TEEMODEOF ACTIONOF SULFONAMIDES
March,1944
459
heat of combustion of a-D-glUCOSe is given as AHR = 669.81 kcal./mole.la Employing the values for carbon dioxide and water previously Discussion of Results mentioned, the heat of formation was calculated Karrer and Fioroni" reported a value for the to be -304.28 kcd./mole. The authors used the heat of combustion of glucose pentaacetate. On value obtained by Huffman and Fox for the heat the basis of the 1942 value for the heat of com- of combustion of 8-D-glUCOSe of - H R = 671.33 bustion of benzoic acid and in units of the defined kcal. per mole. Huffman and Fox state that this calorie, Karrer and Fioroni's value is 1722.4 kcal. value is not of the highest precision, but it is per mole for -AUB. It is not clearly stated that probably very near to the true value. While its these authors were dealing with a-D-glucose penta- agreement with a value calculated from solution acetate, but this is assumed to be the case. No data is good, Huffman and Fox point out that the value has been reported previously for 8-D-glucose same type of irregularities may have complicated pentaacetate both measurements. The calculated heat of The following equation indicates that the formation from the data of Huffman and Fox for acetylation of glucose with acetic acid is an endo- 8-D-glucose is -302.76 kcal. per mole. The heat thermic reaction for both isomers. of formation of acetic acid was calculated to be D-glucose (s) 5 acetic acid (1) = D-glucose pentaacetate - 116.20 kcal./mole, from the heat of combustion (SI ~ H Y (1) O reported by Schjanberg.'* The heat of formation a-isomer, AH = 6.32 kcal./mole of acetic anhydride was calculated to be 149.20 @-isomer,A H = 8.92 kcal./mole kcal./mole from the heat of combustion by The use of acetic anhydride, however, produces Thomsen. l4 the acetylation with a considerable evolution of While the conversion of 8- to a-D-glucose is energy. accompanied by a heat evolution of about 1.5 D-Glucose (s) 5/2 acetic anhydride (1) = D-glucose kcal./mole, l 2 the conversion of 8- to a-D-glucose pentaacetate (s) 5/2Hn0 (1) pentaacetate is accompanied by a heat evolution a-isomer, AH = -30.88 kcal./mole of about 4.0 kcal./mole. How much of this heat @-isomer.AH = -28.29 kcal./mole effect is to be attributed to the 8- to a-shift about The rather large exothermic value for AH in the the saccharide carbon cannot be estimated a t latter reaction suggests that the use of the acetic present on the basis of information now available anhydride will produce a favorable yield of the summary pentaacetates since the A F value will probably have the same order of magnitude. This is in Values for the heats of combustion at 25' and harmony with experience. 1 atm. pressure are given for a- and 8-D-glucose In making the indicated calculations the follow- pentaacetate. The value for the specific heat at ing thermal values were employed. The values 25' is also reported. From these and other data, employed have been recalculated by the authors the heats of formation and heats of acetylation in terms of the defined calorie and based on the were computed. 1942 value for the heat of combustion of benzoic (12) Huffman and For. THISJOUXKAL, 60, 1403 (1938) (13) Schjanberg, Svetrsk. Kern. rids, 44, 227-231 (1932). acid. This places all values secured by and util(14) Thomsen, Z . ghysik. Chcm., 0 ,343 (1905). ized by the authors on a comparable basis. The PITTSBURGH, PA. (11) Karrer and Fioroni, H c b . Chim. Arlo, 6, 306 (1923) RECEIVED MAY14, 1943 for the heats of formation of liquid water and gaseous carbon dioxide.
-
.
+
+
+
-
+
[CONTRIBUTION FROM THE CHEMICAL LABORATORY OF NORTIWESTERN UNIV'RRSTY
1
The Mode of Action of Sulfonamides BY IRVING M. KLOTZ Since the discovery that p-aminobenzoic acid inhibits the action of sulfonamides,' attempts have been made to correlate the activity of these drugs with their structure. Some investigators2 soen observed that the sulfonamide potency seemed to be directly related to the amount of the ionic form of the drug. The work of Cowlesa indicated that sulfonamide activity increased as (1) Woods, Brit. J . Erptl. Path., SI, 74 (1940). (2) Fox and Rose, PTOC.SOC.Exptl. BWE. Mcd., 60, 143
(194Y); Schrnelkes. W y s . hfarkb. Ludwig and StrandRkov. ibid.. 60, 145 (1942). (3) Cnalca. I'uk J . B i d . M r d . . 14. 599 (194.2)
.
