Stochastic formulations of a clock model for temporally regulated generation of oligodendrocytes in vitro

It is possible to grow oligodendrocyte type-2 astrocyte (O-2A) progenitor cells in vitro in such a manner that they divide and generate oligodendrocytes with a timing which recapitulates the timing of normal development in vivo. The most widely accepted model of this process assumes a cell-intrinsic biological clock that resides in the O-2A progenitor cell and counts the number of mitotic divisions. The intrinsic clock model, originally proposed in 1985, remains to be the dominant theoretical concept for the analysis of timed differentiation in this cell lineage. In this paper, we proceed from different biologically plausible assumptions to provide a stochastic description of the clock model based on the theory of multitype age-dependent branching processes. This approach makes it possible to interpret the observed pattern of oligodendrocyte generation and its modification in the presence of thyroid hormone in terms of parameters that have a clear biological meaning.