Dave Brain

Ofer Cohen

Kevin France

Yoshifumi Futaana

Alex Glocer

Mats Holmstrom Parker Hinton

François Leblanc

Yingjuan Ma

Ennio R Sanchez

Neesha R Schnepf

Robert J Strangeway

The Influence of Planetary and Stellar Characteristics on Atmospheric Escape and Habitability. (Whitepaper #037 in the Decadal Survey

  L'archive ouverte pluridisciplinaire

I. Motivation

'Atmospheric escape' is a catch-all term that refers to several distinct processes that provide sufficient energy to particles in planetary atmospheres that they escape to space. We know that planetary atmospheres lose particles to space over time, based both on direct observations and the telltale chemical signatures that escape processes create in atmospheres. This evidence indicates that escape can play an important role in the history of a planet's atmosphere and surface habitability by influencing the evolution of atmospheric abundance and composition.

Presently, scientists who study escape processes at Earth, solar system planets, and exoplanets employ varied strategies to estimate atmospheric escape rates, often focusing on a single planet, process, or set of physics in isolation. This fractured approach has prevented a comprehensive understanding of how atmospheric escape works at any planet, with the result that our understanding of escape at all planets is deficient. For example:

• It is unclear whether a planetary magnetic field inhibits atmospheric escape

• The community does not have consensus on what fraction of outflowing ions ultimately escape Earth's magnetosphere

• The role that atmospheric escape played in the divergent climate histories of Venus, Earth, and Mars is not well understood

• The interaction of Earth's atmosphere with the near-Earth space environment during periods of geomagnetic reversal is a poorly-explored topic

• We are not certain which of the thousands of detected exoplanets (orbiting a wide variety of stars) are likely to retain atmospheres

We argue that a major scientific goal for the next decade, then, should be to bring together observers, modelers, and theoreticians from the terrestrial, planetary, and exoplanetary communities in order to determine what properties of a planet and its host star lead to escape (or retention) of an atmosphere. Working together, these communities should develop common tools, approaches, and understanding that allow answers to the questions posed above. A key aspect of this work should be the evaluation of uncertainty in estimates of atmospheric escape. Though the topic is broadly interdisciplinary in its nature, the escape processes themselves are heliophysics processes that have been the subject of study for many decades. The heliophysics community should therefore take the lead in organizing the community around this exciting topic.

II. Current State of the Field

In broad terms, any particle near the top of an atmosphere (where collisions are rare) can escape a planet's gravity if it is given enough energy and is directed "upward" [see reviews of atmospheric escape processes in, e.g., [START_REF] Moore | Stellar ablation of planetary atmospheres[END_REF][START_REF] Brain | Atmospheric escape from unmagnetized bodies[END_REF].

Energy can be imparted by several different processes, depicted in Figure 1. For neutral particles, escape energy can come from heating by solar photons (thermal escape), from chemical reactions (photochemical escape), or from collisions (sputtering). Since ions are charged particles, they have access to additional important sources of energy through interactions with electric fields. If enough energy is deposited in an upper atmosphere (typically through solar photons) then atmospheric particles can escape as a fluid (hydrodynamic escape). Each escape process can be relevant for a planet's atmosphere in different ways -the processes can have differing results for different atmospheric species and at different times in a planet's history. For example, thermal escape is important only for hydrogen at Venus, Earth, and Mars. Photochemical escape results in the direct escape of oxygen, but only at Mars due to its low escape velocity relative to Earth or Venus. Sputtering is not an escape process today for any species at Venus, Earth, or Mars, but appears to have been important in the past at Mars for heavy noble gases such as Argon. , and H + (all climatically important) at Venus, Earth, and Mars. Hydrodynamic escape is thought to have been responsible for removal of the primordial H and He atmospheres of all terrestrial planets early in solar system history.

Observations relevant to atmospheric escape have been made since the earliest spacecraft missions in the 1960's. Neutral escape (hypothesized as early as 1846) was inferred from UV observations of the upper atmospheres of Mars and Venus [e.g. [START_REF] Barth | Ultraviolet Emissions Observed near Venus from Mariner V[END_REF][START_REF] Mcelroy | Molecular Hydrogen in Atmosphere of Mars[END_REF][START_REF] Barth | Mariner-6 -Untraviolet Spectrum of Mars Upper Atmosphere[END_REF][START_REF] Anderson | Mariner-6 and Mariner-7 Ultraviolet Spectrometer Epxeriment -Analysis of Hydrogen Lyman-Alpha Data[END_REF]. Ion escape/outflow was first measured at Earth [START_REF] Shelley | Satellite Observations of Energetic Heavy-Ions during a Geomagnetic Storm[END_REF], followed by Venus, comets, Mars, Titan, and Pluto [e.g. Mihalov, 1980;[START_REF] Balsiger | Ion Composition and Dynamics at Comet Halley[END_REF][START_REF] Gloeckler | Cometary Pick-up Ions Observed near Giacobini-Zinner[END_REF][START_REF] Lundin | 1st Measurements of the Ionospheric Plasma Escape from Mars[END_REF][START_REF] Gurnett | The Structure of Titans Wake from Plasma-Wave Observations[END_REF][START_REF] Mccomas | Pluto's interaction with the solar wind[END_REF]. Figure 2 shows ion measurements from Earth, Venus, and Mars to scale. [START_REF] Nilsson | Heavy Ion Energization, Transport, and Loss in the Earth's Magnetosphere[END_REF] in a cylindrical coordinate system. Analogous maps of escaping O + flux from Venus [START_REF] Fedorov | Comparative analysis of Venus and Mars magnetotails[END_REF] and Mars [START_REF] Ramstad | Global Mars-solar wind coupling and ion escape[END_REF] are inlaid with the same scale. Escape flux estimates vary by study, but all lie within about an order of magnitude of each other, sparking debate about the importance of a magnetic field. Figure courtesy R. Ramstad. In parallel with observations, models of different escape processes have progressed over the past five decades. The sophistication of models has increased with time, spurred by increases in computational resources and by new observations that reveal important physics that influences escape rates. The community now has a variety of models for the atmospheric reservoirs for escape (thermosphere, ionosphere, exosphere) as well as the escape processes themselves (thermal, photochemical, ion, sputtering, and hydrodynamic escape). These models have become sufficiently sophisticated that there are now typically planet-specific versions of models. For example, one can find separate 3D thermosphere models for Earth, Venus, Mars, Jupiter, Titan, and exoplanets -and in most cases there are multiple examples of each. This situation has both advantages and disadvantages. Competing models can be compared with each other, providing increased confidence in a result when models agree, and a jumping-off point for further investigation when they disagree. It is difficult, however, to develop a unified understanding of atmospheric escape processes that bridges different planets.

In recent decades there has been increased attention on the influence of stellar characteristics (e.g. solar EUV flux, solar wind, flares and CMEs) on atmospheric escape rates. However, the "one planet at a time" nature of both spacecraft observations and existing models has made synthesis of the lessons learned at each planet difficult, and has made studies of the influence of planetary characteristics on atmospheric escape virtually impossible. Understanding of the influence of both stellar and planetary properties on atmospheric escape is required to answer the big picture questions posed in Section I, and is essential for understanding which exoplanets are most likely to retain habitable atmospheres.

