Huan Yu

Jean Auriol

Miroslav Krstic

Output-Feedback PDE Control of Traffic Flow on Cascaded Freeway Segments

Keywords: Traffic network, ARZ traffic model, PDE control, Backstepping

We develop in this paper a boundary output feedback control law for an underactuated network of traffic flow on two connected roads; one incoming and one outgoing road connected by a junction. The macroscopic traffic dynamics on each road segment are governed by Aw-Rascle-Zhang (ARZ) model, consisting of second-order nonlinear partial differential equations (PDEs) of traffic density and velocity. The control objective is to stabilize the traffic network system on both roads around a chosen reference system. Using a ramp metering located at the outlet of the outgoing road, we actuate the traffic flux leaving this considered domain. Boundary measurements of traffic flux and velocity are taken at the junction connecting the two road segments. A delay-robust full state feedback control law and a boundary observer are designed for this under-actuated network of two systems interconnected through their boundaries. Each system consists of two hetero-directional linear first-order hyperbolic PDEs. The exponential convergence to the reference system is achieved.

INTRODUCTION

Traffic flow networks based on macroscopic modeling have been intensively investigated over the past decades. The macroscopic modeling of traffic dynamics is used to describe the evolution of aggregated traffic state values including traffic density, velocity and flow rate on road. The traffic flow network based on the first-order Lightill-Whitham-Richards (LWR) model is theoretically proposed by [START_REF] Coclite | Traffic flow on a road network[END_REF] and studied for numerical simulation and applications in [START_REF] Treiber | Traffic Flow Dynamics-Data, Models and Simulation[END_REF]. The LWR model corresponds to a conservation law of the traffic density. It can predict the formation and propagation of traffic shockwaves on freeway, but fails to describe the stopand-go phenomenon which can be properly addressed by the second-order Aw-Rascle-Zhang (ARZ) model [START_REF] Aw | Resurrection of "second order" models of traffic flow[END_REF] [START_REF] Zhang | A non-equilibrium traffic model devoid of gas-like behavior[END_REF]. This second-order ARZ traffic model consists of a set of nonlinear hyperbolic PDEs describing the evolution of the traffic density and velocity. The macroscopic modeling of road networks based on the ARZ model has been developed in [START_REF] Garavello | Traffic flow on a road network using the aw-rascle model[END_REF], [START_REF] Herty | Coupling conditions for a class of second-order models for traffic flow[END_REF].

In this paper, we use the state-of-art ARZ model traffic flow network to describe the traffic dynamics of two interconnected freeway roads. The traffic network modeling proposed in [START_REF] Herty | Coupling conditions for a class of second-order models for traffic flow[END_REF] is adopted. The modeling of the junction of two connected roads conserves the mass and the other traffic property as detailed later in the paper. This property is not smooth across the junction in [START_REF] Garavello | Traffic flow on a road network using the aw-rascle model[END_REF]. In comparison, the solution in [START_REF] Herty | Coupling conditions for a class of second-order models for traffic flow[END_REF] is a weak solution (in the sense of the conservative variables of the ARZ model) that guarantees the well-posedness of the closed-loop system for our control design.

Traffic network control strategies are developed and implemented for the traffic management infrastructures such as ramp metering and varying speed limits. Previous contributions, in-cluding [START_REF] Gomes | Optimal freeway ramp metering using the asymmetric cell transmission model[END_REF], Jin and Amin (2018), [START_REF] Goatin | Speed limit and ramp meter control for traffic flow networks[END_REF], [START_REF] Zhang | Combined variable speed limit and lane change control for highway traffic[END_REF], mostly focus on the spatially discretized approximation of LWR model, namely cell transmission model and its derivation. The ramp metering optimal control problem is studied to improve various performance indexes including total travel time, ramp metering queue, throughput maximization, avoidance of capacity drop. Boundary feedback control algorithms are developed for traffic PDE modeling of a single freeway segment in [START_REF] Bastin | Stability and boundary stabilization of 1-d hyperbolic systems[END_REF], [START_REF] Karafyllis | Feedback control of scalar conservation laws with application to density control in freeways by means of variable speed limits[END_REF], [START_REF] Yu | Varying speed limit control of aw-rascle-zhang traffic model[END_REF], Yu and Krstic (2019), [START_REF] Zhang | P I boundary control of linear hyperbolic balance laws with stabilization of arz traffic flow models[END_REF]. These control laws are restricted to control problem of one segment and traffic network PDE control problems have not been studied to authors' best knowledge.

In authors' previous work Yu and[START_REF] Yu | Varying speed limit control of aw-rascle-zhang traffic model[END_REF]Krstic (2019), backstepping boundary control laws are designed for ramp metering and varying speed limits to suppress the stopand-go traffic oscillations on one freeway segment either upstream or downstream of the ramp. The problem of controlling the downstream and the upstream traffic simultaneously with a single boundary actuation remained open. More recently, Yu et al. (2019) considers a boundary state feedback control problem for a traffic flow network system in its most fundamental form: one incoming and one outgoing road connected by a junction. The macroscopic traffic dynamics on each road segment are governed by Aw-Rascle-Zhang (ARZ) model. This results into a network of two interconnected PDE systems coupled through their boundaries. Each subsystem corresponds to a 2 × 2 coupled hyperbolic system. The authors have considered a ramp metering located at the connecting junction actuating the traffic flow rate entering from the on-ramp to the mainline junction. The objective is to simultaneously stabilize the upstream and downstream traffic to steady states. In this paper, we consider the same traffic PDE model as the one given in Yu et al. (2019) but the actuation is now located at the outlet of the outgoing road segment. The main contribution of this thread of work is to provide an explicit PDE control design that simultaneously stabilizes the traffic flow on the two connected roads.

L L 0 ⇢ 1 , v 1 ⇢ 2 , v 2
The main contribution and novelty of this work, as a counterpart to Yu et al. (2019), lie in the following three aspects: different controlled boundary requires theoretically a new control design; different actuation locations allow the flexibility of implementation of the either of the control algorithms in practice; two control strategies can be evaluated under various performance objectives of the freeway traffic such as fuel consumption, comfort, and total travel time and therefore it is offered a choice when there are trade-offs between these objectives.

Despite the fact that numerous theoretical results in the literature are focused on the boundary control of this class of hyperbolic system based on the backstepping approach Anfinsen and Aamo (2019) Auriol and Meglio (2016) [START_REF] Coron | Local exponential H 2 stabilization of a 2× 2 quasilinear hyperbolic system using backstepping[END_REF][START_REF] Deutscher | Finite-time output regulation for linear 2 × 2 hyperbolic systems using backstepping[END_REF], the control of the network of PDEs remains a challenging research topic. This is due to the fact that in most cases, these systems are underactuated (only the PDE located at one extremity of the network can be actuated). To tackle this problem, multiple approaches have been proposed: PI boundary controllers by [START_REF] Bastin | Exponential stability of networks of density-flow conservation laws under PI boundary control[END_REF]; [START_REF] Bastin | Stability of linear density-flow hyperbolic systems under PIboundary control[END_REF], flatness based design of feedforward control laws by [START_REF] Schmuck | Flatness-based feed-forward control of an HVDC power transmission network[END_REF], boundary feedback control using weighted Lyapunov function by [START_REF] Herty | Feedback boundary control of linear hyperbolic systems with relaxation[END_REF] and more recently backstepping-based control laws by Auriol et al. (2019). In this paper, we will mainly adopt the theoretical result of full-state feedback design of Auriol et al. (2019). In addition, we propose boundary observer design to construct the output feedback controller which is a new theoretical contribution that has not been developed before.

The paper is organized as follows. In Section II, we introduce the freeway traffic flow system on two connected roads under consideration. In particular, we introduce the PDE model and boundary conditions describing the dynamics of the traffic density and velocity. These equations are then linearized around a given steady-state. A stabilizing state-feedback control law is obtained in Section III for this underactuated system using backstepping approach. In Section IV we design the boundary observer. Finally, some concluding remarks are given in Section V.

PROBLEM STATEMENT

We consider a model for two connected road segments with unidirectional traffic flow. The outgoing road segment corresponds to x ∈ [0, L] and the incoming road segment to x ∈ [-L, 0]. They are connected at the junction through the boundary x = 0. The traffic dynamics of each road segment are described with two systems of PDE models and the junction is given as a set of boundary conditions for the PDE model, which allows weak solutions for the traffic network problem [START_REF] Herty | Coupling conditions for a class of second-order models for traffic flow[END_REF].

ARZ PDE model

The evolution of traffic density ρ 1 (x,t) and velocity v 1 (x,t) for ) is modeled by the following ARZ model (as shown in Fig. 1):

(x,t) ∈ [0, L] × [0, ∞) and traffic density ρ 2 (x,t) and velocity v 2 (x,t) for (x,t) ∈ [-L, 0] × [0, ∞
∂ t ρ i + ∂ x (ρ i v i ) =0, (1)
∂ t (ρ i w i ) + ∂ x (ρ i v i w i ) = - ρ i (v i -V i (ρ i )) τ i , (2)
where the variable w i is interpreted as "friction" or drivers' aggressiveness of each vehicle that transports in the traffic flow. The traffic flow velocity v i is related to w i by

v i = w i -p i (ρ i ).
(3) where the traffic pressure is defined as an increasing function of the density,

p i (ρ i ) = (v m /ρ γ i m,i )ρ γ i i .
The traffic pressure p i (ρ i ) can be interpreted as the effect that forces drivers to slow down when there is a denser traffic density. The maximum velocity v m is assumed to be the same for the two road segments while the maximum density ρ m,i and coefficient γ i ∈ R + representing drivers' property are allowed to vary in the different segments, due to different compositions of drivers and vehicles or road attributes.

The equilibrium density-velocity relation V i (ρ i ) on each road is given in the form of Greenshield's model

V i (ρ i ) = v m 1 - ρ i ρ m,i γ i . (4)
The time scale of τ i ∈ R + is assumed to be constant. If we consider an empty road so that ρ i = 0, then V (ρ i ) = v m and w i = v i . Therefore, the state variable w i represents the heterogeneity of traffic flow, namely, the property of each vehicle, with respect to aggregated equilibrium density-velocity relation V (ρ). We denote the traffic flow rate on each road as q i = ρ i v i .

