Journal o f Pharmacokinetics and Biopharmaceutics, Vol. 3, No. 2, 1975

Calculation of the Gastric Absorption Rate Constants of 5-Substituted Barbiturates Through the Rm Values or Substituent AR m Constants in Reversed-Phase Partition Chromatography Jos6 M. Plfi-Delfina, 1 Joaquin Moreno,1 Juan Durfin, 1 and Altbnso del Pozo ~ Received May 20, 1974--Final Oct. 16, 1974

A linear correlation between the logarithm of the in situ gastric absorption rate constants (ka) of 5-substituted barbiturates and their R m values in selected reversed-phase partition chromatographic systems is demonstrated, as well as between the A log k a and the AR m derived parameters. On the basis of the chromatographic behavior of 14 closely related compounds of this series, the substituent AR~. constants for the main functional groups are calculated, so that the gastric absorption constants of nontested barbiturates can be predicted with close approximation. Predicted Rm and log k a values show an excellent correlation with log 1/C values taken from pharmacological literature data. The migration mechanisms involved in reversed-phase partition chromatography are discussed in connection with the results obtained with other types of partition systems and with bulk-phase solvents. The possible relationships between chromatographic parameters and absorption rate constants found from absorption sites other than the stomach are outlined; as well as the advantages and limitations of the procedure.

KEY W O R D S : barbiturates; absorption rate constants; partition chromatography; reversed-

phase chromatography; R,. values; ARm values; R,,]log k, correlations.

INTRODUCTION

Although chromatographic partition parameters have been successfully related to pharmacological effects for some series of drugs (1-5), little attention has been paid to the direct correlation between true penetration constants and chromatographic partition values. From a pharmacokinetic standpoint, the correlations involving absorption constants, k, (i.e., the first-order rate constants of any individual drugs across a membrane by a 1Practical Pharmacy Department, Section of Biopharmaceutics, Faculty of Pharmacy, University of Barcelona, Barcelona, Spain. 115 9 1975 Plenum PublishingCorporation, 227 West 17th $1reet, New York, N.Y. 1001I. No part of this publication may he reproduced, stored in a retrieval system,or transmitted, in any form or by any means,electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permissionof the publisher.

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passive diffusion process, in time- 1), are of great interest for prediction of the absorption behavior of new or unknown related compounds as well as for their derived pharmacological implications. In a preliminary report (6), a linear correlation between Rm and gastric log k~ values was suggested for several barbiturates on the basis of independent sets of data reported in the available literature. Described herein are the results obtained by means of a reversed-phase partition technique, suitable for the calculation and even for the prediction of the gastric absorption rate constants for the 5-substituted barbituric acid derivatives through their R m values or with the aid of properly established substituent ARmconstants. THEORETICAL

BASIS

The basis for the existence of a correlation between Rm a function of the Rf value, equivalent to log ( 1 / R e - 1)--or ARm--the positive or negative increment due to the introduction of any particular substituent into a given structure--and the logarithm of the absorption rate constant, ka, or its increment, for series of closely related drugs consistent with the pH-partition theory was outlined in our previous paper (6). The equations to be confirmed here, as far as the gastric absorption of the tested barbiturates is concerned, are logk~ = a + b. Rm (1) A log ka = b. ARm

(2)

where a and b are constants for a given technique. It will be also shown that, with C as the compound concentration required for achieving a constant pharmacological response and a l , b l , a2, b2, and c 2 constants for the technique, the linear and parabolic correlations already established for miscellaneous series of drugs including some barbiturates (1-5), expressed as log 1/C = a , + b 1 9 R

m

log 1/C = a2 " R 2 4- b 2 9 Rm + c2

(3) (4)

are of general application for the 5-substituted barbiturate series, the type of correlation depending mainly on the pharmacological effect evolved. From equations 1, 3, and 4, it becomes obvious that, for a particular series of drugs, log 1/C = a 3 + b 3 . 1 o g k a

(5)

log 1/C = a4(log ka) 2 -~- b4.. log ka + c4

(6)

Calculation of Gastric Absorption Rate Constants

117

As will be pointed out later, equations 5 and 6 also arise from the data reported in specialized literature (7-9); they will be discussed here in connection with the chromatographic properties of the compounds tested. MATERIALS AND METHODS Barbiturates

Fourteen 5-substituted barbiturates were included in the chromatographic experiments. Solutions to be chromatographed were prepared by dissolving 0,5 g of the free acids in 100 ml of a mixture of chloroform and methanol. Only compounds of commercial origin, kindly supplied by proprietary manufacturers, were tested. The constitutional features of the barbiturates tested for chromatographic behavior are outlined in Table I. Seven of the compounds were selected for having known k, values ; the remaining ones were selected on the basis that they had sufficient structural differences from the former ones for the calculation of ARm substituent constants. Table I. C o m m o n Names, Chemical Constitution, and Some Physical and Physiological Constants of the Barbiturates Tested

No.

C o m m o n name

1 2 3 4 5 6 7 8 9 10 11 12 t3 14

Barbital Ethallobarbital Heptobarbital Allobarbital Aprobarbital Secbutobarbital Phenobarbital Butobarbital Cyclobarbital Talbutal ldobutal Pentobarbital Amobarbital Secobarbital

5-Substituents

Ethyl-ethyl Ethyl-allyl Methyl-phenyl Allyl-allyl Allyl-(1-methyl)ethyl Ethyl-(l-methyl)propyl Ethyl-phenyl Ethyl-butyl Ethyl-cyclohexenyl Allyl-(1-methyl)propyl Allyl-butyl Ethyl-(l-methyl)butyl Ethyl-(3-methyl)butyl Allyl-(1-methyl)butyl

Partition Partition Partition Absorption coefficient coefficient coefficient constant W P~ P~ k. d 4.47 7.08 e 8.32 e 11.2 14.1 28.2 26.3 44.7 15.9 44.7 e 70.8 e 89.1 89.1 141

0.035 0.063 -0.109 --0.233 -0.297 --0.927 0.944 --

3.82 9.59 -16.80 --34.40 -4.14 --106.00 113.00 --

0.053 0.036 -0.092 --0.135 -0.142 --0.194 0.195 --

aBetween octanol and water. Data are from Hansch and Anderson (7). The figures are.the antilogarithms of the reported values. Used for the Rm/log P correlations excepting the. value of cyclobarbital. bBetween tetrachloromethane and a pH 1.1 buffer solution. Data are from Kakemi et al. (8), which have been used in this report for the R,,]log P correlations. ~Between isopentyl acetate and a pH 1.1 buffer solution. Data are from Kakemi et al. (8), used for the R,,/log P correlations, excepting the value of cyclobarbital. aData are from Kakemi et al, (8), expressed in hr-~. They have been used in this report for establishing the R,,/log ka correlations, excepting the value of ethallobarbital. eValues calculated from the data of Hansch and Anderson (7).

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Partition Coefficients

For the proper selection of partition chromatographic systems, preliminary correlation were outlined between the R m values found in each examined system and the log P values reported in the available literature (P being the partition coefficient). The n-octanol-water (7) and the tetrachloromethane-pH 1.1 buffer (8) partition coefficients were used for this purpose (Table I). Chromatographic Technique

Fifteen grams of Avicel SP (microcrystalline cellulose) was dispersed into a mixture of 15 ml isopropanol and 30ml water and the resultant suspension was distributed on five 20- by 20-cm glass plates. A layer thickness of 300/~m was obtained by means of the "Stratomat" (Chemetron) automatic apparatus. The plates were allowed to dry for 24 hr. The dried, nonactivated plates were impregnated with a 5 % benzene solution of the selected lipophilic material, a mixture of purified castor oil (Spanish Pharmacopoeia, IX) and Ricilan B, a ricinoleic acid ester of lanolin alcohols (American Cholesterol), at 8:2 by weight, which was selected after a laborious screening of several lipophilic materials. Impregnation was conducted by means of a blank run until the solvent front had just attained the upper edge of the plate. The directions of the impregnation were alternatively the same as followed by the cellulose slurry extension and the one perpendicular to this. The solvent was evaporated and the plates were immediately spotted with the barbiturate solutions by means of a "Link" micropipette of 1/~l capacity (equivalent to 5/~g of each particular compound), with the aid of a 14-lane template. Development was carried out in 21- by 21- by 9-cm "Desaga" chambers in the usual way, at 20~ with an aqueous 0.1 M solution of HC1 (pH 1.07) previously saturated with the impregnating oily phase. The chamber was equilibrated with the solvent for 6 hr prior to development, which was carried out in the same direction as the impregnation. The total development time was about 2 hr for a height of run of 14 cm from the starting line. Detection of the spots was achieved using the Ahmed (10) silver nitrate reagent. The solvent action results in demixing, so that the/~-front may be seen without any difficulty after detection. Since the ke value found was about 0.80, the mobility of solutes was referred to the/~-front in order to obtain reliable partition R~ values (11). Under these conditions, R~ values ranging from 0.17 to 0.85 were used for migration-gastric absorption relationships and from 0.10 to 0.85 for the establishment of ARm substituent constants. The reason for the occurrence of demixing will be discussed later.

