SUBSTITUENT IXDICES AXD TETRACYCLINE POTENCIES
January 1970
93
Predictability of Correlations between in Vitro Tetracycline Potencies and Substituent Indices1 ARTHURCAMMARATA AND SUHJENY.4u Temple University, School o j Pharmacy, Philadelphia, Pennsylvania
19140
Received J u l y SI, 1969 Eleven btructurally related tetracyclines having a single substitution on the D ring have had their inhibition potencies against Escherichia colz W correlated with substituent indices using three alternative analytical approaches. -4compound not included in one of the analyses had its in vitro activity predicted satisfactorily. The three approaches taken are shown to be equivalent and the results of the correlations were applied to predict activities for tetracyclines having multiple substitutions on the D ring. Many of the predicted inhibition potencies against Escherichia coli W are of the same relative ordei of potencies a- is observed with Staphylococcus atireus as the test organism.
I n a recent communicationzathe bactericidal potencies of three and the bacteriostatic potencies of six monosubstituted tetracyclines of general structure I against synchronous and nonsynchronous cultures of Escherick ia coli, respectively, were correlated with the square of the Hammett substituent index (u'). The
xm N(CHJ2
CONHz
9\
OH 0
OH 0 I
unprecedented use of u' alone2bin order to gain a correlation with biological pot'encies mas clarified at least part'ially by the observation of a correlation between E , and u2. While E', was initially defined as a free-
E,
=
n s r 0 . 5 0 ~ ~0.07 12 0.06 0.94
+
(1)
radical index,3 and correlations of biological activities with this index have been r e p ~ r t e dthe , ~ observation of a correlat'iori bet'ween E , and u2 suggests the possibility that this index may also be a suitable measure of a frontier-controlled interaction in which t'he desolvation requirement is dominant.5,6 Hence, correlations of biological potencies with either E, or u z may or may not imply the participat'ion of a free-radical-like species in giving rise to the observed biological activity. Recognizing that the actual physical significance of E , and u2 is obscure at present (see conjecture at, end of paper), we have used t,hese physically indefinite parameters as indices of convenience in correlating the bacteriostat,ic potencies of 11 tetracyclines. The activities of these tetracyclines againt Escherichia coli W were determined using bacterial growth kinetics and a comparison of viable with total cell counts was made t80 show that these activites are suitable inhibition p~t~encies.' Three alternative, but demonstrably (1) This x o r k was supported under XIH G r a n t AI-09199. (2) (a) A . Cammarata, S. J. Yau, J. H . Collett, a n d A. N. Martin, M o l . Pharmacol., accepted for publication; (b) a correlation which is essentially a n arbitrary linear combination of u a n d 0 %has been reported: C , Hansch, A. R . Steward, and J. Iwasa, J . M e d . Chem., 8 , 868 (1965). (3) T. Tamamoto a n d T. Otsu, Chem. Ind. (London), 787 (1967). (4) (a) C. Hansch, J. M e d . Chem., 11, 920 (1968); ( b ) C. Hansch, E. K u t t e r , and A. Leo, ibid., l a , 746 (1969). (5) A. Cammarata, ibid., 11, 1111 (1968). (6) A . Cammarata, ibid., l a , 314 (1969). ( 7 ) G . H. lfiller, S. Khalil, and A . N. Martin, J . P h a r n . Sci. in press.
equivalent, approaches were taken in correlating the data and tests of the predictability of the correlations obtained were made. Method 1.-The compounds in Table I of structure I n-ere grouped depending on whether the substitution was a t the 7 or the 9 position, and at no other position. The uizsubsiituted compound zras considered conzmoiz io each set. A number of trial analyses in which the model equation for each set was a linear combination of nieta and para substituent constants were not found suitable for correlating the data. Considering the aromatic D ring as a simple substituted phenol, however, led t o a correlation for the 7-substituted set log k log k
+ = 2.483, + 1.73
=
s r 0.17 0.96
(2a)
4 0.30 0.87
(2b)
7%
0 . 6 4 ~ ~ 1.87 4
and for the g-substit,uted set log k
=
log k
=
n s r 0.57u2 - 0.46rD 2.56 4 0.11 0.98 ( 3 4 ( i 0 . 3 1 ) (hO.09) 0.85Er - 0 . 4 7 ~ ~2.59 4 0.09 0.97 (3b) (i0.28) (h0.05)
+ +
where YD is the van der Waals contact distance for a 9 substituent on the D ring.8 The parameter r D is constant with the 7-substituted set and was therefore not included. Combining the two sets provided the relation log k
=
log k
=
1 . 3 3 ~ '(*0.38) 2.70Er (il.64)
n s r 0 . 5 7 1 ' ~ 2.51 7 0.21 0.93 (4a) (*0.11) 0 . 5 5 r ~ 2.51 7 0.45 0.67 (4b) (i0.34)
+ +
Based on standard deviations the use of u2 in place of E , leads to better correlations with the 7-substituted and the combined sets of data. No great physical significance should be attached to this apparent statistical discrepancy since with the limited number of data points a wide separation between two or three points 011 the E , scale relative to the u2 scale can lead to statistically disappointing correlations in one instance but not in the other (see footnote g, Table 11). The statistically more satisfying correlations show a definite negative (8) M. Charton, J . Amer. Chem. Soc., 91, 615 (1969).