(5) The equilibrium flow rate and density relation, also known as the fundamental diagram, is then given by

Q i (ρ i ) =ρ i V (ρ i ) = ρ i v m 1 - ρ i ρ m,i γ i . ( 6
)
For the fundamental diagram in (6), the critical density ρ c,i is given by ρ c,i = ρ m,i

(1+γ i ) 1/γ i such that Q i (ρ i )| ρ i =ρ c,i = 0 .
The critical density segregates the free regime and congested regime of equilibrium traffic states. The traffic flow is said to be in free regime when the density satisfies ρ i < ρ c,i . The traffic flow is said to be congested when the density satisfies ρ i > ρ c,i . The traffic flux reaches its maximum value at the critical density q c,i = Q(ρ c,i ) which is also referred as the road capacity. In this work, we focus on the congested traffic for both segments. Notice that we allow different road capacities q c,i for the two segments. We adopt in this paper the traffic PDE network model given in [START_REF] Herty | Coupling conditions for a class of second-order models for traffic flow[END_REF]. This model allows weak solutions of the network system. Regarding the boundary conditions at the junctions, the Rankine-Hugoniot condition is satisfied. This implies the conservation of the mass and drivers' property. We assume the continuity of the flux and drivers' property across the boundary condition at x = 0,

ρ 1 (0,t)v 1 (0,t) =ρ 2 (0,t)v 2 (0,t), (7)
w 2 (0,t) =w 1 (0,t).

(8) We assume for the open-loop system, a constant incoming flow rate q for the inlet boundary x = -L and the same constant outgoing flow rate q at the outlet boundary for x = L in the open-loop system. The outgoing flow rate is actuated by a control input U(t) in the closed-loop system, q 2 (-L,t) =q , (9) q 1 (L,t) =q +U(t).

(10) The control objective is to stabilize the traffic flow in both the incoming and outgoing road segments with the single control of the flow rate at the outlet, as shown in Fig. 2.

Steady states

(ρ 1 , v 1 , ρ 2 , v 2 )
In this paper, we want to stabilize the traffic flow in the two segments around the corresponding steady states. These arbitrary steady states (ρ 1 , v 1 , ρ 2 , v 2 ) are chosen such that the boundary conditions ( 7) and ( 8) are satisfied, i.e.

ρ 1 v 1 =ρ 2 v 2 = q , (11) w 1 =w 2 = v m , (12)
where the steady state velocities satisfy the equilibrium densityvelocity relation v i = V i (ρ i ). The constant flux q in (11) satisfies (q = Q 1 (ρ 1 ) = Q 2 (ρ 2 )) according to (6). The steady state densities ρ 1 and ρ 2 are chosen such that this relation is satisfied. The constant driver's property in ( 12) implies that we have the same maximum velocity v m for the two segments (which corresponds to our initial assumption).

Linearized model in the Riemann coordinates

The linearized model is given in the following Riemann variables defined as wi =w iw i , (13) ṽi =v iv i .

(14) where w i and v i are the steady states value defined above. We then apply a spatial transformation wi (x,t) = exp x τ i v i wi (x,t) to simplify the linearized model ( wi , ṽi ). One can check that with such a change of variable, the system (1),( 2), ( 7),( 8),( 9), (10) rewrite (for i ∈ {1, 2}) as

∂ t wi + v i ∂ x wi =0, (15)
∂ t ṽi -(γ i p i -v i )∂ x ṽi =c i (x) wi , ( 16
) ṽ1 (L,t) =r 1 exp - L τ 1 v 1 w1 (L,t) (17)
+ v 1 (1 -r 1 ) q U(t), (18)
w1 (0,t) = w2 (0,t),

w2

(-L,t) = exp -L τ 2 v 2 1 r 2 v2 (-L,t), ( 20
) ṽ2 (0,t) =δ r 2 r 1 ṽ1 (0,t) + r 2 (1 -δ ) w2 (0,t), ( 21
)
where the spatially varying coefficients c i (x) are defined as

c i (x) = -1 τ i exp -x τ i v i . The constant coefficient δ is defined by δ = γ 2 p 2 γ 1 p 1 > 0.
It represents the ratio between the drivers' aggressiveness and the traffic pressure of the two segments. The constant coefficients r i are defined as r i = - p i p i i ). For the congested regime we have ρ i > ρ (1+γ i ) 1/γ i so that the characteristic speed γ i p i -v i > 0. Thus the following inequalities are satisfied, -1 < r i < 0.

v i γ i p i -v i
(22) The more traffic is congested, the smaller the absolute value of the ratio constant r i . Detailed calculations regarding the linearization and spatial transformation can be obtained following Yu and Krstic (2019). The control diagram for the closed-loop system ( 15)-( 21) is given in Fig. 2.

The corresponding initial condition are denoted by ( ṽ0 ) i = ṽi (•, 0) and ( w0 ) i = wi (•, 0). The objective of this paper is to design a control law U that stabilizes the system ( 15)-( 21) around its equilibrium in the sense of the L 2 -norm. Such an interconnected system has already been considered for fullstate feedback design in Auriol et al. (2019) for a a general framework in the case of an actuator located at one of the extremity of the network. It has been proved in [START_REF] Logemann | Conditions for robustness and nonrobustness of the stability of feedback systems with respect to small delays in the feedback loop[END_REF] that a system can be delay-robustly stabilized only if its open-loop transfer function has a finite number of zeros on the complex right half plane. For the considered class of linear hyperbolic system, it has been proved in Auriol and Meglio (2019) that such a condition is equivalent to requiring (15)-( 21) with zero in-domain couplings (i.e. c 1 ≡ c 2 ≡ 0) to be exponentially stable in the open-loop. This requirement can be expressed in terms of the following assumption (see Auriol and Meglio (2019), Yu et al. (2019) for details) Assumption 1. The boundary couplings of the system (15)-( 21) are such that

|1 -δ | exp -L τ 2 v 2 + δ exp -L τ 1 v 1 exp -L τ 2 v 2 < 1. (23)
Indeed, if c i ≡ 0, it is straightforward (using the method of characteristics) to express w2 (t, 0) as a solution of a neutral system whose stability is only guaranteed if Assumption 1 holds. Due to the transport structure of ( 15)-( 21), the convergence to zero of w2 (t, 0) implies the stabilization of the system. Then, ( 15)-( 21) with zero in-domain couplings is exponentially stable in open-loop and the system can be robustly stabilized.

Here, we consider that δ < 1 which means the drivers are more aggressive and traffic pressure is greater in segment 2 than that of segment 1. Thus, Assumption 1 is satisfied. If we consider the traffic conditions in the two segments to be the same, then δ = 1 and (23) becomes exp -L

τ 2 v 2 + -L τ 1 v 1 < 1. The
Assumption 1 easily holds and thus the system can be delayrobustly stabilized.

STATE FEEDBACK CONTROL DESIGN

In this section, we consider a full state feedback law that stabilizes the system ( 15)-( 21) in the sense of the L 2 -norm.

Our approach is directly adjusted from Auriol et al. (2019), which explains why we will only present the main ideas of the design. Inspired by [START_REF] Coron | Local exponential H 2 stabilization of a 2× 2 quasilinear hyperbolic system using backstepping[END_REF], we first consider the two invertible backstepping transformations ᾱ1 (t, x) = w1 (t, x), (24)

β1 (t, x) = ṽ1 (t, x) - x 0 Kvw 1 (x, ξ ) w1 (t, ξ )dξ - x 0 Kvv 1 (x, ξ ) ṽ1 (t, ξ )dξ , (25) ᾱ2 (t, x) = w2 (t, x), ( 26
) β2 (t, x) = ṽ2 (t, x) - x -L Kvw 2 (x, ξ ) w2 (t, ξ )dξ - x -L Kvv 2 (x, ξ ) ṽ2 (t, ξ )dξ , ( 27
)
where the kernels Kvw 1 and Kvv 1 are defined on the set

T 1 = {(x, ξ ) ∈ [0, L] 2 , ξ ≤ x},
(γ i p i -v i )∂ x Kvw i -v i ∂ ξ Kvw i = c i (ξ ) Kvv i , (28)
∂ x Kvv i + ∂ ξ Kvv i = 0, ( 29
) along with the boundary conditions

Kvw i (x, x) = - c i (x) γ i p i , Kvv 1 (x, 0) = 0, ( 30
) Kvv 2 (x, -L) = v 2 γ 2 p 2 -v 2 exp -L τ 2 v 2 1 r 2 Kvw 2 (x, -L). (31)
We have the following lemma. Lemma 1. [START_REF] Coron | Local exponential H 2 stabilization of a 2× 2 quasilinear hyperbolic system using backstepping[END_REF] For system ( 28)-( 31), there exists a unique solution Kvw

1 , Kvv 1 in L ∞ (T 1 ) Kvw 2 , Kvv 2 in L ∞ (T 2
). Moreover, the transformations ( 27)-( 27) are invertible, that is there exists Lβα

1 , Lββ 1 in L ∞ (T 1 ) and Lβα 2 and Lββ 2 in L ∞ (T 2 ) such that ṽ1 (t, x) = β1 (t, x) - x 0 Lβα 1 (x, ξ ) ᾱ1 (t, ξ )dξ - x 0 Lββ 1 (x, ξ ) β1 (t, ξ )dξ (32) ṽ2 (t, x) = β2 (t, x) - x -L Lβα 2 (x, ξ ) ᾱ2 (t, ξ )dξ - x -L Lββ 2 (x, ξ ) β2 (t, ξ )dξ (33)
The transformation ( 25)-( 27) maps the original system ( 15)-( 21) to the decoupled target system

