminantanalysis (LDA) (34, 35) to fit the classification functions. Themodel deals with the discrimination of agranulocytosis-causing

chemicals from nontoxic compounds. In this connection, wedevelop a discriminant function with the general formula:

Here, Θk are the molecular descriptors codifying molecularstructure. In total, we used 16 Θk (from Θ0 to Θ15) as input.The activity (output of the model) was codified by a dummyvariable (AGRAN). This variable indicates either the presence(AGRAN ) 1) or the absence (AGRAN ) 0) of chemicallyinduced agranulocytosis. In eq 6, bk represents the coefficientsof the classification function, determined by the least-squaresmethod as implemented in the LDA modulus of STATISTICA6.0. Backward stepwise was fixed as the strategy for variableselection (35).

Previously, we used tree joining cluster analysis (TJCA) (36)to design the training and predicting sets. Single distance wasused as the clustering method, and Euclidean distance wasselected as the linkage distance. The quality of the model wasdetermined by examining Wilk’s λ statistic, Mahalanobis squareddistance (D2), Fisher ratio (F), and the p level (p). We alsoinspected the percentage of good classification and the ratiosbetween the cases and the variables in the equation andvariables to be explored in order to avoid overfitting or chancecorrelation. Validation of the model was corroborated by meansof an external prediction set; these compounds were never usedto develop the classification function (35).

Table 1. Calculation of kΠ, AΠk, and Θk(j) for Two Z/E Isomers When k Varies from 0 to 2 and j Is a Specific Atom or theMolecule as a Whole (SUM)

(E)-HFCdN-Cl

Xij H F C N Cl SUMj H F C N Cl SUM

H 2.1 0 6.8 0 0 8.9 AΠ0F 0 4 6.8 0 0 10.8 [0.09 0.17 0.28 0.34 0.12] 1C 2.1 4 6.8 8.2 0 21N 0 0 6.8 8.2 3 17.9 Θ0(j) Θ0Cl 0 0 0 8.2 3 11.2 0.128 0.1787 0.21 0.22 0.156 0.896

1Π(E)H F C N Cl SUM AΠ1 SUM

H 0.24 0 0.76 0 0 1 [0.049 0.115 0.391 0.355 0.09] 1F 0 0.4 0.63 0 0 1C 0.10 0.2 0.32 0.39 0 1 Θ1N 0 0 0.38 0.45 0.17 1 [0.088 0.1492 0.22 0.22 0.13] 0.808Cl 0 0 0 0.73 0.27 1

2Π(E)H F C N Cl SUM AΠ2 SUM

H 0.1 0.1 0.4 0.3 0 1 [0.071 0.1724 0.35 0.286 0.11] 1F 0.1 0.4 0.3 0.1 0.1 1C 0.1 0.2 0.4 0.3 0.1 1 Θ2N 0.1 0.1 0.3 0.3 0.2 1 [0.113 0.1817 0.22 0.215 0.14] 0.879Cl 0 0 0.5 0.4 0.1 1

(Z)-HFCdN-Cl

Xij H F C N Cl SUMj H F C Cl SUM

H 2.1 0 0.9 0 0 3.02 AΠ0F 0 4 0.9 0 0 4.92 [0.16 0.31 0.07 0.22 0.23] 1C 2.1 4 0.9 2.8 0 9.82N 0 0 0.9 2.8 3 6.72 Θ0Cl 0 0 0 2.8 3 5.8 [0.178 0.218 0.11 0.199 0.204] 0.911

1Π(Z)H F C N Cl SUM AΠ1 SUM

H 0.7 0 0.3 0 0 1 [0.13 0.28 0.14 0.22 0.22] 1.00F 0 0.8 0.2 0 0 1C 0.2 0.4 0.1 0.3 0 1 Θ1N 0 0 0.1 0.4 0.4 1 [0.16 0.21 0.17 0.20 0.20] 0.94Cl 0 0 0 0.5 0.5 1

2Π(Z)H F C N Cl SUM AΠ2 SUM

H 0.5 0.1 0.2 0.1 0 1 0.11 0.22 0.37 0.16 0.14 1.00F 0 0.6 0.3 0 0 1C 0.1 0.3 0.4 0.2 0 1 Θ2N 0 0 0.4 0.3 0.3 1 0.15 0.20 0.22 0.17 0.16 0.90Cl 0 0 0.5 0.3 0.3 1

Θk ) - ∑j)1

n

Θk(j) ) -kB ∑j)1

n

[Aπk(j)] ‚ ln[Aπk(j)] (5)

AGRAN ) b + b0 Θ0 + b1 Θ1 + b2 Θ2 + ... + bkΘk (6)

Prediction of Chemically Induced Agranulocytosis Chem. Res. Toxicol., Vol. 16, No. 10, 2003 1321

Chemical Data. The general data set was composed of 211organic chemicals. Two groups of chemicals containing 57agranulocytosis-causing chemicals and 94 nontoxic ones wereused as a training series. The collection of the data set wascarried out by performing the following steps: (i) Initially, 1000chemicals belonging to a diverse range of drug families wereselected at random from Martin Negwer’s and Kleeman’sdatabases (37, 38). Figure 4 depicts a representative sample ofsuch compounds. (ii) This data set was filtered in order to verifytheir chemically induced agranulocytosis power from the lit-erature (39, 40). (iii) The remaining chemicals were split intotraining and predicting series by mean of cluster analysis.

