Angie Molina
email: amolinad@unav.es

Frédéric Bonnet
email: fbonnet@mdibl.org

V Lobjois

Sophie Bel-Vialar
email: sophie.vialar@univ-tlse3.fr

Jacques Gautrais
email: jacques.gautrais@univ-tlse3.fr

Fabienne Pituello
email: fabienne.pituello@univ-tlse3.fr

Eric Agius
email: eric.agius@univ-tlse3.fr

G1 PHASE LENGTHENING DURING NEURAL TISSUE DEVELOPMENT INVOLVES CDC25B INDUCED G1 HETEROGENEITY

Keywords: neural stem cells, neurogenesis, proliferation, differentiation, cell cycle kinetics, G1 phase, CDC25 phosphatase, neural tube, vertebrate embryo

While lengthening of the cell cycle and G1 phase is a generic feature of tissue maturation during development, the underlying mechanism remains still poorly understood. Here we develop a time lapse imaging strategy to measure the four phases of the cell cycle in single neural progenitor cells in their endogenous environment. Our results show that neural progenitors possess a great heterogeneity of the cell cycle length. This duration variability is distributed over all phases of the cell cycle, with the G1 phase being the one contributing primarily to cell cycle variability.

Within one cell cycle, each phase duration appears stochastic and independent except for a surprising correlation between S and M phase. Lineage analysis indicates that the majority of daughter cells display longer G1 phase than their mother's suggesting that at each cell cycle a mechanism lengthens the G1 phase. We identify an actor of the core cell cycle machinery, the CDC25B phosphatase known to regulate G2/M transition, as an indirect regulator of the duration of the G1 phase. We propose that CDC25B acts via a cell to cell increase in G1 phase heterogeneity revealing a novel mechanism of G1 lengthening associated with tissue development.

INTRODUCTION

Building a multicellular functional organ requires tight coordination between cell proliferation, cell fate specification and differentiation. In the developing nervous system, the spatio-temporal regulation of these processes is of key importance to generate the relative proportion of the numerous classes of neurons and glia cells essential to construct functional neuronal circuits.

The cell cycle and components of the core cell cycle machinery have been shown to play a major role in the decision to proliferate or differentiate in embryonic stem cells, pluripotent stem cells and neural stem/progenitor cells (for a review see [START_REF] Liu | The cell cycle in stem cell proliferation, pluripotency and differentiation[END_REF]. In numerous cell types including neural stem/progenitor cells, cell cycle and G1 phase lengthening is a general feature accompanying cell maturation and differentiation. During mammalian corticogenesis where consecutive types of progenitors have been described, lengthening of the G1-phase is associated with the transition from neural-stem-like apical progenitors (AP) to fate restricted basal progenitors (BP) and a shortening of the S phase with the transition from proliferative to neurogenic divisions [START_REF] Arai | Neural stem and progenitor cells shorten S-phase on commitment to neuron production[END_REF]. Reducing G1 phase length results in an inhibition of neurogenesis, while lengthening G1 duration promotes neurogenesis [START_REF] Lim | Loss of Cdk2 and Cdk4 induces a switch from proliferation to differentiation in neural stem cells[END_REF][START_REF] Artegiani | Overexpression of cdk4 and cyclinD1 triggers greater expansion of neural stem cells in the adult mouse brain[END_REF][START_REF] Lange | Cdk4/cyclinD1 overexpression in neural stem cells shortens G1, delays neurogenesis, and promotes the generation and expansion of basal progenitors[END_REF][START_REF] Pilaz | Forced G1-phase reduction alters mode of division, neuron number, and laminar phenotype in the cerebral cortex[END_REF]. In the developing spinal cord, different cell cycle kinetics are observed in discrete domains of neural progenitors [START_REF] Molina | Playing with the cell cycle to build the spinal cord[END_REF]. Differentiation here progresses from ventral to dorsal with time. When the maximum differentiation rate is reached in the ventral domain, neural progenitor cells (NPCs) exhibit a long G1 phase and short S and G2 phases [START_REF] Kicheva | Coordination of progenitor specification and growth in mouse and chick spinal cord[END_REF][START_REF] Saade | Sonic hedgehog signaling switches the mode of division in the developing nervous system[END_REF][START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF]. In contrast, the dorsal domain mainly composed at the same age of proliferative NPCs, shows a short G1 phase accompanied by long S and G2 phases [START_REF] Kicheva | Coordination of progenitor specification and growth in mouse and chick spinal cord[END_REF][START_REF] Saade | Sonic hedgehog signaling switches the mode of division in the developing nervous system[END_REF][START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF]. Overexpressing D-type Cyclins in young neural tube increases the pool of proliferating progenitors and induces a transient reduction of neuron production [START_REF] Lacomme | NEUROG2 drives cell cycle exit of neuronal precursors by specifically repressing a subset of cyclins acting at the G1 and S phases of the cell cycle[END_REF][START_REF] Cao | YAP regulates neural progenitor cell number via the TEA domain transcription factor[END_REF], while more mature NPCs will differentiate regardless of Cyclin D overexpression and cell cycle exit [START_REF] Lobjois | Forcing neural progenitor cells to cycle is insufficient to alter cell-fate decision and timing of neuronal differentiation in the spinal cord[END_REF]. Shortening of the G2 phase associated with neurogenesis results from the upregulation in NPCs of a regulator of the G2/M transition, the CDC25B phosphatase. CDC25B promotes entry into mitosis by dephosphorylating its canonical substrates, the cyclin-dependent kinases (CDKs) complexes. Surprisingly preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint for a positive regulator of the core cell cycle machinery, CDC25B has been shown to promote neurogenesis in mouse, chicken and Xenopus embryos [START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF][START_REF] Gruber | MCPH1 regulates the neuroprogenitor division mode by coupling the centrosomal cycle with mitotic entry through the Chk1-Cdc25 pathway[END_REF][START_REF] Ueno | FoxM1-driven cell division is required for neuronal differentiation in early Xenopus embryos[END_REF]. Gain and loss of function experiments performed in chicken neural tube show that CDC25B induces the conversion of proliferating NPCs into differentiating neurons by promoting neurogenic divisions [START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF]. CDC25B acts using both CDK independent and dependent molecular mechanisms [START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF]. A mathematical model has allowed us to hypothesize that CDC25B expression in neural progenitors progressively restricts the proliferative capacities of embryonic neural stem cells [START_REF] Azaïs | Timing the spinal cord development with neural progenitor cells losing their proliferative capacity: a theoretical analysis[END_REF].

A weak point common to all these studies is that cell cycle analyses have been performed at the population level. Cell cycle and phases lengths were calculated from fixed tissues and correspond to estimated average length values considering the population of NPCs as homogeneous [START_REF] Nowakowski | Bromodeoxyuridine immunohistochemical determination of the lengths of the cell cycle and the DNA-synthetic phase for an anatomically defined population[END_REF]. Whether this neural progenitor population is homogeneous or heterogeneous relative to cell cycle kinetics is poorly documented. An indication that the population of NPCs is indeed heterogeneous comes from a study where the total cell cycle length (Tc) was determined from the length of time measured between two cell divisions using timelapse imaging in chick embryo slice cultures [START_REF] Wilcock | Mitotic spindle orientation distinguishes stem cell and terminal modes of neuron production in the early spinal cord[END_REF]. These single cell measurements reveal that the neural progenitor population displays marked heterogeneity regarding the Tc, which ranges from 9 hours to 28 hours. Moreover, previous data indicate that the cell cycle length of cells dividing to produce two progenitors was shorter than that producing one neuron and one progenitor [START_REF] Wilcock | Mitotic spindle orientation distinguishes stem cell and terminal modes of neuron production in the early spinal cord[END_REF].

The goal of this study was to determine at the cellular level the features of NPCs cell cycle kinetics in their endogenous environment and the link between cell cycle kinetics and cell aging. To do so, we set up a high-resolution time-lapse imaging technique to measure the duration of each phase of the cell cycle in single NPCs within the developing neural tube and to track the behavior of daughter cells after mitosis.

We found that the NPCs population is highly heterogeneous regarding the distribution of cycling time. We showed that the duration of each phase can be described by a stochastic process and found no coupling between phase length within a cell cycle. All phases, but M phase, are very heterogeneous, and the total cell cycle (Tc) length variation can be primarily explained by G1 heterogeneity. Time lapse imaging showed that the majority of daughter cells display a longer G1 phase than their mother's preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10. 1101/2020.11.06.370833 doi: bioRxiv preprint .11.06.370833 doi: bioRxiv preprint suggesting that gradually at each cell cycle a mechanism lengthens the G1 phase.

Because CDC25B affects both cell cycle kinetics and neurogenesis, we tested its effect and showed that it increases cell-to-cell G1 length heterogeneity, thereby raising tissue-scale G1 length without affecting cell phase independence. We propose that in a context of cell cycle phases independence, CDC25B expression and reiteration at each cell cycle, increases heterogeneity in G1 phase durations and promotes the restriction of the proliferative capacities of embryonic neural stem cells, their maturation and commitment to differentiation.

preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint

MATERIALS AND METHODS

Embryos

Fertile hens' eggs were incubated at 38°C in a humidified incubator to yield embryos appropriately staged [START_REF] Hamburger | A series of normal stages in the development of the chick embryo[END_REF].

