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Relationship Between the Solubility Parameter and the Binding of Drugs by Plasma Proteins
Relationship Between the Solubility Parameter and the Binding of Drugs by Plasma Proteins PIUR BUSTAMANTE' AND EUGENIO SELL& Received April 30, 1985, from the Departamento de Farmacia Galbnica, Facultad de Farmacia, Universidad de Alcaltl de Henares, Madrid, Spain. Accepted for publication April 14, 1986. Abstract 0An equation, based on regular solution theory, was used to relate the solubility parameter to the binding of drugs by plasma
proteins. The equation was tested on a homologous series and a good correlation was found. Sulfonamides showed maximum binding when their solubility parameters were similar to the solubility parameters of the amino acids situated in a sequence with one tryptophan residue. This observation supports the assumption that this sequence is the primary binding site for the sulfonamides. Binding peaks were also found at solubility parameters in other drug series corresponding to the solubility parameters of human serum albumin (HSA) or bovine serum albumin (BSA) amino acids. It is suggested that the solubility parameter could be used to predict the binding of drugs to plasma proteins. ~~
The solubility parameter has been used as an index of drug activity,' and has been investigated for its correlation with absorption p r o c e s ~ e s . ~The . ~ binding of drugs to plasma proteins has been correlated with physical properties such as polarizability, parachor, molecular weight, and the partition coefficient.4 This report demonstrates a relationship between the solubility parameter and the binding of drugs to plasma proteins.
Theoretical Section The solubility parameter or Hildebrand parameter (6) is defined as the square root of the cohesive energy densitys and is a measure of the cohesion between molecules. Since physiological interactions may occur a t a molecular level, it is assumed that solution properties are operative.'j Barton? observed that cohesive energy density is related to physical properties; accordingly, it is not surprising to find a relationship between cohesive energy density and drug-protein interactions. A high 6 value indicates a high cohesive energy as well as high solubility in water. If one assumes that, in pharmacokinetic terms, there are two different compartments (one for plasma and the other for plasma proteins), then a drug with a high 6 value should have a greater affinity for plasma than for the proteins since plasma is an aqueous medium, whereas proteins are relatively less hydrophilic. Since the solubility parameter is a measure of hydrophilic character, the binding to proteins should increase within a homologous series of a drug with a decrease in the 6 value of the analogue. Therefore, the slope and the correlation coefficient for a plot of protein binding versus the solubility parameter will have a negative sign. This was shown in an earlier work,* and is compatible with studies that relate binding with lipid solubility.9 Like regular solution properties, the binding to proteins can be analyzed by an expression similar to the Hildebrand equation.= Thus, under equilibrium conditions, the activity coefficient of the drug (a)in the albumin compartment is related to both albumin and drug solubility parameters: 0022-3549/86/0700-0639$0 1 .0010
0 1986,American
Pharmaceutical Association
In a
=
In ( B ~ / B ~=)RT
where S, and S, represent the solubility parameters of albumin (subscript E) and drug (subscript D),respectively, VD is the molar liquid volume of the drug, T is the absolute temperature, R is the gas constant, and & is the volume fraction of the albumin compartment. The activity coefficient (a)is written as a term involving the maximum binding (BDM) and the real drug binding (BD), expressed as percent of the bound fraction, by analogy to the ideal solubility, X, and the mole fraction in the Hildebrand equation. In dilute solutions, the volume fraction of the solvent becomes one (4 -1). If this condition applies to the albumindrug interaction, where V$D<
-In
BD =
where the slope,
-In B g A
=
+ A(&
- b)2
(2)
VD RT'
Accordingly, the most favorable condition for drug-protein interactions may occur when the intermolecular affinity is the greatest, i.e., where both solubility parameters are similar:
&=b Under this condition, the term (S,binding rises to its highest value:
B~
(3) in eq. 2 is zero and
= B::
(4)
Following a more simplified approach, eq. 2 does not take into account the contribution of.Flory and Huggins on molecular size differences.7 With an additional degree of approximation, VD may be considered constant for a given series of drug molecules.10 Hence, eq. 2 could be used as a model equation in a linear regression analysis of -In B D on the independent variable (S, - &I2, where A is the slope and -In BFis the intercept. Equation 2 assumes a phase saturation model similar to the model formulated in terms of the regular-solutions approach proposed by Cammarata and Yau.10 Since S,is unknown, the application of eq. 2 requires the use of different values of S,,and a choice must be made of the value that yields the best least-squares line. The S, value can be estimated more accurately when eq. 2 is transformed into an expression where In B D is regressed against a polynomial in &: lnBD=InBg-A&+&i&S,-A&
(5)
Journal of Pharmaceutical Sciences / 639 Vol. 75, No. 7,July 1986
where:
-b = 1nBF- A&
(7)
2A&
(8)
-a2 = -A
(9)
a1 =
The sign of the intercept must be negative, since A& is > In B#. By substituting the regreasion coefficientsin eqs. 8 and 9, one obtains the S, value. Likewise, from eq. 7, one obtains the maximum binding, B#. The proposed equilibrium binding approach can be compared with a distribution model which is also derived from regular solution theory.aJ0-13 "his model assumes that the equilibrium binding of the drug exists between two compartments due to a partitioning of the drug. An equation derived from this approach could be written 88:
RT In (BIF) = VD&&
- S,I2
- VD&&
- &J2(10)
where the subacripts P, E, and D refer to plasma, albumin, and drug, respectively. The function In (BIF),where B is the percent drug bound and F is the percent free, is directly analogous to an organic solventwater partition coefficient4 and has been used to correlate serum binding results to a substituent constant, w, developed by Hansch and Steward.14 Equation 10 can be written as:
In (BIF) = A[(& -
- (& -
W21
(12)
The tern A may be considered constant for a given series of drug molecules, and since S,and S, are also constants, eq. 13 becomes:
In (BIF) = b - a&
-
Table CExperlmental and Calculatad Solublllty Parametersfor Barbtturlc Acids and Sulfonamldes
(11)
where & and c$p 5 1 and A is the term defined in eq. 2. Equation 11 can be transformed into a linear expression by the following steps:
In @IF) = A[($ - &>+ S, (2& - 2&)1
plasma protein binding data and solubility parameters. Since there are few experimental solubility parameters for pharmaceutical solids, S values are calculated using the method of Fedors.16 This method, which is based on group additive constants, is believed to be superior to that of Small17 because the contribution of a much larger number of functional groups, such as -OH, -NH2, and -COOH, have been evaluated in the approach of Fedors. Fedors observed that deviations between the experimental measures and estimated values of the energy of vaporization and molar volume are generally less than 10%.This method has been employed for pharmaceutical solids's22 and was found to compare favorably with experimental 6 values. As shown in Table I, the calculated 6 values for barbituric acids and sulfonamides, which contain some of the aforementioned functional groups, correlate with experimental values with an error of 8%. Therefore, it is assumed that the method of Fedors can be used as a measure of the Hildebrand parameter. Series of acidic and basis drugs were chosen, and the technique for calculating the solubility parameter is shown in Table 11. Only the solubility parameters for sulfonamides are listed in Table 111, since the data for all series are voluminous.
