Modeling the clonal heterogeneity of stem cells.

Recent experimental studies suggest that tissue stem cell pools are composed of functionally diverse clones. Metapopulation models in ecology concentrate on collections of populations and their role in stabilizing coexistence and maintaining selected genetic or epigenetic variation. Such models are characterized by expansion and extinction of spatially distributed populations. We develop a mathematical framework derived from the multispecies metapopulation model of Tilman et al (1994) to study the dynamics of heterogeneous stem cell metapopulations. In addition to normal stem cells, the model can be applied to cancer cell populations and their response to treatment. In our model disturbances may lead to expansion or contraction of cells with distinct properties, reflecting proliferation, apoptosis, and clonal competition. We first present closed-form expressions for the basic model which defines clonal dynamics in the presence of exogenous global disturbances. We then extend the model to include disturbances which are periodic and which may affect clones differently. Within the model framework, we propose a method to devise an optimal strategy of treatments to regulate expansion, contraction, or mutual maintenance of cells with specific properties.