We previously showed that downregulating CDC25B levels using RNAi in the chicken neural tube results in a G2 phase lengthening and a reduction of the number of neurons (Peco et al., 2012). Here we used a genetic approach to question whether both functions are conserved in mammals, using a floxed allele of Cdc25b and a NestinCre;Cdc25b${}^{\mathrm{+}\mathit{}\mathrm{/}\mathrm{-}}$ mouse line to specifically ablate the phosphatase in the developing nervous system (Figure 1A). In the mouse embryo, Cdc25b is detected in the neural tube from E8.5 onward and remains strongly expressed in areas where neurogenesis occurs, as illustrated in the E11.5 neural tube (Figure 1B). Loss of Cdc25b mRNA was observed from E10.5 onward in NestinCre;Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{-}}$ embryos (Cdc25b${}^{\mathrm{nesKO}}$, Figure 1B). We therefore determined the consequences of the Cre-mediated deletion of the floxed Cdc25b allele on cell cycle parameters and neurogenesis starting at E11.5.

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The proliferation capacity of the neural progenitors in NestinCre;Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{-}}$ embryos, was determined by quantification of EdU labelled replicating neural progenitors. The proliferative index in the dorsal spinal cord (number of EdU+ cells among total number of neural progenitors labelled with Pax7 antibody) was similar between NestinCre;Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{-}}$ and control embryos (NestinCre;Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{+}}$ or Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{+}}$ or Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{-}}$) (Figure 1C). Similarly, the fraction of mitotic cells assessed by quantifying the number of Phospho-Histone 3 (PH3) mitotic cells in the Pax7+ cells displayed a slight and non-significant reduction in the mitotic index of mutant embryos (Figure 1D). Since downregulating CDC25B in the chicken neural tube resulted in a lengthening of the G2 phase, we next compared the length of the G2 phase in the dorsal spinal cord of NestinCre;Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{-}}$ versus control embryos using the percentage of labeled mitosis (PLM) (Quastler and Sherman, 1959). Embryos were injected with EdU and allowed to recover for 1 hr, 2 hr or 3 hr before fixation and staining with EdU and PH3 antibodies. We found that the percentage of PH3/EdU positive cells was consistently lower in the dorsal domain of NestinCre;Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{-}}$ versus control embryos (Figure 1E). The average G2-lengths extracted from the curve were 2 hr 19 min in mutants compared to 1 hr 49 min in controls (Figure 1E). This indicates that Cdc25b loss-of-function in dorsal neural progenitors results in a G2 phase lengthening.

The question is then whether Cdc25b loss-of-function affects spinal neurogenesis. Neuron production occurs in two phases in the dorsal spinal cord, an early neurogenic phase (between E9.5 and E11.5) and a late neurogenic phase (between E11.5 and E13.5) (Hernandez-Miranda et al., 2017). Neurons emerging from the dorsal spinal cord express numerous transcription factors including Pax2 and Tlx3 that label distinct neuron types and when combined, identify different subtypes of early (Pax2: dl4, dI6; Tlx3: dI3, dI5) and late born neurons (Pax2: dILA; Tlx3: dILB). The use of a NestinCre mouse line allows us to accurately ablate the phosphatase at the time of late neuron production (Hernandez-Miranda et al., 2017). We hence analyze the impact of the deletion at E11.5 and E12.5. At E11.5, the number of Tlx3+ cells is reduced in the NestinCre;Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{-}}$ compared to control embryos. Pax2+ neurons are also reduced yet non-significantly (Figure 1F,G). One day later, a clear and significant reduction of 25.7% and 28% in the number of Pax2+ and Tlx3+ neurons, respectively, is observed following Cdc25b deletion. Progenitor domain size measured at E11.5 and E12.5 using Pax7 or Sox2 immunohistochemistry shows non-significant differences (Figure 1—figure supplement 1). Analysis of dorsal progenitor nuclear density using DAPI shows a small and constant 7.5% and 7.3% reduction at E11.5 and E12.5, respectively, in mutant versus control embryos (Figure 1—figure supplement 1), indicating that neuronal reduction is at least partly due to this small reduction in the progenitor population. Quantification of active caspase three immunostaining (E12.5) does not reveal an increase in cell death, showing that the reduction in neuron number is not due to apoptosis (not shown). The ratio of dILA to dILB neurons is similar in control (0.68) and mutant embryos (0.71), confirming that Cdc25b does not impact specific neuronal cell type but rather has a generic effect on neuron production. Together, these observations demonstrate that efficient spinal neuron production requires CDC25B in mammalian embryos and illustrate that this function is conserved among higher vertebrates.

The fact that CDC25B downregulation impedes neuron production in mouse and chicken embryos, prompted us to test whether CDC25B gain-of-function is sufficient to stimulate neurogenesis. It is not possible to perform CDC25B gain-of-function using a robust ubiquitous promoter, because an unscheduled increase of the phosphatase during the cell cycle leads to mitotic catastrophe and subsequent apoptosis (Peco et al., 2012). To circumvent this technical impasse, we express CDC25B using the mouse cell cycle dependent CDC25B cis regulatory element (ccRE) that reproduces the cell cycle regulated transcription of CDC25B (Körner et al., 2001) and prevents apoptosis (Kieffer et al., 2007). We verify that ccRE is sufficient to drive lacZ reporter expression in the entire chicken neural tube after transfection by in ovo electroporation (Figure 2—figure supplement 1A). Under the control of ccRE, the eGFP-CDC25B fusion protein is expressed in a subset of transfected cells (Figure 2A). The level of chimeric protein detected results from the periodic expression induced by the promoter and the intrinsic instability of CDC25B actively degraded at the end of mitosis. The fusion protein can be observed both in the nucleus and cytoplasm of neuroepithelial progenitors located close to the lumen (L) and in mitotic progenitors (Figure 2A, arrowhead). The gain-of-function does not induce apoptosis, as revealed by quantification of active caspase three immunostaining (Figure 2—figure supplement 1B–D). To ascertain that the phosphatase is functional, we analyze its impact on G2 phase duration. As expected, ectopic expression of the phosphatase shortens the G2 phase (Figure 2B, blue curve) without significantly modifying the mitotic index or the proliferation index (Figure 2—figure supplement 1E–F).

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Quantitative analysis performed on the entire neural tube using NeuroD-reporter assay indicates that increasing CDC25B is sufficient to promote neuronal commitment (Figure 2—figure supplement 2). In the neural tube, development of the ventral progenitor population is usually considered more advanced than its dorsal counterpart (Kicheva et al., 2014; Saade et al., 2013). Accordingly, the temporality of neuron production progresses from ventral to dorsal (Kicheva et al., 2014; Saade et al., 2013) and correlates with endogenous CDC25B expression (Peco et al., 2012). We therefore analyze separately the fraction of neurons generated following CDC25B gain-of-function in the ventral and dorsal halves of this structure. In the ventral neural tube, CDC25B gain-of-function increases the percentage of HuC/D⁺ GFP⁺ cells from 61.6 ± 1.5% to 76.5 ± 0.9%. Similarly, in the dorsal spinal cord, the proportion increases from 30.7 ± 1.34% to 41.8 ± 2.64% with the CDC25B gain-of-function (Figure 2F,G). A significant increase in neurogenesis is also observed using Pax2 immunostaining, from 11.4 ± 1% to 20 ± 1.8% (Figure 2C,D). Conversely, CDC25B gain-of-function reduces the proportion of cells expressing the progenitor marker Sox2 (Figure 2E). Together, these results indicate that CDC25B is sufficient to stimulate neuron production.

An increase in CDC25B activity has been shown to induce a shifted cleavage plane and precocious neurogenesis during corticogenesis in mouse (Gruber et al., 2011). We therefore tested the effect of CDC25B gain-of-function on spindle orientation in spinal neural precursors. We measured the angle of the mitotic spindle as previously described (Saadaoui et al., 2014), and we did not observe a significant change in spindle orientation (Figure 3A,B). Another element implicated in asymmetric cell fate in neural progenitors is the spindle-size asymmetry (SSA), that is, the difference in size between the two sides of the spindle (Delaunay et al., 2014). Our CDC25B gain-of-function experiments did not induce a significant modification of the SSA in chick spinal neural progenitors (Figure 3C–D). In summary, our analyses did not reveal an effect of CDC25B activity on the orientation or the size of the mitotic spindle.

