CROATICA CHEMICA ACTA CCACAA 62 (3) 449-458 (1989)

CCA-1873YU ISSN 0011-1643

UDC 541.6OriginaL Scientific Paper

Classification of Steroid Partition Coefficients by a PatternRecognition Technique

A. J. Harget* and D. S. EllisDept. of Computer Science and AppLied Mathematics, Aston University,

Aston TriangLe, Birmingham B4 7ET, UK

Received August 9, ~988

A pattern recognition technique, the linear learning machinemethod, has been used to determine structure-activity relatiorr-ships for certain steroids. The steroids used in this study wereclassified into two categories according to their observed parti tioncoefficient and a correlation made with certain substructuraldescriptors. The linear learning machine method was employedto calculate a suitable decision surface that would classify eachsteroid into its correct category. The resulting structure-activityrelationship and the relative contributions of the various structuralvariables are discussed, and a comparison made with resultsobtained from a study using a different approach.

INTRODUCTION

In the design and development of bioactive compounds considerableattention must be given to the particular physicochemical properties, thesolubility and partition coefficient. The reason for this is that the partitioncoefficient together with the solubility of a drug, influences the absorptionand transport processes in a biological system and so determines the biologicalactivity of the drug. Drugs taken orally in tablet or capsule form must firstdisintegrate after swallowing to have any medicinal effect. Slow dissolutionof drug particles then occurs and the drug is transported to the gut, whereactive drug molecules can diffuse into the bloodstream. The fraction of drugthat reaches the desired receptor is largely dependent on the dissolution anddiffusion processes which are governed by solubility and membrane-waterpartion coefficient of the drug.

Several methods exist for the ca1culation of partition coefficients suchas the group contribution approach proposed by Hansch-.s and by a methodof correlation with other molecular properties as demonstrated by Yalkowskyand Valvani". These methods result in good estimates of partition coefficientsfor most groups of compounds. However, the group contribution approachcannot account for any interactions of non-bonded atoms 01' groups or forany intramolecular interaction due to branching. Hence, for certain types ofcompounds and certain bulky or flexible molecules, estimated values can

* To whom correspondence should be addressed.

450 A. J. HARGET AND D. S. ELLIS

differ considerably from the experimentally determined partition coefficient.s.Yalkowsky and Morozowich! found that estimation of partition coefficients bya group contribution method worked poorly for steroids.

In this study we have applied a pattern recognition approach, the linearlearning machine methodš-" in an attempt to predict the partition coeHicientsof the steroids. Pattenr recognition methods attempt to categorize data sam-ples into the membership of their observed classes. In this study the class isdefined by a particular range of partition coefficient values. Despite thecriticism leveled? at certain pattern-recognition studies for their choice ofdata and representation, the pattern-recognition method when applied pro-perly, does offer the chemist a useful means of determining the relationshipsexisting in a large amount of high-dimensional data.

PATTERN RECOGNITION

Pattern recognition techniques have been widely and successfully appliedin a number of different domains'':". Such techniques are particularly usefulfor dealing with data of high dimensionality where the deduction of relation-ships in the data is difficult. Although the technique is empirical it can afforda useful insight into any relationships which may exist in the experimentaldata. The sole assumption made by the technique is that relationships existwithin the experimental data, although even this assumption will be inve-stigated

In this study a pattern recognition technique, the linear learning machinemethod, has been used in an attempt to develop classification rules capableof categorising steroids according to their experimental partition coefficients.If each steroid is represented as a point in n-dimensional space, then it mightbe expected that steroids with similar partition coefficients would cluster inone region of the space separated from steroids with vastly diHerent partitioncoefficients. The linear learning machine method was applied in an attemptto create o. linear decision surface that would separate the two clusters. Thecomputer programs were written and developed by the authors in Algol 68for use on the University of Aston's IeL 1904S.

The linear learning machine method has been widely discussed in theIiteratureš-" and so only a brief outline of the method will be given here.The experimental data to be classified is represented as a vector.

where each element XI of the pattern vector represents an experimentaJobservation and the value of N indicates the number of observations requiredto describe the pattern.

Linearly separable data can be separated by a linear discriminant of theform

N+lS = L WI' XI

I~l

where Xr is an element of the pattern vector, and Wr is the element of theassociated weight vector. An N + 1 component is added where XN+l = 1, sothat the category is determined by the dot product S, namely S> O impliescategory 1 and S<O implies category 2.

