A hybrid collision model for safety collision control

T. Noël 1 , T. Flayols 1 , J. Mirabel 1 , J. Carpentier 2 , N. Mansard 1,3 Abstract-Self-collision detection and avoidance are essential for reactive control, in particular for dynamics robots equipped with legs or arms. Yet, only few control methods are able to handle such constraints, and it is often necessary to rely on path planning to define a collision-free trajectory that the controller would then track. In this paper, we introduce a combination of two lightweight, conservative and smooth models to generically handle self-collisions in robot control. For pairs of bodies that are far from one another on average (e.g. segments of distinct legs), we rely on a standard forward kinematics approach, using simplified geometries for which we provide analytical derivatives. For bodies that are moving close to one another, we propose to use a data-driven approach, with datasets generated thanks to a standard collision library. We then build a simple torque-based controller that can be implemented on top of any control law to prevent unexpected self-collision. This controller is meant to be implemented as a low-level protection, directly on the robot hardware. We also provide an open-source library to generate ANSI-C code for any robot model, experimented on the real quadruped Solo.

I. INTRODUCTION

Collision and self-collision avoidance is an important but yet difficult constraint in robotics [START_REF] Lozano-Pérez | An algorithm for planning collision-free paths among polyhedral obstacles[END_REF], [START_REF] Gilbert | A fast procedure for computing the distance between complex objects in three-dimensional space[END_REF]. They are now handled at the planning level, by relying on random-based algorithms [START_REF] Barraquand | Robot motion planning: A distributed representation approach[END_REF], [START_REF] Lavalle | Planning algorithms[END_REF] where only binary detection is needed [START_REF] Lin | Fast contact determination in dynamic environments[END_REF], and efficient implementation are freely available [START_REF] Pan | Fcl: A general purpose library for collision and proximity queries[END_REF]. Two difficulties prevent to dynamically handle collisions at the control level. First, in control, we need to compute the distance to collision, and not only a binary collision test [START_REF] Ong | Fast versions of the gilbert-johnsonkeerthi distance algorithm: Additional results and comparisons[END_REF].

Yet it has been several times observed that the distance between two general collision objects is a non-differentiable function [START_REF] Escande | Continuous gradient proximity distance for humanoids free-collision optimized-postures[END_REF]. This is because the witness points (i.e. points on the surface of each of the two collision objects that are the closest) may jump on the surfaces even for small relative motions of the pair. Only the strict convexity of the collision geometry can guarantee smoothness properties of the distance function.

To work with the exact robot geometry, a possible approach is to split the collision volumes into a union of strictly convex objects, and consider all the collision pairs resulting from this union [START_REF] Kuffner | Self-collision detection and prevention for humanoid robots[END_REF], [START_REF] Kanehiro | A local collision avoidance method for non-strictly convex polyhedra[END_REF]. Yet the number of pairs drastically scales with the geometry complexity. In addition, control implies to compute collision distances and not only binary collision test, which is about 3 times more expensive [START_REF] Pan | Fcl: A general purpose library for collision and proximity queries[END_REF].

Another approach is to accept to approximate the collision geometries to enable better control properties or performances. A very classic and simple geometry is the so-called capsule [START_REF] Dube | A model of the humanoid body for self collision detection based on elliptical capsules[END_REF], [START_REF] Tassa | Synthesis and stabilization of complex behaviors through online trajectory optimization[END_REF], i.e. a cylinder with spherical extremities [START_REF] Lin | Collision detection between geometric models: A survey[END_REF], which is convex but not stricly convex. Capsules belong to the family of inflated volumes, that we discuss later in the paper. In [START_REF] Escande | A strictly convex hull for computing proximity distances with continuous gradients[END_REF], a strictly convex volume, composed of patches of sphere and torus, is proposed along with an algorithm to build it around a given mesh to be encapsulated, and used in control in [START_REF] Khansari-Zadeh | A dynamical system approach to realtime obstacle avoidance[END_REF] or trajectory optimization in [START_REF] Lengagne | Generation of whole-body optimal dynamic multi-contact motions[END_REF]. Simplified models of collision can also be learned offline from the robot model or directly from trajectories of the system. Various machine-learning algorithms have been used to learn to predict collision (binary query) using either support vector machine (SVM) [START_REF] Pan | Efficient configuration space construction and optimization for motion planning[END_REF], neural networks (NN) [START_REF] García | A neural network approach for real-time collision detection[END_REF], [START_REF] Heo | Collision detection for industrial collaborative robots: a deep learning approach[END_REF], Gaussian Mixture Models (GMM) [START_REF] Huh | Learning high-dimensional mixture models for fast collision detection in rapidly-exploring random trees[END_REF]. In [START_REF] Jiang | Data-driven approach to simulating realistic human joint constraints[END_REF], collision and joint limits are learned together from motion-capture recordings of a human actor.

While computing a single collision distance is faster than machine-learned approximation, especially with a simple geometry, learned representations on all collision pairs of a robot manage to also capture what are the active pairs for which the distance should be considered, hence discarding the information and computational burden related to pairs that are too far away. On the other hand, simple geometries can be made as smooth as desired, and distance derivatives are also straight forward to compute. In [START_REF] Okada | A hybrid approach to practical self collision detection system of humanoid robot[END_REF], a hybridization is proposed to take advantage of both approaches. The authors proposed to combine simple encapsulating volumes and collision tables for complex joints. Yet the hybrid model was only considered for detecting collisions.

In this paper, we extend this idea of hybrid model, to compute distances and their derivatives and build a controller preventing collisions, illustrated on the quadruped Solo [START_REF] Grimminger | An open torque-controlled modular robot architecture for legged locomotion research[END_REF]. More precisely, we propose to rely on simplified geometries to handle pairs of collisions that are far from each other on average. On the quadruped robot for example, that would correspond to segments of distinct legs. We have chosen to use capsules, for which the distance computation is minimal as quickly reported in section II. We also provide the expression of the distance derivatives which are needed for any controller. The drawback to pay for the simplicity and the derivability is some conservatism (i.e. false positive detections and a reduced workspace) which however remains negligible compared to the total range of motion. Yet this conservatism is not acceptable for pairs of bodies moving very close to one-another. On the quadruped, that would be the upper-leg to torso collision. In general, this case covers any pairs on both sides of a complex joint, like shoulder or wrist joints with a composed 2-or 3-DoF mechanism. To handle these cases, we propose to rely on a datadriven representation, trained on data easily generated from a collision-detection library. We propose in section III several representations, along with their derivatives and the method to train them. The complete self-collision model is then composed of a hybridisation between simple geometries and data-driven approximation. We empirically show in section V that our model is an appropriate approximation, detecting all true collisions and raising only a small ratio of false detections. We also show how to evaluate the model along with its derivatives at a low computational cost. It is then suitable to implement a self-collision safety controller at the lowest level. At the end of this section, experiments on the real robot Solo, presented in [START_REF] Grimminger | An open torque-controlled modular robot architecture for legged locomotion research[END_REF] and extended here in a 12-DoF version, demonstrate the interest of the approach to prevent collision, for example during fast locomotion where front and rear legs have to cross.

II. DISTANCE AND DERIVATIVES FOR INFLATED

GEOMETRIES

A. Mesh-to-capsule approximation

As a first step, relevant pairs can be approximated by simple geometries. As we want to use the collision model in our controllers, we select piece-wise smooth objects. We argue here that inflated volumes (i.e. the level set at equal given distance to a simple geometry) are a good trade-off between smoothness and lightness. For the sake of readability, the equations are described here for capsule pairs, but they can be directly extended to any other inflated volumes, e.g. sphere, swept-sphere rectangles or cubes, etc. Mathematically, the definition of a capsule, based on its generating segment S is as follows :

C = p ∈ R 3 | d(p, S) ≤ ρ (1)
The capsule geometry is thus completely characterized by its radius ρ and the length of S. Capsule parameters (placement w.r.t. the parent joint, length and radius) can be selected to fit at best the real geometry (i.e. conservatively covering the mesh and minimizing the extra volume) for example by a non-linear optimization program. For Solo, we obtained 2 sets of capsules parameters (the lower legs are thinner than the upper legs), visualized along with the robot model on Fig. 1. The resulting loss of motion range is negligible, as quantified in section V.

