MATHEMATICAL-MODEL OF THE CUTOFF EFFECT IN THE HOMOLOGOUS SERIES OF TERTIARY AMINE LOCAL-ANESTHETICS

It is proposed a simple mathematical model explaining the quasi parabo lic dependence of the local anesthetic activity on the length of hydro phobic substituent in the homologous series of tertiary amines (TA). I t is suggested that the molecules of TA intercalate between the lipid molecules in bilayers. Due to the mismatch between the lengths of lipi d and TA hydrocarbon chains the intercalation results in a decrease in the bilayer thickness. The quasi parabolic dependence is the result o f 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 depen dent on the lipid: aqueous phase volume ratio. The empirical parameter s used in the model are obtained from the X-ray diffraction on multila mellar egg yolk phosphatidylcholine (EYPC) dispersions with the monohy drochloride of [2-(heptyloxy)phenyl]-2-(1-piperidinyl)ethyl ester of c arbamic acid and from the partition equilibria of its alkyloxy homolog s with unilamellar EYPC liposomes.