Anal. Chem. 1991, 63, 828-833
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Quantitative Retention-Biological Activity Relationship Study by Micellar Liquid Chromatography Emelita D. Breyer,’ Joost K. Strasters,2and Morteza G . Khaledi* North Carolina State University, Department of Chemistry, P.O. Box 8204, Raleigh, North Carolina 27695
I n a previous paper, the usefulness of micellar liquid chromatography (MLC) in predicting octanoi-water partition coefficients of organic compounds was reported. This paper is the first succWul report of a quantitative retentkn-actklty relationship study uslng the retention factor in MLC for predicting the biological activity of a group of phenolic compounds. Excellent correlation was obtalned between the capaclty factor in MLC and the bioactkity (measured as log 1/C, where Cis the 50% inhibitory growth concentration) of 26 para-substituted phenols. A slngie MLC retention parameter is capable of describing the bloactlvity of phenols, while three conventional molecular descriptors (log Po,, pK,, and R ) are needed to achleve a shniiar correlation. This lndkates that both hydrophobic and electronic interactions are Incorporated In a slngie MLC retention parameter, which is due to the amphiphiiic nature of surfactants in the system. I n situations like this, QRAR is a suitable alternative to QSAR since measuring MLC retention Is much easier than measuring different molecular descriptors needed to build the QSAR model. Addition of 10% 2-propanol to a micellar system (hybrld system) proved to be the best chromatographic system for the best estimation of the phenols bioactivity. Other chromatographic factors such as pH and stationary phase also showed significant effect on the correlation between capacity factor k’and log 1/C.
INTRODUCTION The development of quantitative structure-activity relationship (QSAR) studies has had a tremendous impact in the fields of drug design, toxicology, and environmental monitoring. This approach is based on the premise that the behavior of biologically active compounds can be explained on the basis of molecular interactions and in terms of molecular structure and physicochemical properties of the compounds (1-8). Hansch demonstrated that biological activity could be quantitatively related to physicochemical properties, mainly to the partition coefficient between octanol and water (8,9). He also introduced the concept of activity as being described by more than one parameter (i.e. application of multiple linear regression). In QSAR, biological activity is viewed as a summation of the different interactions that a compound undergoes both during the transport through the biological membranes and in the reaction with the active site. These interactions are assumed to be governed by the chemical structure of the compound. A change in the structure can result in a change in biological response (10-12). Physicochemical characteristics such as hydrophobicity and electronic and steric properties *To whom correspondence should be addressed.
University of North Carolina, Clinical Chemistry Division,
Ch; el Hill, NC 27514. Eelft University of Technology, Department of Biochemical
Engineering, Julianalaan 67, 2628 BC, Delft, The Netherlands.
are used as parameters to correlate activity with structures (13, 14). To date, Hansch’s hydrophobicity parameter, the partition coefficient between octanol and water (log Po,), is the most widely used reference to characterize the hydrophobic contribution to the free energy change in the biological response; dipole moment and Hammett’s u are used to describe electronic contributions; Taft’s steric parameter, molar refractivity, and Van der Waals volume are often used for size and steric contributions. One of the limitations in the use of structural descriptors, specially for newly synthesized compounds, is their limited availability. As a consequence, computer programs have been developed to estimate commonly used descriptors such as log Po, and pK, (15). Another approach has been the application of chromatographic techniques (mostly reversed-phase liquid chromatography, RPLC) in QSAR studies. Chromatography is a powerful technique for the measurement of physicochemical parameters. Most of the work in this area has focused on exploring the correlation of RPLC retention parameters with log Po, (or the hydrophobic substituent constant, T ) . There have been only a few reports on the relationships between chromatographic retention and biological activity. The application of chromatographic parameters in QSAR give rise to a new field, quantitative retention-activity relationship (QRAR) (10-12). We have recently reported excellent correlations between retention in micellar liquid chromatography and log Pow for a wide range of compounds (16,17). The initial objective of this study, however, has been to evaluate the usefulness of micellar liquid chromatography in QSAR studies. The transport of compounds through the biological membranes is one of the major factors that affect their bioactivity. Micelles have long been recognized as simple chemical models for biomembranes due to their amphiphilic properties. A combination of the unique characteristics of micelles and the capabilities of HPLC in physicochemical studies should be quite useful in QSAR research. In this paper, we report the first successful application of MLC in predicting the biological activity of 26 para-substituted phenols through a direct retention-activity relationship. Interestingly, a single micellar retention parameter is capable of describing the bioactivity of phenols, while three conventional molecular descriptors are needed to achieve a similar correlation.