(14)
(caVmL)%
(cal/mL)%
69
AS, %
13.50 13.00 12.85 12.40 12.40 11.95 11.90 11.75 11.30 11.30 13.40 12.60 13.90 12.70
12.55 13.03 12.34 12.00 12.24 11.20 12.19 11.54 11.50 11.85 12.85 12.58 12.89 12.58
7.6 -0.2 3.9 3.2 1.3 6.3 -2.4 1.8 -1.8 -4.8 4.1 0.1 7.3 0.9
8'1
Compound Barbital Phenobarbital Allobarbital Aprobarbital Cyclobarbital Butalbital Butobarbital Pentobarbital Secobarbital Hexobarbital Sulfamerazine Sulfamethazine Sulfameter Sulfisomldlne ~
~
'Experimental S values: barbituric acids from ref. 1; sulfamerazine, sulfamethazine, and sulfameter from Sunwoo, C.; Eisen, H. J. fhann. Sci. 1971, 60,236-244; sulfisomidine from ref. 18. bCalculated according to ref. 16.
where the slope is:
and the intercept is:
b
= A($
- &I
(16)
+,
The variable In (BIF) could be regressed against and S, and S, can be estimated from eqs. 15 and 16. The slope (a) must have a negative sign because the plasma solubility parameter (aqueous medium) is larger than the albumin solubility parameter. Equations 6 and 14 can be applied to a homologous series of a drug, and from the results obtained, one may verify which is the more satisfactory model.
Results and Discussion The data used for protein binding are found in the literature and are expressed as percent of the bound fraction. This measure is frequently used with a homologous series of a drug, and has been correlated with the partition coefficient.4.15 The present work suggests a correlation between 640 /Journal of fharmaceutical Sciences Vol. 75,No. 7,July 1986
Table Il-Group Contrlbutlon Method for Calculatlng Molar Volume and Solublllty Parameter of Sulfadlmethoxlne*
Atom or Group
Number of Groups
A€, cal/mol
AV, mUmol
1 1 2 1 2 2 5 5 6 2
3000 2000 5600 2950 1600 2250 5150 5150 2400
19.2 4.5 10 23.7 7.6 67 67.5 -27.5 - 13.2 32 P A V = 190.8
~
-NHI -NH-
-N= S O T b
0 -CHI -CH= C=
Olefinic bond Ring closure
S, = (30600/190.8)'"
500 PA€ = 30600
= 12.66 (cal/mL)'/2
'2,6-Dimethoxy-4-amino-N4-pyrimidinylbenzenesulfonemide;calculated according to ref. 16. bFrom ref. 18.
Table Ili-Solublllty Parameters, Molar Volumes, and Blndlng Data for Sutfonamides
1’ &b
%
&
13.17 12.89 12.58 12.62 12.66 12.16 12.58 11.70 12.66 12.19 1 1.39 11.95 12.07 12.39 12.16 12.07 12.90 12.35
154.2 175.5 183.2 185.0 188.8 223.0 183.2 246.0 188.8 220.9 260.9 239.1 231.9 206.9 223.0 231.9 206.6 203.1
48 85 86 96 98 99 82 61 94 98 97 99 94 96 96 87 98 98
154.2 168.5 168.5 184.8 172.5 183.2
30 62 78 94 85 69
172.5
60
183.2
90
Compound
6-Methoxy2,g-Dimethyl2-Methyl-6-methoxy2,6-Dimethoxy2,bDiethoxy5,B-DirnethyC 2-Butyl5,6-Dimethoxy2-Ethyl-5,6,-dimethoxy5,6-Diethoxy5-6UtOxy5-Isapropoxy.6-methoxy5-Methoxy-6-ethoxy5-Methoxy-B-propoxy 5-Methoxy-6-isopropoxy5-Phenyl5-Ethyl-6-rnethoxv-
26
-
13.17 12.85 12.85 12.54 12.89 12.58
6-Methyl5-Methyl5-Ethyl5-Methoxy4,6-Dimethyl-
CH30
12.89 CH3
4‘ 12.58
a 4-Amino-N-4-pyrimidinylbenzenesuIfonamide. Solubility parameter (cal/rnL)”2and molar volume (rnUmol) calculated according lo ref. 16. Percent bound from ref. 23. d4-Amino-N2-pyrimidinylbenzenesuIfonamide. ’3-Methoxy-4-amino-N-2-pyrazinylbenzenesulfonamide. ’2.4-Dimethyl-4-amino-N5-pyrimidinylbenzenesuIfonamide.
The binding of sulfonamides to human serum albumin is plotted against the calculated solubility parameters in Fig. 1. The experimental binding is expressed as the percent bound at zero drug c o n c e n t ~ a t i o nsince ~ ~ the concentration of any substance can affect the percent bound.24The data disposition in Fig. 1. suggests a parabolic curve, and a maximum binding is observed. By applying eq. 6 to the sulfonamide data, one obtains the following for the equilibrium binding model: In BD
=
-176.345(?30.665)+ 29.353(?4.915)S,(17)
10
11
I2
13
14
solubility parameter Flgure 1- Relationship between solubility parameters and binding to human serum albumin of sulfonamides. Key: (0)obsen‘ed values for sulfonamides; bound Concentrationdata (pH 7.4, T = 25 -c 0.05 “C, and 1.0 x 10-‘ M HSA) from ref. 23; solubility parameters calculated calculated line using eq. 17. according to ref. 16 and Table 111; (-)
where the statistical yields26 are: n = 26, r = 0.840,s = 0.159,F = 27.50,and F (2,23,0.001) = 9.47.The value of S, calculated from regression coefficients (eqs. 8,9 and 17),is 12.33(cal/mLP, and the maximum binding, B$, calculated from eqs. 7 and 17,is 96.5%. As is the case with regular solution theory, the solubility parameter of the drug a t peak binding should equal the solubility parameter of the albumin or the solubility parameter of the site binding the sulfonamide. Agren et al.9 suggested that the primary binding site for sulfonamides in human serum albumin is situated in a sequence of seven amino acids that form a cavity having one tryptophan residue in the bottom and positive charges around the edges of the cavity. The amino acid sequence is Lys-Ala-Trp-Ala-Val-Ala-Arg. Table IV shows the solubility parameter calculated for some amino acids. An average solubility parameter for this amino acid sequence, calculated from individual amino acid solubility parameters and volume fractions, is 12.37 (cal/mL)’q,a value that is similar to the estimated & value for albumin obtained by use of the sulfonamide binding data. This agrees with suggestions that the amino acids cited here constitute the binding moieties for sulfonamides in human serum albumin.9 Accordingly, the closer the solubility parameter of a sulfonamide to the average solubility parameter for this amino acid sequence, the greater attraction of albumin for the drug. To improve the fit of eq. 17,the dependent variable, In BD, is also regressed against S, in a power series. The criteria for determining the more appropriate polynomial equation are based on the examination of r2, the Fisher F ratio, the residual analysis, and also the t test for regression coefficients. From the analysis of various polynomial expressions, only a quartic equation provides significant t values. The polynomial regression for the sulfonamides is: In BD = 59316.98 + 19124.57b - 2311.85%
124.196% - 2.502%
+ (18)
where n = 26,r = 0.894,s = 0.470,F = 6.38,and F (4,21, 0.01)= 4.37.The general aspect of the cuwe is not changed by the use of eq. 18,and the ? value is increased by 9%. Application of eq. 14 to the sulfonamide data yields the following for the distribution model: Journal of Pharmaceutical Sciences / 641 Vol. 75, No. 7, July 1986
ln BD = -239.337(+33.047)
Tabb IV-Solublllty Parameter8 and Molar Volume8 of Some Amino Add8 In Bovlne or Human Serum Albumin
Amino Acid Lysine Alanine Tryptophan Valine Arginine Aspartic acid Histidine
s*, (caI/mL)"*
Va, mUmol
11.79 12.23 13.10 10.94 14.13 14.11 15.25
130.3 79.7 129.6 112.7 99.0 91.3 83.8
+ 37.431(25.105)S, (20a)
41b
0.1832 0.3369 0.1822 0.1584 0.1392
-
a Calculated according to ref. 16. Volume fraction of amino acids in the sequence preferred by sulfonamides. The approximate solubility parameter for this sequence is: S, = I 4 = 12.37 (cal/mL)l".