STEROID PARTITION COEFFICIENTS 451

The procedure adopted is as follows, a training set composed of steroidswas c1assified into one of two categories according to experimentally observedpartition coefficients. The training set was used to develop an effectivedecision surface, that is, to determine the set of weights (WJ,W2, W3 ••• W;,)such that each member of the training set is assigned to the correct categoryaccording to its partition coefficient. The members of the training set arepresented to the learning machine program one at a time and when anincorrect c1assification is made the weigth vector is altered. Numerous error--correction feedback algorithms exist for modifying the weight vector. Theone used in this study modifies the weight vector such that the lineardecision surface is reflected about the misclassified point, in other words,the dot product S has the same magnitude but the opposite, and hence correct,sign. This algorithm was chosen because of its simplicity and because itgurantees convergence when the data is linearly separable, although therate of convergence cannot be guaranteed. In this study the sole criterion forconvergence was the correct c1assification of each member of the trainingset. In the event of convergence not being obtained the program was instru-cted to terminate after a predetermined number of iterations.

A requirement of the linear learning machine method is that the numberof compounds in the training set should exceed by at least a factor of 3 thenumber of descriptors if chance separation is to be avoid". A further requ-irement states that the population of the least populated category shouldbe greater than the number of descriptors!'. Both of these requirements weremet in the present study and consequently the derived weight vectors mustbe considered meaningful.

Correct c1assification of the training set would allow relationships to bededuced from the resulting weight vectors. Furthermore, the weight vectorsobtained from the training process may allow the partition coefficients ofunknown or unsynthesized steroids to be predicted wit.h a certain measureof confidence. The predictive power of the method is expected to increaseas the training set becomes larger and more representative.

The application of the linear learning machine method to steroids ofknown partition coefficients and the results obtained are discussed in asubsequent section.

PARTITION COEFFICIENTS

The definition and theory of partition coefficinets is well known'" andso only a brief description will be given here.

In general terms, if an excess of liquid 01' solid is added to a mixtureof two immiscible liquids, it will distribute itself between the two phasesso that each phase becomes saturated. In the case where the amount ofmaterial added to the immiscible solvents is insufficient to reach saturation,it will become distributed between the two layers in a definite concentrationratio.

If YI, Y2 and Cl, C2 are the activity coefficients and the concentrations ofthe two solvents respectively, then the equilibrium expression becomes

452 A. J. HARGET AND D. S. ELLIS

where the equilibrium constant K is known as the distribution ratio or puart-ition coefficient.

In dilute solutions, the activity coefficients can be approximated to unityand then the above equation reduces to

Many experimental methods have been devised for determining the partioncoefficient. The most common method is simply to shake a solute withtwo immiscible solvents and then analyse the solute concentration in oneor both phases after equilibrium has been reached. In the present case,Cz refers to the concentration in water.

An extensive literature search was undertaken to determine the partitioncoefficient of as many steroids as possible. Numerous sources were foundbut a lack of standardisation in experimental technique precluded many ofthem from inclusion. Two principal sources of data were found, namely, thesteroid partition coefficients measured in an ether-water system by F'lynn!"and the coefficients measured in an octanol-water system by Leo, Hansch andElkins". The latter coefficients were translated into ether-water values usingthe method of Leo, Hansch and Elkins? so that the experimental data wouldbe sufficient to meet the criteria required of a pattern recognition study.

The data set comprised 43 steroids after eliminating those steroids conta-ining unique substituents. This elimination was necessary if meaningfulstructure-activity relationships were to be obtained. The remaining steroidswere classified into two categories of approximately equal membership bydefining a threshold value of l.45 for the partition coefficient. Table 1 liststhe steroids together with their partition coefficients.

RESULTS AND DISCUSSION

Steroids because of their similar molecular structure facilitate computat-ional description. Since steroids have the same basic nucleus and only differfrom one another by the groups that are attached to thatnucleus, then eachsteroid can be unambiguosly described by specifying the position and typeof each of its substituents; substructural descriptors are used to indicate thepresence or absence of the associated substructure.

