Abstract
In the adult hippocampus, neurogenesis—the process of generating mature granule cells from adult neural stem cells—occurs throughout the entire lifetime. In order to investigate the involved regulatory mechanisms, knockout (KO) experiments, which modify the dynamic behaviour of this process, were conducted in the past. Evaluating these KOs is a non-trivial task owing to the complicated nature of the hippocampal neurogenic niche. In this study, we model neurogenesis as a multicompartmental system of ordinary differential equations based on experimental data. To analyse the results of KO experiments, we investigate how changes of cell properties, reflected by model parameters, influence the dynamics of cell counts and of the experimentally observed counts of cells labelled by the cell division marker bromodeoxyuridine (BrdU). We find that changing cell proliferation rates or the fraction of self-renewal, reflecting the balance between symmetric and asymmetric cell divisions, may result in multiple time phases in the response of the system, such as an initial increase in cell counts followed by a decrease. Furthermore, these phases may be qualitatively different in cells at different differentiation stages and even between mitotically labelled cells and all cells existing in the system.
Highlights
In the adult hippocampus, neurogenesis occurs in the subgranular zone of the dentate gyrus [1]
Recent data obtained from single cell level analysis demonstrate that stem cells perform four different types of events in order to produce progeny: symmetric divisions by dividing into two stem cells; two types of asymmetric divisions by either dividing into a stem cell and an astrocyte or a stem cell and a neural progenitor and astrogenic transformation; the direct conversion of a stem cell into an astrocyte [2]
It was shown that the number of stem cells, neural progenitors and immature neurons decreases during the ageing process [3,4] and alongside the number of newborn neurons depletes with time [5]
Summary
Neurogenesis occurs in the subgranular zone of the dentate gyrus [1]. Evaluating the results of such experiments is a non-trivial task owing to the multifactorial nature of the neurogenesis process These complex dynamics severely limit intuitive interpretation of experimental data and call for tools such as mathematical modelling and analysis. Because KO experiments had targeted stem cell compartments, a mathematical model describing the dynamics of cell counts for a given set of stem cell parameters provides a theoretical framework to identify the function of such KOs. Mathematical and computational models have been applied before to study adult neurogenesis. Because we aim to model short-term dynamics of labelled cells, and there is no experimental evidence of feedback loops governing this process, we propose a linear model. We introduce parameters that model the dynamics of neural stem and progenitor cells, namely the fraction of self-renewal, the proliferation rate and the division probability. Basic notation: we occasionally write x(t; p) to emphasize the dependence of the solution x(t) of a differential equation on a parameter p and sgn(a) denotes the sign of a real number a
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