In (BIF) = 26.729 - 1.950b
(19)
where n = 25, r = 0.489, s = 1.330,F = 7.55, F (1,24,0.05)= 4.26, S, = 11.85, and S, = 15.99 (cal/mL)h (calculated from eqs. 15, 16, and 19). Davis'l has observed that the choice of a value for the solubility parameter of an aqueous phase is worth discussing. Generally, the water solubility parameter is in the region of 25, but some authors have shown that it is in the range 15.516.1. According to the work of Davis, a solubility parameter of 15.8 for plasma ($, aqueous phase) is reasonable. This value is near to that obtained for S, (15.59). However, the correlation coefficients in eqs. 17 and 18 are considerably higher than that in eq. 19, and it is evident that the sulfonamide data is better fit by the saturation model presented in eq. 2. The degree of binding for some penicillins versus the calculated solubility parameters is shown in Fig. 2. The binding to human plasma was investigated by Bird and Marshall' who selected a penicillin concentration <20 pg/mL because of its small effect on percent bound. A greater dispersion of data points appears in Fig. 2 than in Fig. 1. This may be due to the binding of the penicillins to human plasma that contains fatty acids and bilirubin which compete for the albumin binding sites.26 For this reason, the penicillins are grouped in two data sets which are fitted by separate regression equations. By applying eq. 6 to the first subset, one obtains:
where n = 59, r = 0.712, s = 0.356, F = 28.15, and F (2, 56, 0.001) = 9.47. The estimated S, value (eqs. 20a, 8, and 9) is 13.03 (cal/mL)h and the maximum binding is 93.3%. To improve the r value of eq. 20a, a polynomial in S, of one degree higher than a quartic expression is required. A polynomial of seventh degree is the only one that provides significant t values. Although the 3 value is a 19%greater than that in eq. 20a, the use of this polynomial better fits only some observed values. However, it does not change the general aspect of the curve provided by eq. 20a. For this reason, the polynomial of the seventh degree is not included. The regression equation for the other penicillin subset, also from eq. 6 is:
where n = 15, r = 0.981, s = 0.116, F = 157.77, and F (2, 12, 0.001) = 9.47. The estimated S, value of 12.45 (ca1lmL)h is similar to that for the sulfonamides, and corresponds to the solubility parameters for alanine and lysine in Table IV. This fact suggests that the binding site in the amino acid sequence for the sulfonamides could also provide an interaction site for the penicillins. The fit of eq. 20b is not appreciably improved by an expression of a higher degree. Equation 14 does not provide satisfactory results for penicillins; i.e., the correlation coefficient obtained is not significant. Penicillin data like the data for sulfonamides are better fit by a saturation model (eq.2). The binding to human serum albumin for barbital, phenobarbital, hexobarbital, butalbital,*' and aprobarbital,zs as well as the experimental solubility parameters (Table I), +re available. Although there are only a few compounds in this series, it may be useful to apply eqs. 6 and 14, because both variables are experimental. The regression equation from eq. 6 is: In BD
=
-16.116(+9.739)
+ 3.430(21.574)& -
0.145(2 0.0631% 100
-
wheren = 5,r = 0.954, s = 0.073,F = 10.13,andF(2,2,0.1) = 9. The S, estimated value (eqs. 21, 8, and 9) is 11.83 (call mL)h near to that of lysine (Table IV), and BF is 65%.The regression equation from the distribution model, eq. 14, for barbituric acids is:
M C
.-0
(21)
7 5 -
c.
z
c . '
C
al
0 50 C
.
In (BIF) = 4.953 - 0.371b
.
wheren = 5, r = 0.802,s = 0.275,F = 5.51,andF(1,3,0.1)= 5.5. The S,value is 13.02 and S, is 13.65 (caYmLP (eqs. 22, 15, and 16). The correlation coefficient in eq. 21 is higher than in eq. 22. In addition, the Sp value calculated in the distribution model does not agree with Davis' suggestion for the aqueous phase." These two facts provide a rationale for choosing the saturation model (eq. 2) for this series. Figure 3 shows three series of drugs of a basic nature: benzodiazepines, xanthine derivatives, and phenothiazines. For benzodiazepines and xanthine compounds, the data needed to precisely estimate the binding peaks are lacking. However, their peaks Beem to correspond to solubility parameters between 11.5 and 12.5 (similar to the solubility parame-
(22)
0
u
U
c
15
3
0
a
I 10
-
'
11
.
I
' 12
~
. 13
' 14
~
'
*
.
15
solubility parameter Flgurr 2-Relationship behveen solubility parameters and binding to human serum albumin of penicillins. Key: (0) observed values for penicillins; bound concentration data (pH 7.4, T = 25 "C,and 5.7 x laM HSA) from ref. 4; solubility parameters calculated according to ref. 16; (-) calculated line using eq. 2Ob; (---) calculated line using eq. 20s. 642 / Journal of Phannaceutical Sciences Vol. 75, No. 7, July 1986
100
1
eq. 24 does not agree with that in eq. 14.Also, the calculated S,value is not reasonable. Therefore, the data of this series are not fitted by the distribution model (eq. 11). In all series, the correlation coefficients for the regression equations obtained from eq. 6 are significant and, in all cases, the signs of the regression coefficients are those in this equation. These results suggest that the relationship between the solubility parameter and the binding involves a saturation-type process, rather than a distribution-type process. This fact is corroborated by the decrease of the percent bound observed with the increase of the total concentration. This is due to the saturation of the binding sites in albumin.2‘ A similar result has been obtained by Cammarata and YauiO who applied the regular solution theory to the analysis of erythrocyte hemolysis.
