## H

In a box diagram, if any three of the equilibrium constants are known, the fourth may be readily calculated from Eq. (4.6), taking into account that octanol causes the pKa of weak acids to increase, and that of weak bases to decrease.

In mixtures containing high lipid: water ratios, HCl will appreciably partition into solutions with pH <2.5, as will KOH when pH >11.5 [162,284]. General box diagrams reflecting these caveats have been discussed [275].

### 4.2 CONDITIONAL CONSTANTS

The constants in Eqs. (4.4) and (4.5) are conditional constants. Their value depends on the background salt used in the constant ionic medium reference state (Section 3.1). In the partition reactions considered, the ionized species migrating into the oil phase is accompanied by a counterion, forming a charge-neutral ion pair. The lipophilic nature and concentration of the counterion (as well as that of the charged drug) influences the values of the the ion pair constants. This was clearly illustrated [277] in the study of the partitioning of the charged form of chlor-promazine into octanol at pH 3.9 (pKa 9.24 [150]) in the 0.125 M background salt concentrations: P1 = 56 (KBr), 55 (NaPrSO3), 50 (KNO3), 32 (KCl, NaCl), 31 (NH4Cl), 26 (Me4NCl), 25 (NaEtSO3), 19 (Et4NCl), 16 (Pr4NCl), 15 (Na2SO4, NaMeSO3), 13 (KCl + 2M urea), and 5 (no extra salt used), suggesting the counterion lipophilicity scale: Br~ > PrSO3~ > NO3~ > CP > EtSO3~ > SO42~, MeSO3~. An additional example along this line was described by van der Giesen and Janssen [279], who observed the relationship logP1 = 1.00log[Na+]+ 0.63 for warfarin at pH 11, as a function of sodium concentration. In all the following discussions addressing ion pairs, it is be assumed that 0.15 M KCl or NaCl is the background salt, unless otherwise indicated.

### 4.3 log P DATABASES

A large list of log P values has been tabulated by Leo et al. in a 1971 review [364]. Commercial databases are available [365-369]. The best known is the Pomona College MedChem Database [367], containing 53,000 logP values, with 11,000 confirmed to be of high quality, the ''logP-star'' list. (No comparably extensive listing of log D values has been reported.) Table 4.1 lists a set of "gold standard'' octanol-water log PN, log P1 and log D7 4 values of mostly drug-like molecules, determined by the pH-metric method.

The distribution ratio D is used only in the context of ionizable molecules [229,270-276]. Otherwise, D and P are the same. The partition coefficient P, defined in Eq. (4.2), refers to the concentration ratio of a single species. In contrast, the distribution coefficient D can refer to a collection of species and can depend on pH. In the most general sense, D is defined as the sum of the concentrations of all charge-state forms of a substance dissolved in the lipid phase divided by the sum of those dissolved in water. For a simple multiprotic molecule X, the distribution ratio is defined as

([X(ORG)]' + [XH(ORG)]' +[XH2(qrg)]' + •••)/([X] + [XH] + [XH2 ] + •••)

where r is the lipid-water volume ratio, v(ORG)/v(H2O). The primed quantity is defined in concentration units of moles of species dissolved in the organic phase per liter of aqueous phase. Assuming a diprotic molecule and substituting Eqs. (3.7), (3.8), (4.2), and (4.4) into Eq. (4.7) yields pa + pha10+(pKa2 pH) + pH2A10+(pKa2+pKai-2pH) 8

where PA refers to the ion pair partition coefficient of the dianion; PHA, to that of the anion, and PH2A, to the partition coefficient of the neutral species. If no ion pair partitioning takes place, then Eq. (4.8) further simplifies to logD = logPN - logf 1 + 10-(pK"2+pK"1-2pH + 10-(pKd-pH)} (4.9)

Note that the distribution coefficient depends only on pH, pKa values, and P (not on concentration of sample species). Equation (4.7) is applicable to all lipophilicity calculations. Special cases, such as eq. 4.9, have been tabulated [275].

Figures 4.2a, 4.3a, and 4.4a show examples of lipophilicity profiles, log D versus pH, of an acid (ibuprofen), a base (chlorpromazine), and an ampholyte (morphine). The flat regions in Figs. 4.2a and 4.3a indicate that the log D values have reached the asymptotic limit where they are equal to log P: at one end, log PN and at the other end, log P1. (The morphine example in Fig. 4.4a is shown free of substantial ion pair partitioning.) The other regions in the curves have the slope of either — 1 (Fig. 4.2a) or +1 (Fig. 4.3a) or ±1 (Fig. 4.4a). Ibuprofen has the octanol-water logPHA 3.97 (indicated by the flat region, pH < 4, Fig. 4.2a) and the ion pair logPA —0.05 in 0.15 M KCl (flat region, pH > 7) [161]. Chlorpromazine has logPB 5.40 and an ion-pair logPBH 1.67, also in 0.15 M KCl (Fig. 4.3a) [161]. Ion pairing becomes significant for pH < 6 with the base. The equation that describes the sigmoidal curve, valid for monoprotic acids and bases for the entire pH range, is log D = log(Px + PXH10+pKa—pH)— log(1 + 10+pKa pH) (4.10)

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