Lipopbilicity and drug activity
`
`By Hugo Kubinyi
`Chemical Research and Development of BASF Pharma Division,
`Knoll AG, D-6700 LudwigshafeniRhein, Germany
`
`Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`1
`The additivity concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`2
`Lipophilicity parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3
`3.1 Partition coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.2 Calculation of partition coefficients. nand fvalues . . . . . . . . . . . . . . . . .
`3.3 Dissociation and partition coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.4 The rate constants of drug partitioning. . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.5 Chromatographic parameters ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.6 Molecular connectivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`3.7 Other parameters related to lipophilicity . . . . . . . . . . . . . . . . . . . . . . . . . .
`4
`Linear dependence of biological activity on lipophilicity. . . . . . . . . . . . .
`5 Nonlinear dependence of biological activity on lipophilicity. . . . . . . . . .
`5.1 Reasons for nonlinear relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.2 The parabolic model and related empirical models. . . . . . . . . . . . . . . . .
`5.3 Equilibrium models of drug partitioning. . . . . . . . . . . . . . . . . . . . . . . . . .
`5.4 Kinetic models of drug transport. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.5 The bilinear model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`5.6 Models for transport and distribution of ionizable drugs. . . . . . . . . . . . .
`5.7 Consequences for additive de novo models. . . . . . . . . . . . . . . . . . . . . . . .
`6
`The future development of QSAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`Acknowledgments.. . ... .. ..... . . . .. . ... . . . . . . .. . . ... . .. . . .. . . .
`References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
`
`97
`
`98
`99
`102
`102
`107
`112
`119
`122
`126
`132
`137
`148
`148
`151
`156
`161
`168
`174
`185
`187
`189
`189
`
`H. Kubinyi et al., Progress in Drug Research / Fortschritte der Arzneimittelforschung / Progrès des
` recherches pharmaceutiques © Birkhäuser Verlag Basel 1979
`
`Micro Labs Exhibit 1063
`Micro Labs v. Santen Pharm. and Asahi Glass
`IPR2017-01434
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`