Figure 3

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To elucidate CDC25B function, we investigate whether it promotes neurogenesis by controlling the division mode of neural progenitors. We take advantage of a strategy recently developed by E. Marti and colleagues, described to distinguish the three modes of division, PP, PN and NN, occurring in the developing chicken spinal cord (Le Dréau et al., 2014; Saade et al., 2017; Saade et al., 2013). Briefly, the neural tube is electroporated with Sox2::GFP and Tis21::RFP reporters, and 24 hr later the number of neural progenitors expressing these markers is quantified at mitosis. Thus, Sox2⁺Tis21^– cells expressing only Sox2::GFP correspond to PP divisions, Sox2^–Tis21⁺ cells correspond to NN divisions, while cells co-expressing both biosensors Sox2⁺Tis21⁺ correspond mostly to asymmetric neurogenic divisions, PN (Figure 4A). Using these biomarkers in the dorsal neural tube, we obtained comparable results to the ones previously described (Figure 2B in Le Dréau et al., 2014). Because the number of electroporated cells in mitosis is very small, we determine whether counting neural progenitors displaying green, yellow or red fluorescence is equivalent to counting only mitotic cells in the dorsal spinal cord 24 hr post electroporation. We do not detect a significant difference in the distribution of cells in total neuroepithelial progenitors (55.4 ± 6.2% Sox2⁺Tis21^– cells, 29.3 ± 3.9% Sox2⁺Tis21⁺ cells and 15.2 ± 2.9% Sox2^–Tis21⁺ cells) and during mitosis (57.9 ± 9.3% Sox2⁺Tis21^– cells, 23.2 ± 8.5% Sox2⁺Tis21⁺ cells and 19 ± 7.3% Sox2^–Tis21⁺ cells) (Figure 4B). Because of reporter stability, the temporal window of analysis of Sox2/Tis21 reporters is restricted to 24 hr (Saade et al., 2013). Recent data indicate that Sox2 mRNA expression can be sustained in some neurogenic progenitors (Albert et al., 2017). A fraction of the Sox2⁺Tis21⁺ cells might therefore correspond to NN rather than PN divisions, suggesting that the use of these biomarkers is not sufficient to separate PN and NN divisions in our experimental conditions. Therefore, even if we quantified separately the three populations, we considered the Sox2⁺Tis21⁺ and the Sox2^–Tis21⁺ progeny as a whole, producing neurogenic divisions, and compared it to the Sox2⁺Tis21^– cells performing proliferative divisions.

Figure 4

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CDC25B RNAi electroporation leads to a consistent and strong downregulation in CDC25B transcripts located in the intermediate neural tube (Figure 4C, bracket). We therefore determine the impact of CDC25B downregulation on the mode of division in progenitors located in this domain. We co-electroporate the biomarkers with either the CDC25B-RNAi plasmid, or the control scrambled plasmid at stage HH11, and quantify the distribution of Sox2⁺Tis21^–, Sox2⁺Tis21+ and Sox2^–Tis21⁺ cells 24 hr later at stage HH17 (Figure 4D–E). When compared to the control scrambled RNAi, the CDC25B RNAi induces a massive increase in Sox2⁺Tis21^– progeny (13.4 ± 1.3% to 35.1 ± 1.8%), and a decrease in Sox2⁺Tis21⁺ progeny (from 72.1 ± 1.85% to 56.2 ± 1.70% and to some extent, in Sox2^–Tis21⁺ progeny (from 14.6 ± 1.43% to 8.74 ± 0.8%, Figure 4E). Therefore CDC25B RNAi increases proliferative divisions from 13.4 ± 1.3% to 35.1 ± 1.8% and decreases neurogenic divisions from 86.6 ± 1.3% to 63.9 ± 1.8% (P-value < 0,0001). This observation indicates that CDC25B downregulation hinders neuron production by maintaining proliferative divisions and reducing neurogenic divisions.

We then tested how CDC25B gain-of-function affects the mode of division using two different approaches: the Tis21/Sox2 assay (Saade et al., 2013) (Figure 5A,D,F), and a clonal analysis using the Brainbow technique (Tozer et al., 2017) (Figure 5B,C,E). Analyzing the distribution of the mode of division with the Tis21/Sox2 strategy in the entire neuroepithelium at 24 hr after electroporation, showed that CDC25B leads to a decrease in Sox2⁺Tis21^– progeny (from 46.1 ± 2.1% to 27.3 ± 1.8%), an increase in Sox2⁺Tis21⁺ progeny (from 43.4 ± 1.9% to 50.9 ± 1.6%), and Sox2^–Tis21⁺ progeny (from 10.5 ± 0.8% to 21.8 ± 1.5%, Figure 5A,D). This shows that CDC25B gain-of-function reduces proliferative divisions from 46.1 ± 2.1% to 27.3 ± 1.8% and increases neurogenic divisions from 53.8 ± 2.1% to 72.7 ± 1.8% (P-value < 0,0001). Embryos co-transfected with the Nucbow vector (Loulier et al., 2014), limiting amounts of Cre recombinase (Morin et al., 2007) and the various gain-of-function constructions, were harvested after 40 hr at stage HH21 and labelled using HuC/D immunostaining (Figure 5B,C). Two cells clones located in low electroporated density area were selected on the basis of color identity (Tozer et al., 2017) and categorized as proliferative divisions: HuC/D^–-HuC/D^– (upper panel in Figure 5C), and neurogenic divisions either HuC/D⁺-HuC/D^–(middle panel in Figure 5C) or HuC/D⁺-HuC/D⁺ (lower panel in Figure 5C).

Figure 5

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Using this alternative strategy, we showed that the expression of CDC25B leads to a decrease in HuC/D${}^{-}$-HuC/D${}^{-}$ cells (from 76.5 ± 2.6% to 60.7 ± 2.3%) and to an increase in HuC/D${}^{-}$-HuC/D${}^{+}$ cells (from 9.4 ± 1.5% to 16.3 ± 1.7%) and HuC/D${}^{+}$-HuC/D${}^{+}$ (from 14.1 ± 2.3% to 23.0 ± 2.1%, Figure 5E). We observe a decrease in proliferative divisions from 76.5 ± 2.6% to 60.7 ± 2.3% and an increase of neurogenic divisions from 23.8 ± 2.5% to 39.4 ± 2.3% (P-value < 0.001). While the mode of division repartitions were probably different due to inherent differences in the two strategies, CDC25B gain-of-function results in consistent modifications in both assays : a reduction of 15.8 percentage-points (pp) (from 76.5% to 60.6%) and 18.8 pp (from 46.1% to 27.3%) in proliferative divisions and a corollary increase of 15.8 pp (from 23.7% to 36.4%) and 18.8 pp (from 53.8% to 72.7%) in neurogenic divisions in the Nucbow and the Tis21/Sox2 assays, respectively (Figure 5D,E). These results indicate that CDC25B gain-of-function in spinal neural progenitors reduces proliferative divisions and promotes neurogenic divisions.

As previously described, neurogenesis progresses from ventral to dorsal in the developing spinal cord. Accordingly, at the electroporation time (stage HH11), the neural tube contains essentially self-expanding progenitors (Le Dréau et al., 2014; Saade et al., 2013). 24 hr later, (stage HH17), the repartition of the modes of division is not the same in dorsal and ventral control conditions. Dorsal neural tube contains mainly self-expanding progenitors (66.3% Sox2⁺Tis21^– cells, Figure 5A,F) (Le Dréau et al., 2014), whereas ventral neural tube encloses essentially neurogenic progeny (58% of Sox2⁺Tis21⁺ cells and 12.7% of Sox2^–Tis21⁺ cells, Figure 5A,F) (Saade et al., 2013). Because of this difference, we analyze the effects of CDC25B on the dorsal and ventral neural tube separately. In the dorsal neural tube, CDC25B gain-of-function leads to a reduction in the percentage of Sox2⁺Tis21^– progeny (from 66.3 ± 2.6% to 38.6 ± 2.1%) and a concomitant increase in the percentage of Sox2⁺Tis21⁺ progeny (from 25.9 ± 2.1% to 50.1 ± 1.9%). In this tissue, the percentage of Sox2^–Tis21⁺ progeny progresses only slightly (from 7.8 ± 1.2 to 11.3 ± 1%, Figure 5F). This observation indicates that CDC25B gain-of-function in early steps of neurogenesis reduces proliferative Sox2⁺Tis21^– progeny and increases Sox2⁺Tis21⁺ neurogenic progeny. In the ventral neural tube, CDC25B gain-of-function induces a massive reduction in Sox2⁺Tis21^– progeny (from 29.3 ±1.3% to 6.9 ± 1%) and leads to an increase in Sox2^–Tis21⁺ progeny (from 12.7 ±1.1% to 40.7 ± 2.7%), without significantly modifying the percentage of Sox2⁺Tis21⁺ progeny (from 58 ± 2% to 52.3 ± 2.8%, Figure 5F). Thus, CDC25B ectopic expression in a more advanced neural tissue reduces proliferative divisions and increases Sox2^–Tis21⁺ neurogenic progeny.

Together, these results suggest that CDC25B activity in neural progenitors reduces proliferative divisions and promotes neurogenic divisions, depending on the receiving neural tissue.

To test quantitatively data from a dynamical point of view (Míguez, 2015; Saade et al., 2013 ; Appendix Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase), we formalized in mathematical terms our current understanding of what happens in this biological system (Figure 6A). Despite the fact that a fraction of the Sox2⁺Tis21⁺ cells might correspond to NN rather than PN divisions, in the modeling part below, we assumed that the Sox2/Tis21 reporter expression is indicative of PP, PN and NN as described in (Saade et al., 2013).

Figure 6

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Figure 7

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We consider a population of progenitors at time $t_0$, $P(t_0)$, and we assumed that their different modes of division result in expanding either the pool of progenitors $P(t)$ through proliferative divisions (PP divisions), or the pool of neurons $N(t)$ by neurogenic divisions (PN and NN divisions). Denoting $\eta$ the rate at which P cells undergo divisions per unit time (which depends only on the cell cycle duration), the growth rates of the two pools only depend on the relative magnitude of each mode of division.

