Quantitative structure-retention relationships - Analytical Chemistry

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QUANTITATIVE STRUCTURERETENTION RELATIONSHIPS Roman Kaliszan’ Department of Oncology McGill University 3655 Drummond Montreal, Qubbec, Canada H3G 1Y6

If the goal of synthetic chemistry is to produce new chemical entities, it is up to analytical chemists to determine how well the chemical compounds are characterized. In general, it is easier to synthesize a compound with a definite chemical structure than with a certain required property. When referring to standard chemical structures, reaction path ways can readily be deduced, whereas predicting properties of the resulting compounds requires a more or less scientific guess. If we imagine sets of balls (atoms) connected by stronger and weaker springs (bonds and interatomic inter actions) colliding with another ball and spring system, the crackings and fusions leading to a new entity can be understood. Thus reactivity emerges as an innate feature of a molecule. However, that is not the case with what we call a physicochemical (biological) property of a chemical compound. The specific ‘Permanent address: Department of Biopharmaceutics and Pharmacodynamics, Medical Academy of Gdafisk, Gen. J. Hallera 107, Gdafisk, 80-416 Poland

0003- 2700BZ0364 -619A/$02.50/0 0 1992 American Chemical Society

property depends as much on the compound’s internal structure as it does on the environment in which the compound is placed, and that environment is by no means inert with regard to the molecules placed in it. The environment interacts with whole molecules and with molecular fragments. Unlike chemical reac tions, the interactions of molecules that form the environment with those placed in the environment cause neither the breaking of existing bonds nor the formation of new bonds. In assigning properties to individ ual chemical structures, the classic

REPOR’T thermodynamic approach appears inappropriate. Thermodynamic prop erties of a given system are bulk properties reflecting only the net interactive effects in that system. The magnitude of thermodynamic parameters represents the combination of individual interactions t h a t may take place at the molecular (or submolecular) level. In effect, thermodynamic analysis of chemical systems provides information of a physical rather than a chemical nature. To quote Prausnitz, “Classical thermodynamics is revered, honored and admired, but in practice it is inadequate” (1).

Certain approaches lack the rigor of thermodynamics but can provide otherwise inaccessible information. These extrathermodynamic a p proaches combine detailed models of processes with the concepts of thermodynamics. The commonly acknowledged manifestations of extrathermodynamic relationships are linear free - energy relationships (LFERs). Although LFERs are not necessarily a consequence of thermodynamics, it is believed that they suggest the presence of a real connection between some correlated quantities, and the nature of this connection can be explored (2).In other words, it can be assumed that correlations among specific quantities are attributable t o some unknown physicochemical relationships. Having t h e correlations encourages identification of the relationships behind them. Chromatographic retention parameters (i.e., Kovats indices in GC, logarithms of capacity factors in LC, and RM values in thin-layer chromatography) are linearly related to the free - energy change associated with the chromatographic distribution process. Actually, although this assumption should be verified by enthalpy-entropy compensation stud ies (3), it is more common to tacitly assume LFERs in chromatography. The occurrence of LFERs in chromatography was initially reported by

ANALYTICAL CHEMISTRY, VOL. 64, NO. 11, JUNE 1,1992

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REPORT Martin (4). He suggested that a substituent changes solute retention by a factor dependent on the nature of the substituent (but not on the remaining part of the molecule) and on both t h e mobile a n d stationary phases. Following Martin’s work, relationships between retention parameters and carbon numbers, as well as several other molecular- sized related descriptors, were reported for homologous series of solutes. In 1977 publications began to appear on what is now termed quantitative structure-retention relationships (QSRRs) (5). QSRRs result from applying the methodology used for quantitative structure- biological activity relationships (QSARs) (6)to the analysis of chromatographic data. In this REPORT we provide an overview of retention prediction, selection of descriptors, and hydrophobicity-retention relationships. Two kinds of input data are needed for QSRR studies (Figure 1):a set of quantitatively comparable retention data for a sufficiently large set of solutes and a set comprising various quantities assumed to reflect structural features of the solutes being studied. Through the use of computerized statistical techniques, retention parameters are characterized in terms of various combinations of solute descriptors. If statistically signif-