B. Distance

Consider two capsules C 1 , C 2 . We denote F 1 and F 2 two frames positioned at the center of the capsules with the Z-axis aligned with the capsule axis. The placement of the frames with respect to the world is computed from the joint configuration q by forward kinematics. The idea of the distance computation is then to solve for the witness points on both segments and use them to get the distance. In order to compute those points, we first compute the closest points on the lines carrying the segments, and then apply the segments constraints before solving again and get

p 1 = s 1 + ρ 1 n and p 2 = s 2 -ρ 2 n with n = s 2 -s 1 s 2 -s 1 .

C. Derivatives

The distance between the 2 capsules is the distance between the 2 witness points p 1 and p 2 . As ---→ p 1 p 2 is normal to both capsules surfaces, then the variation of the distance between the capsules also is the variation of the distance between the witness points. In the following, we denote by resp. J F 1 ,J F 2 the frame Jacobians, corresponding to the frame movements resp. F 1 and F 2 (6 × n v matrices, corresponding to translation and rotation). The Jacobian corresponding to the displacement of the first witness point p 1 is:

J p 1 = ∂p 1 ∂q = J t F 1 -p 1 × J R F 1 (2)
with J t F 1 (resp. J R F 1 ) denoting the translation (resp. rotation) part of J F 1 . We can then derive the distance gradient which reads:

J dist = ∂ ---→ p 1 p 2 ∂q = (p 1 -p 2 ) T d (J p 1 -J p 2 ) (3)
From (3), we see that the Jacobian is independent from the capsule radius. In practice, we can then directly work with the segment (i.e. the capsule of radius 0). We will see in the description of the proposed controller that we will work with a conservative threshold to activate the collision pair before the collision occurs, which happens to be equivalent to inflate the capsule radius of this threshold. We also see that the capsule distance is only piece-wise C 1 (i.e. its Jacobian is differentiable nearly everywhere), which is expected as the capsule is not strictly convex. But this is enough to produce a good controller, as shown in section V. Distance and derivatives of the capsule are directly derived from the witness points of the segments. Likewise for other inflated volumes, the distance and derivatives can be derived from the witness points returned by any collision library.

III. DATA-DRIVEN COLLISION MODEL

Let us now consider the collision pairs for which the distances are small on average, e.g. the case of the shoulder collision between the base and an upper leg. The previous approach is not suitable anymore here, because the mechanical assembly is such that the pair links are constrained to a very low distance in all configurations. No mesh approximation would be sufficient here. We thus need to define a new collision distance ensuring safe collision detection and affecting the range of motion as little as possible, while keeping good control properties. It might be considered to carefully chose another simplified geometry. We prefer however to rely on machine learning to automatically build a generic geometry representation based on data.

A. Cartesian distance between close geometries

Let us consider a given pair of robot bodies, connected by a sub-part of the kinematic tree. We denote by q R ∈ R NR the corresponding sub-part of the robot configuration q. We recognize here that the dimension of q R is typically small (NR = 2 or NR = 3 on most of the robots we considered). For Solo for example, the shoulder articulation has 2 rotations, and the knee adds 1 more in the more advanced model (see Section IV). Thus, the collision of these pairs only occurs in low-dimensions sub-spaces of the robot joint space. From there, we can use a standard collision library [START_REF] Pan | Fcl: A general purpose library for collision and proximity queries[END_REF] to sample the collision distance. Yet the result is not directly satisfactory because collision algorithms and robot models are typically not designed for the accuracy required to handle such close pairs. The result for the front left shoulder pair of Solo is shown as example in Fig. 2. The obtained distance field clearly displays the collision zone (d = 0) corresponding to the angle range along x for which the upper leg intersects with the base, and which depends on the y rotation of the leg (extension towards front or back of the body). We can notice strong discontinuities near the collision zone, and unintuitive variations in the d > 0 zone. These properties of the distance make it difficult to approximate as is or to interpret from a control point of view. The most useful data we get from this sampling is actually the shape and localization of the collision surface in joint space (i.e. the submanifold in R NR separating free space from collision space), which we now characterize further and use to define a new collision distance. Fig. 2. Example of Solo shoulder collision data subspace (x axis: q 7 , shoulder x rotation, y axis: q 8 , shoulder y rotation). Left : Cartesian distance (meters), right : binary view. We observe a large flat area around q 8 = 1.5, corresponding to a hook-shape of the complex joint, which is always close to the leg but mechanically never colliding. Cartesian distance is hence not a suitable metric in such cases.

S = {q R ∈ R NR | d(q) = 0} (4)
It seems vain to try to get a closed-form representation of S [START_REF] Lozano-Pérez | An algorithm for planning collision-free paths among polyhedral obstacles[END_REF]. We thus proposed to sample it. As S is an implicit submanifold of R NR (i.e. of measure 0), we cannot directly sample it from R NR but rather have to project random points from R NR onto S.

We do so by sampling many random pairs of configurations in free space q free and in collision space q coll . We then use dichotomy to compute the intersection of the segment [q free , q coll ] with the surface S with a given precision. This method can lead to miss some parts of the collision surface if S does not numerically contain enough points; however, the sampling of the configurations can also be chosen more carefully than at random when the shape of the collision surface is easy to interpret in 2 or 3D for example.

2) Collision distance in joint space: As the distance in Cartesian space is not satisfactory to represent the proximity of the two bodies, we propose to rather represent it by the distance in joint space of the configuration to the surface S:

d S (q) = min q S ∈S q R -q S ( 5
)
In our case, we used the standard euclidean distance : q Sq R = (q Rq S ) T (q Rq S ) We can naturally extend this definition to the collision domain, i.e. handle positive and negative distance. The complete definition of the collision distance is thus :

d S (q R ) = min q S ∈S {s coll q R -q S } (6)
with s coll (q) = 1 when q R is in free space and -1 otherwise. Note that d S is properly defined also when S is a union of manifold, as it is the case for example with Solo, as shown in Fig. 3. , ∂ds ∂q 8

)

3) Distance jacobian: The gradient of d S is quite similar to the jacobian expression of section II:

J S (q R ) = ∂d S ∂q = q R -q w d S (q R ) (7)
where q w = arg min q S ∈S q Rq S is the witness configuration.

The distance derivatives for the shoulder of Solo are represented in Fig. 4. The visible irregularities, along the line of maximal distance for example, are due to the jump of the witness configuration when q R crosses this line. Similarly to Section II, the distance field is only piecewise C 1 on each side of such configurations surfaces where the witness configuration jumps.

C. Distance approximation

We now have a properly defined collision distance d S and its derivatives, but its evaluation is inefficient at the moment. In order to use it in a real-time controller, we thus need a fastevaluated approximation of this distance. The formulation we have chosen to introduce d S directly leads to a method to sample d S in the joint space R n R , it can now be used to generate a training dataset for a data-driven approximation. We introduce three approximation models to represent d S , that will be benchmarked in Section V.

1) Fourier transform approximation: Dealing with revolute joints and their natural periodicity, a reasonable idea is to use the nD Fourier transform to approximate the distance field sampled on a grid. For example in 2D, the Fourier transform of the distance on a n × m grid is :

D(u, v) = n/2 j=-n/2 m/2 k=-m/2 d( j, k) e -2iπ(u j n + v k m ) (8)
Inverting this transform requires the evaluation of 2nm trigonometric functions. A classical approximation is thus to filter it and neglect the smallest coefficients to only evaluate the trigonometric functions for the coefficients of significant amplitude. The approximation of the derivatives of d S is also directly obtained from the same coefficients.

The main limit of this method is that for a given resolution, the number of Fourier coefficients needed to represent the distance (and thus the execution time), filtered or not, grows exponentially with the number of dimensions in the relevant subspace. Efficiency at runtime is problematic.

2) Datasets generation: For the following methods, we do not need grid-ordered data. The training datasets are generated with the method described in III-B. We also include the set S of surface configurations in the training data, because this is the zone where the distance should be best approximated. Derivatives of the distance are also part of the dataset.

