Moad Kissai

Bruno Monsuez

Xavier Mouton

Didier Martinez

Adriana Tapus

Model Predictive Control Allocation of Systems with Different Dynamics

Keywords: Model Predictive Control Allocation, Chassis Systems, Vehicle Dynamics, Identification, Robust Control

Several systems are integrated in passenger cars. Some of them are just redundant systems due to safety requirements. Others, are completely different and can interact with each other as long as they are operating inside the same vehicle. Control allocation methods have been successfully implemented in advanced aircrafts to avoid conflicts, especially in the context of redundant systems. In this paper, we will rather focus on coordinating non-redundant advanced chassis systems with different dynamics. This difference in dynamics can be especially problematic when systems exhibit different communication delays. Model Predictive Control Allocation (MPCA) methods are therefore investigated in order to activate the right system at the right moment. Results show that particularly when the most effective system is saturated, another system with a different time delay can be activated few steps before saturation to instantly take over the maneuver. With good knowledge of actuator dynamics and higher computation power, MPCA methods are able to solve complex problems in severe situations.

I. INTRODUCTION

The automotive sector is getting prepared for one of its biggest revolutions. After vehicle's electrification and connectivity, full autonomy has become the headline of many scientific researches. In order to achieve safe autonomous driving, additional sensors and actuators are added to replace the driver or at least assist him/her. Different sensors can be used in order to detect the same object. In the same way, different actuators can influence the same physical variable as the vehicle's yaw rate [START_REF] Kissai | A Comprehensive Comparison of Chassis Systems Coordination Approaches[END_REF]. While the first problem is tackled by sensor fusion methods, Control Allocation (CA) algorithms are more suited for the second problem. To the best of our knowledge, these algorithms have been first introduced in the aeronautical sector [START_REF] Bodson | Evaluation of Optimization Methods for Control Allocation[END_REF]. Advanced aircraft systems equipped with several ailerons, rudders, elevators and so on have been coordinated using CA algorithms [START_REF] Bodson | Evaluation of Optimization Methods for Control Allocation[END_REF], [START_REF] Oppenheimer | Control Allocation for Over-actuated Systems[END_REF], [START_REF] Bai | Fault tolerant scheme design for the flight control systems using adaptive control allocation technique[END_REF]. Most of the time, these algorithms are used to coordinate actuators with the same dynamics, e.g., a right aileron with a left one. Following the same idea, CA methods have been introduced in the automotive sector to manage systems with several actuators having the same dynamics. Although the actuators do have the same Palaiseau Cedex, France {moad.kissai, bruno.monsuez, adriana.tapus}@ensta-paristech.fr {xavier.mouton, didier.d.martinez}@renault.com dynamics, they influence the vehicle differently due to their different positioning and the vehicle's non-uniform mass distribution. The Electronic Stability Program (ESP) is one of the most obvious examples in this case, as it consists of controlling the four brakes of the vehicle [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF]. Another chassis system based on the same principle is the Torque Vectoring. This system attracted the automotive community as it enables controlling the vehicle's yaw rate while keeping it in the move unlike the ESP. Authors in [START_REF] De Filippis | Energy-Efficient Torque-Vectoring Control of Electric Vehicles With Multiple Drivetrains[END_REF] used CA algorithms to ensure Torque Vectoring control of an electric vehicle. Not only the vehicle's yaw rate control has been improved, but also the drive-train power losses have been minimized using appropriate tuning of the reference's understeer characteristics. In [START_REF] Van Den | Optimal Control Allocation on Over-Actuated Vehicles[END_REF], both engine torques and brake torques have been coordinated, considering that both are based on the tire longitudinal forces. CA algorithms have been extended to systems based on different forces in [START_REF] Kissai | Complementary Chassis Systems for Ground Vehicles Safety[END_REF]. A differential braking based Vehicle Dynamic Control (VDC) system and an Active Rear Steering (ARS) system have been coordinated using optimal CA algorithms. Here, the ARS system is rather based on the lateral force of the tire. Both systems have been made complementary to make a secondary different system take over the maneuver in case of failure of the primary system. Fault-tolerance has been then ensured by means of different integrated systems.

However, actuators dynamics have been most of the time ignored when designing control allocation algorithms. This could be acceptable as long as actuators with the same dynamics are involved. Once the actuators become very different, switching from one system to another can be very problematic. In [START_REF] Kissai | Complementary Chassis Systems for Ground Vehicles Safety[END_REF] for example, when the ARS system fails, the VDC system takes over the maneuver instantly thanks to a modified effectiveness matrix in the CA framework that takes into account the actuators' flags. This can only be possible if both systems can be activated fast enough without any communication delays. Experiments showed us that the delay cannot be neglected. Different research works have been carried out to face time-delay issues in the control theory community. The problem has been tackled in [START_REF] Haddad | Stabilization of linear and nonlinear systems with time delay[END_REF] by using modified Riccati equations. In [START_REF] Yue | Delayed feedback control of uncertain systems with timevarying input delay[END_REF], delayed feedback control design for uncertain systems with time-varying input delay has been proposed. Authors of [START_REF] Yue | Delayed feedback control of uncertain systems with timevarying input delay[END_REF] used Lyapunov functions and introduced some relaxation matrices and turning parameters to make results less conservative. Results in [START_REF] Haddad | Stabilization of linear and nonlinear systems with time delay[END_REF] and [START_REF] Yue | Delayed feedback control of uncertain systems with timevarying input delay[END_REF] present theoretical mathematical solutions of the problem. Nonetheless, they remain tedious to implement and non adapted for industrial control applications. An alternative solution would be the Model Predictive Control Allocation (MPCA). First of all, the Model Predictive Control (MPC) is a control method that solves an optimization problem, specifically, a quadratic program (QP), at each control interval. The solution determines the manipulated variables to be used in the plant for a number of successive intervals constituting the prediction horizon. The optimization is based on minimizing several cost functions. The most important one for reference tracking consists of minimizing the difference between the reference and the state to be controlled. The same principle can be adopted for MPCA. Here, the cost function to be minimized would be the difference between the overall effort needed to stabilize the plant and the sum of available control effectors. The delay can be taken into account in the whole prediction horizon to determine when the control request should be submitted. In this context, MPCA has been used in [START_REF] Satzger | A model predictive control allocation approach to hybrid braking of electric vehicles[END_REF] to coordinate Hybrid Braking in electric vehicles. Results showed that the MPCA can offer faster transient response, without compromising the energy recuperation efficiency of the actuators. However, the modeling used for the different brakes is relatively simplified. In [START_REF] Zhao | Model predictive control allocation for stability improvement of four-wheel drive electric vehicles in critical driving condition[END_REF], MPCA has been used to stabilize a four-wheel drive electric vehicle in critical driving condition. While results showed stability improvement in severe situations, the problem exposed remains simple as the actuators considered, namely the in-wheel engines, have the same dynamics.

In this paper, we focus on completely different actuators. Our aim is to control the vehicle's yaw rate by means of the steering-based ARS system1 and the braking-based VDC system. Moreover, as the MPC theory suffers from a lack of robustness due to its dependency on analytic modeling, here, we identify the vehicle and actuators' dynamics to be implemented in the MPCA experimentally. We also add a high-level controller based on H ∞ theory. Comparison with the classic CA approach shows the benefit of the MPCA in case of coordinating different systems with different dynamics, especially when both systems have to operate at the same time.

The rest of the paper is structured as follows: We start in Section II by presenting the vehicle dynamics modeling. The identification issues to be used in case of MPCA design are illustrated in Section III. In Section IV, the control allocation problem is described, along with the adaptation of the MPC theory. Comparison of classic CA methods with the MPCA are shown in Section V. The application of such complex method from an industrial point of view is discussed in VI. Conclusions and future works are outlined in Section VII.

II. VEHICLE MODELING

As its name may reveal, the MPC theory is closely based on the plant model selected. This is also the case for the MPCA. The model chosen should be as precise as possible to ensure acceptable performances in real experiments. Experimental identification seems to be the safer option. However, when carrying different experiments with different speed values, different transfer functions can be obtained. This proves the dependency of vehicle dynamics on the speed, as it was also shown in [START_REF] Anderson | Using GPS with a model-based estimator to estimate critical vehicle states[END_REF]. Therefore, first of all, analytic equations should be developed in order to isolate the constant parameters that need to be identified.

Another difficulty is the modular property of the CA framework. As it was discussed in [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF], the multi-layered control architecture seems to be more appropriate for overactuated vehicles. This architecture is illustrated in Fig. 1. The high-level controller in case of yaw rate control must generate the total yaw moment required M ztot . To synthesize this high-level controller, the following equations coming from Newton's second law of motion should be considered:

                                                 M ψV x + sV y =F y f cos δ fi + F yr cos δ ri + sin δ fi F x f,l + F x f,r + sin δ ri F x r,l + F xr,r I z s ψ =F y f l f cos δ fi -F yr l r cos δ ri + l f sin δ fi - t 2 cos δ fi F x f,l + l f sin δ fi + t 2 cos δ fi F x f,r -l r sin δ ri + t 2 cos δ ri F x r,l -l r sin δ ri - t 2 cos δ ri F xr,r (1) (2)
Where:

• s : Laplace operator, • M : vehicle's mass, • I z : yaw inertia moment of the vehicle, • t : vehicle's track, • l k
: distance between the axle k and the vehicle's centre of gravity, where k designs the front or the rear, • V x : longitudinal speed, • V y : lateral speed, • ψ : vehicle's yaw rate, • F y k : overall lateral force at the axle k, • F x k,j : longitudinal force of each tire, where j designs left or right, • δ ki : the initial steering angle before the application of the tire force. Following equation (2), many research papers on CA in the automotive field consider a pure integrator relationship between the lateral force and the vehicle's yaw rate [START_REF] Soltani | Low Cost Integration of Electric Power-Assisted Steering (EPAS) with Enhanced Stability Program (ESP)[END_REF].

