QUANTITATIVE STRUCTURE-RETENTION RELATIONSHIPS

QUANTITATIVE STRUCTURERETENTION RELATIONSHIPS Roman Kaliszan1 Department of Oncology McGill University 3655 Drummond Montréal, Québec, 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 s t a n d a r d chemical structures, reaction pathways 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 interactions) colliding with another ball and spring system, the crackings and fusions leading to a new entity can be u n d e r s t o o d . T h u s r e a c t i v i t y emerges as an innate feature of a molecule. However, t h a t 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 Gdansk, Gen. J. Hallera 107, Gdansk, 80-416 Poland 0003-2700/92/0364-619A/$02.50/0 © 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 reactions, 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 individual chemical structures, the classic

REPORT t h e r m o d y n a m i c approach a p p e a r s inappropriate. Thermodynamic properties 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 that may take place at the molecular (or submolecular) level. In effect, thermodynamic analysis of chemical systems provides information of a physical r a t h e r t h a n a chemical nature. To quote Prausnitz, "Classical thermodynamics is revered, honored and admired, but in practice it is inadequate" (J).

Certain approaches lack the rigor of thermodynamics but can provide otherwise inaccessible information. These extrathermodynamic approaches 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 t h a t they suggest the presence of a real connection b e t w e e n some c o r r e l a t e d quantities, and the n a t u r e of this connection can be explored (2). In other words, it can be assumed that correlations among specific quantities are a t t r i b u t a b l e to some u n k n o w n physicochemical r e l a t i o n ships. Having the 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 studies (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 · 619 A

REPORT Martin (4). He suggested that a sub stituent changes solute retention by a factor dependent on the nature of the substituent (but not on the re maining part of the molecule) and on b o t h t h e mobile a n d s t a t i o n a r y phases. Following Martin's work, re lationships between retention pa r a m e t e r s and carbon n u m b e r s , as well as several other molecular-sized related descriptors, were reported for homologous series of solutes. In 1977 publications began to ap pear on what is now termed quanti tative structure-retention relation ships (QSRRs) (5). QSRRs r e s u l t from applying the methodology used for quantitative structure-biological activity relationships (QSARs) (6) to t h e a n a l y s i s of c h r o m a t o g r a p h i c data. In this REPORT we provide an overview of retention prediction, se lection 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 sol utes and a set comprising various quantities assumed to reflect struc tural features of the solutes being studied. Through the use of comput erized statistical techniques, reten tion parameters are characterized in terms of various combinations of sol ute 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 struc tural descriptors, gain insight into molecular mechanisms of separation operating in a given chromatographic system, evaluate complex physicochemical properties of solutes (other t h a n chromatographic), and even predict relative biological activities within a set of solute xenobiotic com pounds. To obtain valuable QSRRs, reliable input data must be provided and a stringent statistical analysis must be c a r r i e d out. C h r o m a t o g r a p h y can readily yield a great amount of un equivocally 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 appli cability of individual structural pa r a m e t e r s for property description. The knowledge and skill gained from QSRR analysis may be applicable to other s t r u c t u r e - p r o p e r t y relation ship studies, including the biological QSAR. However, not every published QSRR equation provides reliable in formation. Some equations are sta tistically invalid, and sometimes sta

Chromatographic retention parameters

Numerical descriptors of solute structures

Computerized statistical data processing

QSRRs

Identification of informative descriptors

Determination of molecular separation mechanism

Determination of complex physicochemical properties

Retention prediction

Evaluation of relative biological activity

Figure 1. Methodology and goals of QSRR studies. 620 A · ANALYTICAL CHEMISTRY, VOL. 64, NO. 11, JUNE 1, 1992

tistically valid correlations are developed for chemically i n v a l i d principles. Nonetheless, numerous QSRR studies deserve the interest and attention of analytical, physical, and medicinal chemists. Retention prediction Retention prediction within homolo gous series of solutes will not be dis cussed 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 station ary phases and reversed-phase LC were used in the most successful pre dictions reported. Better results were obtained, using both methodologies, for less polar test solutes. An example of nearly perfect pre dictive 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 indi ces / against boiling point T b and van der Waals volume Vw yield 7 SQ = 2.867/b + 7.06F W - 48.3 « = 16, R = 1.0000, s = 0.7 and /TXP = 7.85T b - 9.057 w + 513.7 η = 16, R = 0.9999, s = 2.7