Denoting ${\alpha }_{pp}$, ${\alpha }_{pn}$ and ${\alpha }_{nn}$ the corresponding proportions of the modes of division (their sum is 1), the growth rates of the two pools (i.e. their time derivatives $\dot{P}(t)$ and $\dot{N}(t)$ for Progenitors and Neurons respectively) can then be directly formalized as:

In this model, the evolution of the pool of progenitors is governed by ${\alpha }_{pp}$ and ${\alpha }_{nn}$ (because ${\alpha }_{pn}$ does not affect the pool of progenitors, only the pool of neurons). Denoting $\gamma ={\alpha }_{pp}-{\alpha }_{nn}$ the difference between the two proportions, we then have $\gamma =1$ when ${\alpha }_{pp}=1$, ${\alpha }_{nn}=0$, corresponding to purely self-expanding progenitors and $\gamma =-1$ when ${\alpha }_{pp}=0$, ${\alpha }_{nn}=1$, corresponding to fully self-consuming progenitors. Hence $\gamma$ is a good indicator of the balance between proliferation and differentiation of the progenitors (Míguez, 2015). Using $\gamma$, the model can be rewritten more simply as:

An explicit solution, for $\gamma \ne 0$, is:

This equation means that if the quantities of progenitors and neurons are determined at a given time ($P(0)$, $N(0)$), for example at HH17, we can compute the expected number of progenitors and neurons at any time later, for example at HH22, provided that the modes of division and cell cycle times can be considered constant over the considered period. Full details of the mathematical work and statistics are given in Appendix 2. We then compare quantitatively the experimental data to the predictions based on our current hypotheses. This comparison is surprisingly auspicious for the control and gain-of-function experiments in the ventral zone (Figure 6C, left). In this zone, considering the ratio between the two pools at HH17 (e.g. the measured fractions of neurons), the measured cell cycle duration (12 hr), the set of modes of division measured at HH17, and the hypothesis that those modes of divisions stay unmodified during 24 hr, the model predicts with good accuracy the ratios between the two pools at HH22. In the dorsal zone, the model correctly predicts the control condition, and it confirms the tendency of CDC25B gain-of-function to promote a greater neuron fraction, albeit with some quantitative discrepancy (the model overestimates the fraction of neurons). This suggests that, notwithstanding biological complexity, the general picture of a pool of progenitors among which cells undergo stochastic modes of division, appears relevant.

Our model is built on the assumption that all cells undergo asynchronous mitosis at the same rate, and that the fate of any mitosis is stochastic and probabilistically distributed according to the fraction of dividing cells undergoing PP, PN or NN divisions, namely a common division rate for all progenitors associated with probabilistic fates (Appendix 3). In this picture, the proportion of mode of division controls directly the numbers of progenitors and neurons that are generated. However, the model is compatible with an extreme alternative interpretation, in which the three modes of division correspond to specific division rates associated with deterministic fates (Appendix 3). In this case, each population of progenitors has a specific mean cycling time and the cell cycle time is instrumental to the mode of division. Namely, cycling at rate ${\alpha }_{pp}\eta$ would result in a PP division, cycling at rate ${\alpha }_{pn}\eta$ would result in a PN division, and cycling at rate ${\alpha }_{nn}\eta$ would result in a NN division. Therefore, the numbers and proportions of progenitors/neurons at HH22 would result from the difference between cell cycle times associated with modes of division. We compute these putative cell cycle times based on the data obtained in the three conditions and the two zones (Table 1). The wide range of specific cycle times, that is, from 17 to 172.7 hr, is incompatible with data usually recorded (reviewed in Molina and Pituello, 2017). This suggests that, in the time window of our analyses, the observed evolution of progenitors and neurons cannot be exhaustively explained by pure differences in cell cycle durations among the three modes of division.

One prediction of our model is that neurogenesis might be affected independently of cell cycle length modification. To test whether the CDC25B-induced G2 phase modification is instrumental in promoting neurogenesis, we use a mutated form of CDC25B that was shown not to affect cell cycle kinetics. The mutation prevents CDC25B-CDK1 interactions without affecting CDC25B phosphatase activity (Sohn et al., 2004). Accordingly, expressing this mutated form of the phosphatase called CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$, does not modify G2 phase length in neuroepithelial progenitors (Figure 7A, red curve). The effects of CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ on the division mode are then compared in the entire neuroepithelium using the Tis21/Sox2 approach, 24 hr after electroporation, and the Nucbow technique, 40 hr after electroporation.

In the Tis21/Sox2 strategy, CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ decreases Sox2${}^{+}$Tis21${}^{-}$ progeny (from 46.1 ± 2.1% to 28 ± 1.6%) and increases Sox2${}^{+}$Tis21${}^{+}$ progeny (from 43.4 ± 1.9% to 61.2 ± 1.5%). The percentage of Sox2${}^{-}$Tis21${}^{+}$ progeny is not modified in that experimental context (from 10.5 ± 0.8% to 10.8 ± 0.8%, Figure 7B). These data show that CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ gain of function reduces proliferative divisions from 46.1 ± 2.1% to 28 ± 1.6% and increases neurogenic divisions from 53.8 ± 2.1% to 72 ± 1.6% (P-value < 0,0001). Analyzes using the Nucbow strategy, show a decrease in HuC/D${}^{-}$-HuC/D${}^{-}$ cells (from 76.5 ± 2.6% to 61 ± 2.4%), an increase in HuC/D${}^{-}$-HuC/D${}^{+}$ cells (from 9.4 ± 1.5% to 17.1 ± 2.5%) and in HuC/D${}^{+}$-HuC/D${}^{+}$ cells (from 14.1 ± 2.3% to 21.9 ± 2.1%, Figure 7C) following CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ expression. Therefore, CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ gain of function reduces proliferative divisions from 76.5 ± 2.6% to 61 ± 2.4% and increases neurogenic divisions from 23.8 ± 2.5% to 39 ± 2.4% (P value < 0,001). CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ gain-of-function results in an equivalent reduction of 15.8 and 18.1 percentage-point for proliferative and a corollary increase in neurogenic divisions in the Nucbow and Sox2/Tis21 strategies respectively (Figure 7B,C).

Together these data show that a mutated form of CDC25B unable to interact with CDKs, still promotes neurogenic divisions.

We then analyze the effects of CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ on the dorsal and ventral progenitors 24 hr after electroporation. CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ gain-of-function in the dorsal neural tube, reduces Sox2${}^{+}$ Tis21${}^{-}$ progeny (from 66.3 ± 2.7% to 40.2 ± 2.5%), increases Sox2${}^{+}$Tis21${}^{+}$ progeny (from 25.9 ± 2.1% to 51.1 ± 2.2%), and has no effect in Sox2${}^{-}$Tis21${}^{+}$ progeny (from 7.8 ± 1.2% to 8.0 ± 1.1%, Figure 7D). In this context, the fraction of HuC/D${}^{+}$ neurons generated 40 hr following CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ expression increases from 30.7 ± 1.3% to 40.4 ± 2.5%. (Figure 7E). Similarly, the percentage of Pax2+ neurons is increased from 11.3 ± 1% to 18.3 ± 1.3% (Figure 7F). In the ventral neural tube, CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ overexpression leads to a reduction in Sox2${}^{+}$Tis21${}^{-}$ progeny (29.3 ± 2.1% vs 16.6 ± 1.2%), an increase in Sox2${}^{+}$Tis21${}^{+}$ progeny (58 ± 2% vs 70.7 ± 1.4%) and no effect on Sox2${}^{-}$Tis21${}^{+}$ progeny (12.7 ± 1.1% vs 12.7 ± 1.1%, Figure 7D). In the ventral neural tube, CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ induces a slight but non-significant increase in HuC/D expression (Figure 7E). We examined our mathematical model to determine whether this slight increase in neuron production is coherent with the fact that the mutated form does not promote Sox2${}^{-}$Tis21${}^{+}$ progeny, and the number of neurons predicted is in agreement with the experimental data (Figure 6C).

To determine whether CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ function on neurogenic divisions and neuronal differentiation requires phosphatase activity, we use a form of the protein containing an additional point mutation inactivating the catalytic domain (CDC25B${}^{\mathrm{\Delta }P\mathrm{\Delta }CDK}$). This construct does not affect the mode of division at 24 hr (Figure 7G). 48 hr post electroporation this mutated form does not modify NeuroD reporter expression (Figure 2—figure supplement 2), the percentage of HuC/D + neurons or the percentage of Sox2+ progenitor’s populations (Figure 7H), indicating that the phosphatase activity is required for the neurogenic function of CDC25B.

Altogether, these results show that CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ stimulates neurogenic divisions and neuronal differentiation without affecting the duration of the G2 phase. This opens the possibility that the phosphatase possesses a function in addition to its canonical role in cell cycle regulation.

To go further in our understanding of this cell cycle independent role of CDC25B, we set up a high resolution time-lapse imaging technique that allows real-time tracking of the behaviour of single neural progenitor nuclei during G2/M/G1 phases. To perform live imaging, E2 embryo neural tubes are electroporated with a GFP-tagged version of PCNA (Leonhardt et al., 2000), then slice cultures of neural tube explants are performed 6 hr after electroporation and analyzed in live experiments starting 12 hr later. Using this approach, nuclear movements are tracked in time and space during G2, M and G1 phase (Figure 8). As previously described (Spear and Erickson, 2012), we observe that mitosis initiates away from the apical side and gets completed against the lumen (Figure 8A–B). Interestingly, nuclei in G1 display two types of behaviours: either a newly formed nucleus remains close to the lumen (Ap) or it rapidly migrates away from the apical side towards the basal side (Bs), giving rise to three mitotic patterns Ap/Ap, Ap/Bs, Bs/Bs (Figure 8A–C and Video 1, Video 2, Video 3). Based on the position of the nuclei 20 min after mitosis (Bs being defined as more than 10 µm away from the apical side at that time), the occurrences of their behaviour were quantified in control and gain-of-function conditions (Figure 8D). Under control conditions, Ap represents 50.6 ± 6.9% of the post mitotic behavior, and Bs 49.4 ± 6,9%. CDC25B and CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ gain-of-function decrease Ap (to 24.1 ± 5.3% and 30.9 ± 4.5%, respectively) and increase Bs (to 75.8 ± 5.3% and 69.1 ± 4.5%, respectively).