EXPERIMENTAL SECTION Apparatus. The chromatographic equipment used in the study consisted of an ISCO (Lincoln, NB) Model 2350 dual-pump system and a V4absorbance detector (ISCO) set at 254 nm. The
entire system is controlled by Chemresearch Chromatographic Data Management System Controller software (ISCO) running on a PC 88 Turbo personal computer (IDS, Paramount, CA). Reagents and Procedure. Stock solutions of Tetradecyltrimethylammonium bromide (C,,TAB) (Aldrich) were prepared in deionized doubly distilled water and were filtered through a 0.45-rm Nylon-66 membrane filter. The ionic strength was adjusted by adding phosphate buffer (pH = 7) such that the total buffer concentration of the final solution was 0.05 M. For the
0003-2700/91/0383-0828$02.50/00 1991 American Chemical Society
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Table I. Bioactivity and Structural Descriptors of 26 Para-Substituted Phenols"
(0.780) (0.830) (0.820) (0.380) (0.140) 0.270 (0.090) (0.430) 0.050 0.520 0.020 0.010 1.420 (0.190) 0.550 0.210 0.680 0.850 0.700 0.470 1.020 0.630 1.380 0.910 1.360 1.714
0.00 0.72 0.80 0.90 1.34 1.35 1.45 1.46 1.55 1.60 1.77 1.87 1.91 1.94 2.39 2.58 2.59 2.91 3.04 3.05 3.07 3.18 3.20 3.31 3.56 3.69
PK,
R
F
HB
MR
9.23 10.12 9.99 9.97 10.20 7.62 8.05 9.99 8.85 7.95 9.89 10.52 7.15 10.26 9.43 10.00 9.34 9.20 10.70 10.32 8.89 10.28 9.55 10.23 10.70 10.19
0.14 (0.01) (0.26) (0.18) (0.51) 0.13 0.20
0.24 0.28 0.21 0.26 0.31 0.32
1.66 0.61 1.41 0.55 0.61 0.61 0.61
9.81 11.84 14.93 10.11
0.00
0.00
0.00
0.20 0.19 (0.34) (0.44) 0.16 (0.13) (0.15) (0.10) (0.17) (0.19) (0.55) (0.10) 0.16 (0.08) (0.08) (0.13) (0.35) (0.01)
0.32 0.51 0.43 0.22 0.67 (0.04) 0.41 (0.05) 0.44 0.40 0.25 (0.05) 0.30 (0.06) 0.08 (0.07) 0.34 (0.08)
0.61 0.55 0.00 0.61
1.03 15.83 6.33 0.92 12.47 7.36 5.65 6.03 10.30 8.88 13.94 21.66 14.96 30.33 14.96 25.36 19.62 27.68 30.01
0.00
7.87
6.88 11.18
1.21
0.00 0.00 0.00 0.00
0.00 0.61 0.00
0.61 0.00 0.00 0.00
0.61 0.00
QP
0.36 (0.06) 0.00
0.01 (0.27) 0.42 0.50 0.00 0.48 0.66 0.06 (0.24) 0.78 (0.17) 0.23 (0.15) 0.23 0.18 (0.32) (0.13) 0.43 (0.13) (0.01) (0.20) (0.03) (0.09)
Abbreviations: log Po,, 1-octanol-water partition coefficient; HB, hydrogen-bonding ability; F,polar or field parameter; R, resonance parameter; MR, molar refractivity;pK,, acid dissociation constant. *Values are obtained from ref 17. Table 11. Correlation Table of Variables"
log
1/c
1% p o w MR PK, F R HB2
log 1/c
1% p o w
MR
PK,
F
R
HB2
1.00
0.850 1.00
0.556 0.635 1.00
-0.148 0.289 0.264 1.00
0.169 -0,236 -0.247 -0.631
0.016 -0.212 -0.048 -0.732 0.076 1.00
-0.349 -0.623 -0.005 -0.331 0.428 0.169 1.00
1.00
" Pertains to the value of the correlation coefficient (R)for the 26 para-substituted uhenols. solutions of micelles in water-organic solvents (we refer to these as hybrid systems), after the required amount of organic modifier (2-propanol) (Fisher Scientific, Pittsburgh, PA) was added, the pH was idjusted to 7. Most of the para-substituted phenol samples were obtained from Aldrich. The analytical columns were an Altex ODS (4.6 x 150 mm) from Beckman and Supelcosil LC-diphenyl (4.6 X 250 mm) from Supelco. A silica precolumn and a dry packed CISguard column were used to saturate the mobile phase with silicates and to protect the analytical column. The silica precolumn, the guard column, and the analytical column were jacketed and thermostated at 38 "C with a Hauk (Karlsruhe, GFR) circulating bath. The void volume of the system was measured from the time of injection to the first deviation from the base line. Average values of 1.08 and 1.99 mL were obtained for the 15-cm ODS column and 25-cm diphenyl column, respectively. Both void volumes have a 2-3% relative standard deviation over 16 measurements.