In order that meaningful structure-activity relationships could be derived,non-essential descriptors were eliminated by the weight-sign change featureselection technique'". In this technique a descriptor is regarded as essentialif the sign of its weight vector component obtained after training is fouridto be invariant to the initial weight value taken for the learning machine.Three descriptors were eliminated by this process. The descriptors removedwere those representing the 17-acetyl group, saturation at the 1, 2 bond andthe 16-methyl group. These findings seem reasonable in the current contextbecause the partition coefficient of a steroid is governed by the steroid-solventinteraction with hydrogen bonding being an important factor. The presenceor absence of a carbon-carbon double bond within the ring structure of thesteroid is unlikely to affect such an interaction. Similarly, the 17-acetyl groupwill not significantly alter the interaction since it is shielded by the carbonylgroup at position 20. The 16-alpha-methyl would be expected to have a

STEROID PARTITION COEFFICIENTS

TABLE I

453

Steroids and Their Experimental Partition Coefficients, [Me-methyl, F-fluoroj

No. Steroid Partition coefficientlog PC

1234567891011121314151617181920212223242526272829303132333435363738

39

40

PrednisoloneCortisoneHydrocortisone6a-F-Prednisolone9a-F-Hydrocortisone6a-Me-PrednisoloneDexamethasonePrednisone (Dehydrocortisone)9a-F,6a-Me-PrednisoloneCorticosteronePrednacinolone6a- F-DexamethasoneFlurandrenalone acetonideTriamcinolone acetonidePrednisolone-21-acetateCortisone-21-acetate6a-F-Triamcinolone acetonideHydrocortisone-21-acetate6a-M-9a-F-21-Deoxy prednisolone6a-Me-Triamcinolone acetonide6a-F-Prednisolone-21-acetate11a-Hydroxy progesterone6a,16a-Difluoro prednisolone-21-acetate9a- F-Hydrocortisone-21-acetate6a-Me-9a-F-21-Deoxy hydrocortisone6a-Me-9a-F-'16a-Hydroxy hydrocor tisone acetonide6a-Me-Prednisolone-21-acetate6a,9a-Difluoro-2'1-Deoxy hydrocortisone-17-acetate6a-Me-9a- F-Prednisolone-21-acetate6a,9a,16a- Trifluoro- Prednisolone-21-acetate6a-Me,9.a-F-21-Deoxy prednisolone-17-acetateHydrocortisone-21-propionate6a-F -Dexamethasone-21-acetateDexamethasone acetateHydrocortisone- 21-isobu tyra teHydrocortisone-21- butyrate9a-F-11~-Hydroxy-6a-Me-4-pregnen-3,20-dione6a-Me-9a-F-16a-Hydroxy prednisolone-16,17-acetonide--21-acetate6a-Me-9a-F-16a-Hydroxy hydrocortisone-16,17-acetonide--21-acetate6a-Me-9a-F-16a-Hydroxy hydrocortisone-16,17-acetonide--21-propionate6a-F-Dexamethasone-21-butyrate6a-Me- Triamcinolone acetonide-21-propionate6a-F-Dexamethasone-21-isobutyrate

414243

0.0530.1460.2040.2860.3650.5370.5880.6000.6200.6560.8200.8751.091.161.321.401.411.411.511.541.561.631.661.671.711.731.831.911.921.931.971.982.162.252.352.382.43

2.93

2.98

3.143.183.233.24

similar effect to the 6-alpha-methyl group, but this is not shown by ourstudy and can only be due to the environment of the 16-alpha-methyl groupcompared to that of its 6-alpha-methyl counterpart. The steroids consideredtogether with their partition coefficients are shown in Table I, and the sub-structural descriptors in Table II.

454 A. J. HARGET AND D. S. ELLIS

TABLE II

Sub structuraL Descriptors and Their Associa1ed Weight VaLu es and ScaLed GroupContribution Factors

Descriptor Weight vector Group Contribution

11a/B-hydroxy6A-fluoro6A-methyl9A-fluoro17-hydroxy16A-fluoro16,17-acetonide21-deoxy21-acetate21-propionate21-butyrate21-isobutyrate