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119

Absorption Constants and Chromatographic Partition Parameters

The gastric absorption rate constants (k~) experimentally found by Kakemi et aI. (8) in rats in situ were used for establishing the R,,/log ka and the ARm/A log k, correlations. The k, value of ethallobarbital was omitted in deriving the equations since the authors did not assess a good fit for this element in establishing logarithmic correlations between absorption constants and bulk-phase partition coefficients. The inclusion of this compound in regression analysis would have led to considerable errors in calculating and predicting k, values for the remaining elements. The R m values of the tested barbiturates were calculated from the experimental R I values (mean of ten chromatograms) with the aid of the usual conversion equation. The R~ values obtained for the elements tested for gastric absorption (except ethatlobarbital) were directly used to verify equation 1 through their comparison with the corresponding log k, series. Arbitrary ARm and Alogk~ values were then calculated from the differences between the experimental Rm or log k~ of each compound mentioned and the corresponding R m or log k, of each of all the remaining elements. The ARm and A log k~ series of values were then correlated to test the reliability of equation 2. To establish ARm values characteristic of functional groups (substituent ARm constants), the 14 elements were used. The Rm differences between compounds differing only in the single group considered (next homologues) were calculated (12); if a next homologue was absent, the AR,~ value early calculated for the proper single substituent was added to (or subtracted from) the Rm of the closest tested element in order to obtain more accurate mean ARm constants for each functional group. The R~ values for 5-ethyl-propyl, 5-allyl-propyl, and 5-ethyl-isopropyl derivatives, which were not commercially available, were assessed using this procedure. Only the comparison of all the possible pairs of next homologues able to be chromatographed in the selected system was thought to give a reliable mean AR~ constant for any substituent. Statistical deviations and errors, linear regression equations, and their correlation coefficients were calculated by means of a Programma 101 (Olivetti) computer. Parabolic correlations were assessed by means of a Hewlett-Packard calculator (model 9100B). RESULTS AND DISCUSSION The results of the chromatographic experiments are given in Table II. As can be seen from the reported statistical deviations, the reproducibility in our experimental conditions is quite good. The spots are circular, without any tailing, so that the measurement of Re values did not present any difficulty.

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Table II. Mean Rs and Rm Values of the Tested Barbiturates in the Selected Reversed-Phase Partition System, and Calculated Absorption Rate Constants Expressed as the Antilogarithms of the Figures Obtained by Substituting in Equation 7 the Rm Value for Each Particular Compound No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Barbiturate Barbital Ethallobarbital Heptobarbital Allobarbital Aprobarbital Secbutobarbital Phenobarbital Butobarbital Cyclobarbital Talbutal Idobutal Pentobarbital Amobarbital Secobarbital

Mean RI value 0.846 0.749 0.653 0.615 0.523 0.393 0.384 0.353 0,348 0.254 0,227 0.170 0.177 0.099

Standard deviation 0.011 0.013 0.018 0.016 0,019 0.018 0.014 0.014 0.014 0.013 0.012 0.005 0.007 0,004

Mean R,. value -0.741 -0.476 -0.274 -0.202 -0.040 +0.188 +0.205 +0.263 +0,273 +0.467 +0.533 +0,688 +0.666 +0.961

Calculated log k." - 1.2572 - 1,1522 - 1.0722 - 1,0437 -0,9795 -0.8891 -0.8824 -0.8594 -0.8554 -0.7786 -0.7524 -0,6910 -0.6997 -0,5828

Absorption constant, k. 0.055 0.070 0.085 0.090 0.105 0.129 0.131 0.138 0.140 0.166 0.177 0.204 0.199 0.261

aFrom equation 7.

R~/log k~ and

ARm/Alog

k. Correlations

The series of R~ values and the series of experimental ka values of the six elements considered (Table I) are correlated t h r o u g h equation 7 : log ka = 0.396. R,, - 0.964

(7)

Since the correlation coefficient found was 0.998 (P < 0.01), the validity of equation 1 is confirmed for this particular group of barbiturates. The calculated log k, and k, values for the 14 c h r o m a t o g r a p h e d elements according to equation 7 are shown in Table II. The c o r r e s p o n d e n c e between ARm and A log k, values was also excellent, as shown in Table III. By means of the "all pairs" procedure outlined above, the following e q u a t i o n relating the two series was established : A log k. = 0.406. ARm - 0.009

(8)

with a correlation coefficient of 0.993 (P < 0.01). E q u a t i o n 8 is a very near a p p r o x i m a t i o n to the theoretical one, which would be in this particular case A log k, = 0.396. ARm

(9)

O n the other hand, the correlation coefficient found between the calculated A log k, values (from e q u a t i o n 8) and their theoretical analogues (from e q u a t i o n 9) is 0.999. Therefore, the validity of e q u a t i o n 2 is confirmed. For practical purposes, equations 8 and 9 can be used equally well. The calculated and theoretical A log k. values are given in Table III.

Calculation of Gastric Absorption Rate Constants

121

Table III. Experimental ARmand A log k, Values Assessed from All Possible Pairs of Barbiturates

Tested for Gastric Absorption Plus Calculated and Theoretical A log go Values Shown to Illustrate the Validity of Equation 2 Pair compared

A R~a

Experimental A tog k,b

Calculated A log k,c

Theoretical A log k,~

1-12 1-13 1-9 1-7 4-12 4-I 3 1-4 7-12 4-9 7-13 9-12 4-7 9-13 7-9 12-13

+ 1.429 + 1.407 + 1.014 + 0.946 + 0.890 + 0.868 + 0.539 +0.483 +0.475 +0.461 +0.415 +0.407 +0.393 + 0.068 - 0.022

+0.564 + 0.566 + 0.428 + 0.406 + 0.324 + 0.326 + 0.240 +0.158 +0.188 +0.160 +0.138 +0.166 +0.138 + 0.022 + 0.002

+0.571 + 0.562 + 0.402 + 0.375 + 0.352 + 0.343 + 0.209 +0.187 +0.183 +0.178 +0.159 +0.156 +0.150 + 0.018 - 0.018

+0.566 + 0.557 + 0.402 + 0.375 + 0.352 + 0.344 + 0.214 +0.I91 +0.188 + 0.183 +0.164 +0.161 +0.155 + 0.027 - 0.009

"From the data of Table II. bFrom the data of Kakemi et al. (8), as shown in Table I. CFrom equation 8. eFrom equation 9. Substituent AR m Constants

T h e c h a r a c t e r i s t i c A R m values of the m a i n f u n c t i o n a l g r o u p s o r subs t i t u t i o n s in the m o l e c u l e o f the tested 5 - s u b s t i t u t e d b a r b i t u r a t e s , c a l c u l a t e d a c c o r d i n g to the " p a i r s o f next h o m o l o g u e s " p r o c e d u r e o u t l i n e d above, are additive. F r o m the series o f c h r o m a t o g r a p h i c d e v e l o p m e n t s achieved, only the A R m c o n s t a n t s for the s t r a i g h t - c h a i n - - C H 2 - - a n d - - C H - - C H - g r o u p s , 1 - b r a n c h e d - - C H 2 - - g r o u p , ethyl -~ allyl r e p l a c e m e n t , a n d straightc h a i n d o u b l e b o n d ( - - A - - ) can be safely established. T h e y have been assessed f r o m all p o s s i b l e p a i r s of next h o m o l o g u e s w h o s e Rm value can be a c c u r a t e l y d e t e r m i n e d in the system selected e x c e p t i n g the 5 - p r o p y l derivatives of b o t h the ethyl a n d allyl series a n d the 5 - e t h y l - i s o p r o p y l or 5-ethyl-(1-methyl)ethyl derivative, whose R,, values have been well a p p r o x i m a t e d , however. T h e AR,~ a n d A log k a c o n s t a n t s (as c o m p u t e d f r o m e q u a t i o n 9) for the m e n t i o n e d g r o u p s o r s u b s t i t u t i o n s are s h o ~ in T a b l e s IV to VI. Since all the p o s s i b l e pairs h a v e been considered, we h a v e a s s u m e d t h a t the small statistical e r r o r f o u n d is a n i n d e x r e l i a b l e e n o u g h for c o n f i r m i n g their additivity. C o n s e q u e n t l y , these m e a n values s h o u l d be c o n s i d e r e d as true c o n s t a n t s for each s u b s t i t u e n t c o n s i d e r e d . T h e A R m c o n s t a n t for the 5-ethyl ~ 5-phenyl r e p l a c e m e n t was c a l c u l a t e d with less accuracy, since fewer pairs of next h o m o l o g u e s were a v a i l a b l e for