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It is possible that the Bs migratory behavior precedes the apical process withdrawal associated with the onset of neuronal differentiation (Das and Storey, 2014; Tozer et al., 2017). We took advantage of our time-lapse set up to identify cells re-entering S phase, by the appearance of a dot-like staining within the nuclei corresponding to the recruitment of PCNA into the DNA replication foci (Figure 8—figure supplement 1, Leonhardt et al., 2000). For all the nuclei whose cell cycle status was identified (Table 2), we quantify 9/16, 32/37 and 40/40 Bs nuclei re-entering S phase in Control, CDC25B and CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ gain-of-function, respectively. A majority of Ap nuclei also re-enter S phase in control (30/36), CDC25B (15/21) and CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ (16/20) gain-of-function experiments (Table 2). Thus, a majority of Bs and Ap nuclei re-enter S phase in gain-of-function experiments suggesting that the change in migratory behavior is not the consequence of a neurogenic division and of neuronal commitment, but either is upstream or is independent of it.

To analyze more profoundly how CDC25B activity affects nuclei migration in G1, we determined the nuclei motion using a statistical measure of the average distance a nucleus travels over time: the mean squared displacement, MSD (Norden et al., 2009). We calculated MSD profiles for the Ap and Bs nuclei under control, CDC25B and CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ gain-of-function conditions (Figure 8E). In both cases, the profile clearly exhibits 2 types of motion: Ap nuclei displaying slow motion (diffusion) and Bs nuclei exhibiting directed movements (advection). In addition, we determined the average speed of the nuclei over the first 20 min after mitosis (Figure 8F). We observed speeds of 0.26 ± 0.03 µm/min (n = 16), 0.27 ± 0,03 µm/min (n = 17) and 0.27 ± 0,04 µm/min (n = 11) for the Ap nuclei and 1.10 ± 0.17 µm/min (n = 14), 0.98 ± 0.1 µm/min (n = 25) of and 0.80 ± 0.1 µm/min (n = 19) for Bs nuclei in control, CDC25B and CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$, respectively.

Together these data suggest that the non-cell cycle dependent activity of CDC25B does not modify much the departure speed of the nuclei, but rather controls the switch from slow to fast nuclei departures from the apical surface.

Altogether, these results show that in the neuroepithelium, the CDC25B phosphatase affects early G1 nuclear behavior, and also is necessary and sufficient to promote neurogenic divisions and neurogenesis. Importantly, CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ without affecting the duration of the G2 phase, still affects early G1 nuclear behavior and stimulates neurogenic divisions and neuronal differentiation. Our results open then the possibility that the phosphatase possesses cell cycle independent and neurogenic functions.

In mammals three CDC25s (A, B, C) have been characterized, whereas only two CDC25s (A and B) have been found in chicken (Agius et al., 2015). In mouse, Cdc25a loss-of-function is embryonic lethal, whereas loss-of-function of Cdc25b or Cdc25c or both has no apparent phenotype except female sterility (Boutros et al., 2007). Crossing our floxed mice to ubiquitous Cre:PGK-Cre${}^m$(Lallemand et al., 1998) also results in female sterility (data not shown). Cdc25a has been described as playing a major role in the G1-S transition and is capable of compensating the loss-of-function of the other Cdc25 members. In the mouse embryonic neural tube, both Cdc25a and Cdc25c display a broad expression pattern, while Cdc25b is mainly expressed in domains where neurogenesis occurs (Agius et al., 2015 and Figure 1). The conditional loss-of-function in the mouse CNS, shows for the first time that Cdc25b is involved simultaneously in the control of G2 phase length and spinal neurogenesis. In the mouse, at least part of the reduction in the number of neurons is probably due to the slight reduction in progenitor population. This observation substantiates our data showing that CDC25B downregulation, performed using RNAi in chicken embryo, induces a reduction in neurogenesis (Peco et al., 2012). Two other studies link CDC25B and neurogenesis. First in Xenopus, FoxM1 and CDC25B loss-of-function has been shown to reduce expression of neuronal differentiation markers, but not early neuroectoderm markers (Ueno et al., 2008). In this context, epistasic analysis shows that FoxM1 loss-of-function can be rescued by CDC25B gain-of-function (Ueno et al., 2008). Second, MCPH1 knock out mice display a microcephalic phenotype due to an alteration of the Chk1-Cdc25-Cdk1 pathway. Indeed, MCPH1 mutants display a decreased level of the inhibitory Chk1 kinase localized to centrosomes, leading to increased Cdc25b and Cdk1 activities. A premature activation of Cdk1 leads to an asynchrony between mitotic entry and centrosome cycle. This disturbs mitotic spindle alignment, promoting oblique orientation and precocious neurogenic asymmetric divisions (Gruber et al., 2011). Moreover, the reduced neurogenic production in the MCPH1 loss-of-function can be restored by a concomitant Cdc25B loss-of-function, demonstrating the phosphatase’s pivotal role in the neurogenic phenotype. Altogether, these observations indicate that Cdc25b activity is broadly used during nervous system development among vertebrate species.

CDC25B downregulation reduces the transition from proliferative to neurogenic divisions. To be able to clarify the role of CDC25B on both types of division, we use the cell cycle cis-regulatory element combined with the rapid degradation of CDC25B at the end of M phase, to reproduce the endogenous cyclic expression of the phosphatase (Körner et al., 2001). Using Sox2/Tis21 biomarkers and Nucbow clonal analyses, we observe differences in the repartition of the mode of division, probably due to intrinsic methodological differences. This discrepancy may be linked to the differences in the method used: one possibility being that one analysis is performed at 24 hr after electroporation, while the other is performed 40 hr after. Nevertheless, CDC25B gain-of-function reduces proliferative and promotes neurogenic divisions independently of the method used. Gain-of-function of the CDC25B mutated form inactive during the cell cycle, also diminishes proliferative divisions. Using the Sox2/Tis21 biomarkers, we observe different results depending on the population of progenitors targeted.

In the dorsal neural tube, CDC25B gain-of-function increases Sox2⁺Tis21⁺ compared to control conditions. In the ventral neural tube, gain-of-function leads to an increase in Sox2^–Tis21⁺, the percentage of Sox2⁺Tis21⁺ progeny being unchanged. We propose that ectopic expression of the phosphatase can be interpreted in different ways depending on the context: CDC25B would have the capacity to convert Sox2⁺Tis21^– into Sox2⁺Tis21⁺ in a young tissue, while in an older tissue CDC25B could convert Sox2⁺Tis21^– into either Sox2⁺Tis21⁺ or Sox2^–Tis21⁺. With respect to what occurs in an older tissue, either the phosphatase converts Sox2⁺Tis21^– into Sox2⁺Tis21⁺ or Sox2^–Tis21⁺, or the phosphatase initially promotes Sox2⁺Tis21^– into Sox2⁺Tis21⁺ and subsequently, using the principle of communicating vessels in an older tissue, promotes Sox2⁺Tis21⁺ into Sox2^–Tis21⁺ progeny.

We speculate that CDC25B acts as a maturating factor in the progression from stem pool to differentiated neurons, and we suggest that this element of the cell cycle machinery has been coopted to regulate independently cell cycle progression and neurogenesis.

The model predicts the ratio of neuron at 48 hr after electroporation, given the ratio at 24 hr and the distributions among the modes of division and the mean cycle length. As a minimal model with no free parameters, its predictions are still quite well consistent with data in the ventral neural tube for the three conditions. In the dorsal neural tube, while its prediction is also well consistent with data for control condition, it predicts however larger fractions of neurons than those experimentally observed in CDC25B and CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ gain-of-functions (Figure 6C), pointing to a missing hypothesis to explain this discrepancy.

We submit several hypotheses. First of all, at HH11, endogenous CDC25B is expressed in the ventral neural tube but not in the dorsal neural tube. This means that electroporation causes a true gain-of-function in the dorsal domain, while in the ventral domain it makes only a dosage modification of a component already present. Then, CDC25B regulation is complex, and an active degradation mechanism in the dorsal neural tube could attenuate the gain-of-function. Another possibility is that electroporated gain-of-function, which is also cell cycle dependent, could be less efficient with time and thereby lead to fewer neurons than expected. Alternatively, the signaling pathway downstream of CDC25B could be expressed differently in the ventral and dorsal neural tubes, and this could limit the gain-of-function effect in the dorsal neural tube. All things considered, we regard the discrepancy between our predictions and our data as a challenging milestone that deserves further investigation. We could have formalized an ‘ad hoc’ model for each hypothesis mentioned above in order to fit the observed fractions of neurons, yet this would have amounted to add free parameters, and free parameters can always be adjusted at will. We prefer to stress that the standard model for these dynamics still requires identifying further elements in order to reconcile the predictions with the data of this study.

