Journal of Medicinal Chemistry 0 Copyright
1969 b y the American Chemical Society
MAY1969
VOLUME12, SVMBER 2
Correlation of Biological Activity with Chemical Structure.
Use of Molar Attraction Constants JAMESA. OSTRENGA Instztute of Pharmacezittcal Sciences, Synten: Research, Stanford Industrial Park, Palo Alto, Calzfornza
94304
Received September 26, 1968 Rlolar attraction constants [F = (EV)I/Z],a physical constant derived from the solubility parameter (6 = F / V ) , was taken to be indicative of the relative degree of drug-receptor interaction for related compounds. For several different groups of structurally related compounds, a high degree of correlation of F with biological activity was obtained in each case from a least-squares fit of the data to a first-order equation indicating that F may be a useful parameter for correlating chemical structure n-ith activity. These molar attraction constants are available for most organic functional groups, are apparently additive on a constitutive basis, and are thus readily obtained for many compounds by simple calculation. -4lthough F may merely be related to the relative lipophilicity of a compound in a series, its use in correlating biological activity with chemical structure may be of value since no experimentation is required. The proposed method of correlation appears to have predictive capability.
basis.1 One of the most recent and successful methods for correlating biological activity with the chemical structure and physical properties of drugs is that of p-u-n analysis as introduced by Hansch and coworkers,1b,2where a mathematical and theoretical treatment of three parameters has been shown to give quite reasonable correlations. Many biologically active compounds owe their activity to a capacity for participating in a chemical reaction or physically interacting with cell constituents. Variations in the biological activity of closely related compounds in those cases where absorption is not the controlling factor most probably are due simply to differences in the affinity between the drug molecules and a substrate. In order to evaluate the extent of interaction between the drug molecule and a substrate, it was theorized that a consideration of a parameter which mould be a measure of the attractive forces involved in this interaction might have significance. The thermodynamic free energy of interaction is such a parameter but its determination mould require experimentation involving equilibrium measurements. I t would be more desirable to use a parameter that could be readily calculated. It was assumed that the stronger the interaction between the drug and the biological substrate, the greater the intrinsic activity. Approaching the problem from this viewpoint led to the consideration of a theory which has been used to explain some solubility phenomena, a situation where electrostatic attractive forces play an important role. A theoretical consideration of the attractive forces and their relationship to the enthalpy of mixing for a two-component regular solu-
A great deal of evaluating and screening of potentially active drugs within numerous pharmacological classes has been done, but unfortunately many of these data have not been published. Illoreover, the reported data have been obtained from semiquantitative and relatively imprecise bioassays. I t is apparent that one of the main impediments to progress with structureactivity correlations is the lack of quantitative pharmacological potency data for structurally related drugs. In the past, investigators have shown that relationships between observed biological activity and an experimentally determined parameter do indeed exist for some structurally related compounds or for some compounds with common pharmacological actions. Correlations have been made with partition coefficients, degree of binding to various protein fractions, lipid solubility, kinetic rate of biotransformation, and other physical parameters. Often structure-activity relationships have been obtained strictly by the methodical compilation of bioassay data. Conclusions have then been drawn from these data by noticing the relative changes in biological potency due to the location and nature of organic functional groups. It has been common to utilize a stereochemical “fit” hypothesis based on the classical notion that a drug must meet certain stereochemical requirements a t a substrate site. Conclusions have then been drawn from these data by observing the effect of change in the stivcture and location of functional groups on biological potency. That is, the correlation comes after the fact. Ideally, structure-activity relationships should attempt to explain as well as correlate. They should contribute insight into a mechanism of action a t the molecular level as well as help define the chemical and physical nature of the biological structure involved in drug action. Such a method would hopefully also have some predictive capability. It is only recently that this subject has been approached on a theoretical
( 1 ) (a) E. R. Garrett, 0. K. Wright, G . H. Miller, and K. L. Smith, J . M e d . Chem., 9 , 2 0 3 (1966), (b) C. Hansch and T Fujita, J . A m Chem. Soc., 86, I616 (1964); (c) A. Cammarata, J . Med. Chem., 10, 525 (1967). (2) (a) C. Hansch and R. A. Steward, zbzd., 7, 691 (1964); (b) C Hansch and S. M. Anderson, ibzd, 10, 745 (1967); ( c ) C. Hansch, R. $1. hIuir, T . Fujita, P. P. Maloney, F. Geiger, and 11. Strelch, J . A m . Chem. Sac., 85. 2817 (1963).
