Permeability estimate from molecular size

Mokiailnr probe method. When the membrane pores reach the molecular dimensions, the molecular sieving effect becomes operative and the membrane can discriminate gas molecules with a diameter difference as low as 0.02 nm. Some methods utilizing molecules of different sizes as molecular probes have been used to estimate the pore size of a membrane. In these cases, the membranes can be characterized by their permeabilities or accessible micropore volumes to different gases. The pore size can be inferred from the permeation rates or micropore volumes of different gases whose molecular dimensions are known or can be calculated. 

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... 

Molecular weight is often taken as the size descriptor of choice, mainly because it is easy to calculate and is generally in the chemist s mind. However, other size and shape properties are equally very simple to calculate and may offer a better guide to estimate potential for permeability. As yet, no systematic studies have been reported which investigate this in detail. Cross-sectional area (Ad, obtained from surface activity measurements) has been reported as being a useful size descriptor to discriminate compounds which can access the brain (Ad < 80 A2) from those that are too large to cross the BBB [62]. Similar studies have been performed to define a cut-off for oral absorption [63]. 

Eq. (7.15) can be used to estimate the optimum particle size squared over the column length. Typical values for the column permeability factor, ko, is I x 10 the Knox parameter, C, is 0.1 and the molecular diffusion coefficient 1 x 10 cm-/s for small molecules and 1 x 10 cm /s for proteins. The SI units for solving these equations are AP (pascal or N/m-), p (Pas or N s/m ) and D, (m /s) to give dp and L in m. Thus, typical units for pressure are converted from psi to pascal, typical units for viscosity are converted from centipoise to poise and typical units for diffusion coefficient are converted from cm /s to m /s. 

On the other hand, the dried cake permeability values were theoretically estimated by the same authors from values of the mean size of the ice crystals by assuming that the freeze-dried cake texture could be represented by a bundle of capillary tubes (mean diameter, denoted ore)- Under conditions of molecular flow in the Knudsen regime (Kn = 4) this theoretical freeze-dried layer permeability, denoted by K odei. was estimated by the following equations ... 

---