However, the relationship between the lateral force and the yaw rate is actually nonlinear. Indeed, considering for example the new linear tire model with varying parameters [START_REF] Kissai | A new linear tire model with varying parameters[END_REF], the lateral tire force can be defined as follows:

F y = C * α (κ, µ, F z ) α (3)
Where:

• C * α : varying lateral stiffness that takes into account the longitudinal slip κ, the friction coefficient µ and the vertical load F z in order to represent the combined slip phenomenon,

• α

: the side-slip angle. In addition, the side-slip angle is defined as follows:

α k = δ k - V y ± l k ψ V x (4)
Therefore, the lateral tire force depends on the lateral speed and the yaw rate. A linear transfer function cannot be expressed between the lateral force in this form and the yaw rate. In the following, we will consider only the rear lateral force related to the 4WS system as our prototype is not autonomous yet. The front lateral force is influenced by the human driver and is used to generate the yaw rate reference as Fig. 1 shows. In order to synthesize a high level controller to generate a total yaw moment, we split the controllable term of the lateral force from the non-controllable one:

F yr = C * αr δ r -C * αr V y -l r ψ V x = F yr c + F yr nc (5)
F yr nc will be then integrated in the state-space matrix, and only F yr c = C * αr δ r is considered as an input. A highlevel controller can be then synthesized to generate the total yaw moment, by considering the influence of the rear angle on the yaw moment as M 4W S = -C * αr l r δ r . After few simplifications and combinations, we find as expected a second-order transfer function between the yaw moment and the yaw rate with a gain and two complex poles depending on the longitudinal speed [START_REF] Ellis | Vehicle Dynamics[END_REF]. Each input comes with a different zero. And finally, as the actuators comes from different suppliers with inner control algorithms in black boxes [START_REF] Kissai | Review of integrated vehicle dynamics control architectures[END_REF], we prefer to identify their dynamics experimentally.

III. EXPERIMENTAL IDENTIFICATION

The difficulty of experimental identification manifest in the few measurable signals as Fig. 2 illustrates. In Fig. 2, the accessible signals are in green, and the inaccessible ones are in red, where:

• T b k,j req : requested brake torque at the k -j wheel,

• T b k,j ef f : effective brake torque at the k -j wheel, • δ rreq : requested rear steering angle, • δ r ef f : effective rear steering angle. The effective brake torques applied are not measurable in our case. Therefore, a direct identification of the brake dynamics is not possible. In contrast, the effective rear steering angle is measurable. The idea is then to identify first the 4WS actuator dynamics and the vehicle dynamics by activating only the 4WS system. Then, when identifying the transfer function between T b k,j req and ψ, we can isolate the already identified vehicle poles to deduce the brake dynamics.

A. The 4WS system identification

Vehicle dynamics depend on the vehicle's speed [START_REF] Ono | Vehicle integrated control for steering and traction systems by µsynthesis[END_REF]. The experiments should be carried out at different speed values. We apply a step to the 4WS system, and we measure both the effective rear steering angle δ r ef f and the yaw rate of the vehicle ψ to evaluate the influence of the 4WS actuator on the vehicle. We use afterwards the System Identification app of Matlab R to identify the dynamic models using input/output data. For a speed of 70km/h for example, we obtain the Fig. 3. We use different transfer function shapes to approach the vehicle response. After several experiments we can conclude that two poles and one zero suffice to represent the vehicle dynamics influenced by the rear steering. Fig. 3 shows that there is no need to add for example a third pole. The zero remains characteristic to the 4WS system. The real dynamics of the vehicle are the two identified poles, which falls right into our expectations. Using several experiments for different speed values, we can finally isolate the constant parameters from the vehicle's speed influence.

The same procedure is carried out for the 4WS actuator only. This time a small delay is needed to fit the real dynamics of the actuator as Fig. 4 shows. The overall system is composed then of two poles characterizing the vehicle dynamics, one zero, one delay and two poles characterizing the 4WS system dynamics.

B. The VDC system identification

We follow the same procedure for the VDC also. Here, we apply a torque of 400N.m at each left wheel, and we measure the yaw rate response of the vehicle. Fig. 5 shows that three By analyzing all the poles and zeros identified (see Fig. 6), we can see that the complex poles of both dynamic models are close enough. The complex poles characterize then the vehicle dynamics. The remaining pole, zero and pure delay characterize the VDC system. These identified models are then used to synthesize both the high-level controller and the MPCA.

IV. MODEL PREDICTIVE CONTROL ALLOCATION

First of all, let us define the control allocation problem [START_REF] Johansen | Control Allocation -A survey[END_REF]: find u ∈ R n such that subject to

B u = v (6)
u min ≤ u ≤ u max ˙ u ≤ ˙ u max (7) (8)
B ∈ R m×n is a control effectiveness matrix, u min ∈ R n and u max ∈ R n are the lower and upper position limits, respectively, ˙ u ∈ R n is the control rate, ˙ u max ∈ R n is the maximum control rate, v ∈ R m are the desired accelerations, n is the number of control effectors, and m is the number of axes to control with n > m.

In our case, v = M ztot . However, the low control-level will differ from a CA approach to another as we will explain in the following paragraphs. In contrast, the same high-level controller can be adopted. As robustness is one of our main concerns, H ∞ synthesis is chosen as a high-level controller. It is an optimization method to minimize the H ∞ norm of the augmented plant containing weight functions. Three weight functions are considered here that penalize the error signal, control signal, and output signal, respectively. As the vehicle dynamics depends on the varying longitudinal speed, gain scheduling is then used to adapt the controller behavior to speed values. This, however, goes beyond the scope of this paper. The interested readers can refer to [START_REF] Kissai | Gain-Scheduled H∞ for Vehicle High-Level Motion Control[END_REF].

A. Classic Dynamic Control Allocation

Here, the control architecture exposed in Fig. 1 is carefully followed. The CA layer generate the virtual tire forces to be applied. Then, low-level controllers are added to take into account the zero of each input along with each actuator dynamics. Regarding this low-level layer, H ∞ synthesis can be adopted again. Nonetheless, the actuators' dynamics present pure input time-delays which add non-linearities in the process. H ∞ cannot be applied directly. Consequently, here we use second-order Padé approximation to approximate the time-delays.

As for the CA algorithm, online optimization techniques can be used. Various techniques have been compared in [START_REF] Kissai | Complementary Chassis Systems for Ground Vehicles Safety[END_REF]. It has been shown that the Weighted Least Squares (WLS) formulation based on Active Set Algorithms (ASA) solves the problem rapidly with good precision and reach the optimum in a small finite number of iterations. The WLS solves the global problem in a one stage ASA by means of different weights to determine the importance of each objective. This gives the following expression:

u opt = arg min umin≤ u≤ umax W u ( u -u p ) 2 + γ W v (B u -v) 2 (9)
Where:

• u p : preferred control vector 2 , • γ : weight that enables favouring an objective over another,

• W u : non-singular weighting matrix affecting control distribution among the actuators, • W v : non-singular weighting matrix affecting the prioritization among the virtual control components when B u = v cannot be attained due to actuator constraints. In our case, u is composed of tire forces, and B is composed of the geometrical coefficients shown in equation [START_REF] Bodson | Evaluation of Optimization Methods for Control Allocation[END_REF]. The limits of the control vector are composed of the minimum of the actuator position and rate limits, and the friction ellipse concept [START_REF] Kissai | A new linear tire model with varying parameters[END_REF].

B. Model Predictive Control Theory for Control Allocation

The previous method takes into account only the most effective effector in the distribution process. However, each system has a different dynamic. In severe maneuvers, the fastest system may constitute a better choice. For missile control for example, fast actuators can be used for good transient response, while slow actuators can be used for steady state flight and therefore improving the power efficiency [START_REF] Hanger | Model Predictive Control Allocation[END_REF]. Other interesting scenarios are when several systems should be activated because of the limits of each one. The less effective systems should be activated as soon as the most effective ones saturate. When the less effective systems present time-delays, as it is the case here, the command should be requested a few steps before the saturation of the most effective systems. To the best of our knowledge, this can only be ensured if a certain prediction of the integrated dynamics are provided.

The MPC is an online optimization-based control technique that aims to solve a finite-horizon optimization problem at each sampling time. An internal discretized dynamic model is used to predict the behaviour of the system, and the optimizer generates the required control inputs in order to satisfy the desired performances along a chosen prediction horizon. The MPC objective cost function is usually taken as follows [START_REF] Hanger | Model Predictive Control Allocation[END_REF]:

J (k) = T i=1 Q (i) (x (k + i|k) -r (k + i|k)) 2 + T i=1 R (i) (û (k + i|k)) 2 ( 10
)
Where k is the current time step, x is the estimated state, r is the reference trajectory, û is the optimal control sequence, and T is the prediction horizon length. The first term in 2 Usually 0 due to energy consumption J (k) represents the reference tracking performance, and the second one represents the control effort mitigation. The weights Q (i) and R (i) enable favoring one objective over another. In addition, as far as an optimization problem is concerned, the MPC is capable of handling constraints at both the control input level and the state level. The principle of the MPC is illustrated in Fig. 7. The optimizer explores Fig. 7. An MPC general scheme (taken from [START_REF] Hanger | Model Predictive Control Allocation[END_REF]).

the state trajectories minimizing the cost over the prediction horizon, and only the first control step is applied to the plant. The procedure is repeated for every sampling time in case of changes in the varying parameters of the integrated model. This technique is also called the Receding Horizon Control (RHC) because the horizon keeps being pushed forward.

Regarding our CA problem, the same philosophy can be applied. Rather than imposing a specific state to follow a desired reference, we can modify the cost function to make the virtual forces track the required total yaw moment. What is more interesting in this approach, is that we can take into account the actuator dynamics with their delays in an explicit manner. The integrated model in that case is not the overall system, but only the actuators' models. Thanks to its predictive nature, this approach can pre-act on the actuators by taking into account the time-delay so the tire forces can be applied at the right moment. To do so, the actuators' models should be first discretized and combined with the virtual forces expressions. Here, we use Tustin method:

                                     F xi,j (k) =a b F xi,j (k -1) + b b1 (V x ) T bi,j req k - τ vdc T s -1 + b b2 (V x ) T bi,j req k - τ vdc T s - 2
F yr (k) =a r1 F yr (k -1) + a r2 F yr (k -2) + b r1 (V x ) δ rreq k - τ 4ws T s -2 + b r2 (V x ) δ rreq k - τ 4ws T s -3 (11) (12)
Where the parameters a i and b i are those obtained by discretization. Note that the parameters b i depend on the vehicle's speed. This is due, as we have mentioned, to the dependency of the zeros on the speed. τ vdc and τ 4ws are the input time-delay of the VDC and 4WS systems respectively. And finally, T s is the sampling time.

