Virgile Batto

Thomas Flayols

Nicolas Mansard

Margot Vulliez

Comparative metrics of advanced serial/parallel biped design and characterization of the main contemporary architectures

The best achievements in bipedal locomotion have resulted from associating an intelligent and efficient design with clever and robust control. While several control frameworks exist, the design of the legs of our biped robots still lacks a systematic approach and remains a crucial challenge for robot mobility. This paper introduces several criteria to characterize the design of bipedal legs. They aim to guide the design choices and could be implemented in a codesign approach. They reflect the leg overall performances (ability to produce dynamic and accurate foot movements, absorb impacts, lower the motor torques needed to stand up) and characterize the design compactness. We give the algorithmic formulations to evaluate them beyond classical serial designs, to account for any parallel mechanisms. To validate these criteria, we developed a library of open-source CAD models describing the main existing biped architectures, which can be used as a database for future design studies. We discuss the comparative performances of these architectures. We hope this quantified discussion can serve as a baseline to better design future biped robots.

I. INTRODUCTION

Many recent advances in locomotion have partly resulted from improvements in hardware. Early robots like M2V2 [START_REF] Pratt | Design of a bipedal walking robot[END_REF], Mabel [START_REF] Grizzle | MABEL, a new robotic bipedal walker and runner[END_REF], EP-War3 [START_REF] Figliolini | Descending stairs with EP-WAR3 biped robot[END_REF] have been able to respectively walk, run and climb stairs relatively easily. These robots have opened the way to new improved robots able to be more dynamic, like Digit [START_REF]Digit advanced mobility for the human world[END_REF], Kangaroo [START_REF] Roig | On the hardware design and control architecture of the humanoid robot kangaroo[END_REF], and Atlas [START_REF] Guizzo | By leaps and bounds: An exclusive look at how Boston dynamics is redefining robot agility[END_REF]. The progress in the design was predominantly based on intuition, i.e., trials and errors. Digit is the successor of Cassie [START_REF] Reher | Dynamic Walking with Compliance on a Cassie Bipedal Robot[END_REF] and Atrias [START_REF] Grimes | THE DESIGN OF ATRIAS 1.0 A UNIQUE MONOPOD, HOPPING ROBOT[END_REF], and is still being improved in his latest version, where the elastic component has been removed. In particular, parallel mechanisms are promising for developing dynamic robots, as the actuators can be placed closer to the hip of the robot. The designers of Cassie proved such dynamic performances since its serial-parallel architecture makes it run 100m in less than 30s.

Optimization of the architecture is a crucial step when designing a robot. Although yet mostly performed for manipulator robots, either the robot topology [START_REF] Amstutz | Topological optimization of structures subject to Von Mises stress constraints[END_REF] or the complete architecture are optimized by codesign, i.e., simultaneously simulating and optimizing the robot hardware and control [START_REF] Dinev | A Versatile Co-Design Approach For Dynamic Legged Robots[END_REF], [START_REF] Stocco | Fast constrained global minimax optimization of robot parameters[END_REF]. For manipulators, classical performance criteria [START_REF] Angeles | Performance 10. Performance Evaluation and Design Criteria[END_REF], [START_REF] Unal | Multi-criteria Design Optimization of Parallel Robots[END_REF] typically involve the dexterity and the workspace [START_REF] Stoughton | A modified Stewart platform manipulator with improved dexterity[END_REF], or the energy efficiency [START_REF] Fadini | Computational design of energy-efficient legged robots: Optimizing for size and actuators[END_REF]. Some specific *This work is suported by [START_REF] Pratt | Design of a bipedal walking robot[END_REF] Défi clé Robotique centrée sur l'humain (funded by Région Occitanie, France), (2) ROBOTEX 2.0 (ROBOTEX ANR-10-EQPX-44-01 and TIRREX-ANR-21-ESRE-0015), (3) Dynamograde (ANR-21-LCV3-0002) and (4) ASAP-HRC (ANR-21-CE10-0002) 1 LAAS-CNRS, Université de Toulouse, CNRS, Toulouse, France 2 Auctus, Inria, centre de l'Université de Bordeaux, Talence, France 3 Artificial and Natural Intelligence Toulouse Institute, France * corresponding author: virgile.batto@laas.fr

(a) (b) (c) (d) (e)
Fig. 1. Examples of advanced leg design: (a) Digit [START_REF]Digit advanced mobility for the human world[END_REF], (b) Talos [START_REF] Stasse | TALOS: A new humanoid research platform targeted for industrial applications[END_REF], (c) Kangaroo [START_REF] Roig | On the hardware design and control architecture of the humanoid robot kangaroo[END_REF], (d) WL16 [START_REF] Lim | Biped walking robots created at Waseda University: WL and WABIAN family[END_REF], and (e) the Disney bipedal robot [START_REF] Gim | Design and fabrication of a bipedal robot using serial-parallel hybrid leg mechanism[END_REF].

criteria have been proposed to characterize legged robot performance accurately. The impact mitigation factor was proposed for quadrupeds [START_REF] Wensing | Proprioceptive actuator design in the mit cheetah: Impact mitigation and high-bandwidth physical interaction for dynamic legged robots[END_REF] and we will extend it to bipeds in the following sections. The centroidal momentum matrix [START_REF] Orin | Centroidal Momentum Matrix of a humanoid robot: Structure and properties[END_REF] was proposed to evaluate the stability of biped robots. However, a lack of specific but comprehensive criteria to design and evaluate humanoid robot legs has been spotted. This paper sets the root of a systematic method to design a bipedal robot's kinematic architecture and actuator placement. We propose several criteria to evaluate the biped performances, and write generic formulations that can evaluate these metrics for legs with parallel mechanisms. We also produce a library of 5 state-of-the-art legged designs, ranging from classical serial walking robots to more dynamic parallel architectures, reported in Fig. 1. The proposed CAD models are unified in format and scaling and released in open source. We validate the relevance of the proposed metrics by discussing the relative advantages of these architectures.

II. BACKGROUND

A. Kinematics

We denote by q ∈ R the robot configuration. Assuming the robot is not over-actuated, and the actuators are bounded to avoid non-mountable configurations, the joints can be separated between actuated q a and free q f joints q = (q a , q f ). The same separation is made for the joint forces: τ = (τ a , τ f ) (disregarding the free-flyer for now).

The parallel mechanism is modeled by the implicit constraint φ (q) = 0 . It might be more convenient to express it explicitly, i.e., as f such that q f = f (q a ). However, in general, only the implicit constraint φ can be evaluated, f is not available in closed form, and no automatic conversion exists. As we want each proposed criterion to work for the most common shape, we only consider φ to be available and we show how the derivative of f can be obtained or approximated from φ , which is the only needed quantity. The fundamental link between implicit and explicit writings is ∀q a , φ (q a , f (q a )) = 0. Then, thanks to the implicit function theorem:

∂ φ ∂ q a + ∂ φ ∂ f ∂ f ∂ q a = 0 (1) Assuming ∂ φ ∂ f is full-column rank ie ∂ φ ∂ f + ∂ φ ∂ f = I, we get: ∂ q ∂ q a = I -∂ φ ∂ f + ∂ φ ∂ q a (2)
The left-inverse [START_REF] Greville | Generalized inverses: theory and applications[END_REF] of ∂ φ ∂ f is not always unique, notably when internal degrees of freedom exist. The pseudo inverse is nevertheless meaningful in that case, as it minimizes such internal movements and corresponds to a relevant approximation. The operation is exact for most of the existing designs, in particular for the five robots of our library.

B. Operational frame

We consider the operational frame F A to be attached to the tip of the foot, of particular interest when computing biped performance criteria. The placement of F A wrt. the world frame F o is denoted by o M A (q) ∈ SE(3), which is a function of the configuration q. We have:

J A = T q a o M A = T q o M A ∂ q ∂ q a (3)
with T q o M A the tangent application (derivative) of o M A (q), which corresponds to the classical robot Jacobian of the underlying open chain, for example, computable with a standard tool such as Pinocchio [START_REF] Carpentier | The Pinocchio C++ library: A fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives[END_REF], and J A the equivalent Jacobian acknowledging for the close-loop constraint φ .

C. Inertia

The robot dynamics can be written through the constrained Lagrangian form following [START_REF] Carpentier | Proximal and sparse resolution of constrained dynamic equations[END_REF]:

M q + b = ∂ φ ∂ q T λ + τ s.t ∂ φ ∂ q q + ∂ φ ∂ q q = 0 (4)
with M the mass matrix, b the nonlinear effects (Coriolis, centrifugal, gravity), and λ the forces exerted by the closedloop mechanisms. For serial chains, the effective inertia of the foot F A is [START_REF] Khatib | Commande dynamique dans l'espace opérationnel des robots manipulateurs en présence d'obstacles[END_REF]:

Λ = ((T q o M A ) M -1 (T q o M A ) T ) -1 (5)
In what follows, we will need an equivalent quantity accounting for the constraint φ . We first project (4) on q a . M a qa + b a = τ a [START_REF] Guizzo | By leaps and bounds: An exclusive look at how Boston dynamics is redefining robot agility[END_REF] assuming the existence of equivalent mass M a and drift b a linking qa to τ a . To find M a we write the robot kinetic energy:

E c = 1 2 ( I -∂ φ ∂ f + ∂ φ ∂ q a qa ) T M( I -∂ φ ∂ f + ∂ φ ∂ q a qa ) (7)
Then by analogy:

M a = I -∂ φ ∂ f + ∂ φ ∂ q a T M I -∂ φ ∂ f + ∂ φ ∂ q a (8)
This leads to the generalization of the effective inertia in the presence of closed-loop constraints:

Λ A = (J A M -1 a J T A ) -1 (9)

III. EVALUATION CRITERIA

We propose several performance criteria of leg design accounting for parallel architectures. The proposition is based on our understanding of which properties are expected from a walking machine: Its foot must move fast, with low apparent inertia and good shock absorption capability. It should easily compensate for its own weight and should be compact.

A. Velocity manipulability

The manipulability of a robot [START_REF] Yoshikawa | Manipulability of robotic mechanisms[END_REF] can be seen as the ellipsoid of speed the effector can produce with constant unit joint velocity qT q = 1. For parallel architectures, only the motor coordinates can be controlled, so we need to rewrite it as qT a qa = 1, which leads to the equivalent ellipsoid given by v T (J A J T A ) -1 v = 1. While J A carries information about translational and rotational movements, we prefer to separate the manipulability between translation and rotation, with

J A = [Jt T A , Jr T A ]
T . This gives two manipulability criteria:

T M =det(Jt A Jt T A ) (10)

RM =det(Jr

A Jr T A ) (11)
With TM and RM, the translation and rotation manipulability indexes, reflecting the volume of the ellipsoids of translational and rotational velocities. These criteria give the global kinematic capability and do not reflect in which direction the robot foot can achieve the highest velocity. As the leg will mainly need to transmit force on the z-axis, this particular direction is studied with its own criteria.

B. The z-reduction ratio

We next characterize the capability of the system to transmit low vertical effort to the actuators. In quasi-static, the actuator forces τ a can be expressed as a function of the ground reaction force on the foot λ A ∈ se(3) * :

τ a = J T A λ A (12)
We define the z-reduction ratio (ZRR) as the norm of the projection of J A on the z-axis.

