Modeling spatial population dynamics of stem cell lineage in tissue growth.

Understanding the dynamics of cell population allows insight into the control mechanism of the growth and development of mammalian tissues. It is well known that the proliferation and differentiation among stem cells (SCs), intermediate progenitor cells (IPCs), and fully differentiated cells (FDCs) are under different activation and inhibition controls. Secreted factors in negative feedback loops have already been identified as major elements in regulating the numbers of different cell types and in maintaining the equilibrium of cell populations. We have developed a novel spatial dynamic model of cells. We can characterize not only overall cell population dynamics, but also details of temporal-spatial relationship of individual cells within a tissue. In our model, the shape, growth, and division of each cell are modeled using a realistic geometric model. Furthermore, the inhibited growth rate, proliferation and differentiation probabilities of individual cells are modeled through feedback loops controlled by secreted factors of neighboring cells within a proper diffusion radius. With specific proliferation and differentiation probabilities, the actual division type that each cell will take is chosen by a Monte Carlo sampling process. With simulations we found that with proper strengths of inhibitions to growth and stem cell divisions, the whole tissue is capable of achieving a homeostatic size control. We discuss our findings on control mechanisms of the stability of the tissue development. Our model can be applied to study broad issues on tissue development and pattern formation in stem cell and cancer research.