Let us define the following vectors:

   u = F x f,l ... F xr,r F yr t δ = T b f,l req ... T br,r req δ rreq t (13) (14)
Where the superscript t means the transpose. By adapting the MPC problem to our CA problem, we can define the MPCA problem as: find δ ∈ R n such that

B u = v (15) subject to                  ˙ u = A d u + B d δ u min ≤ u ≤ u max ˙ u ≤ ˙ u max δ min ≤ δ ≤ δ max ˙ δ ≤ ˙ δ max (16) (17) (18) (19) (20)
Where A d and B d are filled with the discretized parameters a i and b i respectively according to equations [START_REF] Satzger | A model predictive control allocation approach to hybrid braking of electric vehicles[END_REF] and [START_REF] Zhao | Model predictive control allocation for stability improvement of four-wheel drive electric vehicles in critical driving condition[END_REF]. The limits imposed to u are due to the friction ellipse [START_REF] Kissai | A new linear tire model with varying parameters[END_REF], while the limits imposed to δ are due to the actuators' saturations. Since the algorithm generates directly the actuator commands, the mild-level layer and the lowlevel layer in Fig. 1 are now merged into one layer as Fig. 8 shows. Following the MPC framework, the cost function to be minimized here is therefore:

J mpca (k) = T i=1   5 j=1 B j u j (k + i) -v (k + i)   2 + γ T i=1 5 j=1 W u (j) (δ j (k + i)) 2 (21)
The major motivation that drove us to use MPC theory for CA problems is the presence of input time-delays. In this context, the prediction horizon T should be at least superior to the bigger time-delay. In our case, the VDC system has a time-delay of almost 180ms while the 4WS system has a time-delay of almost 50ms. Therefore, we choose T = 200ms. The idea is then to compute the evolution of states through the prediction horizon, and choose as an output the commands that should be applied at the time step k by taking into account the time-delays. This is especially relevant when the 4WS system, as the most effective system [START_REF] Kissai | A Comprehensive Comparison of Chassis Systems Coordination Approaches[END_REF], saturates, and the VDC system has to be activated instantly afterwards. Following the same representation as in Fig. 7, an illustration of our case is presented in Fig. 9. We can see that thanks to Fig. 9. The MPCA scheme (adapted from [START_REF] Hanger | Model Predictive Control Allocation[END_REF]).

the prediction of the saturation of the effective rear steering angle, the algorithm can request the braking torque few steps before the saturation taking into account the delay and raising time of the VDC. In this way, as soon as the 4WS is saturated, effective braking torques can be applied and complete the maximum effort generated by the 4WS system.

Finally, one major difference with respect to other researches in MPCA [START_REF] Satzger | A model predictive control allocation approach to hybrid braking of electric vehicles[END_REF], [START_REF] Zhao | Model predictive control allocation for stability improvement of four-wheel drive electric vehicles in critical driving condition[END_REF], [START_REF] Hanger | Model Predictive Control Allocation[END_REF], is the solver used to solve the problem. In most of these researches, the computation effort constitute one of the major drawbacks. As shown in [START_REF] Kissai | Complementary Chassis Systems for Ground Vehicles Safety[END_REF], the ASA solver coupled with the WLS formulation gives fast and reliable results in a limited number of iterations. Therefore, ASA is again used here to solve the MPCA problem. The only additional effort required from the control designer is to transform the problem in a WLS formulation.

V. SIMULATION RESULTS

As a first step, the algorithm should be first validated by simulation. However, in order to present realistic simulation results, we test the control architecture using the experimentally identified models via Matlab R2017b R in a CORE i7 7 th generation machine. One can think of using co-simulation of Matlab R and a high-fidelity software as LMS Imagine.Lab AMESim R [START_REF] Kissai | Complementary Chassis Systems for Ground Vehicles Safety[END_REF], [START_REF] Zhao | Model predictive control allocation for stability improvement of four-wheel drive electric vehicles in critical driving condition[END_REF], however, even these high-fidelity softwares do not encompass the latest advanced chassis systems with their real dynamics.

In order to evaluate the relevance of the MPCA, we test both the classic dynamic CA and the MPCA when the 4WS saturates. This could happen when avoiding a pop-up obstacle and turning the front steering wheel really fast. We represent simply this situation as a step command applied to the yaw rate target. The results for both methods are illustrated in Fig. 10. As Fig. 10 shows, the response of the vehicle using the MPCA is faster than the classic dynamic CA. To understand the reason behind this, we analyse the effective commands in each approach. The effective rear angle and the effective front-left brake torque3 in case of the classic CA is depicted in Fig. 11. Because the control allocator acts only after the saturation of the 4WS system, the VDC is activated only after its characteristic input time-delay of 180ms. This explains also the deflection of the yaw rate signal in case of the classic dynamic CA in Fig. 10.

In contrast, as Fig. 12 shows, this is not the case when using the MPCA algorithm. Thanks to the prediction ability of the MPCA and the precise description of the actuators' dynamics, the request of brake torques is generated before the 4WS saturation. Not only the brake torques are activated as soon as the 4WS is saturated, but they are activated few steps before in order to get the right amount of the brake torques after the saturation.

VI. INDUSTRIAL LIMITS

Our motivation is to make commercial passenger cars safer, more comfortable, and increase their performance. However, all these advantages come with a price, which is an increased complexity. In general, this induces a higher computation effort demand in case of the existence of a solution. For the MPC theory, an additional challenge is added, which is robustness.

A. Computation Effort

Classic dynamic CA algorithms run an optimization solver online. This is already a challenging task when it comes to the automotive control where the dynamics can change in milliseconds. Regarding the MPCA, the same procedure should be redone through all the prediction horizon. If the prediction horizon is 200ms, and if we take a sampling time of 10ms, 20 CA problems should be solved at each step. Needless to say that faster and more expensive Electronic Control Units (ECUs) are required. The increase in cost should be justified by the additional features that the MPCA provides. If fault-tolerance is required between the embedded systems, and if a redundant system is more expensive than a faster ECU, then the choice of the MPCA is cost-effective. Another option is to well tune the MPCA algorithm. The designer can reduce the prediction horizon. However, in the presence of time-delays, these latter impose a minimum value to the prediction horizon. The other alternative is reducing the MPC sampling time. The drawback is that the command becomes more aggressive. Last but not least, is to solve the problem offline when it is possible. This is called the explicit MPC [START_REF] Alessio | A Survey on Explicit Model Predictive Control[END_REF]. However, for multi-objectives problems, an analytic solution could be hard to determine. This falls right in our problem as we are aiming for safety, comfort and performance when it is possible. A compromise should be found between the performance of the algorithm and the cost of the ECU.

B. Robustness

The second drawback is the robustness. The performance of the MPCA is closely related to the implemented model. The more precise this model is, the better the control performances are, and vice-versa. This is the reason that drove us to choose the experimentally identified models to design the MPCA, and a high-level H ∞ controller. Nevertheless, important effort have been deployed in the field of Robust MPC. To introduce robustness, a family of systems is considered by adding an unmeasured noise as an input to the system. A survey on Robust MPC is provided in [START_REF] Bemporad | Robust model predictive control: A survey, Robustness in identification and control[END_REF]. The same techniques can be expected for the MPCA.

Adding robustness in this way may reduce the performances of the controller. Another solution could be the online identification of the plant model in the same style as the Model Reference Adaptive Control (MRAC) [START_REF] Alan | High-Performance Adaptive Pressure Control in the Presence of Time Delays: Pressure Control for Use in Variable-Thrust Rocket Development[END_REF]. The problem in our case is that we need the identification of the actuators models. In this case, we need both the request signal and the effective signal at the input and output of each actuator repectively. Regarding the VDC system, we do not measure the effective torque brakes due to the cost of their sensors. An additional challenge of estimating the effective brake torque is expected. With online identification, online optimization and prediction, the complexity might become unmanageable. Both Robust MPC and MRAC theories are expected to be investigated in our upcoming works.

VII. CONCLUSIONS

In this paper, a Model Predictive Control Allocation algorithm has been developed for systems with different dynamics and time-delays. This algorithm has been compared to the classic dynamic control allocation algorithm. The MPCA has proven its relevance especially in the presence of saturation of one of the chassis systems. The prediction of this saturation leads to the activation of the secondary systems at the right moment. This MPCA method requires however higher computation effort and lacks of robustness. Due to the attractive features that this method offers, our future works are focused on the reduction of computation effort through the optimization of the solver, as well as the improvement of the control logic robustness.

Fig. 1 .

 1 Fig. 1. Multi-layered control architecture.

Fig. 2 .

 2 Fig. 2. The identification problem in an over-actuated vehicle.

Fig. 3 .

 3 Fig. 3. Comparison of the measured response and the estimated ones.

Fig. 4 .

 4 Fig. 4. Comparison of the measured response and the estimated ones for the 4WS actuator.

Fig. 5 .

 5 Fig. 5. Comparison of the measured response and the estimated ones for the VDC. poles, one zero, and one delay are needed to represent both the vehicle and the VDC system.By analyzing all the poles and zeros identified (see Fig.6), we can see that the complex poles of both dynamic models are close enough. The complex poles characterize then the vehicle dynamics. The remaining pole, zero and pure delay characterize the VDC system. These identified models are then used to synthesize both the high-level controller and the MPCA.

Fig. 6 .

 6 Fig. 6. Poles-zeros analysis.

Fig. 8 .

 8 Fig. 8. Multi-layered control architecture in case of MPCA.

Fig. 10 .

 10 Fig. 10. Comparison of the classic dynamic CA and the MPCA.

Fig. 11 .

 11 Fig. 11. The commands in case of classic dynamic CA.

Fig. 12 .

 12 Fig. 12. The commands in case of MPCA.

Moad Kissai, Bruno Monsuez, and Adriana Tapus are with ENSTA ParisTech, Autonomous Systems and Robotics Lab, Department of Computer and System Engineering (U2IS), 828 Boulevard des Marchaux, 91762

Called extensively as the 4-Wheel Steering (4WS) system by car manufacturers.

In this scenario, only the left brakes are activated to generate a positive yaw rate. The rear brakes are not illustrated because they have the same shape as the front brakes with just a lower amplitude.