3) Neural network approximation: We now present a standard multi-layer perceptron approximation. The regular shape of the distance field and the relatively low number of inputs allow for good results with a small, quickly evaluated architecture (one hidden layer). The activation function can also be chosen to optimize computational efficiency. Another advantage is the possibility to use the same inference model to obtain a simple evaluation expression for both the distance and its Jacobian. The periodicity of the distance field is accounted for by using , instead of the shoulder configuration q R , x = [cos q R , sin q R ]. The loss used during the training is the usual RMSE of the distance. Concerning architecture, we used models with a tanh activation, and a hidden layer containing 6 to 48 neurons, while still easily satisfying the real-time evaluation constraint. A Sobolev training [START_REF] Czarnecki | Sobolev training for neural networks[END_REF] was also tested, i.e. where the loss also inlcudes the error between the network derivatives and a groundtruth reference; however, the results were not included here because the method brought no significant improvement in our case.

4) Support Vector Machine: The datasets generated to train the neural network models were also used to train a SVM model. We trained it with a gaussian kernel, first as a classifier, expecting a distance representation to naturally appear. As the result was not satisfactory, we finally trained the SVM as a regressor with the same RMSE loss as the neural network. This approach is compared with the other approximations in Section V.

IV. CONTROLLER

We used the proposed hybrid model to implement a torque-based collision controller as an additional safety controller on top of the main torque-based controller driving the robot. To that end, we first quickly describe the controller, based on the classical formulation of a repulsive potential field. This simple formulation allows us to implement it as a default safety layer directly on the robot hardware. We then describe the implementation using code generation.

A. Control torque

We chose to mimic a visco-elastic spring-damper model to implement the virtual repulsive force applied along the collision normal. The amplitude of the force corresponds to:

f r (q, v q ) = 0 if d ≥ d 0 -k e (d(q) -d 0 ) -k v d(q, v q ) if d < d 0 (9)
where d 0 is the pair-dependant distance threshold under which the virtual force should be active, k e (respectively k v ) is the elastic (resp. viscous) gain characterizing the dynamics of the virtual spring, and d the time derivative of d which can be re-expressed as d(q, v q ) = J coll (q)v q . This choice for Fig. 5.

Metrics illustrated in the case of a [4, 8, 1]-architecture, tanh activation neural network. From left to right and top to bottom : ground-truth distance field, approximated distance field, absolute error field, false positives and negatives, false positives after false negatives removal, predicted distance w.r.t. ground-truth distance the amplitude of the repulsive force can lead to a discontinuous control when k v 0; however, these discontinuities are numerically small compared to the maximum amplitude produced. Finally, we have to project the computed virtual force in joint space using the collision Jacobian. The final expression of the collisions avoidance control torque for one pair is :

τ(q) = J T coll (q) f r (q, v q ) (10)
To compute the total control torque, we finally loop on all the relevant collision pairs in the model and sum the corresponding torques. The controller presented here is very simple by design choice, to allow for an implementation on the lowest-level control hardware. Our collision model could also be integrated with task-space inverse dynamics [START_REF] Righetti | Optimal distribution of contact forces with inverse-dynamics control[END_REF], [START_REF] Herzog | Balancing experiments on a torque-controlled humanoid with hierarchical inverse dynamics[END_REF], [START_REF] Del Prete | Robustness to joint-torque-tracking errors in task-space inverse dynamics[END_REF] or an optimal control solver [START_REF] Tassa | Control-limited differential dynamic programming[END_REF], [START_REF] Dai | Whole-body motion planning with centroidal dynamics and full kinematics[END_REF], [START_REF] Mastalli | Crocoddyl: An efficient and versatile framework for multi-contact optimal control[END_REF].

B. ANSI-C code generation

The computation of the control torque only requires the distance and derivatives provided by the collision model. The model itself also relies on a fast forward kinematics implementation, and an offline neural network training library, both open-source [START_REF] Carpentier | The Pinocchio C++ library -A fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives[END_REF], [START_REF] Paszke | Pytorch: An imperative style, highperformance deep learning library[END_REF]. In an effort to produce a fully-embedded module able to run on the robot hardware, we used the code generation capabilities offered by opensource libraries to re-implement the collision model, initially written in C++, as an agnostic ANSI-C library with reduced development effort. An additional step of code generation from Python to C++ is needed for the neural network model. The code will be released with the final version of the paper.

V. EXPERIMENTAL RESULTS

In order to evaluate the proposed model and its efficiency to control the robot, we first adapt the data-driven model for conservatism. Then, we measure the quality of the approximation, and score the efficiency of its evaluation. Finally, we report the behavior of the controller on the real Solo. Fig. 6. Same metrics as in figure 5 for a gaussian kernel SVM with 181 support vectors. We observe a high numerical sensitivity around the collision surface.

A. Joint-space approximation benchmark

We want to compare the shoulder approximation methods on a common basis to chose the best one. First, we want to adjust the parameters of each approximation model to make them conservative, i.e. ensure no false negatives in terms of collision detection. We do so by defining a modified collision distance dS so that dS (q) = d S (q)d 0 . This is equivalent to shifting the collision surface along its local normal direction. The distance offset d 0 can be chosen for each learning model to minimize the number of false positives while forbidding false negatives. After training, the different methods are evaluated with the following metrics :

• False positives : after removing the false negatives, the false positives, for a homogeneous dataset sampling, are a very good proxy for the loss of range of motion due to the approximation. This metric reflects the quality of the boolean collision detection. • RMSE : loss used for neural network training, which reflects the relative quality of the collision distance approximation in the whole space • Execution time Graphical representations of those metrics in the case of the Solo shoulder in 2D are shown for the NN on Fig. 5 and for the SVM on Fig. 6. From the more extensive results presented in Table I, we can conclude that the trade-off between approximation quality and fast evaluation is best handled by the neural network approach, which will be implemented in our final controller. We also validated the model by approximating the geometry of the shoulder (3D) of a Talos humanoid robot [START_REF] Stasse | TALOS: A new humanoid research platform targeted for industrial applications[END_REF]. Due to lack of space, only partial results are reported in Fig. 7.

B. Solo experiments

We present the experiments conducted with the controller integrated in the robot control loop on the Solo platform. The parameters of the collision avoidance control torque chosen for the experimental setup are k e = 60 N.m -1 , k v = 0 N.m -1 .s -1 and d 0 = 0.05 m. The video attached shows the live experiments on the robot along with the collision data visualized in a virtual environment. The results are summarized in the video https://peertube.laas.fr/videos/watch/ b6e911ee-728f-4337-a76e-8138a332b583.

In order to better demonstrate the capability of our controller as a safety feature for additional control strategies, we first run it as the only active controller and manipulate the legs manually with the robot on a stand (motion 1 of the video). This also allows us to reach configurations for which we know the collision detection can be more difficult and easily test the limits of the controller. We then use a PD tracking a reference trajectory which contains colliding configurations. The reference trajectory for the PDtracking is an ellipse described by the robot feet in the (x, y) Cartesian plane. To test the capsule model case, we set the two front feet to follow such intersecting ellipses (motion 2 of the video). For the shoulder, we can force a collision by setting the ellipse plane close to the body plane for one foot (motion 3 of the video). The reference trajectories in Cartesian space and the experimental trajectories with active collision avoidance are shown in Fig. 8. We also show an example of distance threshold violation and corresponding repulsive torques for the capsule model in Fig. 9.

CONCLUSION

We presented a hybrid self collision model capable of estimating complex-joint limits and body-to-body collisions of a rigid multi-body articulated robot in real time. The proposed method is able to handle collisions of bodies which are naturally distant from one another as well as collisions between links forming hook-shaped joints. Our approach is based both on Cartesian distances between conservative inflated-volume approximations of body geometries and joint-space distances of complex joints via data-driven neural networks. The smooth evaluation of collision distances and their derivatives allow us to use them in a collision avoidance control algorithm while marginally reducing the robot workspace. Those quantities are of major importance for highlevel controllers but can also be a crucial information for last-resort safety controllers. We proposed a simple collision avoidance controller which applies a visco-elastic repulsive force, moving away the robot links from imminent collision. Using automatic code generation, our hybrid collision model can be embedded on limited low-level robot controller hardware. We demonstrated and evaluated the safety controller capabilities on the quadruped platform Solo.

