P permeability coefficients

TABLE 1. Biophysical characteristics of human fetal liver CD34 CD38 cells. Legends Vo - cell volume in isoosmotic solutions, Vb - osmotically inactive volume, Lp - permeability coefficient of membranes for water, p - permeability coefficient of membranes for DMSO cryoprotectant, a - reflection coefficient. 

N number of elementary particles (e.g., molecules, groups, atoms, electrons) Avogadro number (Loschmidfs number) n amount of a substance (mole) n refractive index P permeability coefficient Pr production p probability p dipole moment p, induced dipolar moment p pressure p extent of reaction... 

P permeability coefficient, K/. partition coefficient, diffusion coefficient n = 3 for each sample. 

Nodes, E.E., Mazur, P., Watson, P.F., Kleinhans, F.W., Critser, J.K. (1993). Determination of water permeability coefficient for human spermatozoa and its activation energy. Biol, of Reprod. 48,... 

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. 

Artursson P and Karlsson J. Correlation between oral drug absorption in humans and apparent drug permeability coefficients in human intestinal epithelial (Caco-2) cells. Biochem Biophys Res Commun 1991 175 880-5. 

Another relatively new lipophilicity scale proposed for use in ADME studies is based on MEKC [106]. A further variant is called BMC and uses mobile phases of Brij35 [polyoxyethylene(23)lauryl ether] [129]. Similarly, the retention factors of 16 P-blockers obtained with micellar chromatography with sodium dodecyl sulfate as micelle-forming agent correlates well with permeability coefficients in Caco-2 monolayers and apparent permeability coefficients in rat intestinal segments [130]. 

In PAMPA, the effective permeability coefficient, Pe, is related to the membrane and ABL permeability coefficients, P and Pabl. respectively, as... 

The solubility-diffusion theory assumes that solute partitioning from water into and diffusion through the membrane lipid region resembles that which would occur within a homogeneous bulk solvent. Thus, the permeability coefficient, P, can be expressed as... 

Two hypotheses have been proposed to explain how phenolic acids directly increase membrane permeability. The first is that the compounds solubilize into cellular membranes, and thus cause a "loosening" of the membrane structure so that minerals can leak across the membrane (28-30, 42). Support for this hypothesis comes from the fact that the extent of inhibition of electrical potentials correlates with the log P (partition coefficient of a compound between octanol and water) for various benzoic and cinnamic acid derivatives (Figure 5). 

To illustrate the above point, take the set of largest values given for the diffusion coefficients found in Table 8, that is, 10-9 cm2/s for the stratum corneum, 10-7 cm2/s for sebum, and 10-6 cm2/s for the viable tissue, and convert them to cm2/h. Conversion of these from reciprocal seconds to reciprocal hours eventually leads to permeability coefficients that are more easily compared with literature values (P in units of cm/h) When these values are substituted into Eq. (7) along with... 

The permeability coefficient Kpcr is just the flux divided by Cw. It is apparent that the permeability coefficient is linear with P for small distribution coefficients and constant for large P. Thus, for small P the epithelium is the barrier, and for large P the stroma is the barrier. A fit for steroid permeability is shown in Fig. 12, where the regression analysis gave De = 1.4 x 10 9cm2/s and Ds = 2.0 x 10 6cm2/s for 4 = 4 x 10 3 cm and 4 = 3.6 x 10 2 cm [205]. These values for the diffusion coefficients are reasonable compared with those of aqueous gels and lipid membranes. 

Using regression analysis on a data set of about 50 different molecules, it was found that a. = —4.4,8 = —0.5, Df = 12 cm2/s, and =2.5x 10 5 cm2/s [192], A graphic representation of the effect of relative molecular mass (Mr) and distribution coefficient on corneal permeability is shown in Fig. 13. One observes a rapid reduction in permeability coefficient with decreasing P and increasing Mr. The addition of pores to the model, a mathematical construct, is necessary to account for permeability of polar molecules, such as mannitol and cromolyn. These would also be required for correlating effects of compounds, such as benzalkonium chloride, which may compromise the... 

Karlsson, J. P. Artursson, P., A method for the determination of cellular permeability coefficients and aqueous boundary layer thickness in monolayers of intestinal epithelial (Caco-2) cells grown in permeable filter chambers, Int. J. Pharm. 7, 55-64 (1991). 

