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CONDITIONAL CONSTANTS
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The constants in Eqs (44) and (45) are conditional constants Their value depends on the background salt used in the constant ionic medium reference state (Section 31) 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) in uences the values of the the ion pair constants This was clearly illustrated [277] in the study of the partitioning of the charged form of chlorpromazine into octanol at pH 39 (pKa 924 [150]) in the 0125 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 > Cl > EtSO3 > SO42 , MeSO3 An additional example along this line was described by van der Giesen and Janssen [279], who observed the relationship log PI 1:00 log 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 015 M KCl or NaCl is the background salt, unless otherwise indicated
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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 log P values, with 11,000 con rmed to be of high quality, the log P-star list (No comparably extensive listing of log D values has been reported) Table 41 lists a set of gold standard octanol water log PN ; log PI and log D7:4 values of mostly drug-like molecules, determined by the pH-metric method
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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 coef cient P, de ned in Eq (42), refers to the concentration ratio of a single species In contrast,
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PARTITIONING INTO OCTANOL
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the distribution coef cient D can refer to a collection of species and can depend on pH In the most general sense, D is de ned 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 de ned as X ORG 0 XH ORG 0 XH2 ORG 0 = X XH XH2 r 4:7
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where r is the lipid water volume ratio, v ORG =v H2 O The primed quantity is de ned in concentration units of moles of species dissolved in the organic phase per liter of aqueous phase Assuming a diprotic molecule and substituting Eqs (37), (38), (42), and (44) into Eq (47) yields PA PHA 10 pK a2 pH PH2 A 10 pKa2 pKa1 2 pH 1 10 pK a2 pH 10 pK a2 pK a1 2 pH
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where PA refers to the ion pair partition coef cient of the dianion; PHA , to that of the anion, and PH2 A , to the partition coef cient of the neutral species If no ion pair partitioning takes place, then Eq (48) further simpli es to log D log PN logf1 10 pKa2 pKa1 2pH 10 pKa1 pH g 4:9
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Note that the distribution coef cient depends only on pH, pKa values, and P (not on concentration of sample species) Equation (47) is applicable to all lipophilicity calculations Special cases, such as eq 49, have been tabulated [275] Figures 42a, 43a, and 44a show examples of lipophilicity pro les, log D versus pH, of an acid (ibuprofen), a base (chlorpromazine), and an ampholyte (morphine) The at regions in Figs 42a and 43a 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 PI (The morphine example in Fig 44a is shown free of substantial ion pair partitioning) The other regions in the curves have the slope of either 1 (Fig 42a) or 1 (Fig 43a) or 1 (Fig 44a) Ibuprofen has the octanol water log PHA 397 (indicated by the at region, pH < 4, Fig 42a) and the ion pair log PA 005 in 015 M KCl ( at region, pH > 7) [161] Chlorpromazine has log PB 540 and an ion-pair log PBH 167, also in 015 M KCl (Fig 43a) [161] Ion pairing becomes signi cant 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 PXH 10 pKa pH log 1 10 pKa pH 4:10
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