,-
‘s^
A
I ,I
0
I
l$
0 I
01 10
10
11
1p
,
J,
13
14
,
,
,
15
solubility parameter Flgure 3-Relationship between solubility parameters and binding to bovine and human serum albumin of xanthines, benzodiazepines, and phenothiazines. Key: (A) observed values for xanthine derivatives; bound concentration data (pH 6.85,T = 9 f 1 “C,and 2.9 x iffs M BSA) from ref. 29; (0) observed values for benzodiazepines; bound concentration data (pH 7.4,T = 22°C.and 1.4 x 1C4M HSA) from Muller, W.; Woller, U.Naunyn Schmiedebergs Arch. Pharmacol. 1973, 280,229-237;(0) observed values for phenothiazines; bound concentration data (pH 5.3,T = 20 f 0.1“C,and 5.8 x 10- M HSA) from ref. 15;solubility parameters calculated according to ref. 16;(-) calculated line using eq.23;(- -) approximate line showing the peak between 6 values of 14 and 15 for benzodiarepines and xanthines.
-
ters of lysine and alanine; Table N), and between 14 and 15 (similar to the 8 value for aspartic acid which may be one of the amino acids involved in the binding of basic drugs). Eichman et al.,28in their study of xanthine molecules with bovine serum albumin, suggested that these bases have a negative charge on the oxygen bound to Cc, which may interact, through hydrogen-bond formation, with protonated e-amino groups of lysine. Phenothiazines also show a binding peak between 11.5 and 12.56 values. This maximum can be estimated by application of the saturation model (eq.6):
In BD = -111.280(+52.028)+ 19.739(?9.159)b 0.841(?0.402)%
(23)
= 17, r = 0.662,s = 0.349,F = 5.47,and F (2,14, 0.05)= 3.74.The estimated S, value (eqs. 23, 8,and 9) is 11.74(cal/mL)hnear to that of lysine (Table IV), andBF(eqs. 23 and 7)is 100%. The fit of eq. 23 can be improved with the use of an eighth power in &; the r value yielded by this polynomial expression is 0.897.Therefore, 9 is >36%. How-
where n
ever, the t values of the regression coefficients are not significant and the general aspect of the parabolic curve obtained from eq. 23 is not changed. The only advantage of using this polynomial is a better fit of some observed values. Consequently, it is not included. Application of eq. 14 to the phenothiazine data yields the following for the distribution model:
In (BIZ9 = -13.188 + 1.236b
References and Notes 1. Khalil, Said A.; Moustafa, M. A.;Abdallah, 0.Y.Can. J . Pharm. Sci. 1976,11, 121-126. 2. Khalil, S.A.; Abdallah, 0. Y.; Modtafa, M. A. Pharm. Acta Helv. 1983,58,301313. 3. Aqei, A.; Newburger, J.; Stavchansky, S.; Martin, A. J . Pharm. Scr. 1984,73,142-745. 4. Bird, A. E.; Marshall, A. C. Biochem. Phurmacol. 1967, 16, 2275-2290. _ . - _ _ .. 5. Hildebrand J. H.; Prausnitz, J. M.; Scott, R. L. “Re lar and Related Sohions”; Van Nostrand Reinhold Co.: #w York, 1970:DD 64-88. 6. Breon; ?’. L.;Paruta, A. N. J . Pharm. Sci. 1970,59,1306-1313. I. Barton, A. F.Chem. Rev. 1975,75,131-153. 8. Bustamante, P.; Sell&, E. “Solubility Parameters as an Index of Drug Binding to Plasma Proteins’’; Second Euro an Congress of Biopharmaceutics; Salarnanca, Spain, 1984; 11, pp 385393. 9. Agren, A.; Elofseon, R.; Nilseon, S. 0.Acta. Pharm. Suec. 1971, R. -, 475-48d - .- - - - . 10. Cammarata, A.; Yau, S. J. Pure Ap 1. Chem. 1973,35,495-508. 11. Davis, S.S.ExperientM 1970 26,h1-612. 12. Cammarata, A.; Rogers, K. J . Med. Chem. 1971, 14, 1211-
8.
1212.
A.
13. Srebrenik, S.;Cohen, S. J . Phys. Chem. 1976,80, 996-999. 14. Hanech, C.; Steward, A. R. J . Med. Chem. 1964,7,691. 15. Thoma, R.;Aming, C. Arch. Pharm. (Weinheim, Ger.) 1976,309, 945-959. -- - - - . Sci. 1974,14,141-154. 16. Fedors, R.F . Polym. E 11. Small, P. A. J . Ap 1. C%m. 1953,3,71-80. 18. Martin, A.; Wu, RL.; Velasquez, T. J . Pharrn. Sci. 1985, 74, 211-282. 19. Martin, A.; Paruta, A. N.; Adjei, A. J . Pharm. Sci. 1981, 70, 11 15-1 120. 20. Martin, A.; Wu, P. L.; Adjei, A.; Mehdizadeh, M.; James, K. C.; Metzler, C. J . Pharrn. Sci. 1982,71,1334-1340. 21. Martin, A.;Newburger, J.; Adjei, A. J . Pharm. Sci. 1980,69, 487-491. 22. Martin, A.; Miralles, M. J. J . Phurm. Sci. 1982,71,439-442. 23. Elofsson, R.;Nilsson, S.0.;Klunykowska, B. ActaPharm. Suec. 1971,8,465-414. 24. Goldstein. A. Pharmacol. Rev. 1949,1, 102. 25. The f value in parentheses associated with each regression coefficient is the standard error of the regression coefficient; r is the multiple correlation coefficient. 26. Koch-Weeser,J.; Sellers, E. N. Engl. J . Med. 1976,294,311416. 27. Juarrero, V.P. Arch. Inst. Farmacol. Exper., Madrid 1959,11, 134-158. 28. Lous, P. Acta Pharmacol. Toxicol. 1954,10, 141-165. 29. Eichman, M. L.;Guttman, D. E.; Winkle, Q.; Guth, E. P. J . Pharm. Sci. 1962,51,66-11.
(24)
where n = 17,r = 0.603,s = 0.704,F = 8.56,and F (1,15, 0.05)= 3.74.The estimated S, value is 11.33 and S,is 10.08 (caVmL)h (eqs. 24, 15, and 16). The correlation coefficient observed in eq. 23 ia not significantly greater than that in eq. 24.However, the sign of the regression coefficientobtained in
Acknowledgments The authors wish to,thank Dr. Alfred Martin, Drug Dynamics Institute of the University of Texas, College of Pharmacy, for helpful criticism in the preparation of this report.