While this model can already serve as a low-level safety controller preserving the robot hardware from a destructive high-level control output, we would like to use it in higherlevel controller such as whole-body controllers, and model predictive controllers to better enforce feasibility of the computed motions.

Fig. 1 .

 1 Fig. 1. Capsules notations (left) and approximations for Solo legs meshes (right) : the quadruped legs are properly approximated by capsules

Fig. 3 .

 3 Fig. 3. Left: Shoulder collision distance d S after redefinition as minimal euclidean distance in 2D joint-space. Right: Taking the knee joint into account adds a third dimension to the distance field

Fig. 4 .

 4 Fig. 4. x and y shoulder rotations components of the collision distance derivatives for Solo shoulder (i.e. ∂ds ∂q 7

Fig. 7 .

 7 Fig. 7. Left : Joint-space distance (negative part masked) for the Talos shoulder joint. The free configurations outside the main free zone correspond to mechanically forbidden configurations with the shoulder contained inside the torso. Right : (top) neural network appoximation of the distance field and (bottom) corresponding distance predictions w.r.t groundtruth distances.

Fig. 8 .

 8 Fig. 8. Reference trajectory tracking with active collision avoidance : the dashed line represents the reference trajectory, and the full line is the experimental result on Solo for (left) a capsule pair collision i.e. motion 2 of the video, (right) a shoulder collision i.e. motion 3 of the video.

Fig. 9 .

 9 Fig. 9. (Top) Distance threshold violation and (bottom) avoidance torque for a capsule collision (motion 2 of the video).

This work has been supported by the MEMMO European Union project within the H2020 Program under Grant Agreement No. 780684.

Companion video available at https://peertube.laas.fr/ videos/watch/b6e911ee-728f-4337-a76e-8138a332b583


Denise Paulin

Yeranuhi Hovannisyan

Serdar Kasakyan

Onnik Agbulut

Dr Zhenlin Li
email: zhenlin.li@sorbonne-universite.fr

Zhigang Xue

Synemin-related skeletal and cardiac myopathies: an overview of pathogenic variants

Keywords: Intermediate Filament, Cytoskeleton, Desmuslin, Desmin, polymorphism, genetic variant

Introduction

Intermediate filament (IF) proteins are constituents of the cytoskeleton encoded by a dispersed multigene family of up to 70 genes. IFs are formed by nonglobular flexible protein units, which consist mostly of α-helices. IF protein structure comprises a central α-helical rod domain as its main part, flanked to a variable head and tail parts. IF proteins are chemically heterogeneous, have different rates of assembly and produce discrete types of filaments [START_REF] Herrmann | Intermediate filaments: molecular structure, assembly mechanism, and integration into functionally distinct intracellular Scaffolds[END_REF].

In most vertebrate cells, cytoplasmic IFs are tethered to the nucleus. They extend into the cytoplasm providing a scaffold for mitochondria, the Golgi complex, microtubule organizing centers and other cytoskeletal elements [START_REF] Godsel | Intermediate filament assembly: dynamics to disease[END_REF]. In the periphery, IFs associate with the plasma membrane. The resulting network integrates and organizes the cytoplasm providing mechanical integrity, which is essential to tissue function. This process has been highlighted in more than 75 human genetic diseases. They are the result of deficiencies in this network resulting in skin fragility and epidermolytic disorders, laminopathies, myopathies, cardiomyopathies, neuropathies, cataracts and premature aging (Human Intermediate Filament Mutation Database, http://www.interfil.org).

SYNM is a new candidate gene which shows numerous sequence polymorphisms. However, few data have been available from pathologists with regards to synemin. Synemin is considered as IF associated protein (IFAPs) [START_REF] Green | Intermediate filament associated proteins[END_REF]. In this respect, synemin is associated with multiple partners such as desmin, vimentin, keratins, glial fibrillary acidic protein (GFAP), neurofilaments and is present in muscle cells, in a few neural cells and in various other nonepithelial cell types. Accordingly, it can be responsible for human diseases of unknown etiology. Data are summarized here concerning patients with cardiomyopathy or skeletal myopathy in whom a variation in the SYNM gene exists. Moreover, in silico modeling of helical salt-bridges between residues is presented, allowing for the evaluation of the impact of synemin networks, which are crucial to interactions with cytoskeletal proteins.

Gene expression

In humans, SYNM, also known as desmuslin (DMN), was localized to chromosome 15q26.3 by electronic screening of the human DNA sequence database and using the GB4 radiation hybrid panel [START_REF] Mizuno | Desmuslin, an intermediate filament protein that interacts with alpha -dystrobrevin and desmin[END_REF]. It was located in a 4-cM interval flanked by the microsatellite markers D15S212 and D15S642, and close to D15S120 [START_REF] Titeux | Human synemin gene generates splice variants encoding two distinct intermediate filament proteins[END_REF], (GRCh38:chr15:99098217-99135593).

Synemin was first identified as a high-molecular-mass protein associated with desmin and vimentin filaments in chicken muscles [START_REF] Granger | Synemin: a new high molecular weight protein associated with desmin and vimentin filaments in muscle[END_REF]. Synemin expression was later detected in different tissues, including the nervous system, endothelial cells, retinal cells and hepatic stellate cells (18-20, 41, 47, 50, 53). The SYNM gene encodes three isoforms in mice and humans via an alternative splicing mechanism giving rise to three isoforms: high (H) or α (170 kDa), middle (M) or ß (140 kDa), and low (L) (41 kDa) synemin with the same head and rod domains but differing in the tail domain of the protein (see Figure 1) [START_REF] Mizuno | Desmuslin, an intermediate filament protein that interacts with alpha -dystrobrevin and desmin[END_REF][START_REF] Titeux | Human synemin gene generates splice variants encoding two distinct intermediate filament proteins[END_REF][START_REF] Xue | The mouse synemin gene encodes three intermediate filament proteins generated by alternative exon usage and different open reading frames[END_REF]. SYNM expression is regulated in an isoform specific manner during the development and regeneration of different tissues.

During mouse embryo development, synemin M was present as early as in 5-day-old embryo (E5) of mice with vimentin and nestin. Synemin H was found later at E9 in the nervous system and mesodermic derivatives concomitantly with angiogenesis and the migration of neural crest cells. Synemin L appeared later in neurons at E15 [START_REF] Izmiryan | Synemin isoforms in astroglial and neuronal cells from human central nervous system[END_REF]. Moreover, de Souza Martins et al. demonstrated that synemin M is expressed in mouse pluripotent embryonic stem cells while synemin H was produced only in neural precursors when neural differentiation began, concurrently with synemin M, nestin and glial fibrillary acidic protein (GFAP) [START_REF] De Souza Martins | Dynamic expression of synemin isoforms in mouse embryonic stem cells and neural derivatives[END_REF]. The expression of synemin H and M was reported in multipotent neural stem cells, particularly in the subventricular zone of the lateral ventricle of the adult brain; a neurogenic germinal niche of mice [START_REF] Izmiryan | Different expression of synemin isoforms in glia and neurons during nervous system development[END_REF].

The expression of synemin has also been demonstrated in skeletal muscle satellite cells [START_REF] Li | Synemin acts as a regulator of signalling molecules during skeletal muscle hypertrophy[END_REF].

