The Dynamic Behavior of a Discrete Vertical and Horizontal Transmitted Disease Model under Constant Vaccination

In this paper, a class of discrete vertical and horizontal transmitted disease model under constant vaccination is researched. Under the hypothesis of population being constant size, the model is transformed into a planar map and its equilibrium points and the corresponding eigenvalues are solved out. By discussing the influence of coefficient parameters on the eigenvalues, the hyperbolicity of equilibrium points is determined. By getting the equations of flows on center manifold, the direction and stability of the transcritical bifurcation and flip bifurcation are discussed.

Characterization of hippocampal Cajal-Retzius cells during development in a mouse model of Alzheimer's disease(Tg2576)

Cajal-Retzius cells are reelin-secreting neurons in the marginal zone of the neocortex and hippocampus. The aim of this study was to investigate Cajal-Retzius cells in Alzheimer＇s disease pathology. Results revealed that the number of Cajal-Retzius cells markedly reduced with age in both wild type and in mice over-expressing the Swedish double mutant form of amyloid precursor protein 695 （transgenic （Tg） 2576 mice）. Numerous reelin-positive neurons were positive for activated caspase 3 in Tg2576 mice, suggesting that Cajal-Retzius neuronal loss occurred via apoptosis in this Alzheimer＇s disease model. Compared with wild type, the number of Cajal-Retzius cells was significantly lower in Tg2576 mice. Western blot analysis confirmed that reelin levels were markedly lower in Tg2576 mice than in wild-type mice. The decline in Cajal-Retzius cells in Tg2576 mice was found to occur concomitantly with the onset of Alzheimer＇s disease amyloid pathology and related behavioral deficits. Overall, these data indicated that Cajal-Retzius cell loss occurred with the onset and development of Alzheimer＇s disease.

Development of the cerebellar cortex in the mouse

The cerebellum is a highly conserved structure in the central nervous system of vertebrates, and is involved in the coordination of voluntary motor behavior. Supporting this function, the cerebellar cortex presents a layered structure which requires precise spatial and temporal coordination of proliferation, migration, differentiation, and apoptosis events. The formation of the layered structure in the developing cerebellum remains unclear. The present study investigated the development of the cerebellar cortex. The results demonstrate that the primordium of the cerebellum comprises the ependymal, mantle, and marginal layers at embryonic day 12 （E12）. Subsequently, the laminated cerebellar cortex undergoes cell proliferation, differentiation, and migration, and at about postnatal day 0 （P0）, the cerebellar cortex presents an external granular layer, a molecular layer, a Purkinje layer, and an internal granular layer. The external granular layer is thickest at P6/7 and disappears at P20. From P0 to P30, the internal granular cells and the Purkinje cells gradually differentiate and develop until maturity. Apoptotic neurons are evident in the layered structure in the developing cerebellar cortex. The external granular layer disappears gradually because of cell migration and apoptosis. The cells of the other layers primarily undergo differentiation, development, and apoptosis.