K Mariette
email: kevin.mariette@insa-lyon.fr

Eric Bideaux

Federico Bribiesca Argomedo

Damien Eberard

Sylvie Sesmat

Y Haffner

J Borée

T Castelain

Marc Michard

É Bideaux

F Bribiesca-Argomedo

D Ébérard

Wake symmetrization of a bluff Ahmed body based on sliding mode control

Keywords: Fluid flow control, crosswind, sliding mode control, delay compensation

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

For the sector of road transport, saving energy is a critical issue. At high velocity, the aerodynamic drag is the main contributor to the vehicle fuel and energy consumption. Most of this force comes from the pressure loss at the back of the vehicles [START_REF] Wood | Aerodynamic Drag and Drag Reduction[END_REF]) generating a large recirculation region (RcRg). Then, by modifying the shear layers structures at the boundaries of the RcRg, the pressure levels on a vehicle base can be influenced by control devices, as in [START_REF] Barros | Bluff body drag manipulation using pulsed jets and Coanda effect[END_REF]. Hence, many studies on drag reduction focus on passive (curved surfaces, flaps, cavities) [START_REF] Englar | Improved Pneumatic Aerodynamics for Drag Reduction, Fuel Economy, Safety and Stability Increase for Heavy Vehicles[END_REF]) and active open-loop control strategies (air jets, active flaps) [START_REF] Bideaux | Drag reduction by pulsed jets on strongly unstructured wake: towards the square back control[END_REF]) in order to increase the pressure in the RcRg. For example, El-Alti (2012) showed 39% of base pressure improvement with continuous air jets on a truck mock-up. Recently, closedloop control have shown encouraging results [START_REF] Plumejeau | Ultra-local model-based control of the square-back Ahmed body wake flow[END_REF]) because of promising robustness and adaptability. However, applications of closed-loop approaches still remain difficult to implement on real conditions because of the lack of reliable flow models.

A particular drag reduction strategy for bluff bodies consists in the conservation of the wake symmetry. Indeed, the pressure in the wake is non homogeneous and asymmetries can increase the pressure drag by 4 to 8% (Grandemange Founded by the French ANR, Activ'Road (Ampre laboratory (INSA, Lyon), P' Institute (ENSMA, Poitiers), LMFA (ECL, Lyon), PSA & Renault Trucks companies) et al. ( 2012)). The base pressure asymmetries can have different origins: a cross wind on the vehicle or, for aligned wind flow, natural bistability in the wake.

Hence, symmetry enforcement methods have been previously employed on bluff bodies in order to obtain additional drag reduction. For example, [START_REF] Brackston | Stochastic modelling and feedback control of bistability in a turbulent bluff body wake[END_REF] used movable flaps with a predictive closed loop model leading to a net drag reduction of 2% ; [START_REF] Li | Feedback control of bimodal wake dynamics[END_REF] worked with pulsed jets at 200 Hz on the bistable wake to symmetrize the pressure gradients with a pressure raise of 2%. Finally, [START_REF] Plumejeau | Ultra-local model-based control of the square-back Ahmed body wake flow[END_REF] proposed a model-free closed-loop control of the wake asymmetries thanks to drift-force feedback with air knives blowers and showed 2.5% drag reduction. In the continuity of such experimental studies, this paper focuses on the improvement of wake symmetry thanks to closed-loop control of the centre of pressure (CoP) on a bluff vehicle mock-up backward face. We use high frequency pulsed air jets and a sliding mode control approach which only requires surface pressure measurements.

In Section 2, we present the experimental set up before describing, in Section 3, the behaviours of the CoP subjected to bistability and under open-loop actuation. Finally, Section 4 presents the sliding mode control and ends with the results of the wake symmetry control for different cross wind directions. ), the flow velocity direction (-→) and mock-up dimension parameters ; c) Close up view of the Coanda surfaces deviating the actuation jets.

EXPERIMENTAL SET-UP

In this experimental study, we use a modified Ahmed body mock-up model [START_REF] Ahmed | Some Salient Features Of The Time-Averaged Ground Vehicle Wake[END_REF]) with a straight backward face, called the base. Fig. 1 and Table 1 present this mock-up shape and dimensions. The present bluff profile allows the conversion of the mock-up from a carslike shape to a trailer truck shape by a simple rotation 90 • around the x-axis. The base of the mock-up (see Fig. 2.b) is equipped with 35 low-bandwidth sensors and 12 fast transducers, with respective bandwidths of 200 Hz and 2 kHz, providing average values of pressure levels as well as fast fluctuations useful for closed-loop control. We use, as pressure level indicator, the mean pressure ratio γ p defined as the ratio between the mean pressure value when the control is activated, and the pressure without control. We define analogously the drag force ratio, γ Cx from the controlled an uncontrolled drag coefficient C x :

C x = Fx / 1 2 ρSV 2 ∞
(1) where F x is the drag force, ρ the air density at the wind tunnel temperature, V ∞ the flow velocity, and S the cross section of the body relative to the x-direction. As shown in Fig. 2.c), the supply pressure 1 P i ( 2 ) is kept constant thanks to a PID controller in an upstream tank placed inside the Ahmed body (see Fig. 2.a). This

1 expressed relatively to the atmospheric pressure pressurized air passes through 14 ON/OFF valves ( 3 ) connected to 26 diffusion slits 2 to generate pulsed jets ( 4 ). The slits are distributed all around the edges of the base as described in Fig. 2.b). All the valvles on the same edge share a single control signal consisting of a variablefrequency square TTL signal (VFSS) computed by a dSpace rapid prototyping system at a sampling frequency of 4 kHz. In summary, the computed control signal defines the edges to be activated, the frequency of the opening an closing of the valves on each activated edge, and the target tank pressure P i . The duty cycle of the VFSS can also be included in the command vector but its variation is limited at high frequencies due to opening/closing times of the valves. Here, the duty cycle is fixed at 0.5. The actuation set-up allows to explore jet frequencies up to 1 kHz and maximum jet velocities up to 80 m/s at a supply pressure of 0.4 MPa. These jets are deviated toward the low pressure region by additional curved surfaces, called coanda surfaces (see Fig. 1.c), placed below the diffusion slits as proposed by [START_REF] Barros | Bluff body drag manipulation using pulsed jets and Coanda effect[END_REF] or Haffner (2018), in order to increase the impact of the pulsed jets on the wake.

Finally a 6-axes aerodynamic balance gives access to the forces acting on the Ahmed body. This balance is linked to the body reference frame and implemented on a pole that enables rotations around the z-direction. The rotation angle β is referenced to an orientation corresponding to an aligned flow with the x-direction along the mock-up (see Fig.

FEATURES OF THE CENTRE OF PRESSURE

Natural bistability and forced transition through open-loop control

In this paper, the symmetry of the wake is described by the y-coordinate of the CoP on the base which is taken as the state of the controlled system, and noted X. X is a time varying value and is computed from the 12 fast pressure sensors measurements, p k , and y-positions, y k from:

X(t) = 12 k=1 p k (t)y k 12 k=1 p k (2)
As shown in Fig. 3 [START_REF] Grandemange | Reflectional symmetry breaking of the separated flow over three-dimensional bluff bodies[END_REF], for a natural aligned flow, the bistability induces an important loss of symmetry of the bluff body's wake. A low pressure area, from where the wake develops, can jump randomly from one fixed position to its mirrored position. For an aligned flow at V ∞ = 35 m/s, with the experimental mockup body, such bistable transitions occur and are illustrated in the middle of Fig. 4. The left part (negative time) consists of the uncontrolled time series of X and exhibits two possible states of equilibrium where the CoP is stuck most of the time. These uncontrolled bistable positions are better depicted by the power density function of X (P DF X ) on the left part of Fig. 4: two maxima exist in symmetric positions relatively to y = 0. We call deviation from 0, noted d X the absolute position of the maxima of the P DF X curve:

d X = {y / P DF X (y) = max(|P DF X |)}
(3) For the uncontrolled case, the natural deviation from 0 is:

d X, nat = 0.046 (4)
Next, on the right part of Fig. 4, we activate the right edge of the base and trigger a forced transition of the wake from left (X < 0) to right (X > 0). We use pulsed jets at a frequency of 1050 Hz on the right edge with a supply pressure P i = 0.25 MPa which results in the CoP being moved to the right and locked at the right asymmetric equilibrium (see Fig. 4 on the rightmost graph). We denote this control signal: u = +1.

The symmetric behaviour is observed for the actuation on the left side denoted: u = -1. Table 2 summarizes the symmetry parameters obtained for the asymmetric control and the natural flow over longer time periods.

Frequency effects

Thanks to the previous open-loop tests of CoP displacement, we tested successive forced lateral transitions with Table 2. Symmetry indicators for the uncontrolled (u = 0) and one side actuated cases (u = ±1). Open-loop switching could not comply with the objective of wake symmetrization and drag reduction. Indeed, at high frequency, the average value of X did not tend to y = 0 ; on the other hand, small values of f m created bistable states with transitions observed also in the case of forced transition as in the inclusion of Fig. 4. For the resonant configuration, even though we are able to centre the CoP on average without generating nonsymmetric static states, it generated harmonic oscillations of the wake at a rate corresponding to the vortex shedding frequency.

u = 0 u = +1 u = -1 X 0.
The vortex shedding is characterised by low pressure states and vortex generation behind the body. This instability is not desirable since it increases drag and generates vibrations [START_REF] Roshko | Free Shear Layers, Base Pressure and Bluff-Body Drag[END_REF]). Although not displayed here, the actuation at high frequencies of the L and R edges (or of the four edges at the same time) does not really control efficiently the CoP horizontal position. Even though these actuation profile can impact positively the pressure in the RcRg, the wake is still bistable. As a conclusion, this section showed the limitations of open-loop switching actuation for the regulation of X towards 0.