Siem Van Der Laan

Nikolay Tsanov

Carole Crozet

Domenico Maiorano
email: domenico.maiorano@igh.cnrs.fr

High Dub3 expression in mouse ES cells couples the G1/S checkpoint to pluripotency

Keywords:

The molecular mechanism underlying G1/S checkpoint bypass in mouse embryonic stem (ES) cells remains unknown. DNA damage blocks S-phase entry by inhibiting the CDK2 kinase through destruction of its activator, the Cdc25A phosphatase. We observed high Cdc25A levels in G1 that persist even after DNA damage in mouse ES cells. We also found higher expression of Dub3, a deubiquitylase that controls Cdc25A protein abundance. Moreover, we demonstrate that the Dub3 gene is a direct target of Esrrb, a key transcription factor of the self-renewal machinery. We show that Dub3 expression is strongly downregulated during neural conversion and precedes Cdc25A destabilization, while forced Dub3 expression in ES cells becomes lethal upon differentiation, concomitant to cell cycle remodelling and lineage commitment. Finally, knockdown of either Dub3 or Cdc25A induced spontaneous differentiation of ES cells. Altogether, these findings couple the self-renewal machinery to cell cycle control through a deubiquitylase in ES cells. Highlights (85 character per point)  Cdc25A persistence upon DNA damage sustains G1/S checkpoint bypass in ES cells  Dub3 is rapidly downregulated during neural conversion and Cdc25A is destabilized  Dub3 is a target of Esrrb, a key transcription factor of the self-renewal machinery  Dub3 or Cdc25A knockdown induces heterogeneous differentiation in the presence of LIF

Introduction

Eukaryotic cells have developed checkpoints to block cell cycle progression upon

DNA damage or replication stress [START_REF] Ciccia | The DNA damage response: making it safe to play with knives[END_REF]. Two distinct pathways pertain to the G1/S checkpoint by directly reducing CDK2 activity: a) rapid destruction of the Cdc25A phosphatase resulting in increased CDK2 phosphorylation [START_REF] Mailand | Rapid destruction of human Cdc25A in response to DNA damage[END_REF][START_REF] Sexl | A rate limiting function of cdc25A for S phase entry inversely correlates with tyrosine dephosphorylation of Cdk2[END_REF], and b) a slower, p53-mediated, transcriptional response that activates expression of, amongst others, the potent CDK2 inhibitor p21 (Brugarolas et al., 1995;Dulic et al., 1994). Importantly, rapid p21 degradation observed after exposure to low UV doses may be important for optimal DNA repair (Bendjennat et al., 2003;Chen et al., 2004;Lee et al., 2006), while inhibition of CDK2 activity following Cdc25A degradation is sufficient for cell cycle arrest (Bendjennat et al., 2003). Cdc25A protein levels are tightly regulated by two E3 ubiquitin ligases, the Anaphase Promoting Complex/Cyclosome (APC/C Cdh1 ) as cells exit mitosis, and the Skp1-Cullin1-Fbox (SCF TrCP ) during both S and G2 phase and following DNA damage [START_REF] Busino | Degradation of Cdc25A by beta-TrCP during S phase and in response to DNA damage[END_REF][START_REF] Donzelli | Dual mode of degradation of Cdc25 A phosphatase[END_REF].

Compared to somatic cells, mouse embryonic stem (ES) cells appear to have a relaxed G1/S checkpoint [START_REF] Aladjem | ES cells do not activate p53-dependent stress responses and undergo p53-independent apoptosis in response to DNA damage[END_REF][START_REF] Hong | Restoration of an absent G1 arrest and protection from apoptosis in embryonic stem cells after ionizing radiation[END_REF][START_REF] Koledova | DNA damage-induced degradation of Cdc25A does not lead to inhibition of Cdk2 activity in mouse embryonic stem cells[END_REF][START_REF] Prost | p53independent DNA repair and cell cycle arrest in embryonic stem cells[END_REF]. The molecular mechanism underlying this feature remains unclear. Moreover, mouse ES cell cycle has remarkably short G1 and G2 phases, with little S phase length variation [START_REF] Ballabeni | Cell cycle adaptations of embryonic stem cells[END_REF][START_REF] Savatier | Analysis of the cell cycle in mouse embryonic stem cells[END_REF][START_REF] White | Developmental activation of the Rb-E2F pathway and establishment of cell cycleregulated cyclin-dependent kinase activity during embryonic stem cell differentiation[END_REF]. This is underpinned by high CDK2/Cyclin E activity [START_REF] Stead | Pluripotent cell division cycles are driven by ectopic Cdk2, cyclin A/E and E2F activities[END_REF] and reduced APC/C activity leading to limited oscillation in substrate levels [START_REF] Ballabeni | Cell cycle adaptations of embryonic stem cells[END_REF]. Interestingly, knockdown of CDK2 protein was shown to increase G1 length although DNA damage-dependent degradation of Cdc25A was reported not to affect CDK2 activity, nor to induce a G1 arrest [START_REF] Koledova | DNA damage-induced degradation of Cdc25A does not lead to inhibition of Cdk2 activity in mouse embryonic stem cells[END_REF][START_REF] Neganova | An important role for CDK2 in G1 to S checkpoint activation and DNA damage response in human embryonic stem cells[END_REF][START_REF] Neganova | Expression and functional analysis of G1 to S regulatory components reveals an important role for CDK2 in cell cycle regulation in human embryonic stem cells[END_REF]. In contrast, a previous study reported that Cdc25A is not degraded upon -irradiation in ES cells [START_REF] Hong | Restoration of an absent G1 arrest and protection from apoptosis in embryonic stem cells after ionizing radiation[END_REF].

Maintenance of pluripotency depends upon expression of pluripotency genes under the combinatorial control of a regulatory network of transcription factors such as Nanog, Sox2 and Oct4 [START_REF] Festuccia | The role of pluripotency gene regulatory network components in mediating transitions between pluripotent cell states[END_REF][START_REF] Van Den Berg | Estrogen-related receptor beta interacts with Oct4 to positively regulate Nanog gene expression[END_REF].

Differentiation of ES cell induces cell cycle remodelling, including appearance of longer G1 and G2 phases, but how this regulation is achieved is unknown. Moreover, how the pluripotency regulatory network impacts onto cell cycle control remains obscure. Aside from its well-known role in somatic cell cycle, very little is known about Cdc25A function in ES cells. In human ES cells, Cdc25A expression was shown to be regulated by Nanog [START_REF] Zhang | A role for NANOG in G1 to S transition in human embryonic stem cells through direct binding of CDK6 and CDC25A[END_REF]. A recent report shows that Nanog knockdown in mouse ES cells results in G1/S transition delay by an unknown mechanism [START_REF] Chen | Cell growth arrest and apoptosis induced by Oct4 or Nanog knockdown in mouse embryonic stem cells: a possible role of Trp53[END_REF]. Equally, the role of p53 in ES cells G1/S DNA damage checkpoint still remains controversial [START_REF] Aladjem | ES cells do not activate p53-dependent stress responses and undergo p53-independent apoptosis in response to DNA damage[END_REF][START_REF] Sabapathy | Regulation of ES cell differentiation by functional and conformational modulation of p53[END_REF][START_REF] Solozobova | Nuclear accumulation and activation of p53 in embryonic stem cells after DNA damage[END_REF]. Despite its high abundance, p53 has been proposed to be inactive in ES cells due to a predominant cytoplasmic distribution [START_REF] Solozobova | Nuclear accumulation and activation of p53 in embryonic stem cells after DNA damage[END_REF].

In this study we sought to understand the molecular grounds for inefficient G1/S DNA damage checkpoint in ES cells. We found that high Cdc25A abundance sustains G1/S checkpoint bypass in ES cells. We show that Cdc25A abundance depends upon high expression of Dub3, a deubiquitylase that fine-tunes Cdc25A steady-state levels [START_REF] Pereg | Ubiquitin hydrolase Dub3 promotes oncogenic transformation by stabilizing Cdc25A[END_REF]. Moreover, we identify Dub3 as a novel target gene of estrogen-related-receptor-b (Esrrb), a key transcription factor of the selfrenewal machinery [START_REF] Festuccia | Esrrb is a direct Nanog target gene that can substitute for Nanog function in pluripotent cells[END_REF][START_REF] Ivanova | Dissecting self-renewal in stem cells with RNA interference[END_REF][START_REF] Martello | Esrrb is a pivotal target of the Gsk3/Tcf3 axis regulating embryonic stem cell self-renewal[END_REF]. Strikingly, we observed acute downregulation of Dub3 expression upon differentiation and its knockdown induced spontaneous ES cell differentiation. In sum, our data interconnect the self-renewal machinery to cell cycle control and highlight the importance of deubiquitylases in stem cell and developmental biology.

Results

ES cells arrest in early S phase upon induction of DNA damage in G1

Circumstantial data suggest an impaired G1/S checkpoint in ES cells [START_REF] Hong | Restoration of an absent G1 arrest and protection from apoptosis in embryonic stem cells after ionizing radiation[END_REF][START_REF] Koledova | DNA damage-induced degradation of Cdc25A does not lead to inhibition of Cdk2 activity in mouse embryonic stem cells[END_REF][START_REF] Aladjem | ES cells do not activate p53-dependent stress responses and undergo p53-independent apoptosis in response to DNA damage[END_REF][START_REF] Prost | p53independent DNA repair and cell cycle arrest in embryonic stem cells[END_REF]. We observed that irradiation of ES cells with increasing doses of UV light induced a decrease in the number of G1 cells (Figure S1A). Time course analysis with a single UV dose (6 J/m 2 ) resulted in cell cycle delay at the G1/S boundary (Figure S1B, t=2).

We pulse-labelled nocodazole synchronized cells with BrdU (a nucleotide analogue) to allow exact distinction between late G1 (BrdU-negative) and early S-phase (BrdUpositive, Figure 1A). While analysis of total DNA content suggests a G1 arrest (Figure 1B), analysis of BrdU incorporation revealed that both untreated (Mock) and UV-irradiated cells (+ UV) entered S phase with very similar kinetics (Figure 1C-D). In contrast, synchronized mouse embryonic fibroblasts (NIH-3t3), which are Oct4negative differentiated cells (Figure S1C), did not progress to S phase after UV irradiation in G1 (Figure 1E), in line with the presence of a stringent G1/S checkpoint.