DNA constructs and in ovo electroporation

In ovo electroporation experiments were performed using 1.5-to 2-day-old chicken as described previously [START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF]. To detect the four phases of the cell cycle we developed the mKO-zCdt1-pIRES-NLS-eGFP-L2-PCNA biosensor. In the pCAG plasmid, we inserted the Fucci G1 probe derived from zebrafish Cdt1 [START_REF] Sugiyama | Illuminating cell-cycle progression in the developing zebrafish embryo[END_REF] and downstream the IRES element, the NLS green fluorescently tagged proliferating cell nuclear antigen (PCNA, [START_REF] Leonhardt | Dynamics of DNA replication factories in living cells[END_REF]. This FUCCI G1-PCNA vector is transfected at 0.5µg/µl by in ovo electroporation in the chicken neural tube to reproducibly obtain a high degree of mosaicism compatible with lineage tracing [START_REF] Wilcock | Mitotic spindle orientation distinguishes stem cell and terminal modes of neuron production in the early spinal cord[END_REF]. The hCDC25B or hCDC25B ΔCDK gain-of-function experiments were performed at 1.5µg/µl as in [START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF]. The Fucci S/G2/M mAG-hGem [START_REF] Sakaue-Sawano | Visualizing spatiotemporal dynamics of multicellular cell-cycle progression[END_REF] and the fucci G1 mKO2-zCdt1 (1/190) [START_REF] Sugiyama | Illuminating cell-cycle progression in the developing zebrafish embryo[END_REF] were used at 0.5 µg/µl.

Immunohistochemistry

Embryos or neural tube explants are fixed in 3.7% formaldehyde for 2 hours and sliced using a vibratome (Leica). Proteins were detected on 50 µm vibratome sections, as previously described [START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF]. The antibodies used are: anti-Olig2 (Milipore), anti-Islet1/2, anti-MNR2 (Developmental Studies Hybridoma Bank), antiactive caspase 3 (Becton Dickinson Biosciences).

Determination of S-phase length (Ts) and total cell cycle length (Tc) were based on the relative numbers of cells that incorporated one or two thymidine analogs (Martynoga et al., 2005). For in ovo incorporation 10 µl of bromodeoxyuridine (BrdU Sigma, St Louis, MO, USA) (500 µM) were injected into embryos and followed after 90 minutes by EdU (500 µM, Invitrogen) incorporation. Embryos were fixed 30 minutes later. EdU was detected first (Click-iT EdU Alexa Fluor 647 Imaging Kit, Invitrogen), followed by BrdU detection using the G3G4 antibody that does not recognize EdU. For BrdU incorporation, 10 µl of BrdU (500 µM) were injected into embryos, reincubated for 30 minutes before fixation. BrdU immunodetection was performed on vibratome preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint sections using anti-BrdU (mouse monoclonal, G3G4) as in [START_REF] Lobjois | Specific regulation of cyclins D1 and D2 by FGF and Shh signaling coordinates cell cycle progression, patterning, and differentiation during early steps of spinal cord development[END_REF]. Cell death was analyzed by immunofluorescence, using the anti-active caspase 3 antibody.

Flow cytometry analysis

1.5-to 2-day-old chicken embryos were electroporated with H2B-GFP or NLS-eGFP-L2-PCNA constructs. Neural tubes were dissected 24 h following electroporation, incubated at 37°C for 10 min in trypsin-EDTA to obtain a single-cell suspension, and fixed for 30 minutes in 4% formaldehyde. Cell suspensions were incubated for 30 min in 400 µl of propidium iodure (PI) (20µg/ml)/ RNAse (100µg/ml) cocktail (Sigma). PI and GFP fluorescence were acquired with a FACSCalibur cytometer (Cat#342975, Becton Dickinson), and DNA content analysis was performed using the FlowJo software.

Embryonic neural tube culture and Time-lapse Imaging

Electroporated E2 embryos were collected in PBS and 100 µm slices were obtained using a McIlwain tissue chopper (WPI), from the brachial region corresponding to somites 12 to 17 which generates the greatest number of motoneurons [START_REF] Oppenheim | Early regional variations in motoneuron numbers arise by differential proliferation in the chick embryo spinal cord[END_REF]. 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 embedded into 10 µl of rat type I collagen (Roche Diagnosis; diluted at 80% with 1X MEM (GIBCO), 1X GlutaMax (GIBCO) and neutralizing bicarbonate (GIBCO). 4 neural tube-containing collagen drops (5 µl) were distributed on a 35 mm glass-bottom culture dish (IBIDI) (procedure modified from [START_REF] Das | High-resolution live imaging of cell behavior in the developing neuroepithelium[END_REF] Collagen polymerization was performed at 38°C for 30 minutes and 1.5 ml of complete culture medium is added (Medium 199 (Gibco) supplemented with 1X GlutaMax (Gibco), 5% Fetal calf Serum (FCS, Fisher Scientific) and Gentamycin (Gibco, 40ug/mL). The culture dish is placed in a humid atmosphere incubator with 5% CO2 for 12 hours before time lapse imaging.

Alternatively, explants were cultured for 24 or 48 hours and then fixed in 3.7% formaldehyde (FA) and processed for immunostaining.

For time-lapse, images were acquired on an inverted microscope (Leica inverted DMI8) equipped with a heating enclosure (set up at 39°C) in an atmosphere containing 5% CO2, a spinning disk confocal head (CSU-X1-M1N, Yokogawa), a SCMOS camera and a 63X oil immersion objective (NA 1,4 -0,7). Attenuation of laser beam pulses were preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint performed to reduced cell damage due to photo-toxicity [START_REF] Boudreau | Excitation Light Dose Engineering to Reduce Photo-bleaching and Photo-toxicity[END_REF]. We recorded 40 µm thick z stacks (2 µm z-steps) at 5 min intervals for 48h.

Imaging, data analysis and statistics

IMARIS® and ImageJ® softwares were used for image processing and data analysis.

Statistical analyses were performed using GraphPad Prism and R software. Details for methods used in SI-Data are given in the relevant sections.

RESULTS

A new method to measure the four cell cycle phases length of NPCs in real time

In order to determine cell cycle kinetics of individual spinal NPCs, we developed a combination of biosensors to detect unambiguously the four phases of the cell cycle in living cells. To label the G1 phase, we used the zebrafish G1 marker mKO2-zCdt1 (FUCCI G1, [START_REF] Sugiyama | Illuminating cell-cycle progression in the developing zebrafish embryo[END_REF] instead of the human Cdt1, which in chick NPCs, persists in all cell cycle phases, suggesting that it is not properly degraded (data not shown). We verified the zebrafish FUCCI G1 specificity in G1 by co-electroporating mKO2-zCdt1 with FUCCI S/G2/M (mAG-hGeminin) and quantifying, 24 hours later, red, green and yellow cells corresponding to cells expressing respectively FUCCI G1, FUCCI S/G2/M or both (Fig. 1A). We quantified 43,7% and 41,4 % of cells expressing FUCCI G1 or FUCCI S/G2/M respectively and 14,9 % expressing both markers illustrating their transient overlap as already reported [START_REF] Sakaue-Sawano | Visualizing spatiotemporal dynamics of multicellular cell-cycle progression[END_REF]. This result was comparable to previous quantifications performed by flow cytometry analysis (FACS, [START_REF] Benazeraf | Identification of an unexpected link between the Shh pathway and a G2/M regulator, the phosphatase CDC25B[END_REF]. To time more precisely the G1/S transition and to identify the S/G2 transition, we used NLS-eGFP-L2-PCNA protein [START_REF] Leonhardt | Dynamics of DNA replication factories in living cells[END_REF]. S phase onset was detected by the punctuated appearance of NLS-eGFP-L2-PCNA. PCNA is recruited within the DNA replication forks that change in location and size as S phase progresses. A 30 minute BrdU pulse confirmed that the punctate labelling observed with NLS-eGFP-L2-PCNA corresponds to S phase cells (Fig. 1B). We tested whether electroporated NLS-eGFP-L2-PCNA induces cell cycle disturbances by means of FACS analysis using propidium iodide as a DNA intercalating agent. As shown in Fig. 1C, there is no difference in the cell cycle profile or in the corresponding quantifications following NLS-eGFP-L2-PCNA or H2B-GFP electroporation. These results confirm that NLS-eGFP-L2-PCNA overexpression does not interfere with cell cycle timing, as previously reported in zebrafish neuroepithelia [START_REF] Leung | Apical migration of nuclei during G2 is a prerequisite for all nuclear motion in zebrafish neuroepithelia[END_REF]. According to this, we constructed a pCAG plasmid containing mKO-zCdt1 and NLS-eGFP-L2-PCNA (Fig. 1D) to perform proper mosaic expression through in ovo electroporation into 2-day-old chick neural tube (Fig. 1E), and thereby visualize the four cell cycle phases in individual cycling neural progenitors (Fig. 1F).

To analyze cell cycle parameters, E2 embryonic neural tubes were electroporated with the FUCCI G1-PCNA vector. After 6 hours (E2.25) or 24 hours (E3) of incubation, embryos were sliced, and tissue cultures recovered for 12 hours prior preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint imaging (Fig. 1E). This step of recovering is important to bypass the lengthening of the cell cycle and the delayed increase in the population of progenitors and neurons observed following slicing and cultivation (Sup Fig1 A-D). Time-lapse imaging was performed for 48 hours using a confocal microscope. It is important to stress that the use of 5% fetal calf serum in the culture medium and using spinning disk confocal microscopy associated with attenuation of laser beam pulses to reduce phototoxicity [START_REF] Boudreau | Excitation Light Dose Engineering to Reduce Photo-bleaching and Photo-toxicity[END_REF] are critical to perform cell cycle measurements. Visualization of the FUCCI G1-PCNA vector by time-lapse imaging revealed that the different transitions in the cell cycle could be discerned using nuclear expression of both proteins (Fig. 1F): G1 phase was characterized by the co-expression of mKO-FUCCI G1 and NLS-eGFP-L2-PCNA. S phase was detected by the appearance of punctuated NLS-eGFP-L2-PCNA associated with the gradual disappearance of the FUCCI-G1 reporter. In G2 phase, NLS-eGFP-L2-PCNA was evenly distributed inside the nuclei, and finally mitosis was detected by nuclear envelope breakdown accompanied by morphology changes of NPCs, which become rounded (Fig. 1F).