∂ t ᾱ1 + v 1 ∂ x ᾱ1 =0, ( 34
)
∂ t β1 -(γ 1 p 1 -v 1 )∂ x β1 = -v 1 Kvw 1 (x, 0)α 2 (t, 0), ( 35
)
∂ t ᾱ2 + v 2 ∂ x ᾱ2 =0, ( 36
)
∂ t β2 -(γ 2 p 2 -v 2 )∂ x β2 =0, ( 37
) with boundary conditions β1 (L,t) =r 1 exp - L τ 1 v 1 ᾱ1 (L,t) + v 1 (1 -r 1 ) q Ū(t) (38) ᾱ1 (0,t) = ᾱ2 (0,t), (39) ᾱ2
(-L,t) = exp -L τ 2 v 2 1 r 2 β2 (-L,t), (40) β2
(0,t) =δ r 2 r 1 β1 (0,t) + r 2 (1 -δ ) ᾱ2 (0,t) + 0 -L ( Lβα 2 (0, ξ ) ᾱ2 (t, ξ ) + Lββ 2 (0, ξ ) β2 (t, ξ ))dξ . (41)
In what follows, U(t) is given related to Ū(t) in (38) by

U(t) = Ū(t) + q v 1 (1 -r 1 ) L 0 Lβα 1 (L, ξ ) ᾱ1 (t, ξ ) + Lββ 1 (L, ξ ) β1 (t, ξ )dξ .
(42) Let us now consider the following affine transformation

β1 (t, x) =η 1 (t, x) - x 0 G(x, ξ )η 1 (t, ξ )dξ - 0 -L M α (x, ξ ) ᾱ2 (t, ξ ) + M β (x, ξ ) β2 (t, ξ )dξ (43) β2 (t, x) =η 2 (t, x), (44)
where the kernels M α (x, ξ ) and M β (x, ξ ) are defined on the domain

T = {(x, ξ ) ∈ [0, L] × [-L, 0]} while G(x, ξ ) is defined on T 1 . They satisfy the following set of PDEs (γ 1 p 1 -v 1 )∂ x M α -v 2 ∂ ξ M α = 0, (45)
(γ 1 p 1 -v 1 )∂ x M β + (γ 2 p 2 -v 2 )∂ ξ M β = 0, (46)
∂ x G + ∂ ξ G = 0, (47)
with the boundary conditions

M α (0, ξ ) = r 1 δ r 2 Lβα 2 (0, ξ ), M β (0, ξ ) = r 1 δ r 2 Lββ 2 (0, ξ ), (48)
M α (x, 0) =(1 -δ )M β (x, 0) - v 1 v 2 Kvw 1 (x, 0)) (49) M β (x, -L) = -exp -L τ 2 v 2 M α (x, -L) (50) G(x, 0) =δ r 2 r 1 γ 2 p 2 -v 2 γ 1 p 1 -v 1 M β (x, 0). (51)
We have the following lemma. Lemma 2. Auriol et al. (2019) Consider system (45)-( 51), there exists a unique solution

M α , M β in L ∞ (T ), G in L ∞ (T 1 ).
The transformation (43) maps ( 34)-(41) to the system

∂ t ᾱi + v i ∂ x ᾱi =0, (52)
∂ t ηi -(γ i p i -v i )∂ x ηi =0, (53)
with the boundary condition

η 1 (L,t) =r 1 exp - L τ 1 v 1 ᾱ1 (L,t) + v 1 (1 -r 1 ) q Ū(t) + 0 -L M α (L, ξ ) ᾱ2 (t, ξ ) + M β (L, ξ )η 2 (t, ξ )dξ + L 0 G(L, ξ )η 1 (t, ξ )dξ , (54)
ᾱ1 (0,t) = ᾱ2 (0,t), (55) ᾱ2
(-L,t) = exp -L τ 2 v 2 1 r 2 η 2 (-L,t), (56)
η 2 (0,t) =δ r 2 r 1 η 1 (0,t) + r 2 (1 -δ ) ᾱ2 (0,t). (57)
Let us now define Ū(t) in (54) as

Ū(t) = q v 1 (1 -r 1 ) L 0 G(L, ξ )η 1 (ξ ,t)dξ + 0 -L M α (L, ξ ) ᾱ2 (ξ ,t) + M β (L, ξ )η 2 (ξ ,t)dξ , (58)
Therefore the full state feedback control law U(t) is obtained by substituting (58) into (42). With this control law the target system ( 52)-( 57) is exponentially stable due to Assumption 1 (see Auriol and Meglio (2019) for detials). Due to the invert-ibility of the backstepping transformations ( 25)-( 27) and ( 43), it can easily be proved that there exist L ∞ functions R w 2 , R v 2 , R w 1 and R v 1 such that the resulting stabilizing control law U(t) can be rewritten

U(t) = 0 -L R w 2 (ξ ) w2 (ξ ,t) + R v 2 (ξ ) ṽ2 (ξ ,t)dξ + L 0 R w 1 (ξ ) w1 (ξ ,t) + R v 1 (ξ ) ṽ1 (ξ ,t)dξ . (59)
As this control law is only composed of integral terms, it is strictly proper. It can be shown following the ideas of Auriol et al. (2019) that it is robust to delays in the actuation.

OBSERVER DESIGN

In this section we design an observer that relies on the measurement of qi and ṽi at the left side of the junction. Since we have w2 (0,t) = γ 2 p 2 q q2 (0,t) -1 r 2 ṽ2 (0,t), the measurement Y 0 (t) = w2 (0,t) is obtained.

Observer equations

Inspired by R. [START_REF] Vazquez | Backstepping boundary stabilization and state estimation of a 2×2 linear hyperbolic system[END_REF], the observer equations read as follows

∂ t ŵi + v i ∂ x ŵi = µ i (x)( w2 (0,t) -ŵi (0,t)), (60)
∂ t vi -(γ i p i -v i )∂ x vi = c i (x) ŵi + ν i (x)( w2 (0) -ŵi (0)), (61) with boundary conditions v1 (L,t) = r 1 exp - L τ 1 v 1 ŵ1 (L,t) + v 1 (1 -r 1 ) q U(t), (62) ŵ1 (0,t) = ŵ2 (0,t), (63) ŵ2
(-L,t) = exp -L τ 2 v 2 1 r 2 v2 (-L,t), (64)
v2 (0,t) = δ r 2 r 1 v1 (0,t) + (1δ )r 2 ŵ2 (0,t),

where ŵi (x,t), vi (x,t) are the estimates of the state variables wi (x,t) and ṽi (x,t). The terms µ i and ν i are output injection gains that have to be designed. They are L ∞ functions respectively defined on ([0, L]) 2 and ([-L, 0]) 2 . The corresponding initial conditions are L 2 functions. Defining the error estimates wi = ŵiwi and vi = viṽi and using the fact that ŵ1 (0,t) = ŵ2 (0,t), the error system is obtained by subtracting the observer equations in ( 60)-( 65) from ( 15)-( 21),

∂ t wi + v i ∂ x wi = µ i (x) wi (0,t), (66)
∂ t vi -(γ i p i -v i )∂ x vi = c i (x) wi + ν i (x) wi (0,t), ( 67
) v1 (L,t) = r 1 exp - L τ 1 v 1 w1 (L,t), (68)
w1 (0,t) = w2 (0,t), (69)

w2 (-L,t) = exp -L τ 2 v 2 1 r 2 v2 (-L,t), (70)
v2 (0,t) = δ r 2 r 1 v1 (0,t) + (1δ )r 2 w2 (0,t), (71)

Backstepping transformations

Let us consider the following backstepping transformations

w1 (t, x) = α1 (t, x) - x 0 N ww 1 (x, ξ ) α1 (t, ξ )dξ , (72) v1 (t, x) = β1 (t, x) - x 0 N vw 1 (x, ξ ) α1 (t, ξ )dξ , ( 73
) w2 (t, x) = α2 (t, x) - 0 x N ww 2 (x, ξ ) α2 (t, ξ )dξ , (74) v2 (t, x) = β2 (t, x) - 0 x N vw 2 (x, ξ ) α2 (t, ξ )dξ , (75)
where the kernels N ww 1 and N wv 1 are L ∞ functions defined on the set T 1 , while the kernels N ww 2 and N wv 2 are L ∞ functions defined on the set T 3 = {(x, ξ ), ∈ [-L, 0] 2 , ξ ≥ x}. On their corresponding domains of definition, they satisfy the following set of PDEs:

∂ x N ww i + ∂ ξ N ww i = 0, ( 76
) (γ i p i -v i )∂ x N vw i -v i ∂ ξ N vw 1 = -c i (x)N ww i , (77)
along with the boundary conditions

N vw 1 (x, x) = c 1 (x) γ 1 p 1 , N vw 2 (x, x) = -c 2 (x) γ 2 p 2 , (78)
N ww 1 (L, x) = 1 r 1 exp L τ 1 v 1 N vw 1 (L, x), (79)
N ww 2 (-L, x) = exp -L τ 2 v 2 1 r 2 N vw 2 (-L, x). (80)
The well-posedness of this kernel PDE-system is guaranteed by the following lemma. Lemma 3. R. [START_REF] Vazquez | Backstepping boundary stabilization and state estimation of a 2×2 linear hyperbolic system[END_REF] Consider system ( 76)-( 80). There exists a unique solution N vw 1 , N vv 1 in L ∞ (T 1 ) and N vw 2 , N vv 2 in L ∞ (T 3 ). Let us now define the output injection gains µ i and ν i as

ν 1 (x) = -v 1 N vw 1 (x, 0), µ 1 (x) = -v 1 N ww 1 (x, 0), (81)
ν 2 (x) = v 2 N vw 2 (x, 0), µ 2 (x) = v 2 N ww 2 (x, 0). ( 82
) With this choice of injection gains, differentiating the transformations (72)-( 73) and ( 74)-( 75) with respect to time and space, the error system (66)-( 71) is mapped to the following system

∂ t αi + v i ∂ x αi =0, (83)
∂ t βi -(γ i p i -v i )∂ x βi =0, (84)
β1 (L,t) =r 1 exp -L

τ 1 v 1 α1 (L,t), (85)
α1 (0,t) = α2 (0,t),

(-L,t) = exp -L τ 2 v 2 1 r 2 β2 (-L,t), (86) α2
β2 (0,t) =δ r 2 r 1 β1 (0,t) + (1 -δ )r 2 α2 (0,t). ( (87)
) 88
This system is exponentially stable due to Assumption 1. Due to the invertibility of the Volterra transformations ( 72)-( 73) and ( 74)-( 75), we have the following theorem Theorem 4. Consider the PDE system ( 60)-( 65) with the output injections gains defined in ( 81)-( 82). Then for any initial condition ( ŵi (•, 0), vi (•, 0)), the states ( ŵi , vi ) exponentially converge to the states ( wi , ṽi ).