Laboratory Animals and Biological Assay. Sufficientquantities of analytical grade G-1 for biological assays werepurchased from the Chemicals Bioactive Center. Differentialcounting of granulocytes was carried out as recommended inthe literature (40). Balb/c mice were selected as a biologicalmodel (41). Healthy Balb/c mice of both sexes were purchased,along with food, from the “Centro Nacional de Animales deLaboratorio (CENPALAB)”, Cuba. Quarantine, labeling, ac-climatization, and good maintenance conditions of animals werestrictly adhered (42).

Results and Discussion

MEDNEs-Based QSTR Modeling of Agranulocy-tosis using LDA. Drug-induced injuries of the blood aretermed blood dyscracias. Many authors refer to the four

major types of drug-induced blood dyscracias (DIBD) asbeing hemolytic anemia, thrombocytopenia, aplastic ane-mia, and agranulocytosis/neutropenia. Agranulocytosisis defined as a severe form of neutropenia with a totalgranulocyte count <500/mm3 (43, 44).

The first step in this study was the design of thetraining and predicting series’ to prevent nonrandomdistribution of chemicals between the two sets. This wasachieved using TJCA (36). In this study, we selected fortraining and predicting sets chemicals from all subclus-ters in Figure 5. The Euclidean distance was selected asthe linkage distance and the single linkage as the linkagemethod on an ad hoc basis. The results of the TJCA aredepicted in Figure 5.

Once the training and predicting series’ had beendesigned, LDA was carried out. The backward stepwisevariable selection strategy was used to select the moresignificant variables and to limit its number in the model.This analysis produced a discriminant function that gaverise to an efficient separation of 93.38% of chemicals (i.e.,141 of 151 chemicals in the training set) into two groups:

Figure 4. Random, but not exhaustive, sample of the molecular families of compounds studied here.

Figure 5. TJCA used to design training and predicting series of agranulocytosis-causing (I) and innocuous (II) chemicals.

AGRAN ) (1191.44 × Θ5) - (2651.32 × Θ7) +(5165.66 × Θ13) - (3699.29 × Θ15) - 14.0 (7)

1322 Chem. Res. Toxicol., Vol. 16, No. 10, 2003 Dıaz et al.

where N ) 151, λ ) 0.357, F(4,146) ) 65.55, D2 ) 7.54,and p < 0.000.

This particular model was selected out among manyothers (results not shown) for several reasons: (i) First,comparison of the experimental F value with the tabu-lated one gave a p level < 0.05. This signifies that wecan reject the hypothesis of nonseparation of groups witha low 5% probability of error, so eq 7 can be accepted asstatistically significant (35, 45). (ii) The model showedthe best accuracy in training and predictability inpredicting series. (iii) This equation presented a lowerchance correlation probability prevented by bearing inmind that the number of variables to explore (16) mustbe less than (N/2) - 1 ) 74, where N is the number ofobservations.

In addition, the model classifies correctly 87.72% ofagranulocytosis-causing chemicals, 50 cases out of 57 inthe training series (see Table 2 for names and posteriorprobabilities). The value ∆P% ) [P(+) - P(-)] × 100 wasused here as the cutoff value for taking the decision aboutcorrect/incorrect compound classification, where P(+) isthe posterior probability that the chemical is predictedto be toxic, while P(-) is the posterior probability withwhich the chemical is predicted to be harmless. The plevel threshold limit is p ) 0.05, and so, a chemical with-5% ∆P% < 5 may be considered as nonclassified. Thismethod is the one proposed by the software used (34).

The model classifies 96.81% of nontoxic compounds (seeTable 3), i.e., 91 cases out of 94. Several chemicals weremisclassified as toxic when our literature review statedthat they are innocuous and vice versa. These cases canbe explained in terms of the model lacking some aspectsof structural pattern recognition (outliers).

Employing an external validation series (60 com-pounds) tested the total predictability (86.67%). The

model recognizes as toxic 86.36% of these compounds, i.e.,19 chemicals out of 22 (see Table 4). In addition, themodel correctly classifies 86.84% of nonagranulocytosis-causing chemicals, i.e., 33 cases out of 38 in the predictingseries (see Table 5). Equation 7 can therefore be usedfor the prediction of drug-induced agranulocytosis.

Another aspect worth considering is the selection of alarge and structurally heterogeneous series of compoundsin order to develop QSTRs. Certainly, many reportedQSTRs for specific or even unspecific properties arederived from homologous series’ (27). However, it hasbeen widely demonstrated that the use of very hetero-geneous series’ of organic compounds may yield potentQSARs, even for highly specific properties (12). Morespecifically, agranulocytosis is mediated by quite complexbut very diverse and, in this sense unspecific, toxicologi-cal properties (44). Thus, apart from the discussion aboutthe use of QSAR techniques for heterogeneous series’ ofcompounds to predict specific properties, we can assertthat the present results are promising in terms of thesearch for novel 3D indices.

