Permeability coefficient modeling molecular weight

Mathematical models relate skin permeability of exogenous molecules to physicochemical parameters of the permeant (octanol/water partition coefficients and molecular weight [a surrogate marker of molecular size]). Similar models for animal and human skin relate normalized equations of best-fit regressions based on ... 

Eqn. 5 provides a very clear theoretical basis for the data of Fig. 1 (and similar data on other systems, as we shall see). The measured permeability coefficients for a set of solutes should parallel the measured partition coefficients, if the model solvent corresponds exactly in its solvent properties to the permeability barrier of the cell membrane. In addition, the molecular size of the solute is very likely to be an important factor as it will affect the diffusion coefficients within the membrane barrier phase. Data such as those of Fig. 1 will convince us that we have in our chosen solvent a good model for the solvent properties of the membrane s permeability barrier. We can now calculate values of PLx/K for the various solutes, and obtain estimated values of the intramembrane diffusion coefficient, and are in a position to study what variables influence this parameter. Fig. 3 is such a study in which data from Fig. 1 are plotted as the calculated values of f>n,c,n/A.t (calculated as P/K) against the molecular weight of the permeating solute. The log/log plot of the data has a slope of — 1.22, which means that one can express the dependence of diffusion coefficient on molecular weight (A/) in the form where... 

For some compounds in the Wilschut database more than one permeability coefficient was gathered from literature. In some cases, the differences in kp were greater than one log unit underlining the interlaboratory variations of such measurements. For the development of a new QSPR model one may now either choose one representative data point for each molecule or combine the multiple data points in a reasonable way. In some cases authors even employed all the available data for a single compound. Apart from the permeability data, the data on the partition coefficient and even on the molecular weight may vary from one report to another. Differences in the partition coefficient are easily explained Some collections list experimentally determined values which depend on the experimental procedure employed... 

PK-Map and PK-Sim (Bayer Technology Services, Wuppertal, Germany), that are based on the models described by Willman et al. [54], In these software packages, the intestinal permeability coefficient can be calculated using a compound s lipophilicity and molecular weight [52,54] and hence, no experimental permeability data is needed. Different to the model described by Willman et al. [54], the commercial prediction tools model the dissolution rate taking the particle size distribution of the solid particles into account (www.pk-sim.com). 

The use of distributed pharmacokinetic models to estimate expected concentration profiles associated with different modes of drug delivery requires that various input parameters be available. The most commonly required parameters, as seen in Equation 9.1, are diffusion coefficients, reaction rate constants, and capillary permeabilities. As will be encountered later, hydraulic conductivities are also needed when pressure-driven rather than diffusion-driven flows are involved. Diffusion coefficients (i.e., the De parameter described previously) can be measured experimentally or can be estimated by extrapolation from known values for reference substances. Diffusion constants in tissue are known to be proportional to their aqueous value, which in turn is approximately proportional to a power of the molecular weight. Hence,... 

Figure 1 Summary of solution-diffusion model relationships. Typically the diffusion coefficient, Dj, decreases as the penetrant molecular weight increases. On the other hand, the solubility coefficient, Sj, tends to increase with increasing penetrant molecular weight. As a result, the permeability, Pj, may either decrease...

Clearly, from Fig. 1, the solubility of a solute in an organic solvent correlates very well with the permeability of the Nitella membrane for that solute. But it is also clear that the correlation is only partial. Thus, of two solutes with the same partition coefficient the one with smaller molecular weight would seem to permeate faster. Solute size as well as hpid solubility are both important determinants of permeation rate. The particular solvent chosen, olive oil, seems however to be a very good model for the ability of the membrane barrier to discriminate between the various permeants, since the overall increase in permeability as the structure of the permeant is varied correlates closely with the increase in partition coefficient. Were the two parameters to be strictly linked all the data would fall on the line of unit slope in the figure, the line of identity. Later we shall see cases where the data do not support such a close similarity between certain membranes and model solvents. 

In terms of the descriptors used in the prediction of skin permeability coefficients, the octanol-water partition coefficient F is a well-established measure of hydro-phobicity (Dearden, 1990). There is a variety of algorithms to calculate log P, including Web-based programs and the KOWWIN software, which is part of the EPISuite utility. EPISuite is available free from the U.S. Environmental Protection Agency (see Cronin and Livingstone, 2004b, for more details EPISuite can be downloaded from http //www.epa.gov/oppt/exposure/docs/episuite.htm). Molecular size is well modeled by molecular weight, which of course is fimdamental and trivial to calculate. 

A QSAR model was developed by Potts and Guy (1992) to predict the permeability of a wide range of structurally different chemicals and was based upon the size of the permeant and its octanol/water partition coefficient. Flynn (1990) compiled data on 90 compounds for which (33), below, was used to derive Kp values. The compounds ranged in molecular weight from 18 to >750, and in log Koa from —3 to -i-6. 

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