RESULTS AND DISCUSSION S t r u c t u r e A c t i v i t y Relationships. Recently, Schultz et al. derived QSAR models for the toxicity of para-substituted phenols (28). The toxicity of these compounds is measured as log 1/IGC5O (log l/C); IGC5O is defined as the 50% inhibitory growth concentration of phenols in the culture of Tetrahymena pyriformis. In this work a subset of 26 compounds reported by Shultz (18)was selected and log Powvalues were derived from the literature (19). The structural properties and biological ac-
t
P
1'
Log 1/c
45-
Log Pow
Flgure 1. Plot of log 1/C vs log Pow.
tivity of these phenols are given in Table I. Table I1 summarizes the correlations (in terms of correlation coefficient R ) among the structural descriptors and between them and the biological activity of the 26 para-substituted phenols.
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 8, APRIL
15, 1991
Table 111. Summary of Stepwise Regression Analysis"
param est std dev intercept log Pow
PK, R
2.723 0.668 -0.405 -0.614
0.613 0.046 0.067
0.291
type I1
R2
SSb
0.929 10.070 1.699 0.209
t
pressc MSEd
a-
0.7232 3.614 0.140 0.8924 1.794 0.054 0.9105 1.607 0.047
Correlation between log 1/C and structural descriptors for 26 phenols. bThe improvement in the model sum of squares upon addition of the variable in the model that contains all the other variables. 'The sum of the squared differences between predicted and observed biological activity; the predicted response is calculated by using leave-one-out technique. Mean-squareerror is the difference between the predicted and observed value of biological activity divided by the number of degrees of freedom.
60.
.
K (C-18)
10-
m-
1
0
Table IV. Influence of Stationary and Mobile" Phases
I
-0
rP'
Pfp'
I
I
I
I
n
m
SD
Q
50
RZ log Pow
log
1/c
Flgure 2. Comparison between the capacity factors obtained In the two columns, C,, and diphenyl, at the following mobile-phase composition: 0.04 M CTAB-100% H,O, pH 7.0.
k '(log k 9 values
Diphenyl Column 0.9129 0.04 M CTAB-10% PrOH 0.8405 0.7220 0.12 M CTAB-100% HzO 40% MeOH-60% H,O 0.9210 0.04 M CTAB-100% HZ0
0.8412 0.8936 0.8730 0.6595
CI8 Column
0.04 M CTAB-100% HzO 0.04 M CTAB-10% PrOH 0.12 M CTAB-100% H20 40% MeOH-60% H20 1% P " W log 1 / c
0.9210 0.9189 0.9330 0.8699
0.8132 0.8308 0.6880 0.5308 0.7230 1.0000
1.oooo
0.7230
"All chromatographicexperiments were performed at pH 7 and 0.05 M buffer; k'values were used for micellar systems, and log k', for hvdroorranic svstems. Of the seven variables screened, log Powgave the best single-variable model to describe toxicity (Figure 1) log l/C = 0.583(10g Pow)- 0.908
n = 26
R2 = 0.723
(1)
mse = 0.133
where n is the number of compounds involved in the study;
R2 is the determination coefficient, defined as the fraction of Y that can be explained by X; and mse is the mean square error of the model. The plot of log 1/Cvs pK, did not show any significant trend. However, the plot of pK, versus the residual obtained from the model in eq 1 showed that it contains some information that can help explain some variation in log 1/C.In fact stepwise regression (SR) results show that pK, is the best second variable to improve the model as
+
log 1/C = 0.668(10g Pow)- O.303(pKa) 1.812 (2)
n = 26
R2 = 0.892
mse = 0.054