We noticed that upon UV irradiation, BrdU incorporation was slightly reduced compared to mock-irradiated cells, confirmed by calculating the mean fluorescent signal of BrdU-positive cells (Figure 1E, green boxes), and suggesting DNA synthesis slowdown in very early S phase. Analysis of chromatin-bound proteins shows that recruitment of both Cdc45 and DNA polymerase-two replication forkassociated factors, was considerably reduced upon UV irradiation, but not abolished (Figure S1D, compare lanes 2-4 with 5-7), suggesting activation of the S phase checkpoint preventing late replication origins firing [START_REF] Karnani | The effect of the intra-S-phase checkpoint on origins of replication in human cells[END_REF].

Consistent with this possibility, phosphorylated H2AX histone variant (H2AX), an ATR substrate, accumulated onto chromatin. Moreover UV-induced DNA damage did not significantly change the transcriptional program driven by E2F transcription factors required for S phase entry, as monitored by Cyclin A2 and E1 production (Figure S1E). We also observed UV damage-dependent p53 phosphorylation on chromatin (Figure S2A), and transactivation (amongst other) of p21 gene expression (Figure S2B-D), demonstrating a functional p53 transcriptional response, in line with a previous study [START_REF] Solozobova | Nuclear accumulation and activation of p53 in embryonic stem cells after DNA damage[END_REF].

Persistent high levels of Cdc25A in ES cells sustain G1/S checkpoint bypass

Cdc25A functions as a critical CDK2 regulator by removing an inhibitory phosphorylation on Tyrosine 15 (CDK2 Y15P ) that in turn regulates S phase progression. We compared Cdc25A and CDK2 protein abundance between ES cells and NIH-3t3 cells (Figure 2A). Strikingly, while CDK2 abundance is marginally higher in ES cells, the levels of Cdc25A in asynchronously growing ES cells are exceedingly high compared to NIH-3t3 cells. As expected, upon UV-induced DNA damage, Cdc25A was degraded in both cell lines (Figure 2A). However, one hour after irradiation, Cdc25A level remained about 4-fold higher in ES cells compared to unperturbed NIH-3t3 cells (lanes 1 and 7 and Figure S3A), indicating that high levels of Cdc25A persist even upon UV-induced DNA damage. Since cell cycle distribution of asynchronously growing ES and NIH-3t3 cells is different, we analysed Cdc25A abundance in synchronized cells (Figure 2B). We observed that in G1, ES cells contained about 7-fold more Cdc25A protein than NIH-3t3 cells (lanes 3 and 11 and Figure S3B). Proteolysis of Cdc25A mediated by the E3 ubiquitin ligase APC Cdh1 occurs at mitotic exit [START_REF] Donzelli | Dual mode of degradation of Cdc25 A phosphatase[END_REF]. Polyubiquitylated forms appear as a polypeptide ladder of higher molecular weight than the unmodified protein. In NIH-3t3 cells synchronized in G1 and S phase, we could observe such ladders by western blot using a specific Cdc25A antibody (Figure 2B,dark). Strikingly, in synchronized ES cells, these isoforms are much less abundant, whereas levels of unmodified Cdc25A are 7-fold higher than in NIH-3t3 cells (Figure S3B). Cdc25A immunoprecipitation from either ES or NIH-3t3 cells cotransfected with GFP-Cdc25A and HA-tagged ubiquitin, confirmed the presence of much more Cdc25A polyubiquitylated forms in NIH-3t3 than in ES cells (Figure 2C), corroborating recent data [START_REF] Buckley | Regulation of pluripotency and cellular reprogramming by the ubiquitin-proteasome system[END_REF].

Next we tested whether incomplete Cdc25A degradation may be due to impaired function of the ATR-Chk1 pathway. To this end, we treated cells with a Chk1 inhibitor and analyzed Cdc25A protein levels upon UV irradiation. In contrast to a previous report in which degradation of Cdc25A was not affected by both Chk1 and Chk2 inhibitors [START_REF] Koledova | DNA damage-induced degradation of Cdc25A does not lead to inhibition of Cdk2 activity in mouse embryonic stem cells[END_REF], we observed that Cdc25A degradation in ES cells is entirely dependent on Chk1 activity (Figure 2D). One explanation for this discrepancy may be that we analysed Cdc25A protein turnover in presence of cycloheximide to inhibit translation, since it is known that Cdc25A abundance is also regulated at this level [START_REF] Gautier | The cell cycle regulator CDC25A is a target for JAK2V617F oncogene[END_REF].

Treatment of asynchronously growing ES cells with roscovitine (a selective

CDKs inhibitor) induced dose-dependent increase of G1 cells and reduced the fraction of S phase cells (Figure S3C), demonstrating that, similar to somatic cells, in ES cells CDK activity is necessary for the G1/S transition. Inhibitory CDK2 Y15 phosphorylation is mediated by Wee1 kinase and relieved through dephosphorylation by Cdc25A [START_REF] Busino | Cdc25A phosphatase: combinatorial phosphorylation, ubiquitylation and proteolysis[END_REF][START_REF] Malumbres | To cycle or not to cycle: a critical decision in cancer[END_REF]. We therefore analysed changes in protein level of Wee1, Cdc25A, and CDK2 Y15P during G1/S transition in ES cells, which, according to BrdU uptake experiments, occurs between 2-3 hours after nocodazole release (Figure 1C). Mitotic exit was monitored by histone H3 phosphorylation at serine 10 (H3 S10P ), and S phase entry by H3 and Cyclin A production. Interestingly, Wee1 levels did not show significant cell cycle-dependent variations, while Cdc25A levels decreased and inversely correlated with CDK2 Y15P abundance (Figure S3D-E), suggesting that in ES cells, cell cycle-dependent fluctuation of Cdc25A levels may specifically regulate CDK2 Y15P .

To further pinpoint the specific role of Cdc25A in the G1/S checkpoint, we examined whether interfering with Cdc25A levels by RNAi affects S-phase entry upon DNA damage (Figure S3F-G). To avoid undesired differentiation of ES cells due to G1 phase extension upon Cdc25A downregulation that would interfere with the interpretation of this experiment (see below and Figure 6E-F), knockdown was performed over a short period (24 hours). Interestingly, Cdc25A knockdown (Figure 2E) resulted in a significant, UV-dependent, increase of BrdU-negative cells with 2N DNA content (Figure 2F) mirrored by increased CDK2 Y15P levels (Figure 2E, compare lane 3 with lane 6 and Figure S3H). Importantly, the slight increase of CDK2 Y15P levels between 2 and 4 hours after release (Figure 2E, lane 3), also observed in synchronized undamaged cells entering S-phase (Figure S3D), did not result in an apparent difference in S phase entry in mock and UV-treated cells transfected with control RNAi (Figure 2F). Altogether, these data show that ES cells contain high levels of Cdc25A and that its knockdown leads to a UV-dependent G1 delay.

ES cells express high Dub3 deubiquitylase

Elevated Cdc25A protein levels can be explained by increased gene expression, increased translation or reduced protein degradation. We analysed protein turnover in the presence of cycloheximide to inhibit de novo protein synthesis (Figure S4A-B).

Using this approach, we found a 3-fold longer half-life of Cdc25A in ES cells (t 1/2 = 24 min) compared to NIH-3t3 cells (t 1/2 = 8 min). Of note, since unsynchronized cells were used, we cannot exclude that the observed difference is partly due to distinct cell cycle distribution of both cell types. However, this data strongly suggests alterations in protein stability that, according to data shown in Figure 2B-C, might reflect differences between polyubiquitylation and ubiquitin removal by hydrolysation (deubiquitylation). To address this point, we compared gene expression of Cdc25A, Cdh1, -TrCP and that of the recently described Dub3 deubiquitylase [START_REF] Pereg | Ubiquitin hydrolase Dub3 promotes oncogenic transformation by stabilizing Cdc25A[END_REF], between ES and NIH-3t3 cells. Whereas mRNA levels of Cdc25A, Cdh1 and TrCP in ES cells hardly differ from NIH-3t3 cells, Dub3 mRNA level was 4-fold higher in ES cells (Figure 3A). Moreover, RNAi-mediated knockdown of Dub3 in ES cells (Figure 3B) did not affect Cdc25A mRNA level (Figure 3C) but resulted in 3-fold reduction of Cdc25A protein abundance (Figure 3D). These data are consistent with previous work in human cells [START_REF] Pereg | Ubiquitin hydrolase Dub3 promotes oncogenic transformation by stabilizing Cdc25A[END_REF] [START_REF] Ballabeni | Cell cycle adaptations of embryonic stem cells[END_REF].

Orphan receptor Esrrb regulates Dub3 gene expression

Based on previously described consensus sequence for binding motifs of key transcription factors involved in reprogramming [START_REF] Chen | Integration of external signaling pathways with the core transcriptional network in embryonic stem cells[END_REF][START_REF] Thomson | Pluripotency factors in embryonic stem cells regulate differentiation into germ layers[END_REF], we analyzed the proximal promoter (6 kb) of the Dub3 gene. Strikingly, while no Oct4, Nanog, Klf4, Smad1, Stat3, c-Myc nor n-Myc consensus sites could be detected, we originally (NCBI37/mm9) found up to seven estrogen-related-receptor-b (Esrrb) putative binding motifs (consensus: 5'-TNAAGGTCA-3') [START_REF] Deblois | Genome-wide identification of direct target genes implicates estrogen-related receptor alpha as a determinant of breast cancer heterogeneity[END_REF] and two Sox2 putative response elements (consensus: 5'-CATTGTT-3'). However the latest update of this genomic sequence (GRCm38/mm10) displays only three Esrrb sites (Figure 4A, Esrrb-RE). Esrrb is a nuclear receptor belonging to the superfamily of nuclear hormone receptors. Together with Sox2, it is part of the core self-renewal machinery [START_REF] Festuccia | Esrrb is a direct Nanog target gene that can substitute for Nanog function in pluripotent cells[END_REF][START_REF] Ivanova | Dissecting self-renewal in stem cells with RNA interference[END_REF][START_REF] Martello | Esrrb is a pivotal target of the Gsk3/Tcf3 axis regulating embryonic stem cell self-renewal[END_REF]. Esrrb knockdown using a previously validated RNAi sequence [START_REF] Feng | Reprogramming of fibroblasts into induced pluripotent stem cells with orphan nuclear receptor Esrrb[END_REF] resulted in significant decrease of endogenous Dub3 transcript level (Figure 4B), to a similar extent than the previously described Esrrb target gene Nanog (van den [START_REF] Van Den Berg | Estrogen-related receptor beta interacts with Oct4 to positively regulate Nanog gene expression[END_REF]. Inversely, ectopic expression of Esrrb in ES cells, and not of its C-terminal truncated form (∆-Cter) lacking the activation function 2 (AF2) domain, led to significant increase in endogenous Dub3 mRNA level (Figure 4C). Moreover, treatment of ES cells with increasing dose of DY131, a previously described selective Esrrb and Esrrg agonist [START_REF] Yu | Identification of an agonist ligand for estrogenrelated receptors ERRbeta/gamma[END_REF], boosted Dub3 gene expression and increased Cdc25A protein abundance without affecting Cdc25A transcript level (Figure S5A-B). Inversely, Esrrb knockdown resulted in a 40% decrease of DY131mediated Dub3 transcription (Figure S5C), while Sox2 knockdown using a previously published RNAi sequence [START_REF] Walker | Prediction and testing of novel transcriptional networks regulating embryonic stem cell self-renewal and commitment[END_REF] did not strongly affected Dub3 expression, though slightly increased it (our unpublished observations).

