Distinguishing between multiple mathematical models of neural stem cell quiescence and activation during age-related neural stem cell decline in neurogenesis

Abstract

Stem cells are required for tissue maintenance and homeostasis during an organism’s lifetime. Neural stem cells (NSCs) can be in an actively dividing state or in a quiescent state. The balance between stem cell quiescence and cycling activity determines the rate of neurogenesis. With age, more NSCs enter the quiescent state, while the total number of NSCs decreases. Here we reconsider an existing mathematical model of how neural stem cells switch between active and quiescent states from the point of view of control theory by considering the activation rate, self-renewal probability, and division rate as control parameters rather than as pre-defined functions. Our goal is to test whether those modifications to the basic model could explain the observed decline of neural stem cells with age better than Gomerzian time-dependent parameters, and compare the output from different model variants to experimental data from mice using AIC. We find that time-dependent activation rate provides the best fit to the activated cell fraction (ACF) of NSCs over time, but that other model variants with constant parameter values can better fit the total number of NSCs over time. We also consider an alternate model for NSCs with nonlinear feedback from progenitor cells that affect NSC parameters, and compare all models to experimental stem cell and progenitor data. However, all of the feedback models considered provide a worse fit to the experimental data. This suggests that when switching between active and quiescent stem cells is considered, a time-dependent linear model outperforms the integral feedback mechanism considered by other models of stem cell lineages. Fitting progenitor data for both the time varying models and feedback models indicates that four or five intermediate transit amplifying progenitor states are necessary. Our modeling suggests that in order to determine whether an increase in age-related neural stem cell quiescence is determined by by a decreasing stem cell activation rate or an increased stem cell depletion rate, additional experiments should be designed to explore whether or not depletion of the stem cell pool is occurring, and that a higher resolution time series for activated cell fraction (ACF) would be best to resolve this issue.