CLOSED LOOP CONTROL BY SLIDING MODE

4.1 Sliding mode control: Law 1

Based on these remarks, the second step of this study explored closed-loop control approaches. A sliding mode control (SMC) was chosen here since this technique may provide good robustness even with highly non linear systems. The SMC consists in driving a given system towards a chosen trajectory, called the sliding surface, as fast as possible and then maintaining the system on this trajectory by adjusting its deviations in real time [START_REF] Slotine | Sliding controller design for nonlinear systems[END_REF]). This regulation technique is particularly suitable for the present experimental system because of the discontinuous nature of the pulsed jets and the finite number of stable positions for the CoP [START_REF] Utkin | Sliding Modes in Control and Optimization[END_REF]).

First, the control was designed to reduce the error = X 0 -X, (5) where X 0 = 0 is the desired value for the CoP lateral position. The command u( ) determines the edge to be activated according to:

u( ) = -1 if < 0 0 if = 0 +1 if > 0 (6)
In other words, the left edge (resp. the edge) is activated for < 0 (resp. for > 0). Compared to the open loop case the modulation frequency driving the edge time is not fixed but according to measured deviation sign. This SMC law (Law 1 ) was tested experimentally on the Ahmed body under aligned flow condition with a constant flow velocity V ∞ = 35 m/s and a jet actuation frequency of 1050 Hz at a P i value of 0.2 MPa. In Fig. 6 we can observe that the command u switches from left actuation (u < 0) to right actuation (u > 0) according to the sign of X, and by doing so, it suppresses the bistable states. However, a resonant behaviour appears with an excitation frequency of 23 Hz, close to the vortex shedding frequency (around 18 Hz at V ∞ = 35 m/s). At the same time, the pressure in the RcRg drops dramatically.

In conclusion, with the SMC Law 1 , the actuation switches according to the sign of but, unfortunately, the control acts with a delay on the CoP position. Even if the Fig. 7. Block diagram of the SMC laws 2 and 3 including the Smith predictor and a dead-band [-0 , + 0 ] around X 0 = 0. For the SMC Law 2 , 0 = 0. bistability was suppressed, the SMC Law 1 could not increase the base pressure nor decrease the drag because of the vortex shedding excitation.

Sliding mode based on a prediction: Law 2

Referring again to Fig. 6, we used the observation of the signal shapes of the measured output X(t) and the applied command u(t) to improve the SMC. The quasisquare input u is converted to triangular fluctuations like an integrator would do, but with a + π 4 phase shift. Thanks to this observation we used a simple integrator model and built a delay compensator similar to a Smith predictor (Normey-Rico ( 2007)). The objective was to perform an adjusted SMC, the SMC Law 2 , without exciting turbulent instabilities as the vortex shedding.

The identified model is as follow: Ẋ(t) = Ku(t -τ ) ( 7) where

• Ẋ expresses the derivation with respect to the time of X • u is the control signal to the lateral jets • K corresponds to a speed of transition of X • τ , the time delay is supposed constant, with τ = 12 ms (see Fig. 6)

The block diagram in Fig. 7 presents the prediction architecture. X is computed at the time t + τ in the Prediction block based on the applied control during τ by:

X(t + τ ) = X(t) + τ 0 Ku(t -τ + r) dr (8)
Then the new error is evaluated by:

τ = X 0 -X(t + τ ) (9)
Using the same test configuration as in Section 4.1, the SMC laws 1 and 2 were compared. Fig. 8 shows the values of the pressure ratio γ p recorded by five pressure sensors on the middle line (z = 0) of the base (see Fig. 2.b) as a function of time. Three test were performed sequentially:

1 Uncontrolled flow, natural bistable wake ; 2 SMC Law 1 without compensation of the delay ; 3 SMC Law 2 with Smith predictor compensating the delay (see Fig. 7).

As stated before, for the SMC Law 1 , in part 2 , the CoP was no longer bistable but important pressure decreases were observed (darkest blue patches in Fig. 8, part 2 ). In comparison, for the SMC Law 2 in part 3 , the pressure levels displayed are higher. The difference of shade colours between 2 and 3 shows the positive effects of the delay predictor on the pressure.

Nevertheless, the delay compensation generates important chattering effects and decreases the performance of the SMC Law 2 control performances.

Effects of wake symmetry forcing: SMC Law 3

To counter the chattering, a dead-band around the objective value of X 0 = 0 was defined. For values of X inside the dead-band, the control was stopped (El Makrini et al. ( 2016)). This dead-band is parametrized by 0 and the control Law 2 is modified to the SMC Law 3 with:

u( τ ) = -1 if τ < -0 0 if | τ | < 0 +1 if τ > 0 (10)
Basically, the SMC Law 3 uses 0 > 0 and its structure is also described by the block diagram 7. Results obtained with the SMC Law 3 including the dead-band, for 0 = 0.8 × d X, nat = 0.0370, jets frequency of 1050 Hz, supply pressure of 0.2 MPa and V ∞ = 35 m/s are presented in Fig. 9. The upper part a) presents the time series of X with and without control. With the SMC Law 3 , the bistable states have disappeared and the associated PDF graph at the right proves the control to be efficient in terms of symmetry compared to the natural P DF X at the left. In the controlled configuration, the deviation from 0, X , was reduced by 94.2% with respect to the uncontrolled case and the standard deviation X was reduced by 35.3%.

The lower part b) a close up view the upper time series at the control activation time showing when the control activates (positives and negatives orange peaks).

The brief activations are enough to re-centre X and, the rest of the time, the control is stopped. The CoP stays around the unstable symmetric state: X = 0.

Whereas the control is always activated (positively or negatively) with the SMC Law 2 (Fig. 6), the dead-zone removes the bistability without enhancing the vortex shedding and at a low energetic cost. This sparse actuation led to the reduction of the bistability and slight modifications of the drag as shown in Table 3. It shows, for different pressures P i , the variation ∆ (in %) of the pressure ratio γ p , the drag force ratio γ Cx , and the symmetry parameters for X: X, σ and d X . These variations are computed relatively to the uncontrolled cases and every negative value corresponds to a diminution of the associated parameter. Fig. 9. a) Time series for the evolution of X whith the SMC Law 3 (see Fig. 7) and PDF graphs associated to the uncontrolled and controlled cases ; b) close up view at the control activation.

From the symmetry point of view, the SMC Law 3 impacts positively the CoP lateral location. The mean value is maintained close to 0 while d X is centred in comparison to the data in table 2. Within the range of tested supply pressures, the best gain for the drag ratio is obtained for a supply pressure P i = 0.18 MPa, where the pressure ratio decreased by 2%. The drag force ratio kept decreasing with the reduction of P i and it seems that lower supply pressure for the jets could have generated clear drag gains.

Although the two ratios show the same variation with the reduction of pressure supply P i , obtaining negative pressure ratio is not sufficient for net drag reduction. Studies, as in [START_REF] Szmigiel | Effet du flux de soubassement sur la dynamique du sillage d'un corps non profilé à culot droit[END_REF], show that jets create a localised loss of pressure on the base edges surfaces. It is possible that our operating configurations generated sufficient jets for pressure raise but also significant body forces which reduced the net drag gains.

Application to crosswind configurations

Up to here, our experiments were conducted with the mock-up aligned with respect to the wind direction. Based on the previous results, the SMC was applied to the mock-up in a drift configuration. This configuration is characteristic of a vehicle direction change or non aligned wind. The drift is parametrized by the yaw angle β (see Fig. 1.b) and can be monitored during the experiment with a small amplitude of ±1.7 • . It has been verified that this drift is able to create a fully non-symmetric static wake.

The SMC Law 3 has been applied in different drift configurations in order to evaluate its capacity to maintain a symmetric wake in nonsymmetric flow conditions. The results presented in ever, for the configuration with a higher drift angle of β = 1.7 • , a drag reduction of 1.70% and a pressure raise of 3% are observed.

Even though, for the strongest drifts, the CoP position is only re-centred by 48.5%, the impact on the shear layers is visible on the wake pressure and on the drag values. On the other hand, in the case of small angles or β = 0, the jets strength is too large to produce a pressure raise up as seen in Table 3. Referring to the results of Tables 3 and4, a lower tank pressure could be used for small drift angle while higher values of P i could be required under important crosswind conditions. Therefore the development of SMC for wake symmetry with adapted supply pressure with measurement of the wind direction could be an effective way of reducing drag with a reduced energy cost.

CONCLUSION

The previous developments have presented the effects of asymmetries and their control on aerodynamic drag of bluff bodies. The nonsymmetric states of the wake of an Ahmed body with straight back were investigated to develop an active control based on pulsed air jets at the lateral edges of the body's backward face. The implemented sliding mode control on the centre of pressure lateral position was successful for symmetry preservation in aligned configuration but presented important drawbacks in terms of pressure in the wake. The control was improved by a delay compensation Smith like predictor and a deadband domain around the desired centred position. For an aligned vehicle mock-up, it largely reduced the bistability and efficiently rose the pressure level by 2% but no significant drag gain were concomitantly recorded. However, evidences of relation between jet strength and drag force were observed. With a further reduction of the jet strength, we believe that the proposed sliding mode control and its sparse actuation could lead to net drag reductions.