349
3 50
JAMES A . OSTRENGA
tioii has been giveii by Hildebraiid and Scott.3 For many organic substances the inaiii coiitributioii to the total attractive forces existing het~veeiitwo iiioleculcs is iriatle liy dispersioii forces, the main exception being those system where hydrogen Iiondiiig f0rct.s or tlipolv intcractioiis predominate. Even for the relatively polar orgaiiic liquid acetolie, 96% of the total attractive force Iictwecn two acetoiie iiioltudes is tlric to tlispersioii i’orces.4 The energy requiretl for the formatiou of physical 1,oiids clue to dispersion forccs is thivecl froiii the pairing of dipoles inoinentaiily intiucetl I)\’ pc~itur1,ations hi the electron clouds of mo~c~culc3s i l l chsc prosimity. These forces a iiondi~~ectioiid iii iiatrii*c. a i l t i itre additive over all p s of iiiolecules in n Tlic1 over-all distribution :uitl iiaturc of tli tive forces will b c 7 reflected iii the thcrinotlyiin~iiicf i w c w ~ g of y interaction, l C l , the itlenl quaiitity to cxxiiiiiir niid m i r a which is Idirect iiiclicatioii of tlic tlrgrec of iiiteractioii d i e r e ii 1 c :tiit1 ~icgutive frcwciicigy ~liaitgccorrcspoiids to :L strong uitcr:ictioii or high :ifinity. Thus, Iusecl on tlw :iforc~iicwt i o n ~ l:~bb;iiiipt ioiis. the most l~iologicallya r t i w cmnpountl of :I aciic>i !vi11 correspoiitl to the situatioii d i e r e t l i i h therniotlyiiaiiiic change is at a iiiaxiiiiuni. For such mi iiitcrxctioii ~~roccss, the thel.riiotl!.ii:iiiiic cbiitlinlp~.(AN,) :iii(I twtrop\of the (;ilil;s cquntioii (1) iii:ij 11c eitlicar
positive or iiegative and the sigii may clcpentl oil tlic role of the interaction medium. For biological systeiiib, this medium is most often Tvater. I11 those cases where the enthalpy is positive, one :ippro:ich iiiay be to d e f i i i ( ~ this thermodynamic quantity hi terms of other physical parameters by an equation tlerivctl liy Hildebrantl ani1 Scott5 and Scatchard6 for tT\o-c~ompoiieiit regular solutioiis
where 1- = iiiolar volunie, X = inole fraction, + = volunie fraction, 6 = (E i.)”z = solubility parameter. arid the subscripts 1 aiid 2 refer to the two iiiteractiiig species. In the derivation of cq 2, it was assumed that the geometric ineaii rule lioltls for the relationship hetween the potential energies ( E ) or the cohesivc cnergy densities ( E 1‘) of the individual compoiieiits aiid the interaction mixture, that the interaction forces are central aiid additii e. that there is iio volume change (1I. % O), and that mixing is randoin. The solubility parameter has found some practical use in predicting the mutual compatibility of organic solvents and iii selectiiig solvents for various synthetic polymer^.^ ;I\lulliiiss has suggested its usefulness iii estimating activity coefficients in an attempt to correlate theriiiodynamic with biological activity. while othersg have (3) J. H. Hildebrand and 12. L. Scott, “The Solubility of 1Jon-Electrolytes,“ 3rd ed, Dover Publications, Inc., New York, X, Y., 1964, Chapter 111. (4) P. A . Small J . .AppZ. Chem., 3, i l (1953). (5) J . H. Hildebrand and R. I.. Scott, ref 3, p 129. ( 6 ) G. Scatchard, Chem. Rev., 8, 321 (1931). (7) (a) J. Brandrup and E. H . Immergut, “Polymer Handbook,” Interscience Publishers, Inc., New York, N. Y,, 1966, p IT’, 341; (b) H. Burrell, O f i c . Dig. Federation SOC.Paint Technol., 29, 1069 (1957). ( 8 ) L. J. Mullins. Chem. Rev., 54, 289 (1954). ( 9 ) S. A . Khalil and 4. N. X a r t i n , J . Pharm. Sei., 5 6 , 1225 (1967).