icant, physically meaningful QSRRs are obtained, they can be exploited to predict retention for a new solute, identify the most informative structural descriptors, gain insight into molecular mechanisms of separation operating in a given chromatographic system, evaluate complex physicochemical properties of solutes (other than chromatographic), and even predict relative biological activities within a set of solute xenobiotic compounds. To obtain valuable QSRRs, reliable input data must be provided and a stringent statistical analysis must be carried out. Chromatography can readily yield a great amount of unequivocally precise and reproducible data. In a chromatographic process all conditions may be kept constant; thus, solute structure becomes the single independent variable in the system. QSRR studies appear to be the best method for testing the applicability of individual structural parameters for property description. The knowledge and skill gained from QSRR analysis may be applicable to other structure-property relationship studies, including the biological QSAR. However, not every published QSRR equation provides reliable information. Some equations are statistically invalid, and sometimes sta-

tistically valid correlations a r e developed for chemically invalid principles. Nonetheless, numerous QSRR studies deserve the interest and attention of analytical, physical, and medicinal chemists. Retention prediction Retention prediction within homologous series of solutes will not be discussed here, although the problem is by no means trivial. Predictive QSRR should also comprise nonhomologous solutes. In practice, however, reliable retention prediction is possible only within sets of related (congeneric) compounds. GC on nonpolar stationary phases and reversed-phase LC were used in the most successful predictions reported. Better results were obtained, using both methodologies, for less polar test solutes. An example of nearly perfect predictive QSRR equations (actually, quantitative structure-retention and property-retention relationships) may be that provided by Bermejo et al. (7) for chlorinated dimethylbenzenes chromatographed on squalane (SQ) and 2,4-trixylenyl phosphate (TXP) phases. Multiple regression of gas chromatographic retention indices I against boiling point T b and van der Waals volume Vw yield

Ise = 2.86Tb + 7.06Vw - 48.3 n = 16, R = 1.0000, s = 0.7

(1)

and

I-

Figure 1. Methodology and goals of QSRR studies. 620 A

ANALYTICAL CHEMISTRY, VOL. 64, NO. 11, JUNE 1, 1992

= 7.85Tb- 9.05Vw + 513.7 n = 16, R = 0.9999, s = 2.7

(2)

where n is the number of solutes used to derive the regression equation, R is the multiple correlation coefficient, and s is the standard estimate error. The explanation for the empirical observation expressed by Equations 1 and 2 is not straightforward, however. (See Reference 5, p. 182 for details.) Jurs and Hasan (8)reported a typical QSRR strategy for predicting retention of an unknown based on the structural features and chromatographic properties of other representative compounds. (Examples of de scriptors are contained in the box on the opposite page.) The multiparameter approach consists of generating a multitude of solute descriptors that are regressed against retention data. Observing all the statistical rules and recommendations, one selects the minimum number of descriptors needed to produce an equation with good predictive ability. The number of descriptors that can be assigned to an individual solute is large enough to pose a statistical

challenge, especially if various trans formations and combinations of par ticular descriptors are included. The ADAPT software system developed by the Jurs group can process 200 regressors. For example, a representative QSRR equation developed from the multiparameter approach de scribing liquid chromatographic re tention indices RI of polyhalogenated biphenyls is

relative retention on an octadecylsilica (ODS) column, with pure methanol as the mobile phase, within the series of polyhalogenated biphenyls. However, it is difficult to assign physical meaning to the descriptors selected. The first two descriptors represent the surface areas of either positively or negatively charged por tions of the molecule divided by the total surface area. It is not clear

2469 (f455) [fraction of negatively charged surfac -72.9 (k18.8) [number of ortho substituei + 3351 (f954) [relative positive charge -15.8 (k7.0) [path-3 kappa Kier index I- 840.“

where n = 53, R = 0.968, s = 55, and F ( 6 , 48) = 285. The parenthetical numbers represent 95% confidence limits and F is the value of a statistical significance test (f-test) for the model (8). Equation 3 satisfactorily predicts

vlolecular voiu Solvent-accessible surfacc V a r i t y - related (electronic) 4tomic excess charg Superdelocalizabili ometry- related (sh Vloments of inertia

r graph-derived ( jacency matrix indices Iistance matrix indices nformation content indice: Indicator variables vsicochemical p iydrophobic constants iammett constants Solubilitv Darameters