Finally the control was used on an unaligned configuration to test its effects in case of cross wind on the body. In this last case, we obtained interesting gains in term of pressure and drag, respectively of 3% and 1.7% with a drift angle of 1.7 • . While the employed jets were too powerful for net drag reduction in the aligned and nearly aligned configurations, highly energetic jets could be used in the case of important cross wind. Therefore, in real situation where wind surges can appear suddenly, our closed-loop control approach with adapted jets forces could mitigate efficiently the drag.

Fig. 1 .

 1 Fig. 1. The experimental mock-up: a) Front view ; b) Back view (schematic) with symmetry plan location ( ), the flow velocity direction (-→) and mock-up dimension parameters ; c) Close up view of the Coanda surfaces deviating the actuation jets.

Fig. 2 .

 2 Fig. 2. a) Top-view of the mock-up : 1 air supply, 2 pressure tank , 3 ON/OFF valves, 4 diffusers ; b) Sensor locations: Fast (2 kHz) • ; Static (200 Hz) * ; and slits for air jet output ( ) viewed from the rear. (L) and (R) give the convention for the left and right sides ; c) Block diagram of the control and recordings of the experiment with references to the physical elements in a): the control block C regulates the tank supply pressure P i and generates the activation signal for the ON/OFF (Valves) valves pulsing jets into the wake. The pressure signals are treated in M before being recorded (in R) with the forces collected by the balance B. The box () indicates the parts implemented in a dSpace rapid prototyping system.

Fig. 3 .

 3 Fig. 3. The bistability : a) Left positioned wake ; b) Transition ; c) Right positioned wake (Grandemange et al. (2012))

Fig. 4 .

 4 Fig. 4. Time series of the triggered transition of X for u = +1 and P DF X for the uncontrolled and actuated states. A close-up view of the transition (black rectangle) is displayed at the right bottom of the main Fig.. The colour correspond to: ( ) raw signal ; ( ) 2 Hz filtered data; ( ) control start. alternating left and right edge activation. The actuation frequency was set to 975 Hz, the supply pressure to P i = 0.27 MPa and the flow velocity V ∞ to 25 m/s. Here the control is a low-frequency modulating signal f m that defines the time of actuation for each side. In Fig. 5, we selected representative results of three different modulation frequencies leading to distinct regimes for the wake: a) Under-actuated (f m = 4 Hz): according to the activated side, X moves towards the left or the right unstable equilibrium position ; b) Resonant (f m = 16 Hz): X oscillates between the two unstable equilibrium positions without reaching a steady state. The time 1/f m is close to twice the characteristic transition time for the actuated wake ; c) Over-actuated (f m = 54 Hz): X shows smaller fluctuation magnitudes but its average value is not 0: this open-loop control does not improve the wake asymmetry, even in average.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Open-loop control locations for X for alternated forced transitions at a low frequency fm (from left to right: fm = 4 Hz, 16 Hz, 54 Hz). Control starts at the red dashed lines.

Fig. 8 .

 8 Fig. 8. Pressure ratio levels: 1 bistable pressure states, 2 pressure levels for the SMC Law 1 , 3 delay compensation scheme. The red dashed lines separate the control parts.

Table 1 .

 1 Experimental mock-up dimensions

	Length	L = 1.00 m
	Width	W = 0.36 m
	Height	H = 0.30 m
	Gap under body clearance	G = 0.05 m
	The mock-up is placed on a raised floor in a closed-
	loop wind tunnel (ENSMA, Poitiers, France) in order to
	recreate an homogeneous flow around it. This wind tunnel
	can generate wind velocities up to 60 m/s and create a
	fully turbulent flow around the experimental body with a
	Reynolds number Re about 10 5 .

Table 3 .

 3 Effects of the SMC Law 3 for different tank pressure P i on the pressure, drag ratio and symmetry parameters.

	P i [MPa]∆γp [%] ∆γ Cx [%] |X|	σ	d X
	0.25	+1.73	+2.15	3.10 -4	0.031	0.008
	0.24	+1.25	+1.73	7.10 -5	0.030	0.006
	0.23	+0.34	+1.14	6.10 -4	0.030	0.002
	0.22	-0.78	+0.59	5.10 -4	0.031	0.003
	0.21	-0.89	+0.53	3.10 -4	0.031	0.004
	0.20	-1.41	+0.09	4.10 -4	0.030	0.002
	0.19	-2.11	-0.11	2.10 -4	0.031	0.007
	0.18	-2.03	-0.19	1.10 -4	0.031	0.006
	a)
		b)

Table 4 .

 4 Symmetry parameters X, σ, d X with the pressure and drag ratio variations (respectively ∆γp and ∆γ Cx ) expressed in % for different yaw angles β with the SMC Law 3 .

		Uncontrolled		SMC Law 3
		X	σ	d X	∆γ p [%] ∆γ Cx [%]	|X|	σ	d X
	-0.7	-0.042 0.025 0.049	+0.53	+2.23	0.001 0.030 0.012
	0	0.003 0.047 0.046	+1.73	+1.71	0.001 0.030 0.008
	+1.7 0.044 0.014 0.044	-2.95	-1.70	0.012 0.029 0.020

Table

4

are obtained with a jet frequency of 1050 Hz, a supply pressure P i = 2.5 × 10 5 Pa, and V ∞ = 35 m/s. As displayed, for this important pressure, no improvements in terms of pressure nor drag are achieved for small drift angle or for the aligned configuration. How-

β [ • ]


Idris Boudhabhay

Victoria Poillerat

Anne Grunenwald

Carine Torset

Juliette Leon

Marie V Daugan

Francesca Lucibello

El Khalil

Amandine Karoui

Sophie Ydee

Chauvet

Patrick Chauvet

Steven Girardie

Conrad A Sacks

Peter Farrar

Romain Garred

Moglie Berthaud

Marion Le Quintrec

Pascale Rabant

Caroline De Lonlay

Viviane Rambaud

Veronique Gnemmi

Marie Fremeaux-Bacchi

Lubka T Frimat

Roumenina

Khalil El Karoui

Amandine Ydee

Sophie Chauvet

Patrick Girardie

Steven Sacks

Conrad A Farrar

Peter Garred

Romain Berthaud

Moglie Le Quintrec

Marion Rabant

Pascale De Lonlay

Caroline Rambaud

Viviane Gnemmi

Veronique Fremeaux-Bacchi

Marie Frimat

Ph.D Lubka T Roumenina
email: lubka.roumenina@sorbonne-universite.fr

Complement activation is a crucial driver of acute kidney injury in rhabdomyolysis

Keywords: Boudhabhay, 2020 C3 deposition, complement, heme, hemopexin, lectin pathway, rhabdomyolysisinduced acute kidney injury, Translational

Introduction

Rhabdomyolysis is a life-threatening condition caused by skeletal muscle injury and subsequent release of breakdown products into the circulation. The causes are multiple, but dominated by trauma ("crush syndrome"), muscle hypoxia, genetic defects, medication or drug abuse. [START_REF] Bosch | Rhabdomyolysis and acute kidney injury[END_REF] Acute kidney injury (AKI) is the major complication of rhabdomyolysis, seen in up to 50% of the patients. [START_REF] Candela | Short-and long-term renal outcomes following severe rhabdomyolysis: a French multicenter retrospective study of 387 patients[END_REF][START_REF] Huerta-Alardin | Bench-to-bedside review: Rhabdomyolysis -an overview for clinicians[END_REF] Rhabdomyolysis-induced AKI (RIAKI) occurs in adults, due to trauma or intoxication, and in children due to inherited muscle disorders. There is no specific treatment for RIAKI and patients' management is mostly symptomatic. Myoglobin and its oxygen-carrying moiety heme play a key role in RIAKI through: (i) renal vasoconstriction; [START_REF] Kurtz | Renal cortical blood flow in glycerol-induced acute renal failure in the rat[END_REF] (ii) direct injury of proximal tubular cells through oxidative stress, lipid peroxidation, [START_REF] Boutaud | Mechanism-based therapeutic approaches to rhabdomyolysis-induced renal failure[END_REF] and macrophage activation; [START_REF] Belliere | Specific macrophage subtypes influence the progression of rhabdomyolysis-induced kidney injury[END_REF][START_REF] Okubo | Macrophage extracellular trap formation promoted by platelet activation is a key mediator of rhabdomyolysis-induced acute kidney injury[END_REF][START_REF] Rubio-Navarro | CD163-Macrophages Are Involved in Rhabdomyolysis-Induced Kidney Injury and May Be Detected by MRI with Targeted Gold-Coated Iron Oxide Nanoparticles[END_REF] (iii) myoglobin precipitation with uromodulin, forming pigmented casts in distal tubules. RIAKI was considered complement-independent, since no C3c-positive staining was detected in the renal biopsies in the few published case reports. Nevertheless, complement may be implicated in RIAKI, since C3 depletion improved renal function in a rat model. [START_REF] Huang | The role of complement activation in rhabdomyolysis-induced acute kidney injury[END_REF] Complement is an essential effector of innate immunity. [START_REF] Merle | Complement System Part I -Molecular Mechanisms of Activation and Regulation[END_REF] However, complement overactivation is implicated in diseases affecting kidneys and/or associated with heme release. [START_REF] Merle | Intravascular hemolysis activates complement via cell-free heme and heme-loaded microvesicles[END_REF][START_REF] Merle | Circulating FH Protects Kidneys From Tubular Injury During Systemic Hemolysis[END_REF] Indeed, cell-free heme activates the alternative pathway. [START_REF] Roumenina | Heme: Modulator of Plasma Systems in Hemolytic Diseases[END_REF] Moreover, complement is pathogenic in ischemia-reperfusion injury (I/R). [START_REF] Arumugam | The role of the complement system in ischemia-reperfusion injury[END_REF][START_REF] Zhou | Predominant role for C5b-9 in renal ischemia/reperfusion injury[END_REF][START_REF] Thurman | Altered renal tubular expression of the complement inhibitor Crry permits complement activation after ischemia/reperfusion[END_REF][START_REF] Franzin | Inflammaging and Complement System: A Link Between Acute Kidney Injury and Chronic Graft Damage[END_REF] Here, we demonstrate that complement is activated in RIAKI in mice and patients and describe the mechanisms, by which it contributes to the AKI.

