Table SI: Macroscopic Property Data for All Chemical Permeation Enhancers

Supplementary Material

Table SI: Macroscopic Property Data for all Chemical Permeation Enhancers

Mean standard deviations for raw data are 0.07, 0.09, and 0.12 for EP, TP, and LP, respectively.Please note that while most K values fall between 0 and 1, negative values may occur when LP > EP (see Discussion section). Additionally, it is important to be aware that very small EP and/or LP values yield less meaningful K values, since the magnitude of EP and/or LP values is similar to the magnitude of the error in the system.

THEORY

The passive permeability of an epithelial membrane to a solute or an ion, P0, can be described by the following equation.

(S1)

where  is the fractional area of the entire epithelial membrane through which paracellular transport occurs,Pp is the inherent permeability of the paracellular route and Pt is the inherent permeability of the transcellular route. Equation S1 can be written separately for the control (no enhancer, denoted by a superscript C) and a test case (in the presence of enhancer, denoted by a superscript E).

(S2)

(S3)

An enhancement ratio of permeabilities can be obtained by dividing Eq. (S3) by Eq. (S2) as follows:

(S4)

Equation (S4) can be simplified with the following approximations. First, it is assumed that in the control, the permeability of the transcellular route is negligible, an assumption valid for ionic and polar solutes, PtC = 0. This assumption is supported by reports indicating that the transport of ions and polar solutes such as mannitol across unperturbed epithelium is an indication of paracellular transport (1). This simplifies Eq. (S4) as follows:

(S5)

Next, it is assumed that the transcellular permeability in the presence of an enhancer, PtE, is proportional to the amount of LDH leaked, that is, PtE = LDH, where  is a constant. This argument is based on the assumption that once pathways are created in the membrane to release an intracellular macromolecule such LDH, solutes exterior to epithelial cells can also traverse the membrane through the same pathways. The converse of the above statement is also assumed to be true, that is, pathways through which a solute of interest diffuses across the membrane are also accessible for LDH leakage. With this assumption, Eq. (S5) can be rewritten as follows:

(S6)

It is further assumed that even in the presence of an enhancer, the area fraction, E for paracellular transport is relatively small, that is, E < 1. This assumption follows the fact that cells in the epithelium are well-spread and occupy a substantial area of the monolayer. Accordingly, the area of the paracellular transport (the gap between the cells) is much smaller than the area of the cells themselves. Equation (S6) can then be simplified to the following:

(S7)

where,Eo is the enhancement ratio in overall solute or ion permeability,, Ep is the enhancement in the paracellular component of the permeability, , and .

To further simplify Eq. (S7), we use the results of a positive control (1% Triton X-100) where maximum enhancement (Emax) and maximum LDH release (LDHmax) are simultaneously observed, giving

(S8)

The constant  can be found by assuming that in cases where LDH release approaches its maximum value, indicating maximum opening of the transcellular route, the contribution of transcellular component dominates the paracellular component due to its high area fraction (that is, ). This gives. With these approximations, Eq. (S7) can be rearranged as follows:

(S9)

By using the definitions of enhancement potential (EP) and LDH potential (LP)described in the methods section, Eq. (S9) can be further simplified as the following:

(S10)

Equation (S10) gives a direct relationship between enhancement potential and LDH potential based on LDH release. Equation (S10) is used in the Results section to identify contributions of transcellular and paracellular pathways in passive transport across the epithelial monolayer in the presence of chemical permeation enhancers.

Reference:

1.V. Pade and S. Stavchansky. Estimation of the relative contribution of the transcellular and paracellular pathway to the transport of passively absorbed drugs in the caco-2 cell culture model. Pharm Res. 14:1210 - 1215 (1997).

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