Feedback Control in Planarian Stem Cell Systems

In planarian flatworms, the mechanisms underlying the activity of collectively pluripotent adult stem cells (neoblasts) and their descendants can now be studied from the level of the individual gene to the entire animal. Flatworms maintain startling developmental plasticity and regenerative capacity in response to variable nutrient conditions or injury. We develop a model for cell dynamics in such animals, using methods of nonlinear dynamics, assuming that fully differentiated cells exert feedback control on neoblast activity. Our model predicts a number of whole organism level and general cell biological and behaviours, some of which have been empirically observed or inferred in planarians and others that have not. As previously observed empirically we find: 1) a curvilinear relationship between external food and planarian steady state size; 2) the fraction of neoblasts in the steady state is constant regardless of planarian size; 3) a burst of controlled apoptosis during regeneration after amputation as the number of differentiated cells are adjusted towards their correct homeostatic/steady state level. In addition our model describes the following properties that can inform and be tested by future experiments: 4) the strength of feedback control from differentiated cells to neoblasts (i.e. the activity of the signalling system) and from neoblasts on themselves in relation to absolute number depends upon the level of food in the environment; 5) planarians adjust size when food level reduces initially through increased apoptosis and then through a reduction in neoblast self-renewal activity; 6) following wounding or excision of differentiated cells, different time scales characterize both recovery of size and the two feedback functions; 7) the temporal pattern of feedback controls differs noticeably during recovery from a removal or neoblasts or a removal of differentiated cells; and 8) the signaling strength for apoptosis of differentiated cells depends upon both the absolute and relative deviations of the number of differentiated cells from their homeostatic level. We offer the first analytical framework for organizing experiments on planarian flatworm stem cell dynamics in a form that allows models to be compared with quantitative cell data based on underlying molecular mechanisms and thus facilitates the interplay between empirical studies and modeling. This framework is the foundation for studying cell migration during wound repair, the determination of homeostatic levels of differentiated cells by natural selection, and stochastic effects.