what represents the relative positive charge descriptor, defined as the charge of the most positive atom in the molecule divided by the total charge of the molecule. The least significant among the descriptors in Equation 3 is a molecular graph - derived index, path - 3 kappa, introduced by Kier (9).Kappa indices are calculated by a n algorithm that uses the number of atoms and the number of bond (edge) paths connecting the atoms in the graph. (In molecular graphs, the vertices denote atoms and the edges represent bonds.) The path-3 kappa Kier index might encode the “general shape of the molecules,’’ but what would be that shape raised to the third power? There would most likely be several equations with predictive abilities similar to those of Equation 3, but they would comprise different sets of variables. Analogous reservations apply to a number of QSRRbased expert systems aimed a t retention prediction. Physical structural descriptors One can argue that good retention prediction proves the validity of the approach and that we should try to discover the physical sense hidden in an effective descriptor. Certainly one cannot exclude the possibility that trial and error will result in the identification of universal descriptors that can easily be computed from structural formulas. The danger is that, in striving for that modern philosopher’s stone, one occasionally tends to play a numbers game. The alternative is to start from the existing theories of chromatographic separations and attempt to quantify

the abilities of the solutes to participate in the postulated intermolecular interactions. However simple the fundamental intermolecular interactions involved in chromatographic processes may appear, the problem becomes extremely complex if one realizes that retention is the net effect of solute-stationary phase, solutemobile phase, and mobile phase-stationary phase interactions (not to mention the interactions among the components of individual phases). Even if the intermolecular interactions-known to determine the state of all matter-are quantified, there is no working theory that rigorously accounts for their combinations. This does not preclude the possibility that, if all variables except solute structure are kept constant, the structural factors that differentiate retention will clearly manifest themselves. The fundamental intermolecular interactions are dipole-dipole (Keesom), dipole-induced-dipole (Debye), instantaneous dipole-induced dipole (London), hydrogen bonding, and electron pair donor-electron pair acceptor interactions, and possibly solvophobic interactions. The potential energy E of the first three types of interaction is approximated by

E = -FV2e-’r -6[2pfpz/3kT + azcLtfl+ alp22 +

3I1&a1%/%I1 + 1211 (4) wherewand k are constants; E is relative electric permittivity of the medium; r is the distance between the interacting molecules; T is the absolute temperature; and p, a,and I are the interacting molecules’ dipole moments, polarizabilities, and ionization potentials, respectively. Equation 4 provides the basis for the assumption that, within a series of solutes chromatographed under identical conditions, the retention parameters can be approximated by a linear combination of polarizabilities, ionization potentials, a n d squares of dipole moments. In preQSRR days, attempts were made to select solutes of either similar dipole moments and varying polarizability (10)or of similar polarizability and varying dipole moments (11),and to relate retention to the variable. Ionization potentials could be assumed to be fairly constant at about -10 eV for most organic solutes. Those first correlations were rather moderate but clearly illustrated trends implied in Equation 4. An important observation was the poor performance of the total dipole moment as a retention descriptor. It


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REPORT appeared that, for molecules such as 1,4-dioxane with a n overall dipole moment of zero, better correlation with retention was obtained when assuming the effective dipole moment as twice that of diethyl ether. The two dipoles in 1,4-dioxaneare in opposition and, therefore, cancel each other. In chromatography, however, single dipoles interact at close range with molecules of the stationary and mobile phases. In the QSRR studies that followed, the dipole moments calculated for individual energetically favored confor mations provided better descriptions of retention than the experimental, overall dipole moments (12).Although the squared total dipole moment is still occasionally reported as a significant parameter in QSRR equations, it cannot be used to describe all the specific polar features of the compounds (13). The ability of a solute to participate in structurally specific intermolecular interactions can be better characterized by submolecular polar ity parameters. The availability of molecular mechanics and quantum chemical software makes it feasible t o calculate t h e excess electron charge distribution within the molecule and the orbital energies. An especially promising polarity descrip tor is the parameter A, defined as a maximum excess electron charge difference for a pair of atoms in a molecule. The parameter A, in combination with the energy of the highest occupied molecular orbital EHoMo and total energy ET, allow for the satisfactory description of Kovats indices I for diverse nitrogen compounds on the methylphenylsilicone stationary phase, OV- 101 (14)