We have thus designed a long-term time-lapse imaging method to measure accurately the four cell cycle phases in individual cycling neural progenitors in an endogenous environment, the neural tube.

Neural progenitor nuclei display INMs in phase with the cell cycle and three distinct behaviors after mitosis

Electroporation and imaging of the FUCCI G1-PCNA vector in E2 (HH12) stage embryos, showed cycling NPCs displaying G1 nuclei (orange) moving to the basal side, nuclei in S phase (green punctuated) located in the basal half of the ventricular zone and G2 nuclei (green) moving back to the apical side where mitosis occurs (Fig. 2A; Movie 1). These characteristic positions indicate that in neuroepithelia, INM occurs in phase with the cell cycle (Fig. 2B) as previously described by a large number of studies [START_REF] Molina | Playing with the cell cycle to build the spinal cord[END_REF][START_REF] Laguesse | Progenitor genealogy in the developing cerebral cortex[END_REF][START_REF] Kosodo | Regulation of interkinetic nuclear migration by cell cycle-coupled active and passive mechanisms in the developing brain[END_REF][START_REF] Langman | Behavior of neuro-epithelial cells during closure of the neural tube[END_REF]. We also observed nuclei on the basal side of the neural tube expressing brighter orange fluorescence (Fig. 2A), probably due to the accumulation of FUCCI G1 in differentiating G0 neurons after cell cycle exit, as previously described [START_REF] Sakaue-Sawano | Visualizing spatiotemporal dynamics of multicellular cell-cycle progression[END_REF].

Nuclear tracking after mitosis reveals three different behaviors in daughter cells (Fig. 2C): both daughter cells re-enter S phase and nuclei switch from FUCCI G1 to preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint PCNA-punctuated labeling, this behavior clearly corresponds to cells performing proliferative divisions (PP) (P2 giving P2.1 and P2.2); only one daughter cell re-enters the cell cycle, while the nucleus of the other remains orange and will migrate to the periphery (P3 giving P3.1 and N3.2); the two daughter cells nuclei remain orange and will migrate to the periphery (P1 giving N1.1 and N1.2). These orange nuclei located at the basal side and displaying a G1 phase longer than 1000 min (16h40), were never observed re-entering S phase. We thus assumed that they correspond to cells primed to differentiate into neurons (Fig. 2A-Movie 1). The G1 lengths measured for these cells are excluded from our analyses. Hence our strategy allows us to follow the nuclei of NPCs across the cell cycle and to determine, after mitosis, whether the daughter cells re-enter the cell cycle or remain in G1 phase for a long time (marked PLG1).

Cell cycle kinetics are highly heterogeneous in the population of NPCs

Cell cycle kinetics analysis was performed with E2 (HH12) stage embryo to ensure that we analyze young proliferative progenitors (Fig. 3A). We first compared, at the population level, the cell cycle data measured using time-lapse imaging with those obtained on fixed tissues. The mean value measured using time lapse for the total cell cycle (Tc) is 14h01 (n=33), G1: 5h09 (n=50), G2: 1h17 (n=54) and M : 31 min (n=50, Table 1). These data are in agreement with those described for fixed embryos at equivalent developmental stages (brackets in Fig. 3B), Tc : 10h and 16h, G1 : 4h30 and 7h, G2 : 1h18 min and 2h and mitosis : 30 minutes [START_REF] Kicheva | Coordination of progenitor specification and growth in mouse and chick spinal cord[END_REF][START_REF] Dreau | The strength of SMAD1/5 activity determines the mode of stem cell division in the developing spinal cord[END_REF][START_REF] Saade | Sonic hedgehog signaling switches the mode of division in the developing nervous system[END_REF][START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF][START_REF] Wilcock | Mitotic spindle orientation distinguishes stem cell and terminal modes of neuron production in the early spinal cord[END_REF]. The S phase length measured using time lapse (7h18 ± 23 min) presents an average value higher than reported in fixed tissues (3h42 min and 5h54 min). Thus, except for this phase, which was slightly increased in our conditions (see discussion), the mean data obtained at the population level are consistent with those reported for fixed tissues at equivalent developmental stage.

At the single cell level, our analyses showed a high degree of heterogeneity regarding Tc duration, as it ranges from 9h55 min (595 min) to 24h45 min (1485 min) (Table 1; Fig. 3A,B) recalling previous time lapse measurements reporting a total cell cycle length between 9 hours and 28 hours (see FigS2 in [START_REF] Wilcock | Mitotic spindle orientation distinguishes stem cell and terminal modes of neuron production in the early spinal cord[END_REF]. The use of the FUCCI G1-PCNA biomarker allowed us to determine how this heterogeneity was translated at the level of the different cell cycle phases (Table 1; Fig. 3A). G1 phase durations were comprised between 2h20 (140 min) and 16h20 (980 min). S preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint phase durations spanned from 2h10 (130 min) to 15h45 (945 min), the G2 phase from 35 min to 2h55 (175 min), and Mitosis from 20 min to 55 min. Since data are durations before exiting the phase, we characterized the corresponding distributions using survival analysis (Fig. 3C-F). Each phase can be characterized by a minimal duration (Dmin) and a mean exit time (𝜏) corresponding to the average duration spent in the phase after that minimal duration (Table 1, SI-Data section 1.2). Mean exit time reflects the slope of the survival function after minimal duration. The gentler the slope, the larger the mean exit time, the more heterogeneous the distribution. At the opposite, a very homogeneous population would display durations close to the minimal duration and a vanishing mean exit time. Hence, the mean exit time is a meaningful readout of the phase duration heterogeneity. The shapes of the survival curves and their mean exit times indicate that all the phases are heterogeneous (Table 1, Fig. 3C,E, SI-Data section 1.3).

To identify the quantitative relationships between phases, we performed further analyses using the subset of 33 cells for which a complete cell cycle was monitored (Fig. 3G, Table 1, SI-Data section 2). In this sample, NPCs cells spent 37% of the cell cycle in G1, 52% in S phase, 9% in G2 and 4% in mitosis, in accordance with previous data obtained on fixed samples [START_REF] Saade | Sonic hedgehog signaling switches the mode of division in the developing nervous system[END_REF]. Variation partitioning analysis showed that 58 % of Tc variation is due to G1 heterogeneity alone (Fig. 3G, SI-Data section 2.2). We then tested correlations within each pair of phases, and found no patterns, except for an unexpected significant positive correlation between S and M durations (Fig. 3H). No correlation was identified between G1 length and S/G2/M lengths (P>>0.05, SI-Data section 2.3.1), suggesting that phases durations are independent from each other within the same cell cycle.

To further test the likelihood of the hypothesis of full independence among phases durations, we examined how it would correctly predict the observed distribution of Tc. To build this prediction analytically, the survival curves of exit times for each phase in the subset have been approximated by a simple exponential decay (red line in Suppl Fig. 2, SI-Data section 2.5.1), which would correspond to a model in which cell cycle phase exit is a stochastic exit process driven by a constant probability per unit time to exit after minimal duration. Under such a hypothesis, for each phase, duration can be described by a stochastic exit process D defined as

𝐷 ∼ 𝐷 𝐸

preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint where 𝐸 ∼ 𝐸𝑥𝑝 𝜏 is an exponentially distributed variable with mean time 𝜏.

Under this hypothesis, the complete cell cycle duration would then obey a stochastic process Dc simply defined as:

𝐷 𝑐 𝐷 𝐺1 𝐷 𝑆 𝐷 𝐺2 𝐷 𝑀 that is, the total duration would just result from the sum of four independent exit processes as defined above, each with its corresponding parameters for minimal duration and mean time before phase exit (see SI-Data section 2.4.1 for the analytical expression for Dc distribution under this hypothesis). We found that the predicted survival function for Dc under this hypothesis (brown curve in Fig. 3I) is actually well compatible with the observed one (black line in Fig. 3I) suggesting that the phases are independent. This is confirmed using Monte Carlo permutation, a random sampling technique (red line in Fig. 3I, SI-Data section 2.4.2). To challenge this finding, we illustrate the opposite hypothesis where Tc length would result from the dataset reordered so that the lengths of G1 and S/G2/M phases are fully anti-correlated (blue line in Fig. 3I, SI-Data section 2.4.3). In this case, the heterogeneity of Tc is greatly reduced compared to the experimental one.

Together these data show that the spinal NPCs population is highly heterogeneous regarding the distribution of cycling time. Duration of each phase seems largely stochastic and independent within one cell cycle, suggesting the absence of coupling between phases. The phase mostly responsible for Tc variation is the G1 phase.

