Laura Digan

Pierre Horgue

Gérald Debenest

Sébastien Pommier

Etienne Paul

Claire Dumas

AN IMPROVED HYDRODYNAMIC MODEL FOR PERCOLATION AND DRAINAGE DYNAMICS IN LEACH BED REACTORS

Keywords: Solid-state anaerobic processes, leach-bed reactor, dual-porosity model, water retention, macroporous reservoir

This study concerns the hydrodynamic modelling of percolation and drainage cycles in the context of solid-state anaerobic digestion and fermentation (VFA platform) of household wastes (HSW) in leach bed reactors. The focus was made on the characterization of the water distribution and hydrodynamic properties of the bed. A numerical model, set up with experimental data, highlighted that the simple dual-porosity model was not able to correctly reproduce all the hydrodynamic features and particularly the drainage dynamics. The model was improved by adding a reservoir (immobile) water fraction to macroporosity and allowed to correctly simulate dynamics. This model enabled to explain more precisely the water behaviour during percolation processes and these results should be useful for driving either solid-state anaerobic digestion or fermentation reactors.

INTRODUCTION

Municipal solid wastes include a high organic fraction, especially coming from the residual household solid wastes. Organic wastes are usually transformed into biogas for heat and power Municipal solid wastes include a high organic fraction, especially coming from the residual household solid wastes.

Organic wastes are usually transformed into biogas for heat and power generation through anaerobic digestion but an alternative approach is carbon resource recovery. The LBR is a solid-state fermentation process in which the solid substrate remains static while the leachate is recirculated through the bed. This concept was initiated by Chynoweth et al. (1992) whose objective was to develop a process overcoming usual limitations encountered with high solid substrates. . Recirculation aims at maintaining a sufficient humidity in the bed, facilitating inoculation and mass diffusion between the solid and the flowing liquid [START_REF] Jha | Research Advances in Dry Anaerobic Digestion Process of Solid Organic Wastes[END_REF][START_REF] Francois | Leachate Recirculation Effects on Waste Degradation: Study on Columns[END_REF][START_REF] Lü | Impact of Recycled Effluent on the Hydrolysis during Anaerobic Digestion of Vegetable and Flower Waste[END_REF][START_REF] Stabnikova | Anaerobic Digestion of Food Waste in a Hybrid Anaerobic Solid-liquid System with Leachate Recirculation in an Acidogenic Reactor[END_REF]. The main highlighted advantages of this technology are: (i) its simple design and thus its relatively low cost [START_REF] Dogan | Performance of Leaching Bed Reactor Converting the Organic Fraction of Municipal Solid Waste to Organic Acids and Alcohols[END_REF][START_REF] Cysneiros | The Effect of PH Control and "Hydraulic Flush" on Hydrolysis and Volatile Fatty Acids (VFA) Production and Profile in Anaerobic Leach Bed Reactors Digesting a High Solids Content Substrate[END_REF][START_REF] Yap | Pilot-Scale Testing of a Leachbed for Anaerobic Digestion of Livestock Residues on-Farm[END_REF]) ; (ii) the improvement of bacterial activity due to wetting [START_REF] Pommier | A Logistic Model for the Prediction of the Influence of Water on the Solid Waste Methanization in Landfills[END_REF]), (iii) the acceleration of the first degradation stages, particularly acidogenesis [START_REF] Francois | Leachate Recirculation Effects on Waste Degradation: Study on Columns[END_REF]. For VFAs production application, it has the advantage to enable simultaneous production and withdrawal of VFAs. In the LBR, a fraction of water is flowing between solid particles (macro-scale) while another fraction which is not flowing enables to wet the solid (micro-scale). VFAs are produced in contact of the substrate, in the micropores; then they are transferred to the macropores and can be recovered via the liquid flow [START_REF] Veeken | Effect of Substrate-Seed Mixing and Leachate Recirculation on Solid State Digestion of Biowaste[END_REF]. Dual-porosity models are usually proposed to simplify the description of water flow in a porous medium and has been previously used for modelling water behaviour in waste [START_REF] Tinet | Experimental and Theoretical Assessment of the Multi-Domain Flow Behaviour in a Waste Body during Leachate Infiltration[END_REF], Han 2011). The model remains difficult to parametrize correctly since it requires exhaustive data such as relative permeability and retention curves (Gerke and Van Genuchten (1993)) . In the present study, the protocol and the dual-porosity model proposed by [START_REF] Shewani | Assessment of Percolation through a Solid Leach Bed in Dry Batch Anaerobic Digestion Processes[END_REF] were adapted and improved in order to better capture the experimental results. Waste beds were evaluated in terms of physical structure, and water flow through the wastes materials. .The model parameters were calculated from experimental data in order to compare the wastes, and to be able to predict wetting and drainage process to improve biological reactions.

EXPERIMENTAL MATERIAL AND METHODS

Waste materials

Two different wastes were used in this study: real wastes (from household wastes treatment centre Cavigny (Manche, France) and artificial household wastes. Real wastes were sorted to remove the largest pieces, before being introduced into the percolation column. Artificial household solid wastes (aHSW) were made from commercial products in order to mimic real household solid wastes. The composition was established according to a national household wastes characterization campaign (ADEME 2010). Once completely reconstituted, the aHSW were stored at ambient temperature for one week before use in order to simulate pre-fermented wastes such as the rHSW received. For percolation operations, no mechanical pre-treatment was carried out. The wastes were chemically characterized in terms of total solids (TS) and volatile solids (VS). For rHSW and aHSW samples, the drying was performed at 80°C until obtaining a constant mass, in order to prevent any loss of the waste's organic fraction by combustion [START_REF] Stoltz | Moisture Retention Properties of Municipal Solid Waste in Relation to Compression[END_REF]). The VS content was determined for all wastes by ignition of previously dried samples at 550°C for 2 hours.

Experimental set-up

The experimental device for the hydraulic tests was the same as that used by [START_REF] Shewani | Assessment of Percolation through a Solid Leach Bed in Dry Batch Anaerobic Digestion Processes[END_REF] and composed of a steel column with a diameter of 0.40 m and a height of 0.75 m. A grid placed at the bottom of the column allowed to stop large solid particles from flowing out and clogging the exit nozzles. A drainage layer composed of gravel (size of 6 to 14 mm) was added under the rHSW and aHSW beds to facilitate the leachate flow and avoid clogging by particles. The gravel layer had a height of 0.04 m, representing 10% of the total bed height. The dry solids volume represented decreasingly 13.7, 7.1% m3.m-3 of total volume for respectively rHSW, aHSW. These values suggest a high total porosity fraction whatever the wastes considered (more than 86%). For feeding of the column, a tank containing water was connected to a peristaltic pump (Masterflex 77800-50).Water could be injected either through the bottom of the column (immersion phase for pre-wetting) directly from the pump to the central exit nozzle, or on top of the waste bed (percolation assays for hydrodynamic characterisation. In all cases, the liquid was drained through the five exit nozzles and collected into a drainage tank placed under the column. The feeding and drainage tanks were weighed continuously and the weights of injected and drained water were recorded every 20 seconds.

Hydraulic test protocol

The protocol for the hydraulic characterisation of the waste beds consisted in 5 successive steps : immersion and drainage, percolation-drainage, bed compaction (to mimick a supplementary upper layer of waste exerting a pressure over the bed), immersion and drainage, and finally percolation-drainage step. The wastes bed height was measured all along the experiment. Settlement was supposed to be physical and not due to waste biodegradation. This assumption was made because: (i) no inoculum was introduced in the process and (ii) the total time of the experiment was relatively small compared to typical biodegradation times (one week). Thus, the dry solid mass was considered to remain constant [START_REF] Shewani | Assessment of Percolation through a Solid Leach Bed in Dry Batch Anaerobic Digestion Processes[END_REF][START_REF] Stoltz | Moisture Retention Properties of Municipal Solid Waste in Relation to Compression[END_REF].

Calculations

From these measurements, the micropores volume (Vm) was calculated as the sum of initial water content with the injected volume which remained trapped. The dry solids volume (VDS) was estimated as the ratio between the dry solids mass (calculated with the total solids content measured prior to the experiment) and the dry solids particles density (ρSP). ρSP (kgTS.L-1) was computed as proposed by [START_REF] Agnew | The Physical Properties of Compost[END_REF].

𝜌 𝑆𝑃 = ( 𝑉𝑆 1.55 + (1 -𝑉𝑆) 2.65 ) -1
Where VS is the volatile solids content expressed in kgVS.kgTS-1. Finally, the macropores volume was deduced using the previously computed values VDS and Vm.

RESULTS AND DISCUSSION

HSW leach beds structure

The waste beds underwent water additions and compaction which modified their structure (total porosity, macropores, and micropores). The three main fractions (dry solids, micropores and macropores volumes) were quantified using the protocol described in Section 2.3 at each step.

Wastes beds settlement and compressibility

A bed settlement occurred during the step 1 of the hydraulic characterization protocol (initial immersion and drainage). The rapid drainage of leachate under the effect of gravity creates a suction that drove the solid matrix towards the bottom , leading to the rearrangement (consolidation) of the bed. Understanding and measuring the effects of the settlement process on physical properties is crucial. They alter the flow behaviour and this has been already studied [START_REF] Stoltz | Liquid and Gas Permeabilities of Unsaturated Municipal Solid Waste under Compression[END_REF]. For HSW, the first settlement might be mostly due to the 18 kg weights added on top of the beds to avoid flotation during step 1. From state CL 0 to CL 1, the bed porosity decreased from 86.3% to 81.1% for rHSW and from 92.9 to 88.9% for aHSW. No further settlement was observed over the first percolation series. At CL 2 stage, the total bed porosity (micro and macroporosity) accounted for 79.5% and 87.6% of total bed volume for rHSW and aHSW respectively. The compaction slightly amplified bed subsidence (step 4). For both HSWs, the bed volume did not decrease over the second percolation series. The total volume lost represented 33% and 43% of the initial bed volume for rHSW and aHSW respectively.

It is assumed that compressibility is characterized by the relative volume loss due on one hand to physical compression, and on the other hand to water drainage. The less the initial dry solids (or the more the initial void) volume fraction, the more the total volume loss. Compressibility was thus a wastedependent parameter. Indeed, this parameter is driven by the waste composition (i.e. organic and mineral matter contents) [START_REF] Chen | Aging and Compressibility of Municipal Solid Wastes[END_REF], the elements size and their arrangement inside the matrix. At industrial scale, the bottom layer in the wastes bed is susceptible to compaction due to layers staking, and this could foster the reduction of leachate flow.