Synemin M was present in all types of smooth muscles (blood vessels, bladder, and stomach) whereas synemin H and L were detected solely in the bladder [START_REF] Xue | The mouse synemin gene encodes three intermediate filament proteins generated by alternative exon usage and different open reading frames[END_REF]. Furthermore, a study identified synemin as a novel serum response factor (SRF)-independent target of myocardin that is abundantly expressed in all smooth muscle cells [START_REF] Swärd | Identification of the intermediate filament protein synemin/SYNM as a target of myocardin family coactivators[END_REF]. In striated muscles, the predominant synemin isoforms was M but all three synemin isoforms were produced by an alternative splicing of the synemin pre-mRNA and their expression was regulated in a developmentally specific manner [START_REF] Xue | The mouse synemin gene encodes three intermediate filament proteins generated by alternative exon usage and different open reading frames[END_REF]. The temporal distributions of the three synemin isoforms in striated muscles were distinct. The H/M isoforms were detected in the epaxial muscles (myotomes) and the heart as early as E10 in mice, and they persisted throughout all embryo stages and in the adult. In contrast, the L isoform was found only in a subset of adult muscles [START_REF] Xue | The mouse synemin gene encodes three intermediate filament proteins generated by alternative exon usage and different open reading frames[END_REF]. These differences probably reflect differing functions of the synemin isoforms during development.

Synemin interactions with other proteins

Synemin consists of a short head domain, a missing conserved TALL sequence in the 2A subdomain that is characteristic of all IFs, and the TYRKLLEGEE motif in the 2B subdomain that differs from all other IFs [START_REF] Khanamiryan | Self-assembly incompetence of synemin is related to the property of its head and rod domains[END_REF]. In this respect, synemin is associated with multiple partners such as desmin, vimentin, keratins, GFAP, neurofilaments to form the filament in different tissues. Synemin co-assembles with desmin and vimentin to become heteropolymers in striated and smooth muscle tissues [START_REF] Xue | The mouse synemin gene encodes three intermediate filament proteins generated by alternative exon usage and different open reading frames[END_REF]. It interconnects Z-discs to costamere in skeletal muscle [START_REF] Bellin | Synemin may function to directly link muscle cell intermediate filaments to both myofibrillar Z-lines and costameres[END_REF] and to desmosomes in the heart [START_REF] Lund | Synemin isoforms differentially organize cell junctions and desmin filaments in neonatal cardiomyocytes[END_REF] as well as participates in mitochondria positioning, a process that probably involves plectin [START_REF] Konieczny | Myofiber integrity depends on desmin network targeting to Z-disks and costameres via distinct plectin isoforms[END_REF]. The synemin protein interacts with and is closely related to desmin [START_REF] Paulin | Desminopathies in muscle disease[END_REF]; a protein encoded by a locus mutated in some forms of hereditary distal myopathy [START_REF] Mizuno | Genomic organization and single-nucleotide polymorphism map of desmuslin, a novel intermediate filament protein on chromosome 15q26.3[END_REF]. In myopathies caused by desmin mutation, synemin is associated with cytoplasmic desmin aggregates in skeletal muscles [START_REF] Capetanaki | Desmin related disease: a matter of cell survival failure[END_REF][START_REF] Carlsson | Cytoskeletal derangements in hereditary myopathy with a desmin L345P mutation[END_REF][START_REF] Chourbagi | Desmin mutations in the terminal consensus motif prevent synemin-desmin heteropolymer filament assembly[END_REF][START_REF] Olivé | Expression of the intermediate filament protein synemin in myofibrillar myopathies and other muscle diseases[END_REF][START_REF] Paulin | Desminopathies in muscle disease[END_REF][START_REF] Titeux | Human synemin gene generates splice variants encoding two distinct intermediate filament proteins[END_REF].

Interestingly, in desmin mutations located into the highly conserved amino acid motif of helix 2B (E401K, R406W, E413K), synemin is excluded from desmin containing aggregates [START_REF] Chourbagi | Desmin mutations in the terminal consensus motif prevent synemin-desmin heteropolymer filament assembly[END_REF]. In this study, using in silico constructs the authors demonstrated that such behavior with these mutants was correlated to the abnormal salt-bridges of desmin-dimer which prevent longitudinal annealing and/or radial compaction during desmin filament formation. This perturbs synemin-desmin heteropolymer filament assembly [START_REF] Chourbagi | Desmin mutations in the terminal consensus motif prevent synemin-desmin heteropolymer filament assembly[END_REF]. Co-transfection and immunolabeling experiments indicate that both synemin H and M isoforms are incorporated to desmin to form heteropolymeric IFs. Furthermore, using desmin-and vimentin-deficient mice whose synemin was unstable and delocalized in cells, there is direct evidence of association with desmin or vimentin in skeletal and smooth muscles [START_REF] Carlsson | Differences in the distribution of synemin, paranemin, and plectin in skeletal muscles of wild-type and desmin knock-out mice[END_REF][START_REF] Izmiryan | Different expression of synemin isoforms in glia and neurons during nervous system development[END_REF][START_REF] Jing | Synemin is expressed in reactive astrocytes in neurotrauma and interacts differentially with vimentin and GFAP intermediate filament networks[END_REF][START_REF] Xue | The mouse synemin gene encodes three intermediate filament proteins generated by alternative exon usage and different open reading frames[END_REF]. Synemin also interacts with plectin, zyxin, α-actinin, dystrophin, utrophin, α-dystrobrevin, vinculin and metavinculin, which highlights its role as a bridging protein [START_REF] Bellin | Molecular characteristics and interactions of the intermediate filament protein synemin. Interactions with alpha-actinin may anchor synemin-containing heterofilaments[END_REF][START_REF] Bhosle | Interactions of intermediate filament protein synemin with dystrophin and utrophin[END_REF][START_REF] Hijikata | Plectin 1 links intermediate filaments to costameric sarcolemma through beta-synemin, alpha-dystrobrevin and actin[END_REF][START_REF] Jing | Intermediate filament protein synemin is present in human reactive and malignant astrocytes and associates with ruffled membranes in astrocytoma cells[END_REF][START_REF] Konieczny | Myofiber integrity depends on desmin network targeting to Z-disks and costameres via distinct plectin isoforms[END_REF][START_REF] Mizuno | Desmuslin, an intermediate filament protein that interacts with alpha -dystrobrevin and desmin[END_REF][START_REF] Paul | Synemin: Molecular Features and the Use of Proximity Ligation Assay to Study Its Interactions[END_REF][START_REF] Sun | Human alpha-synemin interacts directly with vinculin and metavinculin[END_REF][START_REF] Sun | Synemin interacts with the LIM domain protein zyxin and is essential for cell adhesion and migration[END_REF] (see Figure 2). Phosphorylation of IF proteins in serine and threonine residues causes rearrangements and interactions with other cellular proteins [START_REF] Clemen | Desminopathies: pathology and mechanisms[END_REF][START_REF] Tsikitis | Intermediate filaments in cardiomyopathy[END_REF][START_REF] Winter | Posttranslational modifications of desmin and their implication in biological processes and pathologies[END_REF]. It has been demonstrated that synemin is an A-kinase-anchoring protein (AKAP) (40) that anchors protein kinase A (PKA) and modulates the PKA-dependent phosphorylation of several cytoskeletal substrates such as desmin and as such, may influence muscle growth and repair by regulating the phosphorylation of proteins of the Z-disks and sarcolemma [START_REF] García-Pelagio | Myopathic changes in murine skeletal muscle lacking synemin[END_REF][START_REF] Li | Synemin acts as a regulator of signalling molecules during skeletal muscle hypertrophy[END_REF]. In addition, synemin also interacts with Akt (36); a kinase important for the normal growth of fast twitch muscles.

These observations collectively reinforce the idea that synemin has dual functions acting both as a bridging cytoskeletal protein and as a regulator of signal transduction pathways.