(1)

(2)

where η is the number of solutes used to derive the regression equa tion, R is the multiple correlation co efficient, and s is the standard esti mate error. The explanation for the empirical observation expressed by Equations 1 and 2 is not straightfor ward, however. (See Reference 5, p. 182 for details.) J u r s and Hasan (8) reported a typ ical QSRR strategy for predicting re tention of an unknown based on the structural features and chromato graphic properties of other represen tative compounds. (Examples of de scriptors are contained in the box on the opposite page.) The multiparam eter approach consists of generating a multitude of solute descriptors t h a t 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 t r a n s formations and combinations of par ticular descriptors are included. The ADAPT software system developed by the J u r s group can process 200 regressors. For example, a representa tive QSRR equation developed from the m u l t i p a r a m e t e r approach de scribing liquid chromatographic re tention indices RI of polyhalogenated biphenyls is

relative retention on an octadecylsilica (ODS) column, with pure metha nol 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

RJ= -66511 (±3646) [fraction of positively charged surface area] -2469 (±455) [fraction of negatively charged surface area] -72.9 (±18.8) [number of ortho substituents] + 3351 (±954) [relative positive charge] -15.8 (±7.0) [path-3 kappa Kier index]3 + 840.2

where η = 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 statisti cal significance test (f-test) for the model (8). Equation 3 satisfactorily predicts

Examples of structural descriptors used in QSRR Bulkiness-related (nonspecific) parameters Molecular mass Refract ivity Molecular volume Total energy Solvent-accessible surface Polarity-related (electronic) parameters Dipole moments Atomic excess charges Orbital energies Superdelocalizabilities Partially charged surfaces Geometry-related (shape) parameters Moments of inertia Length-to-breadth ratio Angle strain energy Molecular graph-derived (topo logical) parameters Adjacency matrix indices Distance matrix indices Information content indices Indicator variables Physicochemical parameters Hydrophobic constants Hammett constants Solubility parameters Boiling points

(3)

what represents the relative positive charge descriptor, defined as t h e 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 molec u l a r g r a p h - d e r i v e d index, p a t h - 3 kappa, introduced by Kier (9). Kappa indices are calculated by a n algo rithm t h a t 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 repre sent bonds.) The p a t h - 3 kappa Kier index m i g h t encode t h e " g e n e r a l shape of the molecules," but what would be t h a t 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 reserva tions apply to a number of QSRRbased expert systems aimed at reten tion prediction. Physical structural descriptors One can argue t h a t good retention prediction proves the validity of the approach and t h a t we should try to discover the physical sense hidden in an effective descriptor. Certainly one cannot exclude the possibility t h a t trial and error will result in the iden tification of u n i v e r s a l descriptors t h a t can easily be computed from structural formulas. The danger is that, in striving for that modern phi losopher'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 partici pate in the postulated intermolecular i n t e r a c t i o n s . However simple t h e fundamental intermolecular interac tions involved in chromatographic processes may appear, the problem becomes extremely complex if one re alizes that retention is the net effect of solute-stationary phase, s o l u t e mobile phase, and mobile p h a s e - s t a tionary phase interactions (not to mention the interactions among the components of individual phases). Even if the intermolecular interac tions—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 struc ture are kept constant, the structural factors t h a t 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 ac ceptor interactions, and possibly solvophobic interactions. The potential energy Ε of the first three types of interaction is approximated by Ε = -W W

- 6 [2μ?μ!/3*Τ + α 2 μι + α χ μ | + 3/ 1 / 2 α 1 α 2 /2(/ 1 + / 2 )]

(4)

wherein and k are constants; e is rel ative electric permittivity of the me dium; r is the distance between the interacting molecules; Τ is the abso lute temperature; and μ, α, and / are the interacting molecules' dipole mo ments, polarizabilities, and ioniza tion 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 polarizabili ties, ionization potentials, and 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. Ion ization potentials could be assumed to be fairly constant at about - 1 0 eV for most organic solutes. Those first correlations were r a t h e r 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