Physical Interpretation of the QSTR Model. Thecentral theorem of limit demonstrates the stationarybehavior of properties derived using MCHs, includingMEDNEs (28). It is therefore to be expected that after acertain number of steps, MEDNEs will become stronglyintercorrelated with one another. In fact, the resultsshown in Table 5 demonstrate that all regression coef-ficients between the MEDNEs in the model are higherthan 0.99. It is known that interrelatedness among thedifferent descriptors can result in highly unstable regres-sion coefficients. However, the small fraction of informa-tion inherent in a descriptor, which is not reproduced byits strongly interrelated pair, can enhance the quality ofthe model in some cases.

Table 2. Name and Posterior Probabilities (∆P%) of Agranulocytosis-Causing Chemicals in Both Predicting andTraining Series

name ∆P%a name ∆P% name ∆P%

agranulocytosis chemical inductor training seriespenicilina G 99.80 quinina 99.74 tioridazina 9.46penicilina V 99.00 primaquina 93.13 ketazolan 57.50feneticilina 96.04 acetohexamida 97.68 pinacepan 74.84ampicilina 99.65 tolazamida 97.58 prazepan 10.20amoxicilina 99.14 IPTD -44.44 brorizolan -43.26carbenicilina 19.23 ceftriaxona 99.99 hidroxizina 32.58meticilina 98.53 gliburida 68.81 piritinol 95.81oxacilina 99.15 gliburnurida 98.62 quinaprilo 10.61dicloxacilina 99.05 vindesina 99.77 ramiprilo 13.41floxacilina 64.61 gliseofulvina 45.36 labetalol 70.77ticarcilina 99.56 pentaquina 92.24 betaxolol 99.84piperacilina 98.41 phenobarbital -21.77 bisaprolol 61.87cefapirina 99.95 amodiaquin -6.61 celiprolol 99.76cefalexina 99.27 dipyrrone -50.42 carvediol 65.78cefradina 97.23 dipyridamole 99.97 timolol 69.94cefamandol 99.73 acvalproico 24.29 ketoconazol 96.63cefalofina 86.49 bupivacaina 33.34 propifenazona 99.07aurotioglucosa -11.66 periciazina -31.47 gemfibrozilo 99.13sulfametoxipiridazina 88.91 pimozida 76.45 piperacetazina 71.52

agranulocytosis chemical inductor predicting seriesnafalina 98.51 glibenclamida 33.09 perindoprilo -26.41carindcilina 99.64 vinblastina 99.82 etuzolina 59.01cloxacilina 98.74 reserpina 99.06 carteolol 22.04cefazolina 99.93 indometacina 66.26 teniposiclo 87.48cefoxilina 97.18 haloperidol 96.71 acmeclofenamico -37.17colchicina 49.44 camazepan 50.19 probucol 99.99tolbutamida 50.41 alprazolan 62.13 mexiletim -48.13

a ∆P% ) [P(+) - P(-)] × 100, where P(+) is the posterior probability with which the chemical is predicted as toxic and P(-) is theposterior probability with which the chemical is predicted as innocuous. The p level threshold limit is 0.05, and so, a chemical with -5%∆P% < 5 may be considered as nonclassified.

Prediction of Chemically Induced Agranulocytosis Chem. Res. Toxicol., Vol. 16, No. 10, 2003 1323

Several years ago, Randic introduced the orthogonal-ization process for molecular indices as a way to improvethe statistical interpretation of the model when descrip-tors are correlated with one another (46-48). Fortu-nately, MEDNEs are accumulative entropies; this meansthat Θk is the entropy involved in the movement ofelectrons in the interval ∆t0k ) tk - t0 ) k (remember t0

) 0). After applying Randic’s procedure, the new orthogo-nal MEDNEs, mO(Θk) takes into account only the infor-mation related to the movement of the electrons exactlyat time k and not at times <k. The symbol O meansorthogonal, and m is the degree of importance of thedescriptor to explain the property determined by the

order in which it is selected by forward stepwise analysis(49).

