Permeability and partition coefficient

On the Energy of Activation. The temperature dependence of many processes, such as diffusion, permeability, and partition coefficients, has been represented often in terms of the Arrhenius plots (52). It would appear that ki in Equation 14 also could be treated in this manner by defining... 

To test whether the barrier for steroids was the same as the barrier for the smaller solutes, Giorgi also measured the permeabilities and partition coefficients for some smaller molecules. Some of these data are reproduced in Fig. 10 as a log/log plot of permeabihty coefficients against n-octanol partition coefficients. Clearly the data for the small solutes and for the steroids fall on a fairly good straight line, suggesting that the same rate law holds for the permeation of the steroids as for that of the smaller solutes. All seem to encounter a rate-limiting permeability barrier which has... 

Table 9—Computed values of permeability, diffusion and partition coefficients for different formulations...

Other fatty acids as absorption enhancers have been reported. Ogiso et al. [112] demonstrated that lauric acid (C12) produced the largest increase in permeation rate, penetration coefficient, and partition coefficient of propranolol. Onuki et al. [113] reported that docosa-hexaenoic acid (DHA) has a strong insulin permeability enhancement effect and little toxicity, compared to oleic acid and eicosapentaenoic acid (EPA) using a water-in-oil-in-water (W/O/W) multiple emulsion with no or little mucosal damage. 

The substance-specific kinetic constants, kx and k2, and partition coefficient Ksw (see Equations 3.1 and 3.2) can be determined in two ways. In theory, kinetic parameters characterizing the uptake of analytes can be estimated using semiempirical correlations employing mass transfer coefficients, physicochemical properties (mainly diffusivities and permeabilities in various media), and hydro-dynamic parameters.38 39 However, because of the complexity of the flow of water around passive sampling devices (usually nonstreamlined objects) during field exposures, it is difficult to estimate uptake parameters from first principles. In most cases, laboratory experiments are needed for the calibration of both equilibrium and kinetic samplers. 

The rate of transmembrane diffusion of ions and molecules across a membrane is usually described in terms of a permeability constant (P), defined so that the unitary flux of molecules per unit time [J) across the membrane is 7 = P(co - f,), where co and Ci are the concentrations of the permeant species on opposite sides of membrane correspondingly, P has units of cm s. Two theoretical models have been proposed to account for solute permeation of bilayer membranes. The most generally accepted description for polar nonelectrolytes is the solubility-diffusion model [24]. This model treats the membrane as a thin slab of hydrophobic matter embedded in an aqueous environment. To cross the membrane, the permeating particle dissolves in the hydrophobic region of the membrane, diffuses to the opposite interface, and leaves the membrane by redissolving in the second aqueous phase. If the membrane thickness and the diffusion and partition coefficients of the permeating species are known, the permeability coefficient can be calculated. In some cases, the permeabilities of small molecules (water, urea) and ions (proton, potassium ion) calculated from the solubility-diffusion model are much smaller than experimentally observed values. This has led to an alternative model wherein permeation occurs through transient hydrophilic defects, or pores , formed by thermal fluctuations of surfactant monomers in the membrane [25]. 

Fig. 4 depicts the data of Sha afi et al. [11], of Savitz and Solomon (12) and of Klocke et al. [13] on the penetration of 23 different compounds into human red cells plotted as a log/log plot (cf. Fig. 1) against the relevant ether/water partition coefficient. The strong dependence of permeability on partition coefficient that was noted by Collander for plant cells is somewhat less obvious for the human erythrocyte. Values of the partition coefficient vary over a range of 10 for molecules which have the same permeation rate. Molecules with the same partition coefficient have permeation rates which vary over a range of 10. But a line of unit slope can be drawn through many of the points on the log/log plot showing the strong dependence of permeation coefficients on partition coefficients. 

The bridge that divides in vitro and in vivo transporter correlation remains wide. Unlike direct enzyme kinetic correlations where a clear product is generated when substrate is added to enzyme, transporter outcomes are affected by many parameters. The physicochemical properties of compounds, such as lipophilicity, pKa, permeability, solubility, and partitioning coefficient,... 