ANALYTICAL CHEMISTRY, VOL. 64, NO. 11, JUNE 1,1992 · 621 A

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 t h e effective dipole m o ment as twice that of diethyl ether. The two dipoles in 1,4-dioxane are in opposition a n d , therefore, cancel each other. In chromatography, how ever, single dipoles interact a t close range with molecules of the station ary and mobile phases. In the QSRR studies that followed, the dipole moments calculated for in dividual energetically favored confor mations provided better descriptions of retention than the experimental, overall dipole m o m e n t s (12). Al though the squared total dipole mo ment is still occasionally reported as a significant p a r a m e t e r in QSRR equations, it cannot be used to de scribe all the specific polar features of the compounds (13). The ability of a solute to partici pate in structurally specific intermolecular interactions can be better characterized by submolecular polar ity parameters. The availability of molecular mechanics a n d q u a n t u m chemical software makes it feasible to c a l c u l a t e t h e excess e l e c t r o n charge distribution within the mole cule and the orbital energies. An es pecially promising polarity descrip tor is t h e parameter Δ, defined as a maximum excess electron charge dif ference for a pair of atoms in a mole cule. The parameter Δ, in combina tion with the energy of the highest occupied molecular orbital £ H O M O and total energy ET, allow for t h e satisfactory description of Kovats in dices / for diverse nitrogen com pounds on the methylphenylsilicone stationary phase, OV-101 (14)

and retention d a t a determined in systems in which dispersive interac tions are decisive (i.e., when polar interactions are either meaningless or constant). Numerous such correla tions are reported for homologous or nonpolar solutes in GC on nonpolar stationary phases. Solvent-accessi ble surface area reportedly is a better dispersive descriptor in LC. The pa rameter is obtained by applying a spherical approximation of the sol vent over the van der Waals surfaces of the molecule (Figure 2). In most chromatographic systems the steric effects on retention a r e generally of minor importance in comparison to differences resulting from polar a n d dispersive interac tions. 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 quantita tive description of this separation was achieved after the introduction of the length-to-breadth ratio as a structural parameter. This shape pa rameter is defined as the ratio of the longer to the shorter side of a rectan gle having a minimum area that can envelop a molecule. It h a s 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 sol utes; they are planar and nonpolar, and they form a number of isomers. In general, the parameters of molec-

(a)

W - i o i = -16.59 (±3.34) ET 7098 (±3798) £ H O M O -

1988 (±766) Δ - 3077 (5) where n = 22,R = 0.96, and s = 50. In Equation 5, ΕΎ is a descriptor of the solute's ability to take part in non specific dispersive (London) intermolecular interactions. This ability is related to solute size, or bulkiness, and t h u s ET is a s i z e - r e f l e c t i n g q u a n t i t y . Structurally nonspecific bulk properties such as polarizability and molecular refractivity can be cal culated even more easily. The latter is conveniently calculated from atom and bond increments (15). The molecular bulkiness parame ters used in QSRR studies are reli able descriptors of dispersive inter actions, as evidenced by excellent correlations among these parameters

(b)

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

622 A · ANALYTICAL CHEMISTRY, VOL. 64, NO. 11, JUNE 1, 1992

ular shapes cannot be determined by use of a single q u a n t i t y . Modern computational chemistry provides a multitude of data on the structure of compounds. Obtaining shape-rele v a n t information is a n i m p o r t a n t task in all structure-property rela tionship studies. New HPLC station ary phases known to interact s t e reospecifically w i t h solutes (e.g., stationary phases based on h u m a n 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 study ing 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). Topo logical indices derived for closely congeneric compounds, such as ali phatic hydrocarbons, can be com pared. However, the myriad indices proposed are empirical modifications of graph-derived theoretical indices. The Randic connectivity index pro vides an excellent description of GC retention indices for branched a l kanes (20, 21). The performance of various other indices has also been reported (9). Unfortunately, when at tempting 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 individ ual indices. Applications of various transformations (squares, square roots, reciprocals) of indices in differ ent QSRR equations can often result in chance correlations. Molecular graph-derived descrip tors differentiate molecular formulas of solutes. Whether they also differ entiate the properties of compounds represented by individual formulas remains an open question. I n f o r m a t i o n c o n t e n t indices of neighborhood symmetry of different orders are also calculated from struc tural formulas (22). These indices are calculated by using the general infor mation theory equation (Shannon's equation) from probabilities of find ing equivalent atoms (or patterns of atoms) in a given structural formula (Figure 3). Among the reported QSRR equa t i o n s , some c o n t a i n i n d i c a t o r 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

