Periodic and quasi-periodic behavior in resource-dependent age structured population models.

To describe the dynamics of a resource-dependent age structured population, a general non-linear Leslie type model is derived. The dependence on the resources is introduced through the death rates of the reproductive age classes. The conditions assumed in the derivation of the model are regularity and plausible limiting behaviors of the functions in the model. It is shown that the model dynamics restricted to its omega-limit sets is a diffeomorphism of a compact set, and the period-1 fixed points of the model are structurally stable. The loss of stability of the non-zero steady state occurs by a discrete Hopf bifurcation. Under general conditions, and after the loss of stability of the structurally stable steady states, the time evolution of population numbers is periodic or quasi-periodic. Numerical analysis with prototype functions has been performed, and the conditions leading to chaotic behavior in time are discussed.

Spatial associations of centromeres in the nuclei of hematopoietic cells: evidence for cell-type-specific organizational patterns.

It is believed that the 3-dimensional organization of centromeric heterochromatin in interphase may be of functional relevance as an epigenetic mechanism for the regulation of gene expression. Accordingly, a likely possibility is that the centromeres that spatially associate into the heterochromatic structures (chromocenters) observed in the G1 phase of the cell cycle will differ in different cells. We sought to address this issue using, as a model, the chromocenters observed in quiescent normal human hematopoietic cells and primary fibroblasts. To do this, we analyzed the spatial relationships among different human centromeres in 3-D preserved cells using nonisotopic in situ hybridization and confocal microscopy. We showed quantitatively that chromocenters in all cell types do indeed represent nonrandom spatial associations of certain centromeres. Furthermore, the observed patterns of centromere association indicate that the chromocenters in these cell types are made of different combinations of specific centromeres, that hematopoietic cells are strikingly different from fibroblasts as to the composition of their chromocenters and that centromeres in peripheral blood cells appear to aggregate into distinct "myeloid" (present in monocytes and granulocytes) and "lymphoid" (present in lymphocytes) spatial patterns. These findings support the idea that the chromocenters formed in the nucleus of quiescent hematopoietic cells might represent heterochromatic nuclear compartments involved in the regulation of cell-type-specific gene expression, further suggesting that the spatial arrangement of centromeric heterochromatin in interphase is ontogenically determined during hematopoietic differentiation. (Blood. 2000;95:1608-1615)