the acid pK of the drug decreased toward 7, but that further increase in acid strength resulted in diminished activity. A more comprehensive study by Bell and Roblin4has shown that bacteriostatic activity is a parabolic type of function of acid strength of the sulfonamide, with maximum potency being obtained, in a solution of pH 7, with drugs whose pK's are approximately 6.7. Inasmuch as current opinion attributes sulfonamide activity to the blocking of an enzyme system,' it was considered advisable to examine (4) Rrll
and Rnhlin. Tmrs JOURNAL, 64, %go6 (1948)
IRVING M. born
460
Vol. 66
the available data from the point of view of the general concepts of acidity and the law of mass action. A brief qualitative description of the approach has been given previously.s A detailed account of the treatment and results is presented in this paper.
at a given PH one must minimize S with respect to KHDwhile (PD-) and the PH are held constant.
Bacteriostatic Effect of Sulfonamides Consider a buffer solution with a fixed hydrogen ion concentration, (H+), a fixed total concentration, T, of the enzyme or protein, P, and a given total concentration, S, of the sulfonamide, HD. Since the buffer equilibrium and the ionization product of water are fixed and known we need consider only the following equilibria in the solution.
Inspection shows quickly that the factor within the brackets must be the vanishing one. Rearrangement of terms within the brackets and use of (11) to replace A, leads to the following form of the minimizing condition
H+fDH+ f P P +OHP D-
-+
=HD = PH'" =POW = PD-
(1) (2) f3) 14)
(For basic sulfonamides HD would be replaced by HD+, D- by D and PD- by PD.) For each of these equilibria we may set up the corresponding mass law expression.
-d =S- - =
1
dS
~ K H D (H+) BX
(PD-) U K P D ( H + ) [ T - (PD-)] { ( l $-
i)
where K k D is the acid ionization constant of the drug which is active at a minimum S. Using the symbol f to represent the left-hand side of (16) and then converting the latter equation into its logarithmic form, one obtains (17)
Were f known for the bacterium-sulfonamide complex, one could calculate KR,, and for E. coli, for example, the value so obtained could be compared with that observed by Bell and Roblin.' In the absence of the pertinent data, one can still Since the total concentration of sulfonamide must test (17) by using the known value of &, equal the sum of the concentrations of the various calculating f for the E. coli-sulfonamide complex, forms in which the drug is present in solution, we and compaxing the value so obtained with that can write the equation which may be derived from the work of Davis and Wood" for the plasma protein-sulfonamide S = (I>-) + (HD) + (PD-' (9) complex. Similarly for the protein Bell and Roblin4 fomid that a plot of bacterioT = (P) + (PH+) f (POH-) + (PD-) (10) static effectiveness versus pK for about a hundred It is now possible to derive an expression for S sulfonamides in a solution a t pH 7 showed a in terms of variables having experimental signifi- maximum at a p K of about 6.7. Substituting the cance. For convenience in algebraic manjpula- appropriate values into (17) we findf = 0.3. Davis and Wood,6 using a dialysis technique, tion, the following definitions have been made. have determined the amounts of sulfonamide (11) bound to plasma protein for a series of seven drugs. They have expressed their results "as the per(H+j ( O H ] 1 +- -- 4--= " (12) centage of the value of the unbound drug which is KPE+ KPOHbound per gram of protein.'I6 If we designate this Using (6) and (7) to eliminate (PH+) and (POH-) percentage by 100a,and in view of the approxifrom (10) and re-grouping terms one obtains the mate nature of the following calculation consider expression P directly proportional to T (see equation (13)>, 7' = u(P) + 1I'W.l (13) then (Round drug) = w ( P ) (Unbound drug) (18) Similarly, making use of (11) and (8) .one can eliminate (D-) and (HD) in (9) and then use (13) where the parentheses represent concentrations. to replace (P) in the resultant expression and Since the unbound drug may consist of HD and obtain D-, (18) becomes (PD-) = d P ) [ ( H D ) (D-11 (19) s = [(l f + 11 (PU-\ (14) Making use of (5) one obtains It seems reasonable to assume that bacteriostasis occurs when a given amount of the sulfon(Prj 1 = [(D-) (Hf) K H D +- (D-I] (20) amide-enzyme complex, PD-, has been formed. If S is the quantity of sulfonamide just sufficient Since the PH of the solutions used by Davis and to produce bacteriostasis, (PD-) in (14) must be a Wood was 7.4, one may insert the numerical value constant. To find the drug of maximum potency of (H+) and transform (20) into
+
;) y&)
( 5 ) Klotz, Science, 98. 6 2 (13.13)
1 0 1 Ild\.i%and Wood,
Pvoc Suc. E r p f l . B i d .+led,, 51, 288 (1942).