These results are similar to those observed by Schultz. Three variables were selected by SR analysis a t the 95% significance level: log Po,, pK,, and F. These results (Table 111) indicate that there are two major interactions that influence the activity of the 26 para-substituted phenols used in this study: nonpolar dispersive interaction characterized by log Powand electrostatic properties represented by F and pK,. However, as mentioned previously, the direct measurement of these parameters is tedious and time consuming. The influence of the nature of the stationary and mobile phase in MLC is summarized in Table IV. Note that in MLC, the capacity factor (in the nonlogarithmic form) is linearly
related to bioactivity. We have previously reported similar relationships between k ' vs log Pow and k ' vs numbers of carbons in homologous series (16,ZO). This behavior is rather unusual since on the basis of linear free energy relationships, log k', which represents the free energy change in a chromatographic system, should be related to changes of free energy in another system with similar mechanisms. For example, in conventional RPLC with hydroorganic eluents, log k 'is linearly related to log Powand n,, or log Powis related to log 1/C in QSAR. The reason for the good correlation between k'(instead of log k') in MLC with log Po,, n,, and log 1/C is not yet known. Effect of Stationary Phase. As shown in Table IV, the micellar system gave better models and prediction of toxicity than the conventional RPLC system with a hydroorganic mobile phase. The R2values obtained by using MLC in both the C18and diphenyl columns are significantly higher than the corresponding values in the hydroorganic system. Between the two stationary phases, k'obtained in the diphenyl column gave a slightly better correlation with toxicity than that in C18column. The reason for the better model obtained by using the diphenyl column as compared to the Cla is illustrated in Figure 2. A linear relationship exists between the capacity factors in the two columns for the less lipophilic phenols. However the diphenyl column can differentiate between the more hydrophobic phenols better than the (&column as indicated by the break in the line (Figure 2). The polarizability and configuration of the stationary phase, and the possibility of T-T interactions between the solute and stationary phase may have considerable effect on the retention of the more hydrophobic phenols. Effect of Mobile Phase. Addition of 10% 2-propanol to the micellar aqueous phase (hybrid system) results in a better correlation between the capacity factor obtained in the two stationary phases. The presence of organic modifier in the system can alter the configuration of the stationary phase, and its incorporation in the micelle can result in additional interaction with solutes. A graphical representation of the effect of the mobile and stationary phase is given in Figure 3a-c. Capacity factors obtained by using diphenyl columns in all three mobile phases gave better estimates of log 1 / C than their corresponding values in CIScolumns. Of the three mobile phases, hybrid systems gave the highest R2value (0.8936) and the lowest error
ANALYTICAL CHEMISTRY, VOL. 63,NO. 8, APRIL 15, 1991
831
Table V. Influence of pH and Buffer Concentration'
R2 PH 7.0 3.0
It
. -
I
17
0.050 M
log Po,vs k ' 0.913 0.946
0.0050 M 0.909 0.950
log 1/C vs k' 7.0 3.0
0.841 0.725
0.843 0.727
'Correlation between log 1/C and k'obtained at different chromatoerauhic conditions for 26 substituted uhenols.
m
P
30
40
50
K
lt
0
P7
P1
I r?=aa5M
I e PM
Figure 3. Comparison between the correlation of k'and log 1/C at different chromatographic conditions: (a, top) 0.04 M CTAB-100% H,O, pH 7.0, diphenyl; (b, middle) 0.04 M CTAB-10% PrOH, pH 7.0. diphenyl; (c, bottom) 40% MeOH-60% H,O, pH 7.0, diphenyl.