It must be highlighted here that the orthogonal de-scriptor-based model coincides with the collinearMEDNEs-based model (7) in all statistical parameters.Therefore, mO(Θk) may be classified according to thedistance k into short- (0-5), mid- (6-10), and long-rangeelectron delocalization entropies (k > 10). The informa-tion in Table 5 clearly shows that the major contributionto agranulocytosis is provided by long-rage MEDNEs.These kinds of electron movement are only detected inhighly condensed aromatic systems. It would thereforebe expected that the presence of such systems creates a

Table 3. Name and Posterior Probabilities of Nonagranulocytosis-Causing Chemicals in Training Series

nonagranulocytosis chemical inductors training series

name ∆P%a name ∆P% name ∆P%

flucitosina -99.80 fumagilin -75.73 nitroglicerina -99.86mecloretamida -1.35 imipramine -82.80 tetranitrato -90.12estreptozocina -98.15 isoprenalina -2.94 minoxidilo -92.26clorzotozina -96.69 metapyrilene -99.63 tiocarlida -100.00fluorouracilo -99.55 aminopirine -95.29 amantadina -92.30floxundina -99.79 difenilhidramina -98.92 lidocaina -86.01clorodeoxiundina -92.26 trimethoprin -75.62 tetracaina -99.96bromodeoxiundina -68.21 amrinona -66.57 etidocaina 34.78indoxuridina -98.06 theophyline -92.17 fenazopiridina -24.45trifluorometil deoxiuridina -99.75 phenantoin -99.61 diazoxido -85.57citanabina -99.41 lisurida -66.29 sulindac -56.76azaundina -99.75 clozapina -98.95 fenoprofen -98.19acnalidixico -90.87 zopicolona -99.56 VUT B6 31.25nitrofurantoina -99.94 pentamidina 0.40 sulfinpinazona -50.62rifampicina -63.77 carbucisteina -72.83 piroxican -80.23dapsona -96.23 acquenodesoxicolico -93.74 sulfasalazina -68.74sulfuxona -89.39 ciprohephadin -89.22 tiabendazol -98.70acetanilida -99.95 ticlopidina -47.68 tioguanina -99.17anilina -99.50 oxprenolol -50.55 mitoxantrona -100.00P-fenetidina -99.81 cilastatina -99.59 probenecid -100.00doxorrubicina -50.38 metronidazol -92.87 vit C -92.67hidroxiurea -99.87 prednimustina -99.98 vit K (K3) menadiona -94.91naproxeno -99.66 paclitaxel -66.15 levodopa -99.61oxido de benceno -99.98 flurbiprofeno -99.93 acebutolol -52.37ciclofosfamida -89.75 protacina -84.82 trifuoroperacina -99.57adnamicina -82.76 halotano -99.90 fenil butazona -95.92mostasa vacilica -99.83 diflunisal -99.57 acetophenetidin -96.49carmustina -93.71 pirifibrato -89.99 ASA -95.70lomustina -87.96 ziduvudina -96.52 chlordano -79.51dacarbazina -99.93 nimodipina -93.28 chlorophenothane -99.39fenitoina -97.12 mononitrato de liusurbida -98.78 xilocaine -99.42caffeine -83.07a ∆P% ) [P(+) - P(-)] × 100, where P(+) is the posterior probability with which the chemical is predicted as toxic and P(-) is the

posterior probability with which the chemical is predicted as innocuous. The p level threshold limit is 0.05, and so, a chemical with -5%∆P% < 5 may be considered as nonclassified.

Table 4. Name and Posterior Probabilities of Nonagranulocytosis-Causing Chemicals in Predicting Series

nonagranulocytosis chemical inductors predicting series

name ∆P%a name ∆P% name ∆P%

melfalan 16.10 ethimate -99.63 propatilnitrato -99.95busulfan -97.13 methaminodiazepoxide -85.34 hidralazina 35.40deoxundina -98.88 disulfiran -99.68 aciclovir -99.66trimidina -91.07 furosemida -97.65 zalcitabina 47.76azanibina -96.00 doxilamina -83.03 mepivacaina -86.93metildopa -53.23 ganciclovir -98.71 hidaclorotiazida -89.86acetaminofeno -94.77 citazaprilo -99.95 vit A -54.68dauronobicina -49.99 tolueno -99.27 tiouracilo -99.52benceno -96.26 nifenazona -91.33 bishydroxycoumann 13.66epinubicina -44.88 carbamacepina -99.40 chlorothiazide -97.27semustina -64.38 dinitrato de Isosurbide -98.58 chlorpromazine 41.60tetraciclina -98.16 carbimazol -96.67 cimetidina -93.63hexacloruro de benceno -99.95 captopril -16.75

a ∆P% ) [P(+) - P(-)] × 100, where P(+) is the posterior probability with which the chemical is predicted as toxic and P(-) is theposterior probability with which the chemical is predicted as innocuous. The p level threshold limit is 0.05 thence a chemical with -5%∆P% < 5 may be considered as nonclassified.

1324 Chem. Res. Toxicol., Vol. 16, No. 10, 2003 Dıaz et al.

certain predisposition of a drug to cause chemically in-duced agranulocytosis. Indeed, many agranulocytosis in-ductors have aromatic rings in their structure. However,the influence of mid- and short-term electron movementsthat could result from the effect of specific substituentsor small chemical groups seems to act as an importantmodulator. The present paper represents the first use ofRandic’s orthogonalization procedure in LDA, despite thewider use of this technique in linear and nonlinearregression (50).

