Abstract
During development of the vertebrate neuroepithelium, the nucleus in neural progenitor cells (NPCs) moves from the apex toward the base and returns to the apex (called interkinetic nuclear migration) at which point the cell divides. The fate of the resulting daughter cells is thought to depend on the sampling by the moving nucleus of a spatial concentration profile of the cytoplasmic Notch intracellular domain (NICD). However, the nucleus executes complex stochastic motions including random waiting and back and forth motions, which can expose the nucleus to randomly varying levels of cytoplasmic NICD. How nuclear position can determine daughter cell fate despite the stochastic nature of nuclear migration is not clear. Here we derived a mathematical model for reaction, diffusion, and nuclear accumulation of NICD in NPCs during interkinetic nuclear migration (INM). Using experimentally measured trajectory-dependent probabilities of nuclear turning, nuclear waiting times and average nuclear speeds in NPCs in the developing zebrafish retina, we performed stochastic simulations to compute the nuclear trajectory-dependent probabilities of NPC differentiation. Comparison with experimentally measured nuclear NICD concentrations and trajectory-dependent probabilities of differentiation allowed estimation of the NICD cytoplasmic gradient. Spatially polarized production of NICD, rapid NICD cytoplasmic consumption and the time-averaging effect of nuclear import/export kinetics are sufficient to explain the experimentally observed differentiation probabilities. Our computational studies lend quantitative support to the feasibility of the nuclear concentration-sensing mechanism for NPC fate determination in zebrafish retina.