Wastes beds porosity evolution with compaction

The total porosity was globally high (from 79.4 to 86.3% for rHSW and from 87.6% to 92.9% for aHSW) at every stage of the experiment. After the first compaction (CL 1), the microporosity of the beds reached 56.8% and 48.0 % of the total volume for rHSW and aHSW respectively. At compaction level CL 2, microporosity fraction increased, representing 65.7% and 57.8% of total bed volume for rHSW and aHSW respectively. This increase of microporosity is made to the detriment of macroporosity fraction accounting for rHSW from 24.2% at CL 1 to 13.6% at CL 2, and for aHSW from 40.9 to 30.0% which suggests a bed rearrangement. Macropores volume was partially converted into microporous volume, which affects hydrodynamic properties of the medium. These results are consistent with those of [START_REF] Stoltz | Moisture Retention Properties of Municipal Solid Waste in Relation to Compression[END_REF] who studied the evolution of pore size distribution with compression. They observed that mechanical compression of the solid material induced an increase of smaller pores and a decrease of larger pores. Since the fluid phases flow in the macropores, the reduction of macroporous volume may affect the water flow through the material [START_REF] Reddy | Hydraulic Conductivity of MSW in Landfills[END_REF]. At the same time, a gain in microporosity may increase the water retention capacity and could foster efficient contact (due to higher surface) between the substrate and the bacterial populations.

Behaviour of leach-bed with respect to water

Waste imbibition, micropores saturation

From the experimental masses of water injected in the leach bed and of leachate recovered, it is possible to calculate the amount of injected water retained in the wastes leach bed. Figure 2 shows a typical evolution of the total water content over cumulated contact time. For the immersion-drainage step, the contact time was defined as the sum of injection time, rest time and the drainage time at which 90% of the total drained volume was collected. For each percolation-drainage cycle, the contact time was equal to the injection time added to the drainage time at which 90% of the total drained volume was collected. The cumulated contact time was thus the sum of each contact time (for a series of experiments).

𝐶𝑜𝑛𝑡𝑎𝑐𝑡 𝑡𝑖𝑚𝑒 = 𝑖𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒 + (𝑟𝑒𝑠𝑡 𝑡𝑖𝑚𝑒) + 𝑑𝑟𝑎𝑖𝑛𝑎𝑔𝑒 𝑡𝑖𝑚𝑒 (90%)

Successive injection and drainage phases led to a progressive increase of total water retained in the bed due to the imbibition of the waste. From the total water content evolution in time, the dynamic and static water contributions were dissociated using the values of water trapped in the solid waste bed after each percolation-drainage cycle. This allowed to evaluate the imbibition dynamics of the waste. Numerical simulations were then used to determine the filling rate of the microporosity 𝛼 𝑚𝑖𝑐𝑟𝑜 (see Section 3.3.2).

Following the microsaturation against total cumulated contact time shows that the time needed to reach 80% microsaturation is around 3 days which is relatively short compared to the characteristic time of anaerobic digestion process which generally runs over more than 20 days. However, acidogenic fermentation processes are operated for a few days only and the transient wetting period of 3 days could reduce the overall performance. During the compaction step, a small volume of water trapped in the microporosity flowed out of the waste beds due to the pressure exerted. At the same time, the microporosity volume increased (see Section 3.1.2) and therefore, micropores saturation fell down from 100% and was over 89% for all waste beds After compaction, the filling behaviour was similar to the one observed before compaction.

Hydraulic conductivity, mobile water analysis

Hydraulic conductivity reflects the ability of a fluid to flow through a multiphase material [START_REF] Richard | Air-Filled Porosity and Permeability Relationships during Solid-State Fermentation[END_REF]). As described in previous works [START_REF] Shewani | Assessment of Percolation through a Solid Leach Bed in Dry Batch Anaerobic Digestion Processes[END_REF][START_REF] Solé | Hydromechanical Behaviour of a Heterogeneous Compacted Soil: Experimental Observations and Modelling[END_REF], the apparent (or effective) hydraulic conductivity (KL) is the relationship between the volume of active water (that is flowing) inside the porous medium and the flow rate applied during percolation assays. An accurate characterisation of KL allows to predict water volume used for transport. This volume is necessary to correctly predict water transfer between macro-and microporosity and solute transfer (such as VFA, see [START_REF] Shewani | Assessment of Solute Transfer Between Static and Dynamic Water During Percolation Through a Solid Leach Bed in Dry Batch Anaerobic Digestion Processes[END_REF] (non characterized in this study). A good knowledge of water and flow distribution is then useful to adapt the leachate management strategy to the objective of the process (washing VFAs or increasing the concentration).

KL is defined as the product of the intrinsic hydraulic conductivity (kM) (which considers a saturated porous medium) and relative hydraulic conductivity (or permeability) (kr,L) :

𝐾 𝐿 = 𝑘 𝑀 ⏟ intrinsic conductivity . 𝑘 𝑟,𝐿 ⏟ relative conductivity
While kM is an intrinsic function of medium parameters (porosity, tortuosity, pore size distribution and shape), kr,L is a function of medium parameters and dynamic variables such as macropores saturation [START_REF] Wu | Multiphase Fluids in Porous Media[END_REF]). The apparent conductivity KL was directly deduced from the experimental flow rate applied. For both cases CL 1 and CL 2, the aHSW bed showed lower macropores saturations than rHSW which means that the conductivity of aHSW was higher and would be able to accept larger flow rate, without overflow on the reactor sides. This was particularly true in the rHSW-CL 2 case where pores were almost saturated for the highest flow rate (macropores saturation > 0.8) while it remains relatively unsaturated for aHSW (macropores saturation < 0.4). The fact that the aHSW bed can accept higher flow rates is possibly due to a more homogeneous structure related to the reconstitution of an artificial HSW. In a real case, as for rHSW, the wastes bed is heterogeneous, composed of elements having various sizes which may therefore show lower apparent hydraulic conductivity.

Modelling water behaviour in wastes leach-beds

Experiments allowed to observe water behaviour during percolation and drainage in wastes beds. By implementing a model, the objective was to describe more precisely the experimental observations, to predict water retention and water transfer and to correctly reproduce wetting and drainage processes. This can help in predicting the coupling of water transport phenomena with the biological reactions present during the fermentation/anaerobic digestion process.

Limitation of simplified dual-porosity model applied to household solid wastes

In a previous study [START_REF] Shewani | Assessment of Percolation through a Solid Leach Bed in Dry Batch Anaerobic Digestion Processes[END_REF], a simplified capillary-free dual-porosity model was used to simulate water evolution in solid waste beds during series of percolation-drainage cycles.

In the present study, the simplified dual-porosity model was applied to real and artificial household wastes (rHSW, aHSW). The comparison between experimental and numerical simulation of dynamic water curves showed that whatever the wastes and compaction level considered, the water dynamics were not completely reproduced (see Figure 1) especially the drainage part as observed by [START_REF] Shewani | Assessment of Percolation through a Solid Leach Bed in Dry Batch Anaerobic Digestion Processes[END_REF] for cattle manure. Indeed, the drainage dynamics depend both on relative permeability and water retention curves of the two porosities which are not handled in the simplified dual porosity model . The drainage dynamics, which were numerically too fast compared to the experimental observations, cannot be calibrated independently using only relative permeability curve. Moreover, the observation of the experimental drainage curves showed that whatever the flowrate applied, the drainage dynamics were similar. The similarity between the curves suggested that the "slow drainage part" is independent from the flow rate applied.

Implementing reservoir water to the mathematical model: description of the proposed model

In this work, the dual-porosity model was improved to obtain a more realistic and predictive model of the drainage process. For that purpose, it was hypothesized that during the percolation process a part of the water located inside macroporosity is not actually flowing but temporarily immobile in the internal cavities of the waste and hereby called: reservoir water. In the standard dual porosity model (Gerke and Van Genuchten 1993), when percolation occurs, the mobile water content increases such as the head pressure inducing water transfer from macro to micro-porosity (to equilibrate macro-head pressure with the micro-head pressure). When injection is stopped, the reduction of saturation in macro-porosity reduce macro-head pressure inducing a reverse water transfer from micro-to macro porosity. The system reaches the equilibrium when gravity forces in macro-porosity is balanced by capillary forces and when head pressure in both macro and micro-porosity are at the equilibrium (which generally correspond to high level of saturation in micro-porosity and low level in macro-porosity since capillary effects are higher in micropores). In the proposed model, the micro-porosity of usual dual-porosity model is dissociated into two porosities, (i) the static water which remains trapped even after drainage and (ii) the reservoir which is trapped temporarily when mobile water is flowing. This dissociation is made possible by considering that the filling and drainage time of the mobile water are negligible compared to that of the reservoir water.

The 3 conservation equations numerically related to saturation (S) are:

𝜖 𝑀𝑎𝑐𝑟𝑜 𝜕𝑆 𝑀𝑎𝑐𝑟𝑜 𝜕𝑡 ⏟
Mobile macroporosity saturation

+ 𝛻. 𝑈 𝑤𝑎𝑡𝑒𝑟 ⏟

Mobile water transport

= -𝑞 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 ⏟

Mobilereservoir exchange

-𝑞 𝑚𝑖𝑐𝑟𝑜 ⏟

Mobile -𝑠tatic exchange (Equation 1)

𝜖 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 𝜕𝑆 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 𝜕𝑡 ⏟

Macroporous reservoir saturation

= 𝑞 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 ⏟

Mobilereservoir exchange (Equation 2)

𝜖 𝑚𝑖𝑐𝑟𝑜 𝜕𝑆 𝑀𝑖𝑐𝑟𝑜 𝜕𝑡 ⏟ Micro𝑝𝑜𝑟𝑒𝑠 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑞 𝑚𝑖𝑐𝑟𝑜 ⏟
Mobile-static exchange (Equation 3)

Where 𝜖 𝑀𝑎𝑐𝑟𝑜 , 𝜖 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 and 𝜖 𝑚𝑖𝑐𝑟𝑜 are the "mobile" macroporosity, the "reservoir" macroporosity and the microporosity fractions, respectively.

