Time Delay and Epo Dose Modulation in a Multilevel Model for Erythropoiesis

In this paper we have extended and adapted a multi-level model in ordinary differential equations accounting for erythropoiesis. At the subcellular level, the model includes equations for the regulation of red blood differentiation through Epo stimulated JAK2-STAT5 activation, while at the cell population level the model describes the basic physiological features involved in erythropoiesis. Furthermore, we included additional equations describing the exogenous injection of Epo, one of the usual treatments for several haematological diseases. Our analysis indicates that time-delay associated with the proliferation-differentiation process can provoke pathological sustained oscillations in the erythropoiesis, while other (shorter) time-delays in the model accounting for nucleo-cytoplasmic shuttling of STAT5 or hypoxia-mediated control of Epo synthesis cannot. The consequences of time delays on the dynamics of the multi-level model are analysed using Hopf's bifurcation theorem. We also investigated the effects that subcellular-level downregulation of the proteins involved in the JA2-STAT5 pathway have in the dynamics of red blood cells population. We found that downregulation of Epo receptor or STAT5 synthesis can reduce considerably the mean value of red blood cells concentration. Our analysis revealed that a realistic scenario for Epo injection (twice-per-day short pulses) can compensate effects of low-medium downregulation, while for intense down regulation Epo injection seems not able to restore the desired hematocrit levels.