Maturation correlates with individual NPC G1 phase lengthening

Long-term time-lapse imaging allow one to perform lineage tracing at the single cell level and determine whether a link exists between cell cycle kinetics of mother cells and the fate of daughter cells after mitosis. A proliferating progenitor (P) is characterized when after mitosis it performs a complete G1 phase and enters into S phase. A cell which stop cycling (G1>1000 min; open dot in Fig. 4A) is referred as PLG1. We were able to correctly identify the fate of 15 pairs of daughter cells, 14 being P-P and 1 P-PLG1. We then attempted to backtrack the cell cycle features for the preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint corresponding 15 mother cells and measured the duration of 15 mitoses and G2 phases, 7 S phases and 6 G1 phases (colored dots in Fig 4A). Identification of the 14 PP divisions allowed us to compare their cell cycle characteristics to the rest of the population. Regarding the S, G2 and M phases, there is no difference between the distribution of the PP-performing cells and the whole population (p-values of 0.973, 0.141 and 0.215 for S, G2 and mitosis, respectively). However, when considering the G1 phase and Tc lengths, they were significantly decreased by 42.3% and 12.3%, respectively, compared to the phase length measured in the total population (p = 0.001 and 0.041, for the G1 and Tc respectively, Table 1). This is clearly illustrated by the localization of PP-generating mother cells within the lower quartile for the Tc and G1 phase (red dots in Fig. 4A). Extending this analysis to all the PP divisions observed in our various experimental conditions (Suppl. Fig. 3A) confirmed that PP divisions are most often associated with short G1 phase (14 out of 20). Noteworthy, PP division can still be observed with long G1 phase (Suppl. Fig. 3A) suggesting that a long G1 phase does not preclude proliferative division.

Further lineage analyses revealed that mother and daughter cells displayed differential behavior in terms of cell cycle kinetics. One example of lineage is given in Fig. 4B). For the G1 phase, 13 out of 17 daughter cells (76.5%) presented a longer G1 phase than their mother without difference in the S, G2, and Tc cell cycle phases (Fig. 4C). The mean difference between these "longer G1 daughter cells" and their mothers is of 1h42 min (Fig. 4D). The 4 other cells (arrowheads in Fig. 4C) display a shorter G1 phase with a reduction of 50 min (Suppl. Fig. 3B). Our results suggest that G1 phase lengthening occurs from generation to generation.

If our statement is true, at later developmental stages when the population of neurogenic NPCs increases at the expense of progenitors performing PP divisions, we should observe a modification in the distribution of the G1 phase length. We therefore electroporated E2 embryos, waited for 24 hours before processing them for live imaging (Fig. 1E) and performed cell cycle live imaging in E3 (HH20) embryonic neural tube explants. As observed in Fig. 5A, out of the 30 G1 nuclei analyzed, 20 display a G1 phase longer than 1000 min after mitosis (open circle in Fig. 5A) as expected from a population of NPCs containing numerous progenitors committed to neuronal differentiation. The other 10 cells performed a complete G1 phase and start an S phase. The total cell cycle length was measured on 5 out of these 10 cells (colored dots in Fig. 5A, Table 1). The Tc, S, G2 and M phases showed similar mean values preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint with those measured at E2 while the average duration of G1 phase was increased (8h54 at E3 vs 5h09 at E2; p = 0.316). The frequency distribution comparison between E2 and E3, revealed for G1 phase, the appearance of cells with G1 around 900 min creating a second peak on the left of the figure (Fig. 5B). S phase data show an asymmetrical skewed distribution with a difference in the peak position and data spreading revealing a right shift in the distribution indicating a lengthening and a left shift in G2 phase representing a shortening (Fig. 5C-5D). Unfortunately, out of 10 cycling G1 nuclei, we were only able to backtrack the cell cycle of one mother cell whose two daughters performed long G1s (blue dot in Suppl. Fig. 3A). Altogether these data suggest that NPCs performing PP divisions will mainly execute a short G1 phase.

G1 lengthening from generation to generation is correlated with NPCs maturation and possibly neuronal fate commitment.

CDC25B activity induces G1 phase lengthening in a CDK dependent manner

As mentioned above, single cell analysis reveals a high degree of heterogeneity in G1 phase length at the population level. Lineage experiments indicate that daughter cells display most often a longer G1 phase than their mother suggesting that G1 phase lengthens hereditarily. One possibility is that a mechanism intrinsic to the cell cycle induces a lengthening of the G1 phase in individual NPCs. Recently, we showed that CDC25B is involved in NPCs maturation [START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF][START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF], we then decided to test the effects of the phosphatase on cell cycle kinetics using our time lapse strategy. We performed gain of function using a vector that reproduces the iterated cell cycle regulated expression of CDC25B [START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF]. As observed in control condition, cell cycle kinetics is highly heterogeneous in CDC25B gain-offunction (Fig. 6A andTable 1). As expected from its role in G2/M transition [START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF][START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF], CDC25B gain of function induced a significant 12.7% decrease of the mean G2 phase length (p = 0.029, Fig. 6C andTable 1). This effect on G2 is associated with a mean Tc length increase of 32.8% (p=0.004 when compared to control; Table 1) resulting from a slight increase in the length of the mean S and M phase lengths (12.4% and 5.5% respectively) and from a drastic 59.9% increase in the mean G1 phase length (p<0.0001 when compared to control; Fig. 6C,Table 1). Survival curves and the corresponding frequency distribution histograms representation were then compared to analyze the dispersion of the data in various conditions (Fig. 6D-H). The 4h16 min (256 min) increase observed in mean Tc length preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint induced by CDC25B is associated with a rise of the exit time (from 247 to 503 min) without modification of the minimal duration (583 min vs 586 min, Table 1). This clearly define that CDC25B increases the dispersion of the dataset. The pace at which CDC25B expressing cells exit the cell cycle is about three times slower (hazard ratio of 0.35) than that of control cells (red curve compared to black curve in Fig. 6D, SI-Data section 3.1). When comparing phase by phase, CDC25B induces a significant increase in both G1 and S phase distribution compared to control (compare red and black curve in Fig. 6E-G). Minimal durations do not appear altered, but rather exit times are affected, with a mean lengthening of 2h45 (165 min) and 1h02 (62 min) and 0.41 and 0.65 hazard ratios for G1 and S phases, respectively (SI-Data section 3.2 and 3.3). No significant effect was found on the G2 or M phase survival distributions (Fig. 6F-H, Table 1, SI-Data section 3.4 and 3.5). We note that mean G2 length shortening appears to be associated with a shorter minimal duration, with no effect upon its heterogeneity (shape of the curve in Fig. 6 F,Table1). These data suggest that CDC25B affects primarily G1 phase heterogeneity.

Variation partitioning using complete cell cycle revealed that about 52 % of Tc variation are explained by G1 heterogeneity alone and 21% by S phase alone in CDC25B condition (Suppl. Fig. 4A). In this condition, correlation analysis between phase lengths showed that phases are uncoupled (SI-Data section 2.3.2). Monte Carlo permutations of the data set (10 4 samples) suggest that the distribution of Tc is compatible with independent cell cycle phase durations (compare red and black curve in Suppl. Fig. 4B and SI-Data section 2.6.2). Because CDC25B effectors control directly G2 phase length, we tested for a correlation between the mother cells G2 phase length and the daughter cells G1 phase length. We could not detect a heritable correlation neither in control nor in the gain of function condition (Suppl. Fig. 4C,D).

We then wanted to know whether the effects of CDC25B on the G1 phase was dependent on the interaction with CDK. We electroporated a CDC25B ΔCDK mutant form of CDC25B unable to interact with CDK but still displaying neurogenic activity albeit less important than the wild type protein [START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF]. In line with the neurogenic effect of this mutant protein, we observed 4 cells with a G1>1000 minutes in this condition (open circles in Fig. 6B). In our experiments, CDC25B ΔCDK neurogenic mutant was not able to significantly change cell cycle phases length and dispersion compared to control conditions (Fig. 6B,C; Table 1, SI-Data section 3). Thus, the G1 phase modification induced by CDC25B is dependent on its interaction with CDK.

preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint All these results show that in a context where each cell cycle phase duration is stochastic and independent, CDC25B enhances heterogeneity in G1 phase duration leading to a lengthening of G1 and Tc mean values at the population level, which is reminiscent of what is observed in maturing neural tissue.

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The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint

Discussion

In this paper we detailed a live imaging strategy allowing us to follow the behavior of single NPCs over 48 hours in their endogenous environment. We show that the cell cycle duration and, more interestingly, the length of each phase is very heterogeneous and with no apparent links between phase lengths within one cell cycle or between mother cells G2 phase and daughter cells G1 phase. Though, we find that G1 phase length increases with cell generations and is the one which contributes mainly to the total cell cycle lengthening. We show that expression of the G2/M regulator CDC25B enhances G1 length heterogeneity in NPCs participating to neural tissue maturation.

Neuroepithelial single cell imaging of the cell cycle in its endogenous environment

Measuring the four phases of the cell cycle in real time with a single cell resolution within a tissue remains challenging. Here, we performed ex ovo live imaging using chick embryo slice cultures [START_REF] Das | High-resolution live imaging of cell behavior in the developing neuroepithelium[END_REF][START_REF] Pituello | Activin A inhibits Pax-6 expression and perturbs cell differentiation in the developing spinal cord in vitro[END_REF]. In our hands, three parameters are then critical: cell cycle biosensor, culture conditions and imaging methods. Dynamic analysis of cell cycle progression by real-time imaging has become feasible with the generation of the FUCCI reporter system [START_REF] Sakaue-Sawano | Visualizing spatiotemporal dynamics of multicellular cell-cycle progression[END_REF] recently improved for the detection of the four phases (FUCCI4, [START_REF] Bajar | Fluorescent indicators for simultaneous reporting of all four cell cycle phases[END_REF]. We did not favor the FUCCI4 strategy because the increased light illumination required for four laser illumination can be detrimental to cell survival. Our biosensor assay combines the mKO-zCdt1 and the NLS-eGFP-PCNA discriminates the four phases of the cell cycle with only two different wavelengths illuminations per time point.