`98
`
`1
`
`Introduction
`
`Hugo Kubinyi: Lipophilicity and drug activity
`
`The understanding of drug potency in biological systems requires an un(cid:173)
`derstanding of chemical structures in terms of physical and chemical
`properties: transport and distribution of a drug in a biological multicom(cid:173)
`partment system, the affmity of the drug to a complementary - structur(cid:173)
`ally unknown - receptor, and the interaction of the drug with its receptor
`obviously depend on these properties.
`In drug design the fIrst step is the more or less systematic variation of a
`lead compound to derive some hypotheses of relationships between
`chemical structure and biological activity. In the next step these hypo(cid:173)
`theses are used to arrive at improved derivatives of the original lead com(cid:173)
`pound with minimal effort. The introduction of the Hansch model in
`1964 enabled medicinal chemists to formulate their hypotheses of struc(cid:173)
`ture-activity relationships in quantitative terms and to check these hypo(cid:173)
`theses by means of statistical methods. From such quantitative structure(cid:173)
`activity relationships (QSAR) it is possible to elucidate the influence of
`various physicochemical properties on drug potency and to predict activ(cid:173)
`ity values for new compounds within certain limits.
`The main purpose of this review is to sum up some developments of
`QSAR since 1971, when the review 'On the understanding of drug po(cid:173)
`tency' [1] appeared in this series. Three excellent books on QSAR have
`been published in the meantime, the introductory book by Purcell, Bass
`and Clayton [2] and two comprehensive monographs by Martin [3] and
`Seydel and Schaper [4]. Monographs on selected topics [5, 6], several
`symposia proceedings [7-10], review articles [11-28], and a rapidly in(cid:173)
`creasing number of publications reflect the growing importance of QSAR
`in medicinal chemistry.
`During the last decade QSAR started.to develop from a merely intuitive
`and empirical discipline to a more and more theoretically based science.
`Drug design will remain a sophisticated art all the time; however, from
`QSAR medicinal chemists gained new insights which allow the applica(cid:173)
`tion of more rational approaches, especially in lead structure optimiza(cid:173)
`tion. The largest progress has been made in describing the lipophilicity of
`drugs and in understanding the dependence of drug activity on lipophil(cid:173)
`icity. Therefore special emphasis is placed on lipophilicity and drug ac(cid:173)
`tivity in this review.
`
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`Hugo Kubinyi: Lipophilicity and drug activity
`
`99
`
`2
`
`The additivity concept
`
`The fundamental basis of all quantitative structure-activity analyses is the
`concept of additivity: all substructures of a drug are assumed to contrib(cid:173)
`ute to biological activity in an additive manner, each part of the structure
`irrespective of all other variations in the molecule. There is no sharp defi(cid:173)
`nition of the term substructure, each substituent and each partial struc(cid:173)
`ture with unique chemical properties can be regarded as a substructure:
`sometimes single atoms, e.g. the halogens, sometimes larger groups, e.g. a
`sulfonamido or pyridyl group, are taken as substructures.
`The environment of a substructure has of course a significant influence
`on its chemical properties and therefore different activity contributions
`may be observed for identical groups in different positions of a molecule.
`For drugs interacting with a specific receptor additional differences result
`from the asymmetric topology of the receptor. Taking this into considera(cid:173)
`tion the different biological activities of optical enantiomers are compat(cid:173)
`ible with the additivity concept.
`Is there a rationale of the additivity concept of drug-receptor interac(cid:173)
`tions? There is one: if the aflinity of a drug to its receptor depends only
`on the physicochemical properties of the complementary binding sites
`and if these physicochemical properties are additive themselves, also the
`receptor affInity of a drug should be an additive molecular property. It
`must be emphasized that the structure and the physicochemical proper(cid:173)
`ties of the receptor binding site need not be known because this part of
`the system remains constant. Such 'simple' drug-receptor interactions can
`be studied e.g. in isolated enzyme systems or in receptor preparations.
`As far as hydrophobic interactions are concerned, the additivity concept
`can be illustrated by the driving forces of hydrophobic interactions (fig. I )
`[3, 29, 30]. A nonpolar drug and a hydrophobic region of a receptor are
`surrounded by water molecules which are more or less ordered and
`therefore in a higher state of energy than in free solution. In the drug(cid:173)
`receptor complex a smaller number of water molecules is in contact with
`hydrophobic surfaces; the resulting increase in entropy leads to a stabili(cid:173)
`zation of the drug-receptor complex. It is obvious that the gain in free
`energy should be proportional to the number of water molecules chang(cid:173)
`ing from an ordered to an unordered state, i.e. proportional to the surface
`area of the nonpolar part of the drug. Specific polar, electronic and steric
`effects may add to these unspecific interactions.
`
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`

`100
`
`Hugo Kubinyi: Lipophilicity and drug activity
`
`R
`
`)
`
`~
`
`Figure I
`b.c O 0 0 0
`Schematic representation of
`00000 0
`0000000""
`hydrophobic interaction.
`0 0°0 0 0 00 ('0
`R= hydrophobic part of
`OO~
`receptor covered by c water
`molecules; D= approaching
`drug enveloped by a + b water
`molecules; D-R= drug-receptor
`interaction complex with a
`representing ordered water
`molecules covering D-Rand
`b + c are the displaced,
`disordered water molecules
`(reprinted from [29] with
`permission of the copyright
`owner).
`
`O- R
`
`In more complex systems like isolated cells, bacteria, isolated organs, or
`whole animals the biological activity of a drug depends not only on the
`receptor affmity but also on the absorption and distribution of the drug:
`the more complex the system is, the more important will the influence of
`absorption and distribution be.
`Lipophilicity is the main factor governing transport and distribution of
`drugs in biological systems. Although these drug characteristics are - for
`a given biological system - unequivocally a function of chemical struc(cid:173)
`ture and time, the relationships are not as simple as in the case of drug(cid:173)
`receptor interactions. Nonlinear lipophilicity-activity relationships have
`been known since long but they could not be described mathematically
`until fifteen years ago; today the understanding of the dependence of
`drug distribution in biological systems on lipophilicity is much better
`than in the early days of QSAR.
`However, there are some other effects which cause departures from the
`additivity concept. Metabolism of drugs is - because of the specifIty of
`the involved enzymes - no simple function of a defmite molecular prop(cid:173)
`erty, but depends on the presence of certain substructures. As long as
`these substructures are common to all molecules of a series, one can be
`confident that a quantitative relationship can be derived for these meta(cid:173)
`bolic conversions too. If the metabolic conversions take place at a
`position of substituent variation, the additivity concept is seriously dis(cid:173)
`turbed. Examples for such metabolic conversions are e.g. the hydroxyl(cid:173)
`ation of aromatic rings, the reduction of nitro groups to amino groups
`and the cleavage of ethers, esters, ami des and amines.
`
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`
`