A particularly intriguing planetary characteristic that may influence escape is the presence of a global dipole magnetic field. [START_REF] Mcelroy | Upper Atmosphere of Venus[END_REF] first proposed that planetary magnetic fields inhibit atmospheric escape, and evidence from atmospheric isotopes [e.g. Donahue et al., 1982;[START_REF] Owen | Deuterium on Mars -the Abundance of Hdo and the Value of D/H[END_REF] and some spacecraft observations of escape [START_REF] Wei | Enhanced atmospheric oxygen outflow on Earth and Mars driven by a corotating interaction region[END_REF][START_REF] Jakosky | Loss of the Martian atmosphere to space: Present-day loss rates determined from MAVEN observations and integrated loss through time[END_REF] have lent support for this idea, which became prevailing wisdom for several decades. The idea that planetary scale magnetic fields lead to reduced escape rates has been questioned over the past decade or more. One of the first to propose that magnetic fields do not protect atmospheres was [START_REF] Strangeway | Does a Planetary-Scale Magnetic Field Enhance or Inhibit Ionospheric Plasma Outflows?[END_REF], who noted that the reported ion escape rates at Venus, Earth, and Mars agree to within about an order of magnitude (Figure 3). It may be that an intrinsic magnetic field encounters more power from the solar wind than an unmagnetized planet due to the large size of the magnetosphere relative to the planet, and that solar wind energy is transferred along magnetospheric field lines to the top of an atmosphere in the cusp regions, possibly resulting in more ion escape than results in the absence of a global field. Initial modeling investigations suggest that neither argument is fully correct. Atmospheric ion escape is not purely correlated or anti-correlated with increasing planetary magnetic field strength. Instead, these global plasma models hint that atmospheric escape rates are maximized for intermediate magnetic field strengths [e.g. [START_REF] Sakai | Effects of a Weak Intrinsic Magnetic Field on Atmospheric Escape From Mars[END_REF][START_REF] Egan | Planetary Magnetic Field Control of Ion Escape from Weakly Magnetized Planets[END_REF][START_REF] Sakata | Effects of an intrinsic magnetic field on ion loss from ancient Mars based on multispecies simulations[END_REF]. Too strong a magnetic field prevents outflowing planetary ions from escaping the system, while too weak a magnetic field results in planetary ions being accelerated by the solar wind back into the atmosphere. However, these models do not yet capture all of the relevant physics, and are often limited by computational resources to relatively weak planetary magnetic field strengths.

III. Needs

Our goal is to understand atmospheric escape as a suite of interconnected heliophysics processes that occur at all planets, and to understand how the different characteristics of stars and planets, in combination, influence whether escape is significant. In other words, we want to move the community from a "How does this apply to my planet of interest?" mindset to a more holistic approach where each planet is considered in its region of a larger parameter space. To accomplish this we have identified three main needs in the next decade. They are described here without regard to priority -an ideal outcome would be comparable progress in all three areas.

A. Development and validation / verification of models that bridge the gap between currently siloed communities

Physics-based models provide a powerful means of computing escape rates from planets. Unlike spacecraft data, models can tell us about the entire system at any given moment and for a variety of conditions, and can be used to probe the physics responsible for energizing and removing atmospheric particles. Models can vary a single parameter (e.g. the composition of the atmosphere, the luminosity of the star) to determine its influence on the system. Useful models include all physical processes which may influence the modeled escape rate. They are validated by observations where it is possible to do so, and verified against theory and/or other models where it is not possible to validate (i.e. outside the range of parameters for which observations are available). Model verification is especially important when considering exoplanets, where few direct observations of escape are available.

Over the past few decades the communities that study atmospheric escape from Earth and other planets have diverged in their modeling tools and approach, driven by key differences in the objects that they study.

One notable example is how ion escape is modeled at unmagnetized planets vs. at Earth. For unmagnetized planets, where the solar wind interacts directly with the upper atmosphere, an ionosphere needs to be included self-consistently in order to properly simulate the interaction process and reproduce observed features [e.g. [START_REF] Ma | A global multispecies single-fluid MHD study of the plasma interaction around Venus[END_REF].

For magnetized planets, modeling ion outflow is an extremely challenging task, and fully self-consistent models for Earth are currently not feasible. A major reason for this is the difficulty in simulating plasma motion in strong magnetic fields (Alfvén speed scales with magnetic field strength, requiring a small timestep that makes long-term calculation difficult) [Toth et al., 2012]. As a result, most Earth magnetosphere models have a lower boundary that is well above the ionosphere, and separate models for the ionosphere and magnetosphere must be coupled to compute escape rates. Glocer et al.

[2018] only recently presented the first two-way coupled ionospheric outflowmagnetosphere model for Earth that includes kinetic ion effects.

Steady advances in computational resources over the past decade or so have made it possible for global models for unmagnetized planets to add planetary magnetic fields [e.g. [START_REF] Sakai | Effects of a Weak Intrinsic Magnetic Field on Atmospheric Escape From Mars[END_REF][START_REF] Egan | Planetary Magnetic Field Control of Ion Escape from Weakly Magnetized Planets[END_REF][START_REF] Sakata | Effects of an intrinsic magnetic field on ion loss from ancient Mars based on multispecies simulations[END_REF], though the models are not validated in this regime and there may be missing or poorly-captured physics in the low-altitude cusp regions most important for ion acceleration and escape.

To evaluate atmospheric escape from any star-planet combination it is important to have tools that work across the full parameter space of planetary and stellar characteristics, rather than relying on a patchwork of models (that have different implementation and assumptions) to cover the parameter space. This requires substantial funded joint model development efforts to promote discussion and collaboration between modelers.

B. Directly comparable measurements of atmospheric energization and escape at a variety of solar system objects, along with simultaneous measurements of the solar inputs that drive escape

Measurement-based estimates of atmospheric escape have been made for many solar system objects (e.g. Venus, Earth, Mars, Titan, comets, Pluto). Several caveats make directly comparing published escape rates between planets problematic. First, published escape rates vary depending upon the instrument capabilities, spacecraft orbit, data selection, and data treatment. Second, there is also natural variability in escape rates with different drivers associated with the solar Extreme Ultraviolet (EUV) flux [e.g. [START_REF] Kollmann | Properties of planetward ion flows in Venus' magnetotail[END_REF][START_REF] Ramstad | The Martian atmospheric ion escape rate dependence on solar wind and solar EUV conditions: 1. Seven years of Mars Express observations[END_REF]solar wind [e.g. Slapak et al., 2017;[START_REF] Ramstad | Global Mars-solar wind coupling and ion escape[END_REF][START_REF] Persson | The Venusian atmospheric oxygen ion escape: Extrapolation to the early Solar System[END_REF]. This suggests that the time period over which data were taken influences the escape rate. Third, the range of solar and solar wind drivers experienced by these objects is different, even over the same period, due to their different heliocentric distances and longitudes.