Output feedback law

We are now able to give the main theorem of this paper. Theorem 5. Consider the system ( 15)-( 21) with the control law

U(t) = 0 -L R w 2 (ξ ) ŵ2 (ξ ,t) + R v 2 (ξ ) v2 (ξ ,t)dξ + L 0 R w 1 (ξ ) ŵ1 (ξ ,t) + R v 1 (ξ ) v1 (ξ ,t)dξ . ( 89
)
where the states ŵi and vi satisfy the observer equations ( 60)-(65). Then for any L 2 initial condition, the states w and ṽ exponentially converge to zero. This implies the local convergence of the initial states of ρ i and v i to the steady states ρ i and v i .

Proof. The proof uses the same ideas as the ones given in (Lamare et al., 2018, Theorem 5). As we have ṽ =vi + vi and w =wi + ŵi , the control law (89) can be rewritten as

U(t) = 0 -L
R w 2 (ξ ) w2 (ξ ,t) + R v 2 (ξ ) ṽ2 (ξ ,t)dξ

+ L 0 R w 1 (ξ ) w1 (ξ ,t) + R v 1 (ξ ) ṽ1 (ξ ,t)dξ + D(t),
where D is given by U in (89) in which the terms vi and ŵi have been replaced by vi and wi respectively. Since vi and wi converge to zero due to Theorem 4, the term D can be seen as a bounded disturbance that converges to zero. The rest of the proof is based on Assumption 1 and on the variation of constants formula (Theorem 7.6, page 32 in [START_REF] Hale | Introduction to functional differential equations[END_REF]). It is omitted here due to space restrictions.

CONCLUSION

In this paper, we develop a boundary state feedback control law for an interconnected two-segment traffic PDE system and then construct the output feedback with a collocated observer design. The control input acts on the traffic flow rate from the downstream outlet and stabilizes the traffic states to segmentspecific steady states using the measurement of density and velocity at the inlet.

Fig. 1 .

 1 Fig. 1. Traffic flow on an incoming road and an outgoing road connected with a junction, actuation is implemented at the outlet with ramp metering.

  and

Fig. 2 .

 2 Fig. 2. Control diagram for the closed-loop system.

  on the set T 2 = {(x, ξ ) ∈ [-L, 0] 2 , ξ ≤ x}. They satisfy the following set of PDEs on their corresponding domains of definition

  Comparison between this result with Yu et al. (2019) (different actuation locations) over performance objectives is of authors' interest. The control design of this paper can be extended to the traffic PDE model of multiple connected road segments.


Ariane Dimitrov

Vincent Paupe

Charles Gueudry

Jean-Baptiste Sibarita

Graça Raposo

Ole Vielemeyer

Thierry Gilbert

Zsolt Csaba

Tania Attié-Bitach

Valérie Cormier-Daire

Tania Attie-Bitach

Valérie Cormier

Pierre Gressens

Pierre Rustin

Franck Perez
email: franck.perez@curie.fr

Vincent El Ghouzzi
email: vincent.elghouzzi@inserm.fr

Vincent El Ghouzzi

-Franck Perez

The gene

Keywords: DMC syndrome, Dymeclin, myristoylation, Golgi apparatus, FRAP, nocodazole

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Dymeclin is a protein recently identified as the translation product of the FLJ20071/FLJ90130/Dym gene (DYM) which mutations are responsible for a severe autosomal-recessive skeletal dysplasia associated with mental delay, Dyggve-Melchior-Clausen syndrome (DMC, MIM#223800) and a clinical variant without mental impairment, Smith-McCort syndrome (SMC, MIM#607326), (1 , 2). DMC/SMC skeletal features consist of a short trunk dwarfism with particular radiological features, severe proximal limb shortening and microcephaly associated with a peculiar facial dysmorphism [START_REF] Paupe | Recent advances in Dyggve-Melchior-Clausen syndrome[END_REF]. Mental retardation is consistently observed in DMC with an average IQ between 25 and 65. Children are often hyperactive, display autistic features and do not speak. Both skeletal and mental features are progressive in DMC, and the phenotype often leads to severe orthopedic complications [START_REF] Paupe | Recent advances in Dyggve-Melchior-Clausen syndrome[END_REF].

Dymeclin is a 669-aminoacid protein which does not belong to any identified protein family.

Except for five or six putative transmembrane domains and a N-terminal myristoylation site, search for predictive structural and/or functional motives failed to provide any clue as to the function of Dymeclin (1 , 2). Most of the mutations identified in DYM predict the generation of a truncating product; however, a few frameshift mutations in the last exon predicting an elongated protein, two complex genomic duplications resulting in exon repetition, and two missense mutations have also been reported (1 , 2, 4). At the ultrastructural level, DMC cells disclose enlarged endoplasmic reticulum (ER) network and accretion of intracytosolic membranous vesicles (2 , 3, 5 , 6 ). It has therefore been proposed that Dymeclin may be an integral membrane protein of the ER possibly involved in the transport of intracellular compounds [START_REF] Kinning | Insights as to the function of Dymeclin, the protein product of the Dyggve-Melchior-Clausen syndrome (DMC) gene[END_REF]. Because the DMC phenotype resembles that of type IV mucopolysaccharidosis (Morquio disease), a lysosomal disorder due to either Nacetylgalactosamine-6-sulfatase or β-galactosidase deficiency, it has also been hypothesized that Dymeclin has a role in intracellular digestion of proteins. However, the cellular phenotype of DMC rather evokes abnormal storage and/or membrane trafficking involving specifically the endoplasmic reticulum network. It therefore clearly differs from that of the Morquio disease in which ultrastructural anomalies involve lysosomes. In addition, biochemical analyses failed to reveal any enzymatic deficiency or accumulation of specific substrate in DMC cells [START_REF] Paupe | Recent advances in Dyggve-Melchior-Clausen syndrome[END_REF].

In order to obtain additional clues about Dymeclin function, we studied the expression pattern of the DYM gene in human embryonic and foetal tissues using in situ hybridization and investigated the sub-cellular localization and the dynamics of the protein in living cells. We show that DYM transcripts are widely expressed throughout human development and that Dymeclin is not an integral membrane protein of the ER, but rather a peripheral membrane protein dynamically associated with the Golgi apparatus. Using different mutations previously identified in DMC and SMC patients, we show that all mutated proteins are mis-localized and subsequently degraded except for one particular mutation reported in SMC.

Results

DYM transcripts are widely expressed during human development

Northern blot analysis of mRNA derived from human tissues previously showed that DYM has two transcripts (3.1 and 5.6 kb) abundantly expressed in foetal brain [START_REF] El Ghouzzi | Mutations in a novel gene Dymeclin (FLJ20071) are responsible for Dyggve-Melchior-Clausen syndrome[END_REF]. Using two nonoverlapping riboprobes selected in either the 5'-half of DYM (probe A, 0.85 kb) or its 3'-half (probe B, 0.5 kb, not shown), we revealed the same two RNA species, thus confirming their specificity. We also show that DYM is abundantly expressed in primary chondrocytes and osteoblasts (Fig. 1A). Because mutations in DYM specifically affect the cognitive development of children and their bone growth in a progressive manner, we questioned whether DYM expression was specific to nervous and osseous tissues or if it was more widely expressed during human development. To address this question, a human multiple tissue expression array was probed with probe A. Consistent with a wide range of expression, DYM transcripts were detected in most adult tissues (Fig. 1A). Highest levels of expression were seen in the cerebellum, kidney, lung and stomach, but in the heart and the pancreas as well. However, very low or no expression was observed in the spleen, thymus, oesophagus, bladder and thyroid gland. DYM was also expressed in a variety of human cell types, including HeLa, SaOs2 and skin fibroblasts and was detected in murine ES cells (Fig. 1A).

As to investigate the spatio-temporal expression pattern of DYM during human development, we performed in situ hybridization on human embryonic and foetal tissues at different developmental stages, Carnegie Stage 17 (CS17, 40 day embryo), Carnegie Stage 19 (CS19, 47-48 day embryo), 17 and 22 weeks of gestation foetus. At CS17, expression of DYM was slightly detectable in numerous structures of the embryo, including the neural tube, the cranial nerve nuclei, the mandible, the stomach, and the limb bud, but no structure showed a particularly marked signal (data not shown). Hybridization at CS19 confirmed the widespread expression of DYM with a higher expression in the germinative zone of the prosencephalon, mesencephalon and cerebellum anlage (Fig. 1B,a,b,c) but also in mesenchymal condensations of the lung and intestinal epithelia (Fig. 1B, a,d,e,f,g). Surprisingly enough, no specific signal could be detected in the vertebrae of the CS19 embryo. Specific expression in the cerebellum was confirmed at later stages. In the 17 week cerebellum, DYM was mostly expressed in the external granule cell layer, the germinative zone which gives rise to the internal granule neurons between 16 and 40 weeks (Fig. 1B, h,i,j,k). At 22 weeks of age, DYM was highly expressed in the external granule layer, in the Purkinje neurons and in the internal granule layer (Fig. 1B, p,q,r,s). At both 17 and 22 weeks, specific labelling was observed in the neocortical plate and corresponding ventricular zone (germinative zone) as well as in the hippocampus (Fig. 1B, l,m,n,o and t,u,v,w). No specific labelling was detected in areas of neuronal migration at any stage.

Together, these data show that human DYM expression is not restricted to nervous and osseous tissues but is also expressed in most embryo-foetal and adult tissues.