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

also be different. In the case of qual itatively similar separation systems, the differences in properties of sta tionary phases may be reflected by the magnitude of the regression coef ficients for individual descriptors. Comparative QSRR studies are espe cially i m p o r t a n t w h e n 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, C . On each column the solutes were chro matographed with several different compositions of methanol-water mo bile phase X. As expected in t h e case of r e versed-phase LC, logarithms of ca pacity factors, log k\ of solute i on phase j were linearly related to X. Also, log k' of solute i eluted by sol vent of composition X was linearly

QSRR and the molecular mechanism of chromatographic separations If physical meaning can be assigned to i n d i v i d u a l v a r i a b l e s in QSRR equations, then such equations can be interpreted in terms of the molec ular or submolecular mechanism of the chromatographic processes. Different structural parameters will d e t e r m i n e gas c h r o m a t o g r a p h i c retention on polar and nonpolar sta tionary phases. The descriptors in QSRR equations derived for normaland reversed-phase LC systems will

Id

ICo EA

d ...c7 H

1 —H 8

0,

Po 7/16 8/16 1/16

EA

IC2 Pi 1/16 5/16 1/16 8/16 1/16

Ci 02 --Cg

c7 Hi —He θ!

EA Ci

d'C^ C3 ...Cs

c 7 ... H, ...H 5 Hg ...Hg

d Ί 0 0 = 1.2718

I d = 1.7744

P2 1/16 2/16 3/16 1/16 5/16 3/16 1/16

IC;, = 2.5550

ΙΟ* = - Σ p,«log2p,·

/ 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, 111"24 is at the C 2 atom, which means that C 2 is connected by a single bond with a one-valence atom (H,), by another single bond with a four-valence atom (C3), and by a double bond with a four-valence atom (C,). Of 16 atoms in the structural formula, seven are carbons (C,-C 7 ), and five of these (C 2 -C 6 ) have identical first-order neighborhoods. However, a second-order neighborhood analogous to C2 has only the atom C6. The values underneath the table are the indices, and the equation is Shannon's equation.


related to the hydrocarbon coverage of stationary phase Cy 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 Δ (maximum excess charge difference). In effect, a QSRR equation was derived, simulta neously accounting for changes in solute structure, mobile-phase com position, and stationary-phase char acteristics log fc'ij,x = [0.0454 (+0.0071) £ T i + 2.6493 (±0.9187) Δ 0.1053 (±0.0672) Ç 0.4946 (±0.5828)] X 0.0381 (±0.0039) £ T i + 2.1659 (±0.4919) Δ + 0.1696 (±0.0359) Ç + 1.2963 (±0.3120) (6) The c o r r e l a t i o n between t h e 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 s t r u c t u r a l l y s i m i l a r solutes, does supply information relevant to a general theory of r e v e r s e d - p h a s e 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 r e versed-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 sign i f i c a n t in r e v e r s e d - p h a s e L C , whereas the significance of polar descriptors increases as the solute's polarity increases. In normal-phase or adsorption LC the chemically specific, size-independent intermolecular interactions are assumed to play the main retentiond e t e r m i n i n g role, and QSRR evidence supports this assumption. For example, the LC retention parameters determined for substituted benzenes on porous graphite carbon and spherical palladium stationary p h a s e s w e r e described by QSRR equations comprising polarity descriptors b u t no bulk descriptors (24). Because it is difficult to quantify the polarity d e s c r i p t o r s p r e cisely, 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