A first order model is applied for the mobile-reservoir exchange term 𝑞 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 : 4)

𝑞 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 = { 𝛼 𝑟𝑒𝑠,
And the mobile-static exchange term 𝑞 𝑚𝑖𝑐𝑟𝑜 (exclusively in charge since water remains trapped in microporosity):

𝑞 𝑚𝑖𝑐𝑟𝑜 = 𝛼 𝑚𝑖𝑐𝑟𝑜 ⏟ Exchange coefficient for micropores charge (1 -𝑆 𝑚𝑖𝑐𝑟𝑜 ⏟ Micropores saturation
) (Equation 5)

𝛼 𝑟𝑒𝑠,𝑐ℎ𝑎𝑟𝑔𝑒 and 𝛼 𝑟𝑒𝑠,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 (s -1 ) stand respectively for the exchange coefficient between "mobile" and "reservoir" macroporous water during the charge and discharge cycles. 𝛼 𝑚𝑖𝑐𝑟𝑜 is the exchange coefficient between "mobile" macroporous water and static water. 𝑆 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 and 𝑆 𝑚𝑖𝑐𝑟𝑜 (m 3 .m -3 ) are the macroporous reservoir and micropores saturations, respectively.

The water-mobile velocity 𝑈 𝑤𝑎𝑡𝑒𝑟 (m.s -1 ) is modelled and computed using the generalized Darcy's law with a classical Brooks and Corey (power law) model for relative permeability [START_REF] Brooks | Hydraulic properties of porous media[END_REF]:

𝑈 𝑤𝑎𝑡𝑒𝑟 ⏟

Mobile water velocity = 𝐾 𝐿 ⏟ Hydraulic conductivity .

𝑆 𝑀𝑎𝑐𝑟𝑜 𝑝 ⏟ Mobile macroporosity saturation (Equation 6)

Where 𝐾 𝐿 (m.s -1 ) is the hydraulic conductivity of the porous medium, 𝑆 𝑀𝑎𝑐𝑟𝑜 (m 3 .m -3 ) is the mobile macroporous water saturation, and 𝑝 is the Brooks and Corey coefficient. The Brooks and Corey parameters 𝐾 𝐿 and 𝑝 are evaluated in order to fit experimental points available. This allows the evaluation of the mobile water content (macrosaturation) for a given flow rate during numerical simulation. The Brooks and Corey model is one of the models used for permeability (and therefore hydraulic conductivity) correlations. [START_REF] Stoltz | Moisture Retention Properties of Municipal Solid Waste in Relation to Compression[END_REF] also calibrated this type of model with real municipal solid wastes for drainage retention properties and concluded that it was applicable to these wastes.

For a given waste composition, all the parameters need to be characterized by experimental measurements: the 3 porosities (𝜖 𝑀𝑎𝑐𝑟𝑜 , 𝜖 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 and 𝜖 𝑚𝑖𝑐𝑟𝑜 ), the 3 exchange rates (𝛼 𝑟𝑒𝑠,𝑐ℎ𝑎𝑟𝑔𝑒 , 𝛼 𝑟𝑒𝑠,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 and 𝛼 𝑚𝑖𝑐𝑟𝑜 ) and the coefficients (𝐾 𝐿 and 𝑝) for the relative permeability law. An 8parameter optimization is complex to set up and would require excessive computation times. Moreover, characteristic times between processes are different (imbibition of the waste is much slower than filling/emptying the reservoir part and the mobile saturation variations are fast and considered as instantaneous) which allows a progressive parametrisation as described in Section 3.3.3.

Application of improved dual-porosity model to HSW

In this part, it is considered that static/dynamic water decomposition has been delineated in independent experiments as described in Section 3.2.1 (𝜖 𝑚𝑖𝑐𝑟𝑜 and 𝛼 𝑚𝑖𝑐𝑟𝑜 are already characterized) and only the dynamic water evolution (which cannot be reproduced by simplified model) is studied. To determine the reservoir macroporosity, the experimental drainage curves are time-shifted and plotted such as initial time corresponds to the moment when injection is stopped.

In these conditions, the drainage curves are similar for all flow rates tested, i.e. starting with a quasiinstantaneous drainage of a part of the water content followed by an inflection of the curve which indicates the beginning of the slower drainage part. The distinction between fast and slow drainage part is purely conceptual and cannot be determined precisely. From the experimental data, we determine the beginning of the slower drainage as the moment when the drainage flow-rate measurement reaches the experimental precision (0.01 L/min) which corresponds in our case to 10% of the maximal drainage flow rate measured. In this study, the evaluated reservoir water content is equal to 2.28 L ±0.12. The reservoir porosity 𝜖 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 is then directly computed from reservoir water volume evaluated. 𝜖 𝑀𝑎𝑐𝑟𝑜 is simply deduced from the already known microporosity and solid fractions. This hypothesis allows the decomposition of dynamic water into mobile and reservoir macroporous water.

From this decomposition, the Brooks and Corey parameters (𝐾 𝐿 and 𝑝) can be directly fitted using the series of plateaus (as described in Section 3.2.2) while the charge 𝛼 𝑟𝑒𝑠,𝑐ℎ𝑎𝑟𝑔𝑒 and discharge 𝛼 𝑟𝑒𝑠,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 rate are calibrated using numerical simulations.

In Figure 2, a comparison of dynamic water retention from experiments and numerical simulations are presented for both rHSW and aHSW at two compaction levels (CL 1 and CL 2). The comparison between simulated and experimental data reveals a quite good representation of the percolation and drainage dynamics whatever the state of the beds and the wastes considered.

The general behaviour for both wastes are similar with the same charge rate of the reservoir macroporosity (𝛼 𝑟𝑒𝑠,𝑐ℎ𝑎𝑟𝑔𝑒 =1.29 day -1 ). The discharge of reservoir macroporosity was a little bit slower for rHSW 𝛼 𝑟𝑒𝑠,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 =0.26 day -1 than for aHSW 𝛼 𝑟𝑒𝑠,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 =0.35 day -1 . These observations were consistent with the higher hydraulic conductivity for aHSW than rHSW (53.1 cm.h -1 and 43.4 cm.h -1 respectively).

Note that for both wastes, the second percolation cycle at low flow rate (6L/h) shows higher water content than for the last percolation cycle although the flow rate is identical (Figure 8). This highlights that partial wetting of the substrate has a non negligible influence on dynamic saturation during the first phase of imbibition Compaction seems to have no influence on the charging rate of reservoir water whatever the wastes considered (rHSW or aHSW). However, it affects discharge rate of reservoir macroporous water in the case of aHSW with a decrease from 0.35 to 0.17 day -1 . Compaction involved a rearrangement of the bed structure that might make the reservoirs drainage slow. This was not the case for rHSW beds.

CONCLUSIONS

In this study, the various water dynamics occurring during percolation and drainage through solid wastes leach-beds were investigated for different types of wastes under two compaction levels. The simplified capillary-free dual-porosity model was not able to completely reproduce the water dynamics, particularly the drainage dynamics. Thus the model has been extended by adding an immobile (reservoir) fraction to macroporosity which to calibrate the model using only water content measurements without retention curves.

An improved experimental procedure was developed to correctly evaluate the effective parameters described in the model. The model enabled to correctly simulate dynamics for all configurations and to explain more precisely the behaviour of leachate and water during leaching processes. The new description of water flow highlighted the presence of water in macroporous reservoirs. It is important for leachate recirculation strategy in wastes digestion context.

Figure 1 .

 1 Figure 1. An example of dynamic water modelling with classical porous medium model.

Figure 2 .

 2 Figure 2. Measured and simulated evolution of dynamic water retention over a percolation-drainage series for rHSW and aHSW. Dynamic water is plotted for all the different percolation flow rates.

  𝑐ℎ𝑎𝑟𝑔𝑒 ⏟

	1 -	𝑆 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 ⏟		if charge
	Exchange coefficient for reservoir charge (		Macroporous reservoir saturation	)	(Equation
	-𝛼 𝑟𝑒𝑠,𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 ⏟	.	𝑆 𝑀𝑎𝑐𝑟𝑜,𝑟𝑒𝑠 ⏟	if discharge
	Exchange coefficient	Macroporous reservoir
	for reservoir discharge		saturation

AKNOWLEDGEMENTS

This work was supported by the project RECOWER funded by the Carnot Institute 3BCAR. The authors want to acknowledge French research ministry for Laura Digan PhD financial support. The authors would like to acknowledge also Anil Shewani, Zhe Li, Matthieu Peyre-Lavigne, Mansour Bounouba, Evrard Mengelle, Simon Dubos, Chantha Kim, Michel Mauret and Xavier Lefebvre for their numerous contributions to the work.


Safa Hayouni

Christophe Michon
email: cmichon@unistra.fr

Didier Morvan

Virginie Bellière-Baca

Francine Agbossou-Niedercorn

Homogeneous palladium-catalyzed enantioselective hydrogenation of 5methylenhydantoin for the synthesis of L-Valine

In this article, we present the development of a synthetic methodology based on homogeneous catalysis for the preparation of enantioenriched L-Valine aminoacid. The enantioselective hydrogenation of 5-methylenhydantoin has been developed through broad screenings of chiral ligands, metal precursors and reaction conditions including scale-up experiments and recyclability studies. A palladium catalyzed asymmetric hydrogenation of 5-methylenhydantoin afforded the corresponding hydrogenated product in a 70 % enantiomeric excess using a substrate/catalyst ratio of 500/1. A partial racemization was observed upon hydrolysis and recovery of L-Valine.

Introduction

Chiral amino acids are key molecules in the pharmaceutical, food, cosmetic and agricultural industries. 1 Due to increasing costs and sustainability issues, the feedstuff industry has gradually developed reduced protein diets for animals. Such strategy has led to a growing demand of L-Valine which is implied in several vital functions in animals. [START_REF] Efsa Feedap Panel | EFSA Panel on Additives and Products or Substances used in Animal Feed). Scientific Opinion on the safety and efficacy of L-valine produced by Escherichia coli NITE SD 00066 for all animal species[END_REF] Indeed, the use of L-Valine in reduced protein diets has been shown to increase the feed conversion and therefore the animal body weight while reducing water consumption and nitrogen waste excretions. Among hydantoins, which are saturated heterocycles comprising 2 lactam functions, 5-substituted hydantoins can be found in a wide range of natural and synthetic chemicals of biological and pharmaceutical interests. More particularly, the simple and low cost 5-substituted hydantoins have been useful intermediates in the synthesis of aminoacids. 3 Though the asymmetric hydrogenation of 5-ylidenhydantoins allows a direct access to enantioenriched aminoacids, it has scarcely been studied. 4 In this article, we present the development of a synthetic methodology based on homogeneous catalysis for the preparation of enantioenriched L-Valine 3 based on a catalyzed asymmetric hydrogenation of 5-methylenhydantoin 1 5 into 2 6 and a subsequent hydrolysis (Scheme 1).