Another critical point is the culture conditions. To ensure cell survival and obtain cell cycle parameters comparable to those measured on fixed tissue, it is important to add 5% FCS and to allow tissue recovery for 12 hours. In such conditions NPCs perform proliferative and neurogenic divisions. Finally, time lapse imaging systems are also critical for cell survival and normal cell behavior. We observed that not only limiting illumination by exciting a focal plane (wide field vs confocal microscope) but also acquisition velocity (confocal vs spinning disk equipped confocal microscope), were crucial to decreasing cell death by phototoxicity (as also described by [START_REF] Icha | Phototoxicity in live fluorescence microscopy, and how to avoid it[END_REF]. Similarly, laser beam pulses frequencies play a role in cell cycle kinetics and survival, this is why we opted for a spinning disk system with laser attenuation preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint [START_REF] Boudreau | Excitation Light Dose Engineering to Reduce Photo-bleaching and Photo-toxicity[END_REF] to reduce the stress to the cells. We nevertheless observed a slightly longer S phase as already described in another study [START_REF] Leung | Apical migration of nuclei during G2 is a prerequisite for all nuclear motion in zebrafish neuroepithelia[END_REF].

The lengthening of the cell cycle results from enhanced heterogeneity

We show that the total cell cycle length exhibits a high degree of heterogeneity, ranging from 9h55min to 24h45 min without apparent patterns or coupling between the phase length except a surprising link between the S and M phase. Such a heterogeneity of the total cell cycle length has already been observed using time lapse imaging in neural stem/progenitor cells including spinal NPCs [START_REF] Wilcock | Mitotic spindle orientation distinguishes stem cell and terminal modes of neuron production in the early spinal cord[END_REF], mice neural stem cells in culture [START_REF] Roccio | Predicting stem cell fate changes by differential cell cycle progression patterns[END_REF], or human nervous system primary tissues and organoids [START_REF] Subramanian | Dynamic behaviour of human neuroepithelial cells in the developing forebrain[END_REF]. This cell cycle heterogeneity is also observed at different levels for each phase of the cell cycle, the phase that contributes the most to the total cell cycle variability being the G1 phase.

Usually, analyses of cell cycle parameters were performed on fixed tissues, considering that neural stem cells are a homogenous population of asynchronous proliferating cells. Using this approximation, these analyses showed that as developmental time progresses, the proliferation rate of neural progenitors decreases and their cell cycle lengthens [START_REF] Molina | Playing with the cell cycle to build the spinal cord[END_REF][START_REF] Kicheva | Developmental Pattern Formation in Phases[END_REF][START_REF] Kicheva | Coordination of progenitor specification and growth in mouse and chick spinal cord[END_REF]. This evolution of the cell cycle length most often associated with differentiation was also observed in various stem cell types [START_REF] Julian | Formula G1: Cell cycle in the driver's seat of stem cell fate determination[END_REF][START_REF] Dalton | Linking the Cell Cycle to Cell Fate Decisions[END_REF]. If the population of NPCs was homogeneous, an increase of the mean cell cycle duration with time would correspond to an increase of the cell cycle duration in each individual NPCs. Instead, we observed that the population of NPCs is heterogeneous, and in this case the increase in the mean cell cycle duration occurring with time correlates with an increase in heterogeneity. To test possible relationships between the four phase lengths, we developed a mathematical model in which Tc length results of the sum of cell cycle phase duration stochastic and independent of each other. The experimental and theoretical Tc survival curves display a very similar pattern, suggesting that indeed cell cycle phase durations are stochastic and independent. One hypothesis is that permitting such stochastic variations at the single cell level is cost efficient for the population, which does not need to strictly control the cell cycle kinetics of each single cell and thereby is probably more robust. These results are reminiscent of experimental data and modeling obtained using NIH3T3 cell cultures that showed that lengthening one phase does not imply lengthening other phases, suggesting that preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint durations of cell cycle phases can be regarded as independent [START_REF] Mura | Mathematical modelling reveals unexpected inheritance and variability patterns of cell cycle parameters in mammalian cells[END_REF]. This is also observed for three independent human cell lines, where each cell cycle phase has been shown to be independent of the others and that cell cycle correspond to a series of uncoupled memoryless phases [START_REF] Chao | Evidence that the human cell cycle is a series of uncoupled, memoryless phases[END_REF].

We propose that i) the total cell cycle length in NPCs corresponds to addition of independent and stochastic phase lengths, ii) the increase of cell cycle length observed during development, is due to an increased heterogeneity of cell cycle length in the NPCs population. This suggests that there is no regulatory system that controls connections between each phase length and that a mechanism increasing cell cycle heterogeneity might be responsible for the modifications observed during stem cell maturation. In the mouse epidermal stem cells, a pronounced heterogeneity of cell cycle length has been recently described using time-lapse [START_REF] Xie | A G1 Sizer Coordinates Growth and Division in the Mouse Epidermis[END_REF].

Their analysis of the 3D volume growth and cell-cycle progression of single epidermal stem cells showed that cell cycle length is controlled by cell growth through a sizer operating in the G1 phase of the cell cycle [START_REF] Xie | A G1 Sizer Coordinates Growth and Division in the Mouse Epidermis[END_REF]. In this case, cell growth heterogeneity would control cell cycle heterogeneity. We can imagine that a similar mechanism takes place in the neuroepithelium. One way to control cell size is to affect cell metabolism, and several links have been described between modification of metabolic pathways and modulation of neurogenic activities during adult neurogenesis [START_REF] Knobloch | Metabolism and neurogenesis[END_REF] or embryonic neurogenesis [START_REF] Fawal | Cross Talk between One-Carbon Metabolism, Eph Signaling, and Histone Methylation Promotes Neural Stem Cell Differentiation[END_REF].

A novel mechanism to control the G1 and cell cycle lengthening

Time lapse analysis showed that even if all cell cycle phase lengths are heterogeneous the S and the G1 phase contribute the most to the total cell cycle heterogeneity, and that the G1 phase is the most affected one upon development. G1 phase heterogeneity has already been observed in neuroepithelial cells in culture [START_REF] Roccio | Predicting stem cell fate changes by differential cell cycle progression patterns[END_REF], in human embryonic stem cells in culture [START_REF] Jang | Control over single-cell distribution of G1 lengths by WNT governs pluripotency[END_REF], and in mouse epidermal stem cell in vivo [START_REF] Xie | A G1 Sizer Coordinates Growth and Division in the Mouse Epidermis[END_REF]. Here we identified a new trigger of the G1 phase lengthening, the CDC25B phosphatase. CDC25B proteins have long been known to regulate G2 phase to mitosis transition by activating CDK1/cyclin B complexes [START_REF] Kumagai | The cdc25 protein controls tyrosine dephosphorylation of the cdc2 protein in a cell-free system[END_REF]. We have shown that the expression of the phosphatase in NPCs correlates spatially and temporally with neurogenesis [START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF][START_REF] Agius | Cell cycle and cell fate in the developing nervous system: the role of CDC25B phosphatase[END_REF][START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF]. In preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10.1101/2020.11.06.370833 doi: bioRxiv preprint agreement with this expression pattern, using both gain and loss of function, we showed that CDC25B is a positive regulator of neurogenesis [START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF][START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF] and contributes to neural tissue aging [START_REF] Azaïs | Timing the spinal cord development with neural progenitor cells losing their proliferative capacity: a theoretical analysis[END_REF][START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF].

Part of CDC25B neurogenic activity is independent of its effect on the cell cycle, however, its full neurogenic potential requires a cell cycle dependent action [START_REF] Bonnet | Neurogenic decisions require a cell cycle independent function of the CDC25B phosphatase[END_REF]. Here we show that CDC25B induces a lengthening of the mean G1 phase duration in a cell cycle dependent manner. It acts by increasing G1 heterogeneity, as illustrated by the fact that exit time is almost doubled and exit rate is more than twice slower than control. The full neurogenic activity of CDC25B will then be the sum of its ability to induce neurogenic division independently of CDK interaction and its action as a maturating factor reducing the proliferative capacities of the NPCs.

Electroporation in chick neural tube leads to mosaic expression. We therefore considered whether part of the G1 heterogeneity observed results from the method we used. The primary activity of CDC25B is to control G2/M transition and thereby affects G2 phase length. In our experiment, the effect observed on G1 heterogeneity is associated with a reduction of the G2 minimal duration in the absence of an effect on the G2 phase heterogeneity (compare the slope of the survival curves, see Fig. 6E and6F). This suggests that the mosaic expression induced by electroporation, does not increase heterogeneity in a non-specific way.

Lengthening of the G1 phase has long been associated with neurogenesis (Kuzmicz-Kowalska and [START_REF] Kuzmicz-Kowalska | Regulation of size and scale in vertebrate spinal cord development[END_REF][START_REF] Molina | Playing with the cell cycle to build the spinal cord[END_REF][START_REF] Takahashi | The cell cycle of the pseudostratified ventricular epithelium of the embryonic murine cerebral wall[END_REF]. Multiple molecular mechanisms link G1 phase length and choice between proliferation and differentiation in multiple stem cell types, including various pluripotent stem cells [START_REF] Julian | Formula G1: Cell cycle in the driver's seat of stem cell fate determination[END_REF][START_REF] Dalton | Linking the Cell Cycle to Cell Fate Decisions[END_REF] and neural stem cells [START_REF] Liu | The cell cycle in stem cell proliferation, pluripotency and differentiation[END_REF].