and retention data determined in systems in which dispersive interactions are decisive (i.e., when polar interactions are either meaningless or constant). Numerous such correlations are reported for homologous or nonpolar solutes in GC on nonpolar stationary phases. Solvent -accessible surface area reportedly is a better dispersive descriptor in LC. The parameter is obtained by applying a spherical approximation of the solvent over the van der Waals surfaces of the molecule (Figure 2). In most chromatographic systems the steric effects on retention are generally of minor importance in comparison to differences resulting from polar and dispersive interactions. In some systems, however, shape effects manifest themselves clearly. For example, isomers of polycyclic aromatic hydrocarbons (PAHs) can be separated by GC on nematic stationary phases. A good quantitative description of this separation was achieved after the introduction of the length-to-breadth ratio as a structural parameter. This shape parameter is defined as the ratio of the longer to the shorter side of a rectangle having a minimum area that can envelop a molecule. It has been used to describe the bioactivity of PAHs (16)and their retention in reversedphase (17) and normal- phase (18,19) HPLC systems. PAHs are a unique group of solutes; they are planar and nonpolar, and they form a number of isomers. In general, the parameters of molec-

Iov-lol = -16.59 (k3.34) ET -

7098 (k3798) EHoMo 1988 (k766) A - 3077 ( 5 ) where n = 22, R = 0.96, and s = 50. In Equation 5, ET is a descriptor of the solute’s ability to take part in nonspecific dispersive (London) intermolecular interactions. This ability is related to solute size, or bulkiness, and thus E , is a size-reflecting quantity. Structurally nonspecific bulk properties such as polarizability and molecular refractivity can be calculated even more easily. The latter is conveniently calculated from atom and bond increments (15). The molecular bulkiness parameters used in QSRR studies are reliable descriptors of dispersive interactions, as evidenced by excellent correlations among these parameters 622 A

Figure 2. Contours of (a) the van der Waals surface and (b) the solventaccessible surface of a molecule of the drug delorazepam.


ular shapes cannot be determined by use of a single quantity. Modern computational chemistry provides a multitude of data on the structure of compounds. Obtaining shape-rele vant information is a n important task in all structure-property relationship studies. New HPLC stationary phases known to interact stereospecifically with solutes (e.g., stationary phases based on human serum albumin) offer a means for rapid testing of the proposed shape descriptors. Indices derived from hydrogensuppressed molecular graphs are of great interest to researchers studying QSRRs. The indices are derived by mathematical calculations from a vertex (atom) adjacency relationship in the graph or from the topological distances (i.e., the number of edges or bonds connecting the vertices on the shortest path between them). Topological indices derived for closely congeneric compounds, such as ali phatic hydrocarbons, can be compared. However, the myriad indices proposed are empirical modifications of graph-derived theoretical indices. The Randie connectivity index provides an excellent description of GC retention indices for branched alkanes (20, 21). The performance of various other indices has also been reported (9).Unfortunately, when attempting to apply a specific set of graph-derived indices to a given set of chromatographic data one is often disappointed. It is difficult to assign a definite physical sense to individual indices. Applications of various transformations (squares, square roots, reciprocals) of indices in different QSRR equations can often result in chance correlations. Molecular graph - derived descrip tors differentiate molecular formulas of solutes. Whether they also differentiate the properties of compounds represented by individual formulas remains an open question. Information content indices of neighborhood symmetry of different orders are also calculated from structural formulas (22).These indices are calculated by using the general infor mation theory equation (Shannon’s equation) from probabilities of finding equivalent atoms (or patterns of atoms) in a given structural formula (Figure 3). Among the reported QSRR equations, some contain indicator or “dummy” variables, which account for the presence or absence of a given structural feature in individual sol Utes. Used in QSRR studies, these variables help improve statistics but

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have no real analytical value. In numerous QSRR studies retention is related to other empirical parameters resulting from inter- and intramolecular interactions. The re lationships among retention parameters and the measures of solute hydrophobicity have been studied extensively.

also be different. In the case of qualitatively similar separation systems, the differences in properties of stationary phases may be reflected by the magnitude of the regression coefficients for individual descriptors. Comparative QSRR studies are especially important when new chro matographic phases and systems are introduced. Let us analyze briefly the QSRRs derived for a classic reversed-phase LC system (23).The test solutes were chromatographed on ODS columns of varying octadecyl coverage, Cj.On each coluqn the solutes were chromatographed with several different compositions of methanol-water mobile phase X. As expected in the case of reversed-phase LC, logarithms of capacity factors, log k', of solute i on phase j were linearly related to X. Also, log k' of solute i eluted by solvent of composition X was linearly

QSRR and the molecular mechanism of chromatographic separations If physical meaning can be assigned to individual variables in QSRR equations, then such equations can be interpreted in terms of the molecular or submolecular mechanism of t h e chromatographic processes. Different structural parameters will determine gas chromatographic retention on polar and nonpolar stationary phases. The descriptors in QSRR equations derived for normaland reversed-phase LC systems will

.. 14 7

14 8

4

Hl'

H5\

111424

IC,

ICn EA

c1 ...c, H i ...He 01

Pa 7116 8/16 1/16

EA Cl

PI 1116 5116 1116 0116 1/16

c2 ...c6

c, H i ...Ha 01

EA C1' c25c6

c, ...c, c, ...