J o u r n a l P r e -p r o o f

Results

Complement activation in kidneys of RIAKI patients

Ten biopsies of RIAKI patients were collected. The main features of patients (RIAKI 1-RIAKI 10) are summarized in Table 1. Kidney biopsies revealed a typical pattern of RIAKI, characterized by acute tubular necrosis (ATN) associated with tubular casts (Fig. 1A). C3c staining was negative in the tubules in 8/10 RIAKI patients, and in 2 controls: a patient with AKI (Cr=420 µmol/L) caused by ATN without rhabdomyolysis and in an allograft kidney biopsy from a patient 2 days post-transplantation, used as example of I/R (Fig. 1B).

Nevertheless, C3d staining, regardless of rhabdomyolysis etiology, revealed a strong cytoplasmic and granular staining within the tubular cells. C3d staining was tested in 4 patients with ATN. With the exception of one patient with hypovolemia-associated ATN, C3d staining was positive in ATN induced by ischemic causes especially in I/R but negative in other causes such Cisplatin toxicity (Fig. 1C). Vascular C5b-9 staining was detected in big vessels and on arterioles (Fig S1A,B) in 6 tested biopsies. We found evidence for localization of C5b-9 staining together with C3d in 3/6 cases (Fig S1C), although not in all vessels, as described in graft rejection. [START_REF] Goutaudier | C5b9 Deposition in Glomerular Capillaries Is Associated With Poor Kidney Allograft Survival in Antibody-Mediated Rejection[END_REF] Systemic markers of complement activation were analyzed in the plasma of 13 patients with rhabdomyolysis (P1-P13) (Table S1). No patient had auto-immune disease. One patient (P2) had chronic kidney disease related to Bardet Biedl syndrome and type 2 diabetes mellitus was present in three patients (P2, P6 and P11). Soluble C5b-9 (sC5b-9) was increased in only 2 patients one of which, P2, developed septic shock early after admission which could explain this result. P7 also had inflammatory syndrome, but not so severe. In P12 the sC5b-9 was borderline. Plasma P13 corresponds to the patient with biopsy RIAKI 9.

Validation of the RIAKI mouse model

We studied the implication of complement in RIAKI using a mouse model in C57BL/6 mice (Fig. S2A). Immediately after glycerol injection (GLY), all mice presented with lameness of the injected limb (Fig. S2B). Rhabdomyolysis biomarkers, CK and ASAT, were elevated in GLY vs PBS mice (p=0.0042 and p<0.0001 respectively) (Fig. S2C). A dark discoloration of the urine of GLY mice at 6h was indicative of necrotic tubules and myoglobinuria (Fig. S2D).

AKI was evident by the increase in both blood urea nitrogen (BUN) (Fig. S2E) and creatinine (Cr) (p<0,0001 and p=0,0006 respectively). Likewise, proteinuria increased in GLY mice (p=0,02), mainly composed of albumin (60kDa band) (Fig. S2F). Tubular damage/injury J o u r n a l P r e -p r o o f markers Lcn2 (Lipocalin 2, the mouse ortholog of human NGAL) and Havcr1 (KIM-1), and endothelial activation markers P-Selectin (p<0,0001), E-Selectin (p<0,0001), ICAM-1 (p<0,0001) and VCAM-1 (p<0,0001), (Fig. S2G) were upregulated in GLY mice.

Lcn2/NGAL staining was intense on tubular cells of GLY mice (Fig. S2H). Likewise, VCAM-1 staining appeared positive in peri-tubular capillaries (Fig. S2I).

Complement activation occurs in the kidney and correlates with RIAKI in mice

Histopathological examination of GLY mice kidneys revealed the same lesions as in humans, with ATN and tubular casts (Fig. 2A). Staining with anti-C3b/iC3b antibody revealed the expected weak signal in PBS mice, on the tubular basement membrane and Bowman's capsule. [START_REF] Thurman | Altered renal tubular expression of the complement inhibitor Crry permits complement activation after ischemia/reperfusion[END_REF] However, after glycerol injection, this staining increased dramatically in the tubular lumen and inside the cytoplasm of tubular cells and at the basolateral pole (Fig. 2B,C). No significant difference was found between CD31 staining in PBS, Glycerol and Cisplatin injected mice. The antibody does not recognize intact C3, indicating activation of complement in RIAKI. Conversely, cisplatin-injected mice did not show an increase in tubular C3b/iC3b deposits. Quantification of the staining revealed a linear correlation with AKI markers, assessed by BUN (r 2 =0.64; p<0,0001) and by plasma creatinine (r 2 =0,69; p<0,0001) in GLY mice (Fig. 2D).

Complement activation occurs locally in the kidney

We used a C3 western blot of plasma and urine to investigate complement system activation (Fig. S3A). In plasma, C3 western blot of GLY mice was similar to PBS mice, with no sign of C3 cleavage (Fig. S3B left), whereas in urine C3b (recognized by α' band) appeared at 2 hours following GLY injection and more markedly at 24 hours after GLY injection (right). The same pattern was observed in all 3 tested patients with RIAKI (R1:CK= 88 000 ui/L; Cr=141µmol/L, R2: CK=10000ui/L; Cr=1615µmol/L; R3: CK=17126ui/L; Cr=903µmol/L), with no cleavage in plasma but in urine (Fig. S3C). The urine R2 corresponds to biopsy RIAKI5. Moreover, among 12 tested patients with RIAKI, C3 was decreased for only one case (Table S1).

Systemic C3 mainly contributes to complement activation in the kidney

Further, we tested if plasma and/or local C3 was involved in RIAKI. C3 kidney mRNA was upregulated in GLY mice compared to PBS (p<0.0001), indicating renal production J o u r n a l P r e -p r o o f during RIAKI (Fig. S4A). Moreover, C3d-staining in human and mouse kidneys appeared cytoplasmic and co-localized with LAMP1, indicative of intracellular C3, at least in part with lysosomal localization (Fig. S4B,S4C). To evaluate the role of systemic C3 in RIAKI, we injected glycerol in HepatoFH-/-mice, which have a low concentration of plasma C3 at steady state because of systemic FH deficiency and subsequent C3 consumption (Fig. S4D). [START_REF] Vernon | Partial Complement Factor H Deficiency Associates with C3 Glomerulopathy and Thrombotic Microangiopathy[END_REF] C3 kidney mRNA expression was similar in hepatoFH-/-GLY mice compared to WT-GLY mice (p=0.8), indicating persistent renal production. However, hepatoFH-/-GLY mice tended to be protected from RIAKI (Fig. S4E), with less tubular injury assessed by Lcn2 expression (Fig. S4F), and with less C3-deposits in their kidneys (Fig. S4G). Likewise, WT mice injected with cobra venom factor (CVF) prior to glycerol, displayed persistent plasma C3 consumption, 24h post-injection (Fig. S4H), and nearly no C3b/iC3b deposits within the kidneys in comparison to mice injected with PBS prior to glycerol (Fig. S4I).

The complement system is over-activated through a C4-bypass pathway

In vitro, a dose-dependent increase in C3 activation fragments was observed on renal proximal tubular epithelial cells (RPTEC), incubated with increasing dose of myoglobin and serum (Fig. 3A left). No C4 deposits were detected (Fig. 3A right). Moreover, C4 was negative in 9 RIAKI biopsies tested (Fig. 3B). C1q staining was mostly negative in tubules of 6/8 RIAKI patients. However, 2 patients had a granular staining in scarce tubules (RIAKI 1 and 7), 1 had focal and segmental deposits in glomeruli (RIAKI 4) and 2 had positive staining of peritubular capillaries (RIAKI 8 and 9) (Fig. S5A). C1s staining was positive in vessels and capillaries including glomerular ones with very weak tubular staining in 2/2 RIAKI patients. (Fig. S5B). In mice, Glycerol injection induced an increased glomerular C1q staining (Fig. S5C). Gene expression revealed a decreased C1s1 expression of -0.54 log2 fold-change (p=0.02) without significant difference for C1r (-0.38 log2 fold-change (p=0.19)).