It is obvious from Equation 14.14 that the most important parameter determining the volumetric air flow rate <2W is the intrinsic permeability K of soil. At this point it is important to stress the difference between water permeability (or hydraulic conductivity) k , air permeability ka, and intrinsic permeability K. In most cases, when permeability data are provided for a type of soil or geological formation, these data are based on hydraulic conductivity measurements and describe how easily the water can flow through this formation. However, the flow characteristic of a fluid depends greatly on its properties, e.g., density p and viscosity p. Equation 14.16 describes the relationship between permeability coefficient k and fluid properties p and p ... 

Shah et al. [51] demonstrated the use of a donor-receptor compartment apparatus separated by a cell monolayer to estimate membrane transport parameters. Permeability coefficients, P, were calculated as... 

One observes, comparing Eqs. (45) and (46) for permeating ions of comparable size and valence with Eq. (47), that the diffusion of cations across the negatively charged pore is increased by the potential gradient. In contrast, the diffusion of anions is decreased by the electrical forces. In other words, P+ or P is composed of the permeability coefficient of its neutral image upon which the contribution... 

The quantitative role of electrical factors affecting the transport of charged molecules is obtained by comparing permeability coefficients with the permeability coefficient P(Lcdi for molecular size-restricted diffusion independent of the charge on the molecule (i.e., the neutral image). With Eqs. (45) and (46) one obtains... 

The slow and linear fluxes of hydrocortisone and dexamethasone under various hydrodynamic conditions are quantified in terms of effective permeability coefficients, P by Eq. (9), i.e.,... 

Table 16 Permeability Coefficients of p-B lockers for Caco-2 Cell Monolayers3... 

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. 

Figure 35 Relationship between the uptake permeability coefficient and the free drug concentration. PAEL is the permeability of the free drug across the aqueous boundary layer, and P BL is the same for the drug-albumin complex. [Redrawn from Raub et al. (1993) with permission from the publisher.]...

The initial conditions are CD = CD(0) at t = 0 and CR = 0 at t = 0. Efforts to obtain analytical solutions are tedious and unnecessary. By applying the change in concentrations (or mass) in the donor and receiver solutions with time to the Laplace transforms of Eqs. (140) and (141), the inverse of the simultaneous transformed equations can be numerically calculated with appropriate software for best estimates of a, (3, and y. It is implicit here that P Pap, Pbh and Ke are functions of protein binding. Upon application of the transmonolayer flux model to the PNU-78,517 data in Figure 32, the effective permeability coefficients from the disappearance and appearance kinetics points of view are in good quantitative agreement with the permeability coefficients determined from independent studies involving uptake kinetics by MDCK cell monolayers cultured on a flat dish... 

Instead of using the oral bioavailability of a drug, one can attempt to correlate PM values with permeability coefficients generated from in situ perfused intestinal preparations. Here, one eliminates the complexities of liver metabolism, clearance, and formulation variables. Recently, this type of in vitro-in situ correlation has been conducted using the model peptides (described previously in Section V.B.2). The permeabilities of these model peptides were determined using a perfused rat intestinal preparation which involved cannulation of the mesenteric vein (Kim et al., 1993). With this preparation, it was possible to measure both the disappearance of the peptides from the intestinal perfusate and the appearance of the peptides in the mesenteric vein. Thus, clearance values (CLapp) could be calculated for each peptide. Knowing the effective surface area of the perfused rat ileum, the CLapp values could be converted to permeability coefficients (P). When the permeability coefficients of the model peptides were plotted as a function of the lipophilicity of the peptides, as measured by partition coefficients in octanol-water, a poor correlation (r2 = 0.02) was observed. A better correlation was observed between the permeabilities of these peptides and the number of potential hydrogen bonds the peptide can make with water (r2 = 0.56,... 

Molecules with a large molecular weight or size are confined to the transcellular route and its requirements related to the hydrophobicity of the molecule. The transcellular pathway has been evaluated for many years and is thought to be the main route of absorption of many drugs, both with respect to carrier-mediated transport and passive diffusion. The most well-known requirement for the passive part of this route is hydrophobicity, and a relationship between permeability coefficients across cell monolayers such as the Caco-2 versus log P and log D 7.4 or 6.5 have been established [102, 117]. However, this relationship appears to be nonlinear and reaches a plateau at around log P of 2, while higher lipophilicities result in reduced permeability [102, 117, 118]. Because of this, much more attention has recently been paid towards molecular descriptors other than lipophilicity [86, 119-125] (see section 5.5.6.). The relative contribution between the para-cellular and transcellular components has also been evaluated using Caco-2 cells, and for a variety of compounds with different charges [110, 112] and sizes [112] (see Section 5.4.5). 

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