Loss of synemin in mice leads to cardiac and skeletal myopathies

Two independent synemin deficient mice were generated using homologous recombination method, one of them using the Cre-loxP mediated system to remove exon 1 [START_REF] Li | Synemin acts as a regulator of signalling molecules during skeletal muscle hypertrophy[END_REF], the second model was a constitutive knocked-out (KO) by removing all exons [START_REF] García-Pelagio | Myopathic changes in murine skeletal muscle lacking synemin[END_REF]. The KO mice are viable, fertile and were born at expected Mendelian ratio. Synemin is not required for embryonic development, myogenesis or for the development of the cardiovascular system [START_REF] Li | Synemin acts as a regulator of signalling molecules during skeletal muscle hypertrophy[END_REF]. No anatomic and behavioral defects were observed at birth. However, mice lacking synemin developed a myopathic phenotype, possibly due to its role in linking desmin filaments to costameres and sarcomeres [START_REF] García-Pelagio | Myopathic changes in murine skeletal muscle lacking synemin[END_REF][START_REF] Li | Synemin acts as a regulator of signalling molecules during skeletal muscle hypertrophy[END_REF] and presented a reduced bone mass which underlines that synemin plays also a role in bone homeostasis [START_REF] Moorer | Deficiency of the intermediate filament synemin reduces bone mass in vivo[END_REF][START_REF] Skalli | The cytoskeleton meets the skeleton. Focus on "Deficiency of the intermediate filament synemin reduces bone mass in vivo[END_REF]. In muscle, synemin inactivation leads to a decrease in maximal force, fatigue resistance and alteration of membrane integrity associated with an occurrence of focal muscle degeneration and regeneration. Synemin may play this role through its demonstrated binding to costameric and sarcolemmal proteins, such as α-actinin, vinculin [START_REF] Bellin | Synemin may function to directly link muscle cell intermediate filaments to both myofibrillar Z-lines and costameres[END_REF][START_REF] Sun | Human alpha-synemin interacts directly with vinculin and metavinculin[END_REF] and members of the dystroglycan complex [START_REF] Mizuno | Desmuslin, an intermediate filament protein that interacts with alpha -dystrobrevin and desmin[END_REF]. In desmin KO mice, synemin no longer associates with Z-discs but remains present in myotendinous and neuromuscular junctions, suggesting that synemin association with junctional complexes, but not with Z-discs, is desmin-independent [START_REF] Carlsson | Differences in the distribution of synemin, paranemin, and plectin in skeletal muscles of wild-type and desmin knock-out mice[END_REF]. This phenomenon could be due to differential synemin isoform distribution since synemin H preferentially localizes in cell-cell junctions while synemin M predominates in Z-discs [START_REF] Lund | Synemin isoforms differentially organize cell junctions and desmin filaments in neonatal cardiomyocytes[END_REF]. Moreover, synemin H localizes to the M-band of the sarcomere through interaction with the M10 region of titin [START_REF] Prudner | α-Synemin localizes to the M-band of the sarcomere through interaction with the M10 region of titin[END_REF]. Synemin also affects the behavior of satellite cells. The balance between selfrenewal and differentiation of muscle satellite cells might be compromised in KO mice [START_REF] Li | Synemin acts as a regulator of signalling molecules during skeletal muscle hypertrophy[END_REF].

The authors suggested that synemin might influence satellite cell behavior through its role in the regulation of PKA activity, which is important for myogenesis.

Loss of synemin also leads to cardiomyopathy. As described by Garcia-Pelagio et al. [START_REF] García-Pelagio | Absence of synemin in mice causes structural and functional abnormalities in heart[END_REF], the genetic silencing of synemin in mice causes left ventricular systolic dysfunction as early as the age of 3 months old. Although contractile and costameric proteins remained unchanged in the old synemin KO hearts, some alterations were identified in several signaling proteins (PKA-RII, ERK and p70S6K) critical to cardiomyocyte function. The mice also present a left ventricular hypertrophy and eventual dilation over time. Alterations in calcium handling indicate that abnormalities originate specifically from cardiomyocytes and not from other cardiac cells [START_REF] García-Pelagio | Absence of synemin in mice causes structural and functional abnormalities in heart[END_REF].

Synemin-related disorders

Synemin has also been linked to human diseases including heart disease, cancer, and neurodegenerative disorders [START_REF] Jing | Intermediate filament protein synemin is present in human reactive and malignant astrocytes and associates with ruffled membranes in astrocytoma cells[END_REF][START_REF] Kapoor | Synemin: an evolving role in tumor growth and progression[END_REF][START_REF] Noetzel | Intermediate filament dynamics and breast cancer: aberrant promoter methylation of the Synemin gene is associated with early tumor relapse[END_REF][START_REF] Pekny | Synemin is expressed in reactive astrocytes and Rosenthal fibers in Alexander disease[END_REF][START_REF] Poot | Variable behavioural phenotypes of patients with monosomies of 15q26 and a review of 16 cases[END_REF]. Its expression is upregulated in pathological conditions such as neurotrauma, Alexandre disease and myofibrillar myopathies [START_REF] Clemen | The toxic effect of R350P mutant desmin in striated muscle of man and mouse[END_REF][START_REF] Pekny | Synemin is expressed in reactive astrocytes and Rosenthal fibers in Alexander disease[END_REF]. The complete sequence of the human SYNM gene was reported by Titeux et al. and Mizuno et al. in 2001 (29, 48). As a result of their studies, analyses were performed based on the full transcript of the SYNM gene (transcript ID: ENST00000336292) in an effort to list all protein changing variations (missense, frameshifts, nonsense). The Human Gene Mutation Database and Clin Var database report the disease-causing mutations over the SYNM gene (see Table 1).

In this review, we analyzed the data concerning seven cases with skeletal myopathy or cardiomyopathy associated with a variation in SYNM: Variant c.173C>T (p.A58V) (56); 2).

Synemin variants leading to skeletal myopathy: First, Mizuno et al. [START_REF] Mizuno | Genomic organization and single-nucleotide polymorphism map of desmuslin, a novel intermediate filament protein on chromosome 15q26.3[END_REF] suggested that synemin could be a new candidate gene for myopathies. In that study, SYNM was screened for mutations in 71 patients with various forms of myopathy for which a genetic cause could not be identified. The authors reported 9 single-nucleotide polymorphisms (SNPs) in SYNM that do not change the amino acid sequence and 12 SNPs that do. Nine silent SNPs, which did not modify the amino acid sequence, were also identified in the patient population. Among twelve modifier SNPs, 10 SNPs are common but the remaining 2 are rare. One of these rare SNPs creates a premature stop codon in the first exon of SYNM and was present in a patient with nemaline myopathy (NCBI36/Ensembl54: chr15:97463527, exon 1, c.598C>T, p.Q200*, non-conservative). This SNP was detected in the unaffected father of the patient. Neither the mother nor any of the other patients were carriers of this genetic variation. This variant is currently cataloged in gnomAD_v2.1.1 database (rs5030689) as a rare stop-gain variant presenting in 1/14494 African, 3/24992 Latino, 68/8400 Ashkenazi Jewish, 39/63602 European (non-Finnish), 5/5074 Other origins of alleles. PolyPhen2 and SIFT prediction analysis did not yield any predictions. Mutation Taster predicted this variant as being "disease causing". features a simple and reliable protocol for mutation screening in 25 known and putative candidate genes for familial cardiomyopathy by heteroduplex analysis [START_REF] Zeller | Large-scale mutation screening in patients with dilated or hypertrophic cardiomyopathy: a pilot study using DGGE[END_REF]. Among the screened families, one family carried a synemin mutation. Two simultaneous missense mutations were identified in the patient suffering from dilated cardiomyopathy, one in SYNM (c.2356G>A, p.V746M) and the other in the VEGF receptor 1 (FLT1) (c.411G>C, p.R54S) gene. Both mutations were also found in the patient's mother and daughter. The daughter showed a borderline left ventricular ejection fraction with a normal left ventricular dimension and was clinically asymptomatic. The mother had regular echocardiographic findings and was also asymptomatic [START_REF] Zeller | Large-scale mutation screening in patients with dilated or hypertrophic cardiomyopathy: a pilot study using DGGE[END_REF]. This variant is currently cataloged in gnomAD_v2.1.1 database as a rare missense variant (rs142594053). This variant has an overall minor allele frequency (MAF) of 0.0010476, meaning it is still a rare variant (gnomAD allele frequency <0,5%). It has been reported that this mutation of SYNM and FLT1 is involved in the VEGF-PLC gamma 1 signaling pathway that controls cardiac contractility in the embryonic heart [START_REF] Rottbauer | VEGF-PLCgamma1 pathway controls cardiac contractility in the embryonic heart[END_REF]. Disturbance of both mechanical integrity and calcium homeostasis of the cardiomyocyte is known to cause cardiomyopathy.