Furthermore, glycerol injection in C4-/-mice revealed no protection from RIAKI (Fig. 3C) and even enhanced vascular aggression (up-regulation of P-Selectin (p<0,001), E-Selectin (p<0,001), VCAM-1 (p<0,001), and ICAM-1 (p<0,001) (Fig. 3D). Tubular injury markers, Lcn2 and Havcr1 were not different in C4-/-GLY mice, compared to WT-GLY but significantly upregulated compared to WT-PBS (Lcn2: p=0,02 Havcr1: p=0,04) (Fig. 3E).

Finally, C3b/iC3b staining revealed intense tubular deposits in C4-/-mice, similar to WT-GLY mice, suggesting that complement activation is independent from C4 in this model (Fig.

3F).

J o u r n a l P r e -p r o o f

A C4 by-pass lectin pathway operates in ischemic kidneys through collectin-11/L-fucose interaction. [START_REF] Farrar | Collectin-11 detects stress-induced L-fucose pattern to trigger renal epithelial injury[END_REF] Collectin-11 (CL-11) staining increased in mouse RIAKI kidney tubules.

Moreover, CL-11 and C3b/iC3b showed partial colocalization, indicating that complement was largely deposited at the site of CL-11 binding (Fig. 3G). Human renal biopsies, including those of RIAKI patients, showed CL-11 overexpression on tubular cells, suggesting that this protein is readily available in the kidney (Fig. S6A). CL-11 staining was positive mainly on proximal tubules identified by their auto-fluorescent brush border. (Fig. S6B)

Complement dysregulation contributes to C3 deposits

Complement receptor 1-related protein y (Crry) is the only complement regulator on mouse tubular epithelial cells. [START_REF] Thurman | Altered renal tubular expression of the complement inhibitor Crry permits complement activation after ischemia/reperfusion[END_REF] Staining of Crry revealed a linear repartition at the basolateral pole of tubular cells in PBS mice, but decreased and lost polarity in GLY mice. This could amplify complement activation and explain the basolateral localization of C3 deposits (Fig. S7A). Complement Factor H (FH) is a plasma regulator, which can bind to the cell membrane to control alternative pathway. Cfh gene expression was downregulated in GLY kidneys (Fig. S7B). Kidney tissue from a patient with idiopathic nephrotic syndrome caused by minimal change disease was FH-low/negative whereas liver sections, a biopsy from a patient with lupus nephritis and a biopsy from a patient with ATN without rhabdomyolysis were positive (Fig. S7C). In human RIAKI tissue sections, FH staining was positive in a small portion of the proximal tubules, showing an intracellular granular pattern. Compared to C3d-staining, only a few of the C3d-positive tubules appeared FH-positive (Fig. S7D).

Heme overload promotes complement activation.

Numerous C3 deposits did not colocalize with CL-11. Therefore, alternative pathway could be triggered independently. As cell-free heme is a well-known alternative pathway activator in hemolysis, we studied if myoglobin-released free heme, reflected by HO-1 up-regulation in GLY mice (Fig. 4A), contribute to complement activation and kidney injury. In vitro, incubation of renal proximal tubular epithelial cells (RPTEC) with oxidized heme and serum, increased C3 deposits (Fig. 4B). In vivo, we evaluated the contribution of heme by a preventive injection of its natural scavenger, hemopexin. The injected hemopexin dose was the maximal well-tolerated in heme-overload. [START_REF] Poillerat | Hemopexin as an Inhibitor of Hemolysis-Induced Complement Activation[END_REF] The induction of rhabdomyolysis was efficient since CK and ASAT were not different in GLY mice +/-hemopexin. However, renal function (BUN) improved in hemopexin injected mice (p=0,01) (Fig. 4C). No change in tubular injury markers was observed, but vascular injury markers were markedly J o u r n a l P r e -p r o o f decreased (P-selectin: p=0,0095; E-Selectin: p=0,014; VCAM-1: p=0,03 ICAM-1: p=0,06) (Fig. 4D-E). Finally, C3 deposits significantly decreased (p=0,02) (Fig. 4F-G) whereas renal C3 gene expression was not different from GLY mice (p=0,5; not shown).

Tubular cell and macrophage C5aR1 is upregulated in mouse RIAKI

Renal C3aR1 mRNA expression in GLY-injected mice was not different from PBS mice (p=0,89) (Fig. 5A). However, C5aR1 mRNA was markedly upregulated in GLY mice (p<0,0001) (Fig. 5A). Strong staining for C5aR1 was detected in the tubules of GLY mice and in interstitial cells (Fig. 5B). To identify those cells, C5aR1 was measured on myeloid populations from kidneys by flow cytometry. Eight hours after glycerol injection, there was an increase in macrophage and neutrophil infiltration within GLY kidney compared to PBS (p=0,0152 and p=0,0022 respectively) (Fig. 5C). At 24 hours, there was no quantitative difference in neutrophil and macrophage infiltration, as described. [START_REF] Komada | Role of NLRP3 Inflammasomes for Rhabdomyolysis-induced Acute Kidney Injury[END_REF] No difference was detected for C5aR1 expression on neutrophils in both groups (p=0,18), but in GLY mice both M1 (CCL2, TNFα) and M2 (Arginase 1) markers were co-expressed (Fig. S8). Indeed, intrarenal macrophages showed phenotypic alteration. Expression of C5aR1 was not different among macrophages expressing class II HLA (CD45 + Ly6G - CD68 + IAb + ; p=0,55) and their proportion did not differ between PBS and GLY mice.

However, CD45 + Ly6G -CD68 + IAb -C5aR1 + macrophages increased in GLY mice (p=0,02) mostly because of the emergence of a peculiar sub-population of CD45 + Ly6G -CD68 + IAb - C5aR1 + CD11b hi cells (Fig. 5D). CD11b/CD18 is a receptor for C3b/iC3b. Interestingly, immunofluorescence on frozen kidneys revealed a close relationship between CD11b + cells and C3b/iC3b deposits (Fig. 5E).

C3-/-mice are protected from RIAKI

To explore the causal link between complement and RIAKI, we injected glycerol in C3-/mice. C3-/-GLY mice presented the same lameness of the injected limb and increase in CK and ASAT, compared to PBS WT mice (p=0,03 and p=0,0043 respectively) reaching the same level as WT-GLY mice (p=0,2 and p=0,5 for CK and ASAT). In addition, HO-1 was equally upregulated in WT-GLY and C3-/-GLY mice (Fig. S9A). However, BUN was significantly lower in C3-/-GLY compared to WT-GLY mice (p=0,002) (Fig. 6A), disrupting the correlation between kidney injury and muscle injury (Fig. 6B). In addition, C3-/-GLY mice kidneys displayed very light ATN and rare tubular casts (not shown) following hematoxylin/eosin staining. Even sensitive markers of tubular injury such as J o u r n a l P r e -p r o o f Lcn2 and Havcr1 were reduced in C3-/-mice, (p=0.001 and p=0.0005 respectively) (Fig. S9B), as well as endothelial activation markers (P-Selectin: p=0,001; E-selectin: p=0.01; ICAM-1: p=0;0005; VCAM: p=0,0005) (Fig. S9C).

RIAKI in mice is associated with a pro-inflammatory and apoptotic transcriptomic signature.

Bulk RNA sequencing analysis on kidneys from PBS versus GLY mice revealed 2056 significantly upregulated genes, 1786 significantly downregulated genes and 16683 genes without significant difference (difference was considered significant when p<0,05 and fold change at least superior to 2) (Fig. 6C). Analysis of the 25 most up-regulated and the 25 most down-regulated genes, allowed definition of a rhabdomyolysis transcriptomic signature (Fig. 6D). Interestingly, one of the most upregulated genes was Fucosyltransferase 2 (Fut2) enzyme, responsible for tagging stressed cells with fucosyl residues, recognized by the lectin pathway. [START_REF] Saku | Fucosyltransferase 2 induces lung epithelial fucosylation and exacerbates house dust mite-induced airway inflammation[END_REF] Performing gene ontology on all significantly upregulated genes showed the most up-regulated pathways involved the inflammatory response (cytokine and chemokines such as Cxcl1, Cxcl2, Cxcl3, Cxcl5, Cxcl14, Cxcl17, Ccl2, Ccl3, Ccl4, Ccl7, Ccl9, Ccl11, Ccl12, Ccl17, Ccl20, Il6, Il11, Il24, TNFα, members of the IL1 family, etc), and the cell response to inflammatory processes (response to biotic stimulus such as Glutathione S-transferase A-1 gene, protein phosphorylation and regulation of intracellular transduction), as well as apoptosis (e.g Trib1 and Myc).

Classical tubular injury markers Lcn2 (NGAL) and Havcr1 (Kim1) were dramatically upregulated. The most downregulated pathways affected renal metabolism (drug metabolic processing, small molecule processing and lipid metabolism), and intracellular transports (ion transport and trans-membrane transport such as SLC34a3 coding for Sodiumdependant phosphate transport protein 2C and SLC12A1 gene, coding for the Na + /K + /2Cl - cotransporter).

