D. Uhrikova et al., MATHEMATICAL-MODEL OF THE CUTOFF EFFECT IN THE HOMOLOGOUS SERIES OF TERTIARY AMINE LOCAL-ANESTHETICS, Die Pharmazie, 48(6), 1993, pp. 446-450
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.