Journal of Pharmaceutical Sciences / 643 Vol. 75,No. 7,July 1986
proteins. The equation was tested on a homologous series and a good correlation was found. Sulfonamides showed maximum binding when their solubility parameters were similar to the solubility parameters of the amino acids situated in a sequence with one tryptophan residue. This observation supports the assumption that this sequence is the primary binding site for the sulfonamides. Binding peaks were also found at solubility parameters in other drug series corresponding to the solubility parameters of human serum albumin (HSA) or bovine serum albumin (BSA) amino acids. It is suggested that the solubility parameter could be used to predict the binding of drugs to plasma proteins. ~~
The solubility parameter has been used as an index of drug activity,' and has been investigated for its correlation with absorption p r o c e s ~ e s . ~The . ~ binding of drugs to plasma proteins has been correlated with physical properties such as polarizability, parachor, molecular weight, and the partition coefficient.4 This report demonstrates a relationship between the solubility parameter and the binding of drugs to plasma proteins.
Theoretical Section The solubility parameter or Hildebrand parameter (6) is defined as the square root of the cohesive energy densitys and is a measure of the cohesion between molecules. Since physiological interactions may occur a t a molecular level, it is assumed that solution properties are operative.'j Barton? observed that cohesive energy density is related to physical properties; accordingly, it is not surprising to find a relationship between cohesive energy density and drug-protein interactions. A high 6 value indicates a high cohesive energy as well as high solubility in water. If one assumes that, in pharmacokinetic terms, there are two different compartments (one for plasma and the other for plasma proteins), then a drug with a high 6 value should have a greater affinity for plasma than for the proteins since plasma is an aqueous medium, whereas proteins are relatively less hydrophilic. Since the solubility parameter is a measure of hydrophilic character, the binding to proteins should increase within a homologous series of a drug with a decrease in the 6 value of the analogue. Therefore, the slope and the correlation coefficient for a plot of protein binding versus the solubility parameter will have a negative sign. This was shown in an earlier work,* and is compatible with studies that relate binding with lipid solubility.9 Like regular solution properties, the binding to proteins can be analyzed by an expression similar to the Hildebrand equation.= Thus, under equilibrium conditions, the activity coefficient of the drug (a)in the albumin compartment is related to both albumin and drug solubility parameters: 0022-3549/86/0700-0639$0 1 .0010
0 1986,American
Pharmaceutical Association
In a
=
In ( B ~ / B ~=)RT
where S, and S, represent the solubility parameters of albumin (subscript E) and drug (subscript D),respectively, VD is the molar liquid volume of the drug, T is the absolute temperature, R is the gas constant, and & is the volume fraction of the albumin compartment. The activity coefficient (a)is written as a term involving the maximum binding (BDM) and the real drug binding (BD), expressed as percent of the bound fraction, by analogy to the ideal solubility, X, and the mole fraction in the Hildebrand equation. In dilute solutions, the volume fraction of the solvent becomes one (4 -1). If this condition applies to the albumindrug interaction, where V$D<
-In
BD =
where the slope,
-In B g A
=
+ A(&
- b)2
(2)
VD RT'
Accordingly, the most favorable condition for drug-protein interactions may occur when the intermolecular affinity is the greatest, i.e., where both solubility parameters are similar:
&=b Under this condition, the term (S,binding rises to its highest value:
B~
(3) in eq. 2 is zero and
= B::
(4)
Following a more simplified approach, eq. 2 does not take into account the contribution of.Flory and Huggins on molecular size differences.7 With an additional degree of approximation, VD may be considered constant for a given series of drug molecules.10 Hence, eq. 2 could be used as a model equation in a linear regression analysis of -In B D on the independent variable (S, - &I2, where A is the slope and -In BFis the intercept. Equation 2 assumes a phase saturation model similar to the model formulated in terms of the regular-solutions approach proposed by Cammarata and Yau.10 Since S,is unknown, the application of eq. 2 requires the use of different values of S,,and a choice must be made of the value that yields the best least-squares line. The S, value can be estimated more accurately when eq. 2 is transformed into an expression where In B D is regressed against a polynomial in &: lnBD=InBg-A&+&i&S,-A&
(5)
Journal of Pharmaceutical Sciences / 639 Vol. 75, No. 7,July 1986
where:
-b = 1nBF- A&
(7)
2A&
(8)
-a2 = -A
(9)
a1 =
The sign of the intercept must be negative, since A& is > In B#. By substituting the regreasion coefficientsin eqs. 8 and 9, one obtains the S, value. Likewise, from eq. 7, one obtains the maximum binding, B#. The proposed equilibrium binding approach can be compared with a distribution model which is also derived from regular solution theory.aJ0-13 "his model assumes that the equilibrium binding of the drug exists between two compartments due to a partitioning of the drug. An equation derived from this approach could be written 88:
RT In (BIF) = VD&&
- S,I2
- VD&&
- &J2(10)
where the subacripts P, E, and D refer to plasma, albumin, and drug, respectively. The function In (BIF),where B is the percent drug bound and F is the percent free, is directly analogous to an organic solventwater partition coefficient4 and has been used to correlate serum binding results to a substituent constant, w, developed by Hansch and Steward.14 Equation 10 can be written as:
In (BIF) = A[(& -
- (& -
W21
(12)
The tern A may be considered constant for a given series of drug molecules, and since S,and S, are also constants, eq. 13 becomes:
In (BIF) = b - a&
-
Table CExperlmental and Calculatad Solublllty Parametersfor Barbtturlc Acids and Sulfonamldes
(11)
where & and c$p 5 1 and A is the term defined in eq. 2. Equation 11 can be transformed into a linear expression by the following steps:
In @IF) = A[($ - &>+ S, (2& - 2&)1
plasma protein binding data and solubility parameters. Since there are few experimental solubility parameters for pharmaceutical solids, S values are calculated using the method of Fedors.16 This method, which is based on group additive constants, is believed to be superior to that of Small17 because the contribution of a much larger number of functional groups, such as -OH, -NH2, and -COOH, have been evaluated in the approach of Fedors. Fedors observed that deviations between the experimental measures and estimated values of the energy of vaporization and molar volume are generally less than 10%.This method has been employed for pharmaceutical solids's22 and was found to compare favorably with experimental 6 values. As shown in Table I, the calculated 6 values for barbituric acids and sulfonamides, which contain some of the aforementioned functional groups, correlate with experimental values with an error of 8%. Therefore, it is assumed that the method of Fedors can be used as a measure of the Hildebrand parameter. Series of acidic and basis drugs were chosen, and the technique for calculating the solubility parameter is shown in Table 11. Only the solubility parameters for sulfonamides are listed in Table 111, since the data for all series are voluminous.