`

`Hugo Kubinyi: Lipopbilicity and drug activity
`
`101
`
`Other nonlinear effects may arise from steric crowding of substituents,
`leading to lower than predicted activity, and cooperative binding, leading
`to higher than predicted activity. While the effects from steric crowding
`are easy to understand, cooperative binding can be explained only in
`thermodynamic terms. Each interaction between a drug substructure and
`the complementary receptor site causes an enthalpy and an entropy
`change. Once a drug molecule is fIxed at its binding site by one or more
`specifIc interactions, no entropy loss will result from further interactions.
`Hence, if two or more substructures of a drug molecule fIt to a comple(cid:173)
`mentary structure, the overall binding force may be higher than the sum
`of the individual contributions. Although all single drug-receptor inter(cid:173)
`actions are weak bonds, the high affinity and specifIty of most drugs can
`be explained by this cooperative effect.
`While we are far from a general mathematical model including all fac(cid:173)
`tors responsible for the relationships between chemical structure and bio(cid:173)
`logical activity, the linear free energy related Hansch model in its linear
`[eq. (1)] and parabolic form [eq. (2)] [31-34] and the de novo model of
`Free and Wilson [eq. (3)] [35] have proven their utility for the quantita(cid:173)
`tive description of such relationships and have confIrmed the additivity
`concept of biological activity group contributions.
`
`10gl/C=alogP+ bO'+c,
`
`logl/C= a(1ogp)2+ blogP+ CO'+ d,
`
`logl/C= ~:ai+ fl..
`i
`
`(I)
`
`(2)
`
`(3)
`
`In these equations C is a molar concentration causing a standard bio(cid:173)
`logical response, e.g. an ED 50 or LD 50. P is the partition coefficient, 0' is
`the Hammett constant, and a, b, c and d are constants determined by
`linear multiple regression analysis. Other physicochemical parameters
`can be used instead of or in addition to P and 0' in equations (1) and (2).
`In equation (3) ai are the values of the substituent group contributions to
`biological activity, and fl. is regarded to be the activity contribution of the
`parent system (in Fujita-Ban analysis [36, 37] fl. is the theoretical bio(cid:173)
`logical activity value of the reference compound). Both the Hansch and
`Free-Wilson analysis have been reviewed in the literature [1-4, 11-19];
`only new developments concerning the methodology will be discussed in
`this review.
`
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`

`102
`
`3
`3.1
`
`Hugo Kubinyi: Lipophilicity and drug activity
`
`Lipophilicity parameters
`Partition coefficients
`
`(4)
`
`The lipophilicity of a drug is dermed by the partition coefficient P, which
`is the ratio of equilibrium concentrations of a drug in an organic phase,
`corg> and an aqueous phase, caq [eq. (4)].
`P= corg •
`caq
`n-Octanol/water has proven to be the system of choice for measuring
`partition coefficients for QSAR studies [33, 38, 39] due to its similarity to
`biological systems: like n-octanol biological membranes are made up
`from hydrophobic alkyl chains and polar groups. In addition to this simi(cid:173)
`larity n-octanol has some theoretical and practical advantages as com(cid:173)
`pared with other organic solvents:
`- A much broader spectrum of compounds is soluble in n-octanol than
`in aliphatic or aromatic hydrocarbons; the hydroxyl group of n-octanol
`can act as a hydrogen bond donor as well as an acceptor.
`- While n-octanol is practically insoluble in water, it dissolves an appre(cid:173)
`ciable amount of water (2.3M, which corresponds to a molar ratio ofn-oc(cid:173)
`tanol:water ~4:1) under eqUilibrium conditions. Hydrogen bonds need
`not be broken during the transfer of a solvated drug molecule from the
`aqueous phase to the organic phase. Therefore n-octanol/water partition
`coefficients reflect only hydrophobic interactions, while hydrocarbon!
`water partition coefficients are additionally influenced by desolvation
`energies.
`-
`n-Octanol has low vapor pressure at room temperature.
`It is well suited for direct measurement of concentrations in the ultra-
`-
`violet region due to its low absorption over a wide range.
`-
`n-Octanol/water partition coefficients are available from the literature
`(for a review see [38]) and from the Hansch data bank for a large number
`of drugs. The hydrophobic substituent constant n and the hydrophobic
`fragmental constant f, which allow the calculation of partition coefficients
`(see below), refer to the n-octanol/water system.
`The experimental measurement of partition coefficients has been re(cid:173)
`viewed by Purcell et aL [2], Martin [3] and Rekker [6].
`The use of a model system for drug/biological system interactions is justi(cid:173)
`fied by the Collander equation (5) [40],
`logP2 = alogP 1 + b,
`
`(5)
`
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`