The DYM gene product, Dymeclin, is a Golgi-associated protein

The coding sequence of DYM is predicted to produce a 669-aminoacid protein we have previously named Dymeclin [START_REF] El Ghouzzi | Mutations in a novel gene Dymeclin (FLJ20071) are responsible for Dyggve-Melchior-Clausen syndrome[END_REF]. As to characterize Dymeclin, we generated a polyclonal antiserum against a 16-aminoacid peptide selected in the amino-terminal half of the protein in a region conserved between mouse and human. The sub-cellular localization of Dymeclin was assessed in HeLa cells by immunofluorescence. As shown in Figure 2A, we found endogenous Dymeclin in the cytosol but it was predominantly detected as a perinuclear pattern reminiscent of the Golgi complex. When cells were double-labelled for Dymeclin and GM130, a marker of the cis-Golgi, an extensive overlap was observed. Specificity of our antibody could be checked in immunofluorecence using a mis-localized mutant of Dymeclin (Fig. 2A), although we did not detect a stronger Golgi labelling upon over-expression of exogenous Dymeclin, suggesting that Golgi localization may be saturable. We were also able to immunoprecipitate the recombinant protein fused to GFP at its carboxy-terminus, Dym-GFP (~105kDa, Fig. 2B). However, our antibody did not raise specific signal in western blot.

Importantly, GFP-tagged Dymeclin was similarly found on Golgi elements. HeLa cells were transfected with Dym-GFP and stained for immunofluorescence using various markers of the cis-Golgi (GM130 and Giantin), the trans-Golgi/trans-Golgi Network (Galactosyl Transferase and TGN46) and of the endoplasmic reticulum (PDI, Fig. 4B). Like the endogenous protein, recombinant Dymeclin strongly co-localized with markers of the cis and trans-Golgi and was closely apposed to the TGN marker (Fig. 3A). By contrast, Dymeclin did not co-localize with markers of the endoplasmic reticulum (Fig. 4B). Similar results were obtained using an No conserved domains or signal peptides could be predicted from the Dymeclin primary sequence, except for a putative N-terminal myristoylation site "MGSNSSR" [START_REF] El Ghouzzi | Mutations in a novel gene Dymeclin (FLJ20071) are responsible for Dyggve-Melchior-Clausen syndrome[END_REF]. Protein Nmyristoylation corresponds to the covalent attachment of a myristate, a 14-carbon saturated fatty acid, to the N-terminal glycine of eukaryotic proteins and promotes, in many cases, a weak and reversible membrane association [START_REF] Farazi | Isolation and characterization of mycophenolic acid-resistant mutants of inosine-5'-monophosphate dehydrogenase[END_REF]. Because the MGSNSSR site found in Dymeclin was N-terminal and included a glycine residue in position +2, we tested whether this motif could be myristoylated in vitro. Carrying out in vitro translation of wild type and a G2A mutant in the presence of radioactive myristate, we could show that Dymeclin can be myristoylated on the G at position +2 (Fig. 4A). We then asked whether myristoylation was essential for Dymeclin to localize to the Golgi apparatus. The mutant G2A was expressed fused to GFP in HeLa cells. The cells were fixed 24 hours after transfection and stained for immunofluorescence with the endoplasmic reticulum marker PDI. Although we observed a slight increase in cytosolic localization of Dym-G2A-GFP, it clearly localized on the Golgi apparatus (Fig. 4B). Similarly, we observed that amino-terminal tagging of Dymeclin, while it prevents myristoylation, does not prevent Dymeclin from binding to the Golgi apparatus (data not shown). Altogether, these results indicate that Dymeclin is a Golgi-associated protein and that myristoylation is dispensable for Dymeclin binding to the Golgi apparatus.

Dymeclin is a peripheral Golgi protein

Based of hydrophobic domain analysis, it has been proposed that Dymeclin may be a multispanning transmembrane protein [START_REF] Kinning | Insights as to the function of Dymeclin, the protein product of the Dyggve-Melchior-Clausen syndrome (DMC) gene[END_REF]. To address this question, we used a permeabilization assays in living cells adapted from a protocol described by Lorenz et al. [START_REF] Lorenz | The fluorescence protease protection (FPP) assay to determine protein localization and membrane topology[END_REF]. HeLa cells stably expressing mCherry-Histone were transfected with GFP-tagged Dymeclin and observed by fluorescent microscopy. Cells were then treated by low concentration of digitonin to permeabilize the plasma membrane and observed again. While Dym-GFP was present on the Golgi apparatus and in the cytosol before treatment, it completely disappeared after 1 min upon opening of the cells (Fig. 5). We compared Dymeclin behavior to ARF1 and GRASP65 behavior, two myristoylated proteins associated with the Golgi apparatus. Before treatment, Dymeclin, GRASP65 and ARF1 display very similar localization (Fig. 5 a,c,e). However, the Golgi apparatus was still weakly stained by GRASP65 and ARF1 1 minute after permeabilization (Fig. 5 e,f) suggesting that the association of ARF1-GFP and GRASP65-GFP with the Golgi apparatus is more stable than that of Dymeclin. Because Dymeclin was more rapidly released from the Golgi apparatus than two well known peripheral Golgi proteins that dynamically exchange with the cytosol (10 , 11), we concluded that Dymeclin is not a transmembrane protein but is a cytosolic protein which can be recruited to the Golgi apparatus.

Dymeclin rapidly shuttles between the Golgi complex and the cytosol

Because Dymeclin behaved as a peripherally associated Golgi protein and was also present in the cytosol, we next examined the dynamics of the protein in living cells. HeLa cells were transfected with GFP-tagged Dymeclin and fluorescence recovery after photobleaching (FRAP) experiments were performed on living HeLa cells 24 hours after transfection. GFPtagged ARF1 and GRASP65 were used as references for Golgi-associated myristoylated proteins. We measured the fraction of these proteins which is associated to the Golgi apparatus (Fig. 6A). As reported previously [START_REF] Vasudevan | The distribution and translocation of the G protein ADPribosylation factor 1 in live cells is determined by its GTPase activity[END_REF], we found that 16.5 ± 4% of ARF1 is Golgiassociated. We obtained very similar values for Dymeclin (13.6 ± 3.9%) while a larger pool was measured for GRASP-65 (33.2 ± 10.8%). The recovery of fluorescence was quantified for the three proteins after correction of the photobleaching resulting from the acquisition and subtraction of the background. The quantifications were performed on 3D and 2D images and gave similar results (data not shown). We therefore decided to work with 2D images in order to increase the frequency of acquisition. The normalized intensity measured for 30 seconds after FRAP for all proteins was plotted on the same graph (Fig. 6B). When Golgi-associated Dym-GFP was photobleached, fluorescence recovered to the Golgi area in less than twenty seconds (Fig. 6D and sup. Movie 1); this recovery is faster than that of the two reference proteins (Fig. 6B). We calculated the mean half time of recovery and confirmed that Dym-GFP recovers more rapidly than the two other proteins with a half time of 2.8 ± 0.9 seconds (Fig. 6C). Arf1-GFP, which is known to be a fast shuttling protein (10 , 11) displayed a halftime recovery of 7.1 ± 2.6 seconds while GRASP65-GFP had a slightly slower dynamics with a half-time of 12.4 ± 4.5 seconds. These results demonstrate that Dymeclin is a highly mobile protein as the entire Golgi pool can be exchanged in less than 20 seconds.

Dymeclin specifically binds to a subset of the Golgi apparatus upon nocodazole treatment

We have shown in the past that depolymerization of microtubules by a nocodazole treatment reveals the presence of two separate Golgi pools [START_REF] Nizak | Recombinant antibodies against subcellular fractions used to track endogenous Golgi protein dynamics in vivo[END_REF]. Most of Golgi-associated proteins (like GM130 and GalT) are relocated on the newly formed mini stacks that appear after microtubules disassembly whereas one protein, Giantin, is found only on the old, pre-existing Golgi complex that keeps its juxta-nuclear localization. This may be due to the fact that Giantin being a very large transmembrane protein is recycling very slowly to the newly formed mini-stacks. In order to test whether Dymeclin recognizes a particular set of Golgi stacks, HeLa cells expressing Dym-GFP were left untreated or incubated for 90 minutes in the presence of nocodazole, before being fixed and stained for GM130 and Giantin and observed by immunofluorescence. The three proteins strongly co-localized in control conditions (Fig. 7A, top line). After nocodazole treatment, and as reported before ( 12), GM130 was present on the mini stacks dispersed through the cytoplasm whereas Giantin was still located on "old" Golgi complexes that were present before nocodazole addition and that are still located in the pericentriolar region (Fig. 7A, bottom line). Surprisingly, Dym-GFP was present both as a soluble pool and on the "old" Golgi but not on the newly formed mini stacks. This result was very surprising as we have shown that Dym-GFP shuttles very rapidly between the Golgi apparatus and the cytosol and suggested that Dym-GFP specifically recognizes a subset of the Golgi apparatus. To test this hypothesis, we followed the dynamics of Dym-GFP after nocodazole treatment in living HeLa cells by FRAP. Cells were co-transfected with Dym-GFP and mCherry-GM130 and treated with nocodazole 24 hours after transfection (Fig. 7B).

As expected, GM130 was found on dispersed dots in the cytoplasm while Dymeclin was preferentially located in a subset of cellular structures (see the GM130-positve element indicated by an arrowhead in Fig. 7B). Dym-GFP was photo-bleached and its recovery analyzed. White arrows in Figure 7B indicate the bleached region. Dym-GFP fluorescence had already largely recovered after 9 seconds (top line, Dym-GFP) whereas mCherry-GM130 did not recover during the time of acquisition (middle line, mCh-GM130). Therefore, Dymeclin specifically and dynamically recognizes a subset of the Golgi apparatus while it ignores other Golgi stacks, a behavior revealed in the absence of microtubules.