REPORT analysis is the requirement (regret tably, not always followed) t h a t the descriptors not be intercorrelated. For example, from a group of several bulk descriptors, only one can be se lected for use. Thus some informa tion contained in omitted descriptors is lost. Systematic information dis persed over large sets of more or less i n t e r c o r r e l a t e d d a t a m a y be ex tracted 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 result ing 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 non aqueous rather than an aqueous en vironment, or as a measure of the tendency of two (or more) solute mol ecules to aggregate in aqueous solu tions. 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, con trary 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 de pends mostly on the environment. When comparing behavior of various solutes in the same environment, a q u a n t i t a t i v e scale can be used to demonstrate the abilities of individ ual solutes to participate in hydro phobic interactions. Octanol-water partitioning is a common reference system t h a t provides the most recog nized hydrophobicity measure: the logarithm of the partition coefficient, log Ρ (6). The standard "shake-flask" method for determining partition co efficients in liquid-liquid systems h a s several serious disadvantages (5). If the QSRR is known, partition chromatographic d a t a r a t h e r t h a n equilibration methods can be used to predict log P. Numerous procedures have been proposed to relate chromatographic p a r a m e t e r s to log P. Near-perfect correlation of the reversed-phase LC retention p a r a m e t e r s with s h a k e flask p a r t i t i o n d a t a h a s been r e ported. However, each partition chromatographic system yields an in d i v i d u a l scale of hydrophobicity. Thus t h e question arises whether different chromatographic hydropho

Logfc' calculated

Logfr' determined

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.)


bicity parameters should be used for predictive purposes or whether an LC system should be developed that mimics t h e log Ρ hydrophobicity scale. In either case the chromato graphic measures of hydrophobicity should be defined and reproducible. The advantages of reversed-phase LC methods for hydrophobicity quan titation can be attributed to the use of organic modifiers in binary aque ous eluents. However, the presence of organic modifiers in mobile phases makes the interactions determining c h r o m a t o g r a p h i c s e p a r a t i o n ex tremely complex. When setting up a system for hy drophobicity parameterization, there are no hard and fast rules for choos ing a solvent and its composition. For example, at a fixed concentration of a given solvent, the solute X may ap pear more hydrophobic t h a n the sol ute Y, whereas the reverse seems true at another concentration of the eluent. To avoid ambiguities, the re tention p a r a m e t e r s determined at various organic modifier-buffer com positions are extrapolated to t h e buffer-alone eluent. One can argue t h a t the extrapolated p a r a m e t e r s (log k'w from HPLC and fl^from TLC) have no physical meaning because they often differ from those deter mined experimentally, when possi ble, and depend on the organic modi fier used. Still, extrapolation seems to be a reliable means for normaliz ing retention (27, 28). Hydrophobicity is as much a "pho bia" toward the aqueous environ ment as a "philia" toward nonpolar species, and thus the chemistry in volved in the contact of a solute with the stationary phase cannot be ne glected. For years the ODS station ary phases were commonly used in hydrophobicity studies. However, the retention data obtained using indi vidual ODS columns—even though they are basically the same type of m a t e r i a l — a r e hardly comparable. This is the case in spite of special precautions taken to suppress phasespecific effects. Another disadvan tage of the ODS reversed-phase ma terials is their instability at pH > 8. The log Ρ 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 uni versal, 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 accessi ble free silanols a n d / o r they a r e chemically stable at a wide pH range (see box below) (29). Figure 5 shows a representative relationship between t h e chromato graphic 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 Ρ values. Thus the advantages of the log Ρ hy drophobicity scale—its universality and continuity—are challenged by a much more convenient, reproducible, fast, and inexpensive chromatograp hic approach. A systematic study could produce a large c h r o m a t o graphic hydrophobicity database similar to t h e one collected labori ously for log P. Using chromatographic data to predict bioactivity The works of Overton, Meyer, and Baum, published a t the turn of the century, d e m o n s t r a t e d t h e impor tance of hydrophobic properties of drugs in their bioactivity. Following the first reports on reversed-phase TLC and HPLC methods of hydro phobicity p a r a m e t e r i z a t i o n , h u n dreds of reports on t h e application of chromatographically derived hydro phobicity descriptors in medicinal, agricultural, and environmental chemistry have appeared (5). For most researchers, the only rea son to use the chromatographic mea sure of hydrophobicity is that it con forms to the log Ρ scale. However, several researchers believe t h a t indi vidual chromatographic hydropho bicity parameters correlate very well with given sets of bioactivity data. The discussion appears a bit aca