`Hugo Kubinyi: Lipophilicity and drug activity
`
`103
`
`which relates partition coefficients from similar solvent systems. Collan(cid:173)
`der equations with slopes a and correlation coefficients r close to unity
`are observed for homologous series of compounds. As an example the
`partition coefficients of 4-alkylpyridines in different solvent systems [41]
`are correlated with their n-octanol/water partition coefficients in table 1.
`
`Table 1
`Collander equations for the partition coefficients of homologous 4-alkylpyridines
`in different solvent systems (derived from the data ofYeh and Higuchi [41]).
`log P= a log P OCI+ b.
`
`Solvent
`
`a
`
`b
`
`Hexadecane
`Octane
`Butyl ether
`Carbon tetrachloride
`Chloroform
`
`1.036 (±0.04)
`1.064 (±0.04)
`1.024 (±0.04)
`1.064 (±0.04)
`1.047 (± 0.03)
`
`-1.199 (±0.15)
`-1.139(±O.l7)
`-0.781 (±0.16)
`-0.503 (±O.l6)
`0.462 (±0.1O)
`
`n
`
`7
`7
`6
`6
`7
`
`r
`
`s
`
`1.000 0.070
`0.999
`0.080
`1.000 0.072
`1.000 0.071
`1.000 0.044
`
`No such close relationships can be expected for heterogeneous groups of
`compounds because, in addition to hydrophobic interactions, solvation
`forces will influence the interrelationships between different solvent
`systems. Equation (5) has been extended to a large number of partition(cid:173)
`ing systems by Leo and Hansch [38, 42, 43]. While close correlations are
`obtained between n-octanol/water and other polar systems, like ketone/
`water, ester/water and alcohol/water systems [e.g. eq. (6)-(8)], systems
`with less polar organic solvents, like aliphatic or aromatic hydrocarbons,
`or diethyl ether gave poor correlations with the n-octanol/water system.
`
`Oleyl alcohol
`10gP= 0.999(±0.06)10gP oct- 0.575(±0.11)
`(n= 37; r= 0.985; s= 0.225),
`
`primary butanols
`10gP = 0.697 (± 0.02)logP oct + 0.381 (± 0.03)
`(n= 57; r= 0.993; s= 0.123),
`
`methyl isobutyl ketone
`10gP= 1.094(±0.07)logP oct+ 0.050(± 0.11)
`(n= 17; r=0.993; s=0.184).
`
`(6)
`
`(I)
`
`(8)
`
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`

