Stochastic modeling of stress erythropoiesis using a two-type age-dependent branching process with immigration.

The erythroid lineage is a particularly sensitive target of radiation injury. We model the dynamics of immature (BFU-E) and mature (CFU-E) erythroid progenitors, which have markedly different kinetics of recovery, following sublethal total body irradiation using a two-type reducible age-dependent branching process with immigration. Properties of the expectation and variance of the frequencies of both types of progenitors are presented. Their explicit expressions are derived when the process is Markovian, and their asymptotic behavior is identified in the age-dependent (non-Markovian) case. Analysis of experimental data on the kinetics of BFU-E and CFU-E reveals that the probability of self-renewal increases transiently for both cell types following sublethal irradiation. In addition, the probability of self-renewal increased more for CFU-E than for BFU-E. The strategy adopted by the erythroid lineage ensures replenishment of the BFU-E compartment while optimizing the rate of CFU-E recovery. Finally, our analysis also indicates that radiation exposure causes a delay in BFU-E recovery consistent with injury to the hematopoietic stem/progenitor cell compartment that give rise to BFU-E. Erythroid progenitor self-renewal is thus an integral component of the recovery of the erythron in response to stress.