Diffusional permeability coefficients

In the case of the movement of labelled water (THO), the diffusional permeability coefficient, P., in cm/s can be calculated as follows ... 

Probably the most systematic and complete study on the influence of temperature on water transfer has been performed on mammalian red cells [10,20,28]. The dependence on temperature of both the tracer diffusional permeability coefficient (cotho) 3 nd the hydraulic conductivity (Lp) of water in human and dog red-cell membranes have been studied. The apparent activation energies calculated from these results for both processes are given in Table 2. The values for the apparent activation energies for water self-diffusion and for water transport in a lipid bilayer are also included in the table. For dog red cells, the value of 4.9 kcal/mol is not significantly different from that of 4.6-4.8 kcal/mol for the apparent activation energy of the water diffusion coefficient ( >,) in free solution. Furthermore, it can be shown that the product L — THOV )rt, where is the partial molar volume of water and the viscosity of water remains virtually independent of temperature for dog, hut not for the human red-cell membrane [20]. The similarity of the transmembrane diffusion with bulk water diffusion and the invariance of the... 

Here the problem is to decide whether these solutes permeate by dissolution in the membrane fabric or by crossing the membrane through polar pathways aqueous pores . It is worth pointing out from the start that there is no conclusive evidence which enables one to decide unequivocally between these two possibilities. As will become clearer by the end of this discussion, the data at hand in certain cases (such as mammalian red cells) are merely more consistent with the postulate that these molecules permeate partly through polar pathways and not entirely by dissolution in the membrane fabric. Probably the strongest evidence for this hypothesis is summarized in Table 4. The values of the diffusional permeability coefficient for egg lecithin spherical bilayers are included in the table for comparison. Based on their lipid solubility these molecules should be quite impermeable. In fact, in certain... 

The permeability coefficient of the diffusional-bioconversion pathway can be delineated with the aid of Eq. (Ill) once the permeability coefficients of the ABL, filter support, and paracellular routes are known (Table 18). It is seen that 98% of the diester molecules passing through the cell monolayer take the intracellular route. 

Figure 31 Scheme for the protein-binding, diffusional, and partitioning processes and barriers that are encountered by a highly lipophilic and membrane-interactive drug (D) as it permeates through a cell within a continuous monolayer, h and h, thicknesses of the aqueous boundary layers. kd and ka, dissociation and association binding constants, respectively. P, protein molecule. Permeability coefficients Effective, Pe aqueous boundary layer, PABL and PW apical membrane, Pap basolateral membrane, Pbl. 

When the barrier has two or more independent diffusional pathways present in parallel, the total permeability coefficient Ptotal is the sum of P for each individual pathway as... 

Average ratios and standard deviations of permeability coefficients reported by Peck et al. (1994) determined from 11 HEM samples. "Ratios based upon free aqueous diffusion coefficients corrected by diffusional hindrance factors that were calculated from Eq. 6 for each permeant based upon an Rp of 21 A. 

The basis for comparing the ratios of the free diffusion coefficients and permeability coefficients was the assumption that hindrance considerations could be ignored. In the instance that this assumption is valid (i.e., the case of large pore dimensions relative to solute radii), the free diffusion coefficients are a reasonable approximation to the diffusion coefficients of the solutes in the membrane. In the instance that hindrance considerations are not negligible, due to pore dimensions that lead to diffusion-restricting hydrodynamic interactions between the solute and the membrane, the diffusion coefficient of the solute in the membrane is a function of both the solute parameters and the properties of the membrane. In this case, the effective diffusion coefficient can be approximated by the product of the free diffusion coefficient and a diffusional hindrance factor, HQC) (Deen, 1987) ... 

Because of its apolar interior, the lipid bilayer is a barrier to diffusional equilibration of solutes between the two aqueous compartments that it separates. The ability of most small solute molecules (50 < molecular weight < 300) to cross the bilayer is directly proportional to their ability to partition into hexadecane or olive oil from an aqueous solution (58), which is an observation first made by Overton (59) and is often referred to as Overton s Law. Permeation of lipid bilayers by small polar molecules and ions seems to occur via one or a combination of both of two mechanisms depending on the nature of the permeants and the nature of the bilayers. First, a solubility-diffusion mechanism treats the bilayer as a slab of liquid hydrocarbon sandwiched between two bulk aqueous compartments. The permeant must partition into the bilayer slab from one of the aqueous compartments, diffuse across it, and leave by dissolving into the second aqueous compartment. In this case, the permeability coefficient, P, is given by ... 

In this equation, A is the area of application, D is the apparent diffusion coefficient and h is the diffusional path length (often taken as the thickness of the membrane). The permeability coefficient (A ) is the steady-state flux per unit area divided by the concentration of drug applied in solution and may be calculated from ... 