The most comprehensive set of measurements to date has been made by the MAVEN spacecraft at Mars [Jakosky et al., 2015]. MAVEN has been measuring escape rates via the full suite of escape processes active at Mars, and simultaneously measuring the solar and solar wind energetic inputs that drive escape (EUV and X-ray photon fluxes, solar wind and solar energetic particle energy fluxes, interplanetary magnetic field and associated magnetic pressure). There is, at present, no analogous dataset for other solar system bodies of interest, including Venus, Earth (!), Titan, comets, Pluto, or giant planets. We argue that comprehensive measurements relevant to atmospheric escape (reservoirs for escape, drivers of escape, and escape itself) should be made at other planetary bodies.

Comparing measured atmospheric escape rates from a variety of objects with a range of sizes (from comet to giant planet), external conditions, and magnetization states is the best (only?) way to validate models for escape. For this comparison to be meaningful we must understand (and if possible control or correct for) differences in measurement technique, instrument performance, solar inputs, and planetary characteristics. A particularly helpful situation would be simultaneous measurements of escape and its heliophysical drivers made at multiple solar system objects by similar instruments. It should be possible to make significant progress in this area using SmallSat Missions at different objects, and multipoint measurements (similar to the ESCAPADE mission currently in development for Mars) at a single object.

C. An interdisciplinary approach led by Heliophysics that includes contributions from Planetary Science, Astrophysics, and Earth Science

The physics that drive atmospheric escape are heliophysics processes. Most are ultimately driven by energy from a star, and energize particles in the thermospheres, ionospheres, exospheres, and magnetospheres of planets. It is our view that the Heliophysics community should therefore lead the field on this topic by acknowledging its importance and taking steps to answer outstanding questions about atmospheric escape. However, valuable measurements, models, and insight come from other communities as well, including Planetary Science, Astrophysics, and Earth Science (for example, the influence of atmospheric escape on a planet's bulk atmospheric chemistry).

By promoting discussion and collaboration between the communities, we will be able to better answer big picture questions relevant in all communities. This requires more opportunity for NASA-funded cross-divisional research, and opportunity for Heliophysics investigations on NASA Planetary and Astrophysics missions. NASA's NExSS community and Interdisciplinary Consortia for Astrobiology Research provide two examples of cross-divisional collaboration -the first focused on exoplanets and the second focused on astrobiology. These kinds of efforts should be expanded to better include Heliophysics, or adapted for the specific needs of NASA's Heliophysics Division.

Figure 1 :

 1 Figure 1: Cartoon of atmospheric escape processes acting at generic magnetized (left) and unmagnetized (right) planets. Ion loss (red O + ), thermal escape (red H), photochemical escape (magenta O), and sputtering (yellow O 2 ) are depicted. Hydrodynamic escape is not depicted. Credit: Cameron Pazol (University of Colorado undergraduate), 2021.

Figure 2 :

 2 Figure2: Oxygen ion escape fluxes from the Earth[START_REF] Nilsson | Heavy Ion Energization, Transport, and Loss in the Earth's Magnetosphere[END_REF] in a cylindrical coordinate system. Analogous maps of escaping O + flux from Venus[START_REF] Fedorov | Comparative analysis of Venus and Mars magnetotails[END_REF] and Mars[START_REF] Ramstad | Global Mars-solar wind coupling and ion escape[END_REF] are inlaid with the same scale. Escape flux estimates vary by study, but all lie within about an order of magnitude of each other, sparking debate about the importance of a magnetic field. Figure courtesy R.Ramstad.

Figure 3 :

 3 Figure 3: (left) Artist's sketch of atmospheric charged particles escaping from the Martian atmosphere in response to a Coronal Mass Ejection. MAVEN results confirm that atmospheric escape has played a major role in changing the Martian climate, possibly due to the lack of a global magnetic field at Mars. However, atmospheric ion escape occurs at Earth (right) and is correlated with the energy of the solar wind, despite -or perhaps enhanced by -the presence of Earth's global magnetic field. The escape is concentrated in the magnetic cusp regions. Image credits: NASA / MAVEN and ESA.


Aurélien Gouhier

Vincent Villette

Benjamin Mathieu

Annick Ayon

Jonathan Bradley

Stéphane Dieudonné
email: stephane.dieudonne@ens.fr

Identification and organization of a postural anti-gravity module in the cerebellar vermis

Keywords: Cerebellum, Posture, Vermis, Purkinje cell, Optogenetics Highlights

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

INTRODUCTION

Posture is defined by the arrangement of body parts in space resulting from muscle contractions [START_REF] Horak | Postural Orientation and Equilibrium: What Do We Need to Know about Neural Control of Balance to Prevent Falls?[END_REF]. Mechanisms of postural control obviously operate during movements, but as well by giving anti-gravity support to the body during maintenance of static posture [START_REF] Massion | Coordination Between Posture and Movement: Why and How?[END_REF][START_REF] Horak | Postural Orientation and Equilibrium[END_REF][START_REF] Horak | Postural Orientation and Equilibrium: What Do We Need to Know about Neural Control of Balance to Prevent Falls?[END_REF]. Calculation of the motor commands required to achieve the appropriate tone of effector muscles for static posture is a subconscious process in which the anterior cerebellar vermis plays a crucial role, as lesions of this region cause atonia of the axial muscles as well as stance and gait deficits (Chambers and Sprague 1955a;1955b;[START_REF] Joyal | Effects of Midline and Lateral Cerebellar Lesions on Motor Coordination and Spatial Orientation[END_REF]. While optogenetic tools have been used to directly probe the functional output of some cerebellar regions, a systematic mapping has yet to be produced. Depending on the location and extent of the cortical region targeted, in vivo optogenetic manipulation of the cortical cerebellar Purkinje cells (PC) output can induce either discrete movements [START_REF] Heiney | Precise Control of Movement Kinematics by Optogenetic Inhibition of Purkinje Cell Activity[END_REF], whole limb motions [START_REF] Lee | Circuit Mechanisms Underlying Motor Memory Formation in the Cerebellum[END_REF], locomotor and rhythmic movement perturbations [START_REF] Hoogland | Role of Synchronous Activation of Cerebellar Purkinje Cell Ensembles in Multi-Joint Movement Control[END_REF][START_REF] Sarnaik | Control of Voluntary and Optogenetically Perturbed Locomotion by Spike Rate and Timing of Neurons of the Mouse Cerebellar Nuclei[END_REF][START_REF] Gao | A Cortico-Cerebellar Loop for Motor Planning[END_REF][START_REF] Gaffield | Cerebellum Encodes and Influences the Initiation, Performance, and Termination of Discontinuous Movements in Mice[END_REF], or even whole-body twitches [START_REF] Witter | Strength and Timing of Motor Responses Mediated by Rebound Firing in the Cerebellar Nuclei after Purkinje Cell Activation[END_REF]. Vermal stimulations, however, have thus far failed to reveal a tonic role of the cerebellum in anti-gravity postural control [START_REF] Witter | Strength and Timing of Motor Responses Mediated by Rebound Firing in the Cerebellar Nuclei after Purkinje Cell Activation[END_REF][START_REF] Hoogland | Role of Synchronous Activation of Cerebellar Purkinje Cell Ensembles in Multi-Joint Movement Control[END_REF].