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Table IV. Calculation of the Chromatographic ARm Constant Characteristic of the StraightChain --CH 2 - Substituent by Means of the Procedure of the Pairs of Next Homologues" Pair 3 7 1 8 2 11 5 10 6 12 10 14

Series Phenyl Ethyl Allyl Allyl Ethyl Allyl

Structural change

Rm

AR~

Methyl - 0.274 Ethyl + 0.205 + 0.479 Ethyl - 0.741 Butyl +0.263 + 1.00 Ethyl - 0.476 Butyl + 0.533 + 1.00 (1-Methyl)ethyl - 0.040 (1-Methyl)propyl +0.467 +0.507 (l-Methyl)propyl + 0.188 (1-Methyl)butyl + 0.688 + 0.500 (1-Methyl)propyl + 0.467 (1-Methyl)butyl +0.961 +0.494 AR,. (straight-chain --CH2--) = +0.499 (_+0.008)~

ARm (--CH2--) + 0.479 + 0.502b +0.502 b + 0.504b + 0.504b +0.507 c + 0.500 +0.494

A log k, (straight-chain --CH2--) = + 0.396 ARm = + 0.198 (+ 0.003) "The small statistical error assessed (e = 0.62~o) may be a good appraisal to substantiate the additivity of this parameter. bThe figures are the estimated ARm values between the ethyl and the propyl derivatives and between the propyl and the butyl derivatives of each series, expressed as one-half of the experimental ARm found between the ethyl and butyl barbiturates tested (i.e., 1-8 or 2-11). CThe ARm value between the pair of elements corresponding to the homologous ethyl series [probarbital or 5-ethyl-5-(1-methyl)ethylbarbituric acid and secbutobarbital or 5-ethyl-5(1-methyl)propylbarbituric acid] cannot be calculated since the former compound was unavailable. However, the eventual use of the parameters AR,~ (ethyl--,allyl) and ARm (l-branched --CH2--), which are, respectively, +0.271 and +0.430 (Tables V and VI), makes possible a quite reliable estimation of this value, since Rm (probarbital) = R,, (aprobarbital - ARm (ethyl~allyl) = - 0 . 0 4 0 - (+0.271)= -0.311 Rm (probarbital)= R,, (barbital)+ ARm (1branched --CH2-- ) = -0.741 + (+0.430)= -0.311. The estimated R m for probarbital is therefore -0.311. That gives for the ARm between probarbital and secbutobarbital a value of 0.499 (from -0.311 to +0.188), so that the mean ARm value obtained here for the straightchain --CH2-- substituent would not change. c o m p a r i s o n . F o r t h e n u c l e u s - a t t a c h e d p h e n y l g r o u p , o n e finds a ARm c o n s t a n t a b o u t f o u r t i m e s g r e a t e r t h a n for a single s t r a i g h t - c h a i n - - C H 2 s u b s t i t u e n t , as s h o w n in T a b l e VII. F r o m o u r c h r o m a t o g r a p h i c d a t a , t h e a b s o l u t e v a l u e s o f t h e AR,, c o n s t a n t s for t h e r e m a i n i n g f u n c t i o n s a r e o f m u c h m o r e d o u b t f u l r e l i a b i l i t y since o n l y o n e p a i r of n e x t h o m o l o g u e s has b e e n c o m p a r e d to c a l c u l a t e t h e m in e a c h i n s t a n c e . W e h a v e u s e c l ~ r e s u m p t i v e ARm v a l u e s for t h e 5-ethyl -~ 5c y c l o h e x e n y l r e p l a c e m e n t , as w e l l as for t h e n u c l e u s - a t t a c h e d c y c l o h e x e n y l s u b s t i t u e n t ( f r o m t h e Rm v a l u e s o f t h e e l e m e n t s I a n d 9), for t h e b r a n c h e d - - C H 2 - - g r o u p in p o s i t i o n o t h e r t h a n 1 ( f r o m t h e R,, v a l u e s o f t h e e l e m e n t s 8 a n d 13), a n d for a r i n g - p l a c e d d o u b l e b o n d ( a s s u m e d to be e q u i v a l e n t to o n e - h a l f o f t h e d i f f e r e n c e b e t w e e n t h e R,, v a l u e s of c o m p o u n d s 7 a n d 9). T h e last t w o v a l u e s a r e e s p e c i a l l y u n c e r t a i n , as will be d i s c u s s e d , since s u b s t i t u t i o n s in d i f f e r e n t p o s i t i o n s o n a n a l k y l c h a i n o r in a h o m o c y c l i c

Calculation of Gastric Absorption Rate Constants

123

Table V. Calculation of the Chromatographic A R m Constant for the 1-Branched - - C H 2 Substituent" Pair

Additions or subtractions

1 6 2 5 8 6 {12 1 10 8 12

--(--CHz--) ---

11

--

14

-(--CH2-- )

-+(--CH2 - ) -(--CH2--) -----

Series

Structural change

R m

ARm (found or calculated) (--1--CH2--)

Ethyl - 0.741 (1-Methyl)ethyl +0.188 -0.499= -0.311 Ethyl - 0A76 Allyl (1-Methyl)ethyl -0.046 Propyl +0.263 - 0.499 = -0.236 Ethyl (1-Methyl)propyl +0.188 Propyl\b f-- 0.476 + 0.499 -----+ 0.023 Allyl Propylj /.+0.533-0.499= +9.034 (1-Methyl)propyl + 0.467 Butyl + 0.263 Ethyl (1-Methyl)butyl +0.688 Butyl + 0.533 Allyl (l-Methyl)butyl +0.961 ARm (1-branched --CHz--) = +0.430 (__!0.005y Ethyl

A log k, (1-branched --CHz--) = 0.396 A R

m

+0.430 + 0.436 ' +0.424 9} +0.43 +0,425 +0.428

= +0.170 (+0.002)

"To assess its additive character, the ARm (straight-chain --CH2--) already established (Table IV) has been added to--or subtracted from--the R~ value of some tested barbiturates in order to include assumed Rm values for the unavailable members of the series (~ = 0.53 ~). bThe reference R,, value for the propyl derivative is assumed to be the mean of the two calculated Rm values (+0.028). ~The ARm value for the 1-branched --CHz-- substituent calculated by means of the three pairs of compounds directly available is also + 0.430. ring s h o u l d n o t necessarily p r o d u c e the s a m e v a r i a t i o n s in c h r o m a t o g r a p h i c p a r t i t i o n b e h a v i o r (11). W o r k is in p r o g r e s s to e l u c i d a t e this p o i n t t h r o u g h serial d e v e l o p m e n t s using several b r a n c h e d - c h a i n a n d 5 - h o m o c y c l i c b a r b i t u r a t e s as solutes, b u t we t h i n k that these p r e s u m p t i v e values are sufficiently o r i e n t a t i v e for the p u r p o s e s o f this p a p e r . T h e e s t a b l i s h e d a n d p r e s u m p t i v e ARm a n d A log ka c o n s t a n t s for s o m e f u n c t i o n a l g r o u p s a n d s u b s t i t u t i o n s a r e s h o w n in T a b l e VIII. If R,, a n d log ka values o f a reference e l e m e n t a r e t a k e n for calculations, they will afford a n excellent basis for the p r e d i c t i o n o f the R I a n d ka values o f n o n t e s t e d b a r b i t u r a t e s of the series m e r e l y by inspection of the f o r m u l a of the c o m p o u n d involved, as will be s h o w n later. Migration Mechanisms

By m e a n s o f the d e s c r i b e d r e v e r s e d - p h a s e technique, a full p r e v a l e n c e o f p a r t i t i o n over a b s o r p t i o n m e c h a n i s m s in c h r o m a t o g r a p h y is u n d o u b t e d l y achieved. I m p r e g n a t i o n with suitable l i p o p h i l i c m a t e r i a l s seems to result in an effective d e a c t i v a t i o n o f surfaces a n d a b s o r p t i o n sites o f the cellulosic substrate. M o r e o v e r , the use o f a c o m p l e t e l y d i s s o c i a t e d d i l u t e d acid as

AR m (--CH

2-

~.