In the consideration of therapeutic activity following dermal application, emphasis is placed on quantifying the extent of absorption of a drug through the skin or some relevant pharmacodynamic response. The amount absorbed (Q) may be expressed in terms of the area of application and the exposure time (T). The amount absorbed will be determined by the permeability coefficient of the drug, the diffusional lag time across the barrier (lag) and the concentration of the drug in the vehicle ... 

Figure 14.9 Sample cumulative skin permeation patterns following finite and infinite dosing regimes. With infinite dose, permeation normally reaches a steady-state flux region, from which it is possible to calculate permeability coefficients and diffusional lag times. In finite dosing the permeation profile normally exhibits a plateauing effect as a result of donor depletion.

Again the same convention as described earlier is used, and flow into the cell is considered to be in the positive direction. The osmotic pressure due to the permeant solute is denoted by which is defined as = RT(Cf - Att has units of dyne/cm. In these equations we speak of differences in concentrations in bulk phases since the partition coefficient which relates the concentration in the membrane phase to that of the bulk phase is incorporated in the permeability coefficients. The subscripts i and s refer to impermeant and permeant solute respectively. Lpj is the cross-coefficient for the volume flow arising from differences in the osmotic pressure of the permeant solute, Aw, when there is no difference of either hydrostatic or osmotic pressure produced by impermeant solutes ( Attj = 0). L p is the relative diffusional solute mobility per unit hydrostatic (or impermeant solute) pressure difference when Asr = 0. Although is always positive, and L p are both negative and have the same units as L. If the Onsager reciprocal relation holds, then is the diffusional flow and is a measure of the relative... 

In many cases, the difference between Pf and P can be attributed to the presence of an unstirred layer. On the other hand, in the case of human red cell membrane the difference cannot be accounted for by the presence of an unstirred layer [14]. Additional support for this difference between Pf and Pdealing with the effect of antidiuretic hormone (ADH) on water movement across epithelia. It was found that in the presence of ADH, the osmotic permeability coefficient of this tissue to water is 120 times greater than the diffusional coefficient (see Table 9.5 in [23]). 

Permeability coefficients of representative membranes and tissues to water under both osmotic and diffusional flows ... 

Since the light/dark differences in CO2 uptake hint to the existence of a carrier mediated CO2 uptake (7,11), "Pg values calculated for illuminated cells are not permeability coefficients in the classical sense. They reflect the conductance of a PM, in which a Michaelis-Menten-type of carrier mediated uptake exists beside diffusional uptake. It will depend on the applied external CO2 concentration, whether the total uptake is determined by the carrier mediated uptake system (low external CO2, no saturation of the carrier) or by pure diffusion (high CO2, saturation of the catalyzed uptake). The conductance of the PM iii2 the dark permits at 1 mM CO2 a CO2 influx of maximal 100 nmol CO2 m sec, which2 is incompatible with photosynthetic fluxes of 160 - 500 nmol CO2 m sec. Only the increase conductance in the light permits the experimentally determined photosynthetic fluxes. 

Calix[4]-W5-crowns 1-7 are used as selective cesium-carriers in supported liquid membranes (SLMs). Application of the D esi diffusional model allows the transport isotherms of trace level Cs through SLMs (containing calix[4]-6/5-crowns) to be determined as a function of the ionic concentration of the aqueous feed solutions. Compound 5 appears to be much more efficient than mixtures of crown ethers and acidic exchangers, especially in very acidic media. Decontamination factors greater than 20 are obtained in the treatment of synthetic acidic radioactive wastes. Permeability coefficient measurements are conducted for repetitive transport experiments in order to determine the SMLs stability with time. Very good results (over 50 days of stability) and high decontamination yields are observed with l,3-calfac[4]-Aw-crowns 5 and 6. 

Penetration of a substance is measured by the permeability coefficient, P, which could be converted to a measurable diffusional coefficient, D, if Pick s law applied strictly. In the more complex situation of a membrane barrier, Kedem and Katchalsky (1958, 1961) have shown that under rigidly controlled conditions there exist at least three parameters which must be considered when characterizing the behavior of a membrane toward a particular solute (1) the interaction between membrane and solvent (2) the interaction between solute and membrane and (3) the interaction between solute and solvent. The reflection coefficient, (T, measures relative rates of solute and solvent permeabilities in the system (Staverman, 1952) and is therefore a measure of semipermeability. Lp is the mechanical coefficient of filtration or pressure filtration coefficient, and co is the solute mobility or solute diffusional coefficient. In the case of living membranes, conditions such as volume flow, osmotic gradients, and cell volume can be manipulated in order to measure the phenomenological coefficients cr, o>, and Lp. Detailed discussions of the theories, methods, and problems involved in such... 

The positive diffusional activation energy is larger in absolute value than the negative AH, and so the overall permeability increases as temperature increases, but to a lower degree than the diffusion coefficient itself It should be noted that the use of equation 34 is only strictly valid when the diffusion and solubility coefficients are independent of concentration. 

---