Scheme 1 Enantioselective synthesis of L-Valine 3 through asymmetric hydrogenation of hydantoin 1 and hydrolysis of 2.

Results and discussion

Due to solubility issues (Table S1), the asymmetric hydrogenation of 5-methylenehydantoin 1 was studied in CH3OH, i-PrOH and 1,4-dioxane. At first, we screened various privileged catalysts based on iridium, cobalt and nickel but did not observe any significant conversion and enantioselectivity (Scheme S1). Afterwards, we tried rhodium based catalysts combining [Rh(COD)2]BF4 precursor and specific ligands like BIBOP, 7 UREAphos and METAMORPhos bifunctional phosphoramidites 8 or Zhaophos, [9][10][11] a ferrocene based diphosphine, bearing appended thiourea groups able to interact with one of the lactam function of 1. Though the hydrogenations proceeded in low to quantitative conversions, there was none or low enantioselectivities (0-13% ee) (Scheme S2 and Table S2). According several reports of Zhang et al. on the asymmetric hydrogenation of 3-substituted maleinimides, 9 maleic anhydrides 10 and β-substituted α,β-unsaturated lactams, 11 the failure of such supramolecular bifunctional approach was somehow surprising but tetrasubstituted alkenes like hydantoin 1 are known to be challenging substrates. 7,12 In addition, substrate 1 is a planar molecule and the two methyl substituents are not introducing great steric effects. By comparison, catalysts based on palladium proved to be more active and selective according to the screening of a selection of 15 diphosphine ligands L1-L15 (Scheme 2). Whether the racemic L1 confirmed the chirality from the ligand controlled the stereoselectivity of the hydrogenation, ligands L4-L7 allowed the asymmetric hydrogenation of 5-methylenehydantoin 1 in high conversions and average enantioselectivities at a hydrogen pressure of 100 bar. When the latter was decreased to 30 bar, a significant increase of enantiomeric excesses was observed. It was worth to note L4-L7 were all C2-symmetric diphosphines and comprised chiral phosphorous atoms bearing bulky electron donor alkyl substituents. The latter are likely to have a significant contribution to the enantioselective process thanks to weak noncovalent attractive interactions 13 between the substrate 1 and catalyst's chiral ligand while the palladium centre would coordinate the alkene moiety 4b and activate hydrogen. By affording hydrogenated product 2 in high conversion and good ee, the ligand L6 based on a quinoxaline backbone was selected for further developments.

Among the several acid additives which were subsequently screened (Table 1, entries 1-8), the (S)-(+)-1,1′-Binaphthyl-2,2′-diyl hydrogenphosphate 4 afforded product 2 in a 49% conversion and 50% ee (entry 5). However, the (R)-camphor sulfonic acid (CSA) proved to be the best acid additive when a single equivalent of (R)-CSA was used as respect to the Pd(TFA)2 precursor (entries 8-10). Indeed, the hydrogenated product was obtained in a full conversion and with an enantioselectivity of 70% ee at 30 bar of hydrogen (entry 9). It was worth to note the configuration of product 2 was always (S), independently of the additive used. The asymmetric hydrogenation of 5-methylenhydantoin 1 implying the palladium catalyst based on ligand L6 was next optimized by adjusting the reaction conditions. Regarding the solvent, the use of i-PrOH afforded the best conversions and enantioselectivities by comparison to CH3OH, 1,4-dioxane or mixtures of i-PrOH and CH3OH or trifluoroethanol (TFE). We noticed strict anhydrous conditions were required in order to get a high asymmetric induction (Table S3). The preferred reaction temperature was found at 80 °C and the hydrogen pressure could be set to 30 bar (Tables S4 andS5).

By using these optimized reaction conditions, we studied the effect of the substrate/catalyst and additive/catalyst ratios on the asymmetric hydrogenation of 5-methylenhydantoin 1 (Table 2, entries 1-7). We demonstrated the asymmetric hydrogenation of 1 proceeded well on a 1.84 mmol scale with a catalyst loading decreased to 0.2 mol% by reaching a substrate/catalyst ratio of 500/1 and an additive/catalyst ratio of 2 (entry 5). Indeed, the use of higher or lower additive/catalyst ratios was not favorable (entries 1-4,6) and the enantioselectivity was lower with a substrate/catalyst ratio of 200 (entry 7). No racemization of hydrogenated product 2 was observed while using long reaction times.

The catalyst recycling was first studied through attempts to separate the catalyst from the product by centrifugation but this resulted in poorly active catalytic species. However, we found that, once a reaction was finished, the cautious and direct addition of a new i-PrOH solution of reactant 1 into the autoclave allowed a possible recycling (Table 3). Moreover, the addition of a subsequent catalytic amount of (R)-CSA (1 mol%) was necessary at the beginning of each cycle in order to allow the catalytic reaction to proceed more effectively. However, a gradual decrease of the conversions in 2 and therefore of the catalyst activity (TON) was noticed. (%) [a] Ee (%) [b] 1

Cycle

Conv. (%) [a] Ee (%) [b] TON [c] 1 [d] The hydrolysis of chiral hydantoin 2 was first performed using NaOH in water at 180 °C (Scheme 3, procedure A). 14 A full conversion of hydantoin 2 in L-Valine 3 was only observed after 144 hours of reaction. Afterwards, an acidification with HCl followed by a purification by distillation under vacuum were required in order to separate the product from NaCl by-product and recover L-Valine 3 in a moderate yield. HPLC analyses showed such hydrolysis resulted in a partial racemization of the substrate, L-Valine 3 being isolated with a 33% ee starting from hydantoin 2 with an enantiopurity of 70% ee. Therefore, the hydrolysis of hydantoin 2 was performed following a different procedure using Ba(OH)2 in water at 115 °C (Scheme 3, procedure B). Indeed, the hydrolysis of enantiopure 5-difluoromethyl-5-methyl-hydantoin 15 and 5-phenyl-5-(trifluoromethyl)hydantoin 16 were previously performed without any racemization. In our case, we noticed 96 hours of reaction were required in order to reach a full conversion of hydantoin 2 in the L-Valine product 3. The latter was recovered in a fair yield after acidification with H2SO4, filtration of the BaSO4 and subsequent flash chromatography on an acidic resin like Amberlyst 15. However, a partial racemization was again observed by HPLC analyses, L-Valine 3 being isolated with a 25% ee starting from hydantoin 2 with an enantiopurity of 59% ee. Furthermore, we noticed the purity of reagent 2, e.g. a material purified by flash chromatography or sublimation, had no influence on the observed racemization. By comparison to the previous hydrolysis of enantiopure 5-difluoromethyl-5-methylhydantoin 15 and 5-phenyl-5-(trifluoromethyl)hydantoin, 16 such a racemization may be explained by the substitution pattern of the asymmetric carbon, hydantoin 2 comprising a tertiary stereocenter and compounds of reference 15,16 having quaternary asymmetric carbons. Therefore, the NaOH or Ba(OH)2 base used for the hydrolysis may deprotonate the tertiary stereocenter of hydantoin 2 and allow a racemization. Interestingly, it was previously noticed that other derivatives like tetrahydroisoquinoline hydantoins or 3,5-disubstituted thiohydantoins 17 gradually racemize in aqueous solutions at acid, basic or neutral pH. Nevertheless, according several reports, 18 a hydrolysis of hydantoin 2 through the use of enzymatic methods like the "Hydantoinase Process" is likely to afford L-Valine 3 without racemization.

Conclusion

We developed a synthetic methodology for the preparation of enantioenriched L-Valine 3 based on a catalyzed asymmetric hydrogenation of 5-methylenhydantoin 1 and a subsequent hydrolysis. Selected palladium homogeneous catalysts based on chiral diphosphine ligands were the single effective species allowing the hydrogenation of 5-methylenhydantoin in high yields and good enantioselectivities. Though L-Valine was obtained through hydrolysis of the hydrogenated product, a significant racemization was observed upon hydrolysis. Overall, these results are encouraging considering the asymmetric hydrogenation of tetrasubstituted alkenes like 5methylenhydantoin 1 is challenging. From an industrial perspective, two main goals remain to fulfil in order to produce L-Valine in bulk quantities at a low cost below 10 €/kg. First, a highly active and enantioselective catalytic hydrogenation, i.e. with high turnover numbers and enantiomeric excesses, is desired. Second, the hydrogenated product 2 need to be rapidly hydrolyzed using enzymatic methods to avoid racemization of L-Valine 3. Finally, further applications in flow chemistry 19 may be appreciated.

Scheme 3 .

 3 Scheme 3. Recovery of L-Valine 3 by hydrolysis of hydantoin 2.

Table 1 .

 1 Acid additive screening for the asymmetric hydrogenation of 5methylenhydantoin 1.

	Entry	Additive	Conv.	Ee
		(mol%)	(%) [a]	(%) [b]
	1	pTsOH (2)	97	27
	2	Benzoic acid (2)	3	-
	3	(R)-(-)-O-Acetylmandelic acid (2)	39	0
	4	(S)-(+)-Mandelic acid (2)	61	0
	5	(S)-(+)-1,1′-Binaphthyl-2,2′-diyl	49	50
		hydrogenphosphate 4 (2)
	6	(R)-(-)-1,1′-Binaphthyl-2,2′-diyl	55	31
		hydrogenphosphate 4 (2)
	7	(S)-CSA (2)	100	42
	8	(R)-CSA (2)	100	44
	9	(R)-CSA (1)	100	61 (70 c )
	10	(R)-CSA (0.5)	100	38

[a] Determined by GC;

[b]

Determined by HPLC on a DAICEL CSP CHIRALPAK ID.

[c]

at 30 bar of H2.

Table 2 .

 2 Effect of the substrate/catalyst and additive/catalyst ratios on the asymmetric hydrogenation of 5-methylenhydantoin 1.

	Entry	substrate	additive	solvent	time	conv.
		/catalyst	/catalyst	(mL)	(h)

Table 3 .

 3 Catalyst recycling.

		500	1	10	48	18	-
	2	500	5	6	38	9	-
	3	500	10	7	38	2	-
	4	500	20	7	38	1	-
	5	500	2	6	120	75	70
	6	200	1	6	62	6	-
	7	200	2	4	62	100	62
	[a] Determined by GC; [b] Determined by HPLC on a DAICEL CSP
	CHIRALPAK ID.