The cerebellum is well-known to be organized in cortico-nuclear-olivo loop modules, each encompassing a subregion of the inferior olive (IO), which projects to a translobular parasagittal band of PCs via the climbing fibers (CFs), and to a subregion of the deep cerebellar nuclei (DCN) supposed to be interconnected in closed loops [START_REF] Groenewegen | The Parasagittal Zonation within the Olivocerebellar Projection. I. Climbing Fiber Distribution in the Vermis of Cat Cerebellum[END_REF][START_REF] Groenewegen | The Parasagittal Zonation within the Olivocerebellar Projection. II. Climbing Fiber Distribution in the Intermediate and Hemispheric Parts of Cat Cerebellum[END_REF][START_REF] Sugihara | Molecular, Topographic, and Functional Organization of the Cerebellar Nuclei: Analysis by Three-Dimensional Mapping of the Olivonuclear Projection and Aldolase C Labeling[END_REF][START_REF] Sugihara | Compartmentalization of the Deep Cerebellar Nuclei Based on Afferent Projections and Aldolase C Expression[END_REF][START_REF] Ruigrok | Ins and Outs of Cerebellar Modules[END_REF]. How the DCN outputs relate functionally to this modular organization has been the subject of attention [START_REF] Fujita | Modular Output Circuits of the Fastigial Nucleus for Diverse Motor and Nonmotor Functions of the Cerebellar Vermis[END_REF][START_REF] Heiney | Action-Based Organization of a Cerebellar Module Specialized for Predictive Control of Multiple Body Parts[END_REF][START_REF] Wang | Excitatory Nucleo-Olivary Pathway Shapes Cerebellar Outputs for Motor Control[END_REF]. Recently, specific regions of the brain that are related to several generic posture-motor functions were shown to receive projections from genetically identified subdivisions of the medial nucleus, which are also innervated by PCs of the vermis and the hemispheres [START_REF] Fujita | Modular Output Circuits of the Fastigial Nucleus for Diverse Motor and Nonmotor Functions of the Cerebellar Vermis[END_REF]. The anterior vermis could be subdivided in several broad modules, which may correspond to the ones previously identified by axonal morphology [START_REF] Voogd | The Anatomy of the Cerebellum[END_REF], and zebrin immunolabeling [START_REF] Hawkes | Monoclonal Antibodies Reveal Sagittal Banding in the Rodent Cerebellar Cortex[END_REF][START_REF] Sugihara | Compartmentalization of the Deep Cerebellar Nuclei Based on Afferent Projections and Aldolase C Expression[END_REF]. Several lines of evidence, however, have pointed to a finer modular organization of the vermal PC output. Cutaneous and nerve stimulations have suggested that cerebellar modules could be further divided into microzones of 100-200 µm based on their CF receptive fields [START_REF] Andersson | Climbing Fiber Microzones in Cerebellar Vermis and Their Projection to Different Groups of Cells in the Lateral Vestibular Nucleus[END_REF][START_REF] Jörntell | Functional Organization of Climbing Fibre Projection to the Cerebellar Anterior Lobe of the Rat[END_REF]. Functional microzones have also been identified by large-scale imaging and correlation of CF discharge in the dorsal cerebellar vermis [START_REF] Ozden | Reliable Coding Emerges from Coactivation of Climbing Fibers in Microbands of Cerebellar Purkinje Neurons[END_REF][START_REF] Mukamel | Automated Analysis of Cellular Signals from Large-Scale Calcium Imaging Data[END_REF]Kostadinov, Beau, Blanco-Pozo, et al. 2019). Furthermore, based on retrograde tracings, it was proposed that thin bands of PCs could act to control single muscles [START_REF] Ruigrok | Multiple Cerebellar Zones Are Involved in the Control of Individual Muscles: A Retrograde Transneuronal Tracing Study with Rabies Virus in the Rat: Cerebellar Zones Involved in Muscle Control[END_REF][START_REF] Ruigrok | Ins and Outs of Cerebellar Modules[END_REF]. Thus, the functional organization of the cortical cerebellar output remains ineffectually characterized.

In this study, using spatially confined optogenetic stimulations in freely-moving mice expressing the actuator ChR2 specifically in PCs [START_REF] Chaumont | Clusters of Cerebellar Purkinje Cells Control Their Afferent Climbing Fiber Discharge[END_REF], we aimed at investigating the functional micro-organization of the vermal lobules IV/V/VI output. We found that the vermis is indeed involved in postural maintenance, and more specifically in anti-gravity support. Optogenetic stimulations elicited an initial perturbation of postural maintenance in the quiet animal. This was followed by a sequential postural reflex involving several parts and muscles of the animal's body. Post-stimulation, we then observe a rebound contraction in the affected muscles. Using a custom fiber array to map the output of the vermis, we reveal that the identified postural function is encoded at the scale of the previously identified A zone, encompassing a large part of the vermal region. Moreover, our data strongly suggest an antero-posterior and medio-lateral functional segregation across the lobules IV/V/VI. Together, our results indicate that computations performed by PCs in the anterior vermis likely involve multi-segmental control of the body to ensure postural anti-gravity maintenance.

EXPERIMENTAL PROCEDURES

Mice

We used male and female mice heterozygous for L7-ChR2-eYFP of 6-16 weeks of age [START_REF] Chaumont | Clusters of Cerebellar Purkinje Cells Control Their Afferent Climbing Fiber Discharge[END_REF]. Mice were housed in standard conditions (12-hour light/dark cycles, light on at 7 a.m., with water and food ad libitum). All protocols adhered to the guidelines of the French National Ethic Committee for Sciences and Health report on Ethical Principles for Animal Experimentation in agreement with the European Community Directive 86/609/EEC under agreement #12007.

Implantation procedure

Mice were anesthetized with intraperitoneal injection of ketamine (100 mg/kg) and xylazine (20 mg/kg, Centravet) and received preoperative analgesic (buprenorphine, 0.1 mg/kg). Mice were then fixed on a stereotaxic frame and a ~6*4 mm craniotomy was performed over the vermal region of the cerebellar lobule IV/V/VI. The bottom part (head plate) of a custom designed 3-D printed implant was aligned with the lambda-bregma axis using a custom-made head plate holder and fixed on the skull with a layer of dental cement (Superbond). Mice were then temporarily detached from the stereotaxic frame and reattached using custom head plate holding bars. A custom designed laser-cut coverslip was then lowered on top of the targeted vermal area while vacuum-sucked onto a rectified hollow rod mounted on the stereotaxic apparatus. This protocol ensured that the coverslip laid flat on the brain and was parallel to the head plate surface, so that in subsequent in vivo experiments the optic fiber would lie flat on the coverslip. A 300-600 µm excess z drive was performed, thus applying pressure on the brain with the coverslip, to ensure that there would be no space between the coverslip and the cerebellum, which could enhance bone regrowth and brain movement. The coverslip was then secured with dental cement (Superbond). Finally, the upper part of the implant was screwed on the bottom part using two M1 screws. Mice were allowed to recover for at least 5 days before handling sessions and housed 1-3 per cage. Meloxicam (10 mg/kg, Centravet) was given daily for 48h after the surgery.