DMC mutations but not the E87K SMC mutation result in Dymeclin mis-localization and subsequent protein degradation

Most of the genetic mutations which have been identified in DMC patients are stop mutations, insertions and deletions causing frameshift or splice mutations that predict protein truncation (3). However, one missense mutation (N469Y) has been identified in some DMC patients while another one (E87K) has been associated with the SMC variant with no mental retardation (1 , 2). Since mental retardation is variable in DMC (ranging from mild to severe), and totally absent in SMC, we asked whether the consequence of DYM mutations on the protein could differ between mutations. To this end, three nonsense mutations (R204X, Q483X and K616X) and the two missense mutations (N469Y and E87K) were introduced through site-directed mutagenesis in GFP-Dym. Following over-expression of these constructs in HeLa cells, the localization of the five mutant proteins was analyzed and compared to that of wild-type GFP-Dym and GM130. Although GFP fluorescence was globally found very weak in cells transfected with DMC mutations, numerous small aggregates were observed in many cells in a pattern suggestive of protein degradation (Fig. 8A). However cells transfected with the E87K mutation still displayed a pattern similar to that of the wild-type Dymeclin. Therefore, only DMC mutations resulted in a mis-localization and aggregation of Dymeclin. Since ubiquitin-rich cytoplasmic inclusion is linked to the pathogenesis of many diseases, we performed a double labelling of DMC mutants with an antibody raised against ubiquitin. As shown in Figure 8B, ubiquitin was found co-localized with mutant GFP-Dym aggregates. These results strongly suggest that DMC mutations result in intracellular deposition of mis-folded Dymeclin which then aggregates into ubiquitin-rich cytoplasmic inclusions, most likely inducing its degradation, whereas the E87K SMC mutation does not affect the stability and the location of the protein.

Discussion

Dymeclin, a new peripheral protein of the Golgi apparatus

The gene responsible for DMC syndrome encodes a 669-aminoacid protein we have named Dymeclin. BLASTS, sequence motif and homology searches using multiple databases indicated that Dymeclin is a novel evolutionarily conserved protein with no homology or known conserved functional domains, except for a putative N-myristoylation site [START_REF] El Ghouzzi | Mutations in a novel gene Dymeclin (FLJ20071) are responsible for Dyggve-Melchior-Clausen syndrome[END_REF]. Using electron microscopy and immunofluorescence techniques on both fixed and living cells, we have shown in this study that Dymeclin is a peripheral protein of the Golgi apparatus. We did not observe any significant ER labeling, which is in contrast with data obtained by Osipovich et al [START_REF] Osipovich | Mapping of mitochondrial metabolic competence by cytochrome oxidase and succinic dehydrogenase cytochemistry[END_REF]. However, these authors used an aminoterminally tagged Dymeclin, a tagging position which hampers myristoylation of the protein. Despite many trials with either homemade or commercially available antibodies (12 antibodies tested so far), specific signal for endogenous Dymeclin was hardly detectable in our hands by Western blot. This may be due to a poor ability of Dymeclin to elicit immune response or a high turn-over/instability of the protein in solution. However, we could detect a Golgi/cytosolic signal for many of the anti-Dym antibodies and immunoprecipitate Dym-GFP with one of them (see Fig. 2B). Based on the hydrophobicity profile of the aminoacid sequence, Dymeclin was first thought to be an integral membrane protein with six trans-membrane segments [START_REF] Cohn | Mental retardation and abnormal skeletal development (Dyggve-Melchior-Clausen dysplasia) due to mutations in a novel, evolutionarily conserved gene[END_REF]. Again, owing to the very fast release of Dymeclin from the Golgi (Fig. 6) we could not get conclusive results from classical biochemical fractionation. However, using imaging experiments, we have shown that Dymeclin is not a stably anchored trans-membrane protein but a dynamically localized peripheral protein of the Golgi apparatus. Firstly, short cell permeabilization without protein extraction using digitonin resulted in a complete loss of both soluble and Golgi-localized Dymeclin. In the same condition integral membrane proteins (not shown) but also well known Golgi peripheral proteins like ARF1 and GRASP65 were still membrane-associated. In addition, FRAP experiments revealed that Dymeclin shuttles very rapidly between the cytosol and the Golgi apparatus. Interestingly, it is the fastest Golgi shuttling protein described so far, exceeding the speed observed for ARF1 and GRASP65 (our results and (14, 15)). Dymeclin is thus present as a cytosolic pool that can shuttle very rapidly between the cytosol and the Golgi apparatus, like other myristoylated proteins. However, the Golgi localization of ARF1 or GRASP65 depends on their myristoylation whereas Dymeclin as a second unknown mechanism of localization. Another striking difference which we report here is that while proteins like ARF1 or GRASP65 were not observed to select particular Golgi stacks, Dymeclin dynamically recognizes a subset of the Golgi apparatus revealed by the depolymerization of microtubules. The existence of two Golgi complex subsets was reported previously [START_REF] Nizak | Recombinant antibodies against subcellular fractions used to track endogenous Golgi protein dynamics in vivo[END_REF] but only Giantin was found to preferentially localize on the "old", preexisting, Golgi apparatus. That a shuttling protein like Dymeclin can similarly recognize the "old" Golgi suggests that it can recognize Golgi components specifically found at the surface of mature Golgi apparatus and not on newly formed mini-stacks (Fig. 9 dysplasia (SMC) also revealed a highly dilated rough endoplasmic reticulum [START_REF] Nakamura | Dyggve-Melchior-Clausen syndrome without mental retardation (Smith-McCort dysplasia): morphological findings in the growth plate of the iliac crest[END_REF]. From their observation, the authors concluded that SMC and DMC should be rough endoplasmic reticulum storage disorders. However, the specific compound which would accumulate does not seem to be Dymeclin itself since both nonsense and missense DMC mutations result in degradation of the protein. Several extensive biochemical analyses, including incorporation/degradation assays of sulphated proteoglycans, peroxysomal and lysosomal contents examination, lipid, carbohydrate and protein work up and assays of mitochondrial respiratory chain activities were performed by our group and others. However, no enzymatic deficiency or specific accumulated compound in DMC cells which would have been consistent with a specific storage of a putative mis-degraded metabolite could be found (3 , 16 , 17 , 18 , 19). Although we can not rule out the possibility that DMC and SMC would be the consequence of a metabolic perturbation which we were unable to characterize yet, our data provide a body of arguments in favor of an ER-Golgi membrane trafficking disorder.

However, experiments we carried out on DMC fibroblasts failed to reveal a reproducible defect in anterograde and retrograde membrane trafficking (data not shown). This may not be surprising because fibroblast cells are to affected in DMC patients. This is nevertheless in marked contrast with results reported by Osipovich et al., although the effects were not quantified by the authors [START_REF] Osipovich | Mapping of mitochondrial metabolic competence by cytochrome oxidase and succinic dehydrogenase cytochemistry[END_REF]. Dymeclin has common features with other Golgi proteins such as GRASP65 or ARF1. These three proteins are localized to the Golgi apparatus, they are myristoylated and they shuttle rapidly between a cytosolic pool and a Golgi pool. Dymeclin could therefore be involved in a GRASP like function and have a role in the structure and/or the function of the Golgi apparatus. GRASP65 has been involved in the formation of the mitotic spindle [START_REF] Sutterlin | The Golgi-associated protein GRASP65 regulates spindle dynamics and is essential for cell division[END_REF] but also in the fusion of the Golgi ribbons [START_REF] Puthenveedu | GM130 and GRASP65-dependent lateral cisternal fusion allows uniform Golgi-enzyme distribution[END_REF]. In drosophila, the GRASP65 homologue is involved in non-conventional secretion (22) A related protein, GRASP55 was recently shown to be similarly involved in Golgi unlinking [START_REF] Feinstein | GRASP55 regulates Golgi ribbon formation[END_REF]. Interestingly, unlinked Golgi cisternae are reminiscent of nocodazole-generated mini-stacks that cannot be recognized by Dymeclin. Structural defects were actually observed in patient cells which further argue for a role of Dymeclin in the regulation of Golgi apparatus organization.

Dymeclin could also have a role similar to the role played by ARF1 or Sar1 and be important for the formation of a complex of proteins (like COPI or COPII respectively) involved in a step of the intracellular transport (24 , 25). This hypothesis could also explain the defects observed by electron microscopy in patient fibroblasts. In this context, it is interesting to note that a mutation in a component of the COPII coat component Sec23A leads to craniolenticulo-sutural dysplasia [START_REF] Boyadjiev | Cranio-lenticulo-sutural dysplasia is caused by a SEC23A mutation leading to abnormal endoplasmicreticulum-to-Golgi trafficking[END_REF]. In fibroblasts from these patients, the ER appears swollen and F o r P e e r R e v i e w many tubular protrusions were observed [START_REF] Fromme | The genetic basis of a craniofacial disease provides insight into COPII coat assembly[END_REF]. Sec23A is an ubiquitous protein, like Dymeclin, which is essential for intracellular transport but only affects some cell types.

Most of inherited diseases known to be associated with ER-Golgi anomalies involve cargo molecules that become unable to couple to the export machinery and then either undergo degradation or accumulate in the cell (28 , 29 , 30). So far, few genetic disorders have been reported to involve central constituents of the ER-Golgi budding, presumably because their disruption is lethal. One of them, however, the X-linked skeletal disorder Spondyloepiphyseal dysplasia tarda (SEDT, MIM #313400), is viable and associated with a loss-of-function of Sedlin, the functional counterpart of the yeast transport protein particle (TRAPP) Trs20p (31 , 32). Interestingly, TRAPP is a large cytosolic protein complex (~ 1,000 kDa) required for tethering ER-derived vesicles to Golgi membranes and for intra-Golgi traffic. In addition, SEDT is characterized by several features strikingly reminiscent of DMC (3 , 33): i) both diseases are chondrodysplasias with short-trunk dwarfism, ii) in both cases, the phenotype is not obvious at birth and appears progressively in childhood and iii) in both diseases, clinical features specifically include a broad chest with sternal protrusion and a flattened and humped appearance of the vertebral bodies. Although Dymeclin does not share any sequence homology with Sedlin, it is tempting to speculate that the two proteins may have a functional relationship in cartilage differentiation.