Scheme 2. Catalyst screening for the asymmetric hydrogenation of 5-methylenhydantoin 1.

Acknowledgments

This research was first funded by ADISSEO France SAS. The CNRS, the Chevreul Institute (FR 2638), the Ministère de l'Enseignement Supérieur et de la Recherche, the Région Hautsde-France and the FEDER are acknowledged for supporting and funding partially this work. Mrs C. Delabre (UCCS) is thanked for GC and GC-MS analyses and some HPLC separations.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found on the web (free access).


Eric Van Leen

Victor

Pietro Florencia

Bellaïche Yohanns
email: yohanns.bellaiche@curie.fr

Oriented cell divisions in epithelia: from force generation to force anisotropy by tension, shape and vertices

Mitotic spindle orientation has been linked to asymmetric cell divisions, tissue morphogenesis and homeostasis. The canonical pathway to orient the mitotic spindle is composed of the cortical recruitment factor NuMA and the molecular motor dynein, which exerts pulling forces on astral microtubules to orient the spindle. Recent work has defined a novel role for NuMA as a direct contributor to force generation. In addition, the exploration of geometrical and physical cues combined with the study of classical polarity pathways has led to deeper insights into the upstream regulation of spindle orientation. Here, we focus on how cell shape, junctions and mechanical tension act to orient spindle pulling forces in epithelia, and discuss different roles for spindle orientation in epithelia.

Introduction

During animal development, complex epithelial structures are formed by regulating the spatiotemporal dynamics of cell rearrangements, cell shape changes and cell division [START_REF] Lecuit | Orchestrating size and shape during morphogenesis[END_REF][START_REF] Guirao | Unified quantitative characterization of epithelial tissue development[END_REF][START_REF] Pietro | Regulation of mitotic spindle orientation: an integrated view[END_REF][START_REF] Heisenberg | Forces in Tissue Morphogenesis and Patterning[END_REF]. Intensive work highlighted that the orientation of cell division plays essential roles in fate asymmetric cell divisions and tissue architecture, and allowed the establishment of a paradigm for spindle orientation within the cell [START_REF] Pietro | Regulation of mitotic spindle orientation: an integrated view[END_REF][START_REF] Xiong | Interplay of Cell Shape and Division Orientation Promotes Robust Morphogenesis of Developing Epithelia[END_REF][START_REF] Morin | Mitotic Spindle Orientation in Asymmetric and Symmetric Cell Divisions during Animal Development[END_REF]. The axis of division is set up by cortical pulling forces acting on astral microtubules (MT) [START_REF] Bosveld | Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis[END_REF][START_REF] Grill | Polarity controls forces governing asymmetric spindle positioning in the Caenorhabditis elegans embryo[END_REF]. Therefore, the orientation of division can be ensured by locating force generators at specific cell cortex locations. While force generation has been attributed to the MT minus-end directed motor dynein, the recruitment task was assigned to NuMA (Mud in Drosophila, Lin-5 in C. elegans), which in turn can be recruited to the cortex by LGN (Pins in Drosophila, GPR-1/2 in C. elegans) and the heterotrimeric G protein Gαi [START_REF] Pietro | Regulation of mitotic spindle orientation: an integrated view[END_REF]. Recently, the relative roles of NuMA and dynein in force generation for spindle orientation have been further deciphered.

In symmetric cell divisions in epithelia, mitotic spindles are often oriented along tissue symmetry axes [START_REF] Gong | Planar cell polarity signalling controls cell division orientation during zebrafish gastrulation[END_REF][START_REF] Mao | Planar polarization of the atypical myosin Dachs orients cell divisions in Drosophila[END_REF]. Classical observations in single cells led to the proposition of Hertwig's rule, which states that cells divide according to their longest axis [START_REF] Hertwig | Das Problem der Befruchtung und der Isotropie des Eies, eine Theory der Vererbung[END_REF][START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF]. While true in many contexts, cell divisions that challenge this rule have been reported [START_REF] Gong | Planar cell polarity signalling controls cell division orientation during zebrafish gastrulation[END_REF][START_REF] Scarpa | Actomyosin-Driven Tension at Compartmental Boundaries Orients Cell Division Independently of Cell Geometry In Vivo[END_REF][START_REF] Finegan | Tissue tension and not interphase cell shape determines cell division orientation in the Drosophila follicular epithelium[END_REF]. Recent work has provided novel insights into whether and how epithelial cells adhere to Hertwig's rule, as well as how tension and polarity are integrated by cells to orient their spindles.

In this review, we first discuss how the cortical forces necessary for oriented cell divisions (OCD) are generated within the cell. Second, we describe recent data exploring how cell shape and local or global tissue tension influence spindle orientation in symmetric divisions in epithelia. Finally, we discuss the function of OCD. For more information on spindle orientation in asymmetric divisions and a more complete oversight of OCD molecular regulators, we refer the readers to recent reviews [START_REF] Pietro | Regulation of mitotic spindle orientation: an integrated view[END_REF][START_REF] Morin | Mitotic Spindle Orientation in Asymmetric and Symmetric Cell Divisions during Animal Development[END_REF].

How are spindle orientation forces generated within the cell?

The current paradigm for force generation involves the recruitment of dynein and its cofactor dynactin to the cell cortex [START_REF] Bosveld | Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis[END_REF][START_REF] Grill | Polarity controls forces governing asymmetric spindle positioning in the Caenorhabditis elegans embryo[END_REF][START_REF] Kiyomitsu | Cortical Dynein and Asymmetric Membrane Elongation Coordinately Position the Spindle in Anaphase[END_REF][START_REF] Kotak | Cortical dynein is critical for proper spindle positioning in human cells[END_REF][START_REF] Okumura | Optogenetic localization of proteins to the cortex in mammalian cells and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF][START_REF] Nguyen-Ngoc | Coupling of cortical dynein and Gα proteins mediates spindle positioning in Caenorhabditis elegans[END_REF]. However, recent studies indicate that cortical dynein recruitment is insufficient for OCD [START_REF] Pirovano | Hexameric NuMA:LGN structures promote multivalent interactions required for planar epithelial divisions[END_REF][START_REF] Seldin | NuMA-microtubule interactions are critical for spindle orientation and the morphogenesis of diverse epidermal structures[END_REF]. Here we discuss recent findings on dynein activity and how its interactors assist dynein in force generation [START_REF] Okumura | Optogenetic localization of proteins to the cortex in mammalian cells and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF][START_REF] Pirovano | Hexameric NuMA:LGN structures promote multivalent interactions required for planar epithelial divisions[END_REF][START_REF] Seldin | NuMA-microtubule interactions are critical for spindle orientation and the morphogenesis of diverse epidermal structures[END_REF][START_REF] Gallini | NuMA Phosphorylation by Aurora-A Orchestrates Spindle Orientation[END_REF][START_REF] Fielmich | Optogenetic localization of proteins to the cortex in C. elegans and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF].

Dynein force regulation and spindle orientation

Work in C. elegans and mammalian cells has led to the identification of different dynein regulators required for spindle orientation such as LIS-1, Nde1/NdeL1, and a subset of dynactin subunits [START_REF] Couwenbergs | Heterotrimeric G protein signaling functions with dynein to promote spindle positioning in C. elegans[END_REF][START_REF] Siller | Lis1/dynactin regulates metaphase spindle orientation in Drosophila neuroblasts[END_REF][START_REF] Yingling | Neuroepithelial stem cell proliferation requires LIS1 for precise spindle orientation and symmetric division[END_REF][START_REF] Moon | LIS1 controls mitosis and mitotic spindle organization via the LIS1-NDEL1-dynein complex[END_REF][START_REF] Di Pietro | An RNAi Screen in a Novel Model of Oriented Divisions Identifies the Actin-Capping Protein Z β as an Essential Regulator of Spindle Orientation[END_REF]. Recent structural analyses showed that dynein can form a ternary complex with dynactin and a cargo adaptor [START_REF] Urnavicius | Cryo-EM shows how dynactin recruits two dyneins for faster movement[END_REF]. In vitro reconstitution indicates that this complex is highly processive and capable of transporting cargo over large distances (Figure 1A) [START_REF] Mckenney | Activation of cytoplasmic dynein motility by dynactin-cargo adapter complexes[END_REF]. Two recent structures of dynein/dynactin complexed with the adapters HOOK3 and BICD2 show that their interaction is facilitated by the coiled-coils of the adapter proteins which run along the length of dynactin [START_REF] Urnavicius | Cryo-EM shows how dynactin recruits two dyneins for faster movement[END_REF]. As BICD2 is not essential for spindle orientation in cultured cells, this raises the question whether HOOK3 or another regulator activates dynein during spindle orientation [START_REF] Di Pietro | An RNAi Screen in a Novel Model of Oriented Divisions Identifies the Actin-Capping Protein Z β as an Essential Regulator of Spindle Orientation[END_REF][START_REF] Olenick | Dynein activators and adaptors at a glance[END_REF]. Furthermore, depending on the adapter, one or two dyneins can be part of the ternary complex. Complexes with two dyneins generate higher forces and walk faster on MT [START_REF] Urnavicius | Cryo-EM shows how dynactin recruits two dyneins for faster movement[END_REF]. The binding of the second dynein is facilitated by the CAPZβ subunit of dynactin (Figure 1A) [START_REF] Urnavicius | Cryo-EM shows how dynactin recruits two dyneins for faster movement[END_REF]. Interestingly, recent experiments revealed that CAPZβ regulates spindle orientation in vivo, suggesting that the capacity of binding two dyneins contributes to OCD [START_REF] Di Pietro | An RNAi Screen in a Novel Model of Oriented Divisions Identifies the Actin-Capping Protein Z β as an Essential Regulator of Spindle Orientation[END_REF].

New roles for NuMA during spindle orientation

The respective roles of dynein and NuMA during spindle orientation have recently been investigated by optogenetically positioning components of the spindle orientation machinery at the cortex [START_REF] Okumura | Optogenetic localization of proteins to the cortex in mammalian cells and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF][START_REF] Fielmich | Optogenetic localization of proteins to the cortex in C. elegans and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF]. In these studies, optogenetic recruitment of NuMA to the cortex was sufficient to orient the mitotic spindle [START_REF] Okumura | Optogenetic localization of proteins to the cortex in mammalian cells and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF][START_REF] Fielmich | Optogenetic localization of proteins to the cortex in C. elegans and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF]. By contrast and in agreement with other studies [START_REF] Pirovano | Hexameric NuMA:LGN structures promote multivalent interactions required for planar epithelial divisions[END_REF][START_REF] Seldin | NuMA-microtubule interactions are critical for spindle orientation and the morphogenesis of diverse epidermal structures[END_REF], recruitment of the dynein heavy chain/dynactin to the cortex was insufficient to generate pulling forces on the spindle [START_REF] Okumura | Optogenetic localization of proteins to the cortex in mammalian cells and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF][START_REF] Fielmich | Optogenetic localization of proteins to the cortex in C. elegans and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF]. This suggests that NuMA is not only required for dynein recruitment, but also for force production.