EMG surgeries

For EMG recordings, mice were additionally implanted with chronic electromyographic electrodes (EMGs). For the animals in which we performed EMGs implantation, the surgery was performed on the same day following the above-described implantation protocol. Mice were supplemented in anesthetics with isoflurane (2%) and prepared for aseptic surgery. An incision was made over the muscle intended for implantation. The skin was separated from underlying fascia. For splenius muscle implantation, the overlying trapezius muscle was gently dilacerated in the antero-posterior orientation with soft tip tweezers to allow for muscle access.

Each pair of electrodes was funneled through subcutaneously from the incision to the back of the head plate implant, where the connector pins were cemented. Each wire was then passed through a small surgical needle (Kalt suture needles size 3, Fine Science Tools #12050-03).

The needle was passed through the intended muscles perpendicular to the muscle fibers until the proximal knot pressed against one side of the muscle. Two electrodes were placed in each muscle at a distance of approximately 1 mm. Individual knots were made with the distal ends of the electrodes against the other side of the muscle. The excess of wire was finally cut approximately 2 mm from the muscle surface. After ensuring that the electrodes were in place, incisions were closed with nylon sutures. Mice received postoperative analgesic (buprenorphine, 0.1 mg/kg) and meloxicam (10 mg/kg, Centravet) was given daily for 48h after the surgery.

Construction of EMG electrodes

We built EMG electrodes based on a previously described procedure [START_REF] Tysseling | Design and Evaluation of a Chronic EMG Multichannel Detection System for Long-Term Recordings of Hindlimb Muscles in Behaving Mice[END_REF].

A section of electrode wire (A/M systems, multi stranded stainless steel, Teflon insulated, #793200) was cut whose length depended on the distance between the head plate implant and the targeted muscle (3.5-7.5 cm range). At the proximal end of the wire, a small amount of wire was stripped and soldered to a 1 mm gold pin (19003-00, Fine Science Tools). At the distal end, five overlapping knots were made on each wire, leaving 2-3 cm of wire excess.

Then, approximately 0.5 mm of insulated material was stripped on the distal side of the knot.

Electrodes were stored in pairs until muscle implantation.

Implant design

A custom-made 3D-printed implant was designed using the Solidworks software in order to map the entire accessible vermal area in a single animal. The implant consists of two main parts (Figure 4A). The bottom part is a head plate which is cemented on the skull of the animal.

It features two empty volumes in which small sliding parts are introduced. The upper part of the implant lands on the bottom part and can slide on it over 3 mm, allowing the coverage of the entire medio-lateral extent of the vermis. It also features a hole at its center into which the optic fiber passes. When in position, the top part of the implant is tightened to the bottom part by two screws (DIN 84 M1, Micro-Modèle) passing through the small slits. The relative positions of the two parts are measured using landmarks printed at their surface. The 3D impressions were done with a Form 2 SLA 3D printer (Formlabs). Because the antero-posterior position of the implant relative to the brain of the animal was variable, upper implant parts with optic fiber holes at different antero-posterior positions were printed. This allowed not only to properly align the fiber in a reproductible position, but also to perform an antero-posterior mapping, since this part of the implant is removable.

Optic fiber design

For Figures 1 to 3, regular optic fibers with a 200 µm core diameter (NA = 0.22, MFP _200/220/900-0.22_1m_FCM-MF1.25(F), Doric Lenses) were used. For mapping experiments, a custom patch cord was designed. The distal end of the patch cord, away of the animal, consists of 14 50 µm core optic fibers (NA = 0.22) arranged in a disk (Figure 4A). This end of the patch cord is coupled to a 400 µm optic fiber (NA = 0.22) which serves as a relay for laser illumination. At the proximal end of the patch cord, the optic fibers are arranged in a linear array that covers a surface of 50*960 µm, which allows the stimulation specific PC bands.

Experimental setup

A custom-designed setup was developed to assess postural behavior during optogenetic stimulations in freely moving mice (Figure 1A). The apparatus consists of a clear glass corridor, 45 cm long, 4.5 cm wide and 20 cm high. The corridor is closed on both sides. Mice were filmed while freely behaving with two high-resolution, highspeed cameras (Basler acA1300-3200um). A mirror (45 cm × 15 cm) was placed below the corridor at an angle of ∼45° to allow simultaneous collection of side and bottom views in order to allow for 3-D analysis of the data [START_REF] Machado | A Quantitative Framework for Whole-Body Coordination Reveals Specific Deficits in Freely Walking Ataxic Mice[END_REF]. Lighting consisted of six matrices of 860 nm infrared LEDs (SFH 4557, Osram) which were carefully positioned to maximize contrast and reduce reflection.

A custom optical setup was placed on top of the arena. It consists of a standard optical breadboard on which a laser (473 nm, LRS-0473, Laserglow Technologies) was aligned with the optic fiber core using a custom-made optical block (Doric Lenses). An acousto-optic tunable filter (AOTFnC-400.650-TN, AAOpto-electronic) was placed on the optical path to allow to trigger optogenetic stimulations. A 5 cm diameter hole was drilled in the breadboard below the optical block which was placed just above the arena. During the experiments, the optic fiber passed directly through the hole and was therefore vertical. This minimized the mechanical constraints on the fiber as well as on the mouse body. To allow for optic fiber rotations, a frictionless rotary joint (Doric Lenses) was used.

Data collection and acquisition

Mice were handled by the experimenter and allowed to acclimate the setup environment without being introduced into the arena on multiple occasions prior to data collection. Before each experiment, the mouse was head-fixed on top of a non-motorized running wheel. This allowed to unscrew the upper part of the implant and carefully clean the glass coverslip. The upper part of the implant was then positioned to the desired medio-lateral location and screwed back in place. Finally, the optic fiber was placed inside the implant in contact with the coverslip and maintained with a M1 screw.

During data collection, mice could freely behave in the glass corridor. No food or water restriction or reward was used. A typical experimental session consisted of 50 optogenetic stimulations delivered at random intervals (range: 2-18 s). During the experiment, the irradiance at the tip of the fiber and the duration of the stimulation randomly varied between trials in the 7.5-120 mW/mm² and 50-1600 ms ranges respectively. Tens of sessions could be carried in the same animal over several days to ensure a sufficient number of trials for each set of stimulation parameters. Between each session the mouse was kept in its home cage in order to minimize stress.

Movies were collected at 100 frames per second with a spatial resolution of 1200x220 (bottom view camera) and 1200x800 pixels (side view camera). The acquisition software was written in LabVIEW and uses one National Instruments board (NI-PCIe-6353) and a connection block (BNC-2090A, National Instruments) to trigger the optogenetic stimulations while simultaneously recording the movie of the animal.