It will now be important to unravel Dymeclin's connection to other regulators of ER/Golgi dynamics and function to understand better the role that this protein plays in the development of the DMC/SMCdysplasias.

Materials and Methods

Multiple-tissue expression array and Northern blot

Pre-made human multiple-tissue expression array (MTE; ref 7776-1 Clontech Laboratories)

and Northern blot containing 20 µg of total RNA extracted from human primary chondrocytes, calvarial osteoblasts, immortalized chondrocytes, SaOs2, HeLa and murine ES cells were hybridized overnight at 42°C with either a 0.85 kb cDNA fragment corresponding to the 5'-end of DYM (probe A) or a 0.5 kb cDNA fragment selected in the 3'-end of Dym (probe B), labelled and purified as previously described [START_REF] El Ghouzzi | Mutations in a novel gene Dymeclin (FLJ20071) are responsible for Dyggve-Melchior-Clausen syndrome[END_REF]. Primers used to generate probe A were selected in exons 2 and 9 [START_REF] El Ghouzzi | Mutations in a novel gene Dymeclin (FLJ20071) are responsible for Dyggve-Melchior-Clausen syndrome[END_REF]. Primers used to generate probe B were selected in exon 10 (10Sintra: 5'-CTCCTCTTGTATACCTTGCT-3') and exon 14 (8ASintra: 5'-

Plasmids and site-directed mutagenesis

The coding region of human DYM cDNA (FLJ90130, DDBJ/EMBL/Genbank accession number AK074611) was purchased from the Biological Resource Center, Japan (NBRC) as an insert cloned into the pME18SFL3 plasmid. However, the clone differed by two nucleotides from the human sequence we previously identified (2) changing a glutamate into a lysine at codon 66 and a leucine into a proline at codon 249. These two mismatches were corrected using the QuickChange XL site directed in vitro mutagenesis kit, following the GCTGCTATTCGATGCCATCTTCAAGCT-3'. In FRAP analyses, we used pEGFP ARF1 and pEGFP GRASP65 (kindly provided by F. Barr). All constructs were verified by direct sequencing using the ABI PRISM BigDye Terminator Cycle Sequencing Reaction Kit on an automatic ABI3100 capillary sequencer (Applied Biosystems).

Cell culture and transfection

HeLa cells were grown in Dulbecco's modified Eagle's medium (DMEM, Gibco) containing 4.5 g/l glucose supplemented with 10% fetal calf serum, 5 mM glutamine, 5 mM sodium pyruvate at 37 °C in a 5% CO2 humidified incubator. For transfections, cells were plated on coverslips the day before transfection, and were transfected using lipofectamin 2000 (Invitrogen). The cells were fixed with either 100% methanol at -20°C for 5 minutes or 3%

PFA at room temperature for 15 minutes, washed with PBS, incubated with PBS-0,1M NH4Cl for 5 minutes, washed again with PBS and permeabilized with 0,1% Triton X100 for 5 minutes.

Immunoprecipitation

Immunoprecipitations were carried out by using extracts prepared from HeLa cells overexpressing Dym-GFP with the Protein G-agarose Immunoprecipitation kit from Roche.

Briefly, cell lysates were first incubated on a rocking platform 5 hours at 4 °C with 50 µl of the homogeneous G-suspension and centrifuged 20 seconds at 12000 g. The supernatant was then incubated with 2-4 µg of mouse monoclonal anti-GFP antibody (Roche) overnight at 4

°C and another 50 µl of the homogeneous G-suspension was added for 5 hours. After several washes of the complexes, the immunoprecipitated proteins were separated by SDS-PAGE and electroblotted on PVDF membranes (Immobilon, Millipore). The membranes were preincubated for 1 hour at 4 °C in TBS (20 mM Tris-HCl ph7.4, 150 mM NaCl) containing 5% skim milk. The blots were then incubated overnight at 4 °C with either anti-GFP (control) or anti-Dym antibodies both at dilutions of 1/1000. After membrane washing, a second antibody coupled to peroxidase was added. Proteins were visualized with the ECL detection kit (Amersham).

Permeabilization assays and drugs

For permeabilization assays, cells grown on a glass bottom chamber (Iwaki) were treated directly during imaging with 60 µM digitonin for 1 minute. For Nocodazole treatment, cells described (35 , 36). In nocodazole treated cells Arf1 is localized on the "Old Golgi" and on the newly formed mini stacks whereas Dymeclin is present only on the "Old Golgi" and not on the mini stacks.

F
Both proteins exchange rapidly.

Movies captions (

  GFP-tagged Dymeclin (GFP-Dym) or a myc-tagged Dymeclin (data not shown). Immuno-electron microscopy was used to further analyze the location of Dymeclin within the Golgi apparatus of HeLa cells. Immuno-gold labeling of Dym-GFP on cryosections confirmed the presence of Dymeclin near the membranes of the Golgi apparatus and on vesicular structures of transfected cells (Fig.3B).

  B, green) in contrast to other shuttling proteins like ARF1 (Fig.9B, red). Both to understand the role of Dymeclin in disease development and to characterize further Golgi complex dynamics, it will be important to understand how Dymeclin can recognize a subset of the Golgi apparatus and if lipids are necessary for this localization. Because Giantin is a transmembrane protein of the Golgi apparatus, and is the only known marker of this mature Golgi compartment, it is tempting to speculate that Dymeclin is recruited on Golgi membranes by Giantin. Interestingly, Osipovich et al. identified Giantin as a potential Dymeclin partner by mass spectrophotometry analysis although this result has not be validated[START_REF] Osipovich | Mapping of mitochondrial metabolic competence by cytochrome oxidase and succinic dehydrogenase cytochemistry[END_REF].DYM mutations lead to complete degradation of Dymeclin in DMC but not in SMC.Many mutations have been identified in DMC and SMC dysplasias which lie in various locations along the DYM gene (3). Although most of them predict protein truncation and a likely loss-of-function of Dymeclin, two different missense mutations have been associated specifically with DMC syndrome (N469Y, (1 , 2)) or SMC syndrome (E87K, (1 , 2)). Since mental retardation is constantly observed in DMC and absent in SMC, we asked whether these two specific amino-acid substitutions could result in different consequences on Dymeclin and found that the N469Y but not the E87K mutation results in mis-localization and subsequent protein degradation. So far, DYM mutations associated with SMC syndrome have been identified in only two families which share compound heterozygosity for the same two mutations, namely the E87K substitution (on one allele) and a splicing mutation leading to exon 8 skipping and a premature stop codon (on the other allele, (1 , 2)). Interestingly the latter mutation has been associated with DMC as well[START_REF] Paupe | Recent advances in Dyggve-Melchior-Clausen syndrome[END_REF]. Since heterozygous individuals who bear the exon 8 splice mutation plus one normal allele (like parents of these patients) are not affected, the E87K mutation appears specific to SMC phenotype. Given that this particular mutation neither results in Dymeclin degradation nor induces mis-localization, it is likely that some residual activity of Dymeclin could explain the absence of neurological phenotype in SMC patients. Conversely, since DMC and SMC share similar skeletal features, the E87K mutation likely exerts a deleterious effect in bony tissue. It will be interesting to identify the specific defects induced by the E87K mutation that prevent this Golgi-localized Dymeclin form to normally fulfill its function.What role forDymeclin in DMC syndrome. Although skin anomalies are not part of the DMC phenotype, Dymeclin is present in fibroblasts and the ultrastructural anomalies observed in skin fibroblasts from DMC individuals presumably properly reflect the intracellular consequences of DYM deficiency (3). Indeed, electron microscopy analysis of chondrocytes from two children with Smith-McCort

  ). Blots were washed three times at 42 °C with 2×SSC : 0.1% SDS for 15 minutes and once under more stringent conditions, at 65 °C with 0.1×SSC : 0.1% SDS for 10 minutes and further exposed overnight to Kodak X-Omat films with an intensifying screen at -80 °C.In situ hybridizationHuman embryos and foetal tissues were collected from legally terminated pregnancies in agreement with the French law and Ethics Committee recommendations. Tissues were fixed in 4% paraformaldehyde, embedded in paraffin blocks and sectioned (5 µm). Primers located in exon 7 (7F: 5'-AAGAAGTTTTGCGACAGAGC-3') and exon 9 (9R:5'-GGCCAGAGGGGAAGAAAG-3') of DYM cDNA were selected for PCR amplification of a ') was added at the 5' end of each primer. T7-7F/9R and 7F/T7-9R sets allowed amplification of sense and antisense templates. Ribobropes were labelled using T7 polymerase in the presence of α[ 35 S]UTP (1200 Ci/mmol; NEN) and purified on Sephadex G50 columns. Hybridization and post-hybridization washes were carried out according to standard protocols[START_REF] Wilkinson | In situ hybridization: A practical approach[END_REF]. Slides were dehydrated, exposed to BIOMAX MR X-ray films (Amersham) for 3 days, dipped in Kodak NTB2 emulsion for 3 weeks at +4 °C, then developed and counterstained in toluidine blue, coverslipped with Eukitt, and analysed under dark and bright field illumination. No hybridization signal was detected with the α[35S]-labelled sense probe.