ZRR = ∥Jt T A z∥ (13)
The norm is investigated here to penalize multiple motors that must produce torque to compensate for a z-axis force and to maintain the robot up. Low ZRR is desirable and is somehow antagonist to high translation manipulability in z.

C. Compactness

The compactness of the design must be quantified, as an important footprint may hinder the capability of the biped to navigate in cluttered environments. An easy way to evaluate the volume V 3 occupied by the leg is to compute the convex hull of the leg, as depicted in Fig. 2. In this study, we only consider the hull at the center of the joints. As the leg will mainly move on the sagittal plane ((xz) in Fig. 2), we additionally consider V 2 the area of the convex hull projected on this plane.

D. Foot Effective Inertia

An agile biped robot should have light legs, especially on the vertical axis to generate dynamic motion. We therefore mainly characterize the foot effective inertia along the z-axis. The z-axis inertia (ZAI) index is:

ZAI = [z, 0]Λ A [z, 0] T (14)
It should be as low as possible to get an optimal robot. Since the leg is globally oriented on z, we argue that minimizing the ZAI will impact more joints and links of the leg than globally evaluating the foot inertia.

E. Impact mitigation factor

The impact mitigation factor (IMF) was introduced [START_REF] Wensing | Proprioceptive actuator design in the mit cheetah: Impact mitigation and high-bandwidth physical interaction for dynamic legged robots[END_REF] to characterize the shock absorption capability. It compares how the entire floating system reacts to external forces, to its reaction when the basis is fixed. Due to space limits, we briefly report here how to extend it to parallel kinematics. The apparent inertia Λ A was computed for the fixed-basis mechanism. The exact same developments for the floatingbasis mechanism lead to the free-basis apparent foot inertia, noted Λ A f ree , and the free basis apparent foot inertia when the leg is locked, noted Λ A lock . Following [START_REF] Wensing | Proprioceptive actuator design in the mit cheetah: Impact mitigation and high-bandwidth physical interaction for dynamic legged robots[END_REF], the IMF then is:

IMF = det(I -Λ A f ree Λ -1 A lock ) (15)

IV. STUDIED BIPEDAL ROBOTS

We evaluate the relevance of our metrics on five representative designs of bipedal legs, chosen from the literature and displayed in Fig. I. As several are not reported with accessible open-source description format, we have built the five corresponding open-source packages scaled into similar dimensions. These descriptions have been gathered using the main available data, as explained below, with inertia deduced from uniform equivalent materials. The CAD models are available on GitHub¹. Even though some of the studied designs are not inspired by biology, a unified vocabulary is used to describe them. The hip will designate the 3 degrees of freedom, which generate the rotation close to the torso; the knee will designate, if possible, the next degree of freedom placed after the hip, then the ankle will designate the 2 rotational degrees of freedom of the foot.

Furthermore, the transmission systems of the robots and their additional inertia are not modeled here, as we are not evaluating these components in the proposed criteria and let it for further work. The knee actuation is deported close to the hip, thanks to a rod. The last two dof of the ankle are driven by two motors deported near the knee thanks to two rods. Actuation: Each one of the 6 motorized joints of this leg is in quasi-direct drive. Loop closure: It compounds 3 closed loops per leg. One for the actuation of the knee and two for the actuation of the ankle. In the CAD, each rod is cut in half, and a 6d constraint is set between each two parts.

2) Talos: Talos [START_REF] Stasse | TALOS: A new humanoid research platform targeted for industrial applications[END_REF] is a serial robot with 6 dof on each leg. Kinematics: It adopts a serial architecture, with the dorsiflexion of the ankle deported inside the shin thanks to a parallelogram linkage. Actuation: Each one of the 6 motorized joints are actuated by a motor with a harmonic gearing. Loop closure: It has one closed loop on each leg inside the parallelogram. In the CAD, one rod is cut in half, and a 6d constraint is set between its two parts.

3) Kangaroo: Kangaroo [START_REF] Roig | On the hardware design and control architecture of the humanoid robot kangaroo[END_REF] is a serial-parallel bipedal robot with 6 dof on each leg. Kinematics: It adopts a serial-parallel architecture where the supination of the hip is actuated by one linear motor, and the abduction and the flexion are set in parallel thanks to two rods controlling a universal joint. The knee is controlled by one actuator, and the two dof of the ankle are controlled by two actuators placed near the hip, which transmit their movement through two rods and a referral triangle controlling the universal joint of the ankle. Actuation: Each one of the 6 motorized joints is a prismatic joint made from a ball-screw transmission system to generate translational movement. Loop-closure: It compounds 11 closed loops by leg. Most of them are due to the usage of translational motors. In the CAD, each rod is cut in half, and the 6d constraint is set between each two parts.

4) Disney Bipedal Robot: The Disney Bipedal [START_REF] Gim | Design and fabrication of a bipedal robot using serial-parallel hybrid leg mechanism[END_REF] Robot is a serial-parallel bipedal robot with 6 dof on each leg. Kinematics: It adopts a serial-parallel architecture where the abduction of the hip is actuated by one motor. The supination, flexion of the hip, knee flexion, and ankle inversion are set in parallel thanks to two 5-bar linkages. The dorsiflexion of the ankle is directly controlled by a motor placed on the foot. Actuation: Each one of the 6 motorized joints is driven by a servo motor. Loop-closure: It compounds 3 closed loops: one on each 5-bar linkage and one between the two 5-bar linkages. In the CAD, 3 rods are cut in half, and a 6d constraint is placed between each two parts.

5) WL16: WL16 [START_REF] Lim | Biped walking robots created at Waseda University: WL and WABIAN family[END_REF] is a parallel bipedal robot with 6 dof on each leg. Kinematics: Each leg has the fully parallel structure of a Gough-Stewart platform [START_REF] Dasgupta | The Stewart platform manipulator: a review[END_REF]. Actuation: Each one of the 6 motorized joints is a prismatic joint made from an electric cylinder. Loop-closure: It compounds 5 closed loops, on 5 of the 6 cylinders. In the CAD, the pistons of these 5 cylinders are cut in half, and a 6d constraint is made between each part.

V. QUANTITATIVE EVALUATION AND DISCUSSION

We do not aim here at comparing each leg to the others. Indeed, each architecture is fundamentally different and might have been designed with respect to different goals. We rather seek to validate the criteria and corroborate them with what we know of the characteristics and achievements of the 5 considered robots.

A. Reference trajectories

The benchmark is based on 3 simple reference trajectories defined in operational space and presented in Fig 2 2 .

• A 40cm forward movement of the foot wrt the hip, corresponding to a walking step. • A 20cm upward movement of the foot wrt the hip, corresponding to a squat. • A corner movement (16cm forward then 20cm upward wrt the hip), corresponding to the climb of a stair. These 3 trajectories correspond to common use cases of a bipedal robot. The lengths are set to cover the range of motion that an average robot can do, with a standardized leg height of 80cm. From these 3 references, a collection of trajectories is obtained by randomizing the displacement, chosen so that the standard deviation around the nominal reference is 2.5cm

B. Motion generation

The motion of the robot model is finally obtained by implementing a simple cartesian regulator around the reference trajectories.

Each trajectory is discretized in a set of 100 positions, and to rapidly model the robots, each desired trajectory is tracked by the foot, thanks to the closed-loop Jacobian. The velocity of the actuated joints is set to:

qa = J † A ν * A ( 16
)
With ν * A ∈ se(3), the reference velocity of our operational frame F A (foot tip) set to correct the error wrt the reference 2 See the companion video, available at https://peertube.laas. fr/w/9HoFdHzhHQNfMJrbJxu2F1 trajectory. The velocity of the entire leg (free and actuated joints) is then:

q = ∂ q ∂ q a qa ( 17
)
This velocity is then integrated to obtain the joint trajectory and clipped to stay within the joint limits. We arbitrarily define the joint limits to avoid non-mountable configurations, as discussed in Sec. II-A. For the WL16, we set the bounds of the cylinders to a maximal extension of 150% of their minimal length. The resulting trajectories are discretized into 100 configurations each. Each criterion is computed on each of these samples. The computation is made with Python and the Pinocchio library [START_REF] Carpentier | The Pinocchio C++ library: A fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives[END_REF].

C. Scaling

We have separated translation TM and rotation RM manipulability to avoid the scaling effect due to mixing lengths and angles. Yet most of the criteria are based on Jacobians, and are subject to the same issue due both to prismatic and revolute joints, and to translation and rotation of the effector. In practice, we suggest to introduce a scaling factor to obtain adimensional (unit-free) Jacobians. Alternatively, attention may be paid to the unit used for each dimension, but it would negatively affect the genericity of the approach.

The approach applies to any Jacobian J split into a translational and a rotational component, J T = [J T t , J T r ]. We denote the i th column with [i, :] Depending on the type of the joint corresponding to Column i, we have:

⟨Jt[i, :]⟩ = ⟨.⟩ if Joint i is prismatic ⟨m⟩ else (18) ⟨Jr[i, :]⟩ = ⟨m -1 ⟩ if Joint i is prismatic ⟨.⟩ else ( 19
)
where ⟨-⟩ stands for the unit of the corresponding quantity (meter, adimensional or meter-inverse here).

To obtain an adimensional Jacobian, we choose to scale it by multiplying the translation part and rotation part of the Jacobian by two diagonal matrices D t , D r , following [START_REF] Khan | Jacobian Matrix Normalization -A Comparison of Different Approaches in the Context of Multi-Objective Optimization of 6-DOF Haptic Devices[END_REF]. We choose the scaling matrices D so that they make the unit of the Jacobians invariant to joint type, i.e.:

D t = diag(d i ) with d i = 1 if Joint i is prismatic d t else D r = diag(d i ) with d i = d r if Joint i is prismatic 1 else
To cancel the scaling effect, the weight d t is chosen as the mean of the singular values of the matrix J t where only the columns corresponding to the revolute joints are selected (i.e. only the terms of unit ⟨m⟩ in ( 18)). Respectively, d r is the mean of the singular values of the prismatic columns of J r (i.e. the terms of unit ⟨m -1 ⟩ in ( 19)). The scaling factors D t and D r then account for all the lengths present inside the architecture. The scaled adimensional Jacobian J, invariant to joint-type dimension is finally: The adimensional manipulability TM, RM, and the ration ZRR are then computed from the scaled Jacobian:

J = JtD t JrD r (20)
TM = det(Jt A D t 2 Jt T A ) RM = det(Jr A D r 2 Jr T A ) ZRR = ||D t Jt T A ⃗ z|| (21)
As only the adimensional version of these criteria will be used in what follow, TM, RM and ZRR now abusively refer to these values.

D. Analysis and discussion

1) Z-reduction ratio : The ZRR for each robot and each movement are plotted in Fig. V-D.1. Over the different trajectories, the ZRR stays relatively constant and small, except for the robots that use prismatic actuation. The variation is noticeable for WL16, but particularly remarkable for Kangaroo. Its ZRR is 10 times larger than other robots.The large ZRR of Kangaroo is compensated by the use of a ball-screw transmission system to generate translational movement. This result highlights the relevance of the ZRR, as all these robots are largely capable of withstanding vertical reaction forces.

2) Velocity manipulability: The TM and RM values are shown in Fig. 4. The translation manipulability of Kangaroo is significantly higher than for any other robot. This reflects the particular architecture of this robot, which only requires small actuator displacements to produce all the robot reference trajectories. The rotation manipulability of all the studied robots is similar. Only the Disney robot shows a slight improvement in rotational velocity capabilities. As rapid foot rotations are not expected on a biped, it is likely that it is a side effect of the ankle actuation rather than a careful decision optimized during the design process.