1.01. 12
iiidicantccl th:it a relationship exists hetncmi mlu\)iIit> parameters :tiid ineinbraiie-t 1 aiibport prciport it>> I t may :I160 l,r. t l f $ l l l c ~ t l :ti i=
i.1
J
I
=
F I*
[
3I
where I.’ = (L’1 ~ ~ i i is c l cnllecl thc iiiolar attraction constant. Sulistitiitioii for 6 iii eq 2 and substitution for AHi iii tlic Gilihs cqu:ttioii givt.;
Equatioii 4 thus relates the molar attraction cuiistaiit ti) the thermotlj ii:iiiiic free eiierpy of iiiternctioii for those systems ~ v l ~ ethc r e eiitlinlpy term is positive and wlicrr tlie nforeiii~litiorietl : uiiiptions iirc upproximately truc. If O i l ? l i O \ Y :lssullieb that tile molar volu111e of‘ that part of the drug iiiolwulr n-liich is iiivolvetl iii tlw iiiteractioii is approximately equal t o tlic irioliir volui~it. of tlic effect i T - c purticipatiiig liiological sit(’, t h i thr. frec energy :it c.quilibriuiii IT ill lw most fnvor:il)lc :mil vi11 appro:icti a iniiiiniuiii n.li(~11112, approaches ~ c r oor ivhcii F1 approaclics Fz. Voiiscqueiitly. if the niagiiitutlc response is clirvctly relntecl to thri tlcgretx of the 1iiologic~nI of iiiteractioii. tlie most I;iologicnll;\- 1 oteiit coiii11ornitl Of :t smies \vi11 correspoiid t o thi. one whrrc~tlic (*li:ing~ 111 the frec t v i ~ r g yof iiit twctioii is ni~ixiiiiizetlor \J hmi thcx niolar attiactioii coiistaiit of tlic t1ri.g ant1 q i i l ) > t i :ire equal. BJ. this aiialysib, tlie iiiolnr attrnctioii coiistaiit is talicii t o l i c :I phJ-sical pnramctcr ivhicli is :I inc:iswv of tlic niteriiiolcculxr attractive force5 of ii ( .;pccic~s rclntii c to L: secoiitl (’iitity 111 this 1 ~ 1 g d . F absuniei 11 physical significaiiw :iiialogoi:s 10 tlic \ - m i der TTa:ils coiistaiit {a)js1” nlicrc n rc~m~bciits tlicl iiitcLrnctioii 1)c.tn-ceii tn-o iiiolccular sperics. The riiolar ;ittl*iiction iwiistaiits for various org:iiiic co~npouiitlsinn? o1)t:iiiicd froiii a lino~lctlgct ~ thrir f wluidity paranid (w uiitl iiiolar volumes (q3 \ U>tliotlsfor tlctcrniiiiiiig or ca1ml:Lt iiig soluldit y 1)nrniiietei-s liavtk 1 ICY I I tliscuswtl c ~ l ~ . i v h c r e . $iiiw ~” tIir1 potentid c i i molai~volriiiicl are cxtciisivc tlicriiiotl\iiaiiiic clu:uititi( y > t h y : i r ~n(l(litivc oil a nio1:ir hasis m t l thus i o ‘ i i ~thc, iiio1:ir :ittr~v~ii)ii (viihtaiits, ‘i7i:it i y s sincc
(IO) J. J. Van Law, Z. Physik. Chem., 72, i 2 3 (191Oj.