C3 deficiency attenuates the RIAKI signature in mice

C3-/-mice injected with PBS presented a transcriptomic profile very close to the PBS WT mice. Strikingly, C3-/-mice injected with glycerol (C3-/-GLY) lost the majority of the RIAKI signature, compared to the WT-GLY mice (Fig. 6E). Indeed, inflammatory pathways were drastically less upregulated than in WT-GLY mice and, cellular metabolism or ion transport were less affected. Lcn2 and Havcr1 were significantly reduced in C3-/mice, confirming the data from the RTqPCR (Fig. 6E, Fig. S9B). Comparison of RIAKI J o u r n a l P r e -p r o o f signature genes between WT and C3-/-PBS (WT/C3-/-PBS), or glycerol (WT/C3-/-GLY) allowed us to classify them into 3 groups: 1) genes, which are completely normalized in the C3-/-GLY mice (p-value WT-GLY vs C3-/-GLY<0.05 and p-value C3-/-PBS vs WT-GLY>0.05); 2) genes which are partially normalized in the C3-/-GLY mice (p-value 'WT-GLY vs C3-/-GLY'<0.05 and p-value 'C3-/-PBS vs WT-GLY'<0.05); 3) genes which are not affected by C3 deficiency (p-value 'WT-GLY vs C3-/-GLY'>0.05 and p-value 'C3-/-PBS vs WT-GLY'>0.05). The completely normalized genes included Fut2 among the upregulated and a set of down-regulated genes, involved in pathways related to potassium ion transport and protein dephosphorylation. Partial correction by C3 deficiency was achieved for upregulated genes involved in the cellular response to cytokines (such as: Ccl12, Cxcl1, Fgb, Lcn2, Socs3, Sox9, Spp1, Timp1) and apoptosis (the same set except Cxcl1 but including Fgg and Sfn). Among them Ccl12, Fgb, Lcn2 and Sox9 belong to the cellular response to IL-1 pathway. The set of downregulated genes, attenuated in C3-/mice, were not enriched in any particular pathway. A set of genes, including such involved in the cellular response to hypoxia (Eif4ebp1 and Myc) were not affected by C3 deficiency.

Discussion

In addition to myoglobin casts and acute tubular necrosis which are common histology features for rhabdomyolysis, [START_REF] Najafian | AJKD Atlas of Renal Pathology: Myoglobin Cast Nephropathy[END_REF] complement deposits occurred in kidneys of mice and patients with RIAKI, independent of the rhabdomyolysis cause. Complement activation occurred intrarenally most likely by the lectin pathway via a C4-bypassing mechanism, and by the alternative pathway via heme. Intrarenal macrophages in RIAKI became particularly sensitive to complement, overexpressing C5aR and CD11b. C3-/-mice were protected from kidney injury, demonstrating a direct pathophysiological link and placing complement as a potential therapeutic target in RIAKI.

We discovered C3d-deposits in the kidneys of patients with RIAKI, regardless of the cause of rhabdomyolysis, demonstrating that complement activation is a consequence of a common factor, present during muscle injury. C3d staining was negative in most of the tested ATN without rhabdomyolysis biopsies, suggesting that complement activation is not a consequence of all tubular injuries. Interestingly, C3c staining was negative/weak in RIAKI biopsies. This can be explained by the rapid cleavage of iC3b to C3c then to C3d, since all biopsies were performed more than 24 hours after the initiation of rhabdomyolysis. [START_REF] Schulze | Glomerular C3c localization indicates ongoing immune deposit formation and complement activation in experimental glomerulonephritis[END_REF] In lupus nephropathy (LN) C3c vs C3d staining allows the J o u r n a l P r e -p r o o f differentiation between active and not-active LN. [START_REF] Wilson | Glomerular membrane attack complex is not a reliable marker of ongoing C5 activation in lupus nephritis[END_REF] Noteworthy, C3c but not C3dimmunostaining is performed as routine work-up on kidney biopsies and might explain why C3-deposits have not been described until now in RIAKI. Furthermore, we detected massive C3-deposits in the mouse model. C3 cleavage or consumption did not occur in plasma from the patients or mice. Thus, complement activation occurs locally within the kidney, and we detected C3 fragments in urine of patients and mice. This intrarenal complement activation could be due to the local overexpression of C3, as described in lupus nephritis [START_REF] Passwell | Local extrahepatic expression of complement genes C3, factor B, C2, and C4 is increased in murine lupus nephritis[END_REF] and in graft rejection, [START_REF] Biglarnia | The multifaceted role of complement in kidney transplantation[END_REF][START_REF] Pratt | Local synthesis of complement component C3 regulates acute renal transplant rejection[END_REF] and/or mediated by the systemic C3 as in I/R [START_REF] Renner | Binding of factor H to tubular epithelial cells limits interstitial complement activation in ischemic injury[END_REF] or hemolysis-induced renal injury. [START_REF] Merle | Circulating FH Protects Kidneys From Tubular Injury During Systemic Hemolysis[END_REF] Since glycerol-injected mice with plasma C3 consumption (FHhepato-/-and CVF-treated mice) were protected from complement activation, the major role was played by the systemic C3.

Complement could be activated in RIAKI by different pathways. In rat RIAKI, enhanced C1q staining in tubules was detected [START_REF] Huang | The role of complement activation in rhabdomyolysis-induced acute kidney injury[END_REF] , whereas here C1q was mainly negative in RIAKI biopsies and enhanced only in some glomeruli in the mouse model. Renal fibrosis models revealed increased expression of C1q, C1r, and C1s and classical pathway activation in the interstitial compartment. [START_REF] Xavier | Pericytes and immune cells contribute to complement activation in tubulointerstitial fibrosis[END_REF][START_REF] Xavier | Complement C1r serine protease contributes to kidney fibrosis[END_REF] We detected a decrease of C1s and C1r expression at 24h. Nevertheless, we cannot exclude an involvement of the classical pathway in RIAKI, potentially later in time, with the progression of the fibrotic process as previously suggested. [START_REF] Xavier | Complement C1r serine protease contributes to kidney fibrosis[END_REF] However, C4-/-mice were not protected from RIAKI and C3 deposits, suggesting that classical pathway and C4 have a minor role in RIAKI's complement activation. The alternative pathway is responsible, at least in part, for the observed deposits. Indeed, heme binds C3, activates the alternative pathway [START_REF] Roumenina | Heme: Modulator of Plasma Systems in Hemolytic Diseases[END_REF] and it induced complement activation on primary tubular cells. This process could be mediated also by properdin. [START_REF] Pedersen | Functional and structural insight into properdin control of complement alternative pathway amplification[END_REF][START_REF] Chen | Properdin Is a Key Player in Lysis of Red Blood Cells and Complement Activation on Endothelial Cells in Hemolytic Anemias Caused by Complement Dysregulation[END_REF] Moreover, the injection of heme-scavenger hemopexin, which can be filtered through the glomerular basement membrane, partially improved kidney function and vascular aggression, as described. [START_REF] Okubo | Macrophage extracellular trap formation promoted by platelet activation is a key mediator of rhabdomyolysis-induced acute kidney injury[END_REF] Hemopexin decreased C3-deposits, showing a direct role of heme in the intrarenal complement activation.

Conventional lectin pathway proceeds through C4, [START_REF] Dobo | The emerging roles of mannose-binding lectinassociated serine proteases (MASPs) in the lectin pathway of complement and beyond[END_REF] but a C4-bypass pathway was found in post-ischemic tissue, where CL-11 binds abnormally fucosylating cells and its associated protease MASP-2 cleaves directly C3 to C3b and C3a. [START_REF] Asgari | Mannan-binding lectin-associated serine protease 2 is critical for the development of renal ischemia reperfusion injury and mediates tissue injury in the absence of complement C4[END_REF][START_REF] Yaseen | Lectin pathway effector enzyme mannanbinding lectin-associated serine protease-2 can activate native complement C3 in absence of C4 and/or C2[END_REF] Fucosyltransferase 2 (Fut2) is the enzyme which fucosylates epithelium in case of enhanced inflammation. [START_REF] Saku | Fucosyltransferase 2 induces lung epithelial fucosylation and exacerbates house dust mite-induced airway inflammation[END_REF] In RIAKI, we detected CL-11 staining, partially colocalizing with C3b/iC3b and Fut2 was one of the most up-regulated genes in the transcriptomic signature. Moreover, Fut2 is strongly dependent on complement, as it was completely normalized in the C3-/-mice, J o u r n a l P r e -p r o o f suggesting that complement activation, potentially triggered by heme, creates an environment that promotes a vicious cycle of further lectin pathway activation. The RIAKI is therefore a particular situation, where both the alternative and the lectin pathways may be triggered in the kidney and the alternative pathway is not a mere amplification loop.

Moreover, the reduced regulatory capacity of the stressed tubular cells in RIAKI that we found amplifies the complement activation.