ot large 9 sub,titucrits or1 the bacterio poteticici of theie tetracycline-. With the da. h:iiid, h o u ever, there i- no iridicatiori a i to whethei steric' iiitcixctioii- betweeii thv 9 iubtitueiit :uid thcb ad,j:iceiit hytlrosyl gt oup 01' bet\\ oeii the $1 -ub-titlietit a i i t l t h t l hiolagical receptor -ul)\t:iiicC (or both) i- tht. tlctrlmelltal i:irtor To t:il\e itito a c c o u n t the cflect ot the G-CH, aiid &OH -iib-titiitioii- on the (' iirig :tiid the ;-OH w b d t u t i o i i o t i the I3 riiig it n:ib a-umed th:tt either only the ( K H , : i t i d .S-H or only the fi-OH m d 5-OH came uitli i l i r rweptor .urface. Only the latter : Iccl t o ;I definite contribution ioi, the :\liphatic -111).titucnt + iii the regrewon eqii:ttioii itifluelicr
log I = 0 $ 3 ~ - - 0 42i
1)
+ :fed. Chem., 6, 405 (1963).
95
TABLE I11 RELATIVE ORDEROF TETRACYCLIXE ACTIVITIESCALCULATED FOR Escherichia coli W .is THE TESTORGISISJIASD OBSERVED J v I m Staphylococcus atireits AS THE TESTORGANISM -Substituents-R7
___ Rs
vitro
----In E. coli 11(calcd)a
act.----
S. aureu8 (obsdIb
NH2 2,331 525 S HB 1.900 320 SH2 1,833 2773 XH, 1.723 160 SH, 1.79OC 14oc SO, XO, 2.546‘ 60‘ SO, C1 1.817c 21C Br SO, 1.386 1.5 Based on the parameters, G, found in Table 11. Data of ref 10 expressed as minimum inhibitory concentration relative to tetracycline. e Deleting these data points the agreement is found to n s r be log k(ca1cd) = 0.50 log hIIC(obsd) 0 . 2 3 0.19 0.89 C1 Br KO? NOs Br
+
group parameters, experimental uncertaintie. (e.g., solubilities), or the difference in the teqt organisms may be factors contributing to the large diiparities in these two instances. Possible Origins of 2-Because of the novelty associated with the finding that the use of U ? can provide a correlation with and lead to reasonable predictions of at least the order for the in viti’o activitiec of tetracyclines, it may be desirable to speculate into the possible physical significance of this parameter. Which, if any, of these speculations is correct will only be e-tablished by appropriate studies on additional syqteni-. h correlation based on the tetracycline data uqiiig quantum chemical indices does, however, support the po-iibilities. The significance of the present results re-t- on one fundamental principle : any statistical argument bearing on real data must submit to the te-t of prediction. I n the current instance, method 2 correctly predicts (within, as it is found, one standard deviation) the bacteriostatic activity of tetracycline. Further, method 3 gives the correct order of activitie. for at least five tetracyclines. To appreciate these fact-. it i, necessary to recognize that methods 1-3 are operatzonally independent; the methods are equivalent because they have been demonstrated to be so. A possible way for g 2 to arise is through a coupling mechanism. Consider, initially, the .ituation where a tetracycline bearing a substituent X 011 it. D ring is capable of interacting with a second tetracycline having a substituent ITon its D ring. Tetracycline chelates >IT? which can dissociate into an ionic form -1IT”+ provide a possible example. An ewentially neutral chelate, each of whose tetracycline ligands i5 .ubstituted differently, might be presumed to pa-- through the lipophilic bacterial cell wall, and once in-ide the cell to dissociate into an ionic form XT-AI-TY
XT-LIn+
+ TY or YT-1\17’- + TX
(A)
The bacteriostatic activity of a tetracycline may be considered as being determined by the ability of the neutral chelate to dissociate to an ionic form” which
(11) (a) A . Albert, ‘Vature, 172, 201 (1953); Chem., 6, 16 (1963).
K. Martin, J . M e d .
(b) J. T . Dolvision, and.4.
January 19i0
hXTIJIALARIAL
= $0.78) electrons. Indeed, seven resoiiance forms can be drawn for 4-nitrochlorobenzene, for example, and five resonance forms can be drawn for 4-aminochlorobenzene. Thus, while the delocalization energ\. for conjugation of a substituent with an aromatic nucleus i y proportional to u,16 it appears that the resoiinnce energy of the substituted molecule +hould be proportional to u ? . A general relationship taking into account both Coulombic and reyoliarice effects in the formation of a chelate is obtained by linearly combining u and u2. T h e result is operationally equivalent to eq 16. Proper caution should be exercised in dealing with relatioris such as 16. While there are at least three arguments that can be advanced to explain a nonlinear dependance of biological activity 011 u (ref 6 and the two already detailed) there is always the posiibility that aiio t her parameter exists that is essentially independent of u .
97
QUINONES
Use of t'his parameter in combination lyith u could cause an otherwise parabolic trend in u to become linear. With chelates as an active species, for example, n knowledge of the association constants for reactions X arid B enables a calculation of the fraction of ionic chelate present a t a specified pH. The observed activity could be by multiplying the rate constarits by the calculated fraction. The use of this corrected biological activity could then result in a linear dependence on U . l'or the tetracJ-cliiies involved in this study, insufficient information is available to attempt this type of correction. The basis for the precaution is essentially the same as for the linear free-energy approach talieii by Hansch" in his account of electronic arid lipophilic factors which influence biological activity. It must be concluded that correlations based on eq 16 are most probably physically significant, but the origin of u2 may ti-tke many forms. (17) C. Hansch in ".\nnual Review of lledicinal Chemistry," C. I