--CH=CH--)

- 0.226

- 0.229

- 0.220

- 0.231

-0.228

-0.225

-0.234

ARm ( - - A - - ) b

and for the

"For the comparison of some pairs, the values AR~, ( - - C H 2 - - ) and AR,, (1-branched - - C H 2 - ) have been used in order to include assumed R , , values for the unavailable members of the series. Additivity can be assessed from the little statistical error (e = 0.59 ~). bComputed as the algebraic difference between A R m ( - - C H 2 - ~ - - C H = C H - - ) as found and A R m ( - - C H 2 - - ) as calculated. CThe reference Rm value for 5-ethyl-5-propyl and for 5-allyl-5-propyl derivatives is assumed to be the mean of the two calculated values. dThe A R m values for ( - - C H 2 - - , - - C H = C H - - ) and for ( - - A - - ) obtained directly from the five pairs directly available (+0.272 and -0.227, respectively) are virtually coincident with the values assessed from all possible pairs.

A log ka (straight-chain - - A - - ) = - 0 . 0 9 0 (___0.002)

0.741 + 0.265 0.476 0.476 - 0.274 0.202 -0.311 - 0.311 +0.271 - 0.040 + 0.499 = -0.242 - 0.499 -0.236 + 0.268 + 0,499 = +0.023 - 0.499 +0.034 + 0.188 + 0.279 + 0.467 + 0.263 + 0.270 + 0.533 + 0.688 + 0.273 + 0.961 AR m (straight-chain - - A - - ) = -- 0.228 ( + 0.004) ~

+ 0.430 = - 0.499

R,, (found or calculated)

A log ka (5-CH2-- --, 5 - C H = C H - - ) = +0.107 (__+0.002);

-

--

12

14

----+(I-CH2--) - (--CH2--) -+(--CH2-- ) -(--CH2--) +(--CH2--) -(--CH2-- ) -----

1 2 2 4 1 6 5 1 8 2 11 6 10 8 11

Structural change

Ethyl-ethyl Ethyl-allyl Allyl-ethyl Allyl-allyl Ethyl-0-methyl)ethyl f-0.741 Ethyl-(1-methyl)ethyl L+ 0.188 Allyl-(1-methyl)ethyl Ethyl-propyl\ S-0.741 Ethyl-propyl)'~ \+0.263 Allyl-propyl], f-0.476 Allyl-propylf "/+0.533 Ethyl-(1-methyl)propyl Allyl-(1-methyl)propyl Ethyl-butyl Allyl-butyl Ethyl-(1-methyl)butyl Allyl-( l-methyl)butyl A R m (5-CH 2 - ~ 5 - C H = C H - - ) = +0.271 (•

Additions or subtractions

Pair

Table VL Values of the Chromatographic ARm Constants for the 5-'Ethyl -~ 5-Allyl Replacement (i.e., - - C H 2 - ~ - - C H = C H - - ) Straight-Chain Double Bond (i.e., - - A - - ) "

o

~"

~,

,~"

-(--CH 2- -, --CH=CH--) --

2 7

-@--

+0.959(+0.012)r

- 0 . 4 7 6 -- 0.271 = --0.747 +0.205

- 0 . 4 7 6 - 0.770 = -- 1.246 - 0.274

@

= +0.775 (+0.005)

= +1.96(_+0.012)

+ 0.952

+0.972

+ 0.946

+0.966

AR,, ( - - C 2 H 4 - --,

)

+ 1.95

+ 1.97

+ 1.94

+ 1.96

~ _ AR,,, (

)b

q n order to include some single m e m b e r s of both the 5-ethyt and the 5-allyl series as comparison terms, tile A R m ( - - C H 2 - - ) and the ARm ( - - C H 2 - - -~ - - C H = = C H --) have been used. Even so, the m e a n AR,, values reported should be considered as less accurate than the previously calculated ones ('Fables IV to VI). hCalculated as the algebraic s u m of ARm (ethyl --+ phenyl) as found and two AR m ( - - C H 2 - ) as calculated. CThe A R m (ethyl ~ phenyl) calculated from the only pair directly available would be + 0.946.

A log ka ( - - C 2 H 4 - -

O, 7 4 1

+ 0.205

-

--0.741 -- 0.499 = -- 1,240 -0.274

R,, (found or calculated)

) = +0.380 (__+0.005); A log k, @ - )

Ethyl-ethyl Ethyl-phenyl

AR,,, ( - - C 2 H 4 - -~ ~ - ) =

-(--CH2-- ~ CH=CH--) -(--CH2--7)

2 3

Methyl-ethyl Methyl-phenyl

Ethyl-ethyl Ethyl-phenyl

--

7

1

Methyl-ethyl Methyl-phenyl

(--CH 2-)

Structural change

--

--

Subtractions

1 3

Pair

Table VII. Calculation of the C h r o m a t o g r a p h i c ARm Constant for the 5-Ethyl -+ 5-Phenyl Replacement, as Well as for the Nucleus-Attached 5-Phenyl Substituent"

o

o

>

~~

=,,

r

126

Pl~-Delfina, Moreno, DurUm, and de| Pozo

Table VIII. Experimental R,, and Log k, Values Found for the Basic Molecule (i.e., Barbital or 5-Diethylbarbituric Acid) and ARm and A log ka Constants Found for Some Functional Groups or Modifications by Means of the Procedure of the Pairs of Next Homologues, as Outlined in the Text H O~c;N;c//O CHa--CH~ N [ /C~| CH3--CH 2 C

1 ~.

II

H

O Basic structure: R,, = -0.741, log k, = - 1.275 Functional group or modification

ARm

A log k,

Straight-chain - - C H 2 Straight-chain - C H = C H - Straight-chain - - s (aliphatic) Straight-chain - - A - - (ring)~

+0.499 + 0.770 - 0.228 -0.031

+0.198 + 0.305 - 0.090 -0.012

Straight-chain @

+ 1.96

+0.775

+2.012

+0.797

Straight-chain

+ 2.456

+ 0.973

1-branched - - C H 2 Branched - - C H 2 - (other than 1)a

+0.430 +0.403

+0.170 +0.160

5-Ethyl --, 5-allyl 5-Ethyl ~ 5-phenyl 5-Ethyl ~ 5-cyclohexenyl" 5-Allyl ~ 5-phenyl 5-Allyl ~ 5-cyclohexenyl"

+0.271 +0.959 + 1.014 + 0.688 + 0.743

+0.107 +0.380 + 0.402 + 0.273 + 0.294

Straight-chain ~

"

aPresumptive values.

solvent might result in additional binding of active points of cellulose before the migrating solutes could come in contact with them. On the other hand, this strong solvent-substrate affinity in spite of previous impregnation can account for the occurrence of demixing. Not only the selected stationary phase (constituted chiefly of triglycerides and other esters of ricinoleic acid) has been shown to be effective for achieving this purpose. Selected mixtures of some other moderately polar lipophilic materials, such as natural and semisynthetic unsaturated and low fatty acid glycerides, sorbitan monooleate, isolecithins, and alcohol-soluble silicones, have also led to good results, although care should be taken in adjusting the composition of mixtures in order to obtain sufficiently accurate R,, values for the compounds tested (for practical purposes, this is reached

Calculation of Gastric Absorption Rate Constants

127

when R/values range from 0.10 to 0.90 or less). The Miglyol 812 (Dynamit Nobel) and Rhodorsil 3322 (Rh6ne-Poulenc) 1 : 1 mixture is a good example of an alternative stationary phase with which ARm constants like those reported in Table VIII have been obtained, with only the standard deviations being slightly greater. The entire predominance of partition phenomena in the reversed-phase chromatographic system described becomes apparent when the additivity of the ARm constants for the main functional groups is considered (Tables IV to VI) as well as the correlations between the found Rmvalues and the bulk-phase partition coefficients taken from the literature (7,8). Since the log P values for most solvents are linearly related for true homologous series (13), this becomes a strong basis to account for the role of partition in chromatography (Figs. 1 and 2).

r 1.ot o,sf \\ 0.2

0.1 F.

8 0.02

08 Rm value

I 0.6

~ 0.4

[ 0.2

0I

P 0.2

04!~

01.6

~--~ 0.8

Fig. 1, Correlation between the partition coefficient of s o m e t e s t e d barbiturates in tetrachloromethane-pH 1.1 buffer solution [data from K a k e m i et aL (8)] and the R , , value found in two chromatographic partition systems: (a) the reversed-phase system s e l e c t e d (black circles) and (b) a direct-phase system based on formamide-impregnated Kieselguhr plates and chloroform-tetrachloromethane ( 2 : 1 , v/v) as solvent (white circles). The equations relating the two constants are R e v e r s e d - p h a s e s y s t e m : log P = 0 . 9 9 . R,, - 0.75 Direct-phase system : log P = - 1.66- R,, - 0 . 3 6

(r = 0.996) (r = 0.992)

N o t e the deviation of e l e m e n t 7 (phenobarbital) from the regression line draft for the direct-phase system. For the derivation of the corresponding equation, e l e m e n t 7 has b e e n o m i t t e d . (Numeration is according to Table l.)