`104
`
`Hugo Kubinyi: Lipophilicity and drug activity
`
`Only after categorization of the solutes into 'hydrogen bond donors' and
`'hydrogen bond acceptors' satisfactory correlations could be obtained
`[e.g. eq. (9)-(12)].
`
`Benzene, H-donor solutes
`
`logP= 1.0l5(±0.11)logPoct-1.402(±0.14)
`(n=33; r=0.962; s=0.234),
`
`benzene, H -acceptor solutes
`
`logP= 1.223(±0.19)logP oct- 0.573(±0.20)
`(n= 19; r= 0.958; s= 0.291),
`
`diethyl ether, H-donor solutes
`
`logP= 1. 130(± 0.04)logP oct-O.l70(±0.05)
`(n=71; r=0.988; s=0.186),
`
`diethyl ether, H-acceptor solutes
`
`logP= 1.142(±0.13)logPoct -1.070(±0.12)
`(n= 32; r= 0.957; s= 0.326).
`
`(9)
`
`(10)
`
`(11)
`
`(12)
`
`In the case of chloroform and carbon tetrachloride a third equation was
`needed for 'neutral' solutes, having both donor and acceptor ability [eq.
`(13)-(15)] [42].
`
`Chloroform, H-donor solutes
`
`logP= 1.126(±0.12)logPoct -1.343(±0.21)
`(n= 28; r= 0.967; s= 0.308),
`
`chloroform, neutral solutes
`
`logP= 1. 1O(±0.12)logP oct- 0.649(±0.18)
`(n= 23; r= 0.971; s= 0.292),
`
`chloroform, H-acceptor solutes
`logP= 1.276(±0.14)logPoct+ 0.171(±0.17)
`(n=21; r=0.976; s=0.25l).
`
`(13)
`
`(14)
`
`(15)
`
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`

`Hugo Kubinyi: Lipophilicity and drug activity
`
`105
`
`While the slopes of equations (13)-(15) are parallel, the intercepts show
`significant differences; the intercept of equation (14) is in the middle be(cid:173)
`tween the intercepts of equations (13) and (15), which is to be expected.
`However, the categorization of solutes into donors and acceptors may be
`a too rough differentiation for correlating partition coefficients from dif(cid:173)
`ferent solvent systems. For a group of substituted phenols Leo et aL [38]
`derived equation (16):
`.
`10gP oct = 0.5010gP cyc10hexane + 2.43
`(n=9; r=0.79l; s=0.39l).
`
`(16)
`
`If they accounted for the hydrogen binding ability of the phenols by add(cid:173)
`ing a term 10gKHB [44], they obtained equation (17) with a much better
`correlation coefficient and a significantly lower standard deviation.
`10gP oct = l.00logP cyc10hexane + 1.20logKHB+ 2.35
`(n= 9; r= 0.979; s= 0.140).
`
`(17)
`
`From a much larger set of partition coefficients in cyc10hexane/water and
`aliphatic hydrocarbon/water systems Seiler derived an additive constant
`IH as a measure of the hydrogen binding ability of different substituents
`and substructures [eq. (18)] [45]. Some representative IH values are given
`in table 2.
`
`(18)
`
`Table 2
`IHvalues ofsubstituents and substructures [45].
`
`SubstituenVsubstructure
`
`Aromatic-COOH
`Aromatic-OH
`-CONH-
`-S02NH-
`Aliphatic-OH
`AUphlltic-NH2
`Aromatic-NH2
`-NR IR2 (R I, R2+ H)
`-N0 2
`~ C=O
`-C=N
`-0-
`artha-Substitution to -OH, -COOH, -NRIR2
`
`2.87
`2.60
`2.56
`l.93
`l.82
`1.33
`1.18
`0.55
`0.45
`0.31
`0.23
`0.11
`-0.62
`
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`

`106
`
`Hugo Kubinyi: Lipophilicity and drug activity
`
`The continous range of IH values suggests that the boundaries between
`H-donors and H-acceptors are fluid. The regression coefficients a= 1.00
`in equations (17) and (18) give some evidence that all possible Collander
`equations are strictly parallel if the effect of solvation is accounted for by
`introducing IH or a similar parameter into the correlation equation. The
`only exceptions are systems with very polar organic phases, like butanols,
`pentanols, cyclohexanol or butanone, which lead to regression coeffi(cid:173)
`cients a< 1.0 [compare eq. (7)]; these solvents contain so much water
`(approx. 9-17%) under equilibrium conditions, that the organic phase is
`significantly 'diluted'. On the other hand, dilution of the aqueous phase
`with an organic solvent which is only slightly soluble in the organic phase
`leads to a similar decrease of the regression coefficient a [eq. (19)] [38].
`
`Ether/50"110 aqueous dimethylformamide
`
`10gP = O.400logP oct - 0.321
`(n= 6; r= 0.988; s= 0.058).
`
`(19)
`
`Although equations (6)-(15) and similar equations may be used to con(cid:173)
`vert partition coefficients from one solvent system to another system, the
`results should be considered with suspicion. The standard deviations of
`most Collander equations are higher than those of the equations pre(cid:173)
`sented in table 1 and much higher than the standard deviations of experi(cid:173)
`mental measurements. While partition coefficients predicted within a
`closely related series of compounds will be reliable, only approximate
`values may result for structurally diverse compounds.
`Equation (5) also applies to the binding of drugs to organic and bio(cid:173)
`logical macromolecules and to the distribution of organic compounds be(cid:173)
`tween aqueous phases and biological membranes [e.g. eq. (20)-(22)] [11,
`33,38].
`
`Binding of acetanilides to nylon [46]
`
`logK=0.69(±0.23)logP-7.I6(±0.37)
`(n=7; r=0.96I; s=0.203),
`
`(20)
`
`binding of misc. neutral compounds to bovine serum albumin (1: 1) [47]
`
`10gI/C= 0.75I(±0.07)logP+ 2.300(±0.I5)
`(n=42; r=0.960; s=0.I59)
`
`(21)
`
`Micro Labs Exhibit 1063-10
`
`