In the mouse cortex, overexpression of cyclin D1, cyclin E1, or CDK4, increases selfrenewal and inhibits neurogenic differentiation, establishing a link between G1 length and neurogenesis [START_REF] Lange | Cdk4/cyclinD1 overexpression in neural stem cells shortens G1, delays neurogenesis, and promotes the generation and expansion of basal progenitors[END_REF][START_REF] Pilaz | Forced G1-phase reduction alters mode of division, neuron number, and laminar phenotype in the cerebral cortex[END_REF]. In the spinal cord, forced expression of G1-phase regulators (D-type cyclins) inhibited the neural marker Tuj1 expression 24 hours after electroporation [START_REF] Lacomme | NEUROG2 drives cell cycle exit of neuronal precursors by specifically repressing a subset of cyclins acting at the G1 and S phases of the cell cycle[END_REF]. Conversely, NSCs of Cdk2/Cdk4 double-knockout mice displayed an increased propensity for neuronal differentiation, leading to enhanced neurogenic divisions in the brains of the mutant embryos [START_REF] Lim | Loss of Cdk2 and Cdk4 induces a switch from proliferation to differentiation in neural stem cells[END_REF]. Thus, by lengthening the G1 phase, CDC25B might create conditions for differentiation.

preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

The copyright holder for this this version posted November 6, 2020. ; https://doi.org/10. 1101/2020.11.06.370833 doi: bioRxiv preprint .11.06.370833 doi: bioRxiv preprint What is the link between G1 phase length and cell fate? In hESC it has been shown that differentiation capacity varies during progression of the G1 phase [START_REF] Pauklin | The cell-cycle state of stem cells determines cell fate propensity[END_REF]. In this case, G1 lengthening has been associated with modifications of TGF signaling cascades and ectoderm vs endo mesoderm cell fate choice. They showed that Smad2,3 activates mesoderm and endoderm commitment in early G1, and that ectoderm commitment occurs in late G1, coinciding with nuclear exclusion of SMAD2,3 in a Cyclin D dependent manner. Alternatively, CDKs may regulate by phosphorylation the activity of transcription factors involved in proliferation or differentiation. For example, CDK-dependent phosphorylation of Sox2 at Serine 39 inhibits neurogenesis, and CDK decrease leads to proteolytically cleaved Sox2 species that promotes neurogenesis [START_REF] Lim | Cyclin-Dependent Kinase-Dependent Phosphorylation of Sox2 at Serine 39 Regulates Neurogenesis[END_REF]. In addition, cyclin A-and B-dependent kinases phosphorylate the proneural basic helix-loop-helix transcription factor Neurogenin 2 (Ngn2) and inhibit its ability to bind neurogenic genes and to promote neurogenesis [START_REF] Ali | Cell cycle-regulated multi-site phosphorylation of Neurogenin 2 coordinates cell cycling with differentiation during neurogenesis[END_REF]. Interestingly, Ngn2 can repress expression of cyclins D1 and E2, suggesting the presence of a positive-feedback loop [START_REF] Lacomme | NEUROG2 drives cell cycle exit of neuronal precursors by specifically repressing a subset of cyclins acting at the G1 and S phases of the cell cycle[END_REF]. In CDC25B gain of function experiments, the total cell cycle duration was increased at least partly as a consequence of G1 phase lengthening. In our recent theoretical studies [START_REF] Azaïs | Timing the spinal cord development with neural progenitor cells losing their proliferative capacity: a theoretical analysis[END_REF], we proposed that CDC25B expression in neural progenitors progressively restricts proliferative capacities of the cell. We propose that CDC25B reiteration at each cell cycle will indirectly increase G1 phase heterogeneity, lengthening cell cycle duration associated with differentiation and participating to tissue maturation. Such a mechanism is likely to be applicable to other developing organs or tissues as well as to stem cells including human stem cells

Acknowledgement

We want to thank Bernard Ducommun, Alice Davy and Xavier Morin for critical review of the manuscript. Caroline Monod for improving the English. We thank the CBI preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

Figure 5 preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

FIGURE LEGEND Figure 1 .

 LEGEND1 FIGURE LEGEND

Figure 2 .

 2 Figure 2. Time lapse observation of NPCs displaying three types of cell division after mitosis. A) Still picture of a time lapse video showing the expression of the sensor in the nucleus of NPCs that allows identification of the four cell cycle phases and the corresponding position within the neuroepithelium. B) Schematic representation of the interkinetic nuclear movement (INM) and of the three modes of division (PP, PN and NN) occurring in the neural tube. MZ, mantle zone. VZ, ventricular zone. C) Still images of a E2.25 culture time lapse movie showing the three modes of divisions observed in the spinal cord from progenitors P1, P2, P3: proliferative (PP -P 2.1 -P 2.2 ), asymmetric neurogenic (PN -P 3.1 -N 3.2 ) and terminal neurogenic (NN -N 1.1 -N 1.2 ). Scale bars represent 10 µm.

Figure 3 .

 3 Figure 3. Neural progenitor cell population is highly heterogeneous regarding the cell cycle. A) Scatter dot-plot representing distributed lengths of total (Tc) and cell cycle phases for E2.25 embryonic spinal cord cells observed in live imaging. Colored dots in

Figure 4 .

 4 Figure 4. G1 phase lengthens in daughter cells. A) Scatter dot-plot representing distributed lengths of cell cycle phases for proliferating NPCs measured in live imaging E2.25 cultures linked to cell fate. Red dots represent NPCs performing PP divisions in the following cell cycle, green dots represent a NPC that gives rise to a progenitor and a cell with a long G1 (asymmetric division), and black dots corresponds to NPCs with undetermined offspring. The empty dot corresponds to a cell with a G1 length of 1175 min (19h35min) that does not start S phase. B) S c h e m a t i c r e p r e s e n t a t i o n o f Nuclei tracking over two generations of proliferating NPCs. Cell cycle total (Tc) and phase lengths (G1 in blue, S in orange, G2 in grey and M in yellow) are calculated from time-lapse images. Proportion of each phase in the whole cell cycle according to Tc is represented inside the circles. Light grey represents undetermined values. C) Bar plot illustrating G1 phase length of mother (green) and daughter (blue and orange) NPCs.Arrowheads point to daughter cells with a shorter G1 phase as compared to their

Figure 5 .

 5 Figure 5. Neural progenitor cell population kinetics changes in older embryos. A) Scatter dot-plot representing distributed lengths of total (Tc) and cell cycle phases for embryonic spinal cord nuclei measured from E3 spinal cord cultures live imaging. Colored dots in the Tc column can be found in cell cycle phases columns and correspond to the same tracked nucleus. Empty dots represent cells with G1 phase length superior to 1000 min and correspond to those cells that do not start S phase. B-C-D) Frequency distribution of G1 (B), S (C) and G2 (D) phase lengths comparing E2.25 spinal cord cultures (dark blue) and E3 spinal cord cultures (light blue).

Figure 6 .

 6 Figure 6. CDC25B gain-of-function increases G1 phase length heterogeneity. A-B) Scatter dot-plot representing distributed lengths of total (Tc) and cell cycle phases measured in live imaging E2.25 cultures for cells electroporated with CDC25B (A) or CDC25B ΔCDK (B). Colored dots in the Tc column can be found in the cell cycle phase columns and correspond to the same tracked nucleus. Empty dots represent cells with a G1 length longer than 1000 minutes (16h40min) that do not start S-phase. C) Box and whiskers plots (5-95 percentile) illustrating the comparison of total (Tc) and cell cycle phase lengths for Control, CDC25B, CDC25B ΔCDK gain-of-function. Brackets represent values in fixed tissues. The top and the bottom of each box indicate upper and lower quartiles, respectively; the horizontal line represents the median and the cross indicates the mean value. (D-H) Survival curves and histogram representation comparing Control (black), CDC25B (red), and CDC25B CDK (blue) conditions for the Tc (D), G1 (E), G2 (F), S (G), and M (H), phases. The vertical dotted line in histograms reports the average of the distribution.

  (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

	bioRxiv preprint	doi:	; https://doi.org/10.1101/2020.11.06.370833	this version posted November 6, 2020.	The copyright holder for this
				The normality of the data
	sets was determined, analyses of variance performed and the appropriate t-test
	method used. Values shown are mean ± standard error of the mean (s.e.m.).
	Significance was assessed by performing the Student-Mann-Whitney test. The
	significance values are: *P<0.05; **P<0.01; ***P<0.001. See also SI.

preprint

  Toulouse Regional Imaging platform (TRI) for technical support. We acknowledge the Developmental Studies Hybridoma Bank, created by the NICHD of the NIH and maintained at The University of Iowa, Department of Biology, Iowa City, IA 52242, for supplying monoclonal antibodies. Work in FP's laboratory is supported by the Centre National de la Recherche Scientifique, Université P. Sabatier, Ministère de L'Enseignement Supérieur et de la Recherche (MESR) et Agence Nationale de la Recherche (ANR-19-CE16-0006-01). Angie Molina was a recipient of IDEX UNITI and preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.Fondation ARC. Fréderic Bonnet was recipient of MESR studentships. The funding entities had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

	bioRxiv preprint	doi:	; https://doi.org/10.1101/2020.11.06.370833	this version posted November 6, 2020.	The copyright holder for this

Table 1

 1 (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

	bioRxiv preprint	doi:	; https://doi.org/10.1101/2020.11.06.370833	this version posted November 6, 2020.	The copyright holder for this
			Figure 6

preprint

Author Contributions

A.M., F.B., F.P., J.G. and E.A. conceived experiments. A.M., F.B., and E.A. performed experiments. A.M., F.B., F.P. J.G. and E.A wrote the manuscript. F.P., J.G., V.L. and E.A secured funding. S.B.V and V.L. provided expertise and feedback

Declaration of interests

The authors declare no competing interests.

preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.


