Abstract
Non-monotonic dose response (U-shaped) patterns occur when a toxic substance acts as a stimulant in small doses, but as an inhibitor in large doses. A mechanistically based mathematical model is introduced in this manuscript, and the ability of the model to demonstrate non-monotonic dose response is discussed. The biologically based dose-response model for developmental toxicology derived by Leroux et al. is extended. The original model has two basic states, precursor cells and differentiated cells, with both states subject to a linear birth-death process. As an alternative, we introduce a model that permits a highly controlled birth and death process for the precursor cells. This controlled growth and differentiation (CGD) model is the foundation for more realistic models of mammalian development. The augmented model limits the number of replications allowed in the development of an organ or tissue and more closely reflects the presence of a true stem cell population. As a result, the CGD model can be used to simulate a host of processes related to development. This paper also explores the adaptability of the CGD model to describe biological development as it relates to toxic agents with effects demonstrating non-monotonic dose response.
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