How Does MEDNEs’ Compare to Other MolecularParameters in Terms of Property Spaces? There area many molecular descriptors such as physicochemicalparameters, biological activities, and toxicological proper-ties that may be interrelated by means of propertyspaces. In this sense, one of the authors of the presentpaper has recently collaborated in the use of propertyspaces and factor analysis in chemistry (51). In theresearch described here, factor analysis was used toestablish the relationship between mO(Θk) and otherparameters in addition to toxicological risk. A set of suchdescriptors for halobenzenes, reported by Warne et al.,was used here (52). The results are summarized in Table6, and the three principal factors explain approximately90% of the variance.

The first factor (F1), which is strongly related with0O(Θ0), encodes information that determines the toxicityof these compounds. This factor is related to bulk (MW,MR), volume (VOL), hydrophilic (logP), and accessibilityrelated properties such as SASA and SA. The reliance ofso many different properties on F1 may be caused by thevery similar structures of the compounds under study(halobenzenes). In general, one would expect that the useof a more heterogeneous series would split F1 into morefactors. Otherwise, 1O(Θ1) (encoded by F2) codifies pref-erentially the heat of formation of halobenzenes (E),which characterizes the strength with which the atomsare linked together in these molecules. Frontier orbitalenergies are not exactly linear here. Finally, the thirdfactor (F3) codifies information related to the dipolemoments, which is again related to 2O(Θ2). In thisanalysis, the three first orthogonal-MEDNEs explain theproperties studied for this data set. A logical consequenceof orthogonality is the successive addition of othermO(Θk) to property spaces and the determination of theincrement of principal factors that may explain otherproperties not taken it into account here. However,studies with larger databases must be developed in orderto ascertain with confidence the amount of informationthat the present approach is capable of codifying.

Table 5. Results of Randic’s Orthogonalization Analysis

nonorthogonal MEDNEs

Θ5 Θ7 Θ13 Θ15

Θ5 1 0.9996 0.9966 0.9955Θ7 0.9996 1 0.9985 0.9977Θ13 0.9966 0.9985 1 0.9999Θ15 0.9955 0.9977 0.9999 1

orthogonal MEDNEs3O(Θ5) 4O(Θ7) 1O(Θ13) 2O(Θ15)

1O(Θ5) 1 0.00 0.00 0.002O(Θ7) 0.00 1 0.00 0.003O(Θ13) 0.00 0.00 1 0.004O(Θ15) 0.00 0.00 0.00 1

forward stepwise LDA with orthogonal MEDNEs1O(Θ13) 2O(Θ15) 3O(Θ5) 4O(Θ7) constant λ p % (total) % (+) % (-)

5165.7 6.4 325.4 -51.1 -13.9 0.357 0.00 93.37 87.72 96.804682.5 5.7 303.2 -12.5 0.398 0.00 92.72 85.72 95.743947.9 5.1 -11.0 0.463 0.00 89.46 82.40 93.622964.9 -0.70 0.614 0.00 84.11 71.93 91.49

Table 6. Three-Fold Factorial Space Relating Physicochemical Properties, Toxicology, and Molecular Descriptors

factor analysis explained variance

factors Eigenvalue% total

variancecumulativeEigenvalue

cumulativevariance

F1 8.74 62.44 8.74 62.44F2 2.31 16.49 11.05 78.93F3 1.50 10.68 12.55 89.62

factor loadings (varimax normalized rotation)

variables F1 F2 F3 R variables F1 F2 F3 R0O(Θ0) 0.23 0.94 -0.04 0.99 DMe 0.07 0.14 -0.50 0.971O(Θ1) -0.80 0.24 0.32 0.99 MWf 0.90 0.25 0.12 0.992O(Θ2) 0.39 -0.05 0.78 0.99 MRg 0.95 0.27 0.17 0.9930 m pTa 0.84 0.44 -0.13 0.99 LogPh 0.97 0.18 0.18 0.99Eb 0.06 0.97 -0.15 1.00 SAi 0.97 0.17 0.19 0.99HOMOc -0.46 -0.31 -0.48 0.98 VOLj 0.95 0.23 0.16 0.99LUMOd -0.93 0.24 -0.21 0.99 SASAk 0.96 0.19 0.22 0.99

a Negative logarithm of the mM concentration causing 50% reduction of light emission by P. fluorescence pT50. b Heat of formation.c Energy of the highest occupied molecular orbital. d Energy of the lowest unoccupied molecular orbital. e Dipolar moment. f Molecularweight. g Molar refractivity. h Logarithm of the partion coefficient. i Solvent accessibility. j Molecular volume. k Surface area.

Prediction of Chemically Induced Agranulocytosis Chem. Res. Toxicol., Vol. 16, No. 10, 2003 1325

Biological Results: Comparison with the Predic-tion and Discussion for the Case of G-1. Experimentscarried out in mice do not provide any evidence of theoccurrence of agranulocytosis in groups treated with G-1(as compared to control groups) when the time of admin-istration was varied (see Table 7)sa very importantparameter for the detection of DIBD (43, 44). Statisticallysignificant differences in the neutrophils count could notbe detected after treatment with different doses of G-1at the 0.05 p level by means of a dependent pairwisestudent test (42). Nevertheless, future phase III studiesin humans will provide the ultimate evidence in this case.Additionally, the posterior probability predicted for G-1(∆P% ) -86.62) coincides with the experimental results.