-1473

-131

-79

12151515

-16

114

-144

-92129

The linear learning machine method was applied to the steroids to deter-mine those weight vectors which would correctly categorise each steroidaccording to the partition coefficient given in Table I. Complete convergencewas obtained in the training procedure. The resulting weight vectors areshown in Table II. The magnitude of the weight vector is indicative of thecontribution the feature makes to the classification while the sign of theweight vector indicates whether the contribution increases the partition coef-ficient( given by the positive valu es) or decreases the partition coefficient(given by the negative values). Thus if we consider the weight vectors obtainedit can be seen that there is general agreement between the results andexperiment. An increase in the hydrogen bonding of the system, by theintroduction of more electronegative groups to the steroid molecule willcause adecrease in the partition coefficient, whilst the removal of hydrogenbonding group s from the steroid molecule will cause an increase in thepartition coefficient. Other factor affecting the hydrogen bonding abilityof the steroid include the steric effect (shielding of electronegative groupsby inert methyl groups producing an increase in the partition coefficient)and effects due to conformations. The cyclic acetal group (16, 17-acetonide)decreases markedly the partition coefficients of the parent compounds. Moreparticularly it can be seen from the weight vector values that the presenceof a 17-hydroxy group is predicted to redu ce the partition coefficient quitestrongly, as it increases the hydrogen bonding. Removal of the 21-hydroxygroup from the steroid, the 21-·deoxy feature or even more strongly 'itsesterification, on the other hand reduces the hydrogen bonding and resultsin an increase in the partition coefficient. The relatively low contributionof the ll-hydroxy (-1), as opposed to the value of -13 for the 17-hydroxy isexplained because the ll-keto group is equally active in hydrogen bonding,so its replacement by a hydroxyl group has little effect on the partitioncoefficient. Apart from hydrogen bonding factors, the branching of ati aliphaticchain in a molecule usually affects the partition coefficient", with a straightchain normally having a higher partition .coeff'icient than a branched chain.However, the weight vector values of the 21-butyrate and 21-isobutyrategroup s are identical. This we believe is due to the Iact that here the main

STEROID PARTITION COEFFICIENTS 455

factor is the replacement of OR by OCOR, where R are nonpolar group sof approximately equal size; indeed the 21-propionate also has the sameweight vector value. It should be remembered that the weight vector valuesshown in Table II are relative values, that is, the inclusion of a 21-estergroup will increase the partition coefficient but that the final value for thepartition coefficient is given by the other substituents present in the steriodmolecule.

The linear pattern classifier obtained after training can be tested accordingto its ability to correctly classify the partition coefficient of a steroid notbelonging to the training set. The predictive ability of the classifier wasdetermined by the so-called 'leave-one-out' procedure-", In this procedure,a steroid was removed from the training set, and the remaining steroids weresubjected to training in the usual manner. The steroid was then classifiedand returned to the training set and a second steroid was removed, andthe training and classification procedure repeated. This process was repeatedfor all members of the training set, whereupon the predictive ability of thelinear pattern classifier could be determined. Although this procedure iscomputationally expensive, it does give a good indication of the performanceof the linear pattern classifier. The predictive ability was found to be 81.4010which is gratifying since the probability of guessing the correct classificationis 500/0 for a binary pattern classifier. The following steroids were misclassified:9, 16, 17, 21, 24, 32, 35 and 36 (the numbering refers to compounds in Table I).The misclassification of some of the compounds can be explained by exa-mination of the training set; if a particular descriptor does not occur in manypatterns, then the weight vector component associated with that descriptormay be inaccurate. For example, hydrocortisone-21-butyrate (steroid 36)when removed from the training set during the 'leave-one-out' procedureleft only one other steroid containing the 21-butyrate group (steroid 41).Hence, when the weight vector component corresponding to the 21-butyrategroup was calculated, three was insufficient data available on that descriptorto give an accurate result. When the calculated weigth vector was used toclassify the steroid, the error caused misclassification. A similar situation existswith steroid 35, since removal of this leaves only one other steroid (steroid43) containing the 21-isobutyrate group. Thus it would be expected that inthe 'leave-one-out' procedure, as the size of the training set would increasethe predictive ability would improve, particularly if the expanded trainingset includes steroids containing some of the poorly rep resen ted groups.

As stated earlier, the size of the weight vector component may givesome indication of the relative contribution that the associated descriptormakes to the value of the partition coefficient, and the sign indicates whetherthe contribution is positive or negative. The idea of the relative contributionmade by a particular group to the effect being studied is similar to thatused in 'group contribution' approaches.

The majority of the data used in this study was taken from areport byF'lynn-" which was concerned with the estimation of steroid partition coef-ficients by molecular constitution. This is a group contribution method whichis particularly suitable for comparison as the data used for both studies isidentical.

456 A. J. HARGET AND D. S. ELLIS

o

o

~ 6

Figure 1. 17-deoxy prednisone.