To better understand the molecular mechanisms of RIAKI and the role of complement, we defined a "RIAKI transcriptomic signature" in the mouse model. A clear signature of apoptosis was detected, consistent with the tubular injury. If there was no evidence for increase of TNF alpha expression in kidney, [START_REF] Shulman | Glycerol induced ARF in rats is mediated by tumor necrosis factor-alpha[END_REF] a strong pro-inflammatory signature was observed with a high involvement of genes for response to cytokines and cytokine production. This is concordant with the hypothesis that tubular injury observed in rhabdomyolysis is an inflammatory disease, [START_REF] Shulman | Glycerol induced ARF in rats is mediated by tumor necrosis factor-alpha[END_REF][START_REF] Nishida | Renoprotective effect of long acting thioredoxin by modulating oxidative stress and macrophage migration inhibitory factor against rhabdomyolysis-associated acute kidney injury[END_REF][START_REF] Kim | N-acetylcysteine attenuates glycerol-induced acute kidney injury by regulating MAPKs and Bcl-2 family proteins[END_REF] involving infiltrating immune cells, especially macrophages in glycerol induced RIAKI. [START_REF] Belliere | Specific macrophage subtypes influence the progression of rhabdomyolysis-induced kidney injury[END_REF][START_REF] Nishida | Renoprotective effect of long acting thioredoxin by modulating oxidative stress and macrophage migration inhibitory factor against rhabdomyolysis-associated acute kidney injury[END_REF][START_REF] Homsi | Role of caspases on cell death, inflammation, and cell cycle in glycerol-induced acute renal failure[END_REF][START_REF] Homsi | Endogenous hepatocyte growth factor attenuates inflammatory response in glycerol-induced acute kidney injury[END_REF] Myoglobin was shown to modulate the phenotype of the macrophages. [START_REF] Rubio-Navarro | CD163-Macrophages Are Involved in Rhabdomyolysis-Induced Kidney Injury and May Be Detected by MRI with Targeted Gold-Coated Iron Oxide Nanoparticles[END_REF] Additionally, myoglobin-activated tubular cells in culture express Ccl2 and Ccl7, potent macrophages-recruiting factors. [START_REF] Belliere | Specific macrophage subtypes influence the progression of rhabdomyolysis-induced kidney injury[END_REF] Indeed, significant upregulation of these and other chemokines and cytokines were detected, which could explain the enhanced infiltration of macrophages and neutrophils. Markers of both M1 and M2 macrophages were detected as described. [START_REF] Belliere | Specific macrophage subtypes influence the progression of rhabdomyolysis-induced kidney injury[END_REF] We identified a RIAKI-associated sub-population of macrophages, negative for HLA-II but expressing strongly C5aR1 and CD11b. This population will be highly susceptible to complement overactivation, being responsive to contact with C3b/iC3b as well as with C5a. Macrophage CD11b/CD18 engagement by direct contact with heme-activated platelets triggered macrophage extracellular trap formation and kidney injury. [START_REF] Okubo | Macrophage extracellular trap formation promoted by platelet activation is a key mediator of rhabdomyolysis-induced acute kidney injury[END_REF] C3b/iC3b is a ligand of CD11b/CD18 and since we detected CD11b+ cells in close contact with C3b/iC3b deposits on affected proximal tubules in situ, we hypothesize that macrophage activation and kidney damage could be mediated due to this direct contact. Moreover, the overexpression of C5aR1 on tubular cells, together with its increase on macrophages could contribute to the AKI, as described in renal I/R injury [START_REF] Peng | C3a and C5a promote renal ischemia-reperfusion injury[END_REF][START_REF] Peng | The C5a/C5aR1 axis promotes progression of renal tubulointerstitial fibrosis in a mouse model of renal ischemia/reperfusion injury[END_REF] and hemolysis. [START_REF] Merle | Circulating FH Protects Kidneys From Tubular Injury During Systemic Hemolysis[END_REF] Evaluation of C5a in urine of human and murine RIAKI could be a potential future biomarker, as urine C5a has been associated with AKI. [START_REF] Schröppel | Donor Urinary C5a Levels Independently Correlate With Posttransplant Delayed Graft Function[END_REF] Interestingly, we found no tubular C5b-9 deposits in mice or in humans, contrary to previous report in rat RIAKI. [START_REF] Huang | The role of complement activation in rhabdomyolysis-induced acute kidney injury[END_REF] This might reflect an efficient regulation of C5b-9 at this site, likely due to CD59 overexpression [START_REF] Huang | The role of complement activation in rhabdomyolysis-induced acute kidney injury[END_REF] . A low J o u r n a l P r e -p r o o f sensitivity of the C5b-9 staining cannot be excluded, despite the clear detection of C5b-9 in blood vessels.

To provide direct proof that complement is a mediator of injury in RIAKI, we induced RIAKI in C3-/-mice. C3-/-mice have already been described as protected in a model of mechanical ischemia/reperfusion. [START_REF] Zhou | Predominant role for C5b-9 in renal ischemia/reperfusion injury[END_REF] Remarkably, C3-/-mice were also protected from RIAKI, and mostly lost the RIAKI transcriptomic signature, demonstrating the pathogenic role of C3 and/or downstream complement activation in this model. In particular, the cellular response to cytokines and apoptosis pathways appeared to be C3dependent. Renal tubular injury and dysfunction were markedly attenuated in glycerolinjected mice, deficient in interleukin (IL)-1β or NLRP3 inflammasome. [START_REF] Komada | Role of NLRP3 Inflammasomes for Rhabdomyolysis-induced Acute Kidney Injury[END_REF] Indeed, the cellular response to the IL1 pathway genes were attenuated in C3-/-mice. Complement overactivation and C5b-9 induce macrophages to release IL-1β, [START_REF] Laudisi | Cutting edge: the NLRP3 inflammasome links complement-mediated inflammation and IL-1beta release[END_REF][START_REF] Suresh | Complement-mediated 'bystander' damage initiates host NLRP3 inflammasome activation[END_REF] providing a potential mechanistic link between complement and the IL-1/cytokine response pathway. C3-/-mice were also protected from fibrosis and peritubular rarefaction in a model of unilateral ureteral obstruction and authors proposed that macrophages polarization could be involved with C3a induced M1 macrophages responsible in vitro for angiogenesis suppression. [START_REF] Cui | Complement C3 exacerbates renal interstitial fibrosis by facilitating the M1 macrophage phenotype in a mouse model of unilateral ureteral obstruction[END_REF] Therefore, complement C3 and/or downstream components are directly pathogenic for tubular cells and act in cooperation with macrophages to promote renal injury. However, specific cell types where inflammatory and apoptotic pathways are activated cannot be defined by the bulk RNA sequencing approach. Finally, C5b-9 deposits were detected in vessels of patients, suggesting that endothelial activation could contribute to the vascular aggression in RIAKI.

Consistent with this hypothesis, the vascular aggression observed in the mouse model was attenuated in the C3-/-injected with glycerol.

These results suggest a benefit for complement inhibition in RIAKI. C3b is the central protein of the complement cascade, allowing its own amplification through C3 convertase formation. C3-/-mice protection and loss of RIAKI transcriptomic signature suggest the therapeutic potential of C3 inhibition. Indeed, if C5 inhibition is the gold standard for complement inhibition, there is growing interest for C3 targeted therapies in diseases such as Paroxysmal Nocturnal Hemoglobinuria and many other conditions. [START_REF] Mastellos | Clinical promise of next-generation complement therapeutics[END_REF] In conclusion, our study demonstrates that complement activation, promoted by renal ischemia and heme overload, plays a key role in RIAKI in both mice and humans, independent from the initial cause of muscle damage. Therefore, drugs targeting complement activation and/or heme overload would represent promising therapeutics in critically ill patients.

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Materials and Methods

The complete Materials and Methods are given in Supplement.

Collection of human kidney biopsies, urines and sera.

Patients. Kidney biopsies and clinical data from 10 patients with RIAKI were retrieved.

All biopsies were performed to eliminate an alternative cause of AKI, or as part of the autopsy in one patient who died from rhabdomyolysis (RIAKI 6). All patients gave informed consent for the use of part of the biopsy for scientific purposes. Urine was collected from 3 and plasma from 11 RIAKI patients and leftover samples from the routine diagnostics were used for this study. All procedures were performed according to national ethical guidelines and were in accordance with the Declaration of Helsinki. Staining was performed for C3c, C3d, Lamp1, C4d, C1q, C5b-9, Collectin-11, [START_REF] Bayarri-Olmos | Development of a Quantitative Assay for the Characterization of Human Collectin-11 (CL-11, CL-K1)[END_REF] Factor H and CD31 on the kidney material (Table S2); C3 and sC5b-9 were measured in plasma and western blot for C3 was performed in plasma and urine.

Animal experimentation

C57BL/6 WT, C3-/-and C4-/-and hepatoFH-/-mice [START_REF] Vernon | Partial Complement Factor H Deficiency Associates with C3 Glomerulopathy and Thrombotic Microangiopathy[END_REF]

Transcriptomic analysis.

mRNA was extracted and retrotranscribed in cDNA. Gene markers of kidney injury (Table S3) were analyzed by RTqPCR and RNAseq.

Immunofluorescence (IF) and immunochemistry (IHC) in mice

Frozen kidney sections were used for IF and IHC are summarized in Table S1.

Complement activation on proximal tubular cells in vitro.

RPTEC were exposed to skeletal muscle myoglobin or oxidized species of heme (heme-ox), followed by human serum. Staining for C3 fragments was analyzed by flow cytometry.