H i ...HS H6 He

...

01

P2

1116 2/16 3/16 1116 5116 3/16 1/16

Figure 3. Calculations of information content indices (IC) of the zero, first, and second orders. The probability pi of finding equivalent atoms (EA) with regard to their neighborhood in a structural formula is shown. In the structure, numbered atoms are accompanied by sets of digits characterizing their closest neighbors. For example, 1 l4Z4is at the C2atom, which means that C2is connected by a single and by a bond with a one-valence atom (Hl), by another single bond with a four-valence atom (C3), double bond with a four-valence atom ((2,). Of 16 atoms in the structural formula, seven are carbons (C!-C,), and five of these (CZ-C,) have identical first-order neighborhoods. However, a second-order neighborhood analogous to C2 has only the atom c&The values underneath the table are the indices, and the equation is Shannon's equation.

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ANALYTICAL CHEMISTRY, VOL. 64, NO. 11,-JUNE 1, 1992

related to the hydrocarbon coverage of stationary phase Cj.Individual solutes were differentiated by means of a bulkiness descriptor ETi (total energy) and a submolecular polarity p a r a m e t e r A (maximum excess charge difference). In effect, a QSRR equation was derived, s i m u l t a neously accounting for changes in solute structure, mobile-phase composition, and stationary-phase characteristics 4

log k'ii,x = [0.0454(M.0071)Em

2.6493 (M.9187)A 0.1053(k0.0672)Cj 0.4946(k0.5828>] X0.0381 (k0.0039)En + 2.1659 (k0.4919)A + 0.1696(M.0359)Cj + 1.2963 (k0.3120)

+

4

(6)

The correlation between the 144 pairs of logarithms of the capacity factors determined experimentally and calculated by Equation 6 is illustrated in Figure 4. The predicting power of Equation 6,although probably not sufficient to , discriminate precisely between structurally similar solutes, does supply information relevant to a general theory of reversed-phase LC separations. A detailed QSRR-based analysis of the molecular mechanism of reversed-phase LC separations on silica-based hydrocarbonaceous phases can be found elsewhere (17). QSRR equations reported for reversed-phase LC are characterized by two types of descriptors: one that describes solute bulkiness and one t h a t encodes its polar properties. Bulkiness descriptors are always significant i n reversed - phase LC, whereas the significance of polar descriptors increases as the solute's polarity increases. In normal - phase or adsorption LC the chemically specific, size - indepen- . dent intermolecular interactions are assumed to play the main retentiondetermining role, and QSRR evidence supports this assumption. For example, the LC retention parameters determined for substituted benzenes on porous graphite carbon and spherical palladium s t a t i o n a r y phases were described by QSRR equations comprising polarity de scriptors but no bulk descriptors (24). Because it is difficult to quantify the polarity descriptors precisely, the QSRR for normal-phase LC is generally of lower quality than in reversed-phase LC. One limitation of applying multiple regression methods for QSRR

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analysis is the requirement (regrettably, not always followed) that the descriptors not be intercorrelated. For example, from a group of several bulk descriptors, only one can be selected for use. Thus some information contained in omitted descriptors is lost. Systematic information dispersed over large sets of more or less intercorrelated d a t a may be extracted by factorial methods of data analysis. These methods occasionally have been used to relate retention to changes in chromatographic systems (25, 26). Also, when large sets of structural descriptors are subjected to factorial analysis, the few resulting principal components, containing condensed information on nonspe cific and polar features of the solutes, clearly differentiate the separation mechanism in the systems studied. Hydrophobicity-retention relationships Hydrophobicity is commonly under stood as a measure of the relative tendency of a solute to prefer a nonaqueous rather than an aqueous environment, or as a measure of the tendency of two (or more) solute molecules to aggregate in aqueous solutions. However complex, hydropho bicity manifestations result from the same well-known physicochemical interactions that determine the state of all matter. The problem with hy-