128

Pl~-Delfina, Moreno, Dur~n, and del Pozo

200

100

50

20

g_

\\\\,,,.,~

10

\

5 ~_ 5 3

[

-0.8

l

-06

I

-0.4

L

I

-0.2

0

I

+0.2

I

+0,4

L

+0.6

[

+0.8

I

+1.0

Fig. 2. Same as Fig. 1 except that the partition coefficients of the tested barbiturates between n-octanol and water [data from Hansch and Anderson (7)] have been used for correlation with Rmvalues. The equations are Reversed-phase system (black circles): log P = 0.95. R,, + 1.27

(r = 0.990)

Direct-phase system (white circles): log P = - 1.57 9Rm + 1.64

(r = 0.992)

Again, the 5-phenyl-substituted barbiturates (phenobarbital and heptobarbital) are out of the regression line drawn for the direct-phase system correlation; in deriving the corresponding equation, the elements 3 and 7 have been omitted. (Numeration is according to Table I.) The chromatographic behavior of the 5-phenyl-substituted barbiturates (phenobarbital and heptobarbital) is also highly illustrative in connection with this: these compounds, probably due to the planar character of the benzene ring, appear to be strongly adsorbed on the usual chromatographic substrates in direct-phase chromatograms, even on those in which partition is known to be the main migration mechanism (5). Such compounds could not be fitted along the regression line relating R,, and log P in any aqueous direct-phase system tested by us on several usual substrates. Apparently, not even the previous impregnation with highly polar stationary phases (i.e., formamide) is sufficient to eliminate the adsorption effects described. Consequently, any correlation between Rm and log k, for 5-phenyl-substituted c o m p o u n d s becomes difficult in direct-phase chromatograms, in which, however, the 5-alkyl-substituted ones are frequently well fitted. However, in the reported reversed-phase systems, the two 5-phenylbarbiturates

Calculation of Gastric Absorption Rate Constants

129

tested, p h e n o b a r b i t a l a n d h e p t o b a r b i t a l , b e h a v e like the r e m a i n i n g terms~ This could indicate a critical i m p r o v e m e n t in p a r t i t i o n c o n d i t i o n s d u r i n g chromatography. The phase effects o n the b e h a v i o r of the b a r b i t u r a t e s tested relative to their p a r t i t i o n coefficients in the selected b u l k solvents are illustrated in Figs. 1 to 3 t h r o u g h two representative series of chromatogramso O n the basis of the concepts outlined, the p o o r fit of p h e n o b a r b i t a l a l o n g the line

100 7O

3

/'0 -0.8

-0.6 Rm va{ue

-0.4

-0.2

0

+0.2

+0.4

~0.6

Fig. 3. Same as Fig. ! except that the partition coefficients of the barbiturates between isopentyl acetate and pH 1.1 buffer solution have been

used for correlation with the Rmvalues. Correlations in the reversed-phase system have been made with and without three 1-methyl-substituted barbiturates to illustrate the analogies between the isopentyl acetate and the stationary phase used for impregnation. The equations are Reversed-phase system (black circles): log P = 0.979. R,, + 1.378

(r = 0.996)

(continuous line, excluding 1-methyl compounds) log P = 0.908. R~ + 1.40

(r = 0.964)

(dotted line, including 1-methyl compounds) Direct-phase system (white circles): log P = - 1.59. R,, + 1.73

(r = 0.976)

It can be seen that 1-methyl-substituted barbiturates are fitted together with the nonmethylated ones. The behavior of the 5-phenyl-substituted barbiturates in the direct-phase system is identical to that in the former solvents. (Numeration is according to Tables I and IX.)

130

PIh-Delfina, Moreno, Durfin, and del Pozo

relating log k, and R,, values in direct-phase paper partition c h r o m a t o g r a m s (6) can easily be explained, whereas the s o m e w h a t a n o m a l o u s position of barbital on the plots should be attributed to unavoidable errors in the R~, calculation arising from the extremely low R I values assessed in m o s t paper chromatograms. In c o n n e c t i o n with this, an unusually interesting point is the different behavior of the 1-methyl-substituted barbiturates with respect to the tested ones in reversed-phase partition c h r o m a t o g r a m s . T h r o u g h our experience it has been assessed that only the latter (nonmethylated) series is consistent with e q u a t i o n 7. T h e 1-methylbarbiturates are apparently fitted by a rather similar e q u a t i o n with a considerably greater a intercept, so that they seem to behave as members of another true h o m o l o g o u s series, as shown in Fig. 4,

0"40I 0.30f

0"20I

g

0.1I0

c9 0.0I5 - 08 - 0.6 Rrn value

- 0.4

- 0.2

0

§0.2

+ 0,4

§ 0.6

+0.8

Fig. 4. Correlations between Rmand gastric log k, experimentally found for two different series of barbiturates. The nonmethylated elements are fitted by equation 7, whereas the 1-methyl-substituted compounds tested are fitted by the following equation : log k, = 0.337- Rm - 0.660

(r= 1.00)

In spite of the excellent correlation coefficient found and since only three elements of the series have been investigated, the equation should be considered as an approximation. The different behavior of the mentioned series of barbiturates seems, however, to be consistent with partition, as outlined in the text.

Calculation of Gastric AbsorptionRate Constants

!31

although, in spite of the excellent fit obtained, the number of 1-methylbarbiturates chromatographed was far too insufficient for any statistical comparison against available log k, values, and, consequently, the suggested regression equation should be considered as only an approximation. Contrary to what occurs in direct-phase chromatography, the mentioned behavior would not indicate that an absorptive process is involved in reversedphase chromatography since it can be easily explained in partition terms. It has been shown in the bulk-phase partition coefficient measurements that some proton-acceptor solvents (i.e., isopentyl acetate) give a separate fit for tile two mentioned series, whereas some proton-donor or inert solvents (i.e., tetrachloromethane and chloroform) fit both series together (14). Since it has only proton-acceptor functional groups, it can be reasonably assumed that the lipophilic impregnating phase behaves like the former solvents and therefore that this behavior is consistent with partition. It can be explained assuming hydrogen bond interactions between the ester group of the impregnating fat molecules and the --NH--groups of the barbiturates ; since the 1-methylation should block the proton-donor capacity of the - - I - N H - - group, the mentioned interactions will mainly affect the nonmethylated elements, which consequently will show a lowered migration velocity. It is obvious that the ARm (nucleus-attached - - 1 - - C H 2 - - ) constant must be much lower in absolute value than expected from log k, measurements. From the R,, values experimentally found for barbital, heptobarbital, phenobarbital, and their 1-methyl-substituted homologues, a presumptive ARm(nucleus-attached --1-CH2--) constant of + 0.436 was found (Table IX), a value three times lower than could be assumed from the reported gastric absorption constants (8). For practical purposes, it should be borne in mind that the reversed-phase chromatographic determination of the nucleusattached --1-CH2-- group does not reproduce the actual influence this substitution has in gastric absorption, and consequently care should be taken in applying the proper equation to each series of barbiturates in order to calculate their gastric absorption constants. The practical implications of this phenomenon will be discussed later. Prediction of Migration Velocities and Absorption Rate Constants

The migration and gastric absorption characteristics of" nontested 5substituted barbiturates can be well approximated through the rational use of the substituent ARm constants (Table VIII) by a mere inspection of their constitutional formulas. For this purpose to be achieved in full, a proper structural R,. reference value must be chosen in order to avoid potential deviations from linearity of ARm constants due to steric or electronic interactions.

