Timing the spinal cord development with neural progenitor cells losing their proliferative capacity: a theoretical analysis.

In the developing neural tube in chicken and mammals, neural stem cells proliferate and differentiate according to a stereotyped spatiotemporal pattern. Several actors have been identified in the control of this process, from tissue-scale morphogens patterning to intrinsic determinants in neural progenitor cells. In a previous study (Bonnet et al. eLife 7, 2018), we have shown that the CDC25B phosphatase promotes the transition from proliferation to differentiation by stimulating neurogenic divisions, suggesting that it acts as a maturating factor for neural progenitors. In this previous study, we set up a mathematical model linking fixed progenitor modes of division to the dynamics of progenitors and differentiated populations. Here, we extend this model over time to propose a complete dynamical picture of this process. We start from the standard paradigm that progenitors are homogeneous and can perform any type of divisions (proliferative division yielding two progenitors, asymmetric neurogenic divisions yielding one progenitor and one neuron, and terminal symmetric divisions yielding two neurons). We calibrate this model using data published by Saade et al. (Cell Reports 4, 2013) about mode of divisions and population dynamics of progenitors/neurons at different developmental stages. Next, we explore the scenarios in which the progenitor population is actually split into two different pools, one of which is composed of cells that have lost the capacity to perform proliferative divisions. The scenario in which asymmetric neurogenic division would induce such a loss of proliferative capacity appears very relevant.

Traveling pulse emerges from coupled intermittent walks: A case study in sheep.

Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioural rules that sheep follow at the individual scale in order to sustain collective motion. Individuals alternate grazing mode at null speed and moving mode at walking speed, so cohesive motion stems from synchronising when they decide to switch between the two modes. We propose a model for the individual decision making process, based on switching rates between stopped / walking states that depend on behind / ahead locations and states of the others. We parametrize this model from data. Next, we translate this (microscopic) individual-based model into its density-flow (macroscopic) equations counterpart. Numerical solving these equations display a traveling pulse propagating at constant speed even though each individual is at any moment either stopped or walking. Considering the minimal model embedded in these equations, we derive analytically the steady shape of the pulse (sech square). The parameters of the pulse (shape and speed) are expressed as functions of individual parameters. This pulse emerges from the non linear coupling of start/stop individual decisions which compensate exactly for diffusion and promotes a steady ratio of walking / stopped individuals, which in turn determines the traveling speed of the pulse. The system seems to converge to this pulse from any initial condition, and to recover the pulse after perturbation. This gives a high robustness to this coordination mechanism.

Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase.

A fundamental issue in developmental biology and in organ homeostasis is understanding the molecular mechanisms governing the balance between stem cell maintenance and differentiation into a specific lineage. Accumulating data suggest that cell cycle dynamics play a major role in the regulation of this balance. Here we show that the G2/M cell cycle regulator CDC25B phosphatase is required in mammals to finely tune neuronal production in the neural tube. We show that in chick neural progenitors, CDC25B activity favors fast nuclei departure from the apical surface in early G1, stimulates neurogenic divisions and promotes neuronal differentiation. We design a mathematical model showing that within a limited period of time, cell cycle length modifications cannot account for changes in the ratio of the mode of division. Using a CDC25B point mutation that cannot interact with CDK, we show that part of CDC25B activity is independent of its action on the cell cycle.