Concluding Remarks

Bearing in mind the findings of other authors and ourprevious results, we decided to proceed with the use ofrecognized and novel molecular descriptors in QSTR asan alternative technique (2-7, 27, 53). Unfortunately,many useful drugs have stereoisomers with lower levelsof biological activity or even toxic properties, the so-called“devil twins” (10). Conversely, not all but most moleculardescriptors present difficulties in terms of the codificationof 3D structures in an efficient way (13).

The introduction of the present methodology haspermitted a physically meaningful 3D generalization ofthe concept of molecular negentropy by means of sto-chastic models. Orthogonalization of MEDNEs as wellas the development of a property space has helped toclarify the interpretation of these results and identifylinks with other molecular parameters. The presentapproach has proven to be very useful in QSTR (inparticular the prediction of chemically induced agranu-locytosis). It can therefore be concluded that MEDNEsseem to be a very flexible tool for QSTR when combinedwith simple pattern recognition techniques. We have alsoreported here some preliminary results (theoreticallydetermined and experimentally assessed) on the study

of DIBD upon treatment with G-1. This result is of majorimportance for the preliminary characterization of thetoxicity of this drug. The good classification of G-1 seemsto be a first positive step in the theoretical prediction ofthe chemically induced agranulocytosis of Z/E isomers.

Acknowledgment. We thank unknown referees foruseful comments and the kind attention of the editorProf. Lawrence J. Marnett. Specifically, E.U. and D.H.G.are grateful to the “Xunta de Galicia” (PR405A2001/65-0) for support in purchasing STATISCA 6.1. D.H.G.is also indebted to Dr. J. Luis Garcıa for kind support.Finally, D.H.G. is indebted to Dr. R. Bello, CentralUniversity of Las Villas. We also acknowledge Dr. NeilThompson for language revision.

References

(1) Fentem, J., and Balls, M. (1992) In vitro alternatives to toxicitytesting in animals. Chem. Ind. 6, 207-211.

(2) Purchase, I., Botham, P., Bruner, H., Flint, O., Frazier, J., andStokes, W. (1998) Workshop overview: scientific and regulatorychallenges for the reduction, refinement, and replacement ofanimals in toxicity testing. Toxicol. Sci. 43 (2), 86-101.

(3) Barratt, M. (1998) Integration of QSAR and in vitro toxicology.Environ. Health Perspect. Suppl. 106 (2), 459-465.

(4) Martin, T. M., and Young, D. M. (2001) Prediction of the acutetoxicity (96 h LC50) of organic compounds to the fathead minnow(Pimephales promelas) using a group contribution method. Chem.Res. Toxicol. 14, 1378-1385.

(5) Green, S., Goldberg, A., and Zurlo, J. (2001) Testsmart-highproduction volume chemicals: an approach to implementingalternatives into regulatory toxicology. Toxicol. Sci. 63 (1), 6-14.

(6) Cronin, T. D., and Schultz, T. W. (2001) Development of a novelQuantitative Structure-Activity Relationship for the Toxicity ofAromatic Compounds to Tetrahymena pyriformis: Comparativeassessment of the methodologies. Chem. Res. Toxicol. 14, 1284-1295.

(7) Dearden, J. C., Barrat, M. D., Benigni, R., Bristol, D. W., Combes,R. D., Cronin, M. T. D., Judson, P. N., Payne, M. P., Richard, A.M., Tichy, M., Worth, A. P., and Yourick, J. J. (1997) Thedevelopment and validation of Expert systems for predictingtoxicity. ECVAM Workshop Rep., ATLA 25, 223-252.

(8) Dukes, M. N. G., Aronson, J. K., Eds. (2000) Meyler’s Side Effectof Drugs, Elselvier, Amsterdam.

(9) Hardman, G. J., Lee, E. I., Eds. (1996) Goodman and Gilman’s,The Pharmacological Basis of Therapeutics, 9th ed., McGraw-Hill.

(10) Eliel, E., Wilen, S., and Mander, L. (1994) Stereo Chemistry ofOrganic Compounds, pp 103-112, John Wiley & Sons Inc., NewYork.

(11) Blondeau, J. M., Castanedo, N., Gonzalez, O., Medina, R., andSilveira, E. (1999) In vitro evaluation of G-1: A novel antimicro-bial compound. Antimicrob. Agents Chemother. 11, 1663-1669.

(12) Estrada, E., and Uriarte, E. (2001) Recent advances on the roleof topological indices in drug discovery research. Curr. Med. Chem.8, 1573-1588.

(13) Todeschini, R., and Consonni, V. (2000) Handbook of MolecularDescriptors, Wiley VCH, Weinheim, Germany.

(14) Cramer, R. D., III, Paterson, D., and Bunce, J. (1988) Comparativemolecular field analysis (CoMFA) 1. Effects of shape on bindingof steroids to carrier proteins. J. Am. Chem. Soc. 110, 5959-5967.

