Frontiers in Mathematical Biology

Invasive behavior of lineage-structured cell populations:The interaction of noise and feedback

Shabnam Moobed

University of California, Irvine

We have developed a general framework to model the spatiotemporal dynamics of cell lineages in normal tissues and in tumors. In preliminary work, we have investigated the dynamics between two cell types: stem (undifferentiated) and dif- ferentiated cells. We used a lattice gas cellular automaton model in which cells are represented as discrete, stochastic entities that may proliferate, differentiate and may move throughout a grid in space. The differentiated cells negatively feed- back on the self-renewal probabilities of stem cells, increasing their probability to differentiate. This model is limited to small (e.g., cell) scale processes. To reach larger (e.g., tissue) scales we performed a mathematical upscaling of the small-scale stochastic system to derive deterministic (non-stochastic) equations known as a "mean-field model". We then investigated the speed and stability of an advancing tumor as a function of the feedback processes and the conditions in the tumor mi- croenvironment. Our results show, the speed and stability of the advancing tumor are controlled by the self-renewal capacity of the stem cells, their motilities. The stronger the self-renewal capacity, the faster the tumor advances. The tumor boundary devel- ops invasive fingers and irregular shapes when the feedback strength is large and density is low. Analysis shows that the instability is a noise induced phenomena, i.e. large local fluctuations are necessary components for the development of insta- bility. Front instability is not observed in the mean-field model. The distribution of stem and differentiated cells is heterogeneous with the differentiated cells tending to be located in the tumor interior and the stem cells tending be located at or near the tumor boundary. This is also observed in mean field models and is consistent with recent experimental observations.