in the prediction (predicted residual sum of squares, press = 1.4375). In both columns, hydroorganic systems gave the lowest correlation with log 1 / C (R2= 0.6594 for diphenyl and R2 = 0.5308 for CIS). p-Nitrophenol (p14) showed deviant behavior in the plot between k ' (or log k ' for hydroorganic systems) and log 1/C. Only the hybrid system in combination with the diphenyl column gave a good estimate of the toxicity of p-nitrophenol (p14). Although log Powis presently the best structural descriptor to estimate log 1/C, our results show that the best chromatographic condition which gives a good estimate of log Powis not necessarily the best condition to model biological activity. In fact the opposite trend was observed for the effect of mobile-phase composition on the correlation of k'with log P, with respect to its correlation with log 1/C (Table IV). The effect of the different mobile phases on the estimation of log Powin the C I S column is less pronounced compared to the diphenyl column. A comparable R2 value is obtained for k' vs log Powcorrelations on the C I S column under different mobile-phase conditions, while with the diphenyl column, a significant difference is observed on the value of R2for the corresponding condition. This behavior might be explained by the fact that solutes experience a smaller difference in their microenvironment upon partitioning from micellar eluents to a surfactant-modified C18stationary phase as compared to that in a diphenyl stationary phase. Hydroorganic systems in combination with a diphenyl column gave the best correlations with log Pow,better than the micellar system. While in the c18 column, the micellar system a t a high micelle concentration gave the best result. Hybrid systems gave the best estimate of log 1/C for both columns (Figure 3b). These results, however, are dependent on the type and congenerity of the solutes used in the study. Entirely different result might be obtained for noncongeneric set of solutes. The better correlation between k'and log 1/C, compared to log Powvs log 1/C, proved the limited information incorporated in this structural descriptor. This result also shows that the chromatographic system that gives good correlation with log Powmay not be the optimum chromatographic system to be used in the estimation of biological activity. Two other factors considered in this study were pH and ionic strength. A two-parameter factorial design was employed, resulting in four experiments that would relate the effect of pH and ionic strength on the correlation of k ' with log 1 / C and log Pow. The results are presented in Table V. The capacity factors obtained at lower pH (3.0) gave better correlation with hydrophobicity, while the capacity factors measured at pH 7.0 gave a better estimate of toxicity. These results are in agreement with the definition of log Pow,i.e. the partition coefficient of the molecular form of compounds between octanol and water. For weak acids, lower pH gave better estimates of log Pow, since a t this pH range the compounds migrate in the chromatographic column in a molecular form. The pK, range of compounds under study is from 7.0
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ANALYTICAL CHEMISTRY, VOL. 63,NO. 8, APRIL 15, 1991
Table VI. Comparison of the Predicted Values of the Three-Variable QSAR Model and the One-Variable QRAR Model obsd log 1/C
P7
2
Plf
CONH, CHpCHZOH NHCOCH, CH&N OCH, CHO COCH,
Predicted Log
H
COC~H, CN F OCHpCH3
NO2 '793 (as) 0 a5 1 u 2 CH3 c1
O b m e d L o g l/C
CHpCH3
l5
'I
I 3
p25
p23
b
Br I
I
predicted log 1/C QSAR model' QRAR modelb
(0.780) (0.830) (0.820) (0.380) (0.140) 0.270 (0.090) (0.430) 0.050 0.520 0.020 0.010 1.420 (0.190) 0.550 0.210 0.680 0.850 0.700 0.470 1.020 0.630 1.380 0.910 1.360 1.714
(1.101) (0.889) (0.629) (0.603) (0.200) 0.459 0.309 (0.348) 0.051 0.455 0.109 (0.018) 1.005 (0.057) 0.592 0.458 0.775 1.058 0.758 0.642 1.075 0.733 1.042 0.871 0.982 1.067
(0.766) (0.654) (0.770) (0.480) (0.060) (0.180) (0.270) (0.240) 0.250 0.200 (0.040) (0.080) 1.165 0.063 0.508 0.474 0.595 0.986 1.040 0.790 1.380 0.840 1.206 0.951 0.998 1.207
Predicted values are obtained from the three-variable QSAR model (eq 3). *Predicted values are obtained from the one-variable QRAR model (ea 4).
has difficulty in predicting the toxicity of the highly lipophilic phenols, as indicated by the curvature in this region (Figure 4a). By using the three-variable QSAR model (eq 3) log 1 / C = 0.668 log Pow- O.405pKa - 0.614R 2.723 (3)
+
n = 26
ObsavedLog 1/c Figure 4. Plot of predicted vs observed log 1/C using the model in (a, top) eq 3 and (b, bottom) eq 4.