During EMG recording experiments, EMG signals were acquired at 10 kHz with a 50x custommade amplifier connected to the National Instruments system. Two small diameter (0.5 mm) wires were used to connect the amplifier to the pins cemented on the implant. The wires were passed through a ring above the arena and ran along the optic fiber in order to minimize mechanical constraints on the animal movement.

Behavior analysis

All analyses were done using the MATLAB software (Mathworks) and performed offline. Both camera views of the animals were processed by the same algorithm.

Animal movement quantification

To quantify the movement of the mouse, we computed the frame-to-frame differential movie of the animal. We then applied a threshold on the resulting movie and defined the global movement of the animal as the sum of each frame, i.e., the number of pixels whose values had significantly changed. The threshold was set at mean + 5*SD of the movie noise. The resulting traces were smoothed with a gaussian filter (30 ms width). All traces were normalized by the mean amplitude of MOFF over the whole dataset. The different peaks values and timings were defined as local maxima in a specific temporal window (between 0 and 250 ms for MON peak, from 0 to 250 ms after stimulation termination for MOFF. In Figure 1L, the distributions were split in two based on gaussian fits for low stimulation powers (merged datasets 7.5 and 15 mW/mm²). "Non-failure" of MON was defined as a MON peak value exceeding mean + 3*SD of the first gaussian.

Animal body barycenter extraction

In order to extract the barycenter of the mouse body, each frame of the movie was saturated and binarized using a fixed threshold (100 for an 8-bit grayscale image). Because the tail and paws of the mouse would perturb the measurement, the resulting shape was then eroded using a binary disk (30 pixels radius) to extract the trunk of the animal. The mouse body barycenter was defined as the barycenter of the resulting binary shape. Barycenter trajectories were smoothed using a gaussian filter (30 ms width). In Figure 2E, the posture retrieval was defined as the timing at which Zb (the Z coordinate of the segmented mouse body barycenter) returned to baseline levels (mean ± 3*SD of the Zb values before light stimulation). ΔZbmax was defined as the mean value of ΔZb 30 ms around stimulation termination.

In Figure 1C and 2C, rearing was defined with a threshold on the mouse barycenter altitude in the 100 ms preceding light stimulation (2.5 cm from the ground). Walking was defined with a threshold on the animal speed in the 100 ms preceding light stimulation (>5 cm/s). The state "standing" was defined by excluding the rearing and walking trials.

EMG post-processing

The EMG signals were processed with a custom MATLAB routine. EMGs were band-pass filtered with a 4 th order Butterworth filter (cut-off frequencies, 50 and 1000 Hz) and the envelope of the signal was computed using a sliding RMS window over 30 ms. The envelope amplitude in Figure 3 was defined as the maximum of the envelope in the M ON window (0-250 ms after light stimulation commenced). Muscle contraction was considered significant when it exceeded mean + 3*SD of the baseline levels (-100 to 0 ms before stimulation). Contraction onset was defined as the earliest timing corresponding to a significant contraction during light stimulation.

Points of interest tracking and realignment along the animal body axis

Specific landmarks on the animal body were tracked using the DeepLabCut software [START_REF] Mathis | DeepLabCut: Markerless Pose Estimation of User-Defined Body Parts with Deep Learning[END_REF]. We tracked both the snout and the base of the tail of the mouse for different purposes.

The tail position was used to realign the movie in the mouse referential. First, a movie centered on the barycenter of the animal was extracted from the original bottom view recording. This movie was processed by the DeepLabCut software for tail tracking [START_REF] Mathis | DeepLabCut: Markerless Pose Estimation of User-Defined Body Parts with Deep Learning[END_REF]. Then, the bottom view video was rotated to be aligned with the body axis of the animal, so that on the resulting movie the mouse had a constant orientation. The tail position was also used to horizontally flip the lateral view movie of the mouse in order to keep its body in a constant orientation for all trials. Finally, the resulting movies were again processed through DeepLabCut for snout tracking. The resulting trajectories were smoothed using a gaussian filter (30 ms width). When computing the snout trajectory, we only kept the trials for which its detection was reliable based on the confidence on the detection returned by the algorithm (>0.8).

Statistics

All statistics were performed using the MATLAB software (Mathworks). Unless otherwise noted, paired-test significativity was assessed with a two-sided Wilcoxon rank sum test and unpaired test significativity with a Wilcoxon signed rank test.

Trial number

In Figures 1 and2, each condition comprised between 171 and 513 trials (n = 10 mice). In Figure 3, each condition comprised between 95 and 335 trials (n = 3 mice for the triceps, 2 mice for the trapezius, 4 mice for the splenius and 2 mice for the pectoris). In Figure 4 B, each condition comprises between 132 and 392 trials (n = 8 mice). In Figure 4E-M, each condition comprises between 196 and 258 trials (n = 5 mice).

RESULTS

Optogenetic stimulations of the anterior vermal Purkinje cells elicit a movement sequence

To investigate the role of the cerebellar vermis in postural control, we used a transgenic mouse model expressing channelrhodopsin-2(H134R) uniformly and specifically in PCs [START_REF] Chaumont | Clusters of Cerebellar Purkinje Cells Control Their Afferent Climbing Fiber Discharge[END_REF]. We implanted these mice with a small-core optic fiber (200 µm), which allowed for confined light stimulations of PCs in the freely moving animal. The mice were introduced in a transparent glass arena where they could behave naturally (Figure 1A), thus preventing potential confounding factors encountered in constrained animals. The animal was monitored from the side and the bottom at high frame rate (100 Hz) to allow for a precise 3D spatiotemporal movement analysis.

When optogenetic stimulations were delivered at random intervals to the midline of the lobule IV/V, we observed that a 400 ms stimulation at 30 mW/mm² always elicited a movement (Movies S1 and S2). By computing the frame-to-frame difference of the movie (100Hz), which is a good proxy for the total quantity of movement of the animal, we were able to dissect this movement's dynamics (Figure 1B). The result revealed two peaks of movement (Figure 1C), which were present across behavioral states. The first (M ON) lagged the light stimulation by 163 ± 34 ms (mean ± SD) and the second (M OFF) occurred once the light stimulation was terminated. When the animal was rearing on its hind legs, M ON was in registration with the animal's collapse, while at rest on all four legs, or walking, M ON corresponded to a forward acceleration and a forward step (Movie S2). To exclude confounding factors linked to an ongoing movement we limited our analysis to movements from stimulations of animals that were "at rest" and standing on their four legs (see Experimental Procedures).

