Passive transport across bilayer lipid membranes: Overton continues to rule

According to Overton's rule, membrane permeability (P_M) of a molecule increases with its hydrophobicity. Experiments with a series of carboxylic acids now suggest the opposite: the most hydrophilic acid exhibited the highest P_M (1).

The experiments, however, do not justify this conclusion for the following reasons: (i) The reported membrane resistance (R_M = 1/P_M = 1/2.2 × 10⁻³ cm/s) is much lower than that of near-membrane unstirred layers (UL) (R_UL = 1/P_UL). As every resistance adds to the total resistance (R = 1/P) (2), we arrive at

where D, δ₁, and δ₂ denote the diffusion coefficient and the thicknesses of the first and second ULs, respectively. Thus, in case of acetic acid, R_M is only ≈3% of R. The value increases to 5% for hexanoic acid. Because this increment is 10-fold smaller than the noise-to-signal ratio, its detection is doubtful. Under conditions where R_M > R_UL (pH > pK_a), a P_M of 6.9 × 10⁻³ cm/s was found for acetic acid (3). In contrast to ref. 1, buffer molecules were present and explicitly considered in the model.

(ii) Steady-state equations were applied, although it takes at least 26 times longer than assumed in ref. 1 to reach the steady state. The factor was derived from the half-time of diffusion through the UL (2):

If a steady state was present in ref. 1, there should have been some kind of convection that acted to diminish the UL (Fig. 1).

Fig. 1.

Theoretical pH (Upper) and weak acid (Lower) distributions in the membrane vicinity. To show the effect of unstirred layer size, we performed model calculations in which we fixed δ_UL,1 to 20 μm and δ_UL,2 to 220 (α) or 2,000 μm (β). The calculations represent a minor modification of the previously published model (3). They were carried out analogous to the calculations of bilayer and aquaporin CO₂ permeabilities (5). The differential equations for the combined processes of diffusion and chemical reaction were solved with respect to the boundary conditions (i) that pH is equal to bulk pH at the edge of the second (right) unstirred layer and equal to 4.0 at the edge of the first (left) unstirred layer and (ii) that total acid concentration (the sum of the anionic and protonated acid concentrations) was equal to 1 mM at the −20 μm boundary and 0 at the 220 μm (α) or 2 mm (β) boundary. (Upper) The similarities between the theoretical distribution obtained with the smaller δ_UL,2 and the experiment of Grime et al. (1) indicate that the experiment was not necessarily in the steady state. Because the mathematical apparatus used by Grime et al. does not include any time dependence, it does not allow determination of membrane permeability. Varying the permeability coefficient for acetic acid by 2 orders of magnitude revealed only minor changes in the 2-mm-wide unstirred layer. (Lower) The theoretical concentration distributions of acetic (P_M = 22 μm/s) and hexanoic (P_M = 6.3 μm/s) acids are very close to each other. In both cases, membrane resistance (1/P_M) to acid flux is negligible.

Control experiments (e.g., lowering P_M with cholesterol) would have revealed the above inconsistencies. We conclude that experimental evidence questioning Overton's rule is deficient. Despite continuous debate (4), its impact prevails.