Methodological and analytical issues of progressive ratio schedules: A mathematical framework for a unified theory of schedules of cocaine self-administration behavior in rats

Background. Progressive ratio (PR) schedules of drug delivery are used to determine the 'motivational' state of the animal and breakpoint is the conventional measure of drug 'reinforcing efficacy'. This widely held interpretation is based solely on the observation that the PR breakpoint is proportional to the unit dose of self-administered drug. Previously, we have demonstrated that the compulsion zone theory of self-administration explains the patterns of lever-pressing and cocaine injections under PR schedules in rats. Here we explored whether the shape of the dose-breakpoint function could be mathematically described in terms of the compulsion zone theory. Methods. The experimental dataset used for model validation was derived from our previously published studies. These data are consistent with a proposed mathematical model in which the value of breakpoint is a function of four independent variables: the lower and upper limits of the compulsion zone, the drug elimination half-life, and the local rate of responding; two parameters defined by the experimenter: the drug unit dose and the slope of progression function; and the initial drug level. Results and conclusions. This mathematical framework defines the pharmacokinetic/pharmacodynamic interactions that determine the effects of schedules of cocaine delivery on self-administration behavior and interprets breakpoint simply as the maximal number of responses which rats can perform after an injection while cocaine levels remain within the compulsion zone. Therefore, PR and fixed ratio schedules convey the same pharmacological information and PR schedules offer no scientific advantages. This mathematical modeling approach is also applicable to self-administration behavior observed with other schedules of cocaine delivery.