Evaluation of the myeloid infiltrate in mouse kidneys

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Eight or 24h after injection of PBS or glycerol, mice were sacrificed, and the kidneys were dilacerated, and cell suspension was stained as described in Table S3. measured by BUN in WT-PBS mice (PBS) (blue), WT-GLY mice (GLY) (red) and C3-/-GLY mice (left) (green). B) Correlation between BUN and Creatine Kinase in WT-GLY mice (r 2 =0,56, p=0,0329) and C3-/-GLY mice (non-significant) (right). C) Volcano plot of WT-GLY versus WT-PBS mice. Genes with a fold change >2 and an adjusted p-value of less than 0,05 (red) are differentially expressed between the two groups. D) Heatmap of normalized counts (RSEM) in each mouse for the top 50 most differentially expressed genes (25 upregulated and 25 downregulated), defining the RIAKI signature. A row normalization is applied. (upper panel). Gene ontology analysis of biological pathways modulated in WT-GLY versus WT-PBS mice (lower panel). E) Heat map of normalized counts (RSEM) in each mouse (n=4 mice/group), for the top 50 most differentially expressed genes (25 upregulated and 25 downregulated) in the WT-PBS, WT-GLY and C3-/-GLY mice. A row normalization is applied. (upper panel). on the right column, in red are the genes of the RIAKI signature, which are completely normalized in the C3-/-(p value for the comparison of WT-GLY vs C3-/-GLY < 0.05 + a p value for C3-/-PBS vs WT-GLY > 0.05). In yellow are the genes which are partially normalized in the C3-/-mice (p value for the comparison of WT-GLY vs C3-/-GLY < 0.05 + a p value for C3-/-PBS vs WT-GLY < 0.05). In green are the genes which are not affected by C3 deficiency (p value for the comparison of WT-GLY vs C3-/-GLY > 0.05 + a p value for C3-/-PBS vs WT-GLY > 0.05). Gene ontology analysis of biological pathways modulated in WT-GLY versus C3-/-GLY mice. (lower panel). BUN: blood urea nitrogen J o u r n a l P r e -p r o o f

  at the same genetic background were used for this study. Experimental protocols were approved by the Charles Darwin ethical committee (Paris, France) and by the French Ministry of Agriculture (Paris, France), APAFIS#2148 2019091015099240v1. Rhabdomyolysis was induced by intramuscular injection of 7.5ml/kg 50% glycerol.

Figure 1 .

 1 Figure 1. C3d staining is positive in tubular cells of rhabdomyolysis (RIAKI) kidneys, independent of its cause. A) Masson Trichrome (left) and periodic acid Schiff stain (right) of a kidney section showing casts in the tubular lumen (*) and acute tubular necrosis with loss of the proximal tubule brush border (arrows). B) C3c staining in kidney sections from patients with acute tubular necrosis (ATN) caused by hypovolemia (left), rhabdomyolysis (RIAKI, middle) or from a renal allograft (48 hours post-transplant; ischemia-reperfusion, right) C) C3d staining kidney sections of patients with ATN caused by hypovolemia (left), Cisplatin toxicity (middle) and kidney allograft at 48 hours post-transplant (ischemia-reperfusion, right). RIAKI caused by autoimmune myositis: (RIAKI 1), crush syndrome (RIAKI 2), strenuous exercise (RIAKI 3), unknown cause (RIAKI 4), suspicion of Mac Ardle syndrome (RIAKI 5), LIPN1 deficiency (RIAKI 6), muscle compression (RIAKI 7-8), Dengue fever (RIAKI 9) and sepsis (RIAKI 10). Original magnification x40.

Figure 2 .

 2 Figure 2. C3b/iC3b tubular deposits correlate with RIAKI severity. A) Hematoxylin-Eosin staining of paraffin embedded kidneys from PBS mice (left) and GLY mice (right), original magnification x40. B) CD31 (red) and C3b/iC3b (green) immuno-fluorescence on frozen kidneys from PBS mice(left), glycerol-treated mice (middle) and Cisplatin-injected mice (CIS, right), original magnification x20. C) Quantification of C3b/iC3b tubular deposits using Halo© Software (left, ****p< 0,0001, Mann-Whitney test) (left). D) Correlation between C3b/iC3b tubular deposits and blood urea nitrogen (BUN) (r 2 = 0,64; p<0,0001) (left) and creatinine (r 2 =0,69; p<0,0001) (right). BUN: blood urea nitrogen.

Figure 3 .

 3 Figure 3. Complement system activation in human and murine RIAKI: implication of classical and lectin pathway. A) Flow cytometry analysis of C3 deposits (left) and C4 deposits (right) on renal proximal tubular epithelial cells (RPTEC) incubated with increasing doses of myoglobin prior to addition of normal healthy serum. B) C4 staining on paraffinembedded kidney in RIAKI (left) compared to lupus nephropathy (right) patients. C) Kidney injury measured by blood urea nitrogen (BUN) in WT mice injected with PBS (blue) or glycerol (GLY) (red) and C4-/-(purple) mice injected with glycerol (C4-/-GLY). D) Vascular aggression measured by mRNA expression of P-Selectin and VCAM-1 in WT-PBS (blue), WT-GLY (red) and C4-/-GLY (purple) mice. E) Tubular aggression measured by Lcn2 (NGAL) and Havcr1 (KIM-1) mRNA expression in WT-PBS (blue), WT-GLY (red) and C4-/-GLY (purple) mice. F) CD31 (red) and C3b/iC3b (green) immunofluorescence on frozen kidneys from C4-/-mice injected with PBS (C4-/-PBS) (left) and C4-/-mice injected with glycerol (C4-/-GLY) (right), original magnification x20. G) Representative immunofluorescence of renal cortex showing C3b/iC3b (green), CL-11 (purple), a merged image of C3b/iC3b and CL-11 in WT-PBS (up) and WT-GLY (down) mice. Kruskall Wallis test with Dunn's correction: *p<0,05; **p<0,01; ***p<0,001; ****p<0.0001. BUN: blood urea nitrogen

Figure 4 .Figure 5 .

 45 Figure 4. Hemopexin improves kidney function through vascular protection and decreases complement activation in murine RIAKI. A) Kidney mRNA expression of Heme Oxygenase-1 (HO-1) in GLY and PBS mice. B) FACS analysis of C3d deposits on RPTEC with increasing concentration of Heme (Fe3+). C) Kidney injury measured by BUN in GLY mice (red) and WT mice injected with Hemopexin (IV) prior to glycerol (black). D)

Figure 6 .

 6 Figure 6. C3-/-mice are protected from RIAKI. A) Kidney injury (renal function)measured by BUN in WT-PBS mice (PBS) (blue), WT-GLY mice (GLY) (red) and C3-/-GLY mice (left) (green). B) Correlation between BUN and Creatine Kinase in WT-GLY mice (r 2 =0,56, p=0,0329) and C3-/-GLY mice (non-significant) (right). C) Volcano plot of WT-GLY versus WT-PBS mice. Genes with a fold change >2 and an adjusted p-value of less than 0,05 (red) are differentially expressed between the two groups. D) Heatmap of normalized counts (RSEM) in each mouse for the top 50 most differentially expressed genes (25 upregulated and 25 downregulated), defining the RIAKI signature. A row normalization is applied. (upper panel). Gene ontology analysis of biological pathways modulated in WT-GLY versus WT-PBS mice (lower panel). E) Heat map of normalized counts (RSEM) in each mouse (n=4 mice/group), for the top 50 most differentially expressed genes (25 upregulated and 25 downregulated) in the WT-PBS, WT-GLY and C3-/-GLY mice. A row normalization is applied. (upper panel). on the right column, in red are the genes of the RIAKI signature, which are completely normalized in the C3-/-(p value for the comparison of WT-GLY vs C3-/-GLY < 0.05 + a p value for C3-/-PBS vs WT-GLY > 0.05). In yellow are the genes which are partially normalized in the C3-/-mice (p value for the comparison of WT-GLY vs C3-/-GLY < 0.05 + a p value for C3-/-PBS vs WT-GLY < 0.05). In green are the genes which are not affected by C3 deficiency (p value for the comparison of WT-GLY vs C3-/-GLY > 0.05 + a p value for C3-/-PBS vs WT-GLY > 0.05). Gene ontology analysis of biological pathways modulated in WT-GLY versus C3-/-GLY mice. (lower panel). BUN: blood urea nitrogen

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Acknowledgments: The cytometric and microscopy analyses were performed at the Centre d'Histologie, d'Imagerie et de Cytométrie (CHIC) and the Centre de Recherche des Cordeliers UMRS1138 (Paris, France). We are grateful to the CHIC team for the excellent technical assistance. CHIC is a member of the Université Pierre et Marie Curie Flow Cytometry network (RECYF). We are grateful for excellent technical assistance from the Centre d'Expérimentations Fonctionnelles team of the Centre de Recherche des Cordeliers and for their support with animal experimentation. We are greatful for the team of the GenomIC plateform Cochin Institute INSERM U1016 headed by Dr. F. Letourner for the RNAseq analyses and the Biochemistry platform in Hospital Bichat Centre Recherche sur l'Inflammation-Paris for the evaluation of the renal function parameters in blood and urine of the mice. This work was presented in the form of abstract at the 17th European Meeting on Complement in Human Disease" (EMCHD 2019), Madrid, Spain, 2019.

Funding: This work was supported by INSERM. IB received a fellowship from the Société Francophone de Néphrologie Dialyse et Transplantation (SFNDT). Author contributions: Designed the research: LR, IB, MF. Performed the research: IB, VP, AG, CT, JL, MVD, FL. Provided patient samples and take care for the patients: KEK, AY, SC, PG, MLQ, RB, MLQ, MR, PL, CR, VG. Analyzed the data: LR, IB, VP, AG, MVD, SS, CF, VFB, MF. Provided vital reagents: PG. Wrote the manuscript: IB, VP, AG, MF, LR.

Conflict of interest: Dr. Roumenina reports grants from CSL Behring, outside the submitted work. The other authors have declared that no conflict of interest exists.

Supplementary information is available on Kidney International's website:

Complete Materials and Methods; Supplementary references; Supplementary Tables Supplementary Figures

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