Quantitative analysis of rate and extent of tolerance of biomarkers: application to nicotinic acid-induced changes in non-esterified fatty acids in rats

In this paper we quantitatively evaluate two feedback systems with a focus on rate and extent of tolerance and rebound development. In the two feedback systems, the regulation of turnover of response is governed by one or several moderators. In the basic system, one single moderator inhibits the formation of response. This system has been applied to cortisol secretion and serotonin reuptake inhibition. The basic system has been extended to adequately describe nicotinic acid (NiAc)-induced changes in non-esterified fatty acids (NEFA). In the extended system, the feedback is described by a cascade of moderators where the first inhibits formation of response and the last stimulates loss of response. The objectives of this paper were to analyze these systems from a mathematical/analytical and quantitative point of view and to present simulations with different parameter settings and dosing regimens in order to highlight the intrinsic behaviour of these systems and to present expressions and graphs that are applicable for quantification of rate and extent of tolerance and rebound. The dynamics of the moderators (k(tol)) compared to the dynamics of the response (k(out)), was shown to be important for the behaviour of both systems. For instance, slow dynamics of the moderator compared to the response (k(tol)<<k(out)), resulted in overshoot and pronounced rebound. The extent of tolerance was studied over time at a single constant drug concentration and at steady state for different drug concentrations and was found to be largest at drug concentrations close to IC(50). An upper limit for the response could be identified and included in the quantification of extent of rebound. Especially, for the extended system, the duration of exposure was an important factor affecting size of rebound. The rate of tolerance development was addressed by quantitatively estimating the time to steady state for the two systems, in which the value of k(tol) and the length of the cascade were critical.