KINETICS OF PHARMACOLOGIC RESPONSE .2. EQUATION FOR TURNOVER TIME OF GOLDFISH AS A FUNCTION OF CONCENTRATION OF ETHANOL AND A THEORETICAL DERIVATION BASED ON A COMBINATION OF OCCUPATION AND RATE RECEPTOR THEORIES

Turnover time (T) of goldfish in 2‐8% v/v ethanol‐water (C) was determined in two crossover studies: (a) three body weight groups of six fish each, and (b) six larger fish. Each fish had different treatment schedule. Analyses of variance of log T showed: (a) no residual effects of a treatment, and (b) no significant differences among fish. Log T was linearly related to log C and the variances were homogeneous. For individual fish: T = (a/C)b where a and b are apparently normally distributed with 95% C.I. of 9.31 ± 3.8 and 2.28 ± 1.17, respectively. For all 24 fish, a.b = D, where D is essentially a constant but has a narrow apparently normal distribution with a coefficient of variation of 11.5 %; hence, T = (D/bC)b. This equation was also derived by marrying occupation and rate receptor theories. Basic assumptions are: dT/T = ‐b(dv/v) and v ≪ Vm, where v is the overall reaction rate of the receptor‐ethanol reaction and Vm is the maximum rate. Also note that dv/v = dn/n, where n is the fraction of receptors occupied. Literature data are shown to obey the derived equations. Hence 1/T ∝ C only in those rare instances when b = 1. The theory assumes only a partitioning across the absorbing membranes of the fish. It differs from a previous theory which assumes a first order rate constant for absorption is involved. Copyright © 1969 Wiley‐Liss, Inc., A Wiley Company