3) Compactness: The compactness criteria are displayed in Fig. 5. On the top row, the occupancy volume V 3 of all 5 robots is similar and very low, though the WL16 and Disney bipedal robots tend to span more space over the reference movements. This reflects their general architecture choices, which rely on parallelism more systematically than the others, in particular with no main hip-knee-ankle serial chain. Since the WL16 is not a planar architecture, it takes more space. The Disney bipedal robot loses compactness because of its two five-bar linkages.

The anteroposterior projected convex hull V 2 (sagittal area) is presented in Fig. 5 (bottom). It highlights that parallel architectures such as Digit or Kangaroo tend to occupy more space than serial ones such as Talos. This result validates the relevance of this criterion, in particular when optimizing the volume spanned by an architecture.

4) Relevance of the proposed inertia model: We first recall that each robot part/link is modeled as to be made of plain plastic with a density of 1g/cm 3 for each structural part, and plain material with a density of 4g/cm 3 (half the steel) for the motor part. These assumptions correspond to the mean density of structural and motor parts. We first validate with Table I the relevance of this hypothesis, by comparing our average-inertia model with the open-source ground-truth model of Talos [START_REF] Stasse | TALOS: A new humanoid research platform targeted for industrial applications[END_REF].

The error induced by our simplest modeling hypothesis is rather limited, and is not likely to significantly change the predicted behavior and the relevance of this study.

5) Apparent inertia:

The ZAI of the foot of each robot is presented in Fig. 6. As expected, Talos and the Disney bipedal robot have important leg-effective inertia due to the presence of a motor on the foot. Every other robots with small motors (Digit) or no motors (Kangaroo and WL16) embedded in the leg have a small inertia. The important inertia of the Disney bipedal robot is strongly due to the scaling of the robot, while the robot was optimized with a leg size of only about 40cm. Nevertheless, this criterion highlights the need to reduce the mass near the foot.

6) Impact Mitigation Factor: To compute the impact mitigation factor, the mass of each torso is set at 40kg. The global IMF is presented in Fig. 7. The isotropic IMF is displayed on the top row and is nearly null for all robots except WL16. Indeed, none of the reported architecture is explicitly designed to absorb impacts. WL16 higher IMF is a side-effect of its architecture, as it is derived from a Stewart platform, providing a more isotropic behavior.

These legged machines are rather expected to absorb shock in the z direction when the robot walks/runs/jumps. When we look at the IMF projected on the z-axis (Fig. 7, bottom), the results are much better for every robot. On the z-axis, the WL16 presents high impact-absorption performance, closely followed by Digit, which also shows to absorb impact efficiently. The Disney bipedal robot and Talos have a lower impact-mitigation capability, undoubtedly due to the presence of the big ankle actuators directly on the foot.

We point out here that the inertia of the actuators is not modeled in the proposed library (only the added masses of the motors are modeled, not the apparent inertia induced, e.g., by the rotor inertia multiplied by the reduction ratio). This would likely change the values, in particular for Talos. Yet the results confirm the relevance of the IMF in evaluating

VI. CONCLUSION

This paper proposed a set of new criteria to systematically characterize the design of a bipedal robot leg. These criteria include manipulability, the Z Reduction Ratio, the Z-Axis Inertia, the Impact Mitigation Factor, and the leg convex hull. These criteria can be used to design an efficient leg with a minimal ZRR, a maximal TM, and RM. A Dynamic leg with a minimal ZAI and a maximal IMF or Compact leg with a minimal convex hull.

We also provided the formulations to compute these criteria with any serial or parallel architecture, accounting for the most generic model with implicit constraints.

We have shown the relevance of these criteria by applying them to discuss the performance of 5 existing robots representing the main classical architectures of the literature. This implied to reproduce the 5 CAD models in a consistent scaling and format that we also propose in open source.

This study has successfully demonstrated the effectiveness of the proposed criteria in evaluating the leg design. We argue that they cover the main aspects of the kinematic design, accounting for the ability to quickly move (TM, RM), sustain ground reaction forces (ZRR), react (ZAI), absorb shocks (z-IMF), and navigate in cluttered environments (convex hull V 2 ). The results obtained from the application of these criteria to the selected robots have provided valuable insights into their architectural designs and the overall performance of bipedal robots.

We have limited our study to the kinematic model without yet modeling the actuation and characterizing it. This would need additional criteria, likely considering the full dynamic model and not only the inertia. However, this limitation does not invalidate the proposed criteria but simply calls for an additional batch of them. Finally, the overall objective of our contribution is to set the basis for a systematic optimization of the kinematics of biped legs, which we consider doing next.

Fig. 2 .

 2 Fig. 2. Convex hull and trajectory example

1 1 )

 1 Digit: Digit[START_REF]Digit advanced mobility for the human world[END_REF] is a serial-parallel bipedal robot with 6 dof on each leg. Kinematics: It adopts a serial-parallel architecture where the 3 dof of the hip are placed in serial.

Fig. 3 .

 3 Fig. 3. Z-reduction ration (ZRR)

Fig. 4 .Fig. 5 .

 45 Fig. 4. Velocity manipulability of the foot, in translation (TM, top) and rotation (RM, bottom)

Fig. 6 .

 6 Fig. 6. z-apparent inertia (ZAI) of the foot

Fig. 7 .

 7 Fig. 7. Impact mitigation factor (IMF), isotropic (top) and in z (bottom)

TABLE I MASS

 I OF TALOS PIECES ON DIFFERENT MODEL

https://gitlab.laas.fr/vbatto/closed_loop_ kinematics_pinocchio


Nemanja Milicevic

Lasse Jenner

Alexander Myasnikov

Marat Yusupov

Gulnara Yusupova

mRNA reading frame maintenance during eukaryotic ribosome translocation

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

Main

During protein synthesis, messenger RNA (mRNA) and transfer RNAs (tRNA) must be rapidly translocated through the ribosome to advance the translational reading frame by one codon. The process is susceptible to errors, of which the most severe is shifting of the translational reading frame of mRNA, causing incorrect reading of succeeding codons. The key question is how the eukaryotic ribosome couples mRNA and tRNA translocation during protein synthesis, while securing the integrity of weak codon-anticodon interactions and thus preventing frameshifting.

Many bacterial ribosome intermediates of translocation have been structurally analyzed employing both X-ray crystallography and cryo-EM [START_REF] Rundlet | Structural basis of early translocation events on the ribosome[END_REF][START_REF] Carbone | Time-resolved cryo-EM visualizes ribosomal translocation with EF-G and GTP[END_REF][START_REF] Petrychenko | Structural mechanism of GTPase-powered ribosome-tRNA movement[END_REF][START_REF] Zhou | How the ribosome hands the A-site tRNA to the P site during EF-G-catalyzed translocation[END_REF][10][11] , however, insights into eukaryotic translocation complexes have been hindered by low-to-intermediate resolution [START_REF] Djumagulov | Accuracy mechanism of eukaryotic ribosome translocation[END_REF][START_REF] Flis | tRNA Translocation by the Eukaryotic 80S Ribosome and the Impact of GTP Hydrolysis[END_REF][START_REF] Taylor | Structures of modified eEF2 80S ribosome complexes reveal the role of GTP hydrolysis in translocation[END_REF] . The higher complexity of the eukaryotic 80S ribosome, with approximately 40 % higher molecular mass than its prokaryotic counterpart, and a minimum mass of 3.3 MDa in yeast and plants, hampered the high-resolution structural study of eukaryotic translocation, arguably the most complex operation of protein synthesis. Apart from being more sophisticated in terms of function and regulation [12][13][14] , an increasing number of genetic and biochemical studies report that the eukaryotic translational apparatus relies to a large extent on unique post-transcriptional modifications of ribosomal RNA (rRNA) and tRNAs, as well as kingdom-specific elongation factors, which actively contribute to the accuracy of protein synthesis.

In eukaryotes, the process of translocation is ensured by a five-domain GTP-ase, elongation factor 2 (eEF2). Eukaryotic eEF2 and archaeal aEF2, contain a unique and strictly conserved post-translationally modified histidine residue located at the tip of domain IV, named diphthamide, and shown to contribute to translation accuracy [START_REF] Ortiz | Translation elongation factor 2 anticodon mimicry domain mutants affect fidelity and diphtheria toxin resistance[END_REF][START_REF] Liu | Diphthamide modification on eukaryotic elongation factor 2 is needed to assure fidelity of mRNA translation and mouse development[END_REF] . Its biosynthesis pathway requires the action of at least seven enzymes and even involves non-canonical radical enzyme chemistry.

Diphthamide in human eEF2 is a target of at least two virulent toxins that inactivate eEF2 by ADP-ribosylation and cause lethal effects [START_REF] Ortiz | Translation elongation factor 2 anticodon mimicry domain mutants affect fidelity and diphtheria toxin resistance[END_REF]15,16 . By failing to respond to high oxidative stress, mammalian cells lacking diphthamide are more sensitive to cell death 17 . Moreover, the loss of diphthamide can lead to several neurodegenerative diseases 18,19 and render human cells hypersensitive to Tumor Necrosis Factor-mediated apoptosis 20 . A recent crystal structure of the Saccharomyces cerevisiae ribosome translocation intermediate revealed that domain IV of eEF2 and diphthamide engaged in an extensive stabilization network with the codon-anticodon duplex in an early state of translocation 3 , however the role of diphthamide in other translocation phases remained unanswered.

We determined ten high-resolution cryo-EM structures (up to 1.97 Å) of elongating eukaryotic S. cerevisiae ribosome bound to the full translocation module consisting of messenger RNA, peptidyl-tRNA and deacylated tRNA, seven of which also contained ribosome-bound S. cerevisiae eEF2. Such a collection of translocation intermediates trapped in transition from the early to the late state of translocation reveals how elements of the mRNA-tRNA2-growing peptide module are displaced over distances of approximately 30 to 50 Å and reach a close-to-final position of translocation. Moreover, the early translocation states presented hereinafter demonstrate how the eukaryotic translocase eEF2 engages spontaneously occurring, fully-rotated ribosomal conformations 21 , while promoting peptidyl-tRNA translocation once it is fully accommodated on 80S. We describe the mechanism of maintenance of the eukaryotic translational reading frame on the atomic level, showing how eukaryote-specific elements of the 80S ribosome, eEF2 and tRNAs, undergo large-scale molecular rearrangements to safeguard the mRNA reading frame, from early eEF2 translocase accommodation, until the very late stages of the process.