S1eroid 1 - Prednisolone

S1eroid 3 . Hydrocortisone

S1eroid 10 - Corticosterone

S1eroid 13 - Flu:randrenaJone ace tonide

S1eroid 2 - Cortisone

S1eroid 7· Dexarnethasone

S1I!roid Il - Predn.acinoJone

Figure 2. Structures of selected steroids.S1eroid 1~ - Triamcinolone ecetorude

STEROID PARTITION COEFFICIENTS 457The contributions to the partition coefficient shown by the weight vectors

are relative to that of the steroid 17-deoxy prednisone (Figure 1), whilstFlynn's group contribution values are relative to that of prednisolone (steroid1 in Figure 2.).

The only differences between the two 'standard' steroids are the presencein prednisolone of a hydroxy group at positions 11 and 17. Hence, only twogroup contribution factors require alteration to make the two sets compatible.

Table 2 shows some of the original group contribution facto rs calculatedby Flinn which have been scaled-up for comparison with the weight vectorsderived in this experiment; only the group contribution factors pertinent tothis study are given. It can be seen that the correlation is good, since bothmethods agree on the features which affect the partition coefficient and theorders of magnitude of the facto rs are similar. The group contribution facto rsrelate the effect of a group on the partition coefficient as a multiple of thereference steroid's partition coefficient. For a group which decreases thepartition coefficient, the factor is less than 1, while for a group which causesan increase, the factor is greater than 1.

The results of the present study can clearly only be applied to thosesteroids containing the particular substituents considered in this paper. Steroidscontaining new su.bstituents, or identical substitutents in new positions wouldhave to be subjected to the pattern-recognition process.

The above evidence suggests that the derived pattern classifier could beused to predict the pattern coefficient of unknown, or untested, steroids.Hence the likely biological solubility of a steroid and hence its mobility tothe activity site, can be very quickly determined. The medicinal chemistthus has another tool at his disposal to aid in amore rational approach todrug design.

CONCLUSION

A pattern-recognition technique has been applied successfully to theproblem of predicting the partition coefficients of the steroids. The resultsobtained were shown to be in good agreement with experiment and withthe results derived from another, quite different, study. The elements of theweight vector produced for classification were comparable with the equivalentgroup contribution factors calculated from a structural approach. The predi-ctive ability of the method was found to be good, although improvement isexpected as more data becomes available. The results allow the medicina]chemist to adopt amore rational approach to drug desing.

REFERENCE S

1. T. F u j ita, J. I s a w a, and C. Han s c h, J. Amer. Chem. Soc. 86 (1964) 5175.2. A. Leo, C. Han s c h, and D. El k i n s, Chem. Rev. 71 (1971) 525.3. S. H. Y al k o w sky and S. C. Val van i, J. Med. Chem. 19 (1976) 727.4. S. H. Y al k o w sky and W. Mo r o z o w i c h in Drug Design, E. J. Ari e n s

(Ed.), Academic Press, New York, vol. 9 1980, p121.5. N. J. N i 1s s o n, Learning Machines, New York, McGraw Hill, 1965.6. T. L. I s e n h o u r and P. C. Ju rs, Anal. Chem. 43(10) (1971) 20A.7. C. L. Perrin, Science, 183 (1974) 551; J. T. Clerc, P. Naegeli, and J.

S e i b 1, Chimia 27 (1973) 639.8. P. C. Ju r s and T. L. I s e n h o u r, Chemical Applications of Pattern Reco-

gnition, New York, Wiley, 1975.9. N. B o dor, A. J. Ha r g e t, and E. W. P h i Il i p s, J. Med. Chem. 26 (1983) 318.

458 A. J. HARGET AND D. S. ELLIS

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SAZETAK

Klasifikacija koeficijenata razdjeljenja steroida s pomoću tehnike prepoznavanjaobrazaca

A. J. Harget i D. S. EHis

Jedna od tehnika za prepoznavanje obrazaca - metoda linearnog učećeg stroja(LLM) - primijenjena je za određivanje relacija struktura-aktivnost (SAR) za nekesteroide. Ti su steroidi razvrstani u 2 kategorije na osnovi njihovih koeficijenata raz-djeljenja i nekih (sub)strukturnih deskriptora. Metodom (Ll',M) izračunana je razlučnaploha, s pomoću koje se svaki od proučavanih steroida razvrstava 'u ispravnu kate-goriju. Tako dobivena SAR kao i relativni doprinosi raznih strukturnih varijabliuspoređeni su s rezultatima polučeni ma različitim pristupom.