Synemin variants leading to cardiomyopathies:

In 2016, two variants of synemin were reported in dilated cardiomyopathy patients (c.2456_2457delAG, p.E819fs; c.4555C>T, p.Q1519*) by Ware et al. (51). This study shows the identification of 26 distinct rare heterozygous truncating variants in eight genes. Of the 26 truncated variants, 2 SYNM variants were identified; one being a missense mutation that creates a premature stop codon (c.4555C>T, p.Q1519*) and the second being a frameshift mutation (c.2456_2457delAG, p.E819fs). Mutation Taster predicted the variant c.4555C>T (p.Q1519*) as being "disease causing": it results in the loss of protein tail interacting with Dystrophin (DMD) and Utrophin (UTRN).

Based on its tissue-specific expression profiles and the available data on KO mice phenotypes, Zlotina et al [START_REF] Zlotina | Rare Case of Ulnar-Mammary-Like Syndrome With Left Ventricular Tachycardia and Lack of TBX3 Mutation[END_REF] suggested SYNM as a candidate gene contributing to the Ulnar-mammary syndrome-like phenotype, a group of rare congenital conditions that combine cardiac pathology (structural defect or arrhythmic disorder) and limb abnormality. Employing wholeexome sequencing and bioinformatics strategies, a novel heterozygous missense variant in SYNM was identified (GRCh37/hg19: chr15:99645578, exon 1, c.173C>T, p.A58V, conservative) [START_REF] Zlotina | Rare Case of Ulnar-Mammary-Like Syndrome With Left Ventricular Tachycardia and Lack of TBX3 Mutation[END_REF]. Further comprehensive functional studies are required to evaluate possible involvement of SYNM in genesis of complex heart-limb pathology. That variant is currently cataloged in the gnomAD_v2.1.1 database as a rare missense variant presented only in one allele of African origin among 3938 African alleles (1/3938). No accounts of the same variation have been found in other populations studied and accepted into the gnomAD database to date. That variant, having no "rs" accession number assigned yet, presents a minor allele frequency (MAF) of 0.00000811. When analyzed as a single event, PolyPhen-2 and SIFT prediction algorithm analyses qualified this variant as "benign/neutral", respectively.

Mutation Taster predicted the variant as being "polymorphism".

The study of Zhang and al. (55) concerns the investigation of a Chinese family of three generations in which four patients had dilated cardiomyopathy. Employing whole-exome sequencing and bioinformatics strategies, a novel heterozygous missense mutation of SYNM gene was identified (GRCh37/hg19: chr15:99670180, exon 4, c.1612T>C; p.W538R) and cosegregated in the affected family members [START_REF] Zhang | A novel heterozygous variant p.(Trp538Arg) of SYNM is identified by whole-exome sequencing in a Chinese family with dilated cardiomyopathy[END_REF]. The heterozygous variant was detected in all living patients in this family and all family members carrying the wild-type genotype were healthy. The missense mutation resulting in a substitution of tryptophan by arginine is located in the C-terminal domain of synemin, known as the region close to the encoding AKAP site of synemin which could be crucial for kinase activity. Cross-species alignment analysis of synemin amino acid sequences revealed that this mutated site was highly conserved in mammals, which suggests that the modification of tryptophan at position 538 may affect the structure of synemin. As we demonstrated in Figure 3 using in silico modeling, this missense mutation may cause structural changes in the synemin protein (see Figure 3). This variant is currently cataloged in gnomAD_v2.1.1 database as a rare missense variant (rs551837344) presenting in 8/17520 alleles of East Asian origin and 4/110162 alleles of European (non-Finnish) origin. This variant has a minor allele frequency -10-(MAF) of 0.0000491. (see table 1: in PolyPhen2, probably damaging; in SIFT, deleterious; in Mutation Taster, disease causing).

In silico modeling the structure of synemin protein and characterization of synemin variants

It has been known for several years that all IFs are α-helix type fibrous proteins; that is, they contain coiled-coil helices [START_REF] Steinert | Ten-nanometer filaments of hamster BHK-21 cells and epidermal keratin filaments have similar structures[END_REF]. An amino acid sequence of the rod domain can assume this structure. It contains a succession of seven residue peptides (heptads) (a-b-c-d-e-f-g), where a and d are usually apolar residues, and are normally buried inside the protein core [START_REF] Herrmann | Intermediate filaments: molecular structure, assembly mechanism, and integration into functionally distinct intracellular Scaffolds[END_REF]. Four segments, widely referred to as 1A, 1B, 2A, and 2B, are separated by linkers. Linker L1 connects 1A to 1B; linker L2 joins 2A to 2B. These are interspersed by short linkers that cannot form a coiled-coil sequence of the form (hydrophilic-apolar). Linker L12 joins the segments 1 and 2 [START_REF] Herrmann | Intermediate filaments: molecular structure, assembly mechanism, and integration into functionally distinct intracellular Scaffolds[END_REF].

Table 1 describes the different types of changes (conservative, missense, or stop) for 24 SYNM variant. Among them, 9 variants lead to conservative amino acids, 12 missense amino acids, 2 premature stops, and one is a deletion. Moreover, Table 1 and Figure 2 report the position of the amino acid variants with potential pathogenicity. Variants A58V, Q200*, A272V related to cardiomyopathy or skeletal myopathy are located in the rod domain, characterized by interactions with desmin, vimentin, vinculin, α-dystrobrevin, dystrophin and utrophin. Variant W538R is found near the region 556 to 707 with α-helices described by Russell et al. (40) while also potentially being anchored to PKA. The missense variant V746M is located in the tail region of the M and H synemin but not of the L synemin, which is shorter. The tail region from 909 to 1564, which is known to interact with zyxin, talin, vinculin, α-actinin and dystrophin, includes the variant Q1519* that causes the integration of a premature stop codon.

Helical Wheel analyses performed by Khanamiryan et al [START_REF] Khanamiryan | Self-assembly incompetence of synemin is related to the property of its head and rod domains[END_REF] as well as by Russell et al [START_REF] Russell | The intermediate filament protein, synemin, is an AKAP in the heart[END_REF] show that certain regions of synemin could form an amphipathic structure. The software Helical Wheel Custom Images and Interactive Java Applet software were used to search for potential α-helices within the synemin protein and for modifications of amino acid interactions between the variants. It can be hypothesized that mutations leading to a change of charge, distance and interactions between the amino acids of the helix are deleterious and modify an association with their partners. In order to support our hypothesis, the interactions between amino-acid residues were examined using in silico modeling. The modeling of mutated synemin for missense residue 538 shows that the replacement of a tryptophan neutral apolar hydrophobic residue by a positive hydrophilic arginine residue causes the loss of the hydrophobic interaction between residue 538 and residue leucine 541 (W--L--L vs R L--L) (Table 2, Figure 3A). For missense mutation V746M, a nonpolar hydrophobic residue valine changed to a nonpolar hydrophobic residue methionine does not change the interaction. However, although variant 272 is a conservative mutation, the change of a nonpolar hydrophobic residue alanine residue with a nonpolar hydrophobic residue valine creates a new interaction between residue 272 valine and residue 276 leucine: (I--L A vs I--L--V) (Table 2, Figure 3B). By contrast, for the conservative mutation of A58V, a nonpolar hydrophobic residue alanine to a nonpolar hydrophobic residue valine does not modify the interactions (Table 2, Figure 3B). It is evident that the change of hydrophobic interaction between amino acids in the helix depends not only on the characteristic of the mutant residue, but also on the property of its partner residue.

Concluding remarks: Pathogenic mutations or uncertain significant variants?

To date, among the variants described of the SYNM gene, 7 could be associated in human to a cardiomyopathy or a skeletal myopathy. Data on synemin KO mice suggest that synemin plays an important role in skeletal muscle and in the heart. Synemin is thought to mechanically stabilize the cardiomyocyte by linking the extracellular matrix to the Z-disc.

