Abstract:
A Hill-type time-response curve was derived using a single-step chemical kinetics approximation.
The rate expression for the transformation is a differential equation that provides an interpolation
formula between the logistic growth curve and second order kinetics. The solution is equivalent to the
log-logistic cumulative distribution function with the time constant expressed in terms of a kinetic
rate constant. This expression was extended to a full dose-time-response equation by postulating a
concentration dependence for the rate constant. This was achieved by invoking a modified form of
Haber’s law that connects an observed toxic effect with the concentration of the active agent and the
elapsed exposure time. Analysis showed that the concept of Concentration Addition corresponds to a
special case where the rate constant for the overall transformation rate is proportional to the sum of the
rate constants that apply when the agents act individually. Biodiesel “survival” curves were measured
and used to test the applicability of the empirical model to describe the effects of inhibitor dosage and
binary inhibitor mixtures. Positive results suggest that the proposed dose-response relationship for
the toxicity of agents to organisms can be extended to inanimate systems especially in cases where
accurate mechanistic models are lacking.