Here we show for the first time in the spinal cord that nuclei basalward movements occurring in early G1 display two types of motion: slow or fast departure from the apical surface. During mammalian corticogenesis, two not mutually exclusive mechanisms were described for the basal migration of G1 nuclei. It was proposed to be a passive event, depending on a crowding effect due to the apically G2 phase nuclei migration (Kosodo et al., 2011). Other studies proposed that the actomyosin system (Schenk et al., 2009) or plus-end-directed kinesin/microtubule driven movement (Tsai et al., 2010) are involved in carrying nuclei from apical to basal side. In the spinal cord, we show that CDC25B and CDC25B${}^{\mathrm{\Delta }\mathrm{CDK}}$ control the choice between slow or rapid apical departure and promotes the latter. This establishes a new link between a core cell cycle regulator and INM. Similarly a relationship has been described between CDK1 and the minus-end-directed motor dynein in G2 apical movement (Baffet et al., 2016; Hu et al., 2013). CDK1 phosphorylates the nucleoporin RanBP2, promoting nuclear envelop dynein recruitment.

We observed that the two types of motion in early G1 occur in proliferating progenitors, suggesting that they are either upstream or independent of neurogenesis. A great deal of evidence shows that nuclear movement alterations correlate with neurogenesis modifications, due to alterations in the duration and level of exposure of nuclei to proliferative or differentiation signaling. In zebrafish retina, when the motor protein Dynactin-1 is disrupted, nuclei migrate more rapidly and further into the basal side and more slowly to the apical side. In this context, since Notch signaling is activated on the apical side, mutant progenitors are less exposed to Notch and exit the cell cycle prematurely (Del Bene et al., 2008). In the developing rat brain, INM is driven basally by the microtubule motor protein KIF1A, and downregulating KIF1A results in the maintenance of nuclei on the apical side and a severe reduction in neurogenic divisions (Carabalona et al., 2016). Radial glial progenitors nevertheless display normal cell cycle progression, indicating that the two events can be uncoupled. The authors propose that this change in nuclear movement increases exposure of neural progenitors to proliferative signals at the apical side, or alternatively keeps the cells further away from differentiating signals. Accordingly, the rapid basal movement induced by CDC25B in the neural tube would reduce exposure of the nucleus to proliferative signals, or expose them to differentiating signals. Interestingly, mouse CDC25A, B and C triple KO (TKO) exhibits epithelial cells in the small intestine blocked in G1 or G2, accompanied by enhanced Wnt signalling activity (Lee et al., 2009).

A follow-up to this work could be identifying the CDK independent players downstream of CDC25B. Other CDC25B substrates have been characterised, such as steroid receptors (Ma et al., 2001), and the peri-centriolar material component Kizuna (Thomas et al., 2014). A recent analysis using microarrayed Tyr(P) peptides representing confirmed and theoretical phosphorylation motifs from the cellular proteome, identifies more than 130 potential CDC25B substrates (Zhao et al., 2015). These substrates are implicated in microtubule dynamics, signalling pathways like Delta/Notch or Wnt, transcription, epigenetic modifications, mitotic spindle or proteasome activity (Zhao et al., 2015), and several of them could play a role in INM or cell fate choice (Akhtar et al., 2009; Aubert et al., 2002; Das and Storey, 2012; Götz and Huttner, 2005; Hämmerle and Tejedor, 2007; Jiang and Hsieh, 2014; Kimura et al., 2014; Li et al., 2012; MuhChyi et al., 2013; Olivera-Martinez et al., 2014; Sato et al., 2004; Schwartz and Pirrotta, 2007; Vilas-Boas et al., 2011). Further work will be necessary to dissect the molecular pathway linking CDC25B with INM and to determine whether this link is causal in neurogenesis. In conclusion, we propose that our data illustrate that cell cycle core regulators might have been coopted to elicit additional functions in parallel to cell cycle control. We show that a positive cell cycle regulator, CDC25B, unexpectedly reduces proliferative divisions and promotes differentiation. Cell cycle regulators are routinely described as deregulated in cancers and are associated with increased proliferation. Understanding their function outside the cell cycle is therefore crucial to characterising their molecular and cellular mechanisms of action and to foresee novel therapeutic strategies.

Fertile chicken eggs at 38°C in a humidified incubator yielded appropriately staged embryos (Hamburger and Hamilton, 1992). Animal related procedures were performed according to EC guidelines (86/609/CEE), French Decree no. 97/748 and CNRS recommendations.

Experiments were performed in accordance with European Community guidelines regarding care and use of animals, agreement from the Ministère de l’Enseignement Supérieur et de la Recherche number: C3155511, reference 01024.01, and CNRS recommendations. To disrupt Cdc25b function, we generated a modified allele of Cdc25b (Mouse Clinical Institute, IGBMC, Illkirch). Using Homologous recombination in embryonic cells (ES), we inserted two LoxP sites, flanking exon 4 to exon 7 of the Cdc25b gene (referred to as Floxed allele). Upon Cre-mediated excision, exons 4 to 7 are deleted and following intron splicing, a premature stop codon is generated, leading to a truncated protein of 134 aa. The activity of this remaining peptide has been tested in a cellular model and has no activity (not shown). The mouse strain used is C57BL6/JRj. We first generated a mutant mouse line (Cdc25b${}^{\mathrm{-}\mathit{}\mathrm{/}\mathrm{-}}$) by crossing Cdc25b floxed mice with PGK-Cre mice, resulting in an ubiquitous and permanent deletion of Cdc25b. In order to delete Cdc25b activity specifically at the onset of neurogenesis, we crossed Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{-}}$ mice with transgenic mice expressing the Cre recombinase under the control of the rat Nestin (Nes) promoter and enhancer (Tronche et al., 1999). The effect of expressing Cre recombinase on proliferation and neurogenesis was evaluated by comparing Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{+}}$ and NestinCre;Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{+}}$ littermates. As there were no phenotypic differences between these embryos for any of the parameters that we measured (not shown), they were both included with the Cdc25b${}^{\mathrm{fl}\mathit{}\mathrm{/}\mathrm{-}}$ littermates in the control group.

For each experiment, at least three independent litters and three different slides per embryo were analyzed. To compare the number of neurons between control and conditional mutant embryos, we used a statistical model called the ‘mixed effect model’. This model contains both the fixed effect, that is, the genotype of the embryo (control or conditional mutant) and random effects, that is, the variability induced by the age of the litter and by the embryo nested in the litter. Random effects were excluded using the R software and the package ‘nlme’, and we applied the following formula:

library(nlme)
result.lme <- lme(Neuronnumber ~Genotype,
                       random =~1|Litter/Embryo, data = data, method=``REML'')

To test the effect of the genotype on the number of neuron, we next performed an ANOVA test. * p < 0.05; ** p < 0.01; *** p < 0.001.

In ovo electroporation experiments were performed using 1.5- to 2-day-old chickens as described previously (Peco et al., 2012) . Loss of function was performed as described in (Peco et al., 2012).Gain-of-function experiments were performed using a vector expressing the various human CDC25 isoforms (hCDC25B3, hCDC25B3${}^{\mathrm{\Delta }\mathrm{CDK}}$, hCDC25B3${}^{\mathrm{\Delta }P\mathrm{\Delta }CDK}$) under the control of a cis regulatory element of the mouse Cdc25B called pccRE. A control vector was generated with the $\beta$Gal gene downstream of the pccRE. All gain-of-function experiments were performed at 1.5 µg/µl. For the Brainbow experiments, we used a pCX-Cre gift of X. Morin (Morin et al., 2007), at 0.5 ng/µl; Nucbow a gift of J. livet (Loulier et al., 2014) at 0.5 µg/µl. The Sox2p-GFP, Tis21p-RFP, and NeuroD-luciferase constructs were obtained from E. Marti and used at 1 µg/µl, 0.5 µg/µl and 1 µg/µl, respectively. pNLS EGFP-L2-PCNA was received from M.C. Cardoso (Leonhardt et al., 2000) and used at 0.5 µg/µl.

Mouse embryos were dissected in cold PBS and fixed in 4% paraformaldehyde overnight at 4°C. Then they were embedded in 5% low-melting agarose before sectioning on a Leica vibratome, in 50 µm thick transversal sections. In situ hybridization was performed as published (Lacomme et al., 2012). Riboprobes to detect mCDC25B transcripts were synthesized from linearized plasmid containing the full CDC25B cDNA. Riboprobe sequence : ACTCCTGTCGAAAGGGCTTCTGAAGAAGATGACGGATTTGTGGACATCCTGGAGAGTGATTTAAAGGATGACGAGAAGGTCCCCGCGGGCATGGAGAACCTCATTAGTGCCCCACTGGTCAAAAAGCTGGATAAGGAAGAGGAACAGGATCTCATCATGTTCAGCAAGTGCCAGAGGCTCTTCCGCTCCCCATCCATGCCATGCAGTGTGATCCGACCCATCCTCAAGAGGCTAGAGCGGCCCCAGGACCGGGATGTGCCTGTCCAGAGCAAGCGCAGGAAAAGTGTGACACCCCTGGAAGAGCAGCAGCTTGAAGAACCTAAGGCCCGTGTCTTTCGCTCAAAGTCGCTGTGTCATGAGATTGAGAACATCCTGGATAGTGACCACCGTGGACTGATCGGAGATTACTCTAAGGCCTTCCTCCTGCAGACCGTGGATGGCAAACACCAAGACCTTAAGTACATCTCACCAGAAACTATGGTGGCCCTGTTAACAGGCAAGTTCAGCAACATCGTGGAGAAATTTGTCATTGTGGACTGCAGATACCCCTATGAGTATGAAGGCGGGCATATCAAGAATGCTGTGAACCTGCCCCTGGAACGGGATGCTGAGACCTTTCT. Immunohistochemistry was performed as described in (Lobjois et al., 2004). The antibodies used were the anti-Pax2 (Covance), guinea pig anti-Tlx3 (gift from C.Birchmeier, Müller et al., 2005, anti-Pax7 (Hybridoma Bank), and anti-Sox2 (Millipore). For chick embryos, proteins or transcripts were detected on 40 µm vibratome sections, as previously described (Peco et al., 2012). The antibodies used were: anti-HuC/D (Molecular Probes), anti-Sox2 (Chemicon), anti-PH3 (Upstate Biotechnology), anti-BrdU (mouse monoclonal, G3G4), anti-BrdU (rat anti-BrdU, AbD Serotec), anti-active caspase 3 (BD Biosciences), and anti-GFP (Invitrogen).