(15) Benigni, R., Cotta-Ramusino, M., Gallo, G., Giorgi, F., Giuliani,A., and Vari, M. R. (2000) Deriving a quantitative chiraltymeasure from molecular similarity indices. J. Med. Chem. 43,63699-63703.

(16) Julian-Ortiz, J. V., de Gregorio Alapont, C., Rıos-Santamaria, I.,Garcıa-Domenech, R., and Galvez, J. (1988) Prediction of proper-ties of chiral compounds by molecular topology. J. Mol. GraphicsModell. 16, 14-18.

(17) Kellogg, G. E., Kier, L. B., Gaillard, P., and Hall, L. H. (1996)E-state fields: applications to 3D QSAR. J. Comput.-Aided Mol.Des. 10, 513-520.

(18) Golbraik, A., Bonchev, D., and Tropsha, A. (2001) Novel ChiralityDescriptors Derived from Molecular Topology. J. Chem. Inf.Comput. Sci. 41, 147-158.

(19) Freund, J. A., Poschel, T., Eds. (2000) Stochastic Processes inPhysics, Chemistry, and Biology. In Lecture Notes in Physics,Springer-Verlag, Berlin, Germany.

Table 7. Results of the Differential Count of Neutrophilsat Different Times and Doses after Administration inMouse of G-1, Vehicle, Positive Control, and Negative

Control Solutions

control groups

time (h) 48 72 96

control ∆U/L %a

migliol 0.16 ( 0.04 0.16 ( 0.04 0.16 ( 0.04negative (0 mg/kg

of G-1)0.35 ( 0.005 0.27 ( 0.04 0.22 ( 0.005

groups treated with G-1

time (h) 48 72 96

doses (mg/kg) ∆U/L %a

185.6 0.16 ( 0.01 0.26 ( 0.06 0.24 ( 0.0561.8 0.21 ( 0.01 0.20 ( 0.05 0.19 ( 0.0323.4 0.28 ( 0.16 0.16 ( 0.01 0.11 ( 0.0112.4 0.27 ( 0.16 0.16 ( 0.07 0.16 ( 0.059.8 0.203 ( 0.08 0.17 ( 0.03 0.23 ( 0.10

a Difference (arithmetic mean for the respective group) betweenthe neutrophil count after treatment (U/L (after) with respect toneutrophil count before the treatment U/L (before) in units (cells)per liter, that is, ∆U/L % ) [U/L (after) - U/L (before)] × 100.

1326 Chem. Res. Toxicol., Vol. 16, No. 10, 2003 Dıaz et al.

(20) Gonzales, D. H., Olazabal, E., Castanedo, N., Hernadez, I.,Morales, A., Serrano, H., Gonzalez, J., and Ramos, R. (2002)Markovian Chemicals “in Silico” Design (MARCH-INSIDE), apromising approach for Computer Aided Molecular Design II:Experimental and Theoretical Assessment of a Novel Method forVirtual Screening of Fasciolicides. J. Mol. Model. 8, 237-245.

(21) Gonzalez, D. H., De Armas, R. R., and Uriarte, E. (2002) In SilicoMarkovian Bioinformatics for Predicting 1Ha-NMR ChemicalShifts in mouse Epidermis Growth Factor (mEGF). Online J.Bioinformatics 1, 83-95.

(22) Gonzalez, D. H., Hernadez, I., Uriarte, E., and Santana, L. (2003)Symmetry considerations in Markovian chemicals ‘in silico’ design(MARCH-INSIDE) I: central chirality codification, classificationof ACE inhibitors and prediction of s -receptor antagonist activi-ties. Comput. Biol. Chem. In press.

(23) Shannon, C. E. (1995) The Mathematical Theory of Communica-tion, University of Illinois Press, Urbana.

(24) Bonchev, D., and Trinjastic, N. (1997) Information Theory,Distance matrix and Molecular branching. J. Chem. 67, 4517-4533.

(25) Kier, L. B. (1980) Use of molecular negentropy to encode structuregoverning biological activity. J. Pharm. Sci. 69, 807-810.

(26) Agrawal Vijay, K., and Khadikar Padmakar, V. (2003) Modellingof carbonic anhydrase inhibitory activity of sulfonamides usingmolecular negentropy. Bioorg. Med. Chem. Lett. 13, 447-453.

(27) Katritzky, A. R., and Douglas, B. T. (2001) Theoretical descriptorsfor the Correlation of Aquatic Toxicity of Environmental Pollut-ants by Quantitative Structure-Toxicity Relationships. J. Chem.Inf. Comput. Sci. 41, 1162-1176.

(28) Wilson, E. D. (1992) The Diversity of Life, Harvard UniversityPress, Cambridge.

(29) Landau, L. D., and Lifshitz, E. M. (1963) Mecanica Quantica no-Relativista. In Curso de Fısica Teorica, Vol. 3, pp 1-49, Reverte,Barcelona.

(30) Pauling, L. (1939) The Nature of Chemical Bond, pp 2-60, CornellUniversity Press, Ithaca, New York.