`

`Hugo Kubinyi: Lipophilicity and drug activity
`
`107
`
`partitioning of alcohols between human erythrocyte membranes and
`buffer [48]
`
`10gP= 1.003(±O.l3)logP oct- 0.883(±0.39)
`(n= 5; r=0.998; s=0.082).
`
`(22)
`
`The slope a= 1.00 in equation (22) is a further justification for the use of
`n-octanoVwater as a model system for the interaction of drugs with bio(cid:173)
`logical systems; slopes between 0.5 and 0.8 are observed for equations
`correlating the binding of organic compounds to biological macromole(cid:173)
`cules with n-octanoVwater partition coefficients, indicating the more or
`less polar nature of these binding sites.
`
`3.2
`
`Calculation of partition coefficients.7l and fvalues
`
`If a linear free energy related model like the Hansch model is used to
`describe and predict biological activities in terms of physicochemical
`parameters, these parameters must be known for all compounds included
`in the analysis. In order to simplify QSAR analyses it is desirable to
`predict physicochemical properties from chemical structures; such pre(cid:173)
`dictions can then be used to estimate the biological activity of new,
`hitherto unknown compounds.
`One of the pioneering achievements of Hansch was the demonstration
`that partition coefficients are - in the logarithmic scale - an additive
`constitutive molecular property, like molar volume, molar refractivity,
`parachor and Hammett (J values. In this context additive means that
`partition coefficients can be calculated by simply adding increments of
`partial structures and constitutive means that the increment values de(cid:173)
`pend on the relative position and environment of the partial structures.
`Hansch et al. [49, 50] defmed the hydrophobic substituent constant 1l
`[eq. (23)] of a substituent X as the difference of 10gP values of the substi(cid:173)
`tuted compound R - X and the unsubstituted compound R - H.
`
`(23)
`
`From eight different series of aromatic compounds 1l values for the most
`important aromatic substituents could be derived [49]. Slightly different
`values were obtained for meta and para substituents indicating some elec(cid:173)
`tronic interactions. Today the most often used values are the 1l values
`
`Micro Labs Exhibit 1063-11
`
`

`

`108
`
`Hugo Kubinyi: Lipophilicity and drug activity
`
`derived from substituted phenoxyacetic acids [49] and from substituted
`benzenes [49,51,52]. n- Values [49,53], derived from substituted phenols
`and anilines, should be used for aromatic compounds bearing additional
`electron donor substituents. The differences between nand n- values
`arise from electronic interactions as can be seen from equation (24),
`which correlates n values from substituted phenols and benzenes with
`Hammett a values of the corresponding substituents [49].
`LIn = nphenoI- nbenzene= 0.8230' + 0.061
`(n=24; r=0.954; s=0.097).
`
`(24)
`
`A compilation of nand n- values for selected ortho, meta and para sub(cid:173)
`stituents has been published by Norrington et al. [53], while two parame(cid:173)
`ter collections of Hansch et al. [51, 52] contain some 170 n values derived
`from substituted benzenes.
`The decision which series of n values should be used for the calculation
`of 10gP values depends on the chemical structures of the parent com(cid:173)
`pounds: the closer the relationship between both parent structures, the
`more accurate the calculated partition coefficients. Partition coefficients
`calculated for molecules differing in their parent structure too much from
`the parent structure of the used n system wi11lead to erroneous results, a
`fact which is sometimes neglected in QSAR studies.
`Deviations from n additivity have been observed for polysubstituted aro(cid:173)
`matic compounds, e.g. 1,2,3-trimethoxybenzene [38], for o,o'-disubsti(cid:173)
`tuted phenols [38, 54, 55] and for compounds like salicylic acid, where
`hydrogen bonds between two polar ortho substituents reduce the hydro(cid:173)
`philic nature of both groups [38].
`The extension of the n concept to aliphatic compounds led to some
`serious problems. First, the set of aliphatic n values derived by Hansch et
`al. [50] is based on a too small number of data points. Secondly, the use
`of equation (25) [13] is an incorrect application of the n concept [eq.
`(23)] [6].
`
`(25)
`
`Thirdly, no differentiation was made between nCH3 and nCH2. As a con(cid:173)
`sequence, the n concept failed in the calculation of some 10gP values,
`e.g. the calculation of the 10gP value of 1,2-diphenylethane from
`logPc6H6 and nCH3 [eq. (26)] [56].
`
`Micro Labs Exhibit 1063-12
`
`