to 11.0. Thus a t low pH most of the compounds are virtually completely un-ionized. The above pK, pertains to the ionization of the phenolic group; the difference in the pK,'s of this group of compounds reflects the different molecular interaction of the substituents with the aromatic ring. Since toxicity of the 26 compounds was measured a t a physiological pH of 7.4, the good correlation between k' obtained a t pH 7.0 and log 1/C was not surprising. It is possible that since the micellar system closely mimics the biological system, the same form (molecular,ionized, or partially ionized) of compound responsible for the particular biological response also exists in the chromatographic column. A 10-fold increase in the buffer concentration of the system did not show any significant effect in the correlation between k'and log 1/C. This is probably due to the fact that the effect of the increased buffer concentration on the ionic strength of the system is minimal compared to the effect of micelle concentration. QSAR vs QRAR. The predictive ability of the models derived from the structure-toxicity and retention-toxicity studies was compared in Figure 4a,b. The predicted value of log 1/C was calculated from the model using the leaveone-out technique (the compound to be predictd is left out in the derivation of the model). The QSAR model (Table 111)
R2 = 0.9105
mes = 0.047
an R2 of 0.8623 was obtained when predicted log 1/C was correlated with the experimental value (Figure 4a). While comparable correlation, R2 = 0.8758, was obtained when only k' (capacity factor using a hybrid system) was used in the model (eq 4, Figure 4b). log l / C = 0.08712'- 0.922 (4)
n = 26
R2 = 0.8936
mse = 0.051
The predicted values of log 1/C using the three-variable QSAR model (eq 3) and the one-variable QRAR model (eq 4) are compared in Table VI. This result shows that one variable, k', from a chromatographic system gave as much information about toxicity as the three structural descriptors (log Pow,pK,, and F) conventionally used in QSAR. The addition of other structural parameters (F,R, VWDV, etc.) can further improve the correlation given in eq 4, i.e. log 1/C = 0.087k' + 0.566F - 1.046 (5)
n = 26
R2 = 0.9236
mse = 0.038
Considering the results presented above, it seems that chromatographic techniques offer a considerable potential in the study of solute behavior for drug design and other structure-property related studies. Thus further studies should be done in order to better understand the factors influencing chromatographic processes, and this study should be directed toward the design of a chromatographic system that will be a suitable model for biological activity.
Anal. Chem. 1991, 63,833-839
LITERATURE CITED Bkge, W. J.; Black, J. A. Aquatk Toxlcdogy and Hererd A s s " t ; ASTM Special Technical Publication 891; Bahner, R. C., tiansen, D. J., Eds.; April, 1948; p 51. Richet, M. C. C . R. Seances Soc. B M . Ses. FlI. 1893, 45, 775. Meyer, H. Zur Theorle der Alkolnarkose I . Welche EigenschaR der Anesthetlca bedina lhre narkotlsche wlrkung. Arch. EXD.Pathol. Pharmakol. 1899, 42;109. Overton, E. 2.Phys. Chem. 1887, 22, 189. Lien, E. J.; Guo, Z.-R.; Li, R.-L.; Su, C.-T. J. Pharm. Sci. 1982, 77, 641. Moriguchi, I.; Kanada, Y.; Katsulchlro, K. Chem. Pharm. Bull. 1978, 24, 1799. Cascorbi. I.; Ahlers, J. Toxicology 1989, 58, 197. Hansch, C. Acc. Chem. Res. 1989, 2, 232. Hansch, C. Nature 1982, 794, 178. Kalisran, R. Quantitative Structure Chromatographic Retentbn Re& tionships; J. Wiley and Sons: New York, 1987. Valko, K. Trends Anal. Chem. 1987, 6 , 214. Valko. K. J. Llq. Chromatogr. 1984, 7 , 1405. Konemann, H.; Musch, A. Toxicology 1981, 79, 223.