The imperviousness of the plastic geomembrane material with respect to a certain chemical can be characterised by the permeability coefficient P = Jd/Ac = oD with the dimension m7s which indicates the ratio of the product of permeation rate and depth to the concentration difference and therefore the product of the material parameters diffusion coefficient and partition coefficient. The value J/Ac = P/d with the dimension m/s, may be called diffusive conductivity and is used sometimes as analogous to the hydraulic conductivity of Darcy s law. Its reciprocal value, d/P, may be called the diffusion resistance. 

When the values of permeability for each layer of a n-layer structure are known instead of the diffusion and partition coefficients, by the weU known relationship, is... 

Cb and Ca are the real-time methanol concentrations of the water reservoir and initial methanol concentration of the methanol solution reservoir A, L, and Vg are the effective area of the membrane, the membrane thickness, and the volume of the permeated reservoir, respectively D and K are the methanol diffusivity and partition coefficient between the membrane and the product DK that represents the membrane permeability (P in cm s"0, which can be calculated from the slope of the straight line obtained from plots of methanol concentration versus time, as the typical charts shown in Figure 10.8 [87],... 

This shows that pervaporation depends on two sources of selectivity. The first source, given in the square brackets, is the relative permeability across the membrane. As expected, this relative permeability is the product of diffusion and partition coefficients. Second, the selectivity of the pervaporation is influenced by the relative volatility given in the braces. This volatility, a thermodynamic factor, is independent of any dynamic concerns. This combination of dynamic and equilibrium factors explains why the less volatile species may be concentrated in the permeate stream of a pervaporation process. 

The HYBOT descriptors were successfully applied to the prediction of the partition coefficient log P (>i--octanol/water) for small organic componnds with one acceptor group from their calculated polarizabilities and the free energy acceptor factor C, as well as properties like solubility log S, the permeability of drugs (Caco-2, human skin), and for the modeling of biological activities. 

Physiologically Based Phamiacokinetic (PBPK) Model—Comprised of a series of compartments representing organs or tissue groups with realistic weights and blood flows. These models require a variety of physiological information tissue volumes, blood flow rates to tissues, cardiac output, alveolar ventilation rates and, possibly membrane permeabilities. The models also utilize biochemical information such as air/blood partition coefficients, and metabolic parameters. PBPK models are also called biologically based tissue dosimetry models. 

Mathai and Singh have estimated the permeability coefficient P, using the formula P = kD where k is the partition coefficient and D is the diffusivity. They have used both parallel and series models to calculate P. The experimental values are always greater than measured values. The poor agreement between the experimental and calculated values is attributed to the polar-polar interaction between the epoxy group and nitrile group. 

An analysis of partition coefficient data and drug solubilities in PCL and silicone rubber has been used to show how the relative permeabilities in PCL vary with the lipophilicity of the drug (58,59). The permeabilities of copolymers of e-caprolactone and dl-lactic acid have also been measured and found to be relatively invariant for compositions up to 50% lactic acid (67). The permeability then decreases rapidly to that of the homopolymer of dl-lactic acid, which is 10 times smaller than the value of PCL. These results have been discussed in terms of the polymer morphologies. 

When a two- or higher-phase system is used with two or more phases permeable to the solute of interest and when interactions between the phases is possible, it would be necessary to apply the principle of local mass equilibrium [427] in order to derive a single effective diffusion coefficient that will be used in a one-equation model for the transport. Extensive justification of the principle of local thermdl equilibrium has been presented by Whitaker [425,432]. If the transport is in series rather than in parallel, assuming local equilibrium with equilibrium partition coefficients equal to unity, the effective diffusion coefficient is... 

Lipophilicity is intuitively felt to be a key parameter in predicting and interpreting permeability and thus the number of types of lipophilicity systems under study has grown enormously over the years to increase the chances of finding good mimics of biomembrane models. However, the relationship between lipophilicity descriptors and the membrane permeation process is not clear. Membrane permeation is due to two main components the partition rate constant between the lipid leaflet and the aqueous environment and the flip-flop rate constant between the two lipid leaflets in the bilayer [13]. Since the flip-flop is supposed to be rate limiting in the permeation process, permeation is determined by the partition coefficient between the lipid and the aqueous phase (which can easily be determined by log D) and the flip-flop rate constant, which may or may not depend on lipophilicity and if it does so depend, on which lipophilicity scale should it be based ... 

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