Next we performed chromatin immunoprecipitation (ChIP) experiments to map

Esrrb and Sox2 binding to Dub3 promoter in ES cells. To this end, we designed five primer pairs (Figure 4A, pp) separated by approximately 1kb to scan promoter occupancy by Esrrb and Sox2 within the 6kb upstream of the start codon (ATG+1).

Sonication of chromatin resulted in fragments under 500 bp, limiting signal overlap between primers (Figure S5D). ChIP analysis with an anti-Esrrb antibody (Figure S5E) shows that Esrrb binds to the proximal Dub3 promoter in regions containing the three Esrrb consensus binding motifs (Figure 4D, pp 3-5), while no Esrrb binding was observed in an upstream region that does not contain Esrrb binding sites (pp 1-2).

On the contrary, ChIP analysis with an anti-Sox2 antibody showed high enrichment only at one of the two consensus sites in the Dub3 promoter (Sox2-RE2), around primer pair 3, while in the region containing the second site (Sox2-RE1, pp4-5) Sox2 was bound to much lower levels.

To corroborate abovementioned ChIP data, we cloned the Dub3 proximal promoter (3,2 kb) and analyzed its transcriptional activity in a reporter assay using luciferase activity as readout. For this purpose we used cells that have very low expression of endogenous steroid receptors (CV1 cells). As anticipated, we observed strong induction of luciferase activity upon Esrrb expression in cells cotransfected with the 3.2 kb Dub3 promoter that contains all three Esrrb binding sites (Figure 4E, Esrrb, white bars) while only background activity was observed on a region of the Dub3 promoter (5' far) devoid of Esrrb consensus binding sites (Esrrb, black bars).

Similarly, expression of Esrrb ∆-Cter, resulted in basal promoter activity, comparable to that observed by expression of empty vector (EV, Figure 4E andS5F).

Interestingly, we did not observe stimulation of luciferase activity upon expression of Sox2, but a small and significant repression of basal promoter activity (Figure 4E). Importantly, mutation of the unique Esrrb binding site in a 1kb Dub3 genomic fragment decreased transcriptional activity (Figure 4F). Altogether these observations suggest that Dub3 is a direct Esrrb target gene, having a positive role in regulating transcription of the Dub3 gene, while Sox2 on its own is not sufficient to stimulate Dub3 transcription.

Developmental regulation of Dub3 expression and Cdc25A stability

Esrrb is a pluripotency factor highly expressed in ES cells that, unlike Sox2, is strongly downregulated upon ES differentiation [START_REF] Percharde | Ncoa3 functions as an essential Esrrb coactivator to sustain embryonic stem cell self-renewal and reprogramming[END_REF]. Since Dub3 is an Esrrb target, we analyzed expression of Dub3 during neural conversion of ES cells in vitro. Plating of ES cells in N2B27 culture medium triggers conversion into neuroepithelial precursors [START_REF] Ying | Conversion of embryonic stem cells into neuroectodermal precursors in adherent monoculture[END_REF] microscopically visible as rosette conformations (Figure 5A, day 7). Loss of pluripotency was monitored by expression analysis of specific markers such as Oct4, Nanog, Klf4, and acquisition of neural identity was monitored by Nestin and Sox1 expression. Specificity was controlled by analysis of Sox7 expression, a well-established endoderm marker (Figure S6A-B).

Importantly, Nestin was detectable in just about each individual cell of the differentiating population at day 6, indicating homogenous neural conversion. Acute (within 24 hours) decrease of Esrrb mRNA expression preceded in time a marked and dramatic decrease of Dub3 expression (Figure 5B). Expression of Sox2 also decreased after 24 hours, however of only 50% and increased afterwards. In contrast, neither Cdc25A nor Cdh1 or -TrCP transcript levels significantly changed during differentiation (Figure 5B, middle panel). Expression analysis of three other deubiquitylases implicated in Cdc25A stability, USP13, 29 and 48 [START_REF] Pereg | Ubiquitin hydrolase Dub3 promotes oncogenic transformation by stabilizing Cdc25A[END_REF] revealed a decrease of only USP48 within 24 hours after differentiation (Figure 5B, lower panel) that mirrored Sox2 expression. Importantly, we could not find any consensus Esrrb binding sites within the USP48 proximal promoter. In contrast, USP13 gene expression did not significantly change during differentiation, while USP29 expression strongly increased during neural conversion.

To analyze Dub3 protein levels we raised a specific antibody recognizing, as expected, a 60 kDa polypeptide in SDS-PAGE (Figure S6C-D). Dub3 protein levels dropped massively very early during differentiation, much earlier than Oct4, finely correlating with Dub3 mRNA levels (Figure 5C). Strikingly, lineage commitment between days 2-3, as monitored by Sox1 expression, led to a marked and continuous decrease of Cdc25A protein level, while the protein level of the two other Cdc25 family members, Cdc25B and Cdc25C, remained constant during differentiation (Figure S6E). We further analyzed expression of two additional Dub3 substrates during differentiation, RhoA (de la Vega et al., 2011) and Suds3 [START_REF] Ramakrishna | Lys-63-specific deubiquitination of SDS3 by USP17 regulates HDAC activity[END_REF], and observed no significant variations in gene expression (Figure S6F), nor in protein stability (Figure 5C), although a small decrease in Suds3 level was seen at day 7 after differentiation. Finally, we found very low expression of Esrrg (another member of the subfamily) in ES cells that further increased during differentiation (Figure S6F), corroborating the specificity of Dub3 gene regulation by Esrrb.

Altogether, these findings suggest that reduced Cdc25A protein abundance during neural differentiation is likely governed at the post-translational level.

While retaining self-renewal properties, neural stem cells (NSC) are multipotent stem cells derived from ES cells, isolated and amplified at day 7 following differentiation. Quantification of Cdc25A abundance revealed 8-fold more Cdc25A in asynchronously growing ES cells compared to NSCs (Figure 5D). Similar to NIH-3t3 cells, we detected very low Dub3 transcript levels in NSCs (Figure S6G). Finally, we isolated and analyzed three different genomic fragments of the Dub3 promoter and compared basal transcriptional activity in NIH-3t3 versus ES cells. We observed strong transcriptional activity of all three promoter sequences in ES cells, about 10fold higher than in NIH-3t3 cells (Figure 5E), further corroborating mRNA expression during differentiation (Figure 5B).

Dub3 expression is important for maintenance of pluripotency and cell cycle remodelling during differentiation

Stable transfection of Esrrb in ES cells has been shown to be sufficient to sustain pluripotency in absence of LIF [START_REF] Zhang | Esrrb activates Oct4 transcription and sustains self-renewal and pluripotency in embryonic stem cells[END_REF]. We therefore addressed whether forced Dub3 expression in ES cells could substitute Essrb function in maintaining pluripotency in absence of LIF. To this end, we generated a stable ES cell line, expanded from a single ES colony, expressing eGFP-Dub3 under control of a constitutive strong promoter (Figure 6A). Remarkably, while Pereg et al. (2012) reported that high Dub3 expression induces S-G2/M arrest in human somatic U2OS cells, ES cells overexpressing Dub3 could be propagated without significant differences in cell cycle distribution compared to a control cell line, indicating that in ES cells constitutive Dub3 expression is not toxic (Figure S7A-B). Removal of LIF led to an apparent highly similar morphological differentiation program in both cell-lines, but unexpectedly resulted in massive death of eGFP-Dub3-expressing ES cells two days after, microscopically visible as detached cells with retracted nuclei (Figure 6B, arrows). Of note, five days following LIF withdrawal, hardly any cell survived in the eGFP-Dub3 expressing cell-line. Caspase-3 activity, essential for proper differentiation [START_REF] Fujita | Caspase activity mediates the differentiation of embryonic stem cells[END_REF], was higher at days 3-4 in eGFP-Dub3 expressing cells compared to empty vector, strongly indicative of apoptosis (Figure 6C and Figure S7C). Finally, whereas mRNA and protein levels of pluripotency and differentiation markers were highly comparable in both cell lines, we observed elevated expression of the apoptotic marker Noxa at day two and afterwards in eGFP-Dub3 expressing cells (Figure S7D).

Remarkably, 2-3 days upon LIF removal, a strong reduction of eGFP-Dub3 protein level was evident (Figure 6C), suggesting an additional control at posttranscriptional level, very likely proteolysis, occurring during differentiation. A similar phenotype was observed upon N2B27-mediated neural conversion, and a similar result was also observed with a ES cell line expressing HA N-terminal-tagged Dub3 (Figure S7E-F), ruling out a non-specific effect of the GFP tag or of the differentiation protocol used. Onset of apoptosis, was equally observed by FACS analysis (Figure 6D), that showed the presence of subdiploid (less than 2N) cell debris starting from day three during differentiation and being predominant at day four. Interestingly, appearance of the sub-G1 cell population in ES cells expressing eGFP-Dub3 was concomitant to cell lineage commitment, as monitored by Sox1 and Nestin expression (Figure S6A) and cell cycle remodelling which started at day three in the control cell line (empty vector), resulting in lengthening of the G1 phase (Figure 6D).

Altogether these results strongly suggest that high Dub3 expression is lethal during differentiation at the time when cell cycle remodelling occurs.