Eukaryotic translocation intermediates

To visualize intermediates of the eukaryotic 80S ribosome translocation, we prepared translocating S. cerevisiae 80S ribosome complexes in vitro, using purified components, including naturally occurring S. cerevisiae eEF2. In the first set of experiments, complexes were prepared with the non-hydrolysable GTP analogue, GMPPCP, while in the second and third sets of experiments, the reaction mixture contained eEF2-binding translation inhibitor sordarin 22 , and either GMPPCP or GTP (see Methods). All three reaction mixtures were subjected to singleparticle cryo-EM analysis which yielded an ensemble of nine distinct reconstructions of S. cerevisiae 80S ribosome bound to the complete mRNA-tRNA2 module (39-nucleotide mRNA, fMet-Phe-N-tRNA Phe and deacyl tRNA fMet ). Seven of these contained S. cerevisiae eEF2 bound to the ribosome, respectively representing genuine eukaryotic 80S ribosome translocation intermediates (TIs) (Fig. 1a, b, Extended Data Tables 1,2, Supplementary Table 1). The tenth reconstruction resulted in a non-rotated (NR) state of S. cerevisiae 80S ribosome bound to mRNA, fMet-tRNA fMet and tRNA fMet . Altogether, these structures reflect rotational motions of recruitment is accompanied by the opening of the SSU shoulder domain, while fMet-Phe-N-tRNA and deacyl tRNA fMet maintain A/A* and P/E configurations, respectively (Extended Data Fig. 1, Supplementary Fig. 1). Moreover, during early translocation events (PRE-H1, PRE-H2 and TI-1, TI-1*), the SSU head domain maintains a somewhat tilted position of approximately 1° relative to the body (Extended Data Fig. 1). Hence, the head domain likely acts as the main ligand anchor, modulating the progression of tRNA anticodons. Such importance of the head domain for tRNA translocation is further corroborated by a recent X-ray structure of an early intermediate state of eukaryotic translocation 3 . In this structure, eEF2 is fully accommodated, while the SSU body is still in a highly rotated state (9.5°), however, its SSU head domain has swiveled forward by 13°, coinciding with a major tRNA advancement.

During transitions from TI-2 to TI-5, 80S undergoes substantial large-scale conformational changes, where the SSU body domain rotates backward, being only 0.4° away (TI-5) from the final non-rotated position, while the SSU head domain performed forward rotation of up to 19.8° (Extended Data Fig. 1). Accommodation of eEF2 on 80S, as observed from TI-1 to TI-2 (Fig. 2a), coincides with further SSU shoulder domain opening. Then, as codon/anticodon duplexes undergo modest advancement from TI-2 to TI-5 (Fig. 1d), the mRNA-tRNA2 module remains in the chimeric state (Extended Data Fig. 2, Supplementary Fig. 1). For instance, TI-2 and TI-3 states can be considered as "overlapping", however, even though GTP hydrolysis had already occurred in TI-2, TI-3 was considered more advanced since the SSU body is more back-rotated.

Despite only a minor codon-anticodon advancement in late translocation, 80S undergoes substantial large-scale conformational changes in terms of SSU body back-rotation and SSU head forward swiveling (Extended Data Fig. 1).

Expectedly, the final product of translocation -in which eEF2 would have dissociated from the 80S ribosome complex, and fMet-Phe-N-tRNA Phe and deacyl-tRNA fMet reached P/P and E/E positions, respectively -was not observed in any of the assayed in vitro conditions. This confirms that the translocation process cannot be fully accomplished in the absence of GTP hydrolysis 25 or in the presence of sordarin 22 . Thus, our study supports the proposal that the elongating complex can reach a close-to-final state in a single round of translocation with no requirements for energy coming directly from GTP hydrolysis 26 . Analogously, final translocation events, including notably eEF2 dissociation, would therefore require the hydrolyzed, GDP, form 25 . Ultimately, the translocase is most likely to guard against the slippage of the translational reading frame, while the principal role of GTP hydrolysis is to ensure eEF2 will not be released from the ribosome before completion of the translocation cycle [START_REF] Flis | tRNA Translocation by the Eukaryotic 80S Ribosome and the Impact of GTP Hydrolysis[END_REF]25,27 .

eEF2 engagement and mRNA-tRNA2 movement

Early translocation intermediates TI-1 and TI-1* reveal eEF2 binding to a fully rotated hybrid intermediate ribosome captured in a conformation analogous to PRE-H2 (Fig. 1a,b, Supplementary Fig. 1). Displacement of the elbow domain of peptidyl-tRNA, which prevents the collision with domain IV of eEF2 (Fig. 2b), as well as the movement of the acceptor stem of deacyl-tRNA from P/P to P/E, demonstrate that PRE-H2 represents an authentic translocation intermediate, in which acceptor stems of tRNAs had largely translocated on the LSU. This step occurs spontaneously, in the absence of both eEF2 and GTP, and can be reversible 28 . The TI-1 state is captured during eEF2 recruitment on 80S, with domains I and V bound to the universally conserved sarcin-ricin loop (SRL) of 25S rRNA (Fig. 2c, Extended Data Fig. 4a-d). Moreover, domain I is accommodated on uL6, domain V is in contact with uL11, while domain IV is found between SSU shoulder and head domains. The TI-1 structure also reveals eukaryote-specific points of contact between eEF2 domains I and II and SSU proteins eS6 and eS24 (Extended Data Fig. 4e). In addition, the lysine-rich loop 1 of domain IV forms initial contacts with the peptidyl-tRNA anticodon-stem loop (ASL), notably through a hydrogen bond with proline residue 580 (Fig. 2d,e). Although the interaction is not side-chain-specific, it points to the fundamental importance of proline geometry for domain IV conformation in the context of translocation accuracy. Indeed, single-point mutation of proline 580 to histidine increases the rate of frameshifting events in yeast, while the equivalent P596H in human eEF2 is associated with human neurodegeneration phenotypes, notably autosomal dominant spinocerebellar ataxias 29 .

During progression to TI-2, eEF2 undergoes rotation-like movement by approximately 17° around SRL, and ultimately, accommodates on 80S (Fig. 2c). In the transition from TI-1 to TI-2, unlocking of the decoding center enables eEF2 domain IV to move into the A-site by approximately 19 Å and engage in direct interactions with the minor groove of the codonanticodon duplex formed by peptidyl-tRNA and the A-codon (Fig. 2f, Fig. 3a, b, Supplementary Video 3). Full accommodation of eEF2 occurs together with further SSU back rotation (Fig. 1a-b, 2a, c, Extended Data Fig. 1). These observations further suggest that unlocking of the eukaryotic ribosome decoding center occurs during the transition from TI-1 to the early translocation state characterized by the recent crystal structure of eukaryotic S. cerevisiae 80S ribosome 3 . Disruption of minor groove interactions between rRNA elements of the decoding center and the codonanticodon duplex in the SSU A-site presents a rate-limiting step in enzymatic translocation 30 .

Upon sequential transitions from TI-2 to TI-5, accompanied by further reverse rotation of the SSU body and forward swiveling of the head, the mRNA-tRNA2 cargo reaches its close-to-final position of translocation, while eEF2 domain IV conserves its overall conformation and position on the SSU (Extended Data Fig. 2, 5a-c, Supplementary Fig. 1). Furthermore, structures of TI-1 and TI-3 obtained in the presence of GMPPCP showed that abrogation of GTP hydrolysis does not prevent translocation from reaching a late intermediate state (Extended Data Fig 2, 3, Supplementary Fig. 1). Therefore, eEF2 contributes to translocation most likely by preventing reverse rotation of the SSU head domain, acting as a molecular "doorstop" [START_REF] Djumagulov | Accuracy mechanism of eukaryotic ribosome translocation[END_REF][START_REF] Flis | tRNA Translocation by the Eukaryotic 80S Ribosome and the Impact of GTP Hydrolysis[END_REF] (Supplementary Video 4).

Although we observed gradual dissociation of eEF2 from 80S during transitions from TI-2 to TI-5 (Extended Data Fig. 4b-d), contacts between eEF2 domain IV and peptidyl-tRNA are maintained (Fig. 2d-f, Extended data Fig. 5b). More importantly, eEF2 contributes substantially to the overall stability of the mRNA-tRNA2 module, with an additional contact area of ~430 Å 2 in TI-2, TI-3 and TI-4. As such, it accounts for roughly 25 % of the total contact area found to preserve the integrity of codon-anticodon duplexes, including tRNA ASLs. Our data suggest that codon-anticodon integrity is maintained until the very late stages of the translocation process, pointing to the possible existence of accuracy control mechanisms, not only upon decoding but throughout the elongation cycle.

mRNA reading frame and eEF2 domain IV

Our high-resolution structures reveal an intricate network of interactions preventing the slippage of the translational reading frame (Fig. 3a). First, as eEF2 is recruited on the hybrid 80S complex and TI-1 is formed, the codon-anticodon duplex of peptidyl-tRNA remains locked in the decoding center -as observed in PRE-H1/PRE-H2 -while the stem of peptidyl-tRNA ASL gains additional stability from domain IV of not fully accommodated eEF2 (Fig. 2d-e). In the decoding center, the codon-anticodon duplex is secured by a highly ordered network of interactions, largely resembling the one previously described in prokaryotes 31 . However, we observed additional interactions with the eukaryote-specific glutamine residue 63 of the conserved uS12 protein (Fig. 3a). Then, upon transition from TI-1 to TI-2 and full eEF2 accommodation, the tRNA-like domain IV of eEF2 establishes an intensive network of interactions with the codon-anticodon duplex, in which diphthamide forms a total of three hydrogen bonds with the second base pair (BP2), involving both codon and anticodon nucleotides (Fig. 3a,b). A similar pattern of interactions, although with additional interactions with BP1, was recently described in a TI trapped presumably at a state between TI-1 and TI-2 [START_REF] Djumagulov | Accuracy mechanism of eukaryotic ribosome translocation[END_REF] . Next, reconstructions of TI-3 and TI-4 suggest that the interaction network of diphthamide undergoes remodeling to include an additional contact with the third codon nucleotide, possibly by means of amide O-protonation.

Finally, in TI-5, diphthamide re-establishes the interaction network only with the second codon nucleotide. This suggests that diphthamide acts by maintaining the interaction with BP2 throughout translocation, while transiently probing BP1 during early 3 , and BP3 during late translocation. Stabilization of the codon-anticodon duplex is further ensured by histidine 583 of eEF2 domain IV, found to interact with the phosphate moiety of wybutosine 37 of tRNA Phe (Fig. 2f) from the early 3 to the late state of almost accomplished translocation (TI-5). In addition to the stabilizing effect of eEF2, the codon-anticodon duplex is also secured by RNA nucleotides of the SSU body domain (Fig. 3a) Our cryo-EM data also show that BP2 gains additional stabilization in TI-3 onwards through an additional hydrogen bond with the ribosomal residue U1761. Moreover, wobble base pair geometry in TI-4 and TI-5 is further secured by a hydrogen bond with Cm1639, which complements BP3 interacting counterparts C1637, G1638 and C1640 preserved from TI-2.

Altogether, these interactions mimic the stabilizing effect of the decoding center observed in TI-1. Ultimately, the sterically constrained environment imposed predominantly on BP2 through the arrangement of diphthamide and domain IV residues suggests that the role of eEF2 is not only to stabilize correct Watson-Crick codon-anticodon interactions but also to contribute to tRNA discrimination during translocation (Fig. 3c). By probing the minor groove of the peptidyl-tRNA codon-anticodon duplex, eEF2 could uncover near-cognate peptidyl-tRNA paired to the codon by non-canonical Watson-Crick interactions and trigger dissociation of erroneous peptidyl-tRNA from the eukaryotic ribosome 32 .

