## Application of Shape Analysis to One Point log D Shake Flask Measurement

It is a common practice to measure log D at one buffered pH (often 7.4) and calculate the log P of the substance using case 1 a equation for weak acids and case 1 b equation for weak bases (Table 1). If the pH of the buffer and the pK.d of the molecule differ by

Lipophilicity Profile: Weak Base

Lipophilicity Profile: Weak Base

 pH = . zone 1' PKo t !ogD — !o gPx -y -- - zone 2 /• ; y^zone 3 zone 2 ^logD = togPxH zone 1 1_ — pH = p0 Ka "rn

10 12

logD 5

zone 2'

zone 2

logD 1

Figure 9. (a) Dissection of the lipophilicity profile for a weak base with a pK^ 10, log P 5 and log P (ion pair) 0 (the "Scherrer" pK„ po^a'"", is 5) into zones of zero-slope (1 and 1'), zones of curvature (2 and 2 ) and zone of unit-slope (3). (b) Zone 2 close-up view, (c) Zone 2 close-up view.

more than 1-2 units, the calculation can be in error. This is because ion-pairing may be an unaccounted contribution in a single log D measurement.

Let us take aprindine as an example. The pKit of aprindine is'9.95 and log D was measured as -0.09 at pH , The calculated log Px was reported to be 4.86. How reliable is the "correction"? Let us apply the shape analysis concepts of the last section. If the single log D is in zone 3, then indeed log Px would have to be 4.86. What boundaries can one put on the value of log Pxh? We know that since zone 2 is 1.66 log D units in height, the ion-pair log PXH cannot be greater than -1.75 (-0.09-1.66). This is depicted by curve 1 in Fig. 10. Curve 1' in the figure corresponds to lower values of log Pxh- Therefore, the difference between the neutral log Px and ion-pair log Pxli is greater than 6.6. This is unreasonably high.

For simple monoprotic substances, the difference between log Pneutrai and log Piott is usually 3-4 units [23, 31]. This is substantiated by our own measurements, shown in Table 2 for a variety of drug substances. Bulky, multiprotic molecules with extensive electronic derealization can have substantially lowered differences. Small peptides Figure 10. Several possible interpretations of the aprindine lipophilicity profile (see text).

can even have negative differences (that is, log Pm„ >log Pneulrai), as indicated in Table 2.

Let us test another hypothesis. Let us assume the single log D measurement is from point C in zone 2 (the Scherrer pKa). If that were so, then log Px is 4.57 (1.66 - 0.30 -0.09 + log (1 + 10"'95-5)) and log PXH is -0.39 (-0.30 -0.09). Now the log P difference is 4.96; this is more reasonable. This situation is represented by curve 2 in Fig. 10.

Let us consider the third hypothesis: the log P measurement was made from the zone 1 portion of the lipophilicity curve. This immediately fixes log Pxh to -0.09. What can one say about log Px? It can be no higher than 3.21 (-0.09 + 9.95 -6.65), which is a constraint imposed by curve shape and the pKa. This maximum log P is depicted by curve 3 in Fig. 10. In principle, the value can be lower, as illustrated by the bounding curve 3' in the figure. Therefore, for this case the log P difference is no greater than 3.30.

The hypotheses testing suggests that a single log D measurement (plus "correction") is not an ideal way to determine log P. Had two points been measured, then in principle, eq. (20) could have determined both the ion-pair and neutral log Ps. Of course, many log D measurements for a given molecule would reliably determine the underlying partition coefficients.

 Substance AlogP AlogP AlogP Reference (0.15 m KCl) (0.15 m NaCl) (no added salt) Buprenorphine 4.73 b Ibuprofen 4.02 4.89 c Deprenyl 3.85 d Chlorpromazine 3.73 3.75 5.04 c (2,4-Dichlorphenoxy) 3.65 d acetic acid pF-deprenyl 3.64 d Prostaglandin E2 3.44  Prostaglandin E, 3.43 3.80 3.95 P] Papaverine 3.17 d Lidocaine 2.96 d Niflumic acid 2.65 3.27 
 Substance AlogP AlogP AlogP Reference (0.15 M KCl) (0.15 M NaCl) (no added salt) Quinine 2.60 3.43 c Propranolol 2.59 c Hydroxyzine 2.56 d Diacetylmorphine 2.52 b TRP-Phe 2.16 d Morphine 2.13 2.27 b Buprenorphine 2.13 b 6-Acetylmorphine 1.97 b Terbutaline 1.89,1.97 d 3-Aminobenzoic acid 1.27 d 4-Aminobenzoic acid 1.26 d 4-Methylumbilleferyl- 0.93 b ß-glucuronide Trp-Trp 0.89 d Pyridoxine 0.83 0.23 c Tryptophan 0.80 d Niflumic acid 0.68 1.23  Phe-Phe-Phe 0.57 d Ofloxacin 0.43 0.36 c Morphine-3ß-D- 0.21 b glucuronide Trp-Phe 0.11 d Phenylalanine 0.03 0.00 c Aspartic acid 0.01 c Tryptophan -0.22 d Phe-Phe-Phe -0.31 d Phe-Phe -0.58 d Trp-Trp -0.59 d Trp-Phe -0.61 d Aspartic acid -0.72 c Phe-Phe-Phe -0.80 d

a Bold entries refer to log PneM,i> - log PCH,n„, other entries refer to log P„cum,i - log P. b Avdeef, A., Knaggs, R., Barrett, D., Shaw, P. N., Davis S. S. in preparation, c Avdeef, A., Box, K. J., Takacs-Novak, K., in preparation, d Avdeef, A., Box, K. J., in preparation.

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