Abstract:
Adult hippocampal neurogenesis has become a subject of intense research. We use data obtained from various experiments with mice in the group of Kempermann [1,2,4] which document the different mitotic and postmitotic stages of neuronal development. Such experiments use specific combinations of marker proteins for microscopic counts. They only observe the subpopulation of neurons which arise from cells which are in the S-phase of cell division at time zero.
In order to draw conclusions concerning the total daily production of mature neurons, and the average time which a cell stays within the different stages, we need an appropriate model. Here we discuss a model in discrete time, where the time step is adapted to the length of S-phase of the cells. The model is related with classical Leslie matrices [3] but incorporates cell division. It is is developed mathematically, assuming steady-state conditions for the mitotic stages. Relations between different parameters are derived (length of cell cycle for different stages, rates of symmetric/asymmetric cell division and simple growth, total cell populations and observed subpopulations) which allow a parameter reduction.
We then fit the data of [1,2,4] to the model, discuss the conclusions and possible sources of errors. A main point is how two opposing effects with apparently identical results in the experiments can be distinguished using properties of the model: the dilution of the marker in labelled cells, caused by successive divisions in a growing population, and the mortality of the cells.
[1] M.D. Brandt et. al., Mol. Cell. Neurosc. 24, 603-613 (2003).
[2] G. Kronenberg et. al., J. Comp. Neurol. 467, 455-463 (2003).
[3] L.P. Lefkovich, Biometrics 21, 1-18 (1965).
[4] B. Steiner et. al., GLIA 46, 41-52 (2004).