  manufacturer's instructions (Stratagene). The cDNA of DYM was amplified by PCR and subcloned in the pEGFP-N2 vector (Clontech) between XhoI and BamHI. The QuickChange XL site directed in vitro mutagenesis kit was used to generate the R204X, Q483X, K616X, E87K and N469Y mutations. Primers designed to mutate the myristoylation site of Dymeclin were as follow: G2Afor, 5'-AGCTTGAAGATGGCATCGAATAGCAGC-3', G2Arev, 5'-

  at 4 °C for 1h30, then at 37 °C for 1h30 in the presence of 10 µM Nocodazole (Sigma) before being directly fixed or used for imaging.ImmunofluorescencePrimary antibodies: anti-giantin hFc TA10 1/50, polyclonal anti-GalT 1/1000, sheep TGN46 1/1000, anti-GM130 (Transduction Laboratories, 1/200), anti-transferin receptor OKT9 1/500, DAPI 1/1000. Secondary antibodies: anti-human Cy3 (Jackson, 1/500), anti-rabbit Cy5 1/500, anti-mouse Cy3 1/500, anti-sheep Cy3 1/500, anti-mouse Cy5 1/500, anti-human Cy5 1/500. Fixed cells were visualized using a Leica DM6000B microscope with a CoolSnapHQ camera (obj 100x NA 1.4 oil CS (HCX PL APO), or with a Leica DMRA and a Micromax 5 Mhz, 40x objective NA 1.25 oil ph3 CS (HCX PL APO), and Metamorph. 3D stacks were acquired and deconvolved to build a projection on one plane on Metamorph. Live imaging For FRAP analyses with Dym-GFP, ARF1-GFP and GRASP65-GFP. HeLa cells were maintained in culture medium in glass bottom chambers (Iwaki) and imaged on a Leica DMIRE2 with a Roper Cascade II Camera, Polychrome V and a 100x NA 1.35 oil oblective, twenty-four hours after transfection. Images were collected before bleaching of the Golgi and every 50 milliseconds after photobleaching. Images were processed using Metamorph software. After correction of the photobleaching due to acquisition, the background was subtracted. The intensity of fluorescence was then normalized and the half recovery was quantified. For nocodazole treated cells the images were acquired on a spinning disk microscope. The Spinning disk microscope is based on a CSU-22 Yokogawa head mounted on an inverted TE-2000E Nikon microscope equipped with a motorized Märzhäuser XY Stage. Images are acquired through a 60x 1.4NA Plan-Apo objective with a Photometrics Coolsnap HQ2 CCD camera. Optical sectioning is achieved using a PI Pifoc piezo z-drive mounted between the microscope turret and the objective. A Roper/Errol laser lounge is equipped with 488 nm and 514 nm laser diodes, delivering 50 mW each, coupled to the spinning disk head through a single fiber. Multi-dimensional acquisitions are performed in streaming mode using Metamorph 7.1.7 software. Images were collected before bleaching of the Golgi and every 400 milliseconds after photobleaching for Dym-GFP and mCherry-GM130. The data shown in the movies where obtained using ND-SAFIR (N-Dimensional -Structure Adaptive Filtering for Image Restoration) © INRIA/INRA 2007 as previously

B: 22 (

 22 In situ hybridization analysis of Dym transcripts during human embryo-foetal development. Hematoxylin/eosin stained sections under bright field illumination (A, D, F, H, J, L, N, P, R, T, V) and adjacent Dym-hybridized sections under dark field illumination (B, C, E, G, I, K, M, O, Q, S, U, W). A-C, Sagittal sections of a CS19 embryo (x10); as a negative control of hybridization, the sense Dym probe was used (C). D-E, Magnification of the lung Lu, x25, D) and the intestinal epithelium (x32, F, G) corresponding to the black squares in A; White arrows point to elective signal seen in mesenchymal condensations (E). H-K, Transversal sections of the cerebellum from a 17-week foetus (x10, H, I) and x32 magnification showing Dym expression in the external granule layer (J, K). L-M, Dym expression in the hippocampus from a 17-week foetus (x8). N-O, Dym expression in the neocortical plate and in the corresponding germinative zone from a 17-week foetus (x12). P-S, Dym expression in the cerebellum from a 22-week foetus (x8) and higher magnification showing Dym expression in the external granule layer, the Purkinje neurons and the internal granule layer (x40, R and S). T-U, Dym expression in the hippocampus from a 22-week foetus (x40). V-W, Dym expression in the neocortical plate and in the corresponding germinative zone from a 22-week foetus (x12).

Figure 2 :

 2 Figure 2: Immuno-detection of endogeneous Dymeclin in HeLa cells. A: Intracellular localization of endogeneous Dymeclin in HeLa cells. HeLa cells (Top panel) were fixed and stained with the anti-Dym antibody at dilution 1/400. The Golgi was labeled with GM130 (red). Hela cells transfected with Dym(N469Y)-GFP (Bottom panel) were fixed and stained for Dymeclin (red) and GM130 (pink). B: Immunoprecipitation of Dym-GFP. Lysates from HeLa cells over-expression Dym-GFP (lane 1) were immunoprecipitated with either the anti-GFP antibody (lane 2) or the anti-Dym antibody (lane 3).

Figure 3 :

 3 Figure 3: Intracellular localization of Dym-GFP in HeLa cells. A: Reconstruction from 3D images of HeLa cells transfected with Dym-GFP and stained with antibodies against Giantin (in red, top line) and GalT (in blue, top line) or TGN46 (in red, bottom line) and GM130 (in blue, bottom line). Dym-GFP partially co-localized with the different Golgi markers and was also found as a soluble pool. B: Immunogold labeling on cryosections of Dym-GFP transfected HeLa cells visualized by electron microscopy confirmed that the protein is localized on the Golgi apparatus and in the cytosol.

Figure 4 :

 4 Figure 4: Myristoylation of Dymeclin in vitro and intracellular localization of the G2A mutant in HeLa cells. A: Dymeclin was produced in vitro in the presence of either 35 Smethionine (left panel) or 3 H-myristate (right panel). Wild-type Dymeclin (Dym WT) can be myristoylated in vitro and the mutation of the second Glycine into an Alanine (Dym G2A) prevents the myristoylation. B: Hela cells were transfected with Dym-GFP or Dym-G2A-GFP (green) and stained for GM130 (red).

Figure 5 :

 5 Figure 5: In vivo permeabilization with Digitonin. Hela cells stably expressing mCherry-Histone were transfected with either Dym-GFP, ARF1-GFP or GRASP65-GFP. 3D images were acquired on a spinning disk microscope before treatment and one minute after treatment with 60µM Digitonin. In permeabilized cells Dym-GFP has completely disappeared from the Golgi and the cytosol whereas ARF1-GFP is dimly visible on the Golgi apparatus and GRASP65-GFP is still present.

Figure 6 :

 6 Figure 6: Quantification of Dym-GFP dynamics. Hela cells were transfected with either Dym-GFP, Arf1-GFP or GRASP65-GFP and photobleaching experiments were performed 24hours after. A. The Golgi apparatus of one cell (outlined in white in the movie) was bleached after 10 seconds and images were then acquired every 100 mseconds for 1 minute (see mov.

  1). After 13,5 seconds the fluorescence of Dym-GFP has totally recovered. From these experiments we could quantify the Golgi fraction of the three proteins. The percentage of protein on the Golgi is represented in B. 16,5 ±4% of Arf1-GFP, 13,6 ± 3,9% of Dymeclin and 33,2 ± 10,8% of GRASP65-GFP are on the Golgi. The normalized intensity of fluorescence for the three proteins was plotted on the same graph. The mean value is indicated in black and the SD is indicated in grey. The half time of recovery was calculated from these data as shown in C. GRASP65-GFP recovered more slowly with a half time of 12,4 ± 4,5 seconds, the recovery of Arf1-GFP was faster with a half time of 7,1 ± 2,6 seconds and Dym-GFP was even faster with a half time of recovery of 2,8 ± 0,9 seconds.

Figure 7 :

 7 Figure 7: Intracellular localization and dynamics of Dym-GFP upon nocodazole treatment. A: HeLa cells transfected with Dym-GFP were fixed 24 hours after transfection and the Golgi was labeled with GM130 (red) and Giantin (blue). In non treated cells (top line) the three markers co-localized whereas after 1h30 at 4°C and 1h30 at 37°C with 10µM nocodazole (bottom line) GM130 was present on the mini stacks dispersed in the cell and Giantin and Dym-GFP were co-localized on the "Old Golgi" in the center of the cell. B:FRAP experiments were performed on cells co-transfected with mCherry-GM130 and Dym-GFP (see sup. Movie 2). The first line shows the Dym-GFP before (-1"), immediately after (0") or 9 seconds after (9") the photobleaching (indicated by the white arrows). The second line shows the mCherry-GM130 and the last line corresponds to the overlay of Dym-GFP in green and mCherry-GM130 in red. The insert shows the upper bleach region with a three

Figure 8 :

 8 Figure 8: Mis-localization and degradation of Dymeclin bearing DMC mutations. A:HeLa cells transfected with wild-type (WT) or mutant GFP-Dym (K616X, Q483X, R204X, N469Y, E87K) were fixed 24 hours after transfection and the Golgi was labeled with GM130 (red). B: HeLa cells transfected with GFP-Dym(R204X) or GFP-Dym(N469Y) were fixed 24 hours after transfection and labeled with an anti-ubiquitin antibody (red). Ubiquitin was found co-localized with mutant GFP-Dym aggregates.

Figure 9 :

 9 Figure 9: Schematic representation of Dymeclin dynamic localization. A: This model proposes that, in the non treated cells, Dymeclin (in green) and Arf1 (in red) are present as a soluble pool and a Golgi pool and shuttle rapidly between the two (green and red arrows). B:

Quick Time format) Movie 1 : 6 . 2 :

 162 photobleaching. For details, see Dimitrov et al, Figure7.

25 Figure 1 26 Figure 2 27 Figure 3 28 Figure 4 29 Figure 5 30 Figure 6 31 Figure 7 32 Figure 8 , 33 Figure 9 ,

 251262273284295306317328339 Figure 1, Dimitrov et al

Human Molecular Genetics

Acknowledgments

The authors whish to thank Cécile Martel for strong support during preparation of the manuscript, Florence Jollivet and Noman Kadhom for assistance in cell culture and immunoassays, Jérôme Boulanger and Vincent Fraisier for assistance in data acquisition and treatment, Géraldine Goudefroye and Férechté Encha-Razavi for assistance in situ hybridization. The authors also thank Michel Vekemans for providing the invaluable support for working on human embryos, Valérie Doye for providing the cell line stably expressing mCherry-Histone and Angela M. Kaindl for reading and fruitful comments on the manuscript.

Funding

This work was supported by the Institut National pour la Santé et la Recherche Médicale (INSERM), the Centre National de la Recherche Scientifique (CNRS), the Institut Curie, the Université Paris 7 and the Agence Nationale pour la recherche (ANR).