Ribosome mRNA-tRNA interactions

The most expanded interaction networks between mRNA and the eukaryotic elongating ribosome were observed in hybrid and TI-1 states (e.g. PRE-H1 in Extended Data Fig. 6a,b), when A-tRNA binding to the NR complex led to the narrowing of the downstream mRNA tunnel, as shown in the bacterial ribosome 33 , while the SSU head domain remained unrotated. mRNA is found to interact with uS12 and a number of 18S nucleotides in a base-non-specific manner (Extended Data Fig. 6c). All interacting elements are conserved from prokaryotes, except the eukaryote-specific Gln63 of uS12. The transition from TI-1 to subsequent late TIs leads to simultaneous disruption of the pre-translocation arrangement and formation of new posttranslocation interactions of peptidyl-and deacyl-tRNA ASLs with the SSU body domain (Fig. 4a-d). Unlike deacyl-tRNA, peptidyl-tRNA ASL interacts primarily with the SSU body rather than the head domain. This principally arises from the interactions with decoding nucleotides in TI-1 (Fig. 3a) and hybrid states. During late translocation (from TI-2 to TI-5), a preserved set of SSU body nucleotides ensures both the advancement of peptidyl-tRNA ASL through chimeric states (e.g. TI-4 in Fig. 4c) and the final delivery to the classical state in NR, while deacyl-tRNA is almost exclusively "guided" by the SSU head domain (Fig. 4c,d). Ultimately -as deacyl-tRNA reaches the classical E-site -SSU head domain residues disengage from its ASL as a result of head domain back-swiveling to the classical NR state, and restore the complete P-site setup around peptidyl-tRNA (Fig. 4d). Subsequent disruption of these interactions may be the main energy barrier to the rate-limiting step of unlocking, which is to be solved by eEF2. Indeed, following the unlocking event, eEF2 domain IV mimics the effect of decoding nucleotides to maintain the stability of weak A-codon-anticodon pairing of peptidyl-tRNA and prevent the loss of the reading frame during translocation (Fig. 3a, 4a-d).

Eukaryote-specific RNA modifications

1-methyl-3-α-amino-α-carboxyl-propyl pseudouridine 1191 (m 1 acp 3 Ψ1191) is the only hypermodification identified in S. cerevisiae rRNA. This heavily modified uridine 34 , reported in the hairpin loop of the universally conserved helix 31 of 18S rRNA, lies at the interface of SSU head and body domains, and is known to participate in the architecture of the peptidyl-tRNA site [START_REF] Ben-Shem | The structure of the eukaryotic ribosome at 3.0 A resolution[END_REF]36 (Fig. 5a). The central importance of m 1 acp 3 Ψ1191 is underlined by the fact that its loss (hypo-modification) is associated with the proliferation of colorectal cancer cells 37 . In the classical (NR) state, this hypermodification interacts with the first anticodon nucleotide of the Psite tRNA, while forming a hydrogen bond with C1637 of the SSU body. This SSU head-to-body contact at positions 1191-1637 is then maintained during the transition to the rotated state (Fig. 5a). Despite its subsequent disruption due to eEF2 binding and forward head swivelingassociated translocation of P-site tRNA, m 1 acp 3 Ψ1191 maintains the interaction with tRNA and guides the ASL to the E-site while covering a distance of approximately 11 Å. Finally, as deacyl-tRNA reaches its final position and the head swivels backward, m 1 acp 3 Ψ1191 releases E-site tRNA and immediately reaches to the next P-site tRNA ready to engage in the upcoming step of translocation (Fig. 5a, Supplementary Video 5).

Our structures also revealed additional stabilization of codon-anticodon pairing in which the wyosine moiety of the hypermodified wybutosine 37 of S. cerevisiae tRNA Phe (yW37) cross-strand stacks with the first codon nucleoside paired to peptidyl-tRNA Phe (Fig. 5b). As translocation reaches the late states, tighter compactness of the peptidyl-tRNA ASL can be observed.

Wybutosine modulates this compactness by protruding further into the interior of the ASL and directly interacting with U32, which decreases the conformational flexibility of the anticodon loop 38 . Overall, these findings substantiate previous studies which showed that both the absence of yW37 and its alterations increased the ribosomal frameshifting frequency 39 while being linked to a lower survival of patients with cancer 40 .

Sordarin action and eEF2 dissociation

Reconstructions of TI-1, TI-2, TI-3, TI-4 and TI-5 revealed additional density at the interface of eEF2 domains III and V corresponding to sordarin 41 (Extended Data Fig. 7a-j). Global alignments of ribosome-bound eEF2 in early and late states of translocation suggest that the presence of sordarin has insignificant effects on the overall conformation of eEF2 5 and, more importantly, has little-to-no effect neither on the position nor the conformation of eEF2 domains I and IV relative to the 80S ribosome (Extended Data Fig. 7a-c). However, eEF2 domain III alignment indicates that sordarin bridges the domain III-V interface (Extended Data Fig. 7d-i).

Consequently, the mechanism of sordarin-induced eEF2 stalling on the 80S ribosome most likely proceeds by domain interface remodeling. Late translocation (TI-2 to TI-5) is associated with a stepwise decrease of the overall contact area between eEF2 and, both the full 80S, and the individual subunits (Extended Data Fig. 4b-d), however, the interactions of eEF2 domain II with the SSU shoulder protein uS12 expand as the entire SSU body domain rotates backward (Extended Data Figs. 1, 8a, b). Structural analyses corroborate these findings and reveal that uS12 prevents further progression of eEF2 on the SSU (Extended Data Fig. 8a). The interactions between eEF2 domain III and uS12 follow the overall decreasing trend of eEF2/80S contacts only until the penultimate translocation state TI-4, from where the contact area between domain III and uS12 increases (Extended Data Fig. 4b-d, 8b). Indeed, our structures reveal that the αhelix A of domain III swings in the direction of domain V, which in turn can trigger eEF2 dissociation from the translocating ribosomal assembly, as proposed in earlier works on non- We propose that the mechanism of sordarin action most likely consists in blocking the full remodeling of eEF2 domain III with respect to domain V, which possibly leads to eEF2 stalling on 80S, and ultimately, late translocation arrest. We cannot exclude that sordarin action on eEF2 might inhibit conformational changes of the switch loop 2 (sw2) through a similar mechanism proposed for argyrin B (ArgB) 43 (Extended Data Fig. 7g-i). As for ArgB, sordarin seems to indirectly prevent sw2 remodeling, which is expected to be necessary for eEF2 dissociation. In comparison, fusidic acid (FA), a bacterial EF-G-targeting antibiotic, binds to a distinct site vacated by the released inorganic phosphate and -unlike sordarin and ArgB -blocks eEF2 by directly stabilizing the GTP-like conformation of sw2 6 . However, in contrast to FA and ArgB, which trap the mid-translocation intermediate INT2 [START_REF] Rundlet | Structural basis of early translocation events on the ribosome[END_REF]43 , sordarin allows the eukaryotic translocating assembly to reach the late intermediate state TI-5. Finally, our TI-4 showed density for inorganic phosphate, suggesting that in the presence of sordarin, and without phosphate release or domain IV remodeling, translocation is almost fully accomplished, and a late chimeric state can be formed.

Discussion

Here we present first atomic-resolution structural information for the understanding of the mechanism of movement of the mRNA-tRNA2-growing peptide module during protein synthesis in eukaryotes. We characterize eukaryotic translocation intermediates whose existence had only been hypothesized on the basis of bacterial translocation but their reconstructions had never been reported. Our data describe how the eukaryotic translocase eEF2 is engaged by a spontaneously rotated 80S ribosome and reveal the importance of its contacts with co-evolved eukaryotespecific SSU proteins. This study reveals that the additional complexity of the eukaryotic translational apparatus, in comparison with the prokaryotic system, reflects more sophisticated and more finely regulated mechanisms of maintenance of the mRNA-tRNA2 module during its translocation through the ribosome. An extensive system of eukaryote-specific rRNA and tRNA post-transcriptional modifications, together with eEF2 and its unique post-translational modification, actively contribute to the accuracy of protein synthesis by preventing the slippage of the translational reading frame (Supplementary Video 6).

We propose that the sterically constrained environment imposed by the eukaryote-specific posttranslational modification diphthamide, in the context of domain IV conformation, not only stabilizes correct Watson-Crick codon-anticodon interactions but may uncover the erroneous peptidyl-tRNA by probing the minor groove of the codon-anticodon duplex. Therefore, this additional proofreading mechanism that prevents incorporation of an incorrect amino acid during translocation contributes to higher accuracy of protein synthesis in eukaryotes. Our reconstructions in the presence of GMPPCP demonstrated nearly complete movement of the tRNA2-mRNA module, corroborating the model in which the translocase functions as a molecular "doorstop" which uncouples the mRNA-tRNA2 movement from the thermally driven back-rotation of the SSU body/platform 23,26,27,42,44,45 . Hence, it seems that the primary role of GTP hydrolysis in translocation in all kingdoms of life is to establish an irreversible step that prevents translocase release until both tRNAs and mRNA have moved by one full codon. Such a mechanism would ensure productive translocation and efficient maintenance of the translational reading frame [START_REF] Djumagulov | Accuracy mechanism of eukaryotic ribosome translocation[END_REF][START_REF] Rundlet | Structural basis of early translocation events on the ribosome[END_REF][START_REF] Carbone | Time-resolved cryo-EM visualizes ribosomal translocation with EF-G and GTP[END_REF]25 .

Here we propose the mechanism of translocation inhibition by sordarin. The latter can bind to ribosome-associated eEF2 from the early TI-1 state and seems not to affect global eEF2 conformation or otherwise interfere with subsequent eEF2 accommodation on the ribosome. As translocation then reaches the late TI-5 state, sordarin supposedly stalls eEF2 on the ribosome by preventing domain III remodeling and ultimate dissociation from the ribosome.

Although our results provide atomic resolution information on molecular mechanisms of eukaryotic ribosome translocation, further structural studies, including time-resolved cryo-EM and biochemical investigations of mRNA-tRNA displacement through the eukaryotic ribosome, are needed to provide full understanding of the precise timing of GTP hydrolysis and Pi release, as well as translocation proofreading mechanisms that ensure accurate protein synthesis in eukaryotes.

Fig. 1: Overview of eukaryotic ribosome translocation intermediates solved by cryo-EM

a, Schematic representation of eukaryotic translocation based on high-resolution cryo-EM reconstructions of elongating 80S ribosomal complexes reported in the current study. eEF2catalyzed displacement of peptidyl-(green) and deacyl-tRNAs (yellow) from A to P, and P to E sites, respectively, is associated with SSU body domain back-rotation (dark blue to grey), and SSU head domain forward (cadet blue to violet) and backward swiveling (violet to grey). eEF2 is depicted in red, LSU is shown in grey, and dipeptide in dark grey. b, Overview of reported resolutions and cryo-EM maps, colored as in a. c, LSU alignment reveals tRNA translocation trajectories from PRE-H1 to NR depicted by light-to-dark palettes. TI-1 shows eEF2 in the recruitment phase (pink), while late translocation intermediates TI-2 to TI-5 reflect its fully accommodated state on the ribosome, e.g. TI-5 (red). mRNA is shown in magenta. d, Codon/anticodon duplex advancement displayed relative to PRE-H1 (A-site) and NR states (Pand E-sites). Alignment is performed on the SSU body domain. tRNA Phe hypermodification wybutosine (yW) at position 37 is marked with an asterisk. Positions of peptidyl-(green) and deacyl-tRNA (yellow) anticodons in chimeric states of translocation TI-2 to TI-5 relative to final positions observed in the NR state (white) and the early chimeric ap 0 /P-pe 0 /E state (PDB ID 7OSM). Individually displayed anticodon nucleotides (top to bottom in the 3' -5' direction) reveal distinct SSU sub-chimeric states: ap 1 -pe 1 (in TI-2 and TI-3) and ap 2 -pe 2 (in TI-4 and TI-5).

