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The shapes of permeability pH pro les mirror those of solubility pH (see, Figs 61a, 62a, and 63a), with slopes of opposite signs In solutions saturated with an insoluble compound, the product of solubility and permeability ( ux, as described in 2) is pH-independent! This is indicated in Fig 22 as the maximum ux portions of the curves
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PAMPA: 50 MODEL LIPID SYSTEMS
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Permeability (10-6 cm/s units)
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Pu (approx)
membrane permeability, Pm = Po / ( 1 + 10 -pKa + pH ) effective (measured) permeability, Pe = Pu / {1 + [ 1 + 10 -pKa + pH ] Pu / Po }
Figure 734 Permeability pH pro les of ketoprofen: (a) log log plot; solid curve represents effective permeability, and the dashed curve is the membrane permeability, calculated by Eq (753) The latter curve levels off at the intrinsic permeability, P0 The effective curve levels off to approximately the unstirred water layer permeability, Pu (b) Direct plot; the inset curve for the fraction neutral substance levels of at 100% (scale not shown) [Avdeef, A, Curr Topics Med Chem, 1, 277 351 (2001) Reproduced with permission from Bentham Science Publishers, Ltd]
Figure 735 shows the characteristic log Pe pH curve for a weak base, phenazopyridine (pKa 515) With bases, the maximum permeability is realized at high pH values As in Fig 734, the PAMPA assays were performed under iso-pH conditions (same pH in donor and acceptor wells), using the 2% DOPC in dodecane lipid system
PERMEABILITY
phenazopyridine
pKa 515
N NH2 N N
log Pe (cm/s)
-4 -5 -6 -7 2 3 4 5
Figure 735 Permeability pH pro le of phenazopyridine under iso-pH conditions [Based on data in Ref 558]
H2N N
log Pe (cm/s)
carbamazepine
O H3C N N CH3 CH3 N N
caffeine
antipyrine
O N N CH3
6 pH
Permeability pH pro le of three neutral molecules under iso-pH conditions
PAMPA: 50 MODEL LIPID SYSTEMS
Figure 736 shows the log Pe pH plots for three nonionizable molecules: carbamazepine, caffeine, and antipyrine As is expected, there is no pH dependence shown; neither the molecules, nor the 2% DOPC/dodecane membrane show charge-state changes in the pH interval from pH 3 to 9 Table 715 lists the intrinsic permeabilities and the unstirred water permeabilities of 16 drugs, determined by the Gutknecht method The average unstirred water layer permeability is 16 10 6 cm/s Since the aqueous diffusivity (Daq) of most of the drugs in Table 715 is near 8 10 6 cm2/s, the average thickness of the unstirred water layer on each side of the membrane is $2500 mm in the unagitated 96-well microtiter plates, used by pION s PAMPA system The permeation cell dimensions in typical Caco-2 assays indicate UWL of about 1500 mm (when the plates are unstirred) [554] The thickness of the unstirred water layer can be driven down to values as low as 300 500 mm if the plate is vigorously stirred during permeation [546,554,556] The intrinsic membrane permeabilities in Table 715 span about eight orders of magnitude, whereas the effective (measured in the in vitro assay) permeabilities are con ned to a much narrower range, limited by the UWL Since the in vivo UWL in the gut is estimated to be about 50 mm [541], it is more appropriate to use Pm than Pe values in oral absorption prediction strategies 7763 Determination of UWL Permeabilities using Stirring Speed Dependence Caco-2 assay permeabilities corrected for the UWL usually include Pu determined as a function of the stirring speed (since the cells are not stable over a wide pH range), as in Eq (757) [511 514,552,578] Pu kn x 7:57
where k is a constant descriptive of the diffusivity of the solute and n is the stirring speed (rpm) If the thickness of the UWL is different on the two sides of the membrane, then there are two different values of k [514] Equation (757) may be substituted into Eq (746) to obtain 1 1 1 x Pe Pm kn 7:58
Measurements of Pe in xed-pH solutions but at various different stirring speeds need to be made The double-reciprocal analysis, 1/Pe versus 1/n x, for Caco-2 permeability measurements in the Transwell (Corning Costar) system produced a linear plot for x 08 [514] The intercept yields the membrane permeability for the particular pH value in the study; the slope determines the k constant From the analysis of testosterone transport, for the stirring speed of 25 rpm (planar rotating shaker), the thickness of each UWL (assuming symmetric geometry) was calculated to be 465 mm; at 150 rpm, haq 110 mm [514] Karlsson and Artursson [512] found x 10 to best represent their stirring-based analysis of the UWL permeability