May 1969
351
;\fOLECULAR AkFTRACTION C O N S T A N T S
Letting v = nV, substituting (E/V)1'2for 6, and rearranging gives
Et17t == (nlE1
+ nzEZ)(nlS'l +
?121'2)
TABLE I EFFECTIVE COXCENTRATION
-
I
+ + n2 (Ez
+ E,Vz)'/' + n22E2T'z=
6
n12E1T.'1 2nln2(E1V1 [ n1 (E11'1)
1'2)
1' (E,vt)
"2
=
n1(Ell'1)
n2(E2172)'/2 or Ft = nlF1
FOR THE ACTIVITY OF
PEXICILLIN DERIVATIVES ON Staphylococcus aureus
+ nzF2
+
Results and Discussion The use of molar attraction constants to correlate structure with activity was tested using published biological data for six different classes of compounds. Aii actual tabLlatioii of biological activities and calculated molar attraction constants is given for only one set of data in order to not unduly lengthen this report hy completely identifl ing each structure and its corresponding data values. This tabulation is given for data set 111 in Table 11. For the remainder of the data sets, only the resultant statistical parameters for each correlation are given (Table 11). Complete structures for all the compounds employed in the correlations may he found, hoiTever, in the corresponding references cited along with each set of data in Table 11. The biological activities for the various systems all represent a constant equivalent response such as EDSO, LDho,or isoiiarcotic concentration. Set I corresponds to (i) the inhibition of rat brain cortex respiration by some barbiturates and (ii) the fraction of barbiturates bound to lTo bovine serum albumin, set I1 to the barbiturate inhibition of Arbacia egg cell division, set I11 to the toxic action of substituted phenols on Micrococcus pyogeizes Tar. aureus, set IV to the toxic action of substituted phenols on Salmonella typhosa, set V to the activity of penicillins on Staphylococcus aureus, and set VI to the isonarcotic concentrations (tadpoles) of some esters, ketones, alcohols, and ethers. The molar attraction constants ( F ) were calculated either for the entire molecule (sets 111, IV, VI) or only for that part of the molecule where the chemical structure varied (sets I, 11, V). The use of partial instead of total molar attraction constants merely displaces a plot of biological activity us. F along the abscissa and does not affect its shape. Partial values were used in those cases where F was not known for some functional group comprising the invariant part of the chemical structure. Although eq 4 predicts that a plot of activity us. F for compounds in a series will exhibit a maximum (if biological activity is directly related to A G i ) it does not necessarily tell one what its shape will be away from the maximum. Such plots, however, suggested that the biological data was linearly related to F for each set and
XICE
&N-COOH 0
X
(9)
Small4 has demonstrated that besides being additive on a molar basis, the molar attraction constant appears to be additive on a constitutive and atomic basis, and a table giving molar attraction constants for common functional groups has been Thus, F can be calculated for many organic compounds merely by adding the respective values for the functional groups comprising their chemical strccture.
IN
F
Function
H 4-Cl 4-OCHa a-Et ( n
=
I)
4-SOz
2-c1 2,5-c12 a-Pr ( n = 2 ) 3,5-(CH3)2 a-BU ( n = 3) 2,4Ch 2,4Br2 2,3,6-Cla 4-Cyclohexyl 4-t-Bu 3,4,5-(CH3)3 4t-Amyl, a-Et CIS
1061 1239 1253 1194 1256 1239 1417 1327 1305 1460 1417 1557 1595 1762 1518 1427 1784 1951
-Log Obsd
5.86 5.79 5.6Y 5.54 5.53 5.40 5.24 5.03 5.03 5.01 4.97 4.87 4.72 4.70 4.67 4.65 4.57 4.25
(l/c)--.
Calcd
A log (lit)
5.75 5.43 5.40 5.51 5.40 5.43 5.11 5.27 5.31 5.03 5.11 4.86 4.79 4.49 4.Y3 5.09 4.45 4.15
0.11 0.36 0.29 0.03 0.13 0.03 0.13 0.24 0.28 0.02 0.14 0.01 0.07 0.21 0.26 0.44 0.12 0.10
a least-squares fit of each set of data to a first-order equation was performed. The statistical parameters for each set appear in Table I1 where r is the correlation coefficient, s is the standard deviation, n is the number of data points, and r* is the correlation coefficient when the same biological data was correlated to rll in a comparable manner. A relationship between the sum of molar attraction constants and okserved biological activity appears to exist for each of the data sets examined. In those cases where a comparison can be made and r* is given, the results suggest that F correlates with the biological data a t least as well as T and in some cases slightly better than T . For the data corresponding to the toxic action of phenols on bacteria (sets I11 and IT7), a correlation exists separately for each group of phenols which have substitution a t the same ring position and the statistical parameter for each group is given separately. This result may be due to (1) a significant dependence of molar volume on the ring position of the substituted group, (2) the role of the relative partition coefficient, (3) steric effects, or (4) the fact that the molar attraction constant does not evaluate the significance of the relative location of a functional group within an organic molecule.12 Corrections for the values of F based on the relative position of the substituted group could be made on an empirical basis for each biological system considered. On the other hand, it was found that for the data of sets I11 and IV a smooth curve exhibiting a maximum was obtained when the observed biological (11) r is the parameter defined by Hansoh as the logarithm of the ratio of two partition coefficienta. (12) I t should be pointed out here that it appears that some functional groups take on diiffefent values for F when they are attached to a n aromatic nucleus.
JAMES A. OSTHESGA
352
LI:,t:i
ncit
Iii! iii 1 I1 III(i 1 iii I (iii J (iv!
