A multiscale mathematical model of cell dynamics during neurogenesis in the mouse cerebral cortex.

BACKGROUND: Neurogenesis in the murine cerebral cortex involves the coordinated divisions of two main types of progenitor cells, whose numbers, division modes and cell cycle durations set up the final neuronal output. To understand the respective roles of these factors in the neurogenesis process, we combine experimental in vivo studies with mathematical modeling and numerical simulations of the dynamics of neural progenitor cells. A special focus is put on the population of intermediate progenitors (IPs), a transit amplifying progenitor type critically involved in the size of the final neuron pool. RESULTS: A multiscale formalism describing IP dynamics allows one to track the progression of cells along the subsequent phases of the cell cycle, as well as the temporal evolution of the different cell numbers. Our model takes into account the dividing apical progenitors (AP) engaged into neurogenesis, both neurogenic and proliferative IPs, and the newborn neurons. The transfer rates from one population to another are subject to the mode of division (proliferative, or neurogenic) and may be time-varying. The model outputs are successfully fitted to experimental cell numbers from mouse embryos at different stages of cortical development, taking into account IPs and neurons, in order to adjust the numerical parameters. We provide additional information on cell kinetics, such as the mitotic and S phase indexes, and neurogenic fraction. CONCLUSIONS: Applying the model to a mouse mutant for Ftm/Rpgrip1l, a gene involved in human ciliopathies with severe brain abnormalities, reveals a shortening of the neurogenic period associated with an increased influx of newborn IPs from apical progenitors at mid-neurogenesis. Our model can be used to study other mouse mutants with cortical neurogenesis defects and can be adapted to study the importance of progenitor dynamics in cortical evolution and human diseases.

Multi-scale modelling of ovarian follicular development: From follicular morphogenesis to selection for ovulation.

In this review, we present multi-scale mathematical models of ovarian follicular development that are based on the embedding of physiological mechanisms into the cell scale. During basal follicular development, follicular growth operates through an increase in the oocyte size concomitant with the proliferation of its surrounding granulosa cells. We have developed a spatio-temporal model of follicular morphogenesis explaining how the interactions between the oocyte and granulosa cells need to be properly balanced to shape the follicle. During terminal follicular development, the ovulatory follicle is selected amongst a cohort of simultaneously growing follicles. To address this process of follicle selection, we have developed a model giving a continuous and deterministic description of follicle development, adapted to high numbers of cells and based on the dynamical and hormonally regulated repartition of granulosa cells into different cell states, namely proliferation, differentiation and apoptosis. This model takes into account the hormonal feedback loop involving the growing ovarian follicles and the pituitary gland, and enables the exploration of mechanisms regulating the number of ovulations at each ovarian cycle. Both models are useful for addressing ovarian physio-pathological situations. Moreover, they can be proposed as generic modelling environments to study various developmental processes and cell interaction mechanisms.