Figure 7.36 shows the log Pe-pH plots for three nonionizable molecules: carba-mazepine, 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 7.15 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 x 10-6 cm/s. Since the aqueous diffusivity (Daq) of most of the drugs in Table 7.15 is near 8 x 10- cm 2/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 7.15 span about eight orders of magnitude, whereas the effective (measured in the in vitro assay) permeabilities are confined 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. 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. (7.57) [511-514,552,578]

where k is a constant descriptive of the diffusivity of the solute and v 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 (7.57) may be substituted into Eq. (7.46) to obtain

Measurements of Pe in fixed-pH solutions but at various different stirring speeds need to be made. The double-reciprocal analysis, 1/Pe versus 1/vx, for Caco-2 permeability measurements in the Transwell (Corning Costar) system produced a linear plot for x — 0.8 [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 — 1.0 to best represent their stirring-based analysis of the UWL permeability.

TABLE 7.15 Intrinsic Permeabilities and Unstirred Water Layer Permeabilities Determined from Iso-pH Dependence of Effective Permeabilities: 2% DOPC in Dodecane
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