`

`Hugo Kubinyi: Lipophilicity and drug activity
`
`10gP C6H5CH2CH2C6H5= 2logP C6H6 + 27rCH3= 4.26+ 1.00= 5.26
`exptl.1ogP=4.79 [38].
`
`109
`
`(26)
`
`Folding of co-substituted phenylpropanes, C6H5CH2CH2CH2X, with in(cid:173)
`tramolecular hydrophobic bonding was assumed to explain deviations
`between observed and calculated partition coefficients [38, 57].
`From the deftnition of 7r values [eq. (23)] obviously 7rH must be zero;
`however, this does not imply that the lipophilicity contribution of a hy(cid:173)
`drogen atom per se has to be zero [58]. Rekker [59] reinvestigated the
`problem of folding and criticized the inappropriate application of the 7r
`concept. He formulated a new system of hydrophobic fragmental con(cid:173)
`stants f, defmed by equation (27) [6, 59-61].
`10gP= L ali.
`
`(27)
`
`i
`While 7r values are lipophilicity contributions relative to hydrogen sub(cid:173)
`stitution, the fi values of equation (27) are absolute contributions of sub(cid:173)
`stituents and substructures to the totallipophilicity; ai indicates how often
`a given fragment occurs in the structure. Statistical evaluation of some
`300 partition coefficients led to a ftrst set of aromatic and aliphatic f val(cid:173)
`ues which was further refmed upon by consideration of proximity effects
`and other corrective terms discussed below.
`The main difference between the 7r and f system results from the fact that
`there is a hydrophobic fragmental constant of the hydrogen atom, fH
`=0.175. No branching corrections are needed for aliphatic compounds
`because different f values for -CH3, -CH2-, -CH- and quaternary C
`resulted from the regression analyses. However, the differences between
`these values are not regular (different sets of similar f values - depending
`on the compounds and correction factors used in the calculation - have
`been published by Rekker et al. [6, 59, 60]; the values presented here and
`below are taken from the appendix of [6]):
`
`fcH3 =0.702} A=0.172
`fCH2 = 0.530} A = 0.295
`fCH =0.235 }
`fc =0.15
`(fH=0.175).
`The correct application of Rekker f values requires the consideration of
`certain corrections:
`
`A=0.085
`
`Micro Labs Exhibit 1063-13
`
`

