Mathematical model of erythrocyte maturation regulation
Hematopoietic tissue belongs to the self-renewing systems of the organism that are operated through specific regulatory and self-regulatory mechanisms. Maintenance of certain amount of erythroid cells is one of the necessary conditions for the organism to perform its vital functions. From this standpoint, theoretical research into proliferation and differentiation of hematopoietic tissue cells is of both basic and applied biomedical importance.
The main stages of erythrocyte maturation are regulated by the gene network described in GeneNet database. The hormone erythropoietin interacts with immature erythroid cells (erythroid stem progenitors of CFU-E type) and stimulates their proliferation, syntheses of hemoglobin, and the enzymes involved in heme biosynthesis, that is, maturation and differentiation of erythroid progenitors. Low partial pressure of oxygen in venous blood (hypoxia) is another stimulator of erythropoietin synthesis.
Interacting with cell receptor, erythropoietin activates the transcription factor GATA-1, a key regulator of erythrocyte differentiation. GATA-1 stimulates syntheses of a -, b -globins, and the enzymes of heme biosynthesis. In addition, GATA-1 activates its own gene and gene of erythropoietin receptor (positive feedback). Heme, a -globin, and b -globin form hemoglobin, the major component of the mature erythrocyte.
This biosystem functions according to completely different pattern compared to the system described in the previous section. This gene network is inactive until erythropoietin triggers it to start the irreversible process of erythrocyte maturation, where positive feedbacks are predominant. The model of this gene network performance is described as a sequence of events occurring in the maturating cells of the erythroid lineage. The erythropoietin-responsive progenitor cell opens the lineage closed by mature erythrocyte. The model comprises 119 elementary processes, 68 products, and 178 constants. Brief descriptions of the gene network objects presented in the model as dynamic variables given in the table.
Table. The objects of gene network of erythrocyte maturation regulation presented in the models as dynamic variable
Direct experimental data [Dailey and Karr, 1987; Volland and Felix, 1984; Felix and Brouillet, 1990; Frydman and Feinstein, 1984; Gibbs et al., 1985; Kohno et al., 1996; Mazzetti and Tomio, 1988; Mukerji and Pimstone, 1987; Nakahashi et al., 1990; Smythe and Williams, 1988; Scholnick et al., 1972; Siepker et al., 1987; Tan et al., 1996; Taketani and Tokunaga, 1981; Yoshinaga and Sano, 1980] were used to specify a number of constants. The rest parameters were determined through numerical experiments [Ratushny et al., 2000b] using quantitative and qualitative characteristics known from the literature [Kuhn, 1994; Ponka, 1997]. The model developed predicts that productions of several components of the system follow oscillatory dynamics (Fig. 6). The reason for this pattern is interaction of positive and negative feedbacks with domination of the former regulation mode.
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