# The relationship between permeant size and permeability in lipid bilayer membranes

## Authors

- Received:
- Revised:

DOI: 10.1007/BF00232899

- Cite this article as:
- Xiang, T.-. & Anderson, B.D. J. Membarin Biol. (1994) 140: 111. doi:10.1007/BF00232899

## Abstract

Permeability coefficients (*P*
_{
m
}) across planar egg lecithin/decane bilayers and bulk hydrocarbon/water partition coefficients (*K*
_{w→hc}) have been measured for 24 solutes with molecular volumes, V, varying by a factor of 22 and *P*
_{
m
} values varying by a factor of 10^{7} to explore the chemical nature of the bilayer barrier and the effects of permeant size on permeability. A proper bulk solvent which correctly mimics the microenvironment of the barrier domain was sought. Changes in *P*
_{
m
}/K_{w→hc} were then ascribed to size-dependent partitioning and/or size-dependent diffusivity. The diffusion coefficient-size dependency was described by *D*
_{barrier} = *D*
_{
0
}/*V*
^{
n
}. When *n*-decane was used as a reference solvent, the correlation between log *P*
_{
m
}/*K*
_{w→hc} and log V was poor (*r* = 0.56) with most of the lipophilic (hydrophilic) permeants lying below (above) the regression line. Correlations improved significantly (*r* = 0.87 and 0.90, respectively) with more polarizable solvents, 1-hexadecene and 1,9-decadiene. Values of the size selectivity parameter *n* were sensitive to the reference solvent (*n* = 0.8 ± 0.3, 1.2 ± 0.1 and 1.4 ± 0.2, respectively, for decane, hexadecene, and decadiene). Decadiene was selected as the most suitable reference solvent. The value for *n* in bilayer transport is higher than that for bulk diffusion in decane (*n* = 0.74±0.10), confirming the steep dependence of bilayer permeability on molecular size. Statistical mechanical theory recently developed by the authors suggests that a component of this steep size dependence may reside in size-dependent solute partitioning into the ordered chain region of bilayers. This theory, combined with the above diffusion model, yielded the relationship, *P*
_{
m
}/*K*
_{W→hc}=*D*
_{
0
}exp(™α*V*)*V*
^{
n
}. A fit of the experimental data to this model gave the best fit (*r*=0.93) with α = 0.0053±0.0021 and *n*=0.8 ± 0.3, suggesting that both diffusion and partitioning mechanisms may play a role in determining the size dependence of lipid bilayer permeabilities.