Stem cell control, oscillations and tissue regeneration in spatial and non-spatial models

Normal human tissue is organized into cell lineages, in which thehighly differentiated mature cells that perform tissue functions arethe end product of an orderly tissue-specific sequence of divisionsthat start with stem cells or progenitor cells. Tissue homeostasis andeffective regeneration after injuries requires tight regulation ofthese cell lineages and feedback loops play a fundamental role in thisregard. In particular, signals secreted from differentiated cells thatinhibit stem-cell division and stem-cell self-renewal are important inestablishing control. In this article we study in detail the celldynamics that arise from this control mechanism. These dynamics arefundamental to our understanding of cancer, given that tumorinitiation requires an escape from tissue regulation. Knowledge on theprocesses of cellular control can provide insights into the pathwaysthat lead to deregulation and consequently cancer development