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pH 12 --> 2 pH 12 --> 2 pH 2 --> 12 pH 12 --> 2
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Bjerrum plot for titration of a suspension of 1 mM soy lecithin
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PAMPA: 50 MODEL LIPID SYSTEMS
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between pH 55 and 80 with concentrations in excess of 1 mM For pH > 8, phosphatidic and possibly free fatty acids start to ionize, approximately to the extent of 1% of the total soy content by pH 9 776 Intrinsic Permeability, Permeability pH Pro les, Unstirred Water Layers (UWL), and the pH Partition Hypothesis Up to now we have focused on measurement of permeability and membrane retention at pH 74 Since the GIT covers a range of pH values, with pH 5 8 characterizing the small intestine, it is necessary to address the pH dependence of the transport of drug molecules Even nonionizable molecules may be affected by pH dependence, since several biological membrane components themselves are ionizable (pKa values listed in Fig 74) For example, with PS, PA, and DA (free fatty acid) undergoing changes in charge state in the pH 5 8 interval In this section, we examine the consequences of pH dependence 7761 Unstirred Water Layer Effect (Transport across Barriers in Series and in Parallel) Passive transport across a membrane barrier is a combination of diffusion through the membrane and also diffusion through the stagnant water layers at the two sides of the membrane Stirring the bulk aqueous solution does not appreciably disturb the water layers in contact with the membrane When the solute is introduced into the bulk aqueous phase, convective mixing resulting from applied stirring, quickly positions the drug molecule next to the so-called unstirred water layer (UWL) At that point, the passage through the UWL is governed by the laws of diffusion, and is independent of stirring In simple hydrodynamic models [534 538] the UWL is postulated to have a distinct boundary with the rest of the bulk water The UWL can be made thinner with more vigorous stirring, but it cannot be made to vanish Extensions of the simple UWL models have been discussed in the literature [539,540], but such models are not often used in practice The actual thickness of the unstirred water layer depends somewhat on the transport model system The in vivo UWL is signi cantly different from the in vitro assay measuring cell UWL Because of the ef cient mixing near the surface of the epithelium, the in vivo UWL is estimated to be 30 100 mm thick The UWL in the endothelial microcapillaries of the brain is nil, given that the diameter of the capillaries is $7 mm and the ef ciency of the mixing due to the passage of erythrocytes [612] However, in unstirred in vitro permeation cells, the UWL values can be 1500 2500 mm thick, depending on cell geometry and dimensions It may be assumed that the total resistance to passive transport across the trilamellar (UWL membrane UWL) barrier is the sum of the resistances of the membrane and the UWL on each side of it Resistance is the inverse of permeability So 1 1 1 P e Pm P u 7:46
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PERMEABILITY
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where Pe refers to the measured effective permeability, Pu refers to the total UWL permeability, Pm is the permeability of the membrane (which would be measured if the UWL were made vanishingly thin) If it is possible to separate the donor and acceptor contributions to the UWL, then the total Pu can be allocated between its D A parts according to 1/Pu 1/Pu 1/Pu In Caco-2 literature, equations like Eq (746) often have a tter, Pf ; component, to account for resistance of the water- lled pores of the tter In PAMPA, all pores are lled with lipid, and no consideration of lter contributions are needed The UWL permeability is nearly the same for drugs of comparable size, and is characterized by the water diffusivity (Daq) of the drug divided by twice the thickness of the layer (haq), Pu Daq / (2 haq), in a symmetric permeation cell [40] The unstirred water layer permeability can be determined experimentally in a number of ways: based on pH dependency of effective permeability [25,509,535 538], stirring rate dependence [511 514,552,578], and transport across lipid-free micro lters [25,546]
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7762 Determination of UWL Permeability using pH Dependence (pK flux ) Method a The membrane permeabilities Pm may be converted to intrinsic permeabilities P0, when the pKa is taken into consideration An ionizable molecule exhibits its intrinsic permeability when it is in its uncharged form and there is no water layer resistance The relationship between Pm and P0 is like that between the pH-dependent apparent partition coef cient (log Kd) and the true partition coef cient (log Kp), respectively This relationship can be rationalized by the mass balance Take, for example, the case of a monoprotic acid, HA The total substance concentration is CHA HA A 7:47
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Using the ionization quotient expression [Eq (31)], [A ] may be expressed in terms of [HA]: HA Ka CHA HA H   Ka HA 1 H HA 1 10 pKa pH 7:48
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In the UWL, HA and A diffuse in parallel; the total UWL ux, Ju, is the sum of the two individual ux components If it is assumed that the transport is under steady
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