Local control of cellular proliferation underlies neuromast regeneration in zebrafish

Biological systems are never at equilibrium but maintain stability despite perennial external disturbance. A prime example is organ regeneration, whereby despite intrinsically stochastic damage, organs are rebuilt via controlled cellular proliferation. Here, we use a mathematical approach to understand how a cell decides to re-enter and exit mitosis during organ repair. Using empirical data from regenerating neuromasts in larval zebrafish, we identify a minimal model based on ordinary differential equations (ODEs). Remarkably, the ODEs model reproduces the regeneration kinetics by assuming a cell-proliferation switch that depends on the type and the number of the neuromast cells. Additionally, a two-dimensional Cellular Potts Model (CPM) predicts that cell proliferation is a delayed response to injury. The CPM recapitulates the experimental results qualitatively and quantitatively, showing that cell proliferation is locally controlled by a switch, where each cell division stops when the type-dependent number of neighbouring cells exceeds a deterministic critical value. An intriguing corollary of our results is that a local negative feedback loop among identical cells may be a general property of organ-level proportional homeostasis.