NuMA coiled-coil and MT binding domains are essential for spindle orientation

All NuMA homologs have a coiled-coil domain which has been shown to be required for spindle orientation in Drosophila and HeLa cells [START_REF] Bosveld | Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis[END_REF][START_REF] Okumura | Optogenetic localization of proteins to the cortex in mammalian cells and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF][START_REF] Kiyomitsu | The cortical force-generating machinery: how cortical spindlepulling forces are generated[END_REF]. Therefore, in the light of the recently established ternary dynein complex structure described above, NuMA is a candidate regulator of dynein activity (Figure 1B). Furthermore, NuMA localizes to MT tips in interphase and prometaphase cells, and deletion of the domain responsible for this localization (AA:1811-1985 in human) impaired spindle orientation in cultured keratinocytes and in vivo [START_REF] Seldin | NuMA-microtubule interactions are critical for spindle orientation and the morphogenesis of diverse epidermal structures[END_REF]. In addition, a second NuMA MT binding domain, (AA: 2002-2115 in human) is also essential for spindle orientation in cultured cells [START_REF] Pirovano | Hexameric NuMA:LGN structures promote multivalent interactions required for planar epithelial divisions[END_REF][START_REF] Gallini | NuMA Phosphorylation by Aurora-A Orchestrates Spindle Orientation[END_REF]. Accordingly, this second MT binding is necessary to orient the spindle upon optogenetic recruitment of NuMA to the cortex [START_REF] Okumura | Optogenetic localization of proteins to the cortex in mammalian cells and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF]. Exactly how NuMA and its MT binding domains assist in spindle orientation remains to be defined. For instance, MT tip localized NuMA could regulate MT growth dynamics, cortical capture or cortical dwell time which have all been proposed to regulate spindle orientation [START_REF] Pietro | Regulation of mitotic spindle orientation: an integrated view[END_REF][START_REF] Kwon | Direct Microtubule-Binding by Myosin-10 Orients Centrosomes toward Retraction Fibers and Subcortical Actin Clouds[END_REF][START_REF] Bowman | The Drosophila NuMA Homolog Mud Regulates Spindle Orientation in Asymmetric Cell Division[END_REF].

In summary, these recent data illustrate that MT pulling force generation does not solely rely on dynein, but also requires NuMA. Direct analyses of astral MT dynamics and associated forces, combined with the deletion of the aforementioned NuMA domains and optogenetic recruitment will contribute to a better understanding of dynein regulation in spindle orientation.

How do cell shape and tissue tension result in anisotropic spindle orientation forces?

In the first exploration of the influence of cell geometry on division orientation, amphibian eggs were artificially flattened. As a result the first cleavage plane was perpendicular to the long axis of the egg [START_REF] Hertwig | Das Problem der Befruchtung und der Isotropie des Eies, eine Theory der Vererbung[END_REF][START_REF] Pflüger | H: Entwicklungsmechanische Studien. I. Der Werth der beiden Furchungszellen der Echinodermenentwicklung[END_REF]35]. Predicting spindle orientation based on the cells' long axis later became known as Hertwig's rule. In depth study of the underlying mechanism was possible after advances in microfabrication enabled standardized regulation of cell shape and the application of defined mechanical stress. Combined with automated measurements of spindle orientation and physical modeling, this led to important advances in linking geometry and division orientation [START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF][START_REF] Fink | External forces control mitotic spindle positioning[END_REF][START_REF] Théry | Experimental and theoretical study of mitotic spindle orientation[END_REF][START_REF] Théry | The extracellular matrix guides the orientation of the cell division axis[END_REF].

By culturing single cells on adhesive micropatterns of defined shape, Théry and colleagues found that it was not cell shape but the distribution of actin rich retraction fibers (RF) connecting the mitotic cell with the substrate which best predicts spindle orientation. RF were proposed to provide a memory of the interphase adhesion pattern of the cell since this pattern controls their distribution [START_REF] Fink | External forces control mitotic spindle positioning[END_REF][START_REF] Théry | Experimental and theoretical study of mitotic spindle orientation[END_REF][START_REF] Théry | The extracellular matrix guides the orientation of the cell division axis[END_REF]. The forces for spindle orientation were proposed to be generated in parallel by the NuMA pathway and by RF directed-actin clouds in which Myosin-10 modulates astral MT dynamics [START_REF] Kwon | Direct Microtubule-Binding by Myosin-10 Orients Centrosomes toward Retraction Fibers and Subcortical Actin Clouds[END_REF][START_REF] Fink | External forces control mitotic spindle positioning[END_REF][START_REF] Machicoane | SLK-dependent activation of ERMs controls LGN-NuMA localization and spindle orientation[END_REF]. Following Hertwig's experiments, Minc and colleagues squeezed sea urchin eggs into microfabricated wells which orientated divisions according to the created long axis [START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF]. They proposed that the applied rotational forces on centrosomes scale with MT length, linking cell geometry with division orientation in single cells [START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF].

In epithelia, initial studies identified major roles for planar cell polarity (PCP) and apical-basal (AB) polarity in OCD [START_REF] Gong | Planar cell polarity signalling controls cell division orientation during zebrafish gastrulation[END_REF][START_REF] Mao | Planar polarization of the atypical myosin Dachs orients cell divisions in Drosophila[END_REF]. These studies were instrumental in analyzing spindle orientation in multicellular contexts, and in particular with respect to the AB axis. Recent work explored whether and how geometry and tension play roles in regulating spindle orientation in epithelial tissues.

Two axes of spindle orientation in epithelia: apical-basal and planar

In epithelia, mitotic spindles are typically oriented perpendicular to the AB axis, which is critical to maintain daughter cells in the plane of the epithelium. This orientation generally depends on the lateral distribution of pulling forces [START_REF] Chanet | Myosin 2-Induced Mitotic Rounding Enables Columnar Epithelial Cells to Interpret Cortical Spindle Positioning Cues[END_REF][START_REF] Nakajima | Epithelial junctions maintain tissue architecture by directing planar spindle orientation[END_REF][START_REF] Gloerich | Cell division orientation is coupled to cell-cell adhesion by the E-cadherin/LGN complex[END_REF]. When the actomyosin machinery necessary for cell rounding is impaired, the geometry can override the lateral pulling forces [START_REF] Chanet | Myosin 2-Induced Mitotic Rounding Enables Columnar Epithelial Cells to Interpret Cortical Spindle Positioning Cues[END_REF][START_REF] Nakajima | Epithelial junctions maintain tissue architecture by directing planar spindle orientation[END_REF][START_REF] Mckinley | Cellular aspect ratio and cell division mechanics underlie the patterning of cell progeny in diverse mammalian epithelia[END_REF]. Recently, Box and colleagues found that AB division orientation responds to changes in cell geometry in mouse basal epidermal progenitors. Mutants for the PCP protein Vangl2 fail to close their neural tube, which in turn alters cell geometry, thereby indirectly perturbing division orientation relative to the AB axis [START_REF] Box | Epithelial geometry regulates spindle orientation and progenitor fate during formation of the mammalian epidermis[END_REF].

Spindle orientation is also regulated in the plane of the tissue (planar orientation, Figure 2 top center, Figure 2A, 3A), and is usually set according to Hertwig's rule [START_REF] Tamada | Square Cell Packing in the Drosophila Embryo through Spatiotemporally Regulated EGF Receptor Signaling[END_REF][START_REF] Mao | Differential proliferation rates generate patterns of mechanical tension that orient tissue growth[END_REF][START_REF] Da Silva | Oriented cell divisions in the extending germband of Drosophila[END_REF]. A large variety of cell shapes exist in tissues, ranging from highly anisotropic (elongated) cells to isotropic (round) cells [START_REF] Bosveld | Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis[END_REF][START_REF] Hart | E-cadherin and LGN align epithelial cell divisions with tissue tension independently of cell shape[END_REF][START_REF] Legoff | A global pattern of mechanical stress polarizes cell divisions and cell shape in the growing Drosophila wing disc[END_REF][START_REF] Nestor-Bergmann | Decoupling the Roles of Cell Shape and Mechanical Stress in Orienting and Cueing Epithelial Mitosis[END_REF]. Cells round up during mitosis raising the question of how the interphase long axis is sensed during division [START_REF] Chanet | Myosin 2-Induced Mitotic Rounding Enables Columnar Epithelial Cells to Interpret Cortical Spindle Positioning Cues[END_REF][START_REF] Stewart | Hydrostatic pressure and the actomyosin cortex drive mitotic cell rounding[END_REF][START_REF] Sorce | Mitotic cells contract actomyosin cortex and generate pressure to round against or escape epithelial confinement[END_REF][START_REF] Ramanathan | Cdk1dependent mitotic enrichment of cortical myosin II promotes cell rounding against confinement[END_REF]. Furthermore, epithelial cells are subjected to mechanical forces, which can directly affect planar spindle orientation and modulate cell shapes (Figure 3B) [START_REF] Heisenberg | Forces in Tissue Morphogenesis and Patterning[END_REF]. Central questions in the field are therefore whether tissue stress is able to orient the spindle, and whether this effect is dependent on cell shape changes.