Extended Data Fig. 3: Nucleotide-binding pockets of eEF2 in translocation intermediates from TI-1 to TI-5.

Unfiltered, unsharpened maps (σ=3) of the nucleotide-binding pocket found in domain I of eEF2 (red). TI-1 and TI-3 show density for the non-hydrolysable analogue of GTP (GMPPCP) and switch loop 1 (sw1). GDP-containing TI-2, TI-4 and TI-5 show no density for sw1. Additional density corresponding to inorganic phosphate was identified in TI-4.

Extended

  canonical IRES-mediated translocation 42 . Recently, Carbone et al. observed a similar trend in EF-G domain III rearrangement relative to uS12 in a late bacterial translocation state where EF-G dissociation had already commenced and the GTPase domain had unbound from the ribosome 7 .

Fig. 2 : 2 a,Fig. 3 :Fig. 4 :

 2234 Fig. 2: eEF2 accommodation on the 80S ribosome and interactions of domain IV with ASL of peptidyl-tRNA in TI-1 and TI-2

Fig. 5 : 5 )

 55 Fig. 5: Role of S. cerevisiae hypermodifications m 1 acp 3 Ψ1191 of 18S and wybutosine (yW37) of tRNA Phe.

Data Fig. 4 :

 4 eEF2 interactions with the eukaryotic 80S ribosome. a, Contacts of eEF2 domains (I in green, II in magenta, III in pink, IV in red, and V in blue) with ribosomal elements of large 60S (RNA in light grey and proteins in dark grey) and small 40S subunit (RNA in light blue and proteins in dark blue) in translocation intermediate complexes TI-1 to TI-5. Sordarin is depicted in orange. b-d, Quantification of contact areas of eEF2 domains I to V with 80S, in b, large 60S subunit, in c, and small 40S subunit, in d. Eukaryote-specific interactions between eEF2 and SSU proteins eS6 and eS24 during factor recruitment in early translocation (TI-1), and eS30 once eEF2 is fully accommodated on 80S (TI-2 to TI-5). Black arrows indicate areas of eukaryote-specific contacts. Extended Data Fig. 5: Conformational adaptations of eEF2 and contact areas with the tRNA2-mRNA translocating module. a, Alignment on 25S (left) and global eEF2 alignment (right) on eEF2 in TI-5 for GMPPCP bound intermediates TI-1 and TI-3, and GDP-containing intermediates TI-2, TI-4 and TI-5. Atoms are colored on the basis of root-mean-square deviation values of atomic positions relative to TI-5. b, Buried surface measurements corresponding to contacts of the tRNA2-mRNA module with 80S ribosome (pink) and domain IV of eEF2 (red) in the course of elongation from PRE-H1 to TI-5. c, Unfiltered, unsharpened density of S. cerevisiae eEF2 (e.g. TI-4) contoured at σ = 3. Extended Data Fig. 6: mRNA path on the small subunit of the eukaryotic 80S ribosome a, Lateral view of the full 40S small subunit (SSU) of the eukaryotic 80S ribosome trapped in the PRE-hybrid-1 reconstruction (PRE-H1) reveals the path of messenger RNA (magenta) at the SSU head-body domain interface. Unsharpened, unfiltered high-resolution cryo-EM maps are shown at σ = 3.5. 18S ribosomal RNA and SSU proteins are colored in light and dark blue, respectively. b, Zoom on the thirteen nucleotide-long messenger RNA and interacting residues of 18S rRNA and the conserved SSU protein uS12. +1 indicates the first nucleotide of the start codon. c, Close-up view of the interactions between messenger RNA and ribosomal SSU elements in the PRE-H1 complex. π-π stacking is found between -1 and G1150, while the p-π effect is observed in the following interacting pairs: -3 and G904, and +3 and C1637. Extended Data Fig. 7: Effect of sordarin binding to eEF2 in the context of eukaryotic translocation a-c, Global alignments reflecting general conservation of overall eEF2 conformation during early, in a, and late states of translocation, in b and c. d-f, Domain III alignment shows displacement of eEF2 domain V towards the interface with domain III. g-I, Zoom on the sordardin binding site for respective structural superimpositions on eEF2 domain III, as shown in d-f. The arrow indicates the displacement of domain V relative to domain III. Remodeling of the switch loop 2 (sw2) has not been observed. Structural alignments are performed for late translocation states before, in b, e and h, and after GTP hydrolysis, in c, f and i. eEF2 domains are colored as follows: domain I in green, domain II in magenta, domain III in pink, domain IV in red, and domain V in blue. Unfiltered, unsharpened of sordarin is shown at σ = 4 and depicted in orange. Lighter nuances correspond to structures without sordardin, TI-1* and TI-4*. j, Chemical structure of sordarin. Extended Data Fig. 8: Interactions of eEF2 with small subunit proteins uS12 and eS30 a, Inter-domain remodeling of eEF2 and conformational changes of SSU proteins uS12 and eS30 accompanying SSU back-rotation during respective transitions between translocation intermediates TI-1 to TI-5. b, Curves depicting contacts between SSU proteins uS12 with eEF2 domains II (dark yellow) and III (orange), and eS30 with domain IV (blue).

Acknowledgments

We are grateful to the staff of the Dubochet Centre for Imaging (DCI-Lausanne) for cryoimaging and preliminary data analysis. We thank Dr. Yury Polikanov from the University of Illinois at Chicago for providing the plasmid for the over-expression of the CCA-adding enzyme.

We also thank Corinne Crucifix from the IGBMC cryo-EM platform for her expertise in grid preparation. This work was supported by "La Fondation pour la Recherche Médicale" DEQ20181039600 (to M.Y.).

Data availability

Atomic coordinates and cryo-EM maps generated during this study are available through the Protein Data Bank (PDB) and the Electron Microscopy Databank (EMDB). The complexes have been deposited under following accession codes: PRE-H1 (8CCS, EMD-16563), PRE-H2 (8CDL, EMD-16591), TI-1 (8CF5, EMD-16616), TI-2 (8CDR, EMD-16594), TI-3 (8CG8, EMD-16634), TI-4 (8CEH, EMD-16609), TI-5 (8CIV, EMD-16684), NR (8CGN, EMD-16648), TI-1* (8CKU, EMD-16702), TI-4* (8CMJ, EMD-16729).

Additional information

Correspondence and requests for materials should be addressed to G.Y. (email: gula@igbmc.fr)

the 40S small ribosomal subunit (SSU) from 0° to 11.7° relative to the 60S large subunit (LSU), SSU head-swiveling from 0° to 19.8°, as well as tRNA translocation trajectories accompanied by rearrangements of a number of intersubunit bridges and the L1 stalk (Fig. 1a-d, Extended Data Fig. 1, 2, Supplementary Fig. 1, 2a-d).

The most pronounced inter-subunit rotation of approximately 12° was observed in pretranslocation substrates, referred to as PRE-translocation-hybrid 1 (PRE-H1) and PREtranslocation-hybrid 2 (PRE-H2) complexes. These two early-stage complexes showed densities for peptidyl-tRNA in classical (A/A or A/A*), and deacyl-tRNA in hybrid P/E states (Fig. 1b, Supplementary Fig. 1). As such, the two states, determined at 1.97 Å and 2.72 Å, respectively, precede eEF2 recruitment on 80S and highlight a considerable shift of approximately 23 Å that the elbow of peptidyl-tRNA performs in its transition from A/A, in PRE-H1, to A/A*, in PRE-H2 (Supplementary Fig. 2b,c), confirming that tRNA acceptor arm movements can be uncoupled [START_REF] Carbone | Time-resolved cryo-EM visualizes ribosomal translocation with EF-G and GTP[END_REF]23,24 . The NR complex (2.28 Å) has a non-swiveled head domain with tRNAs that occupy classical P/P and E/E states (Fig. 1a, b, Extended Data Fig. 1, Supplementary Fig. 1).

Although no interactions between mRNA E-codon and tRNA fMet anticodon were found in NR, the latter displays final positions of tRNA translocation and thus reflects a POST-translocation state (POST).

Translocation intermediates 1 to 5 (TI-1 to TI-5) were determined in the presence of sordarinbound native S. cerevisiae eEF2 (2.04-2.71 Å), while TI-1* and TI-4* complexes were reconstructed in the absence of the inhibitor (Fig 1a,b, Extended Data Tables 1,2, Supplementary Table 1). TI-1, TI-1*, TI-3 and TI-4* were captured by GMPPCP, while TI-2, TI-4 and TI-5 were obtained from a single set of conditions in the presence of GTP and showed density for its hydrolyzed, GDP, form. Furthermore, we observed additional density in TI-4 corresponding to inorganic phosphate, Pi (Extended Data Fig. 3). The sequence of translocation events was reconstructed based on observed conformations of SSU domains (body and head rotation) and the exact positions of tRNAs and the L1 stalk (Extended Data Fig. 1, Supplementary Fig. 1, 2a-d, Supplementary Videos 1, 2,). Accordingly, TI-1 was defined as the earliest, while TI-5 represented the latest intermediate of eukaryotic translocation.

TI-1 and TI-1* are -to our knowledge -the first-ever visualized structures of an early eukaryotic ribosome translocation assembly, reflecting eEF2 recruitment events on 80S. Translocase

Methods

Purification of S. cerevisiae 80S ribosome

S. cerevisiae 80S ribosomes were purified from the JD1370-∆Stm1 strain [START_REF] Pellegrino | Structural Insights into the Role of Diphthamide on Elongation Factor 2 in mRNA Reading-Frame Maintenance[END_REF] following a previously published protocol with minor modifications [START_REF] Ben-Shem | The structure of the eukaryotic ribosome at 3.0 A resolution[END_REF] . After cell disruption, ribosomes were isolated by PEG 20,000 precipitation between 4 % and 8.5 % w/v and purified on 15-30 % w/v sucrose gradients (20 mM HEPES/KOH pH 7.5, 120 mM KCl, 10 mM MgCl2, 10 % w/v sucrose, 2 mM DTT, 0.37 mM EDTA, 2.5 mM spermidine). The peak of 80S ribosomes was pooled, precipitated by PEG 20,000 and subsequently re-dissolved in buffer G (10 mM HEPES/KOH pH 7.5, 50 mM CH3COOK, 10 mM NH4Cl, 5 mM (CH3COO)2Mg, 2 mM DTT).

Purification of endogenous S. cerevisiae eEF2

Native eEF2 was isolated from the S. cerevisiae JD1370-∆Stm1 strain according to a previously reported protocol 47 with some modifications. Following microfluidizer cell disruption and lysate dialysis, eEF2 was purified on HiLoad® SP Sepharose® and Q Sepharose®, after which the sample was applied to a HiLoad® 16/600 Superdex® 200 pg gel filtration column (all from GE Healthcare). Eluted eEF2 fractions were concentrated and stored in 20 mM HEPES/KOH pH 7.5, 10 % v/v glycerol, 5 mM MgCl2, 1 mM DTT, 100 mM KCl.