Cell proliferation was evaluated by incorporation of 5-ethynyl-2’-deoxyuridine (Click-iT EdU Alexa Fluor 647 Imaging Kit, Invitrogen). 10 µl of 250 µM EdU solution were injected into chicken embryos harvested 30 min later, fixed for one hour and processed for vibratome sectioning. EdU immunodetection was performed according to manufacturer’s instructions. Mitotic cells were detected using anti-PH3. G2-phase length was determined using the percentage of labeled mitoses (PLM) paradigm (Quastler and Sherman, 1959). EdU incorporation was performed as described above, except that a similar dose of EdU was added every 2 hr, and embryos were harvested from 30 to 180 min later. Embryos were fixed and labeled for both EdU and PH3. We then quantified the percentage of PH3 and EdU co-labeled nuclei with increasing times of exposure to EdU. The progression of this percentage is proportional to G2-phase duration. Cell death was analyzed by immunofluorescence, using the anti-active Caspase three monoclonal antibody (BD Biosciences).

For EdU staining experiments in mouse, 100 µl of 1 mg/ml EdU were injected intraperitoneally into pregnant mice. Litters were harvested 1, 2 or 3 hr following injection.

Slices (40 µm) were analyzed using a SP5 Leica confocal microscope as described previously (Peco et al., 2012). Experiments were performed in triplicate. For each embryo, confocal analyses were performed on at least three slices. Confocal images were acquired throughout the slices at 3 µm z intervals.

For each experimental slice, Z sections were acquired every 3 µm, and blind cell quantifications were performed on one out of every three Z sections to avoid counting the same cell twice. For each slice, the percentage of cells is determined using the sum of counted Z sections. For each experimental condition, the number of embryos analyzed and of cells counted is indicated in the Figure legend.

Embryos were electroporated with the DNAs indicated together with a NeuroDp-Luciferase reporter (Saade et al., 2013) and a renilla-construct (Promega) for normalization. GFP-positive neural tubes were dissected out at 48 hr after electroporation and homogenized in passive lysis buffer. Firefly- and renilla-luciferase activities were measured by the Dual Luciferase Reporter Assay System (Promega), and the data are represented as the mean ±sem from at least 14 embryos per experimental condition.

1.5-days-old embryos were electroporated with a pNLS-EGFP-L2-PCNA (Leonhardt et al., 2000) vector, to distinguish the G2/M/G1 phases of the cell cycle, at 0.5 µg/µl. 6 hr later, embryos were dissected, fluorescent neural tubes were transferred to a tissue chopper (Mc Ilwain) and 100 µm thick transverse sections were sliced. Sections were collected in 199 culture medium (GIBCO) and were sorted out under a fluorescence microscope to control tissue integrity and the presence of isolated fluorescent cells along the dorso-ventral axis. Each slice was imbedded into 10 µl of rat type I collagen (Roche; diluted at 80% with 1X MEM (GIBCO), 1X GlutaMax (GIBCO) and neutralizing bicarbonate (GIBCO)). Four neural tube-containing collagen drops (5 µl) were distributed on a 35 mm glass-bottom culture dish (IBIDI). Collagen polymerization was performed at 38°C for 30 min and 1.5 ml of complete culture medium (199 medium, 5% FCS, 1X GlutaMax, Gentamicin 40 µg/ml) was gently added. For time-lapse, images were acquired on an inverted microscope (Leica inverted DMI8) equipped with a heating enclosure (set up at 39°C), a spinning disk confocal head (CSU-X1-M1N, Yokogawa) a SCMOS camera and a 63X oil immersion objective (NA 1,4–0,7). We recorded 40 µm thick z stacks (2 µm z-steps) at 5 min intervals. IMARIS and ImageJ software were used for image processing and data analysis.

Quantitative data are expressed as mean ± S.E.M. Statistical analysis was performed using the GraphPad Prism software. Significance was assessed by performing ANOVA followed by the Student- Mann-Whitney test, (*P<0.05, **P<0.01, ***P<0.001, ****P<0.0001 and n.s. non significant). See also Appendix 4.

In the appendices, we expose explicitly the hypotheses we made while interpreting the data of CDC25B experiments using a model of cell populations dynamics. In particular, we examine at the importance of a clear distinction between interpretations at the population level or at the cell level (Altschuler and Wu, 2010 ). The model is first exposed at the population scale in Appendix 2. We derive an analytical solution when fate parameters are considered unvaried over the time window of the analyses. We show that the evolution is governed by one parameter: the balance between proliferation and differentiation. The model at the population scale can match many scenarios at the cell scale. In Appendix 3, we consider two contrasted scenarios that produce the same dynamics at the population scale. The first scenario considers that all cells divide at the same rate (all cells share a common cycle length), and that the choice by a cell to produce a symmetric proliferative division, a symmetric neurogenic division or an asymmetric division is stochastic. Such a stochastic choice at the cell scale is a very common interpretation for stem cells dynamics (Harris, 1948; Loeffler and Roeder, 2004; Anderson, 2001; Antal and Krapivsky, 2010; Vogel et al., 1969), even in the presence of (non-autonomous) external signaling (Losick and Desplan, 2008; Johnston et al., 2007; Ramalho-Santos, 2004. In this interpretation, the proportions of the modes of division at the population scale (the statistical measure over a large number of cells) is a direct reflection of the probabilities at the individual scale, provided all cells divide asynchronously with the same cycle length. The second scenario is used to test the opposite possibility: that the proportion of the modes of division at the population scale only comes from differences in cycle lengths, each mode of division having a specific cycle length.

We then present in Appendix 4 how our model statistics were used to enlighten the data. We point out that our model was not designed to ”fit the data” by tuning free parameters, since it has no free parameters at all. It is used to check whether the modes of divisions (MoD) measured at HH17 were well in accordance with the neuronal fractions measured at HH22 given the measured cell cycle length, doing so with as few assumptions as possible.

Models for proliferation/differentiation in the spinal cord have been proposed previously in (Saade et al., 2013 ) and (Míguez, 2015). However, a developmental switch has been incorporated in the first, which we do not use here. Also, we encounter a noteworthy difference between the second in (Míguez, 2015) and our model. In (Míguez, 2015), the model is built starting from cell description, and the limit to continuous-time population dynamics is taken considering that all mitoses are synchronous with a cell cycle length tending to 0 (which is implicit in equations 33-35 of (Míguez, 2015)-SI. Here, we first consider division rates at the population scale, and only then do we consider interpretations at the cell scale. Importantly, this difference between the two models yields different dynamics, especially when the balance between proliferation and differentiation of the progenitors is negative (i.e. in favor of differentiation). In the most extreme case (purely differentiating progenitors), our model still predicts the expected dynamics.

We consider a population of cells ${\displaystyle C(t)}$ at time ${\displaystyle t}$, part of which are proliferating progenitors ${\displaystyle P(t)}$, part of which are differentiated neurons ${\displaystyle N(t)}$, with

The dividing progenitors can undergo three kinds of fate, yielding:

• some proliferative divisions ending with two progenitors ($\mathrm{pp}$-divisions)

• some asymmetric divisions ending with one progenitor and one neuron ($\mathrm{pn}$-divisions)

• some terminal divisions ending with two neurons ($\mathrm{nn}$-divisions)

We consider that the division of a cell in two cells is instantaneous (it is always possible to find a date before which there is one cell, and after which there are two cells).

We also consider that division events occur uniformly in time (asynchronously).

Let us denote :

${\displaystyle \eta }$ the rate at which P-cells undergo divisions (in fraction of the P-pool per unit time)

${\alpha }_{\mathrm{pp}}(t)$ the fraction of dividing cells undergoing $\mathrm{pp}$-divisions

${\alpha }_{\mathrm{pn}}(t)$ the fraction of dividing cells undergoing $\mathrm{pn}$-divisions

${\alpha }_{\mathrm{nn}}(t)$ the fraction of dividing cells undergoing $\mathrm{nn}$-divisions

$P(0),N(0)$ the quantity of P-cells and N-cells known at time $t=0$.

In general, the fractions of pp-, pn- and nn-divisions can evolve with time, under the constraint that ${\alpha }_{pp}+{\alpha }_{pn}+{\alpha }_{nn}=1$, and so might as well the division rate.