(31) Gnedenko, B. (1978) The Theory of Probability, pp 107-112, MirPublishers, Moscow.

(32) Kier, L. B., and Hall Derivation, L. H. (1981) Significance ofvalence molecular connectivity. J. Pharm. Sci. 70, 583-589.

(33) Hernandez, I., and Gonzalez, D. H. (2002) MARCH-INSIDEversion 1.0. CBQ, Central University of “Las Villas”, Cuba(contact: humbertogd@navegalia.com).

(34) STATISTICA version. 6.0 (2002) Statsoft, Inc.(35) Van Waterbeemd, H. (1995) Discriminant analysis for activity

prediction. In Method and Principles in Medicinal Chemistry(Manhnhold, R., Krogsgaard-Larsen, R. M., Timmerman, H., Eds.)Vol. 2, Chemometric methods in molecular design (Van Water-beemd, H., Ed.) pp 265-282, VCH, Weinhiem.

(36) Kowalski, R. B., and Wold, S. (1982) Pattern recognition inchemistry. In Handbook of Statistics (Krishnaiah, P. R., andKanal, L. N., Eds.) pp 673-697, North Holland PublishingCompany, Amsterdam.

(37) Negwer, M. (1987) Organic Chemical Drugs and Their Synonyms,Akademie-Verlag, Berlin.

(38) Kleeman, A., Engel, J., Kutscher, B., and Reichert, D. (2001)Pharmaceutical Substances, 4th ed., George Thieme Verlag,Stuttgart.

(39) Garcıa, A. (1997) INTERCON, Edimsa, Barcelona.(40) Tilton, C. R., Ballows, A., Hohnadel, C. D., and Reiss, F. R. (1992)

Mosby-Year Book, pp 812-994, Clinical Laboratory Medicine,U.S.A.

(41) Loeb, W. F.; Quimby, F. W. (1999) Clinical Chemistry of Labora-tory Animals, 2nd ed., Taylor & Francis, Philadelphia, PA.

(42) Ping, C., and Hayes, A. (1994) Acute toxicity and eyes irritancy.In Principles and Methods of Toxicology, 3rd ed. (Wallace Hayes,A., Ed.) Raven Press Ltd., New York.

(43) Benichou, C., and Celigny, P. S. (1991) Standardization ofdefinitions, criteria for causality assessment of adverse drugreactions. Drug-induced blood cytopenias: report of an interna-tional consensus meeting. Nouv. Rev. Fr. Hematol. 33, 257.

(44) Sasich, D. L., and Sukkari, R. (2001) Drug-induced Blood Disor-ders. In Applied Therapeutics: The Clinical Use of Drugs (KodaKimble, M. A., Lloyd, Y. Y., Kardjan, A. W., and Guglielmo, B.J., Eds.) Vol. 85, pp 1-21, Lippincott Willians & Wilkins,Philadelphia.

(45) Johnson, R. A., and Wichern, D. W. (1988) Applied MultivariateStatistical Analysis, Prentice-Hall, NJ.

(46) Randic, M. (1991) Resolution of ambiguities in quantitativestructure-property studies by use of orthogonal descriptors. J.Chem. Inf. Comput. Sci. 31, 311-320.

(47) Randic, M. (1991) Orthogonal molecular descriptors. New J.Chem. 15, 517-525.

(48) Randic, M. (1991) Correlation of enthalpy of octanes withorthogonal connectivity indices. J. Mol. Struct. (THEOCHEM)233, 45-59.

(49) Estrada, E., Perdomo, I., and Torres-Labandeira, J. (2001)Combination of 2D- and 3D-Connectivity and Quantum ChemicalDescriptors in QSPR. Complexation of R- and â-Cyclodextrin withBenzene Derivatives. J. Chem. Inf. Comput. Sci. 41, 1561-1568.

(50) Randic, M. (1993) Fitting of Nonlinear Regressions by Orthogo-nalized Power Series. J Comput. Chem. 4, 363-370.

(51) Estrada, E., and Gonzalez, D. H. (2003) What Are the Limits ofApplicability for Graph Theoretic Descriptors in QSPR/QSAR?Modeling Dipole Moments of Aromatic Compounds with TOPS-MODE Descriptors. J. Chem. Inf. Comput. Sci. 43, 75-84.

(52) Warne, M. A., Boyd, E. M., Meharg, A. A., Osborn, D., Killham,K., Lindon, J. C., and Nicholson, J. K. (1999) QuantitativeStructure-Toxicity Relationship in two Species of BioluminiscentBacteria, Pseudomona fischeri and Vibrio fischeri, Using andAtom-Centered Semiempirical Molecular-Orbital Based Model.SAR QSAR Environ. Res. 10, 17-38.

(53) Estrada, E., Uriarte, E., Gutierres, Y., and Gonzalez, D. H. (2003)Quantitative structure-toxicity relationships using TOPS-MODE.3. Structural factors influencing the permeability of commercialsolvents through living human skin. SAR QSAR Environ. Res.14, 145-163.

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