demic if one realizes that there is no single, unique, universal, continu ous, u n e q u i v o c a l l y defined, a n d pharmacologically distinguished hy drophobicity scale. Thus there is no reason to prefer the information on properties of solutes provided by the o c t a n o l - w a t e r or a n y c h r o m a t o graphic system over that provided by other methodologies. Although it is often sufficient from the practical medicinal chemistry point of view to use a selected hydro phobicity parameter for bioactivity estimation, a single hydrophobicity scale is unsuitable for characteriza tion of t h e complex interactions be tween drugs and biological systems. The composition of individual parti tioning 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 pharma cokinetic and pharmacodynamic pro cesses, information extracted from diversified retention d a t a may be more useful t h a n information based on individual, one-dimensional hy drophobicity scales. To extract the systematic informa tion from diversified yet often highly intercorrelated sets of data, modern multivariate chemometric methods of data analysis must be used. All re producible retention data provide in formation on solute structures, as do data normally discarded in the tradi tional methods of data analysis. Wold et al. (30) describe one type of multivariate parameterization of bio logical properties of solutes based on chromatographic data. Principal component analysis (PCA) was per formed on TLC data from systems u s i n g different s t a t i o n a r y p h a s e s and compositions of mobile phase.

Stationary-phase materials used in chromatographic methods to determine hydrophobicity Materials dynamically coated with π-octanol, oleyl alcohol, silicone oil, liquid paraffin, glycerol, phosphatidylcholine, and others Physically stable reversed-phase materials, including octadecylsilica and other hydrocarbonaceous silica materials Specially deactivated octadecylsilica-based phases Polymer-coated octadecylsilica Polymeric and monomeric hydrocarbon phases immobilized on alumina Poly(styrene-divinylbenzene) copolymers Polyacrylamide- based materials with bonded alkyl groups Graphite carbon for HPLC Any two immiscible liquid phases used in centrifugal partition chromatogra phy

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Two significant factors were identi fied. These two principal components explained about 70% of the variance in pharmacological activity of a se ries of oligopeptides. Another multivariate approach to the analysis of chromatographic data of chemically and closely related sol utes resulted in their classification according to their diversified phar macological activity (31). Large sets of polycratic LC capacity factors were determined by using various station ary phases, pH, and mobile-phase compositions, and the data were sub jected to PCA. The first principal c o m p o n e n t ( P C I ) a c c o u n t e d for 60.5% a n d t h e 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. Be cause of their chromatographic be havior, the solutes can be grouped into three clusters: a, b , and c. Phar macology t e x t b o o k s classify t h e agents belonging to cluster a as se lective agonists of oc2 adrenoceptor, whereas those belonging to cluster c are considered ctj agonists. Imidazo lines belonging to cluster b possess affinity to both subtypes of α adreno ceptors. When applying chromatog raphy to bioactivity prediction, it ap pears to be more productive to collect a representative set of diverse reten tion parameters than to try to deter mine a universal chromatographic measure of hydrophobicity. Future trends QSRR studies are important for un derstanding the phenomena that de termine the physicochemical proper-

log P= 1.49 log k'+ 2.36

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ties of compounds (i.e., their direct interactions with their environment). These studies also have practical ap plications such as predicting reten tion and other physicochemical pa r a m e t e r s ; however, a good QSRR study t h a t is valid for structurally di verse solutes is still needed. The QSRR approach has been use ful with retention data obtained by GC on nonpolar stationary phases and by reversed-phase LC. The mod eling of solute b e h a v i o r in more s t r u c t u r a l l y selective c h r o m a t o graphic systems is much more diffi cult and has been reported only occa sionally. The main problem is the inadequacy of the available descrip tors in representing the structural features that determine retention. It is anticipated t h a t increased ac cess to modern molecular mechanics and quantum chemical software will lead to identification of easily deter mined s t r u c t u r a l p a r a m e t e r s t h a t better account for physicochemical a n d biological p r o p e r t i e s . W h e n 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 repre senting chemical structures that ac count not only for reactivity but also for properties. In addition, QSRR equations describing retention on enantioselective, protein-based col u m n s and on the immobilized en-

PC1

log k'

Figure 5. Relationship between 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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Figure 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 14 304 ; 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.)

z y m e or r e c e p t o r c o l u m n s s h o u l d be of i n t e r e s t t o a n a l y t i c a l c h e m i s t s a n d other researchers. Support for this research by the Komitet Badan Naukowych, W a r s a w , P o l a n d (Project No. 408319101) is kindly acknowledged.