Varying the duration of the optogenetic stimulation confirmed that M OFF was indeed time-locked to the OFF of light stimulation (Figure 1D-E, R = 0.999, p = 4.5e-9). For all durations of stimulation, we observed the same stimulation latency of M ON (Figure 1D and 1F), except for stimulations under 200 ms, for which M ON and MOFF appeared to overlap. For 50 ms duration stimulations M OFF would fall within the MON latency window. Indeed, a single movement occurred and with a shorter latency than normal MON (Figure 1D, 145 ± 29.8 for 50 ms stimulations vs M ON latency of 164 ± 32.3 ms for stimulations longer than 200 ms, p = 2.7e-17, Wilcoxon rank sum test). Thus, the M OFF is not a correction of MON (the postural defect caused by the stimulation), but is directly caused by stimulation cessation. The amplitude of M OFF increased with stimulation power (Figure 1G-H), but decreased with stimulation duration (Figure 1I). This is consistent with the idea of a movement provoked by rebound firing in the DCN when PC inhibition resumes to its normal level, which may decrease with stimulation time due to DCN cells adaptation [START_REF] Witter | Strength and Timing of Motor Responses Mediated by Rebound Firing in the Cerebellar Nuclei after Purkinje Cell Activation[END_REF][START_REF] Lee | Circuit Mechanisms Underlying Motor Memory Formation in the Cerebellum[END_REF]. To further dissect the effect of the optogenetic Purkinje cells stimulation, we thereon focused on long stimulations (200-1600 ms), for which M ON was fully developed, did not overlap with the MOFF and had a constant amplitude (Figure 1D and1J).

Although MON seemed to increase and saturate with stimulation power (Figure 1D and 1K), closer examination of the response at sub-saturating stimulations power (7,5 and 15 mW/mm²) revealed that it did not occur for every stimulation. In fact, failures resulting in a first mode of amplitude distribution were observed, while full-blown responses had similar amplitudes to those observed at high stimulation power (Figure 1L). The failure probability of M ON gradually decreased towards zero for high stimulation powers (Figure 1M). When we corrected for this factor, the non-failure amplitude was independent from stimulation power (Figure 1K, p = 0.67 between 15 mW/mm² and 120 mW/mm², Wilcoxon rank sum test), thus qualifying for a reflex movement. Movie inspection revealed that M ON generally corresponded to a forward step (Movie S2).

Previous optogenetic stimulation of vermal PCs performed in head-fixed animals was shown to evoke a movement exclusively when light stimulation terminated [START_REF] Witter | Strength and Timing of Motor Responses Mediated by Rebound Firing in the Cerebellar Nuclei after Purkinje Cell Activation[END_REF]). While we also observe this light termination effect in a freely moving animal, we additionally report the occurrence of a M ON. The reflexive nature of this movement raises the possibility that it does not represent the direct effect of the optogenetic stimulation but a secondary consequence of the postural defect through the optogenetic PC stimulation. This led us to analyze in more detail the displacement of the animal body in the period immediately following light stimulation and preceding M ON.

The direct effect of the stimulation is a postural collapse

In order to better characterize the animal movement kinematics, we segmented the mouse, recording simultaneously the body from side and bottom cameras, and extracted the coordinates of the body barycenter, which approximates its center of gravity (Figure 2A, see Experimental Procedures). Surprisingly we discovered that during the light stimulation the segmented mouse body undergoes a striking decrease of the altitude of the barycenter (Zb) which immediately follows light onset (Figure 2B). This effect on the mouse barycenter was observed in all initial postural conditions (Figure 2C). The altitude drop robustly preceded M ON in 85 % of the trials (429/504 trials, 74 ± 38 ms for Zb decrease versus 124 ± 47 for Xb, p = 1.4e-59, Wilcoxon signed rank test). The downward movement of the body therefore likely constitutes the primary effect of our optogenetic PC stimulation, hereafter referred to as M ON- DIRECT, while the MON forward step would constitute a compensatory reflex, hereafter referred to as M ON-REFLEX. To test this interpretation, we varied the stimulation parameters and found that with increasing stimulation duration (at fixed power) the body altitude-collapse gradually developed, and then saturated to a constant altitude during long stimulations. Collapse always started to recover immediately after stimulation termination (Figures 2D and2E), again suggesting that M ON-DIRECT is the primary and direct consequence of increased PC activity.

Varying the power of a fixed short-duration light stimulation (200 ms) led to a graded postural collapse which saturated for high intensities (Figures 2G and2H). Strikingly, the vertical speed of the barycenter at the onset of the collapse (from 25 to 125 ms after commencing stimulation) was linearly correlated to the stimulation intensity (Figure 2G (insert) and 2I), indicating an imbalance in anti-gravity muscle tone proportional to the optogenetic stimulation.

We then looked, in greater detail, at the trial to trial variability in the movement induced from light stimulation. At all stimulation powers the loss of barycenter altitude at steady-state was correlated with the initial altitude of the mouse body (Figure 2J). As the power increased, however, the slope of the linear regression increased and converged towards unity (Figure 2J and K, from -0.44 for 7.5 mW/mm² stimulations to -0.99 for 120 mW/mm² stimulations). At these saturating powers the final loss of barycenter altitude is therefore constant and corresponds to the lowest position that can be reached, essentially when the ventral surface of the mouse body rests on the surface of the arena. At non-saturating powers the stimulation seemed to impose a multiplicative gain on the maintained antigravity muscle-tone (which sets the altitude of the animal), leading to larger falls for those postures where the animal's body was being held farther off the surface of the arena. Part of this effect could arise from the fact that the final position of the barycenter is determined by the fraction of the animal's weight which is already in contact with the ground and supported by it, thus counterbalancing the optogenetic muscle tone loss.

Taken together, these results show that the direct effect of the light stimulation was a loss of anti-gravity maintenance. Overall, the stimulation effect can be decomposed into four phases (Movie S3). First, an anti-gravity postural collapse starts about 40 ms (38 ± 15 ms for a 30 mW/mm² 400 ms stimulation) after the light stimulation commences, M ON-DIRECT. Second, at 120 ms post stimulation, a compensatory reflex engages, M ON-REFLEX, generally a step forward, aiming at restoring balance. Third, the animal undergoes a loss of anti-gravity muscle tone, which is prolonged even while the animal attempts to execute voluntary forward steps during the stimulation. Finally, after termination of the optogenetic stimulation, the mouse performs a phasic motor response, M OFF, most likely triggered by a rebound in the deep cerebellar nuclei, while slowly retrieving its postural altitude.

Body parts are differentially involved during optogenetic PC activation

We sought to investigate the involvement of different body muscles in the postural perturbation evoked by the optogenetic stimulations. To address this, we implanted EMG electrodes in two neck muscles involved in upward head movement (trapezius and splenius), and two muscles involved in body support by the forelimbs (triceps and pectoris), and extracted their muscle tone from the recorded signal by computing the EMG envelope (Figure 3A, see Experimental Procedures). During the optogenetic stimulation, we observed that the movement of the mouse was consistently associated with contractions of all four of the recorded muscles (Figure 3B), and all started to contract at least 100 ms after the stimulation commenced. Therefore, we considered these muscle contractions a signature of the mouse postural reflex. As expected, contractions of these muscles were also observed at posture retrieval (Figure 3B and3C).

Interestingly, based on the timings of contraction after stimulation commenced, we observed that the trapezius and splenius muscles contracted significantly before the triceps and pectoris.