Synemin interacts with type III IFs desmin and vimentin, through the head and rod domain, and interacts with membrane proteins through its long C-terminal tail. Furthermore, through its interaction with cytoskeletal proteins dystrophin, utrophin and vinculin, synemin is able to link those heteropolymers to adherent-type junctions within striated muscle cells, suggesting that it plays an important role in the component assembly of the cytoskeleton and in morphogenesis. In addition, we emphasize that in silico modeling of the helical salt-bridge between residues could evaluate the impact of synemin on network organization or integration into desmin filaments and be crucial to its interaction with cytoskeletal proteins. Two mutations in position 272 or in position 538, corresponding to patients with respectively myopathy or cardiomyopathy, showed a change in neighbor amino acid interactions. The position 538 near the encoding AKAP site of synemin could be crucial for kinase activity and synemin-desmin heteropolymer filament assembly. Taken together, all data support a role for synemin in the integrity of the intermediate filaments.

In this review, we summarized several studies indicate that a single mutant allele of SYNM may cause disease as an autosomal dominant manner. In spite of the amount of accumulated animal model research data and the information directly provided by medical genetic diagnostic studies on human samples, we cannot correlate all SYNM variants related to cardiomyopathy or skeletal myopathies. Like other rare variants, they may contribute to the penetrance of potentially pathogenic structural or nucleotide variants of the genome, leading to disease. Given that current state of exome data lacks the gene network analysis for polymorphisms in myopathies, we propose a careful anlaysis and interpretation of additional variants in SYNM and other related genes to be considered when evaluating a phenotype, both in research and clinical context. Many studies including animal models, in vitro cell culture assay, as well as in silico modeling of helical salt-bridges should be performed in order to validate the clinical significance of SYNM variants.

  variant c.598C>T (p.Q200*) (28); variant c.815C˃T (p.A272V) (28); variant c.1612T>C (p.W538R) (55); variant c.2356G>A (p.V746M) (54); variant c.2456_2457delAG (p.E819fs) (51); variant c.4555C>T (p.Q1519*) (51) (see Table

  In 2006, Zeller et al. (54) reported the first SYNM mutation (c.2356G>A, p.V746M) associated with dilated cardiomyopathy. Zeller et al.

Figure 1 .

 1 Figure 1. Schematic representation of the human synemin gene (SYNM) and protein isoforms (SYNM). (A) Organization of synemin gene. The SYNM encodes three RNA corresponding respectively to M (exons 1-2-3-4-5), H (exons 1-2-3-4a) and L (exons 1-2-3-5) through an alternative splicing mechanism, giving rise to three proteins. (B) Organisation of synemin isoforms. High (H) or α-synemin (170 kDa), Middle (M) or ß-synemin (140 kDa), and Low (L) synemin (41 kDa) with the same head (10 amino acids) and rod domains (312 amino acid) but with different lengths of the C-terminal end (respectively 1243, 931 and 6 amino-acids). AA: amino acid. (C) Immunofluorescence detection of desmin (green) and synemin (red) in human skeletal muscle (from Lars-Eric Thornell, Umeå University, Sweden).Synemin co-localizes with desmin at the myofibrillar Z-lines. Bar: 5 µm.

Figure 2 .

 2 Figure 2. Localization of synemin interacting regions with its partners. Tripartite structure of synemin comprising a central α-helical rod domain (amino acid position from 11 to 322) flanked by non-helical head (amino acid position from 1 to 10) and tail domains (amino acid position from 323 to 1565). Note that the amino acids 1151 to 1463 are absent of M synemin (48). Protein interactions with parts of rod domain of synemin are presented: Desmin (7), Vimentin (3), Vinculin (44), α-Dystrobrevin (29), Dystrophin (3), Utrophin (3) interacting site. Interactions with parts of the tail domain of M and H synemin (from 909 to 1564 amino acid): Zyxin (45), Talin (44), Vinculin (44), α-Actinin (2), Dystrophin (3). Triangles show the positions of 7 variants examined in this review; numbers correspond to the position of mutated amino acids.

Acknowledments

We thank Dr Serge Fermandjian for valuable suggestions, Pr Ali Ladram for helpful advices, Dr Ara Parlakian for critical reading of the manuscript and Sareen Kardjian for linguistic improvements. We express our thanks to Pr L.E.Thornell for the gift of immunolabeling of synemin and desmin presented in Figure 1.

Fundings

Financial support has been provided by Sorbonne Université, CNRS, INSERM, the AFM-Téléthon [contract numbers: 21833 and 22142] and the Fédération Française de Cardiologie. Y.H. was supported by a fellowship from the AFM-Téléthon.

Statement of author contributions

ZX, YH performed in silico modeling of synemin protein; SK, DP, ZX contributed to genetic variant analysis; DP, OA, ZL and ZX wrote the manuscript. [START_REF] Mizuno | Genomic organization and single-nucleotide polymorphism map of desmuslin, a novel intermediate filament protein on chromosome 15q26.3[END_REF][START_REF] Ware | Shared Genetic Predisposition in Peripartum and Dilated Cardiomyopathies[END_REF][START_REF] Zeller | Large-scale mutation screening in patients with dilated or hypertrophic cardiomyopathy: a pilot study using DGGE[END_REF][START_REF] Zhang | A novel heterozygous variant p.(Trp538Arg) of SYNM is identified by whole-exome sequencing in a Chinese family with dilated cardiomyopathy[END_REF][START_REF] Zlotina | Rare Case of Ulnar-Mammary-Like Syndrome With Left Ventricular Tachycardia and Lack of TBX3 Mutation[END_REF] and unpublished data (Z Li, Sorbonne Université, France). For amino acid changes analyses, the sequence of synemin from Titeux et al [START_REF] Titeux | Human synemin gene generates splice variants encoding two distinct intermediate filament proteins[END_REF] were used (GenBank under accession numbers AJ310522 for the α isoform (Synemin H) and AJ310521 for the β isoform (Synemin M). Column 5 indicates effect of mutations: (C) Conservative, (M) Missense, (FS) Frame Shift, Stop. Column 6 indicates the phenotype or associated disease from published data [START_REF] Mizuno | Genomic organization and single-nucleotide polymorphism map of desmuslin, a novel intermediate filament protein on chromosome 15q26.3[END_REF][START_REF] Ware | Shared Genetic Predisposition in Peripartum and Dilated Cardiomyopathies[END_REF][START_REF] Zeller | Large-scale mutation screening in patients with dilated or hypertrophic cardiomyopathy: a pilot study using DGGE[END_REF][START_REF] Zhang | A novel heterozygous variant p.(Trp538Arg) of SYNM is identified by whole-exome sequencing in a Chinese family with dilated cardiomyopathy[END_REF][START_REF] Zlotina | Rare Case of Ulnar-Mammary-Like Syndrome With Left Ventricular Tachycardia and Lack of TBX3 Mutation[END_REF]. nd: non-determined. Column 8 to 10 indicate prediction analyses; SIFT prediction: consequences of mutations: damaging, tolerated, n/a: not available; PolyPhen2 prediction: consequence of mutations for synemin protein NP_663780 (isoform α/H) / NP_056101 (isoform β/M); benign, probably damaging, possibly damaging; Mutation taster prediction: consequence of mutations polymorphism or disease causing. Gray rows indicate the seven variants selected in this review. Different SYNM variants and their consequences: A58V (Ulnar-mammary syndrome) (56), Q200* (Nemaline myopathy) (28), A272V (nd: no-determined) (28), W538R (Dilated cardiopathy) (55), V746M (Dilated cardiopathy) (54), E819fs (Cardiomyopathy) [START_REF] Ware | Shared Genetic Predisposition in Peripartum and Dilated Cardiomyopathies[END_REF], Q1519* (Cardiomyopathy) [START_REF] Ware | Shared Genetic Predisposition in Peripartum and Dilated Cardiomyopathies[END_REF]. Different types of amino acid interaction changes are indicated for four variants: (A58V) conservative without modification, (A272V) with a new hydrophobic bond, (W538R) missense with loss of the hydrophobic bond or (V746M) without modification. (--) indicates hydrophobic interaction. n/a: no applicable (see figure 3).

Exon 1 Conservative

58

Exon 2 Conservative

Exon 4 Missense

538

Exon 4 Missense

746