The time change $\dot{P}(t)$ of pool $P(t)$ (resp. $\dot{N}(t)$) is then driven at time $t$ by:

where in the first equation :

• $-\eta P(t)$ quantifies the rate at which P-cells disappear from the pool $P(t)$ because they divide. The quantity of disappearing P-cells between $t$ and $t+dt$ is then $\eta P(t)dt$

• ${\alpha }_{pp}\eta P(t)$ quantifies the fraction of this quantity that undergoes a pp-division ; it doubles to yield 2 P and adds up to the pool P(t) (hence the factor 2)

• ${\alpha }_{pn}\eta P(t)$ quantifies the fraction of this quantity that undergoes a pn-division ; it doubles to yield 1 P and 1 N, so only half (the P part) adds up to the pool P(t) (hence the factor 1)

correspondingly in the second equation :

• ${\alpha }_{nn}\eta P(t)$ quantifies the fraction of this quantity that undergoes a nn-division ; it doubles to yield 2 N and adds up to the pool N(t) (hence the factor 2)

• ${\alpha }_{pn}\eta P(t)$ is the fraction of this quantity that undergoes a pn-division ; it doubles to yield 1 P and 1 N and only half (the N part) adds up to the pool N(t) (hence the factor 1)

Considering a period of time during which the fractions of pp-, pn- and nn-divisions do not evolve with time, the dynamics can be written:

Let $\gamma =-1+2{\alpha }_{pp}+{\alpha }_{pn}$.

Considering that ${\alpha }_{pp}+{\alpha }_{pn}+{\alpha }_{nn}=1$, we have:

Hence,

and the solutions are of the general form:

Plugging the first into the second, we have:

For explicit solutions, we have to consider two cases: $\gamma =0$ and $\gamma \ne 0$.

For $\gamma =0$, we have:

so that:

In that case, the pool of progenitors is steady, and the pool of neurons increases linearly with time.

For $\gamma \ne 0$, solving the integral in the second equation yields:

so that:

In that case, the evolution of the system depends on the sign of $\gamma$.

We note that, for a given mitosis rate $\eta$, the dynamics only depend upon $\gamma$.

We have $\gamma =2{\alpha }_{pp}+{\alpha }_{pn}-1=2{\alpha }_{pp}+{\alpha }_{pn}-({\alpha }_{pp}+{\alpha }_{pn}+{\alpha }_{nn})={\alpha }_{pp}-{\alpha }_{nn}$.

The case $\gamma =0$ (Equation 12) corresponds to ${\alpha }_{pp}={\alpha }_{nn}$. Here, the P-pool is steady and can be considered as a source of N-cells emitted at the steady rate $\eta P(0)$ (N-cells per unit time):

The case ${\alpha }_{pp}>{\alpha }_{nn}$ yields $\gamma >0$, so that the P-pool will increase with time. At the extreme, a purely proliferative P-pool corresponds to ${\alpha }_{pp}=1$ and ${\alpha }_{nn}=0$, hence $\gamma =1$. In that case, the dynamics simplify to the classical proliferative equation for the P-pool, while the N-pool remains unchanged:

The case ${\alpha }_{pp}<{\alpha }_{nn}$ yields $\gamma <0$, so that the P-pool will decrease with time. At the extreme, a fully differentiating P-pool corresponds to ${\alpha }_{pp}=0$ and ${\alpha }_{nn}=1$, hence $\gamma =-1$. In that case, the P-pool undergoes a classical exponential decay, and the N-pool increases in proportion to the remaining P-pool, up to $2P(0)$:

Regarding the total population $C(t)=P(t)+N(t)$ (Appendix 2—Figure 1), positive (or null) value of $\gamma$ (${\alpha }_{pp}\ge {\alpha }_{nn}$) allows an infinite growth of the total population $C(t)$ whereas the growth saturates as soon as $\gamma <0$ (${\alpha }_{pp}<{\alpha }_{nn}$). Since we made the hypothesis that the fate parameters were considered as steady over time, interpretations for the real biological system should take into account that these fate parameters actually change over longer time in the real system.

Regarding the fraction of neurons in the population, $N(t)/C(t)$ (Appendix 2—Figure 2), it increases as soon as $\gamma <1$, yet at a rate depending on $\gamma$.

Appendix 2—figure 1

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Appendix 2—figure 2

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We have so far described the system at the population scale. At the individual scale, two different kinds of process (at least) would result in the same dynamics at the population scale described in Equation 5.

The most immediate interpretation is to consider that all cells undergo mitosis at the same rate, and that the fate of any mitosis is stochastic and probabilistically distributed according to $({\alpha }_{pp},{\alpha }_{pn},{\alpha }_{nn})$. In that case, only the rate $\eta$ (used in the equations at the population scale) has to be determined from a cell-scale model, since it depends upon the characteristic time ${\tau }_m$ between two mitoses at the cell scale.

Let us consider the hypothesis that mitosis happen exactly every ${\tau }_m$ for all cells (common deterministic division time), still asynchronously so that division dates are uniformly distributed over time (this is the most common hypothesis in the community). We want to express $\eta$ as a function of ${\tau }_m$.

For the sake of simplicity, let us consider the pure proliferative process (${\alpha }_{pp}=1$) so that we deal with only one population $P(t)$.

Let us start at time 0 with an initial pool $P_1(0)$ containing a very large number of cells (so that $P_1(t)$ can be considered as continuous). Since mitoses take a fixed time ${\tau }_m$, their last division occurred before $t=0$, the oldest division happened at $0-{\tau }_m$ and they all will undertake a mitosis in the time interval $[\mathrm{0\hspace{0.33em}..\hspace{0.33em}0}+{\tau }_m]$. Since divisions are uniformly distributed over time, the number performing a mitosis during a small time interval $\mathrm{\Delta }t$ is proportional to $\mathrm{\Delta }t/{\tau }_m$ and $P(0)$. Hence, the loss in $P_1$ between $t$ and $t+\mathrm{\Delta }t$ is given by:

Taking the limit $\mathrm{\Delta }t\to 0$ yields:

Considering $P_1(0)$, we then have:

Logically, ${\displaystyle P_1(t)}$ decreases linearly from ${\displaystyle P_1(0)}$ down to 0 at time ${\displaystyle t={\tau }_m}$. Meanwhile, the output of each division will populate the next generation, say ${\displaystyle P_2(t)}$, at twice the rate ${\displaystyle P_1}$ disappears, up to ${\displaystyle 2P_1(0)}$ at time ${\displaystyle t={\tau }_m}$, from which ${\displaystyle P_2}$ will start decreasing doing mitosis and populate the third generation ${\displaystyle P_3}$ and so on… Such a process would then translate into a population growth which is piecewise linear (Appendix 3—figure 1), but very close to an exponential growth. If we equate at time ${\displaystyle {\tau }_m}$ the piecewise growth, and its exponential approximation at rate ${\displaystyle \eta }$, we have:

Denoting ${\displaystyle {\tau }_c=1/\eta }$ the characteristic time at the population scale, we then have: ${\displaystyle {\tau }_c={\tau }_m/\ln 2}$. Hence, from an observed time ${\displaystyle {\tau }_c}$ at the population scale, we should infer (under this model) that ${\displaystyle {\tau }_m={\tau }_c\ln 2}$, that is ${\displaystyle {\tau }_m\simeq 0.7{\tau }_c}$ (e.g. if population cycle time is 12 hr, cell cycle time should be around 8h20).

Appendix 3—figure 1

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Another way to produce the dynamics described in Equation 5 at the population scale is to consider that each kind of fate result from a specific division time. In such a picture, the time needed to achieve a cycle deterministically determines the kind of fate.

To exhibit this interpretation, we rewrite Equation 5 as follows:

Denoting ${\displaystyle {\eta }_{pp}={\alpha }_{pp}\eta }$ (and correspondingly for ${\displaystyle {\eta }_{pn}}$ and ${\displaystyle {\eta }_{nn}}$), we then have:

The interpretation is then that, from the pool P(t), the cells leaving it at rate ${\displaystyle {\eta }_{pp}}$ yield pp-divisions, those leaving it at rate ${\displaystyle {\eta }_{pn}}$ yield pn-divisions, and the others, leaving it at rate ${\displaystyle {\eta }_{nn}}$, yield nn-divisions. Overall, the pool ${\displaystyle P(t)}$ depletes at the sum rate ${\displaystyle \eta ={\eta }_{pp}+{\eta }_{pn}+{\eta }_{nn}}$.

Correspondingly, the population cycle time ${\displaystyle {\tau }_c=1/\eta }$ would then be given by:

equivalently by:

We also note that the distribution of fates is then completely constrained by the ${\displaystyle {\tau }_{pp},{\tau }_{pn},{\tau }_{nn}}$ (under the constraint that mitosis events are uniformly distributed in time). Indeed, it remains true that the quantity leaving the P-pool during ${\displaystyle \mathrm{\Delta }t}$ to make pp-divisions is proportional to ${\displaystyle \mathrm{\Delta }t/{\tau }_{pp}}$ (corr. for other fates). This implies in turn that the fraction ${\displaystyle {\alpha }_{pp}}$ leaving for an pp-division is ${\displaystyle {\tau }_c/{\tau }_{pp}}$, correspondingly, ${\displaystyle {\alpha }_{pn}={\tau }_c/{\tau }_{pn}}$ and ${\displaystyle {\alpha }_{nn}={\tau }_c/{\tau }_{nn}}$.

As a consequence, if we have experimental measures of ${\displaystyle {\tau }_c}$ and of a distribution among fates ${\displaystyle {\alpha }_{pp},{\alpha }_{pn},{\alpha }_{nn}}$, we must conclude that:

For ${\displaystyle {\tau }_c=12h}$, and a distribution ${\displaystyle (0.6,0.3,0.1)}$, we would obtain:

The main point is then: if the ratios between fractions of fate ${\displaystyle {\alpha }_{pp},{\alpha }_{pn},{\alpha }_{nn}}$ resulted only from differences in rates ${\displaystyle {\eta }_{pp},{\eta }_{pn},{\eta }_{nn}}$, the ratios between rates must be the same as the ratios between fractions:

With ${\displaystyle {\alpha }_{pp}=0.6,{\alpha }_{nn}=0.1}$, we would have ${\displaystyle {\tau }_{nn}=({\alpha }_{pp}/{\alpha }_{nn}){\tau }_{pp}=6{\tau }_{pp}}$.