THEMODE OF ACTIONOF SULFONAMIDES
March, 194
461
Similar results have been obtained by Brueckner’ for Staph. aureus, B. subtilis and Ps.pyocyaneu. The left-hand side of (21) is the inverse of KPD-, the dissociation constant of the serum proteinsulfonamide complex (P being expressed in grams, the other concentrations in moles). Hence, one may write 1
UKPD-
=I
Q
[4.0;R;-8
+ 13
(22)
Using values of 01 given by Davis and Woode and those of KHDin the tables of Bell and Roblin‘ we have calculated UKPD-for six of the seven drugs for which data are available. (The results for sulfaguanidine have been omitted, because of the conflicting data in the literature on its acid ionization constant. If the acidity is actually too small to be measured in water then the ionization constant of the acid form of sulfaguanidine, HD+, should be used in the following graph.) Figure 1 shows that a straight line is a sufficiently good approximation to the relationship between log (UKPD-)and log K H D ,for the available data are not very precise. The slope of the line isf and is 0 8 10 equal to 0.5. Thus if there is any similarity in ~KHD. behavior of the proteins in E. coli to those in blood Fig. 2.-Activity as a function of acidity at various plasma, the value of 0.3 obtained for the former PH’s for E. coli: 0 , PH 6.0; 8, $H 6.8; 0 , PH 7.6. case is apparently a very reasonable one. These results indicate that a reasonable first approximation to the relationship between KPDand K H Dwould be KPD- = kKaof
(23)
the integrated form of d In KPD-
d In K H D = f
f and k being constants. This equation may be
substituted into (14) to give an explicit expression for S, which in turn may be converted into logarithmic form
k’ is a constant for a fixed PH and is given by the equation k’ =
u&(PD-)
T - (PD-) 10 -8 -6 In general, the amount of bound drug, (PD-), Log KHD. will be small compared to the total amount of Fig. I.-Dissociation constants of the plasma protein- sulfonamide. Hence, we may use log S instead of sulfonamide complexes: 8, sulfacetamide; 8, sulfapyrazine; log [S - (PD-)I in equation (25), and obtain 0 , sulfadiazine;8, sulfathiazole; 0, sulfapyridine; 0,sulthe following expression after a simple rearrangefanilamide. ment
-
Equation (17) also predicts that as the pH of the medium is increased, the pK of the sulfonamide of maximum potency should also increase. This relationship affords an alternative and more This is in agreement with the results reported by reliable method of evaluating f from the entire Cowlesafor E. coli. His data, summarized in Fig. range of data, as well as an opportunity for 2, show a definite displacement of the Dotencv evaluating k‘. CUrveS toward higher P k ’ S as the PH is inireased. (7) Brueckner, Yale J . Biol. Mcd.. 16, 813 (1943).
IRVINGM. KLOTZ
462
Using the data of Bell and Roblin,' one can plot the sum of the terms on the left-hand side of equation (27) as a function of log KHDand thus obtain a value off for E . coli. f turns out to be 0.37. Substituting this value for f and -3.46 for log k', the intercept of (27) for E. coli, one obtains an expression for log S in terms of PKHD,which has been plotted in Fig. 3. The experimental curve is shown also, for purposes of comparison. The agreement is quite satisfactory, except possibly for drugs with PKHD'S below 3.5. I t may well be that in this region of high acidity constants an additional limiting factor is the inability of the anions to penetrate the cell walln8 Diffusion experiments in this Laboratory may soon give some information on this factor.
