Stochastic control of proliferation and differentiation in stem cell dynamics.

In self-renewing tissues, cell lineages consisting of stem cell and classes of daughter cells are the basic units which are responsible for the correct functioning of the organ. Cell proliferation and differentiation in lineages is thought to be mediated by feedback signals. In the simplest case a lineage is comprised of stem cells and differentiated cells. We create a model where stem cell proliferation and differentiation are controlled by the size of cell populations by means of a negative feedback loop. This two-dimensional Markov process allows for an analytical solution for the mean numbers and variances of stem and daughter cells. The mean values and the amounts of variation in cell numbers can be tightly regulated by the parameters of the control loop.