(14)
(caVmL)%
(cal/mL)%
69
AS, %
13.50 13.00 12.85 12.40 12.40 11.95 11.90 11.75 11.30 11.30 13.40 12.60 13.90 12.70
12.55 13.03 12.34 12.00 12.24 11.20 12.19 11.54 11.50 11.85 12.85 12.58 12.89 12.58
7.6 -0.2 3.9 3.2 1.3 6.3 -2.4 1.8 -1.8 -4.8 4.1 0.1 7.3 0.9
8'1
Compound Barbital Phenobarbital Allobarbital Aprobarbital Cyclobarbital Butalbital Butobarbital Pentobarbital Secobarbital Hexobarbital Sulfamerazine Sulfamethazine Sulfameter Sulfisomldlne ~
~
'Experimental S values: barbituric acids from ref. 1; sulfamerazine, sulfamethazine, and sulfameter from Sunwoo, C.; Eisen, H. J. fhann. Sci. 1971, 60,236-244; sulfisomidine from ref. 18. bCalculated according to ref. 16.
where the slope is:
and the intercept is:
b
= A($
- &I
(16)
+,
The variable In (BIF) could be regressed against and S, and S, can be estimated from eqs. 15 and 16. The slope (a) must have a negative sign because the plasma solubility parameter (aqueous medium) is larger than the albumin solubility parameter. Equations 6 and 14 can be applied to a homologous series of a drug, and from the results obtained, one may verify which is the more satisfactory model.
Results and Discussion The data used for protein binding are found in the literature and are expressed as percent of the bound fraction. This measure is frequently used with a homologous series of a drug, and has been correlated with the partition coefficient.4.15 The present work suggests a correlation between 640 /Journal of fharmaceutical Sciences Vol. 75,No. 7,July 1986
Table Il-Group Contrlbutlon Method for Calculatlng Molar Volume and Solublllty Parameter of Sulfadlmethoxlne*
Atom or Group
Number of Groups
A€, cal/mol
AV, mUmol
1 1 2 1 2 2 5 5 6 2
3000 2000 5600 2950 1600 2250 5150 5150 2400
19.2 4.5 10 23.7 7.6 67 67.5 -27.5 - 13.2 32 P A V = 190.8
~
-NHI -NH-
-N= S O T b
0 -CHI -CH= C=
Olefinic bond Ring closure
S, = (30600/190.8)'"
500 PA€ = 30600
= 12.66 (cal/mL)'/2
'2,6-Dimethoxy-4-amino-N4-pyrimidinylbenzenesulfonemide;calculated according to ref. 16. bFrom ref. 18.
Table Ili-Solublllty Parameters, Molar Volumes, and Blndlng Data for Sutfonamides
1’ &b
%
&
13.17 12.89 12.58 12.62 12.66 12.16 12.58 11.70 12.66 12.19 1 1.39 11.95 12.07 12.39 12.16 12.07 12.90 12.35
154.2 175.5 183.2 185.0 188.8 223.0 183.2 246.0 188.8 220.9 260.9 239.1 231.9 206.9 223.0 231.9 206.6 203.1
48 85 86 96 98 99 82 61 94 98 97 99 94 96 96 87 98 98
154.2 168.5 168.5 184.8 172.5 183.2
30 62 78 94 85 69
172.5
60
183.2
90
Compound
6-Methoxy2,g-Dimethyl2-Methyl-6-methoxy2,6-Dimethoxy2,bDiethoxy5,B-DirnethyC 2-Butyl5,6-Dimethoxy2-Ethyl-5,6,-dimethoxy5,6-Diethoxy5-6UtOxy5-Isapropoxy.6-methoxy5-Methoxy-6-ethoxy5-Methoxy-B-propoxy 5-Methoxy-6-isopropoxy5-Phenyl5-Ethyl-6-rnethoxv-
26
-
13.17 12.85 12.85 12.54 12.89 12.58
6-Methyl5-Methyl5-Ethyl5-Methoxy4,6-Dimethyl-
CH30
12.89 CH3
4‘ 12.58
a 4-Amino-N-4-pyrimidinylbenzenesuIfonamide. Solubility parameter (cal/rnL)”2and molar volume (rnUmol) calculated according lo ref. 16. Percent bound from ref. 23. d4-Amino-N2-pyrimidinylbenzenesuIfonamide. ’3-Methoxy-4-amino-N-2-pyrazinylbenzenesulfonamide. ’2.4-Dimethyl-4-amino-N5-pyrimidinylbenzenesuIfonamide.
The binding of sulfonamides to human serum albumin is plotted against the calculated solubility parameters in Fig. 1. The experimental binding is expressed as the percent bound at zero drug c o n c e n t ~ a t i o nsince ~ ~ the concentration of any substance can affect the percent bound.24The data disposition in Fig. 1. suggests a parabolic curve, and a maximum binding is observed. By applying eq. 6 to the sulfonamide data, one obtains the following for the equilibrium binding model: In BD
=
-176.345(?30.665)+ 29.353(?4.915)S,(17)
10
11
I2
13
14
solubility parameter Flgure 1- Relationship between solubility parameters and binding to human serum albumin of sulfonamides. Key: (0)obsen‘ed values for sulfonamides; bound Concentrationdata (pH 7.4, T = 25 -c 0.05 “C, and 1.0 x 10-‘ M HSA) from ref. 23; solubility parameters calculated calculated line using eq. 17. according to ref. 16 and Table 111; (-)
where the statistical yields26 are: n = 26, r = 0.840,s = 0.159,F = 27.50,and F (2,23,0.001) = 9.47.The value of S, calculated from regression coefficients (eqs. 8,9 and 17),is 12.33(cal/mLP, and the maximum binding, B$, calculated from eqs. 7 and 17,is 96.5%. As is the case with regular solution theory, the solubility parameter of the drug a t peak binding should equal the solubility parameter of the albumin or the solubility parameter of the site binding the sulfonamide. Agren et al.9 suggested that the primary binding site for sulfonamides in human serum albumin is situated in a sequence of seven amino acids that form a cavity having one tryptophan residue in the bottom and positive charges around the edges of the cavity. The amino acid sequence is Lys-Ala-Trp-Ala-Val-Ala-Arg. Table IV shows the solubility parameter calculated for some amino acids. An average solubility parameter for this amino acid sequence, calculated from individual amino acid solubility parameters and volume fractions, is 12.37 (cal/mL)’q,a value that is similar to the estimated & value for albumin obtained by use of the sulfonamide binding data. This agrees with suggestions that the amino acids cited here constitute the binding moieties for sulfonamides in human serum albumin.9 Accordingly, the closer the solubility parameter of a sulfonamide to the average solubility parameter for this amino acid sequence, the greater attraction of albumin for the drug. To improve the fit of eq. 17,the dependent variable, In BD, is also regressed against S, in a power series. The criteria for determining the more appropriate polynomial equation are based on the examination of r2, the Fisher F ratio, the residual analysis, and also the t test for regression coefficients. From the analysis of various polynomial expressions, only a quartic equation provides significant t values. The polynomial regression for the sulfonamides is: In BD = 59316.98 + 19124.57b - 2311.85%
124.196% - 2.502%
+ (18)
where n = 26,r = 0.894,s = 0.470,F = 6.38,and F (4,21, 0.01)= 4.37.The general aspect of the cuwe is not changed by the use of eq. 18,and the ? value is increased by 9%. Application of eq. 14 to the sulfonamide data yields the following for the distribution model: Journal of Pharmaceutical Sciences / 641 Vol. 75, No. 7, July 1986
ln BD = -239.337(+33.047)
Tabb IV-Solublllty Parameter8 and Molar Volume8 of Some Amino Add8 In Bovlne or Human Serum Albumin
Amino Acid Lysine Alanine Tryptophan Valine Arginine Aspartic acid Histidine
s*, (caI/mL)"*
Va, mUmol
11.79 12.23 13.10 10.94 14.13 14.11 15.25
130.3 79.7 129.6 112.7 99.0 91.3 83.8
+ 37.431(25.105)S, (20a)
41b
0.1832 0.3369 0.1822 0.1584 0.1392
-
a Calculated according to ref. 16. Volume fraction of amino acids in the sequence preferred by sulfonamides. The approximate solubility parameter for this sequence is: S, = I 4 = 12.37 (cal/mL)l".