Vol. 66 (H+)(A-)/(HA) KEA (P)(A-)/(PA-) = KPA-
(30)
(31)
and the following stoichiometric relationships R = (A-) (HA) (PA-) (32) T = (P)
+
+
+ (PH+) + (POH-) + (PD-) + (PA-)
(33)
With these new equations one can derive a suitable expression for R. Rearrangement of (9) gives the equation (D-) =
s - (PI)-) 1 -t 1/x
(34)
4 similar expression, obviously, can be written for (A3 \
- (PA-)
,
(A-) =
where
R 1
+ 1/P
(35)
The quotient of (34)by (35)becomes -(D-) = (A-)
e
S
- (PD-) 1 + 1/p
(37) R - (PA-) 1+1/X Making use of (8) and (31) to obtain another expression for the ratio (D-)/(A-)
e
"E
we can obtain the following equation
r(
3 4
where (40)
3
_-_
I
5
7
9
*KED. Fig. 3.-Bacteriostatic acivity as a function of acidity, for E. coli: - -,calculated; -, experimental.
-
We assume that the bacteriostatic effect of a sulfonamide is inhibited when the (PA-) reaches a value such that (PA-)/(PD-) is equal to some fixed number. Hence, B is constant at a fixed PH. Within the reproducibility of growth experiments, we can assume that [S- (PD-)] does not differ significantly from S and that [R - (PA-)] does not differ significantly from R. Thus, we arrive at the equation
Inhibition of Bacteriostasis by p-Aminobenzoic
Acid
The inhibitory action of p-aminobenzoic acid on sulfonamide activity is also amenable to the
mass law treatment. Consider a buffer solution containing a total concentration, T , of enzyme and a concentration, R , of p-aminobenzoic acid, HA. To this solution the sulfonamide is added until one reaches a concentration, S, beyond which bacteriostasis will set in. For the solution described one must consider two more equilibria in addition to those of equations (1) to (4).
-
H ' 4-A- = HA P APA-
+
(28) (29)
In addition to equations (5), (6), (7), (8) and (9) which the system must satisfy we can set up the following mass law expressions
It is immediately obvious that for a given sulfonamide acting at a fixed PH, the concentration of p-aminobenzoic acid which will counteract the sulfonamideis proportional to the concentration of the latter. Such is the case experimentally as has been found by Strauss, Lowell and Finland,* by Wood,* and by Brueckner.' Furthermore, the following equation can be derived readily from (41) and (23) The data of Rose and Foxlohave been used to test this relationship. Only one constant, log B / k , has been evaluated from their data, and the calcu(8) Straws, Lowell and Finland, J . C l h . Invert., 10, 189 (1941) 19) Wood, J . Exp Mcd., 76, 369 (1942). 101 R o w and F o x Crrrnrr 95, 412 (1942)
T H E MODEOF ACTION OF STJLPONAMIDRS
March, 1944
lated values of log R / S have been compared, in Fig. 4, with the logarithm of the observed ratios. The experimental points do not deviate from the theoretical line to a degree greater than the reproducibility of the results.
463
right-hand side of (44) becomes essentially constant. That the experimental data agree satisfactorily with the quantitative predictions of equation (44)is shown in Fig. 5. The results have been plotted in logarithmic fashion to expand the region of low hydrogen-ion concentration, but it should be noted that this form of representation also magnifies the discrepancies for small SIR ratios.
4
3r/l
3
8 c12
1
4
6
8
10
#KED. Fig. 4.-Ratios of #-aminobenzoic acid to sulfonamide. The solid line is the calculated curve, the circles the experimental points.
Brueckner' has published recently some very interesting data on the variation in the sulfonamide-p.a.b. ratio as the PH is changed. His work shows that for sulfanilamide, SIR falls continuously as the PH range from 6.5 to 8.9 is covered. In contrast, for sulfathiazole, S/R falls from PH 6.0 to 7.0 but remains constant thereafter until PH 8.9. Such behavior is a direct consequence of equation (41). Algebraic manipulation leads one readily to the expression
6
7
8
9
#H. Fig. &-Ratios of +aminobenzoic acid to sulfonamide as a function of pH for Staph. auras: 0 , sulfanilamide; 0,sulfathiazole; -, calculated values.
Conclusion
These calculations show that on the basis of the simple assumption that sulfonamide inhibition of bacterial growth is due to a reversible combination between the basic molecule or anion and an enzyme one can account quantitatively for the various aspects of bacteriostasis and for the resumption of growth by the addition of p-aminobenzoic acid. Other more detailed hypotheses'~' are unnecessary, and do not give as comprehenIn the PH range studied by Brueckner, (Hf)