Metharbital

Heptobarbital

Methylheptobarbital

Hexobarbital

Phenobarbital

Mephobarbital

3

16

17

7

18

1-Methyl 5-Met hyl-cyclohexenyl 5-Ethyl-phenyl 1-Methyl 5- Ethyl-phenyl

5-Methyl-phenyl 1-Methyl 5-Methyl-phenyl

5-Ethyl-ethyl 1-Methyl 5-Ethyl-ethyl

Substituents

0.191

0.382

0.338

0.399

0.643

0.647

0.840

Rs value

+ 0.627

+ 0.209

+0.292

+0.178

-0.256

- 0.263

-0.720

R,, value b

0.354

0.135

0.276

--

--

0.178

0.053

Gastric absorption constant c

+ 1.5

+ 0.237

+ 1.19

--

+ 0.637

-0.787

Presumed R,, value d'e

0.029

0.367

0.061

0,0,74~

0.187

0.860

Presumed R f value d

*In the last columns, under the headings "presumed value," the theoretical Rj- and R,. values which would be obtained for the compounds according to their gastric absorption rate constants are shown (equation 7 has been used to calculate them). It can be seen that the actual ARm (nucleus-attached - - I-CH2-- ) constant has a presumptive value of + 0.436, whereas the same "presumed" constant would be about + 1.357. Therefore, if the partition chromatographic behavior of the 1-methyl-substituted barbiturates exactly reflects their absorption characteristics, the extremely low R s values of most elements would be unsuitable for the R m calculation, bThe AR m (--1-CH2--) constant has a mean presumptive value of + 0.436, as calculated from the pairs of next homologues 1-15, 3-16, and 7-18. ~Data from Kakemi et al. (8), expressed in h r - t. dRs and R,, values calculated according to the gastric absorption rate constants by means of equation 7. ~The AR m ( - - I - C H 2 - - ) constant would have a presumptive mean value of + 1.357, as calculated from the pairs 1-15 and 7-18. IEstimated value (actual R,, - 0.436 + 1.357, converted to RI).

Barbital

1

Barbiturate

l5

No.

Table IX. Mean Ry and R,n Values Found for Some 1-Methyl-Substituted Barbiturates and Their Nonmethylated Homologues in a Series of Developments Other Than Reported in Table II but Using the Same Selected Reversed-Phase System"

~. ~. e,

~,

o

Calculation of Gastric Absorption Rate Constants

133

For several reasons, the 5-diethylbarbituric acid molecule (barbital) is the best reference standard for these types of calculations. Disubstitution shields interactions on the 5-C atom and adjacent groups (7); the use of a 5-disubstituted element instead of barbituric acid should therefore prevent the classical first-element deviations (11). Since the stated interactions can sometimes affect the second chain-substituent (12), the 5-diethyl derivative should be considered as a better reference compound than the 5-dimethyl derivative for the calculation of the ARm constant. Finally, in the partition system selected, the R I values of both the barbituric acid and its 5-dimethyl derivative (being about 1.00 and 0,98, respectively) are unsuitable for any reliable comparison. For practical purposes, the chromatographic behavior of any particular barbiturate can be predicted by merely adding the characteristic AR,, constant of each added group to the R,, of barbital and converting into RI the R,, value obtained. By substituting the predicted R,, value into equation 7, the log ka value for any unknown can be calculated; the antilogarithm of this value will be the predicted gastric absorption rate constant of the barbiturate under consideration. The usefulness of the substituent ARm values for the prediction of the absorption rate constants becomes more apparent if one considers that the k, value prediction range includes elements whose R,, values cannot be assessed from the chromatograms but are easily and accurately calculated by this procedure. In Table X, the predicted R,,, RI, and k~ values of several tested and nontested barbiturates are shown. Although in the case of the elements tested excellent concordance between experimental and predicted values was found (n = 14, r = 0.999 for Rm; n = 7, r = 0.998 for log k~ (P < 0.01 in both cases), previous to any generalization it should be borne in mind that the absolute values of the ARm constants assumed for some functional groups or substitutions are only approximate and that even the wellestablished ARm constants could not be completely true in all instances: it can be observed that the ARm (--CH2--) calculated from the first pair (which includes a 5-methyl-substituted element No, 3 or heptobarbital) and the ARm (--CH2--) calculated from the remaining pairs are slightly different (Table IV). This can be a true deviation from Martin's equation (11) since the ARm value is assumed to be constant only if successive groups are added sufficiently far removed from any potentially interacting structure (12). Therefore, if the AR,. value obtained from the first pair of elements had been omitted from the calculations, the mean AR,, ( - - C H 2 - - ) constant found would have been slightly greater. The smallness of the difference makes this effect negligible in the present case but may be significant in others: for example, a phenyl group added in terminal position to a straight chain could

Hexethal

Secobarbital

Pentobarbital Amobarbital

Butobarbital Cyclobarbital Butalbital

Phenobarbital

Secbutobarbital

Barbital Probarbital Allobarbital Aprobarbital

C o m m o n name

R,n - 0.741 -0.311 -0.199 -0.040 +0.166 +0.188 +0.188 +0.215 +0.257 +0.257 +0.273 +0.437 +0.618 +0.687 +0.665 +0.755 + 0.958 + 0.985 + 1.10 + 1.14 + 1.16 + 1.26 + 1.26 +2.07

value a 0.846 0.672 0.612 0.523 0.404 0.393 0.393 0.379 0.357 0.357 0.348 0.268 0.194 0.170 0.178 0.150 0.099 0.094 0.074 0.067 0.064 0.053 0.053 0.008

Predicted Rf value a 0.055 0.082 0.091 0.105 0.126 0.129 0.129 0.132 0.137 0.137 0.140 0.162 0.191 0.203 0.199 0.216 0.260 0.267 0.295 0.308 0.314 0.341 0.341 0.719

Predicted absorption constant k, ~ 30.9 61.7 61.7 102.3 ---104.7 -251.2 173.8 257.0 707.9 831.8 660.7 660.7 -660.7 660.7 2512.0 -1318.0 -5012.0

1/Cb Inhibition of Arbacia egg cell division

---3020.0 -691.8 --

--2512.0 ---

5623.0

--

4266.0 4266.0 4266.0 2884.0 3548.0 5248.0 --

1230.0 1995.0 --

1/C b Hypnotic activity

1549.0

-229.1 -631.0 -631.0 -1175.0 1318.0

20.9 77.6 -257.0 --

1/Cb Inhibition of brain oxygen consumption

----

--

--

912.0 -398.1 436.5 --3236.0 3311.0

-

91.2 ----

1/Cb Inhibition of N A D H oxidation

"Calculated on the basis of the substituent chromatographic constants AR m or A log ka (Table VIII). bData from different authors, tabulated and correlated with log P (octanol-water) in Hansch and Anderson (7). The figures are the antilogarithms of the reported values. The compounds omitted by the authors in deriving the equations relating log P and log 1/C values have been omitted here also, as well as some other terms containing functional groups for which the AR,, constant has not been assessed (methallyl derivatives).

Ethyl, ethyl Ethyl, isopropyl Allyl, allyl Allyl, isopropyl Ethyl, isobutyl Ethyl, (1-methyl)propyl Propyl, isopropyl Ethyl, phenyl Propyl, propyl Ethyl, butyl Ethyl, cyclohexenyl Allyl, isobutyl Ethyl, (1-ethyl)propyl Ethyl, (1-methyl)butyl Ethyl, isoamyl Ethyl, amyl Allyl, (1-methyl)butyl Allyl, benzyl Ethyl, (1,3-dimethyl)butyl Isopropyl, benzyl Propyl, isoamyl Ethyl, hexyl Eutyl, butyl Ethyl, (2-ethyl)hexyl

5,5-Substituents

Predicted

Table X, Predicted Rm Values (Column 3), Migration Velocities in the Reversed-Phase System Selected, Expressed as R I Value (Column 4), and Gastric Absorption Rate Constants in situ (Column 5) of Some Barbiturates Tested for Pharmacological Activity, Expressed as 1/C (Columns 6 to 9)

O

O

,w,

Calculation of Gastric Absorption Rate Constants

135

not produce the same Rm increment as this group does when added directly to the barbituric acid nucleus. This factor of error could arise in the Rm prediction of the 5-benzyl-substituted compounds in Table X since the ARm ~ constant has been calculated from the 5-phenyl-substituted ones (Table VII). Similarly, the assumed ARm (2-branched --CH2-- ) could not be the same as the ARm (3-branched --CH2--) calculated from the compounds 8 and 13; this can affect the calculated Rm values for the 2branched compounds in Table X. All these differences can be cleared up through a careful chromatographic partition study with suitable barbiturates in the series tested. Here, we intended only to substantiate the possibility of predicting the k, values of unknowns approximately enough for pharmacokinetic purposes and to correlate the predicted Rm or log k, values with some pharmacological effects. The experimental errors inherent in partition coefficient calculations do not seem to be significant since the random errors in pharmacological tests are usually much larger anyway, as Hansch and Anderson (7) have pointed out. Pharmacological Implications

It has been shown (7) that, in the case of the 5-substituted barbiturates, for which the spread in the degree of ionization is small and significant effects due to steric or electronic interactions are not to be expected, good correlations can be established between pharmacological activity (expressed as log 1/C) and bulk-phase partition coefficient (expressed as log P). They may be linear or parabolic, depending on the pharmacological effect considered and on the features of the compounds handled. Most of the 1/C values are indicated in Table X; correlations found are illustrated in Table XI. The same type of correlations should exist between log k~ (or Rm) and log 1/C values. This becomes obvious from the classical work of Collander (9), which correlated log P with penetration rates through vegetal tissues for different compounds, and, in the particular case of barbiturates, from the more recent paper of Kakemi et al. (8), in which a linear correlation between log k~ and log P for some compounds was shown. However, the number of 5-substituted elements included in the last-mentioned paper is perhaps insufficient for reliable statistical comparison against available log 1/C values (7). From the data herein outlined, the log k~ values for almost all the compounds tested for pharmacological activity might be predicted through the use of substituent ARm constants. Since the introduction of a term for pK, in the equations relating log 1/C and log P does not significantly improve the correlation coefficients (7), our predicted k~ values--indicated in Table X, as well as the Rm ones---can be correlated with log I/C in spite of the fact that the latter parameters were obtained at neutral or slightly alkaline pH.

