Mathematical model of the cut-off effect in the homologous series of tertiary amine local anesthetics.

It is proposed a simple mathematical model explaining the quasi parabolic dependence of the local anesthetic activity on the length of hydrophobic substituent in the homologous series of tertiary amines (TA). It is suggested that the molecules of TA intercalate between the lipid molecules in bilayers. Due to the mismatch between the lengths of lipid and TA hydrocarbon chains the intercalation results in a decrease in the bilayer thickness. The quasi parabolic dependence is the result of combination of partition equilibria and of geometrical parameters of interacting molecules in the bilayer. The model predicts that the TA chain length at which the maximum activity is observed should be dependent on the lipid: aqueous phase volume ratio. The empirical parameters used in the model are obtained from the X-ray diffraction on multilamellar egg yolk phosphatidylcholine (EYPC) dispersions with the monohydrochloride of [2-(heptyloxy)phenyl]-2-(1-piperidinyl)ethyl ester of carbamic acid and from the partition equilibria of its alkyloxy homologs with unilamellar EYPC liposomes.