drophobic interactions is that, contrary to the supposition that a force between two particles is a property of the particles themselves, the forces appear to depend more on solvent properties than on the solutes. The hydrophobicity of solutes depends mostly on the environment. When comparing behavior of various solutes in the same environment, a quantitative scale can be used to demonstrate the abilities of individual solutes to participate in hydrophobic interactions. Octanol-water partitioning is a common reference system that provides the most recognized hydrophobicity measure: the logarithm of the partition coefficient, log P (6).The standard “shake-flask” method for determining partition coefficients in liquid-liquid systems has several serious disadvantages (5). If the QSRR is known, partition chromatographic data rather than equilibration methods can be used to predict log P. Numerous procedures have been proposed to relate chromatographic parameters to log P. Near-perfect correlation of the reversed-phase LC retention parameters with shakeflask partition data has been reported. However, each partition chromatographic system yields an in dividual scale of hydrophobicity. Thus the question arises whether different chromatographic hydropho-

Figure 4. Correlation between logarithms of capacity factors determined experimentally and calculated by Equation 6 for a set of substituted benzene derivatives chromatographed using various reversed-phase LC systems. R = 0.9862. (Adapted with permission from Reference 23.) 626 A


bicity parameters should be used for predictive purposes or whether an LC system should be developed that mimics the log P hydrophobicity scale. In either case the chromatographic measures of hydrophobicity should be defined and reproducible. The advantages of reversed - phase LC methods for hydrophobicity quantitation can be attributed to the use of organic modifiers in binary aqueous eluents. However, the presence of organic modifiers in mobile phases makes the interactions determining chromatographic separation extremely complex. When setting up a system for hydrophobicity parameterization, there are no hard and fast rules for choosing a solvent and its composition.For example, a t a fixed concentration of a given solvent, the solute X may appear more hydrophobic than the solute Y, whereas the reverse seems true at another concentration of the eluent. To avoid ambiguities, the retention parameters determined at various organic modifier-buffer com positions are extrapolated to the buffer-alone eluent. One can argue that the extrapolated parameters (log kl, from HPLC and R$ from TLC) have no physical meaning because they often differ from those determined experimentally, when possi ble, and depend on the organic modifier used. Still, extrapolation seems to be a reliable means for normalizing retention (27, 28). Hydrophobicity is as much a “phobia” toward the aqueous environment as a “philia” toward nonpolar species, and thus the chemistry involved in the contact of a solute with the stationary phase cannot be neglected. For years the ODS stationary phases were commonly used in hydrophobicity studies. However, the retention data obtained using individual ODS columns-even though they are basically the same type of material-are hardly comparable. This is the case in spite of special precautions taken to suppress phasespecific effects. Another disadvantage of the ODS reversed-phase materials is their instability at pH > 8. The log P values are determined for neutral, nonionized forms of solutes. Chromatographic determination of hydrophobicity of nonionized forms of organic bases cannot be performed directly on silica-based materials. With the above limitations of ODS in mind, researchers have attempted to introduce a reversed - phase mate rial for the construction of a universal, continuous chromatographic hydrophobicity scale. Certain new

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materials supposedly are devoid of the major problems of regular alkylbonded silicas; they have no accessible free silanols and/or they are chemically stable at a wide pH range (see box below) (29). Figure 5 shows a representative relationship between the chromatographic measure of hydrophobicity (log k') determined on a deactivated phase for a noncongeneric series of nonionized basic, acidic, and neutral solutes, as well as their log P values. Thus the advantages of the log P hydrophobicity scale-its universality and continuity-are challenged by a much more convenient, reproducible, fast, and inexpensive chromatographic approach. A systematic study could produce a large chromatographic hydrophobicity database similar to the one collected laboriously for log P. Using chromatographic data to predict bioactivity The works of Overton, Meyer, and Baum, published at the turn of the century, demonstrated the impor tance of hydrophobic properties of drugs in their bioactivity. Following the first reports on reversed-phase TLC and HPLC methods of hydrophobicity parameterization, hundreds of reports on the application of chromatographically derived hydro phobicity descriptors in medicinal, agricultural, and environmental chemistry have appeared (5). For most researchers, the only reason to use the chromatographic measure of hydrophobicity is that it conforms to the log P scale. However, several researchers believe that indi vidual chromatographic hydropho bicity parameters correlate very well with given sets of bioactivity data. The discussion appears a bit aca-