In (BIF) = 26.729 - 1.950b
(19)
where n = 25, r = 0.489, s = 1.330,F = 7.55, F (1,24,0.05)= 4.26, S, = 11.85, and S, = 15.99 (cal/mL)h (calculated from eqs. 15, 16, and 19). Davis'l has observed that the choice of a value for the solubility parameter of an aqueous phase is worth discussing. Generally, the water solubility parameter is in the region of 25, but some authors have shown that it is in the range 15.516.1. According to the work of Davis, a solubility parameter of 15.8 for plasma ($, aqueous phase) is reasonable. This value is near to that obtained for S, (15.59). However, the correlation coefficients in eqs. 17 and 18 are considerably higher than that in eq. 19, and it is evident that the sulfonamide data is better fit by the saturation model presented in eq. 2. The degree of binding for some penicillins versus the calculated solubility parameters is shown in Fig. 2. The binding to human plasma was investigated by Bird and Marshall' who selected a penicillin concentration <20 pg/mL because of its small effect on percent bound. A greater dispersion of data points appears in Fig. 2 than in Fig. 1. This may be due to the binding of the penicillins to human plasma that contains fatty acids and bilirubin which compete for the albumin binding sites.26 For this reason, the penicillins are grouped in two data sets which are fitted by separate regression equations. By applying eq. 6 to the first subset, one obtains:
where n = 59, r = 0.712, s = 0.356, F = 28.15, and F (2, 56, 0.001) = 9.47. The estimated S, value (eqs. 20a, 8, and 9) is 13.03 (cal/mL)h and the maximum binding is 93.3%. To improve the r value of eq. 20a, a polynomial in S, of one degree higher than a quartic expression is required. A polynomial of seventh degree is the only one that provides significant t values. Although the 3 value is a 19%greater than that in eq. 20a, the use of this polynomial better fits only some observed values. However, it does not change the general aspect of the curve provided by eq. 20a. For this reason, the polynomial of the seventh degree is not included. The regression equation for the other penicillin subset, also from eq. 6 is:
where n = 15, r = 0.981, s = 0.116, F = 157.77, and F (2, 12, 0.001) = 9.47. The estimated S, value of 12.45 (ca1lmL)h is similar to that for the sulfonamides, and corresponds to the solubility parameters for alanine and lysine in Table IV. This fact suggests that the binding site in the amino acid sequence for the sulfonamides could also provide an interaction site for the penicillins. The fit of eq. 20b is not appreciably improved by an expression of a higher degree. Equation 14 does not provide satisfactory results for penicillins; i.e., the correlation coefficient obtained is not significant. Penicillin data like the data for sulfonamides are better fit by a saturation model (eq.2). The binding to human serum albumin for barbital, phenobarbital, hexobarbital, butalbital,*' and aprobarbital,zs as well as the experimental solubility parameters (Table I), +re available. Although there are only a few compounds in this series, it may be useful to apply eqs. 6 and 14, because both variables are experimental. The regression equation from eq. 6 is: In BD
=
-16.116(+9.739)
+ 3.430(21.574)& -
0.145(2 0.0631% 100
-
wheren = 5,r = 0.954, s = 0.073,F = 10.13,andF(2,2,0.1) = 9. The S, estimated value (eqs. 21, 8, and 9) is 11.83 (call mL)h near to that of lysine (Table IV), and BF is 65%.The regression equation from the distribution model, eq. 14, for barbituric acids is:
M C
.-0
(21)
7 5 -
c.
z
c . '
C
al
0 50 C
.
In (BIF) = 4.953 - 0.371b
.
wheren = 5, r = 0.802,s = 0.275,F = 5.51,andF(1,3,0.1)= 5.5. The S,value is 13.02 and S, is 13.65 (caYmLP (eqs. 22, 15, and 16). The correlation coefficient in eq. 21 is higher than in eq. 22. In addition, the Sp value calculated in the distribution model does not agree with Davis' suggestion for the aqueous phase." These two facts provide a rationale for choosing the saturation model (eq. 2) for this series. Figure 3 shows three series of drugs of a basic nature: benzodiazepines, xanthine derivatives, and phenothiazines. For benzodiazepines and xanthine compounds, the data needed to precisely estimate the binding peaks are lacking. However, their peaks Beem to correspond to solubility parameters between 11.5 and 12.5 (similar to the solubility parame-
(22)
0
u
U
c
15
3
0
a
I 10
-
'
11
.
I
' 12
~
. 13
' 14
~
'
*
.
15
solubility parameter Flgurr 2-Relationship behveen solubility parameters and binding to human serum albumin of penicillins. Key: (0) observed values for penicillins; bound concentration data (pH 7.4, T = 25 "C,and 5.7 x laM HSA) from ref. 4; solubility parameters calculated according to ref. 16; (-) calculated line using eq. 2Ob; (---) calculated line using eq. 20s. 642 / Journal of Phannaceutical Sciences Vol. 75, No. 7, July 1986
100
1
eq. 24 does not agree with that in eq. 14.Also, the calculated S,value is not reasonable. Therefore, the data of this series are not fitted by the distribution model (eq. 11). In all series, the correlation coefficients for the regression equations obtained from eq. 6 are significant and, in all cases, the signs of the regression coefficients are those in this equation. These results suggest that the relationship between the solubility parameter and the binding involves a saturation-type process, rather than a distribution-type process. This fact is corroborated by the decrease of the percent bound observed with the increase of the total concentration. This is due to the saturation of the binding sites in albumin.2‘ A similar result has been obtained by Cammarata and YauiO who applied the regular solution theory to the analysis of erythrocyte hemolysis.