`

`110
`
`Hugo Kubinyi: Lipophilicity and drug activity
`
`(I) Proximity effects: if two electronegative groups like -OH, -0-,
`-COOH or -NH2 are separated by only one or two saturated carbon
`atoms, the overalllipophilicity is higher than predicted; correction factors
`0.861 and 0.574, respectively, must be added.
`(2) Hydrogen attached to an electronegative group: a hydrogen atom
`bound to -COOH, -COOR, -COR, -CONH2' etc. has an increased fH
`value of 0.462 instead of the normal value fH=0.175.
`(3) Conjugated and cross-conjugated systems: if two aromatic rings are
`conjugated (e.g. biphenyl) or cross-conjugated (e.g. benzophenone), a
`correction factor of 0.28 must be added.
`(4) Condensed aromatic systems like naphthalene require a correction
`factor of 0.31 for each pair of carbon atoms common to two aromatic
`rings.
`Whether the correction factors and the differences between aliphatic and
`aromatic f values can be explained by a 'magic' constant cM = 0.28 or
`multiples of this value [6], is still subject to discussion. However, the cor(cid:173)
`rect application of the f system does not depend on the right answer to
`this more or less philosophical problem.
`The most impressive result from the use of equation (27) is that 10gP val(cid:173)
`ues of aliphatic and araliphatic compounds can be calculated with high
`accuracy; the problems of folding and intramolecular hydrophobic bonds
`do not exist any longer.
`
`Calculation oflogP C6HS(CH2)3Cl from 7l values:
`
`10gP= 10gPbenzene+ 371CH3 + 7laliph.Cl= 2.13+ 1.50+0.39=4.02. (28)
`
`Calculation oflogP C6Hs(CH2hCl from fvalues:
`
`10gP= fC6Hs + 3fcH2 + faliph.Cl= ·1.886+ 1.590+ 0.061 = 3.537
`exptl.1ogP=3.55 [50].
`
`(29)
`
`Starting from equation (27), but using a different approach, Leo et al.
`[62] derived another set of f values. From the 10gP values of hydrogen
`and some lower hydrocarbons they calculated strictly additive fcH3,
`fcH2, fCH' fc and fH values (see table 3) and used these values for the cal(cid:173)
`culation of all other f values. The disadvantage of this approach is that
`Leo et al. had to consider negative correction factors fb for 'each single
`carbon-carbon bond after the ftrst one' when calculating 10gP values of
`
`Micro Labs Exhibit 1063-14
`
`

`

`Hugo Kubinyi: Lipopbilicity and drug activity
`
`III
`
`larger molecules. A comparison of some representative f values and cor(cid:173)
`rection factors is given in table 3 together with aromatic 7t values. As ex(cid:173)
`pected from the defInition of 7t and f values, the aromatic f values of both
`
`Table 3
`Hydrophobic fragmental constants f and 7t values of selected substructures and
`substituents.
`
`Fragment
`
`Fragmental constants f
`Reller [6]
`aliph.
`
`arom.
`
`Leo et al. [62]
`aliph.
`arom.
`
`0.175
`0.702
`0.530
`0.235
`0.15
`1.886
`1.688
`1.431
`
`-0.462
`0.061
`0.270
`0.587
`-1.491
`-1.581
`-0.954
`-1.428
`-1.825
`-0.939
`-1.970
`-1.703
`0.757
`-1.066
`0.00
`-0.51
`
`0.399
`0.922
`1.131
`1.448
`-0.343
`-0.433
`-0.093
`-0.854
`-0.964
`-0.078
`-1.109
`-0.842
`1.331
`-0.205
`0.62
`0.11
`
`H
`CH3
`CH2
`CH
`C
`CJIs
`CJI4
`CJI3
`
`F
`CI
`Dr
`I
`OH
`-0-
`COOH
`NH2
`NH
`N02
`CONH2
`>C=O
`CF3
`C=N
`SH
`-s-
`
`Correction factors
`Reller
`
`0.23
`0.89
`0.66
`0.43
`0.20
`1.90
`
`-0.38
`0.06
`0.20
`0.60
`-1.64
`-1.81
`-1.09
`-1.54
`-2.11
`-1.26
`-2.18
`-1.90
`
`0.37
`0.94
`1.09
`1.35
`-0.40
`-0.57
`-0.03
`-1.00
`-1.03
`-0.02
`-1.26
`-0.32
`
`-1.28
`
`-0.34
`
`-0.79
`
`0.03
`
`Leo et al.
`
`7tbenzene
`[51]
`
`0.00
`0.56
`
`1.96
`
`0.14
`0.71
`0.86
`1.12
`-0.67
`
`-0.32
`-1.23
`
`-0.28
`-1.49
`
`0.88
`-0.57
`0.39
`
`Proximity effect 1
`Proximity effect 2
`H on electronegative group
`Aryl conjugation
`Condensed aromatic system
`
`0.861
`0.574
`0.287
`0.28
`0.31
`
`fb(chain)
`fb (cyclic)
`Chain branching
`Group branching
`
`-0.12
`-0