Yung-Ta Chen

Yao-Jen Chang

Hideyuki Murakami

Stéphane Gorsse

An-Chou Yeh

Designing high entropy superalloys for elevated temperature application

Keywords: high entropy superalloys, superalloys, cost performance, high temperature

In the context of cast alloy development for high temperature applications, high entropy superalloys (HESA) have exhibited superior cost specific tensile strength than that of superalloys such as CM247LC. Compositions of HESA are distinctively different from those of cast superalloys with higher contents of Fe and Ti, making HESA cheaper and lighter. Comparing to superalloys, although HESA has adopted the template of FCC-structured () matrix and coherent L1 2 -structured () precipitates,  is enriched with solutes with higher intrinsic strength, rendering positive lattice misfit, and the high entropy  matrix may have attributed a good combination of strength and ductility.

properties Superalloys are important materials for gas turbine engines in aerospace and energy industries [START_REF] Reed | The superalloys: fundamentals and applications[END_REF]. Since the homologous temperature of superalloys has already reached the limit, efforts on alloy development have focused on improving the cost-performance by reducing the use of expensive elements such as rhenium (Re) [START_REF] Wahl | Superalloys Int. Symp[END_REF].

For example, CMSX-8 [START_REF] Wahl | Superalloys Int. Symp[END_REF] was developed as a more economical version of CMSX-4, which has been widely used in industry, and with respect to the cost specific tensile strength, the advantage of CMSX-8 over that of CMSX-4 was about 1.6 times.

However, the Ni-based system constrains the composition design space for reduction in cost and density. To search for better cost-performance alloys, High Entropy Alloy (HEA) allows the exploitation of vast composition space [START_REF] Yeh | [END_REF][4][START_REF] Gao | High-entropy alloys: fundamentals and applications[END_REF][START_REF] Miracle | [END_REF][7][8], among different types of HEAs [9], Refractory High Entropy Alloys (RHEAs) possess high melting points and are promising structural materials, however, the development of RHEAs has yet to reach high-temperature oxidation resistance and a balance between high-temperature strength and room temperature ductility [START_REF] Miracle | [END_REF]10], on the other hand, 3d-TM HEAs possess the best specific strength and appears to be the most promising HEA for structural application [9]. The most well-known 3d-TM HEA is CoCrFeMnNi, although single-phase CoCrFeMnNi can possess attractive combination of strength and toughness from ambient to cryogenic temperatures [11],

the strength of single-phase HEA is relatively weak at elevated temperatures [START_REF] Miracle | [END_REF]12,13]. At high temperatures, diffusion driven phase transformation and creep need to be considered [START_REF] Reed | The superalloys: fundamentals and applications[END_REF], FCC phase with lower intrinsic diffusivity than BCC phase should be the choice of structure basis for high temperature alloys [14]. Wu et al. [15] demonstrated that tensile yield strength of CoCrFeNi, CoCrMnNi, CoCrNi, CoNi and Ni dropped sharply with increasing temperature, and Otto et al. [12] found that the yield strength of CoCrFeMnNi was only 76 MPa at 600 o C. So, strengthening mechanisms such as solid solution strengthening, work hardening and grain refinement, are not effective at elevated temperatures.

Conventional superalloys have relied on ordered Ni 3 (Al,Ti)-based L1 2 -structured () precipitates to strengthen the FCC-structured () matrix. And, this type of precipitates has been introduced in HEA systems. Shun et al. [16] and Gwalani et al. [17][18][19][20] investigated Al 0.3 CoCrFeNi, and observed precipitation of fine  precipitates in the  matrix; however, the  phase could only be stable up to 550 o C and was destabilized and replaced by B2-structured () phase at 700 o C. He et al. [21,22] found that addition of Al and Ti in CoCrFeNi could induce formation of  phase in the  matrix, however, excessive addition of these two elements could promote the formation of brittle L2 1 -structured (Ni, Co) 2 TiAl phase. Yeh et al. [23,24] systematically studied the Al x Co 1.5 CrFeNi 1.5 Ti (0.5-x) systems, higher Ti/Al ratio could induce higher  phase fraction and higher hardness; however,  phase was found to be unstable and could transform into brittle η phase after prolonged exposure at 900 o C; higher Al/Ti ratio could promote  phase formation instead. Daoud and Manzoni et al. [25][26][27][28][29] investigated a similar alloy AlCo 2.5 Cr 0.8 Fe 1.5 Ni 3.6 Ti 0.6 , which contained a  matrix with 46 % of  phase and 5 % of  phase by volumes; its yield strength at 750 o C was 473 MPa, although this value appeared to surpass those of solid solution strengthened type superalloys such as 800H and Inconel617, it was still weaker than more advanced superalloys such as CM247LC [30], this was mainly due to relatively low fractions and low solvus of  phase. During the course of developing wrought HEA [31,32], low  solvus had promoted chemical instability at the front of mobile grain boundaries and resulted the formation of cellular - precipitates at grain boundaries during thermo-mechanical processes; this could cause severe hot ductility drop at around 750 o C. So, the development of HEA for high temperature application has been focused on cast type alloy to avoid hot ductility drop associated with cellular precipitation at grain boundaries.

To further increase the elevated temperature strength to compete with superalloys, both the solvus and fractions of the  phase in HEA need to be increased; however, the volume fractions and solvus temperature of the  phase could be restricted by the increase in entropy of the system within the composition range of 5.0 at. %  x  35.0 at. % [START_REF] Gao | High-entropy alloys: fundamentals and applications[END_REF][START_REF] Miracle | [END_REF]. To break through this restriction, alloy design has been shifted to Ni-rich HEA with Ni content beyond 35 at. % [START_REF] Gao | High-entropy alloys: fundamentals and applications[END_REF][START_REF] Miracle | [END_REF]. CALPHAD prediction indicates that an increase in Ni content beyond 35 at % could allow further adjustment in the composition to increase the thermal stability of  matrix and  precipitates, Figure 1(a) and 1(b). Furthermore, the configurational entropy of the nominal composition can still meet the broader definition of HEA, i.e. ΔS conf. > 1.5 R, where R is the universal gas constant. So, the development of Ni-rich HEA has taken the advantage of a broader definition of HEA in order to further expand the alloy design space, as shown in Figure 2(a). Since the microstructure of Ni-rich HEA with  matrix and  precipitates resembles that of advanced superalloys, the name "High Entropy Superalloys (HESA)" has been given to this class of materials [23,[33][34][35][36].

In the context of cast alloys, selected compositions of HESA, i.e. HESA-1 [33], HESA-2 [33] and HESA-3 [34] are shown in Table I. Compositions of HESA and traditional superalloys evolved from different origins; superalloys were designed from the Ni-based corner of the multidimensional phase diagram, and HESA was designed from the high entropy compositions near center of the same phase diagram. Although compositions of superalloys and HESA appeared to converge at the mid-point between the center and the corner of the phase diagram, HESA had taken the path of lower cost and lower density with higher Fe and Ti contents than those of cast superalloys, while cast superalloys accommodated more and more refractory  formers up to the 5 th generation alloy [START_REF] Kawagishi | Superalloys Int. Symp[END_REF]; to visualize the compositions difference, Figure 2(b) shows general contents of elements in 71 cast superalloys (including the latest 5 th generation alloy) [START_REF] Reed | The superalloys: fundamentals and applications[END_REF][START_REF] Kawagishi | Superalloys Int. Symp[END_REF] and HESA [33,34]. Take CM247LC as example, it contains 0 at % Fe and 0.9 at % Ti; HESA-3 contains 8.9 at % Fe and 5.8 at % Ti.

HESA-3 had a density of 7.96 g/cm 3 , and its raw materials cost was 61 % cheaper than that of CM247LC. The Ni contents of HESAs were all higher than 35 at. %, and this allowed significant increase in the solvus temperature and phase fraction of  phase, Figure 1, without the formation of detrimental phases such as , , Laves, TCP phases [START_REF] Reed | The superalloys: fundamentals and applications[END_REF]. The enhanced phase stability of HESA could further accommodate minor W, Mo to strengthen the FCC-structured  matrix, and minor Ta or Nb to strengthen L1 2 -structured  phase in HESA-2 and HESA-3; the solvus temperatures of  phase in HESA-2 and HESA-3 were 1194 o C [33] and 1199 o C [34], respectively, similar to those of superalloys [START_REF] Reed | The superalloys: fundamentals and applications[END_REF]. Furthermore, the fractions of  phase in HESA-2 and HESA-3 were close to 70 vol. %, which is considered as the optimum fraction for high temperature strengthening in cast superalloys [START_REF] Reed | The superalloys: fundamentals and applications[END_REF].

The excellent phase stability of HESA had been confirmed by long term isothermal ageing at temperatures from 700 o C to 1100 o C for up to 1000 hours, only  precipitates in  matrix could be observed without formation of detrimental intermetallic phases [33]. Furthermore, the  phase with high Ti content resulted higher anti-phase boundary (APB) energy than that of conventional superalloys [START_REF] Chandran | [END_REF], which could retard superdislocations and strengthen  phase, for example the APB energies of HESA-1 and superalloy CM247LC were 0.25 and 0.19 J/m 2 , respectively [33], this had resulted higher hardness of HESA L1 2 -structured  phase comparing to that of CM247LC measured by nano-indentation tests [33]. On the other hand, high entropy compositions in the  matrix of HESAs could lead to lower stacking fault energy, which could hinder dislocation cross-slip during deformation by increasing the spacing between the partial dislocations [34] and enhance the toughness by formation of twins [7,11,39]. By comparing to those of conventional HEAs (5.0 at. %  x  35.0 at. %), elevated temperature tensile yield strengths of HESAs were about 200 MPa in average higher than those of reported HEAs from room temperature to 750 o C [34], and a positive temperature dependence of the yield strength of HESAs was identified due to high fractions of L1 2 -structured  phase. Furthermore, the creep rupture life of HESA-3 under 982 o C and 159 MPa was 114 hours, which was similar to several first generation superalloys; the steady state creep rate of HESA-3 was competitive against CMSX-2 [40], this was attributed to strengthening from thermally stable  precipitates, low stacking fault energy of the  matrix, leading to a high creep activation energy of 290 kJ/mol [34]. Due to high solute contents in  phase, lattice misfits between FCC-structured  matrix and L1 2 -structured  phase in HESA were positive, during creep at 982 o C,  phase rafted in parallel to the applied stress direction; this is opposite to that of advanced superalloys with negative misfit between  matrix and  precipitates [START_REF] Reed | The superalloys: fundamentals and applications[END_REF]. Furthermore, HESAs had the ability to form continuous and protective Al 2 O 3 layer after high temperature exposure; the oxidation and corrosion resistances were comparable to that of CM247LC [41]. So, HESAs can possess excellent elevated temperature phase stability and surface stabilities; their high temperature strength can be comparable to those of some commercial superalloys.