Purification and aminoacylation of tRNAs

Amino-tailing of S. cerevisiae tRNA Phe (replacement of the 3'-terminal A76 nucleotide carrying the 3'-OH group with the one carrying 3'-NH2) was performed as previously reported 48 with some modifications. A mixture containing 40 μM deacylated native S. cerevisiae tRNA Phe (Sigma-Aldrich), 1 mM 3'-amino-3'-deoxyadenosine-5'-O-triphosphate (Biolog Life Science Institute GmbH), 1 mM sodium pyrophosphate (Sigma-Aldrich), 70 μM CCA-adding enzyme, 10 mM MgCl2, 100 mM glycine/NaOH pH 9, 1 mM DTT was incubated at 37°C for one hour and 20 minutes. The reaction was terminated by addition of EDTA to 20 mM, treated with 1:1 phenol-chloroform mixture and precipitated with ethanol. The pellet was washed two times, dissolved in 30 µL of 10 mM Hepes/KOH pH 7.5 and purified on a Sephadex ® G-25 spin column (Sigma-Aldrich). The resulting, full-length, S. cerevisiae 3'-NH2-tRNA Phe was enzymatically acylated with phenylalanine as previously described 49 with minor modifications.

S. cerevisiae Phe-N-tRNA

Phe was purified on a Waters™ C4 column (Delta-Pak C4, 300Å, 5 μm, 3.9 mm X 150 mm, 1K -30K, 1/pk) by applying a linear ethanol gradient (as reported in [START_REF] Mesters | Complete Purification of Transfer-Rna, Charged or Modified with Hydrophobic Groups, by Reversed-Phase High-Performance Liquid-Chromatography on a C-4 C-18 Column System[END_REF] ) and stored in 20 mM CH3COONH4 pH 5.

Following purification of its overexpressed form, E. coli initiator tRNA fMet was aminoacylated and formylated according to previously published protocols [START_REF] Mechulam | Protection-based assays to measure aminoacyl-tRNA binding to translation initiation factors[END_REF] . The reaction mix was phenolextracted and the aqueous phase was applied to a TSKgel® Phenyl-5PW column (Tosoh bioscience). Purified fractions of fMet-tRNA fMet were stored in 20 mM CH3COONH4 pH 5.

Formation of 80S ribosome translocation complexes

For reconstitution of translocation complexes 80S/tRNA2/mRNA/eEF2/GMPPCP or 80S/tRNA2/mRNA/eEF2/GTP, S. cerevisiae 80S ribosomes (2.2 µM) and 39 nucleotide-long mRNA (5'-AAAAGAAAAGAAAAGAAAAUGUUUUUUGAAGAAAAGAAA-3', Dharmacon) (10.8 µM) were incubated at 30°C for 10 minutes in 10 mM HEPES/KOH pH 7.5, 50 mM CH3COOK, 10 mM NH4Cl, 5 mM (CH3COO)2Mg, 2 mM DTT. E. coli fMet-tRNA fMet (10.8 µM) and S. cerevisiae Phe-N-tRNA Phe (10.8 µM) were then added in two steps and incubation continued for 5 and 3 minutes, respectively. Separately, S. cerevisiae eEF2 (10.8 µM) was incubated either with GMPPCP (255 µM) or GTP (255 µM) for 10 minutes at room temperature. Each of the two eEF2 mixtures was then added to the ribosome mix and buffer conditions were re-adjusted to 10 mM HEPES/KOH pH 7.5, 50 mM CH3COOK, 10 mM NH4Cl, 6 mM (CH3COO)2Mg and 1.25 mM DTT. Additionally, if present, sordarin (Sigma-Aldrich) was added at this stage to a final concentration of 100 μM. The last incubation step proceeded for another 10 minutes at 30°C.

Cryo-EM grid preparation and data collection

Following complex formation, 3 μL of sample were applied to glow-discharged Ultrathin Carbon Quantifoil® R 2/2 on 300 gold mesh (Jena Bioscience) using a Mark IV Vitrobot™ (Thermo Fisher Scientific). Incubation of grids at 9°C and 95% humidity lasted for 30 seconds and was immediately followed by blotting and flash freezing in liquid ethane, pre-cooled to the liquid nitrogen temperature. Grid screening was performed on a 200 kV Glacios transmission electron microscope (Thermo Fisher Scientific) equipped with a K2 Summit direct electron detector (Gatan).

Single molecule datasets were acquired at the Dubochet Center for Imaging of EPFL and the University of Lausanne (DCI-Lausanne) on a 300 kV Titan Krios G4i transmission electron microscope (Thermo Fisher Scientific) equipped with a Cold FEG emission gun, SelectrisX energy filter and a Falcon IV direct electron detector. Datasets were collected using the EPU automated software (Thermo Fisher Scientific) and a pixel size at detector of 0.450 Å/pix (for eEF2/GMPPCP and eEF2/GTP datasets with sordardin) and 0.726 Å/pix (for the eEF2/GMPPCP dataset without sordarin). Total electron exposure was set to 60 e -per Å 2 for the eEF2/GTP/sordarin dataset and 40 e -per Å 2 for both eEF2/GMPPCP and eEF2/GMPPCP/sordarin datasets.

Cryo-EM data processing of the 80S/eEF2/GTP/sordarin elongation complex

Cryo-EM image processing was performed using cryoSPARC [START_REF] Punjani | cryoSPARC: algorithms for rapid unsupervised cryo-EM structure determination[END_REF] . Raw micrographs were motioncorrected, and CTF estimation was carried out. A total of 616,978 particles were auto-picked and extracted with fourier cropping 4 times (bin4 data). Several rounds of 2D classification were performed, and an ab initio structure was reconstructed and used for initial 3D variability analysis 53 . The resulting volumes were subjected to heterogeneous refinement against a total of 442,508 particles from selected 2D classes. This resulted in four structures, each representing different rotational states of the 40S subunit. Three meaningful classes were selected and subjected to additional 3D variability analysis, resulting in three subclasses for each class.

The first class consisted of 170,386 particles with the fully rotated 40S subunit. Its first subclass contained both deacyl-and peptidyl-tRNAs, but no eEF2. This sub-population was re-extracted (bin2), and homogeneous refinement yielded the PRE-H1 complex (55,455 particles). Although two other subclasses contained the elongation factor and were refined to high resolution, they were not further examined due to the absence of peptidyl-tRNA.

The second class of 133,186 particles with a semi-rotated 40S subunit resulted in subclasses, all of which contained deacyl-and peptidyl-tRNAs and eEF2. Particle re-extraction (bin2), followed by respective homogeneous refinements, resulted in two intermediate translocation structures, TI-2 (58,531 particles) and TI-4 (55,762 particles).

Finally, the third class with 133,186 particles and a non-rotated 40S subunit also yielded three subclasses. The first subclass possessing only tRNAs was pooled and local refinement yielded the NR complex (21,458 particles). Two remaining subclasses contained clear density for eEF2.

The meaningful class (51,517 particles) was subjected to additional 3D variability analysis and a well resolved sub-population was re-extracted (bin2) and processed by homogenous refinement which yielded the TI-5 complex (23,773 particles).

Cryo-EM data processing of the 80S/eEF2/GMPPCP/sordarin elongation complex

Raw micrographs were motion corrected and CTF estimated [START_REF] Punjani | cryoSPARC: algorithms for rapid unsupervised cryo-EM structure determination[END_REF] . 514,460 particles were autopicked and extracted with fourier cropping 4 times (bin4). Two rounds of 2D classification were performed, good 2D classes were selected and 393,786 particles were re-extracted. Consensus homogenous refinement was performed, and the volume was applied to 3D variability analysis 53 .

The class with the rotated 40S subunit (42,053 particles) was subjected to 3D variability analysis which resulted in four subclasses. Only the subclasses possessing density for both tRNAs and eEF2 were selected, particles were re-extracted (bin2) and homogenous refinement yielded the TI-1 complex (23,096 particles).

Classes with the semi-rotated 40S subunit were combined and run through 3D variability analysis yielding five subclasses. Three of the five subclasses showed strong density for both tRNAs and eEF2. They were pooled together, particles were re-extracted (bin2) and refined, yielding the TI-3 complex (73,086 particles).

Cryo-EM data processing of the 80S/eEF2/GMPPCP elongation complex

Raw micrographs were motion corrected, CTF estimated, particles were auto-picked and extracted with fourier cropping 4 times (bin4). Selected 2D classes yielding 561,498 particles were used to refine the initial volume. Next, particles were subjected to 3D variability analysis and separated either on the basis of 40S subunit rotation (workflow 1) or presence of strong density of tRNA and eEF2 ligands (workflow 2).

In workflow 1, the population containing rotated 40S (157,099 particles) was re-extracted (twofold binned) and subject to a new round of 3D variability analysis. One of the resulting subclasses contained deacyl-and peptidyl-tRNAs, but no elongation factor 2. Particles were re-extracted without fourier cropping (fully un-binned, bin1) and supplied to homogenous refinement which yielded the PRE-H2 structure (68,945 particles). The second subclass with the non-rotated 40S (118,986 particles) was re-extracted and subjected to 3D variability analysis, and only the sub-population with strong tRNA density was pooled. Particles were then reextracted (bin2) and applied to homogenous refinement which yielded the TI-4* complex (41,878 particles).

In workflow 2, 276,089 particles possessing strong tRNA and eEF2 density were selected from initial 3D variability analysis. Following, two series of additional 3D variability analysis, only particles with strong ligand density were pooled. This sub-population was re-extracted (bin2) and supplied to homogenous refinement which yielded the TI-1* complex (22,551 particles).

Model building and refinement

PDB ID 7OSM was split into 60S, 40S body and head domains, eEF2 and deacyl-tRNA. Submodels were then rigid fitted into cryo-EM maps using the fitmap command in ChimeraX [START_REF] Goddard | UCSF ChimeraX: Meeting modern challenges in visualization and analysis[END_REF][START_REF] Pettersen | UCSF ChimeraX: Structure visualization for researchers, educators, and developers[END_REF] .

Messenger RNA, peptidyl-tRNA, dipeptide, sordarin and ribosomal RNA modifications were built de novo in COOT. Several cycles of manual building in COOT and real space refinement in Phenix [START_REF] Terwilliger | Improved crystallographic models through iterated local densityguided model deformation and reciprocal-space refinement[END_REF][START_REF] Liebschner | Macromolecular structure determination using X-rays, neutrons and electrons: recent developments in Phenix[END_REF] were then performed for each model. Restraints were generated using the ELBOW algorithm integrated in the Phenix suite [START_REF] Moriarty | electronic Ligand Builder and Optimization Workbench (eLBOW): a tool for ligand coordinate and restraint generation[END_REF] .

Model superimpositions and motion measurements

Models were superimposed using the mmaker command integrated in ChimeraX. Per-residue root mean square deviation (RMSD) values for individual chains were calculated in ChimeraX using the rmsd command. RMSD calculations of entire 40S subunits were performed in PyMOL using the colorbyrmsd script (The PyMOL Molecular Graphics System, Version 2.0 Schrödinger, LLC.). Rotation measurements and axis projections were generated using the measure rotation command in ChimeraX. Contact areas were quantified by applying the measure buriedarea command and default parameters for solvent-accessible surface calculations available through ChimeraX.