References (1) Prausnitz, J. M. Science 1979, 205, 759-66. (2) Reichardt, C. Solvent Effects in Organic Chemistry; Verlag Chemie: Weinheim, Germany, 1979; p. 227. (3) Melander, W.; Campbell, D. E.; Horvath, C. / Chromatogr. 1978, 158, 2 1 3 25. (4) Martin, A.J.P. Annu. Rev. Biochem. 1950, 19, 517-42. (5) Kaliszan R. Quantitative StructureChromatographic Retention Relationships; Wiley: New York, 1987; p. 1. (6) Hansch, C ; Fujita, T.J. Am. Chem. Soc. 1964, 86, 1616-19. (7) Bermejo, J.; Blanco, C. G.; Guillen, M. D. /. Chromatogr. 1986, 351, 4 2 5 - 3 2 . (8) Hasan, M. N.; J u r s , P. C. Anal. Chem. 1990, 62, 2318-23. (9) Kier, L. B. Med. Res. Rev. 1987, 7, 4 1 7 40. (10) Scott, R.P.W. /. Chromatogr. 1976, 122 35—53 (11) Karger, B. L.; Snyder, L. R.; Eon, C. / Chromatogr. 1976, 125, 7 1 - 8 8 . (12) Kaliszan, R.; Holtje, H-D. /. Chro matogr. 1982, 234, 3 0 3 - 1 1 .

GFS

(13) Ong, V. S.; Hites, R. A. Anal. Chem. 1991, 63, 2829-34. (14) Osmialowski, K.; Halkiewicz, J.; Radecki, Α.; Kaliszan, R. /. Chromatogr. 1985, 346, 53-60. (15) Vogel, A . I . Textbook of Practical Or ganic Chemistry; Chaucer: London, 1977; p. 1034. (16) Lamparczyk, H.; Radecki, Α.; Kal iszan, R. Biochem. Pharmacol. 1981, 30, 2337-41. (17) Sander, L. C ; Wise, S. A. Crit. Rev. Anal. Chem. 1987, 18, 299-415. (18) Jinno, K ; Kawasaki, Κ Chromatographia 1984, 18, 4 4 - 4 6 . (19) Rohrbaugh, R. H.; J u r s , P. C. Anal. Chem. 1987, 59, 1048-54. (20) Randic, M. / Am. Chem. Soc. 1975, 97, 6609-15. (21) Bosnjak, N.; Michalic, Z.; Trinajstic, N . / Chromatogr. 1991, 540, 430-40. (22) Sarkar, R.; Roy, A. B.; Sarkar, P. K. Math. Biosci. 1978, 39, 299-312. (23) K a l i s z a n , R.; O s m i a l o w s k i , K.; Tomellini, S. Α.; Hsu, S-H.; Fazio, S. D.; Hartwick, R. A.J. Chromatogr. 1986, 352, 141-55. ( 2 4 ) B a s s l e r , B . J . ; K a l i s z a n , R.; Hartwick, R. A . / Chromatogr. 1989, 461, 139-47. (25) Walczak, B.; Chretien, J. R.; Dreux, M.; Morin-Allory, L.; Lafosse, M.; Szymoniak, K ; Membrey, F. / Chromatogr. 1986, 353, 123-37. (26) Cserhati, T.; Valko, K. / Biochem. Biophys. 1990, 20, 8 1 - 9 5 . (27) Braumann, T. /. Chromatogr. 1986, 373 191—225 (28) Clark, C. R.; Barksdale, J. M.; May-

field, C. Α.; Ravis, W. R.; DeRuiter, J. /. Chromatogr. Sci. 1990, 28, 8 3 - 8 7 . (29) Kaliszan, R. Quant. Struct.-Act. Relat. 1990, 9, 8 3 - 8 7 . (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. /. Chromatogr. 1991, 550, 573-84.

Roman Kaliszan is a visiting scientist at McGill University. He is a professor and chairman of the Department ofBiopharmaceutics 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. andaD.Sc. in medicinal chemis try from the Medical Academy of Gdansk in 1975 and 1982, respectively. He has been working on chromatographic QSRRs since 1975.

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