If we exclude the possibility that a nn-division is six times as long as a pp-division, then the distribution of fates can not be exclusively determined by differences in fate-based cycle times. It does not exclude that a given kind of fate (e.g. proliferative divisions pp) would require a longer time to be achieved than others, it excludes that such differences would suffice per se to explain the differences between the fractions of fates.

We obtain experimental measures with this system at different times after electroporation (time 0 hr): the fractions ${\displaystyle {\mathrm{f}}_N(24)}$ of neurons at 24 hr and ${\displaystyle {\mathrm{f}}_N(48)}$ at 48 hr (the fraction among the electroporated cells), the distribution of fates at 24 hr as well as an estimate of ${\displaystyle {\tau }_c=12}$ hours. We hypothesize that the fate distribution is steady between 24 hr and 48 hr after electroporation, that is the 24 hr between quantification of the mode of division and progenitors and neuron counting. We use the model to check the consistency of these data with the model.

The first test of consistency was to determine the range of distribution of fates which was able to explain the transition from ${\displaystyle {\mathrm{f}}_N(24)}$ to ${\displaystyle {\mathrm{f}}_N(48)}$.

If we had a system with only symmetric divisions (e.g. some value for ${\displaystyle {\alpha }_{pp}}$, ${\displaystyle {\alpha }_{nn}=1-{\alpha }_{pp}}$, with ${\displaystyle {\alpha }_{pn}=0}$), we first ensured that one pair (${\displaystyle {\mathrm{f}}_N(24),{\mathrm{f}}_N(48)}$) would be compatible with only one fate distribution.

Considering ${\displaystyle P(24)+N(24)=1}$ arbitrary total amount of cells at 24 hr, we can plug ${\displaystyle N(24)={\mathrm{f}}_N(24)}$ and ${\displaystyle P(24)=1-{\mathrm{f}}_N(24)}$ into Equation 14 and get:

where ${\displaystyle P(48),N(48)}$ correspond to the amount obtained at 48 hr from this arbitrary amount of 1 at 24 hr. We have ${\displaystyle {\mathrm{f}}_{\mathrm{N}}(48)=N(48)/(N(48)+P(48))}$, yielding :

which holds for any initial cell amount (Appendix 4—figure 1).

Appendix 4—figure 1

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Now considering the full system with the three kinds of division, there is more than one unique triplet (${\displaystyle {\alpha }_{pp}}$,${\displaystyle {\alpha }_{pn}}$,${\displaystyle {\alpha }_{pn}}$) that is compatible with the unique value of observed ${\displaystyle ({\mathrm{f}}_N(24),{\mathrm{f}}_N(48))}$. For instance, less nn-divisions can be compensated for by more pn-divisions, yielding the same ${\displaystyle f_N(48)}$.

We used the model in the same spirit as in Appendix 4—figure 1 to compute the predicted values for ${\displaystyle {\mathrm{f}}_N(48)}$ for all possible fate triplets. For the system with symmetric-only divisions above, the space of parameters for division is one-dimensional: ${\displaystyle \gamma }$ corresponds to one value of ${\displaystyle {\alpha }_{pp}}$, which constrains in turn the value of ${\displaystyle {\alpha }_{nn}}$. With the three kinds of division, this space of parameters becomes two-dimensional: we need to fix ${\displaystyle {\alpha }_{pp}}$ and ${\displaystyle {\alpha }_{nn}}$, and ${\displaystyle {\alpha }_{pn}}$ is then constrained. Hence the predictions should be drawn over a two-dimensional map.

We compute those maps for each experimental condition, starting from the corresponding observed value ${\displaystyle {\mathrm{f}}_N(24)}$ (fixing the observed initial condition corresponds here to drawing only the bold curve in Appendix 4—figure 1). Then, we determine numerically the subset of fate triplets compatible with the ${\displaystyle {\mathrm{f}}_N(48)={\mathrm{f}}_N^{\ast }}$ measured in the condition. We also determined numerically the confidence regions for the distributions of fates that can yield ${\displaystyle {\mathrm{f}}_N^{\ast }\pm 2.5\mathrm{\%}}$, ${\displaystyle {\mathrm{f}}_N^{\ast }\pm 5\mathrm{\%}}$ and ${\displaystyle {\mathrm{f}}_N^{\ast }\pm 10\mathrm{\%}}$.

In the end, we also report the distribution of fates that was actually measured in each condition, and check in which confidence interval it is (Ventral zone: Appendix 4—figure 2, Appendix 4—figure 3, Appendix 4—figure 4, Dorsal zone: Appendix 4—figure 5, Appendix 4—figure 6, Appendix 4—figure 7).

Appendix 4—figure 2

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Appendix 4—figure 3

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Appendix 4—figure 4

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Appendix 4—figure 5

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Appendix 4—figure 6

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Appendix 4—figure 7

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To compute the predicted fractions of neurons at 48 hr (after electroporation) reported in the main text (Figure 6C), we used Equation 31, parametrized by the data obtained for the averaged fraction of neurons at 24 hr (a.e.), the fate distribution at 24 hr (a.e.), and the cell cycle 12 hr.

All predictions are gathered in Appendix 4—figure 8 as a function of the change in the proliferation/differentiation balance of the progenitors, induced by the ${\displaystyle \mathrm{C}\mathrm{D}\mathrm{C}25\mathrm{B}}$ and the ${\displaystyle \mathrm{C}\mathrm{D}\mathrm{C}25{\mathrm{B}}^{\mathrm{\Delta }\mathrm{C}\mathrm{D}\mathrm{K}}}$ experiments. Together, the observations indicate that ${\displaystyle \mathrm{C}\mathrm{D}\mathrm{C}25\mathrm{B}}$ and ${\displaystyle \mathrm{C}\mathrm{D}\mathrm{C}25{\mathrm{B}}^{\mathrm{\Delta }\mathrm{C}\mathrm{D}\mathrm{K}}}$ result in an increased proportion of neurons 48 hr a.e. (HH22).

Appendix 4—figure 8

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Such an increased proportion of neurons is actually compatible with two dynamical scenarios regarding how the absolute amounts of the two pools (progenitors, neurons) are modified by ${\displaystyle \mathrm{C}\mathrm{D}\mathrm{C}25\mathrm{B}}$ gain-of-function: scenario (1) a speed-up of the neuron pool so that it increases faster under the gain-of-function at the expense of the progenitor pool expansion, or scenario (2) a decrease of the progenitor pool while the pool of neurons keeps the same expansion rate. Which scenario is relevant depends on how ${\displaystyle \mathrm{C}\mathrm{D}\mathrm{C}25\mathrm{B}}$ affects the balance ${\displaystyle \gamma }$ between proliferation and differentiation.

The progenitor pool can increase only if ${\displaystyle \gamma >0}$, which implies ${\displaystyle {\alpha }_{pp}>{\alpha }_{nn}}$. In this case, the two pools can increase (scenario 1), their respective growth rates are controlled by ${\displaystyle \gamma }$ and the neurogenic effect of ${\displaystyle \mathrm{C}\mathrm{D}\mathrm{C}25\mathrm{B}}$ gain-of-function will produce a greater absolute number of neurons in the end (at 48h/HH22). Otherwise (${\displaystyle \gamma <0}$, that is ${\displaystyle {\alpha }_{pp}<{\alpha }_{nn}}$), the neuron pool can increase at about the same rate, yielding the same absolute number of neurons at 48 hr/HH22, and the increased fraction of neurons reflects a depletion of the progenitor pool (scenario 2).

The model enlightens which is the most probable scenario for the dynamical impact of ${\displaystyle \mathrm{C}\mathrm{D}\mathrm{C}25\mathrm{B}}$ manipulation, since we can compute the underlying evolution of the absolute amounts of the two pools that determines the evolution of the neuronal fraction (Appendix 4 — figure9C).

Under ${\displaystyle \mathrm{C}\mathrm{D}\mathrm{C}25\mathrm{B}}$ gain-of-function in the dorsal neural tube (Appendix 4 — figure9C-right), the percentage of progenitors performing pp-divisions stays greater than the percentage of those performing nn-divisions (${\displaystyle 38.6\mathrm{\%}>11.3\mathrm{\%}}$, ${\displaystyle {\alpha }_{pp}>{\alpha }_{nn}}$) and the balance is still positive (${\displaystyle \gamma =0.386-0.113=0.273>0}$), so the pool of progenitors still increases but at a lower rate than the control (where ${\displaystyle \gamma =0.663-0.078=0.585}$). The higher percentage of neurons at 48 hr/HH22 then results from an even higher absolute number of neurons (scenario 1).

Appendix 4—figure 9

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By contrast, in the ventral neural tube, the balance shifts from ${\displaystyle \gamma =0.393-0.127=0.266}$ in the control to ${\displaystyle \gamma =0.069-0.407=-0.338}$, becoming negative under ${\displaystyle \mathrm{C}\mathrm{D}\mathrm{C}25\mathrm{B}}$ gain-of-function (scenario 2). Accordingly, the absolute number of neurons at 48 hr/HH22 is poorly affected, but the pool of progenitors declines, explaining the higher fraction of neurons (Appendix 4 — figure9C-left).