Author contributions


Sp C Onference Series

V O Lu M E

D B Onneau

O C Hesneau

D M Ourard

P Stee

U niv. N H Fizeau

Sophia A Ntipol Is,C N R S

Spectro-interferom etric observations of interacting

A bstract. W e obtai ned spectro-i nterferom etri c observati onsi n the vi si bl e of Lyrae and Sgr usi ng the i nstrum ent V EG A ofthe C H A R A i nterferom etri c array. For Lyrae,the di spersed fri nge vi si bi l i ti es and di erenti alphases were obtai ned i n spectralregi ons contai ni ng the H and H eI 6678 l i nes and the H and H eI 4921 l i nes. W hereas the source i s unresol ved i n the conti nuum , the source ofthe em i ssi on l i nes i s resol ved and the photocenter ofthe bul k ofthe H em i ssi on exhi bi ts o sets correl ated w i th the orbi talphase. For Sgr,both the conti nuum and H sources are resol ved,but no cl ear bi nary si gnali s detected. T he di erenti alphase shi ft across the l i ne reveal s that the bul k ofthe H em i ssi on i s cl earl y o set from the pri m ary.

P resentation of the C H A R A array and the V E G A instrum ent

H i gh angul ar resol uti on observati ons by opti cal l ong basel i ne i nterferom etry, com bi ned w i th cl assi cal techni ques l i ke photom etry and spectroscopy provi de deep i nsi ght on the m orphol ogy of the m assi ve i nteracti ng bi nari es and new constrai nts for thei r m odel i ng. H ere we present the rst spectro-i nterferom etri c observati ons of the i nteracti ng m assi ve bi nari es Lyr and Sgr carri ed out w i th thei nstrum entV EG A on theC H A R A i nterferom etri c array. T heC H A R A1 i nterferom etri c array wasconstructed by theC enterforH i gh A ngul arR esol uti on (G eorgi a State U ni versi ty, A tl anta) (B rum m el aar et al . 2005). Located at the M ountW i l son observatory (C al i forni a),i ti sform ed by si x 1m tel escopes pl aced by pai rs on an Y shaped basel i ne. B ase l engths of 34 m to 330 m al l ow to reach an angul ar resol uti on =B up to 1: 0 m as at near i nfrared wavel engths or 0: 3 m as i n the vi si bl e. T he V i si bl e spEctroG raph and pol A ri m eter (V EG A ) of the C ôte d' A zur O bservatory i s a beam com bi ner operati ng i n the vi si bl e range [ 0: 45 0: 85 m ]and o ers three spectralresol uti ons (R = 30000;5000;1700). It i sdesi gned to record si m ul taneousl y the spectral l y di spersed i nterference fri nges w i th two photon counti ng detectors l ooki ng at two di erent spectral bands. A pol ari m etri c devi ce can be i nserted to record the pol ari zed fri nges. V EG A currentl y recom bi nes2 beam sbut3 and 4 beam srecom bi nati on i sforeseen. T he data reducti on process al l ow s to m easure the squared vi si bi l i ty m odul us V 2 or the com pl ex di erenti alvi si bi l i ty V e i' asa functi on ofthe wavel ength. Spectroi nterferom etri c observati ons w i th the V EG A i nstrum entare dedi cated to stel l ar physi c program s for the determ i nati on offundam entalstel l ar param eters or the 2 study ofstel l ar acti vi ty and ci rcum stel l ar envi ronm ent. A detai l ed descri pti on ofthe V EG A i nstrum ent i s gi ven by M ourard et al . (2008).

Lyrae

Lyr (H D 174638) i s a 12. 9 d spectroscopi c and ecl i psi ng bi nary w i th evi dence ofci rcum stel l ar m atter w i thi n and around the system . Fi rst i nterferom etri c observati onshave been carri ed outi n 1994 w i th theG I2T i nterferom eterduri ng the m ul ti -techni que cam pai gn devoted to the study ofthi s system (H arm anec et al . 1996). T he com bi ned anal ysi s ofthe spectro-i nterferom etri c,spectroscopi c and photom etri c observati ons l ead to the concl usi on that the source ofthe H and H eI em i ssi on l i nes can be associ ated w i th m ateri al s outsi de the orbi talpl ane (jet l i ke structure) ofthe bi nary. In 2005,the rst reconstructed i m ages ofthe H em i ssi on atl ow spectralresol uti on were obtai ned by di erenti alphase referenci ng w i th the N PO Ii nterferom eter (Schm i dtt et al . 2009). T he rst resol ved i m agesofthecoreofthesystem ,theecl i psi ng bi nary,wereobtai ned i n 2007 from near i nfrared observati ons (H band) w i th the M IR C beam com bi ner,thanks to the use ofthe l ongest basel i nes ofthe C H A R A array. T he el em ents ofthe relati ve orbi t of Lyr have been deri ved from these i nterferom etri c observati ons (Zhao et al . 2008).

T he observati ons of Lyr was dedi cated to study ofthe m orphol ogy and the ki nem ati c of the H regi on. T hey were carri ed out duri ng four ni ghts i n 2008 (orbi talphases 0. 5, 0. 8, 0. 9 & 0. 2) w i th the m edi um spectralresol uti on. For the observi ng dates the expected behavi or of Lyr can be predi cted usi ng the ephem eri sfrom A k etal . ( 2007)and the el em entsofthe rel ati ve orbi t (Zhao etal . 2008). T he observati onsof Lyrwere bracketed by these ofthe cal i brator Lyr. W i th the 34 m S1S2 basel i ne,the angul ar resol uti on was 4. 0 or 3. 0 m as around H and H ,respecti vel y. T he di recti on ofthe basel i ne projected onto the sky were nearl y perpendi cul ar to the orbi talpl ane. T he data anal ysi s have been done usi ng the m easurem ents ofsquared vi si bi l i ty m odul us i n conti nuum spectralbandsand di erenti alvi si bi l i ty m easurem entsaround the spectrall i nes H and H eI6678 (R = 1650) or H and H eI4921 (R = 1225).

In the spectralconti nuum ,the bi nary Lyri s unresol ved as expected from the short basel i ne used and the ori entati on ofthe orbi t. In the H l i ne,at any orbi talphase,the di p ofthe vi si bi l i ty m odul us show s that the source i s si gnicantl y resol ved. T he di erenti alphase exhi bi ts a si gnali n the l i ne i ndi cati ng a shi ft of the source photocenter correl ated w i th the orbi talphase. In H eI6678 l i ne,the source i s m argi nal l y resol ved at any orbi talphases but no cl ear photocenter shi ft i s detected. For the H l i ne,the source i s resol ved at som e orbi tal phases and there i s som e suspi ci ons of a photocenter shi ft. For the H eI4921 l i ne,there i s no si gnalabove the noi se. W ork i s i n progress to determ i ne the true extensi on of the H em i tti ng source and i ts l ocati on i n the system . T hese resul ts w i l l be com pared w i th those ofthe observati ons of Lyr w i th N PO I(Schm i tt et al . 2009),taki ng i nto account thei r l ow spectralresol uti on (R 40).

Sagittarii

Sgr (H D 181615) i s the bri ghtest ofthe extrem el y hydrogen-de ci ent bi nari es stars (H dB stars), know n as a 137. 9 d spectroscopi c bi nary. A new orbi tal sol uti on and a betterunderstandi ng ofthethecharacteri sti csofthi ssystem were obtai ned from spectroscopi c m oni tori ng (K oubsk y et al . 2006). T he presence of ci rcum stel l ar m atter i n the Sgr system i s evi denced by the com pl ex H absorpti on/em i ssi on pro l es and by a strong i nfrared excess. T he rst m i d-IR i nterferom etri c observati ons of Sgr were carri ed out usi ng the M ID I/V LT I i nstrum ent (N etol i ck y et al . 2009). T he dusty ci rcum bi nary di sk i s resol ved i n the N band w i th a typi calsi ze of20 x 14 m as,an i ncl i nati on i' 50 and a posi ti on angl eP A ' 80 .U si ng theseval uesto constrai nttheorbi talparam eters cl earl y con rm that Sgr i s a m assi ve bi nary w i th a totalm ass > 15 M .

T he observati ons of Sgr were carri ed out duri ng three ni ghts i n 2008 (orbi talphase 0. 06-0. 09) w i th the m edi um spectralresol uti on i n spectralband centered on 660 nm . T he appearance of Sgr (rel ati ve posi ti on ofthe com ponents,l ocati on ofthe H em i ssi on)atthe observi ng datescan be predi cted w i th som e accuracy usi ng the orbi talel em ents (K oubsk y etal . 2006 and N etol i ck y et al . 2009). W i th a l um i nosi ty rati o > 100 thecom pani on i sexpected to beal m ost unseen (D udl ey & Je ery 1990). A 23 m S1S2 basel i ne ( =B ' 5: 9 m as) cl ose to the N -S di recti on wasm ai nl y used and som e data were al so recorded w i th the E-W 100 m W 1W 2 basel i ne ( =B ' 1: 4 m as). T he observati ons of Sgr were bracketed by these ofthe cal i brators Sgr and C ap. For the S1S2 basel i ne, the data anal ysi s can been done usi ng the di erenti al spectrali nterferom etri c anal ysi s(bi nned R = 660)around theH l i ne. M odul usvi si bi l i ty m easurem ents were al so done i n the conti nuum ( = 13 nm at = 641;656 & 666 nm ) for the two basel i nes.

In thespectrum of Sgr,theH l i neexhi bi tsa ' P C ygni 'pro l easexpected at thi s orbi tal phase from K oubsk y et al . (2006). For the two basel i nes, the source appears al m ost resol ved i n the conti nuum . For the S1S2 basel i ne,a di p of the vi si bi l i ty associ ated w i th a shi ft of the di erenti al phase of ' 25 i n the H l i ne show s that the em i tti ng source i s wel lresol ved and di spl aced from the conti nuum source. Prel i m i nary concl usi ons can be draw n from these rst resul ts. A bout 10-20% ofthe total ux m ay com e from an over-resol ved source and 90-80 % from a com pact source. T he extended source coul d be rel ated to the di use l i ghtfrom the i nnerri m ofthe dusty ci rcum bi nary di sk.T he com pact source i s probabl y dom i nated by the ux ofthe bri gth com ponent. T he source associ ated w i th the H em i ssi on i s resol ved and i ts photocenter seem s to be l ocated between the two com ponents as expected by K oubsky et al . (2006). N o si gn ofbi nari ty i s evi denced probabl y because ofthe di erence of ux between com ponents.

W orksare i n progressto esti m ate the true H extensi on and to convertthe phase shi ft i nto photocenter posi ti on ofthe H bul k em i ssi on. Lyr. B ottom : Sgr Left: spectrum recorded by V EG A .R i ght: resul t of the di erenti alvi si bi l i ty anal ysi s. N ote that the l i ne i ntensi ty can be bi ased due to a l ocalsaturati on e ect ofthe photon counti ng cam era. com pact sources i n general ,and m assi ve i nteracti ng bi nari es. To go further i n the study ofthese com pl ex system s,the next step w i l lbe to carry out observati ons at l onger basel i nes to resol ve the bi nary system and al so m ul ti -basel i nes observati ons to m ore stongl y constrai n the m orphol ogy ofthese sources.

C onclusion

T hese rstV EG A /C H

A cknow ledgm ents. V EG A /C H A R A observati onswere possi bl e thanksto the strong support ofthe C H A R A team . O ur parti ci pati on at thi s conference have been supported by the C N R S i nternati onalcol l aborati on program "France -R epubl i que T ch eque"(PIC S 4343) and the French program for stel l ar physi cs (PN PS).

R eferences

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  A R A observati ons of Lyr and Sgr show the potenti al ofthi si nstrum entand the spectro-i nterferom etry techni que forthe study ofhot Fi gure 1. Exam pl e of i nterferom etri c observati ons around H l i ne. Top:

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