136

Phi-Delfma, Moreno, Dunin, and del Pozo

Table XI. Equations Relating Pharmacological Activity of Some 5-Substituted Barbiturates a No.

Effect

n

1

Inhibition of Arbacia egg cell division

19 17 17

log 1/C = 0.801 9log P + 1.076b log 1/C = 0.861. Rm + 2.090 log 1/C = 2.171 9log ka + 4.182

0.960 0.962 0.962

Inhibition of brain oxygen consumption

10 10 10

log 1/C = 1.037. log P + 0.959 b log 1/C = 1.052. R,, + 2,280 log 1/C = 2.650- log k, + 4.835

0.956 0.970 0.970

3

Hypnotic activity

11 11 11

log 1/C = - 0.630 - (log P) 2 + 2 . 0 9 2 . 1 o g p + 1.918 b 0.986 log 1/C = -0.563.(Rm) 2 + 0 . 3 5 4 . R m + 3.575 0.986 log 1/C = - 3.568. (log ka)z - 5.997. log ka + 1.110 0.986

4

Inhibition of N A D H

6 6 6

Correlation equation

log 1/C = 1.107. log P + 1.237 b log 1/C = 1.072. Rm + 2.623 log 1/C = 2.695. log k a + 5.220

r

0.921 0.928 0.928

aExpressed as the log' I/C value obtained from four different series of tests, with (a) their partition coefficients between octanol and water, expressed as log P, (b) their predicted R~ values in the reversed-phase partition system selected, and (c) their predicted absorption rate constants, expressed as log ka. The correlations are linear for effects 1, 2, and 4, and parabolic for effect 3. It can be seen that, as parameters, the R,, or log ka predicted values are as g o o d - - i f not b e t t e r - as partition coefficients for the establishment of structure-activity correlations. bData from Hansch and Anderson (7).

From correlations in Table XI, it can be observed that the nature of the relationships is identical for both log ka (or Rm) vs. log 1/C and log P vs. log 1/C. A linear correlation is already good for effects 1,2, and 4 (probably in the category of in vitro tests) and a parabolic correlation is found for effect 3 (a test in a whole organism). By means of the ARm constant procedure, the correlations between log ka and log 1/C values arising from equations 5 and 6 are therefore substantiated for the 5-substituted barbiturates. It can be observed that the log ka value becomes a linear function of the activity for some pharmacological effects, so that the direct measurement of ka could have, in these instances, an immediate application to the study of structure-activity relationships. On the other hand, it can be observed that the Rm values and their linear functions log ka are slightly better correlated with log 1/C values than are log P values (Table XI). This seems to support the observation made by Dearden and Tomlinson (4) that the chromatographic R m o r ARm constants emerge as better parameters than partition coefficients for being correlated with pharmacological effects, at least in particular instances. This improvement is properly attributed by the authors to the dynamic conditions which prevail in chromatography rather than to the accuracy and reproducibility

Calculation of Gastric Absorption Rate Constants

137

of experimental measurements. It can be added here only that the careful selection of proper stationary and mobile phases might have much to do with obtaining satisfactory correlation coefficients. In this particular case, at least, the selected reversed-phase systems seem to afford partition conditions for all the barbiturates tested; this is not accomplished by other types of partition systems. Advantages and Limitations of the Procedure

The method outlined for the calculation of the gastric absorption rate constants can undoubtedly avoid in many cases the rather cumbersome techniques necessary to perform the bulk-phase partition coefficient determinations, by substituting them for a ready ad simple standard chromatographic development or a short series of them. At the same time, more precision in the calculated k, values would probably be achieved; comparison of the correlation coefficients found between experimental log k, and log P values in the best reported solvent (8)--n = 7, r = 0.921 including ethallobarbital; n = 6, r = 0.987 excluding it--and between the log k~ and R,, values in the selected reversed-phase chromatographic system--0.936 and 0.998, respectively--seems to give evidence for it in the case of the 5-substituted barbiturates. The analogy of the chromatographic reversed-phase partition processes and some absorption mechanisms in vivo has been recently emphasized by Wagner and Sedman (15) through the similarities in the equations governing both processes. Contrarily, a possible limitation of the chromatographic procedure may be that, as far as the direct calculation of k, from R,, is concerned, the number of elements chromatographed should necessarily be scanty, whereas the bulk-phase log P determinations can be carried out without any practical limitation. The previous establishment of substituent ARm constants for the main functional groups is an alternative procedure to enlarge the k, calculation range in most cases. The already mentioned behavior of the 1-methyl-substituted barbiturates with respect to the nonmethylated ones (which means the establishment of t w o different regression equations relating log k, and R,, values) could also be considered as an essential disadvantage of the chromatographic procedure outlined. For practical purposes, however, this is not so : if the migration differences between the two barbiturate series were-to exactly reflect the gastric absorption differences, the chromatographic development of both series of compounds together would be unfruitful due to the extremely low migration velocity the 1-methyl-substituted compounds would show, so that the R s values would be unsuitable for R,, calculations, as illustrated in Table IX. Since the actual ARm (--1-CH2--) constant is three times lower,

138

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the calculation of k, from the R,, values can be readily made for most 1methyl-substituted barbiturates, provided that the appropriate equation was applied. If more pairs of next homologues were available and a proper statistically verified equation was established, the gastric absorption constants for any nontested 1-methyl-barbiturates could be predicted. Another point of interest is the possible extrapolation of the outlined correlations between chromatographic Rm and gastric log k, values to absorption sites other than stomach. The absorption process of barbiturates from the stomach, as occurs from other slow-absorbing sites, is known to be consistent with the pH partition hypothesis (8, 16, 17). The small intestine, however, appears to behave in a rather different way as far as absorption is concerned, since linear correlations between log P and intestinal log k a values have not been substantiated (17, 18). Consequently, care should be taken before generalizing the outlined criteria. To test the relationships between the R,, values of 5-substituted barbiturates and absorption rate constants other than gastric, a new series of reversed-phase chromatograms was developed using a weakly acidic solution as solvent on cellulose plates according to the technique already described. The stationary phase was castor oil alone, whereas the mobile phase was a Clark-Lubs phosphate buffer of p H = 6.0. The results are summarized in Table XII. From them, a linear correlation was assessed between the R,, values and the percentages of drug absorbed from the colon at fixed time intervals as reported by Schanker (16) for a number of 5-substituted barbiturates (n = 7, r = 0.988, P < 0.01), but not between the R,, values and the absorption rate constants experimentally found by Kakemi et al. (18) in the rat small intestine (n = 8, r = 0.277 including cyclobarbital; n -- 7, r = 0.317 if this compound is excluded). Kakemi et al. (18) interpret the intestinal absorption of barbiturates on the basis of a binding process to the proteins of the absorptive mucosal surface, so that the formed weak complex would be easily dissociated in favor of the serosal direction (18). The good correlations found between the percentages of drug absorbed and the percentages of drug bound at fixed time intervals enable the authors to postulate binding to the mucosa as the determining step in the absorption of several nonionized and ionized substances (19). In such a case, the absorption conditions will be difficult to reproduce by means of partition and even adsorption chromatography, as well as by means of bulk-phase-partition measurements. The parabolic correlation between intestinal log ka and R m values (Table XII) is an improvement over the linear correlation, and it becomes statistically significant (r = 0.937) when cyclobarbital is excluded from the regression analysis, so that log k,, = - 0 . 1 9 6 . R~ + 0.106.

