A model of cytotoxic dose-response nonlinearities arising from adaptive cell inventory management in tissues

Why do low-level exposures to environmental toxins often elicit over-compensating responses that reduce risk to an organism? Conversely, if these responses improve health, why wait for an environmental challenge to trigger them? This paper presents a mathematical modeling framework that addresses both questions using the principle that evolution favors tissues that hedge their bets against uncertain environmental challenges. We consider a tissue composed of differentiated cells performing essential functions (e.g., lung tissue, bone marrow, etc.). The tissue seeks to maintain adequate supplies of these cells, but many of them may occasionally be killed relatively quickly by cytotoxic challenges. The tissue can "order replacements" (e.g., via cytokine network signaling) from a deeper compartment of proliferative stem cells, but there is a delivery lag because these cells must undergo maturation, amplification via successive divisions, and terminal differentiation before they can replace the killed functional cells. Therefore, a "rational" tissue maintains an inventory of relatively mature cells (e.g., the bone marrow reserve for blood cells) for quick release when needed. This reservoir is replenished by stimulating proliferation in the stem cell compartment. Normally, stem cells have a very low risk of unrepaired carcinogenic (or other) damage, due to extensive checking and repair. But when production is rushed to meet extreme demands, error rates increase. We use a mathematical model of cell inventory management to show that decision rules that effectively manage the inventory of mature cells to maintain tissue function across a wide range of unpredictable cytotoxic challenges imply that increases in average levels of cytotoxic challenges can increase average inventory levels and reduce the average error rate in stem cell production. Thus, hormesis and related nonlinearities can emerge as a natural result of cell-inventory risk management by tissues.