In single adhesive cells, applying external forces without affecting cell shape was able to induce spindle rotation [START_REF] Fink | External forces control mitotic spindle positioning[END_REF]. Initial studies in the context of Zebrafish epiboly and in cultured epithelial monolayers stretched 30%, also indicated that tension is able to orient cell divisions, while also orienting cell shape [START_REF] Campinho | Tensionoriented cell divisions limit anisotropic tissue tension in epithelial spreading during zebrafish epiboly[END_REF][START_REF] Wyatt | Emergence of homeostatic epithelial packing and stress dissipation through divisions oriented along the long cell axis[END_REF]. In the next section, we discuss recent studies that investigated how epithelial cells sense their interphase shape, as well as how cell divisions are oriented by cell shape and/or tension [START_REF] Bosveld | Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis[END_REF][START_REF] Scarpa | Actomyosin-Driven Tension at Compartmental Boundaries Orients Cell Division Independently of Cell Geometry In Vivo[END_REF][START_REF] Finegan | Tissue tension and not interphase cell shape determines cell division orientation in the Drosophila follicular epithelium[END_REF][START_REF] Hart | E-cadherin and LGN align epithelial cell divisions with tissue tension independently of cell shape[END_REF][START_REF] Nestor-Bergmann | Decoupling the Roles of Cell Shape and Mechanical Stress in Orienting and Cueing Epithelial Mitosis[END_REF][START_REF] Campinho | Tensionoriented cell divisions limit anisotropic tissue tension in epithelial spreading during zebrafish epiboly[END_REF].

Sensing interphase cell shape in mitosis

Work in the Drosophila notum epithelium uncovered a mechanism that translates the interphase long axis into localized forces which can orient the mitotic spindle. This mechanism is based on the localization of Mud/NuMA to tricellular junctions (TCJ, the junctions where three cells come together). This localizes the forces exerted on astral MT to TCJ, leading to spindle orientation according to TCJ distribution, which generally aligns with the cell long axis (Figure 2B). In cases where the angle predicted by cell shape and the distribution of TCJ differ by more than 45 degrees, cells divide according to the TCJ distribution showing that the orientation of TCJ is a better predictor for spindle orientation than cell shape [START_REF] Bosveld | Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis[END_REF].

Tension vs shape in spindle orientation

To analyze whether tension can orient the spindle independently of cell shape, a recent study subjected the Xenopus embryo animal cap to an uniaxial stretch (20%) with a PDMS based device [START_REF] Nestor-Bergmann | Decoupling the Roles of Cell Shape and Mechanical Stress in Orienting and Cueing Epithelial Mitosis[END_REF]. The externally applied stretch induced both cell elongation and cell division orientation along the axis of stretch. By comparing cell shape, cell area and the position of the TCJ vertices, the investigators found that TCJ align with the principal axis of local stress and are a better predictor of spindle orientation than global tissue stress [START_REF] Nestor-Bergmann | Decoupling the Roles of Cell Shape and Mechanical Stress in Orienting and Cueing Epithelial Mitosis[END_REF][START_REF] Nestor-Bergmann | Relating cell shape and mechanical stress in a spatially disordered epithelium using a vertex-based model[END_REF]. Indeed, in cells that do not elongate along the axis of stretch, the spindle is not oriented in the axis of stretch, but according to TCJ distribution (Figure 2B,3C). Mechanistically, TCJ are enriched in Cadherin and LGN, and this distribution is necessary to control planar spindle orientation in this context [START_REF] Nestor-Bergmann | Decoupling the Roles of Cell Shape and Mechanical Stress in Orienting and Cueing Epithelial Mitosis[END_REF]. In contrast to the findings in Xenopus epithelia, dividing cells within MDCK monolayers subjected to low uniaxial stretch (15%), oriented their spindle with respect to the stretch axis, independently of cell shape. The mechanism proposed here involves both Cadherin and the polarization of LGN towards the bicellular junctions (BCJ) that are perpendicular to the axis of stretch (Figure 3D) [START_REF] Hart | E-cadherin and LGN align epithelial cell divisions with tissue tension independently of cell shape[END_REF]. Therefore, the same molecules mediate the link between the orienting cue (geometry or tension) and force generation by localizing to TCJ or BCJ in Xenopus and MDCK cells respectively.

The link between tension and planar spindle orientation has been also studied in developing tissues which undergo elongation or experience localized tensile stress. In the case of the Drosophila embryo, cells that are adjacent to high tensile supracellular actomyosin cables divide according to their long axis only if they are highly elongated. By contrast, slightly elongated cells divide according to the tension cue provided by the actomyosin cables, which run perpendicular to cell shape (Figure 2C) [START_REF] Scarpa | Actomyosin-Driven Tension at Compartmental Boundaries Orients Cell Division Independently of Cell Geometry In Vivo[END_REF]. Another tension dependent mechanism orienting cell divisions was identified in the elongating Drosophila follicular epithelium (FE). In these cells, the cell long axis is perpendicular to the axis of tissue elongation and thus to the stretch force [START_REF] Finegan | Tissue tension and not interphase cell shape determines cell division orientation in the Drosophila follicular epithelium[END_REF]. The embryo and FE constitute immature epithelia which do not harbor classical BCJ and TCJ septate junctions. No clear crescents or TCJ accumulation of LGN or NuMA could be observed and these proteins were not required for planar spindle orientation [START_REF] Scarpa | Actomyosin-Driven Tension at Compartmental Boundaries Orients Cell Division Independently of Cell Geometry In Vivo[END_REF][START_REF] Finegan | Tissue tension and not interphase cell shape determines cell division orientation in the Drosophila follicular epithelium[END_REF]. In mature epithelia with septate junctions (larval wing disc, pupal wing and notum tissues), Mud is enriched at the level of the tricellular septate junction [START_REF] Bosveld | Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis[END_REF][START_REF] Bergstralh | Pins is not required for spindle orientation in the Drosophila wing disc[END_REF]. Therefore, different mechanisms might orient cell divisions according to tension in immature and mature epithelia. In the embryo, the actomyosin cable is proposed to orient the spindle by capturing one centrosome in an actin network, while in the FE, anisotropic cortical stiffness is proposed to bias spindle orientation [START_REF] Scarpa | Actomyosin-Driven Tension at Compartmental Boundaries Orients Cell Division Independently of Cell Geometry In Vivo[END_REF][START_REF] Finegan | Tissue tension and not interphase cell shape determines cell division orientation in the Drosophila follicular epithelium[END_REF].

What emerges from these experiments is that no clear one-size fits all rule can be applied. In highly elongated cells, the predominant cue seems to be cell shape, independently of the mechanism used by cells to interpret this cue [START_REF] Bosveld | Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis[END_REF][START_REF] Scarpa | Actomyosin-Driven Tension at Compartmental Boundaries Orients Cell Division Independently of Cell Geometry In Vivo[END_REF][START_REF] Nestor-Bergmann | Decoupling the Roles of Cell Shape and Mechanical Stress in Orienting and Cueing Epithelial Mitosis[END_REF]. In cells with moderate anisotropy, different scenarios are possible: i) in immature epithelia or MDCK layers, where OCD regulators do not localize to TCJ, spindle orientation responds to global tension independently of cell shape; ii) in mature epithelia, cells use TCJ bipolarity, which aligns with local tension, as the main cue for spindle orientation (Figure 2, 3) [START_REF] Bosveld | Epithelial tricellular junctions act as interphase cell shape sensors to orient mitosis[END_REF][START_REF] Scarpa | Actomyosin-Driven Tension at Compartmental Boundaries Orients Cell Division Independently of Cell Geometry In Vivo[END_REF][START_REF] Nestor-Bergmann | Decoupling the Roles of Cell Shape and Mechanical Stress in Orienting and Cueing Epithelial Mitosis[END_REF]. In this view, one could speculate that TCJ hot spots of LGN or NuMA are more efficient to orient the spindle than other mechanisms that depend on actomyosin forces. Actomyosin based mechanisms remain to be defined in epithelia: could actin clouds and Myosin-10 be involved in spindle orientation like in cultured cells?

Function of mitotic spindle orientation in epithelia

A central question in the field of spindle orientation is the function of OCD in epithelia. Multiple roles have been proposed such as tissue layering, dissipation of tissue stress, changes in tissue morphology, and homeostasis (Figure 4) [START_REF] Heisenberg | Forces in Tissue Morphogenesis and Patterning[END_REF][START_REF] Nakajima | Epithelial junctions maintain tissue architecture by directing planar spindle orientation[END_REF][START_REF] Da Silva | Oriented cell divisions in the extending germband of Drosophila[END_REF][START_REF] Campinho | Tensionoriented cell divisions limit anisotropic tissue tension in epithelial spreading during zebrafish epiboly[END_REF][START_REF] Morin | Control of planar divisions by the G-protein regulator LGN maintains progenitors in the chick neuroepithelium[END_REF].

OCD were proposed to be required for axis elongation during Zebrafish gastrulation [START_REF] Gong | Planar cell polarity signalling controls cell division orientation during zebrafish gastrulation[END_REF]. The PCP pathway can regulate spindle orientation through Mud and via the Anthrax2 receptor [START_REF] Ségalen | The Fz-Dsh Planar Cell Polarity Pathway Induces Oriented Cell Division via Mud/NuMA in Drosophila and Zebrafish[END_REF][START_REF] Castanon | Anthrax toxin receptor 2a controls mitotic spindle positioning[END_REF]. Knock down of the PCP protein Dishevelled resulted in a shortened anterior-posterior axis [START_REF] Gong | Planar cell polarity signalling controls cell division orientation during zebrafish gastrulation[END_REF]. Yet, more directly perturbing spindle orientation by impairing dynein or NuMA function did not affect body axis elongation, challenging the idea that OCD are involved in tissue elongation during Zebrafish gastrulation [START_REF] Ségalen | The Fz-Dsh Planar Cell Polarity Pathway Induces Oriented Cell Division via Mud/NuMA in Drosophila and Zebrafish[END_REF][START_REF] Quesada-Hernández | Stereotypical Cell Division Orientation Controls Neural Rod Midline Formation in Zebrafish[END_REF]. In Drosophila wing imaginal disc, cells in the central wing pouch divide preferentially along the proximal-distal axis, while cells in the periphery divide tangentially along the local tissue boundary [START_REF] Mao | Planar polarization of the atypical myosin Dachs orients cell divisions in Drosophila[END_REF][START_REF] Mao | Differential proliferation rates generate patterns of mechanical tension that orient tissue growth[END_REF][START_REF] Legoff | A global pattern of mechanical stress polarizes cell divisions and cell shape in the growing Drosophila wing disc[END_REF]. In this tissue, loss of Mud/NuMA leads to the formation of smaller but normally shaped wings (Figure 4D-G) [START_REF] Zhou | Oriented Cell Divisions Are Not Required for Drosophila Wing Shape[END_REF]. Spindle misorientation can result in basally born cells being lost from the tissue possibly explaining the size reduction [START_REF] Nakajima | Epithelial junctions maintain tissue architecture by directing planar spindle orientation[END_REF][START_REF] Zhou | Oriented Cell Divisions Are Not Required for Drosophila Wing Shape[END_REF]. As global tissue stress can regulate OCD [START_REF] Mao | Planar polarization of the atypical myosin Dachs orients cell divisions in Drosophila[END_REF][START_REF] Mao | Differential proliferation rates generate patterns of mechanical tension that orient tissue growth[END_REF][START_REF] Legoff | A global pattern of mechanical stress polarizes cell divisions and cell shape in the growing Drosophila wing disc[END_REF], the authors proposed that loss of OCD can be buffered by an increase in tissue stress and cell rearrangements contributing to tissue elongation [START_REF] Zhou | Oriented Cell Divisions Are Not Required for Drosophila Wing Shape[END_REF]. Therefore, planar division within the wing disc epithelium might serve to aid planar tissue extension and reduce cell loss.