R m

-t- 0.151

(10)

Calculation of Gastric Absorption Rate Constants

139

Table XlI. Rf and R~ Values in a Reversed-Phase Partition System Developed

with a Slightly Acidic Solvent and Absorption Velocities in Sites Other Than Stomach"

Barbiturate

Rf valuC

Rm valueb

Absorption in colonc

Intestinal absorption constanr

Barbital Ethallobarbital Heptobarbital Allobarbital Aprobarbital Secbutobarbital Phenobarbital Butobarbital Cyclobarbital Talbutal Idobutal Pentobarbital Amobarbital Secobarbital

0.808 0.713 0.618 0.582 0.491 0.359 0.373 0.320 0.336 0.236 0.209 0.152 0.164 0.088

-0.624 -0.395 -0.209 -0.144 +0.015 +0.252 +0.225 + 0.327 +0.296 + 0.511 +0.578 +0.750 +0.707 + 1.015

12 ---17 -20 24 24 --30 -40

1.014 1.205 -1.320 --1.569 -1.094 --1.279 1.260 1.188

"The absorption from colon is linearly related to R,, values, whereas intestinal absorption constants show an apparently parabolic relationship with R,, values. bReversed-phase system on cellulose plates. Stationary phase: castor oil. Mobile phase: phosphate buffer (pH = 6.0). Preparation and development according to the described technique. cPercentages of drug absorbed from colon at fixed time. From Schanker (16). eIn hr -t, Data from Kakemi et al. (18). A c c o r d i n g to e q u a t i o n 10, the p r o b a b i l i t y of r e a c h i n g the general c i r c u l a t i o n for a b a r b i t u r a t e s h o w i n g a very low o r very high p a r t i t i o n coefficient (or R,, value) will be small, so t h a t there will be an o p t i m u m h y d r o p h i l i c l i p o p h i l i c b a l a n c e for intestinal a b s o r p t i o n . This c o n t r a d i c t s the s t a t e m e n t of W a g n e r a n d S e d m a n (15) t h a t t r a n s p o r t o u t of the m e m b r a n e is ind e p e n d e n t of the p a r t i t i o n coefficient. But it is n o t irrelevant to a s s u m e that a c o r r e c t e d c o r r e l a t i o n p r o p e r l y a c c o u n t i n g for kum (the diffusion rate c o n s t a n t at the serosal layer) c o u l d e x p l a i n the e x p e r i m e n t a l d a t a better. If it c o u l d be d e m o n s t r a t e d , the c h r o m a t o g r a p h i c p a r t i t i o n p r o c e d u r e s , as well as the b u l k - p h a s e p a r t i t i o n coefficient m e a s u r e m e n t s , c o u l d a t t a i n a general a p p l i c a t i o n as a l t e r n a t i v e m e t h o d s for c a l c u l a t i n g the a b s o r p t i o n b e h a v i o r of b a r b i t u r a t e s a n d o t h e r c o m p o u n d s . ACKNOWLEDGMENTS T h e a u t h o r s are i n d e b t e d to P r o f e s s o r J o a c h i m K n a b e , U n i v e r s i t y o f S a a r b r t i c k e n (West G e r m a n y ) , for s e n d i n g s o m e n o n c o m m e r c i a l s a m p l e s of 1 - m e t h y l - s u b s t i t u t e d b a r b i t u r a t e s . T h e a u t h o r s t h a n k B a m a S.A.

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Plfi-Delfina, Moreno, Durfin, and del Pozo

( B a r c e l o n a , Spain), Bayer M e d i c a m e n t o s ( B a r c e l o n a , Spain), B e r g c h e m i e ( L t i d e n s c h e i d , W e s t G e r m a n y ) , C i b a S.A. ( B a r c e l o n a , Spain), D u m e x A / S ( C o p e n h a g e n , D e n m a r k ) , Lefa S.A. ( M a d r i d , Spain), M a y a n d B a k e r Laboratories (Dagenham, England), Promonta Laboratorium (Hamburg, W e s t G e r m a n y ) , Siegfried A . G . ( Z o f i n g e n , S w i t z e r l a n d ) , a n d T h . G e y e r A.G. ( S t u t t g a r t , W e s t G e r m a n y ) for k i n d l y s u p p l y i n g t h e s a m p l e s o f b a r b i t u r a t e s used in this w o r k .

REFERENCES 1. C. B. C. Boyce and B. V. Milborrow. A simple assessment of partition data for correlating structure and biological activity using thin-layer chromatography. Nature 208:537-539 (1965). 2. J. Iwasa, T. Fujita, and C. Hansch. Substituent constants for aliphatic functions obtained from partition coefficients. J. Med. Chem. 8:150-153 (1965). 3. G. L. Biagi, M. C. Guerra, A. M. Barbaro, and M. F. Gamba. Influence of lipophilic character on the antibacterial activity of cephalosporins and penicillins. J. Med. Chem. 13:511-516 (1-970). 4. J. C. Dearden and E. Tomlinson. Correlation of chromatographically obtained substituent constants and analgesic activity. J. Pharm. Pharmaeol. 24:115P-I 18P (1972). 5. M. C. Bonjean, J. Alary, and M. C. Luu Due. Relations "coefficients de partage-Rmactivit6s biologiques" dans la s6rie barbiturique; utilisation de la chromatographic sur couches minces. Chim. Ther. 1:93-97 (1973). 6. J. M. Pl~-Delfina, J. Moreno, and A. del Pozo. Use of chromatographic R,, values as a possible approach to the calculation of the absorption rate constants for some related drugs. J. Pharmaeokin. Biopharm. 1:243-253 (1973). 7. C. Hansch and S. M. Anderson. The structure-activity relationships in barbiturates and its similarity to that of other narcotics. J. Med. Chem. 10:745-753 (1967). 8. K. Kakemi, T. Arita, R. Hori, and R. Konishi. Absorption and excretion of drugs. XXX. Absorption of barbituric acid derivatives from rat stomach. Chem. Pharm. Bull, 15: 1534-1539 (1967). 9. R. Collander. The permeability of plant protoplasts to nonelectrolytes. Trans. Faraday Soe. 33:985-990 (1937). 10. Z. F. Ahmed, Z. I. El-Darawy, M. N. Aboul-Enein, M. A. Abou-EI-Naja, and S. A. E1-Leithy. Identification of some barbiturates by paper and thin-layer chromatography. J. Pharm. Sei. 55:433--434 (1966). 11. J. M. Pl~t-Delfina and J. Moreno. Un m6todo racional de an~_lisisen la industria farmac~utica: La cromatografia en sustratos planos. Cien. Ind. Farm. 2:103-119 (1970). 12. S. Marcinkiewicz, J. Green, and D. McHale. Paper chromatography and chemical structure. II. The chromatography of phenols, alkoxyphenols, coumaranols and chromanols. The use of group and atomic ARm values. Steric and electronic effects in chromatography. J. Chromatog. 1 0 : 4 2 ~ 7 (1963). 13. R. Collander. Partition of organic compounds between higher alcohols and water. Aeta Chem. Scand. 5:774-780 (1951). 14. K. Kakemi, T. Arita, R. Hori, and R. Konishi. Absorption and excretion of drugs. XXXI. On the relationships between partition coefficients and chemical structures of barbituric acid derivatives. Chem. Pharm. Bull. 15:1705-1712 (1967). 15. J. G. Wagner and A. J. Sedman. Quantitation of rate of gastrointestinal and buecal absorption of acidic and basic drugs based on extraction theory. J. Pharmaeokin. Biopharm. 1: 23-50 (1973). !6. L. S. Schanker. Absorption of drugs from the rat colon. J. Pharmaeol. Exp. Theor. 126: 283-290 (1959).

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17. K. Kakemi, T. Arita, R. Hori, R. Konishi, K. Nishimura, H. Matsui, and T. Nishimura. Absorption and excretion of drugs. XXXIV. An aspect of the mechanism of drug absorption from the intestinal tract in rats. Chem. Pharm. Bull. 17:255-261 (1969). 18. K. Kakemi, T. Arita, R. Hori, and R. Konishi. Absorption and excretion of drugs. XXXII. Absorption of barbituric acid derivatives from rat small intestine. Chem. Pharm. Bull. 15:1883-1887 (1967). 19. K. Kakemi, T. Arita, R. Hori, R. Komshi, and K. Nishimura. Absorption and excretion of drugs. XXXIII. The correlation between the absorption of barbituric acid derivatives from the rat small intestine and their binding to the mucosa. Chem. Pharm. Bull. 17: 248-254 (1969).