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demic if one realizes that there is no single, unique, universal, continuous, unequivocally defined, a n d pharmacologically distinguished hydrophobicity scale. Thus there is no reason to prefer the information on properties of solutes provided by the octanol-water or any chromatographic system over that provided by other methodologies. Although it is often sufficient from the practical medicinal chemistry point of view to use a selected hydrophobicity parameter for bioactivity estimation, a single hydrophobicity scale is unsuitable for characterization of the complex interactions between drugs and biological systems. The composition of individual partitioning sites in a living organism is unknown, and there are differences in the properties of specific parts of the body penetrated by a given drug. It can be argued that, for prediction of the net effects of complex pharmacokinetic and pharmacodynamic pro cesses, information extracted from diversified retention data may be more useful than information based on individual, one-dimensional hydrophobicity scales. To extract the systematic information from diversified yet often highly intercorrelated sets of data, modern multivariate chemometric methods of data analysis must be used. All reproducible retention data provide information on solute structures, as do data normally discarded in the traditional methods of data analysis. Wold et al. (30)describe one type of multivariate parameterization of biological properties of solutes based on chromatographic data. Principal component analysis (PCA) was performed on TLC data from systems using different stationary phases and compositions of mobile phase.

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Two significant factors were identified. These two principal components explained about 70% of the variance in pharmacological activity of a series of oligopeptides. Another multivariate approach to the analysis of chromatographic data of chemically and closely related solutes resulted in their classification according to their diversified phar macological activity (31). Large sets of polycratic LC capacity factors were determined by using various stationary phases, pH, and mobile-phase compositions, and the data were subjected to PCA. The first principal component (PC1)accounted for 60.5% and the second (PC2) for 18.9% of the variance in the capacity factors considered. Figure 6 shows the positions of the drugs on the plane spanned by the two principal component axes. Because of their chromatographic be havior, the solutes can be grouped into three clusters: a, b, and c. Pharmacology textbooks classify t h e agents belonging t o cluster a as selective agonists of a2 adrenoceptor, whereas those belonging to cluster c are considered a, agonists. Imidazolines belonging to cluster b possess affinity to both subtypes of a adrenoceptors. When applying chromatography to bioactivity prediction, it appears to be more productive to collect a representative set of diverse retention parameters than to try to determine a universal chromatographic measure of hydrophobicity. Future trends QSRR studies are important for understanding the phenomena that determine the physicochemical proper-

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Figure 5. Relationship betwmi logarithms of capacity factors (log k') and logarithms of octanol-water partition coefficients (log P ) for a diverse set of nonionized basic, acidic, and neutral solutes. Retention data were determined using a deactivated, chemically stable reversed- phase material.


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ties of compounds (i.e., their direct interactions with their environment). These studies also have practical applications such as predicting retention and other physicochemical parameters; however, a good QSRR study that is valid for structurally diverse solutes is still needed. The QSRR approach has been useful with retention data obtained by GC on nonpolar stationary phases and by reversed-phase LC. The modeling of solute behavior in more structurally selective chromatographic systems is much more difficult and has been reported only occasionally. The main problem is the inadequacy of the available descrip tors in representing the structural features that determine retention. It is anticipated that increased access to modern molecular mechanics and quantum chemical software will lead to identification of easily determined structural parameters that better account for physicochemical and biological properties. When structurally dependent retention data can be readily obtained, QSRR studies are preferable for testing new descriptors, and they may be helpful in discerning new means of representing chemical structures that account not only for reactivity but also for properties. In addition, QSRR equations describing retention on enantioselective, protein-based columns and on the immobilized en-


.gure 6. Pharmacologically consistent distribution of imidazoline circulatory drugs on the plane determined by two first principal components extracted from a large set of diversified retention data. The drugs are identified as follows: 1, Medetomidine; 2, Detomidine; 3, Xylazine; 4, Moxonidine;5, UK 14,& 6, Lofexidine; 7, Clonidine; 8, Cirazoline; 9, Tolazine; 10, Tiamenidine; 11, Tetryzoline; 12, Phentolamine; 13, Naphazoline; 14, Antazoline; 15, Tymazoline; 16, Oxymetazoline; 17, Tramazoline; 18, Xylometazoline. (Adapted with permission from Reference 31 .)

zyme or receptor columns should be of interest to analytical chemists and other researchers. Support for this research by the Komitet Badan Naukowych, Warsaw, Poland (Project No. 408319101)is kindly acknowledged.