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833
(14) Lipnlck, R. L.; Bichlngs, C. K.; Johnson, D. E.; Eastmond, D. A.; Aquatic Toxhbgy and Hazard Assessment; ASTM Technical Publication 153; Hansen, D. J., Ed.; 1981. (15) Perrln. D. D.; Dempsey, B.; Sergeant, E. P. pKa Redlctbn for Organlc Acids and Bases; Chapman and Hall: London, 1981. (16) Khaledi, M. G.; Breyer. E. D. Anal. Chem. 1989, 67, 1040. (17) Khaledi, M. G. Trends Anal. Chem. 1988, 7 , 293. (18) Schultz, W.; Riggin, G. W.; Wesley, S. K. QSAR in Mvloronmental Toxkology-II; Kalser, K. L., Ed.; Reidel Publishing Co.; Dordrecht, The Netherlands, 1987; p 333. (19) Hansch, C.; Leo. A. Substnuent Constants for Corre&tion Analysis In Chemistty and Biology; J. Wlley and Sons: New York, 1974; p 45. (20) Khaledi, M. G.; Peuler, E.; Ngeh-Ngwainbi, J. Anal. Chem. 1987, 59, 2738.
RECEIVED for review October 30,1990. Accepted January 18, 1991. We gratefully acknowledge the funding of this project by the National Institutes of Health (FIRST Award, Grant GM 38738).
Determination of Isotherms from Chromatographic Peak Shapes Eric V. Dose, Stephen Jacobson, and Georges Guiochon* Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996-1600, and Analytical Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -6120
A new method for determlnlng equlllbrlum Isotherms from chromatographlc peak shapes Is presented. It dlffers from atternathe methods Hke elutkn by characterlstlc polnt In that the present method accounts for the flnlte efficiency of real chromatographlc columns, and 80 the new method Is used to Its best advantage In systems of low plate number. I n the new method, lnltlal estlmates of the parameters of an Isotherm equation are reflned by finding slmulated chromatographic peak shapes that most nearly approximate the experlmental peak shapes. A serles of example determlnatbns demonstrate the method's utlllty.
INTRODUCTION The equilibrium isotherm describes how an adsorbate concentration on an adsorbent surface depends on the adsorbate chemical potential in either the stationary phase or the fluid, mobile phase in contact with the stationary phase. The isotherm plot deviates from linear behavior due to surface saturation, surface heterogeneity,and/ or adsorbate-adsorbate interactions at the surface. Conversely, measured isotherms can be used to test hypotheses about the extent of heterogeneity and adsorbate-adsorbate interactions exhibited by an adsorbate-adsorbent system ( I ) . Though the equilibrium isotherm is formally defined in terms of the adsorbate chemical potential at the interface, in practice one usually substitutes adsorbate concentration for the chemical potential, and we follow this practice herein. The most straightforward isotherm determination methods are static in nature. Static methods consist of near-equilibrium measurements of the extent of adsorption at specified, constant adsorbate concentrations. The extent of adsorption has been measured by methods including microbalance gravimetry (2),infrared absorption ( 3 ) ,and thermogravimetry (3-5). It was recognized very early that chromatography offered sig-
nificant advantages in measurement speed when it could be used. Several methods have been practiced over the previous 40 years including frontal analysis (FA) ( G l l ) ,frontal analysis by characteristic points (FACP) (12, 13), peak-maxima methods (14),elution by characteristic point (ECP) (15-191, and step-and-pulse (minor disturbance) methods (20-24). These methods have been reviewed by others (25-27). A recurring problem in determining isotherms by chromatography is the approximation caused by the assumption that the adsorption system is always at equilibrium. While the intimate contact of the equilibrated phases yields equilibration rates far exceeding those of static measurement systems, the former rates are not infinite, and the chromatographic peak or front shapes differ from ideal (equilibrium) chromatographic peak shapes. The differences are frequently small (8-1 7), and approximate peak shape corrections have been proposed (28). It is very difficult to demonstrate the validity of these correction methods, and they are not always used in practice. Chromatographic nonideality (low column efficiency) is important, especially in the case of biopolymer separations. Thus, we feel the development of a fast method permitting the use of small amounts of material is warranted. The development of numerical chromatographic simulation methods (29, 30) that explicitly include the effects of finite efficiency (measured as the chromatographic plate number) suggests a different path. A method of successive approximation to the physical isotherm can be designed given a means of computing chromatographic peak shapes from a given isotherm and plate number, provided by the semi-ideal (finite efficiency) model (29);a score measuring the similarity of this simulated peak shape to the experimental shape; and an algorithm that generates new isotherms with increasing similarity scores and that recognizes convergence of the series of new isotherms to a single best isotherm. This last task may be performed by modified simplex optimization methods (31-33). In this article, we describe how to determine iso-
0003-2700/9 110383-0833$02.50/0 0 1991 American Chemical Society