I \.(i 1 (ii (iii 1
O.!)hi
0.900 0.9s2 0.960 0.946 0.7iF5 0.!)::7
iiv J \
\'I
activity was plotted z b . the product of n and F.Id The values of n employed in sets 111 aiid IT were taken from ref 2 anti the resultant correlations arc included in Tablr 11. For tho s? steins investigated :tiid iii light of the assumptions that were required, tlie correlations appear to tie quite reasonable considering the limited accurac) of tlic biological data. In the treatment of sonic of the suiie data hy p -u n analysis, Hniisch has coiicludetl tlint the relative partition coefficient (n)accounted for most of the differelices in biologienl potencj . l b *he Thub, it (vult1I)e concluded that the iiiolar attracltioii constant is actually only a nirasiir~of tlie relative partition coc4icieiit. This was found not to l i e tlie vase ill tliv cvrrelatioii of the structures of it seriea of related steroids with their relative aiitiiiiflanirnatory p o t e n c k where F gave good correlations but 7~ dit1 Tlie results ill this paper, however. do suggest that F is re1:rtrtl to A. $uch a relationship is conceivable bincci partition phciioinena as well as physical interact ions are tlepcxdeir t o i i c+emical structure. The proposed method of correlation unquestioiial)ly has liinitations with regard to its general applicability. ant1 the theoretical basis of this treatment requires pcxrliwps more than the usual number of assumptions. 111 addition, steric factors involved in drug interactions w r e neglected while it is likely that changes in molecular size, shape, and rigidity do indeed affect AS,. HowCWT, it should be stated that for compounds of a series. the magnitude of these effects are probably approximately equal. The limitation that the enthalpy term as tlescribed by eq 1 is directly applicable only to s\ stcbnis n.hc.re this quaiitit>*is positive is perhaps R otttled b\ olle of the I w i e u e l s legdrdlng the enlpiliLai TF 13 ueli taken I t s apparent correlation, houever, m I \ be rationalizrd intuitireli bx colraiderinp that the factor K evpresses th it fractioii of the appJlent conceiitratlon which 16 made available foi interc o r r ~ c t l f~a rc t o r in ab-essing the extent of interaction 11
iict
0.0:;7 0.057 0.0SI 0.146 0.077 0.204 0.212
berious oiie whc.n coupled with tlic f x t tliut tlic sigil ot A H l is usually iiot knoivn for most drug intcractioiih If the drug niter:tction is of a specific nature. ir-hwtd)) M i takes oii iwgative values, it is still possible that :I
correlation lwtween biological activity and inol:ii attraction c~)nstaiitsexists. The relationship to thcrnioc l naniic ~ quantities ~vouldthen take a tliffcrcnt forni thaii I)reseiitccl lierr.. I n order to 1)roatleii tlie applicahility of the propohccl method oiit~ 1 1 ( ~ ~to1 ~obtain a11 expression for t lw theririocl\-ii3iiiic ciithalpy or free energ? which i+ rolatcd to a iiiolar attraction fuiictioit as w l l as :Lsoc011~1 parameter irliicli allo~vsfor those s> stenia n-1ier1.t t l i ~ clisper,iioii foiws (fdt;, do not follow the geoinctric II~(':III rulc aiitl or ~vliwc> othcr attractive forces :lrc sigiiificani . Such air ~ ~ x p r ~ w will i o n permit M i to t a h on po-itivcx or iiegativv vducs. 111 t rc,:itiiig F aiitl its :tpp:trwt :uttiitivity i t i- renlizrd that the validity (Jf ('(I 2 i i depciiclt~iit011 t h c assumption tliat thc rlistrihtioil oI the dispersion torccs follow-s the geonictric incan rul(>. If this ~esuinptioiiis not a vnlid o w iii certain iristimy)-, it in:iy 1 ) ~iiecessary to tlcfiiie LI functioir, c/(f(ij. f01 which thcb tlistriliutioii of attr:tcativc forces Tvouhl i i i o i ~ ~ closely appro-hiatc t h e truc situation. Ai1 ~xpr('siioii for AH which w~ultlacrount for specific.intcr:ictioi~ilia> take the form [
10,
where j s is iiii (qression containing a parameter wliicah describes the relative magnitude of specific iiitwactioiih. For the case where LHi is positi'i's and only clispersioii forces are operative, g(fs) would equal 0 arid r q !f woulcl take the form of eq 2. Acknowledgment.-The author wishes to ~xprcs> thanks to Sheldon Kugler of the Department of Biostatistics. Syiitcx Research. for his help in the statistical analysis.