In the developing Zebrafish embryonic surface layer (pre-EVL), Xiong and colleagues proposed that OCD contribute to tissue layering. In this context, cell shape predicts spindle orientation with squamous and cuboidal cells dividing in perpendicular directions (Figure 4A) [START_REF] Xiong | Interplay of Cell Shape and Division Orientation Promotes Robust Morphogenesis of Developing Epithelia[END_REF]. Cell divisions in cuboidal cells contributed to layering as one of the two daughter cells was displaced from the outer layer into a new layer below. Furthermore, OCD were proposed to buffer changes in the global geometry of the embryo, permitting successful epiboly [START_REF] Heisenberg | Forces in Tissue Morphogenesis and Patterning[END_REF].

In the Zebrafish EVL, cell divisions tend to orient along the axis of tension during epiboly (Figure 4B) [START_REF] Campinho | Tensionoriented cell divisions limit anisotropic tissue tension in epithelial spreading during zebrafish epiboly[END_REF]. In stretched MDCK monolayers, cell divisions reorient according to the axis of stretch (Figure 3D, 4C) [START_REF] Gloerich | Cell division orientation is coupled to cell-cell adhesion by the E-cadherin/LGN complex[END_REF][START_REF] Wyatt | Emergence of homeostatic epithelial packing and stress dissipation through divisions oriented along the long cell axis[END_REF]. These orientations have been proposed to relieve tissue stress by increasing the number of cells along the stress axis [START_REF] Campinho | Tensionoriented cell divisions limit anisotropic tissue tension in epithelial spreading during zebrafish epiboly[END_REF][START_REF] Wyatt | Emergence of homeostatic epithelial packing and stress dissipation through divisions oriented along the long cell axis[END_REF].

Fine tuning AB spindle orientation is essential to ensure faithful epithelial structure. During mouse embryonic epithelial development, a switch from parallel to perpendicular spindle orientation is necessary for progenitor cells differentiation and skin stratification [START_REF] Kulukian | Spindle orientation and epidermal morphogenesis[END_REF]. Impaired AB spindle orientation can also lead to daughter cells being aberrantly displaced out of the epithelial layer [START_REF] Nakajima | Epithelial junctions maintain tissue architecture by directing planar spindle orientation[END_REF]. Therefore, OCD have been proposed to prevent tumor initiation and/or tumor spreading. Nakajima and colleagues showed that by perturbing spindle orientation and inhibiting apoptosis, tumor like masses can form in fly wing disc epithelia (Figure 4G) [START_REF] Nakajima | Epithelial junctions maintain tissue architecture by directing planar spindle orientation[END_REF]. Alternatively, tumor spreading can be prevented by reintegration of cells after misoriented divisions. In the Drosophila FE, the embryonic ectoderm, the neuroepithelium and the wing disc, misplaced cells can reintegrate in the tissue (Figure 4G) [START_REF] Zhou | Oriented Cell Divisions Are Not Required for Drosophila Wing Shape[END_REF][START_REF] Bergstralh | Lateral adhesion drives reintegration of misplaced cells into epithelial monolayers[END_REF]. Further exploration of cell reintegration upon division misorientation will help to understand how epithelial tissues can prevent out of plane born cells from becoming tumorigenic. Finally, how epithelial homeostasis and morphogenesis are affected by aberrant cell loss due to AB spindle misorientation remains to be further investigated.

Future directions

Considerable progress has been made in understanding the mechanisms and roles of mitotic spindle orientation during symmetric epithelial cell division. Accordingly, complementary in vitro and in vivo studies have put forward novel hypotheses. For example, cortical clustering of NuMA is proposed to be critical for spindle orientation in cultured cells, while in epithelial tissues TCJ localization of spindle guidance cues seems to be a predominant mechanism to orient the spindle [START_REF] Okumura | Optogenetic localization of proteins to the cortex in mammalian cells and found that NuMA but not dynein recruitment to the cortex is sufficient to orient the mitotic spindle[END_REF][START_REF] Pirovano | Hexameric NuMA:LGN structures promote multivalent interactions required for planar epithelial divisions[END_REF]. This suggests that NuMA clustering at TCJ, rather than homogenous cortical localization, could be more efficient to generate pulling forces in epithelia. Better characterization of the upstream regulators of spindle orientation and of the mechanisms of force generation will extend our understanding of the many roles of OCD in multicellular contexts. Another exciting direction will be to explore how the interplay between tissue mechanics, vertex dynamics and apoptosis influences spindle orientation.

Figure 1 :

 1 Figure 1: Dynein can bind to dynactin and a cargo adapter such as HOOK3 to form a processive complex (A). Their interaction is facilitated by the coiled-coil in HOOK3. A second dynein can be part of the complex through interactions with the CAPZb subunit of dynactin. Knock-down of CAPZb leads to spindle misorientation. NuMA also possesses a long coiled-coil, which is required for spindle orientation. (B).

Figure 2 :

 2 Figure 2: Planar spindle orientation can be regulated through different mechanisms. Hertwig's rule states that cells divide according to their long axis (A). Cells with Mud orLGN at TCJ divide according to the position of TCJ (B). In the Drosophila embryo cells adjacent to the actomyosin cable divide according to cell shape if their cell shape is highly anisotropic, but spindle orientation is directed towards the cable in moderately anisotropic cells (C).

Figure 3 :

 3 Figure 3: In homeostasis, no apparent global direction of cell division can be observed (A). If a stretch is applied to the tissue, the cells become elongated and divide according to their long cell axis (B). Stretched Xenopus animal caps have enriched LGN at TCJ. The anisotropy of the cell as given by TCJ is the best predictor of local stress and cell division orientation (C). Cell divisions in MCDK layers do no follow cell shape, but divide along the direction of stretch by accumulation of LGN on junctions perpendicular to the axis of stretch (D).

Figure 4 :

 4 Figure 4: Multiple cellular processes have been linked to OCD. In Zebrafish, OCD contribute to the formation of multiple tissue layers in the pre-EVL stage (A). The spreading motion of epiboly generates tissue tension which can be mitigated by OCD along the axis of stretch (B). Similarly, OCD can relieve external stress imposed on MCDK layers (C). In Drosophila, spindle misorientation causes phenotypes in the plane (D) and along the AB axis of epithelia (E). Spindle misorientation in mud mutants leads to smaller wings (F). Furthermore, the loss of AB spindle orientation results in multiple cellular phenotypes. Firstly, a fraction of cells is able to reintegrate into the plane of the tissue. Alternatively, they can be lost through delamination after which the cell can be removed through apoptosis (G). When apoptosis is blocked, these cells can survive and form tumor like masses (G).

Acknowledgements

We thank Floris Bosveld for critical reading of the manuscript. Work in Y.B lab is supported by ERC Advanced (TiMorph, 340784), ARC (PGA1 RF20180206793), ANR Labex DEEP 11-LBX-0044, ANR-10-IDEX-0001-02 PSL grants for funding. E.v.L. is supported by the Marie Skłodowska-Curie Actions Innovative Training Network 675407 and F.d.P. by the Fondation pour la Recherche Medicale (FRM) postdoctoral grant SPF20170938661.


Shigenori Otsuka

Yasumitsu Maejima

Pierre Tandeo

Takemasa Miyoshi

Takemasa Miyoshi Toward

Toward an integrated NWP-DA-AI system for 30-second-update precipitation prediction

teaching and research institutions in France or abroad, or from public or private research centers.

  Array Weather Radar (PAWR) at NICT Kobe -Every 30 seconds, 60-km-range, 100-m range resolution, 300 azimuth, 110 elevation -A high-resolution regional NWP system (SCALE-LETKF, Miyoshi et al., 2016a,b, Lien et al., 2017) -3D optical flow nowcast: https://weather.riken.jp/ (Otsuka et al. 2016, WAF) -A deep-learning-based system to merge observations and forecasts is newly developed.-The Conv-LSTM is extended to 3D. A real-time 3D Conv-LSTM system is implemented with the Kobe PAWR.-The 3D Conv-LSTM captured the evolution of convective cores.-Conv-LSTM with forecast data outperformed that without forecast data.-Future perspective: Training with PAWR data in different seasons / training with other model variables such as winds, humidity -The machine learning architechture will be updated to improve the prediction accuracy.

  2. Deep-learning-based system (NICT/Osaka U./TOSHIBA) PAWR antenna and beam Toward an integrated NWP-DA-AI system for 30-second-update precipitation prediction -Based on Conv-LSTM (Shi et al. 2015, NIPS) -Long Short Term Memory (Hochreiter & Schmidhuber 1997, Neural Comp.) -Suitable for time series -Convolution: taking account of spatial pattern -Weights: copied from the encoder to the forecaster -Conv-LSTM outperforms CNN for two-dimensional precipitation nowcasting -Extended to three-dimensional data -Future data are used in the decoder network 3. Test case -Observation data: Kobe PAWR observations, 250-m mesh, 321x321x57 pixels -Future data: -Optical flow-based 3D nowcast (TREC) -Surface precipitation forecast by SCALE-LETKF -Training period: 15:10:00-17:29:30 UTC, 10 June 2019 -Verification period: 17:40:00-17:59:30 UTC, 10 June 2019 -6 steps for the past data (encoder), 20 steps for the future data (decoder) -Subregions of 61 x 61 x 9 pixels (z = 1.5-3.5 km) with rain echoes are extracted from the original data, and are used for training and inference. -Optimizer: Adam -Loss function: Balanced mean square error -Convolution kernel size:


Vincent Galand

Erwan Flécher

Céline Chabanne

Bernard Lelong

Céline Goéminne

André Vincentelli

Clément Delmas

Camille Dambrin

Septuagenarian population has similar survival and outcomes to younger patients after left ventricular assist device implantation