References ( 1 ) Prausnitz, J . M. Science 1979, 205,

759-66. (2)Reichardt, C. Solvent EAeccts in Oqanic Chemistry; Verlag Chemie: Weinheim, Germany, 1979;p. 227. (3)Melander, W.;Campbell, D. E.; Horvath, C. J. Chromatogr. 1978, 158,21325. (4)Martin, A.J.P. Annu. Rev. Biochem. 1980,19,517-42. ( 5 ) Kaliszan R. Qtlantitative StrtlctureChromatographic Retention Relationships; Wiley: New York, 1987;p. 1. (6)Hansch, C.; Fujita, T.J. Am. Chem. Sot. 1964,86,1616-19. (7)Bermejo, J.; Blanco, C. G.; Guillen, M. D. I. Chromato 1986,351,425-32. (8) Hasan, M. N.; urs, P. C. Anal. Chem. 1990,62,2318-23. (9)Kier, L. B. Med. Res. Rev. 1987,7,41740. (10)Scott, R.P.W. J. Chromatogr. 1976, 122,35-53. (11)Karger, B. L.; Snyder, L. R.; Eon, C. J. Chromatogr. 1976,125,71-88. (12)Kaliszan, R.; Holtje, H-D. J. Chromatogr. 1982,234,303-11.

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(13)Ong, V. S.;Hites, R. A. Anal. Chem. 1991,63,2829-34. (14)OSmiaIowski, K.;Halkiewicz, J.; Radecki, A.; Kaliszan, R. J. Chromatogr. 1985,346,53-60, (15)Vogel, A. I. Textbook of Practical Organic Chemistry; Chaucer: London, 1977; p. 1034. (16)Lamparczyk, H.;Radecki, A.; Kaliszan, R. Biochem. Pharmacol. 1981,30, 2337-41. (17)Sander, L.C.;Wise, S.A. Crit. Reu. Anal. Chem. 1987,18,299-415. (18)Jinno, K.; Kawasaki, K. Chromatographia 1984,18,44-46. (19)Rohrbaugh, R. H.; Jurs, P. C. Anal. Chem. 1987,59,1048-54. (20)Randii, M.J. Am. Chem. SOC.1975, 97,6609-15. (21)Bolnjak, N.;Michalii, 2.;Trinajstii, N. J. Chromatogr. 1991,540,430-40. (22)Sarkar, R.; Roy, A. B.; Sarkar, P. K. Math. Biosci. 1978,39,299-312. (23) Kaliszan, R.; OBmialowski, K.; Tomellini, S. A.; HSU,S-H.; Fazio, S. D.; Hartwick, R. A. J. Chromatogr. 1986,352, 141-55. (24) B a s s l e r , B. J.; K a l i s z a n , R.; Hartwick, R. A. J. Chromatogr. 1989,461, 139-47. (25)Walczak, B.;Chretien, J. R.; Dreux, M.; Morin-Allory, L.; Lafosse, M.; Szymoniak, K.; Membrey, F. J. Chromatogr. 1986,353,123-37. (26)Cserhati, T.; Valko, K. J. Biochem. Biophys. 1990,20,81-95. (27)Braumann, T. J. Chromatogr. 1986, 373,191-225. (28)Clark, C.R.; Barksdale, J. M.; May-

field, C. A.; Ravis, W. R.; DeRuiter, J. J. Chromatogr. Sci. 1990,28,83-87.

(29)Kaliszan, R. Quant. Stmct.-Act. Relat. 1990,9,83-87. (30)Wold, S.;Eriksson, L.; Hellberg, S.; Jonsson, J.; Sjostrom, M.; Skageber, B.; Wikstrom, C. Can. J. Chem. 1987, 66, 1814-20. (31)Gami-Yilinkou, R.; Kaliszan, R. J. Chromatogr. 1991,550,573-84.

Roman Kaliszan is a visiting scientist at McGill University. He is a professor and chairman of the DepaPZmeHt of Biopharmaceutics and Pharmacodynamics at the Medical Academy in Gdansk, Poland, where he received an M.Sc. degree in pharmaceutics in 1968. He also received a Ph.D. and a DSc. in medicinal chemistry fiom the Medical Academy of Gdakk in 1975 and 1982, respectively. He has been working on chromatographic QSRRs since 1975.

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