Discussion

In this study we dissected the G1/S checkpoint signalling pathway in ES cells. We found that ES cells maintain high levels of the Cdc25A phosphatase in G1 that persists even after DNA damage. Knockdown of Cdc25A expression resulted in a G1 delay and increased CDK2 Y15P after UV damage within 24 hours post RNAi treatment (a condition required to avoid natural G1 phase expansion due to differentiation of ES cells). Indeed, prolonged Cdc25A downregulation (or Dub3), resulted in cell differentiation in the presence of LIF, in line with the notion that lengthening of the G1 phase and deregulation of CDK2 activity is linked to differentiation [START_REF] White | Developmental activation of the Rb-E2F pathway and establishment of cell cycleregulated cyclin-dependent kinase activity during embryonic stem cell differentiation[END_REF]. These findings provide an explanation for absent regulation of CDK2 activity upon DNA damage in ES cells [START_REF] Koledova | DNA damage-induced degradation of Cdc25A does not lead to inhibition of Cdk2 activity in mouse embryonic stem cells[END_REF]. This model is also in line with existing evidence linking elevated Cdc25A expression with impaired G1/S arrest followed by radioresistant DNA synthesis in cancer cells [START_REF] Falck | The ATM-Chk2-Cdc25A checkpoint pathway guards against radioresistant DNA synthesis[END_REF].

Interestingly, in addition to Cdc25A, we have also observed down-regulation of Cyclin E (Figure S6H), another CDK2 regulator that is rate limiting during the G1/S transition and opposes spontaneous differentiation of naïve ES cells [START_REF] Coronado | A short G1 phase is an intrinsic determinant of naive embryonic stem cell pluripotency[END_REF]. Moreover, ablation of the SCF Fbw7 -mediated degradation pathway controlling Cyclin E abundance in vivo results in impaired differentiation, genomic instability and hyperproliferation [START_REF] Minella | Cyclin E phosphorylation regulates cell proliferation in hematopoietic and epithelial lineages in vivo[END_REF], illustrating the importance of Cyclin E regulation in mouse development. Taken together, both reduced abundance of Cdc25A and Cyclin E during differentiation of ES cells, likely embody key molecular adaptations that control CDK activity and consequent G1 lengthening.

Importantly, as a result of expanded G1, the p53-dependent response may now become more effective in CDK2 inhibition since this requires a slow transcriptionaldependent induction of the CDK inhibitor p21 protein level. It is anticipated that p21 may have virtually no role in CDK2 regulation in ES cells since these cells spend most of their time in S phase and p21 is efficiently degraded by the PCNA-dependent CRL4 Cdt2 ubiquitin ligase throughout S phase, as well as after DNA damage [START_REF] Abbas | PCNA-dependent regulation of p21 ubiquitylation and degradation via the CRL4Cdt2 ubiquitin ligase complex[END_REF].

We have provided evidence that post-transcriptional regulation of Cdc25A abundance in ES cells depends upon the Dub3 deubiquitylase. Expression of Dub3, and not Cdh1 or -TrCP, is higher in ES cells compared to differentiated cells, and knockdown of Cdh1 or -TrCP did not significantly change the stability of Cdc25A since it is already highly stabilized in ES cells. These observations are consistent with the finding that ES cells have attenuated APC activity that increases during differentiation [START_REF] Ballabeni | Cell cycle adaptations of embryonic stem cells[END_REF]. Of the four additional deubiquitylases implicated in Cdc25A stability in human cells (USP13, 29, 48 and Dub2A), we found that only USP48 mRNA levels significantly decreased during differentiation although its expression remained high and increased towards the end of differentiation, mirroring Sox2 expression. Hence, although we cannot exclude a redundant role for Dub2A and USP48 in Cdc25A stability during differentiation, our data support a key role for Dub3 in this process, as previously shown in somatic cells [START_REF] Pereg | Ubiquitin hydrolase Dub3 promotes oncogenic transformation by stabilizing Cdc25A[END_REF], and suggest that in ES cells the balance of ubiquitylation and deubiquitylation activities, which fine-tunes the steady-state level of Cdc25A, is shifted towards deubiquitylation due to high Dub3 expression.

We showed that downregulation of Esrrb negatively affected the endogenous expression of the Dub3 gene, to a similar extent than a previously characterized Esrrb target gene, Nanog (van den [START_REF] Van Den Berg | Estrogen-related receptor beta interacts with Oct4 to positively regulate Nanog gene expression[END_REF]. However, expression of Oct4, another Esrrb target [START_REF] Zhang | Esrrb activates Oct4 transcription and sustains self-renewal and pluripotency in embryonic stem cells[END_REF] was not found to be much affected by Esrrb knockdown [START_REF] Van Den Berg | Estrogen-related receptor beta interacts with Oct4 to positively regulate Nanog gene expression[END_REF]. These differences likely exist because in ES cells, expression of pluripotency genes is under the combinatorial control of transcription factors of the pluripotency gene regulatory network (van den [START_REF] Van Den Berg | Estrogen-related receptor beta interacts with Oct4 to positively regulate Nanog gene expression[END_REF]. This transcriptional control appears to be very complex, gene-specific and remains to be further clarified.

We observed that while forced Dub3 expression could not inhibit differentiation upon LIF withdrawal, unexpectedly it induced massive apoptosis during differentiation concomitant to lineage commitment and cell cycle remodelling, such as lengthening of the G1 phase. These observations are in line with the recent finding that expression of non-degradable Cdc25A mutants leads to early embryonic lethality in mice (E3.5) showing the importance of fine-tuning the expression level of Cdc25A already at the oocyte and morula stages [START_REF] Bahassi El | A human cancer-predisposing polymorphism in Cdc25A is embryonic lethal in the mouse and promotes ASK-1 mediated apoptosis[END_REF]. Although we have shown that Cdc25A is a critical Dub3 substrate in ES cells, we cannot exclude the implication of other Dub3 substrates (de la [START_REF] De La Vega | The deubiquitinating enzyme USP17 is essential for GTPase subcellular localization and cell motility[END_REF][START_REF] Ramakrishna | Lys-63-specific deubiquitination of SDS3 by USP17 regulates HDAC activity[END_REF] in the toxicity observed by forced Dub3 expression during differentiation. The importance of tight Cdc25A regulation during embryogenesis is also underscored by its function in regulation of pluripotency versus differentiation of ES cells since Cdc25A is expressed in progenitor cells undergoing proliferative self-renewing divisions [START_REF] Peco | The CDC25B phosphatase shortens the G2 phase of neural progenitors and promotes efficient neuron production[END_REF]. We speculate that this developmental regulation might be governed by Dub3 to modify cell cycle dynamics under control of Esrrb.

In conclusion our results couple the Cdc25A-CDK2 cell cycle signalling pathway to the self-renewal machinery through Esrrb-dependent regulation of Dub3 in ES cells, and highlight the importance of deubiquitylases in stem cell and developmental biology. Since cell cycle regulation is a rate-limiting step in reprogramming processes, these findings put Dub3 and Cdc25A as interesting candidate genes in cell reprogramming.

Experimental Procedures

Cell extracts, western blotting and antibodies

Cells were rinsed once in PBS and incubated in lysis buffer. Whole cell extracts were clarified by centrifugation at 12000 g for 10 min at 4°C. Protein concentration of was estimated by BCA (Pierce; see Supplemental information).

Cell culture and transfection

ES cells (CGR8) were cultured on gelatin-coated dishes in the absence of feeder cells with 1,000 U LIF per ml (Millipore). Cells were grown in a humidified atmosphere of 5% CO 2 at 37°C. For transient expression both NIH-3t3 and ES cells were transfected using X-tremeGENE 9 DNA (Roche), and CV1 with JetPEI (Polyplus), according to manufacturer's directions. For infection, retroviral particles were generated by transfecting Platinum-E ecotropic packaging cell line with retroviral expression vector (pLPC) encoding Myc 6 -Dub3 variants using home-made PEI reagent.

Cell synchronization

ES cells were arrested in prometaphase by nocodazole (Sigma) for 4-8 hours. After mitotic-shake off cells were washed 3 times in ice-cold PBS and dissolved in full ES growth medium. Cells were incubated in a humidified atmosphere of 5% CO 2 at 37°C for 45 minutes and placed at 30°C for 1 hour to reduce S phase entry. Cells were mock-or UV-irradiated (6 J/m 2 ) and incubated at 37°C prior collection. To synchronise NIH-3t3 cells in G 0 cells were grown to confluence and incubated for 2-3 days. Next, cells were washed, resuspended and split at 30% confluency. Six hours after release, cells were UV-irradiated.

UV-induced DNA Damage and Drugs

UV-C irradiation at 254nm was performed with microprocessor-controlled crosslinker (BIO-LINK ®) or with a UV-lamp (Hanovia). Cycloheximide and DY131 (GW4716) were from Sigma and Chk1 inhibitor SB218078 from Calbochiem.

Flow cytometry

Single-cell suspensions were prepared by trypsinisation and washed once in PBS.

Cells were fixed in ice-cold 70% ethanol (-20°C) and stored at -20 °C overnight.

Following RNAse A treatment, total DNA was stained with propidium iodide (25 µg/ml). For BrdU uptake analysis, ES cells and NIH-3t3 cells were grown in the presence of 10 µM BrdU for respectively 10 and 30 minutes. The BrdU content was determined by reaction with a fluorescein isothiocyanate (FITC)-conjugated anti-BrdU antibody (BD Biosciences). Cells were analyzed with a FACScalibur flow cytometer using CellQuestPro software.

RNA extraction, reverse transcription and quantitative real-time PCR

Total RNA was isolated with TRIzol reagent (Invitrogen). Reverse transcription was carried out with random hexanucleotides (Sigma) and Superscript II First-Strand cDNA synthesis kit (Invitrogen). Quantitative PCRs were performed using Lightcycler SYBR Green I Master mix (Roche) on Lightcycler apparatus (Roche). All primers used were intronspanning (primer sequences available upon request). The relative amount of target cDNA was obtained by normalisation using geometric averaging of multiple internal control genes (ACTB, HPRT, HMBS, GAPDH, SDHA).

Chromatin Immunoprecipitation

ES cells were formaldehyde cross-linked and sonicated using a Misonix sonicator S-4000. Cells were lysed in ice-cold lysis buffer (Supplemental Information). Primer pairs for promoter scanning (6 kb upstream of transcription start site, TSS) of the Dub3 murine promoter were designed approximately every 1 kb.

