Numerically modelling time and dose dependent cytotoxicity

Dose-response curves are fundamental tools of in vitro toxicology, extensively employed in toxicant or drug screening. They are expressed by a variety of end-points and assays, measured at different time-points in a choice of cell-lines, but are typically quantified only using the mean concentration for 50% response (e.g. drug efficacy or pathway inhibition)as an indicator of overall effect. However, the response is the result of a complex and dynamic cascade of events which occur between the initial exposure and the measured end-point, and the characteristic rates of the contributing stages govern the dose response and ultimately the measured characteristic concentration. A better understanding of the effects and interdependencies of these can help in interpreting the response curves. The system can be modelled according to a phenomenological rate equation approach, in which each stage of the process is characterised by a rate constant, and causal relationships between different processes are incorporated. The current study utilises such an approach to simulate some common response cascades of cell populations to exogenous agents and explores the dependences of the dose dependent response on, for example, number of steps in a cascade, time-point, and scenarios such as additive, synergistic and antagonistic response of multiple exogenous agents.