PERMEABILITY LIPOPHILICITY RELATIONS

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v1 C1 0 v1 C1 1 v2 C2 1 v3 C3 1 Two partition coef cients need to be de ned: K p2 C2 1 =C1 1 and K p3 C3 1 =C1 1 With these, the mass balance may be rewritten as v1 C1 0 v1 C1 1 v2 Kp2 C1 1 v3 Kp3 C1 1 C1 1 v1 v2 Kp2 v3 Kp3 If the organic : aqueous volume ratios are r2 and r3, then the equilibrium concentrations in the three phases can be stated as C1 1 C2 1 C3 1 C1 0 1 r2 Kp2 r3 Kp3 C1 0 Kp2 1 r2 Kp2 r3 Kp3 C1 0 Kp3 1 r2 Kp2 r3 Kp3 7:38 7:39 7:40

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Further reduction is possible To a good approximation, partition coef cients from different organic solvents may be interrelated by the so-called Collander equation a [364,587]: log Kp3 a log Kp2 c, or Kp3 10c Kp2, where a and c are constants Equations (738) (740) can be expressed in log forms as a function of just one partition coef cient (ie, Kp Kp2): Water : Lipid : Receptor : log log log C1 1 a log 1 r2 Kp r3 10c Kp C1 0 C2 1 a log Kp log 1 r2 Kp r3 10c Kp C1 0 C3 1 a a log Kp log 1 r2 Kp r3 10c Kp c C1 0 7:41 7:42 7:43

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Figure 720 is a sample plot of relative equilibrium concentrations, Eqs (741) (743) In the example, the three phases were picked to be water, octanol, and phosphatidylcholine-based liposomes (vesicles consisting of a phospholipid bilayer), with the volumes v1 1 mL (water), v2 50 mL (octanol), and v3 10 mL (liposomes) The Collander equation was deduced from Fig 56: log Kp,liposome 041 log Kp,oct 204 Figure 720 suggests that when very hydrophilic molecules (with log Kp,oct < 6) are placed into this three-phase mixture, most of them distribute into the water phase (solid curve), with only minor liposome phase occupation (dashed-dotted curve), but virtually no octanol phase occupation (dashed curve) In the example, molecules with log Kp,oct of 4 to 3, mostly reside in the liposome fraction, schematically modeling the lipophilic property of a hypothetical receptor site, reaching maximum occupancy for compounds with log Kp,oct at about 15 Very lipophilic molecules, with log Kp,oct > 5 preferentially concentrate in the (more lipophilic) octanol compartment, becoming unavailable to the receptor region

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PERMEABILITY

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10 L liposome

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50 L octanol

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log C / Co

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0 -2 -4

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1 mL water Collander equation from Fig 56 log Kp,liposome = 041 log Kp,oct + 204

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log Kp,oct

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Figure 720 Three-compartment equilibrium distribution model (after Kubinyi [23])

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Kubinyi [23] showed that the bilinear equation (743) can be approximated by a general form log C a log Kp c b log rKp 1 7:44

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where a, b, c, r are empirical coef cients, determined by regression analysis, and C is the concentration in the intermediate phase Equation (744) was used to calculate the curve in Fig 719d Our present topic is the relationship between permeability and lipophilicity (kinetics), whereas we just considered a concentration and lipophilicity model (thermodynamics) Kubinyi demonstrated, using numerous examples taken from the literature, that the kinetics model, where the thermodynamic partition coef cient is treated as a ratio of two reaction rates (forward and reverse), is equivalent to the equilibrium model [23] The liposome curve shape in Fig 720 (dasheddotted line) can also be the shape of a permeability-lipophilicity relation, as in Fig 719d This relationship was further clari ed by van de Waterbeemd in the two-step distribution model [588 590] Later, the model was expanded by van de Waterbeemd and colleagues to include the effects of ionization of molecules, with the use of log Kd, in place of log Kp, as well as the effects of aqueous pores [49,54]

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77 PAMPA: 50 MODEL LIPID SYSTEMS DEMONSTRATED WITH 32 STRUCTURALLY UNRELATED DRUG MOLECULES In the rest of the chapter, we describe over 50 speci c PAMPA lipid models developed at pION, identi ed in Table 73 The lipid models are assigned a two

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