The concept of HESA has led to several recent studies in exploring the strengthening contributions from L1 2 -structured  phase in HEAs, however, these works mostly focused on room temperature properties and have shown that this approach could be effective in increasing the tensile strength while retaining a good level of tensile ductility [29,[42][43][44], e.g.  precipitates strengthened Al(Co, Fe, Ni) 12.3 Ti exhibited a tensile yield strength of 1028 MPa with an elongation up to 47.8 % [42]. On the other hand, microstructure optimization through heat treatment can also be important in order to balance strength and ductility; Zhang et al. [36] studied a Hf containing HESA Al 0.56 CoCrFeNi 3.36 Ti 0.56 Hf 0.015 , in as-cast condition, its ultimate tensile strength could reach 960 MPa at 750 o C but with only 3 % fracture strain; by contrast, the directional solidified form of HESA-3 subjected to post heat treatment to optimize the microstructure could possess a tensile yield strength of 855 MPa at 750 o C with fracture strain greater than 20 % [34]. Due to its relatively low elemental cost and density, with respect to 750 o C yield strength, HESA-3 performed better than all reported HEA data with the same testing condition and could achieve a 3 times increase in cost-specific tensile strength comparing to that of CM247LC, Fig. 3 [30,31,34,45], most importantly, its tensile elongation can be 2.7 times that of CM247LC, making HESA very attractive for elevated temperature applications.

Based on the current state of the art, the development of HESA technology has combined several alloy design strategies; viewpoints of these strategies are described and discussed in the following:

Utilize low cost elements such as Fe to lower down the cost of material:

In an alloy system based on Co-Ni, although Co is relatively expensive, it is utilized in conventional Ni-based superalloys to stabilize the  matrix and also lower the stacking fault energy [START_REF] Reed | The superalloys: fundamentals and applications[END_REF]. Co is also a common element in HEA, while HEA composition space provides the freedom to include significant fractions of cheap elements that can lower the cost. It is important to balance the cost with desired microstructure (FCC-structured  matrix and L1 2 -structured  precipitates) and sufficient phase stability. Fe is an ideal choice of cheap element serving as matrix element, which acts mainly as a substitution to Ni or Co in conventional superalloys, however, Fe is also known to destabilize  phase [START_REF] Durand-Charre | The microstructure of superalloys[END_REF]; CALPHAD has been a useful tool to ensure that Fe-bearing HESA could retain sufficient fractions of stable  phase. Another potential issue regarding to the cost is associated with processing, HESA reported are cast alloys, and the yield of casting can be affected by alloy compositions greatly [START_REF] Reed | The superalloys: fundamentals and applications[END_REF][START_REF] Reed | [END_REF]48]. In advanced superalloys, the tendency to form freckles defects can be related to both the content of refractory elements and their ratios of solid-liquid partitioning, since convection caused by density difference with the mushy zone can cause nucleation of stray grains with undesired chemical compositions. Therefore, HESA with low level of refractories might exhibit good castability for complex part, thorough investigations on castability of HESA should be conducted in the future.

Utilize light weight elements such as Al, Ti, Cr to lower down the density:

Ni-rich HEA design space presents the freedom to utilize higher level of light elements in the system to decrease the density of the alloy. However, the contents of light elements need to be controlled carefully in order to maintain the phase stability. In traditional superalloys metallurgy, Al and Ti are strong  formers, and phase instability associated with TCP phases can be related to the degree of supersaturation of solutes in  matrix [START_REF] Reed | The superalloys: fundamentals and applications[END_REF]49]; Cr also promotes detrimental intermetallic formations such as  [START_REF] Reed | The superalloys: fundamentals and applications[END_REF]; CALPHAD can be an extremely useful tool in maintaining phase stability while performing alloy design for light weight.

And, HESA may possess an advantage over superalloys with a higher entropy matrix to accommodate more solid solutions, hence phase stability for the  matrix [33,50].

Design through elemental partitioning characteristics between  matrix and 

precipitate:

Constituent elements in HESAs possess characteristic partitioning tendencies, e.g. Al and Ti partition to  precipitates and Co, Cr, Fe partition to  matrix, Table II. The partitioning ratios of these elements have significant meanings to the design of HESA. First of all, the degree of entropy in  matrix and  precipitates can be affected; the  matrix needs to be high entropy to utilize the beneficial effects of HEAs, and the  phase has to retain medium entropy state to possess thermal stability. This is demonstrated in Table I & II, from HESA-0 to HESA-1, the substitution of 2.0 at % Ni by 2.0 at % Ti can affect the partitioning characteristics for other elements, resulting an increase in the entropy of  matrix, and a decrease in the entropy for  phase, which in turn could enhance its thermal stability. Furthermore, higher Ti content in  phase can promote an increase in APB energy to further strengthen the  phase. The partitioning ratios can also affect the lattice misfit between the  matrix and  phase, it can influence the morphology of  phase and the evolution of coarsening under stress [START_REF] Reed | The superalloys: fundamentals and applications[END_REF], HESAs developed so far all possess positive misfit, e.g. lattice misfit of HESA-3 was 0.08 % at 982 o C [34].

It has been that positive misfit alloys can possess better cyclic creep resistance than negative misfit alloys [START_REF] Giraud | Superalloys Int. Symp[END_REF][START_REF] Cormier | Superalloys Int. Symp[END_REF], since cyclic creep might be closer to some actual turbine engine operating conditions, HESA should be evaluated against cyclic creep in the future. against oxidation [41]. On the other hand, HESA-1 possesses higher Cr activity and is a Cr 2 O 3 former; HESA-1 can be extremely resistant against slat-coated hot corrosion [41]. The activities of Al and Cr can be influenced by constituent elements in the system, for example, Si addition can greatly enhance both the Al and Cr activity [START_REF] Wang | [END_REF], so the addition of Si may provide further flexibility in alloy design of HESA in the future.

Strengthening through hierarchical microstructure development:

Recent studies have shown that composition complexity in HEAs can induce effective heterogeneous microstructure strengthening at room temperature through phase transformation pathway design [44,[54][55][56][57]. HESA may also utilize its distinct stoichiometric  compositional complexity to accommodate  formers in the metastable condition, this could be done by quenching process and subsequent ageing in order to induce  particles formation inside . Previous studies have shown that this concept could be beneficial for elevated temperature strengthening by retarding coarsening kinetics of  phase [56], and compression creep life at elevated temperature could be improved [58]. So, strengthening through hierarchical microstructures should be explored for HESA in the future, since microstructure strengthening can be an effective mean to provide further strengthening without the use of expensive heavy elements.

Comparing the tensile strength, ductility, cost, density, and surface stability between HESA-3 and CM247LC superalloy, a combined performances chart has been constructed in Figure 4. HESA-3 can outperform CM247LC superalloy in most of these aspects and may be even more useful for applications when cost, density, and ductility are more demanding than high temperature strength. Recent studies have shown that cast type HESA has shown potential for high temperature applications, similar approach may also apply to develop wrought HESA in the future, since the increase in  solvus can be expected to minimize the cellular structure embrittlement at grain boundaries [31]. Recently, artificial intelligence machine learning approach has been utilized to design HEA compositions and to optimize several single property [59,60], the growing interest in the research field of HESA will generate more experimental data, and artificial intelligence machine learning approach can be employed in the future to develop more advanced high entropy superalloys with customized and balanced properties.

4 .

 4 Design oxidation and corrosion resistances of HESAs by promoting the formation of Al 2 O 3 or Cr 2 O 3 layers: Alumina and chromia are effective barriers against oxidation and corrosion, whether Al 2 O 3 or Cr 2 O 3 layers can be protective depends on the compactness and continuity of the external oxide layer. For the formation of protective Al 2 O 3 , certain level of Al content and Al activity are required, for example, HESA-2 and HESA-3 are both Al 2 O 3 formers and can perform as well as advanced superalloys

Figure 1 .

 1 Figure 1. CALPHAD predictions for HESA development (a) isopleth section of the Al-Co-Cr-Fe-Ni-Ti senary system along the line connecting HEA(Al0.2Ti0.3) and HESA-3 in Table I showing that Ni-rich HEA allows alloy design for greater FCC + L1 2 structure phase field, and (b) increase in solvus temperature and L1 2 equilibrium fraction at 800°C with Ni content along the same compositional trajectory as (a).

Figure 2 .

 2 Figure 2. (a) compositions of cast superalloys (including 5 th generation superalloys) vs HESA. (b) The configurational entropy of the nominal composition can meet the broader definition of HEA (Ni x (AlCoCrFeTi) y ), i.e. ΔS conf. > 1.5 R with Ni content greater than 35 at %.

Acknowledgement

Authors would like to acknowledge funding supports from Ministry of Science and Technology (MOST) in Taiwan under Grant MOST108-2218-E-007-005, MOST109-2634-F-007-024, and MOST109-2811-E-007-500; the "High Entropy Materials Center" from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education.