Monolayer differentiation of ES cells into neurectodermal precursors

This protocol was as previously described [START_REF] Ying | Conversion of embryonic stem cells into neuroectodermal precursors in adherent monoculture[END_REF]. (see also Supplemental information).

Isolation and amplification of NSC cells from CGR8 ES cells

ES cells were induced to differentiate into NSC following the protocol described above. At day 6, cells were dissociated in 0.01% Trypsine-EDTA and plated onto Poly-L-Ornithine/Laminin coated dishes in DMEM/N2 medium with 10 ng/ml of both EGF and bFGF (Biosource). For the preparation of Poly-L-Ornithine/Laminin plates, a 0.01% solution of poly-L-ornithine (Sigma) was added to plates for at least 20 min.

The solution was removed and plates were washed 3 times with PBS. A 1 µg/ml solution of laminin in PBS (Sigma) was then applied and incubated at 37°C for at least 3 hrs. Cells can then be cultivated and amplified under these conditions for several subpassages without loosing neural stem cells properties.

Establishment of a monoclonal eGFP-Dub3 expressing ES cells

Wild-type ES cells were transfected with pcDNA3-eGFPDub3, plated at clonal density and selected with G418 (Sigma). eGFP-Dub3 positive clones were expanded in continuous presence of G418 and validated by immunofluorescence and western blotting. and the pellet (Triton-insoluble fraction) was resuspended in CSK buffer and incubated for 10 min on ice. After centrifugation, the pellet (chromatin-enriched fraction) was resuspended in Laemmli Buffer. Equivalent amount of soluble and chromatin fractions were analyzed by immunoblotting.

Statistical analysis

Two-way ANOVA or Student t-test were used to evaluate differences between groups using Prism software (GraphPad Software). P < 0.05 was considered significant and indicated with *, P < 0.001 was indicated with **.

  and indicate that Dub3 function in regulating Cdc25A protein stability is analogous in mouse ES cells. In addition, we also observed a role of Dub3 in Cdc25A stability in unperturbed and damaged NIH-3t3 cells (Figure S4C-D). Of note, GFP-tagged Dub3 shows an exclusive nuclear localization (Figure 3E) as previously observed for Cdc25A in ES cells (Koledova et al., 2010). Finally, to address the role of Cdh1 and -TrCP in regulating Cdc25A levels in ES cells, we performed RNAi-mediated knockdown experiments. In contrast to Dub3 knockdown neither Cdh1, nor -TrCP downregulation affected Cdc25A mRNA expression nor did significantly alter Cdc25A stability (Figure S4E-F). These observations are consistent with a previous study showing that APC/Cdh1 activity is attenuated in ES cells by high levels of the Emi1 inhibitor

Finally

  we analyzed the effect of Dub3 or Cdc25A knockdown in ES cells. Interestingly, prolonged (7 days) RNAi mediated Dub3 knockdown, resulted in an increase of alkaline phosphatase (AP)-negative colonies, as well as heterogeneous morphological differentiation of ES cells even in the presence of LIF, suggesting that Dub3 expression is important for maintenance of pluripotency (Fig 6E-F). A very similar result was also observed upon prolonged Cdc25A knockdown. In sum, these data couple the self-renewal machinery of ES cells through Essrb to the master cell cycle regulator Cdc25A and remodelling of the cell cycle during differentiation through modulation of Dub3 expression.

Figure 1 :

 1 Figure 1: DNA damage in G1 induces transient ES cell cycle arrest in early S-phase

Figure 2 :

 2 Figure 2: Persistence of Cdc25A upon DNA damage in G1 sustains G1/S checkpoint

Figure 3 :

 3 Figure 3: Elevated deubiquitylase Dub3 in ES cells increases Cdc25A abundance.

Figure 4 :

 4 Figure 4: Dub3 is a target gene of the orphan receptor Esrrb.

Figure 5 :

 5 Figure 5: Developmental regulation of Cdc25A protein abundance correlates with

Figure 6 :

 6 Figure 6: Constitutive Dub3 expression leads to massive apoptosis concomitant to

Figure1

  Figure1Click here to download high resolution image

Figure S1 (

 S1 Figure S1 (related to Figure 1). Shows additional information providing evidence for an

Figure

  Figure S2 (related to Figure 1). Shows that the p53 transcriptional response is functional

Figure S3 (

 S3 Figure S3 (related to Figure 2). Provides additional information showing that Cdcd25A is

Figure S4 (

 S4 Figure S4 (related to Figure3). Provides evidence that Cdc25A half-life is higher in

Figure S5 (

 S5 Figure S5 (related to Figure 4). Shows that the Esrrb and Esrrg agonist DY131 boosts

Figure S6 (

 S6 Figure S6 (related to Figure 5). Provides additional data essential to control the

Figure

  Figure S7 (related to Figure 6). Provides additional information for the cell death

Acknowledgments

We thank J-M. Vanacker for Esrrb vectors, H. Te Riele for p53 -/-ES cells, P.

Stambrook and S. Manenti for Cdc25A wild-type and mutant cDNAs, J. Basbous for p53 reporter constructs, and F. Poulat for Sox2 vector. We also thank P. Coulombe and F. Cammas for technical assistance, and D. Hodroj, E. Golfetto and I. Peiffer for technical support. We tank V. Dulic and D. Fisher for critical reading of the manuscript. This project was supported from grants from ARC (grant N° 3156 to D.M. and personal fellowship to S. v. d. L) and FRM ("Equipes").

Supplemental Information

The molecular and cellular phenotype of HA-Dub3 expressing cells was highly comparable to the eGFP-Dub3 expressing cells indicating that the phenotype is independent of the N-terminal tag.

Supplemental Experimental Procedures

Cell culture and transfection

Briefly, ES cells were maintained in Glasgow MEM BHK-21 (GMEM) supplemented with 10% fetal bovine serum, non-essential amino acids, L-glutamine, sodium pyruvate, β-mercapthethanol. NIH-3t3 cells were maintained in Dulbecco's modified eagle's medium (DMEM) supplemented with 10% fetal bovine serum, 2 mM glutamine and antibiotics. The viruses-containing conditioned medium was incubated on exponentially growing NIH-3t3 cells for 24 hours in the presence of polybrene (10 mg/mL). 48 hours post-infection, cells were selected in puromycin (2.5 µg/mL)containing medium for 8-10 days before use. Reverse transfection of ES cells was performed using INTERFERin (Polyplus) according to manufacturer's directions. Cells were collected 24, 36 or 48 hours after transfection for analysis. The Cdc25A RNAi sequence was 5'-GAAAUUUCCCUGACGAGAA-3', Dub3 5'-GGCUGUAAGAUGUGUGCUA-3' and a Esrrb previously described [START_REF] Feng | Reprogramming of fibroblasts into induced pluripotent stem cells with orphan nuclear receptor Esrrb[END_REF]. RNAi for Cdh1 and β-TrCP knockdown were purchased from Darmacon (SMARTpool) 57371 (Cdh1) and 12234 (β-TrCP).

Monolayer differentiation of ES cells into neurectodermal precursors.

ES cells were dissociated and plated in N2B27 medium onto 0.1% gelatine-coated dishes at a density of 1.10 4 cells/cm². N2B27 medium is a 1:1 mixture of DMEM/F12

(Gibco) supplemented with modified N2 (25 µg/ml insulin, 100 µg/ml apo-transferrin, 6 ng/ml progesterone (Sigma), 16 µg/ml putrescine (Sigma), 30 nM sodium selenite (Sigma), 50 µg/ml bovine serum albumine (Gibco), Neurobasal medium supplemeted with B27 (Gibco), β-mercaptoethanol (0.1 mM) and glutamate (0.2 mM) was also added. The medium was replaced every two days until day 7.

Plasmids

The murine Dub3 gene (Gene ID:

Chromatin immunoprecipitation

Cells were lysed in ice-cold lysis buffer (50 mM Tris-HCl pH 7.4, 100 mM NaCl, 50 mM NaF, 5 mM EDTA, 40 mM β-glycero-phosphate, 1% SDS, 1% Triton X-100 and protease inhibitors) for 30 min on ice. Immuoprecipitation was performed by adding 5 µg Esrrb (Sigma SAB2100715), Sox2 (Bethyl A301-739) or control antibodies (Peprotech 500-P00) to lysates and incubation with rotation overnight at 4 °C. BSA and salmon sperm-blocked Protein A-Sepharose (Amersham) beads were added to the lysate.

Luciferase assay

ES cells were transfected with following reporter constructs, pG13-luciferase, p21luciferase and p21-ΔREp53-luc (kindly provided by J. Basbous, IGH, Montpellier). A Renilla luciferase plasmid was cotransfected as an internal control. Cells were harvested 24 hours after transfection and mock or UV-irradiated. Six hours following UV-induced DNA damage, cells were harvested and the luciferase activities of the cell lysates were measured using the Dual-luciferase Reporter Assay system (Promega). The proximal promoter of 1kb upstream ATG start codon was inserted into pGL4.10 plasmid. Three mutations of the Esrrb consensus binding site (TCAAGGTCA) were introduced by PCR to generate a mutated binding site (TCATTTTCA). All constructs were sequence verified.

Immunofluorescence microscopy

For Nestin, Oct4 and active caspase 3 staining staining, cells were fixed in 4% paraformaldehyde and permeabilized with 0,1% Triton X-100. After fixation, cells were blocked in 3% BSA PBS-Tween and incubated overnight with antibody. The slides were mounted using Prolong Gold with DAPI (Invitrogen). For determination of the cellular localisation of Dub3, mouse ES cells were transfected with pcDNA-GFP-Dub3 and directly fixed. All slides were analysed using a Leica DM6000 epifluorescence microscope. Images were acquired using a Coolsnap HQ CCD camera (Photometrics) and the metamorph software (Molecular Devices).

Subcellular fractionation experiments

Chromatin-enriched and soluble fractions were prepared using CSK-extraction procedure. Briefly, pelleted cells were lysed in CSK buffer (10 mM PIPES pH 6.8, 100 mM NaCl, 300 mM sucrose, 1 mM EGTA, 1 mM MgCl 2 , 0.5 mM DTT, 1 mM ATP, 0.2% Triton X-100 and protease inhibitors) for 10 min on ice. After centrifugation at