,-
‘s^
A
I ,I
0
I
l$
0 I
01 10
10
11
1p
,
J,
13
14
,
,
,
15
solubility parameter Flgure 3-Relationship between solubility parameters and binding to bovine and human serum albumin of xanthines, benzodiazepines, and phenothiazines. Key: (A) observed values for xanthine derivatives; bound concentration data (pH 6.85,T = 9 f 1 “C,and 2.9 x iffs M BSA) from ref. 29; (0) observed values for benzodiazepines; bound concentration data (pH 7.4,T = 22°C.and 1.4 x 1C4M HSA) from Muller, W.; Woller, U.Naunyn Schmiedebergs Arch. Pharmacol. 1973, 280,229-237;(0) observed values for phenothiazines; bound concentration data (pH 5.3,T = 20 f 0.1“C,and 5.8 x 10- M HSA) from ref. 15;solubility parameters calculated according to ref. 16;(-) calculated line using eq.23;(- -) approximate line showing the peak between 6 values of 14 and 15 for benzodiarepines and xanthines.
-
ters of lysine and alanine; Table N), and between 14 and 15 (similar to the 8 value for aspartic acid which may be one of the amino acids involved in the binding of basic drugs). Eichman et al.,28in their study of xanthine molecules with bovine serum albumin, suggested that these bases have a negative charge on the oxygen bound to Cc, which may interact, through hydrogen-bond formation, with protonated e-amino groups of lysine. Phenothiazines also show a binding peak between 11.5 and 12.56 values. This maximum can be estimated by application of the saturation model (eq.6):
In BD = -111.280(+52.028)+ 19.739(?9.159)b 0.841(?0.402)%
(23)
= 17, r = 0.662,s = 0.349,F = 5.47,and F (2,14, 0.05)= 3.74.The estimated S, value (eqs. 23, 8,and 9) is 11.74(cal/mL)hnear to that of lysine (Table IV), andBF(eqs. 23 and 7)is 100%. The fit of eq. 23 can be improved with the use of an eighth power in &; the r value yielded by this polynomial expression is 0.897.Therefore, 9 is >36%. How-
where n
ever, the t values of the regression coefficients are not significant and the general aspect of the parabolic curve obtained from eq. 23 is not changed. The only advantage of using this polynomial is a better fit of some observed values. Consequently, it is not included. Application of eq. 14 to the phenothiazine data yields the following for the distribution model:
In (BIZ9 = -13.188 + 1.236b
References and Notes 1. Khalil, Said A.; Moustafa, M. A.;Abdallah, 0.Y.Can. J . Pharm. Sci. 1976,11, 121-126. 2. Khalil, S.A.; Abdallah, 0. Y.; Modtafa, M. A. Pharm. Acta Helv. 1983,58,301313. 3. Aqei, A.; Newburger, J.; Stavchansky, S.; Martin, A. J . Pharm. Scr. 1984,73,142-745. 4. Bird, A. E.; Marshall, A. C. Biochem. Phurmacol. 1967, 16, 2275-2290. _ . - _ _ .. 5. Hildebrand J. H.; Prausnitz, J. M.; Scott, R. L. “Re lar and Related Sohions”; Van Nostrand Reinhold Co.: #w York, 1970:DD 64-88. 6. Breon; ?’. L.;Paruta, A. N. J . Pharm. Sci. 1970,59,1306-1313. I. Barton, A. F.Chem. Rev. 1975,75,131-153. 8. Bustamante, P.; Sell&, E. “Solubility Parameters as an Index of Drug Binding to Plasma Proteins’’; Second Euro an Congress of Biopharmaceutics; Salarnanca, Spain, 1984; 11, pp 385393. 9. Agren, A.; Elofseon, R.; Nilseon, S. 0.Acta. Pharm. Suec. 1971, R. -, 475-48d - .- - - - . 10. Cammarata, A.; Yau, S. J. Pure Ap 1. Chem. 1973,35,495-508. 11. Davis, S.S.ExperientM 1970 26,h1-612. 12. Cammarata, A.; Rogers, K. J . Med. Chem. 1971, 14, 1211-
8.
1212.
A.
13. Srebrenik, S.;Cohen, S. J . Phys. Chem. 1976,80, 996-999. 14. Hanech, C.; Steward, A. R. J . Med. Chem. 1964,7,691. 15. Thoma, R.;Aming, C. Arch. Pharm. (Weinheim, Ger.) 1976,309, 945-959. -- - - - . Sci. 1974,14,141-154. 16. Fedors, R.F . Polym. E 11. Small, P. A. J . Ap 1. C%m. 1953,3,71-80. 18. Martin, A.; Wu, RL.; Velasquez, T. J . Pharrn. Sci. 1985, 74, 211-282. 19. Martin, A.; Paruta, A. N.; Adjei, A. J . Pharm. Sci. 1981, 70, 11 15-1 120. 20. Martin, A.; Wu, P. L.; Adjei, A.; Mehdizadeh, M.; James, K. C.; Metzler, C. J . Pharrn. Sci. 1982,71,1334-1340. 21. Martin, A.;Newburger, J.; Adjei, A. J . Pharm. Sci. 1980,69, 487-491. 22. Martin, A.; Miralles, M. J. J . Phurm. Sci. 1982,71,439-442. 23. Elofsson, R.;Nilsson, S.0.;Klunykowska, B. ActaPharm. Suec. 1971,8,465-414. 24. Goldstein. A. Pharmacol. Rev. 1949,1, 102. 25. The f value in parentheses associated with each regression coefficient is the standard error of the regression coefficient; r is the multiple correlation coefficient. 26. Koch-Weeser,J.; Sellers, E. N. Engl. J . Med. 1976,294,311416. 27. Juarrero, V.P. Arch. Inst. Farmacol. Exper., Madrid 1959,11, 134-158. 28. Lous, P. Acta Pharmacol. Toxicol. 1954,10, 141-165. 29. Eichman, M. L.;Guttman, D. E.; Winkle, Q.; Guth, E. P. J . Pharm. Sci. 1962,51,66-11.
(24)
where n = 17,r = 0.603,s = 0.704,F = 8.56,and F (1,15, 0.05)= 3.74.The estimated S, value is 11.33 and S,is 10.08 (caVmL)h (eqs. 24, 15, and 16). The correlation coefficient observed in eq. 23 ia not significantly greater than that in eq. 24.However, the sign of the regression coefficientobtained in
Acknowledgments The authors wish to,thank Dr. Alfred Martin, Drug Dynamics Institute of the University of Texas, College of Pharmacy, for helpful criticism in the preparation of this report.
Journal of Pharmaceutical Sciences / 643 Vol. 75,No. 7,July 1986