As shown in Figure 3D, the recordings revealed trapezius and splenius starting to contract at 99 ± 38 ms and 112 ± 59 ms respectively (p = 0.58, Wilcoxon rank sum test). Then, at 179 ± 57 ms the pectoris begins to contract, and finally the triceps (183 ± 45 ms for the triceps, p = 6.4e-36 between the two muscle pairs of trapezius & splenius versus pectoris & triceps). On a trial-to-trial basis the trapezius and triceps muscle contractions were highly correlated to M ON- REFLEX amplitude (R = 0.93 and 0,65, p = 5.3e-30 and 1.6e-19 respectively), confirming their involvement in this phase of the movement. Correlations to the two other muscles were weaker albeit significant (R = 0.37 and 0.27, p = 4.5e-8 and 4.72e-4 for the pectoris and splenius respectively). Lower significance could be explained by the smaller impact of these muscles on the global body position, as quantified by the cameras. Thus, the muscles could be placed in two groups. Moreover, we observed that, similarly to the M ON-REFLEX amplitude, the amplitude of the M ON-REFLEX contraction was independent from both the stimulation power (Figure 3E, triceps muscle, 400 ms stimulations, n = 3 mice) and duration (Figure 3F, triceps muscle, 30 mW/mm² stimulations). This provides further confirmation that the optogenetic stimulation of Purkinje cells evokes a compound sequential reflex aimed at stabilizing the head and the trunk of the animal. Moreover, in all the recorded muscles, in particular the splenius, the contraction appeared to be sustained during the stimulation (Figure 3B). This indicates that after the postural reflex the mouse tried to compensate for the still ongoing loss of muscle-tone but despite prolonged contractions could not overcome the effect of the perturbation.

Although the EMG did not reveal any significant muscle relaxations in the 120 ms period during body collapse (the M ON-DIRECT period), we reasoned that muscles which were perturbed when stimulation commenced ought to display a clear rebound of activity upon termination of stimulation. We indeed observed such a rebound in pectoris and triceps, which are both muscles that act to maintain posture by counteracting gravity (Figure 3G, rebound values 0.54 ± 0.51, 0.59 ± 0.22 for triceps and pectoris respectively). In contrast, we did not see a similar rebound in the two neck muscles (Figure 3G, rebound values -0.81 ± 0.20 mV, 0.04 ± 0.28 for the trapezius and splenius respectively). For the triceps, recordings were stable enough to verify that the light-OFF response was graded by the stimulation power and duration (Figures 3E-F). Accordingly, we ascribe these pectoris and triceps contractions to the M OFF rebound activity originating from the DCN. In conclusion, pectoris and triceps are two muscles likely directly affected by the optogenetic PC stimulation.

Optogenetic mapping of the anterior cerebellar vermal output

We next set out to map the output of the anterior vermis. For this, we produced a 3D-printed implant for mounting a custom optic fiber array (14 cores of 50 µm aligned on a linear array) over a cranial window that spanned the whole medio-lateral extent of the anterior vermal cerebellum. Thus, sequential optical stimulations of mild intensity (10 mW/mm², 400 ms stimulation) could be delivered to narrow sagittal bands of PC (Figure 4A) at different mediolateral locations in the cerebellar lobule IV/V. As we gradually moved the fiber from a medial to lateral locations, we observed that the postural collapse amplitude progressively decayed and disappeared once outside of the vermis (Figure 4B-C, n = 4 mice). The mid-effect was found around 500 µm laterally, which is in accordance with a broad (wider than a cortical microzones) module of DCN cells previously defined by genetic profiling, PC axonal projections to the DCN and zebrin immunolabeling patterns [START_REF] Hawkes | Monoclonal Antibodies Reveal Sagittal Banding in the Rodent Cerebellar Cortex[END_REF][START_REF] Sugihara | Projection of Reconstructed Single Purkinje Cell Axons in Relation to the Cortical and Nuclear Aldolase C Compartments of the Rat Cerebellum[END_REF][START_REF] Voogd | Cerebellar Zones: A Personal History[END_REF][START_REF] Fujita | Modular Output Circuits of the Fastigial Nucleus for Diverse Motor and Nonmotor Functions of the Cerebellar Vermis[END_REF].

In order to assess the existence of functional subregions, we refined our analysis of the evoked movement and used machine learning to track points of interest on the animal's body. The base of the mouse tail was tracked, allowing us to realign its body around the body axis (see Experimental Procedures). We then computed the average cumulative differential movie of the animal between 0 to 100 ms after stimulation commenced (before M ON-REFLEX, the postural reflex), which produced a body map of the mouse movement over this period (Figure 4D, 400 ms stimulations, n = 3 mice). Comparing these body maps for different stimulation locations, we found that the mouse movement was lateralized in both lobule IV/V and VI (Figure 4D), which was also observed when measuring the Y coordinates of the mouse body barycenter (Figure 4E and F, ΔYb body lateral displacement of 2.1 ± 1.61 mm and -2.33 ± 1.26 mm for left and right lobule IV/V stimulations respectively, 1.22 ± 1.63 mm and -1.8 ± 1.14 mm in lobule VI, p = 1.4e-20 and 8.4e-15 in lobule IV/V and VI respectively), the mouse body falling ipsilateral to the side of stimulation. In contrast, a straight downward movement of the animal body was seen for midline stimulations (Figure 4D-F, 0.19 ± 0.58 mm and -0.25 ± 0.74 mm ΔZb body vertical displacement in lobule IV/V and VI respectively). As expected, a global body collapse was observed at all locations (Figure 4G, bottom panels). The mouse's snout is a good proxy of head movement (Figure 4E, see Experimental Procedures). While the Y coordinate of the snout reported a lateralization of the stimulation effect (Figure 4H andI, average ΔYsnout at stimulation termination of 1.91 ± 1.32 mm and -3.1 ± 1.69 mm for left and right lobule IV/V stimulations respectively, 1.46 ± 0.99 mm and -2.56 ± 1.25 mm in lobule VI, p = 4.0e-16 and 2.3e-19 in lobule IV/V and VI respectively), the animal's snout also displayed an initial additional forward movement for medial stimulations compared to lateral stimulations (Figure 4J and K, ΔXsnout 150 ms after light onset 2.52 ± 1.25 mm and 1.52 ± 1.34 mm for medial vs lateral stimulations in lobule IV/V, 2.47 ± 1.63 mm and 1.50 ± 1.81 mm in lobule VI, p = 3.3e-4 and 9.7e-3 in lobules IV/V and VI respectively). Stimulations in lobule IV/V produced similar snout (Figure 4L) and body barycenter altitude decrease (Figure 4G). In contrast though, stimulations in lobule VI evoked an increase in the snout altitude during the stimulation (Figure 4L andM, average ΔZsnout at stimulation termination -2.04 ± 1.11 mm in lobule IV/V vs 1.53 ± 0.80 mm in lobule VI, p = 1.4e-85 between the two lobules), although the mouse experienced a postural collapse of the body barycenter (Figure 4G), suggesting a contraction of the dorsal neck muscles. These results indicate that a fine-grain functional somatotopy of the anterior vermis within a genetically and immunohistochemically identified module.

DISCUSSION

Our results from optogenetic stimulations of cerebellar PCs argue for a direct involvement of the anterior vermis in anti-gravity postural maintenance: we find that a postural collapse is the first event to occur upon sustained increased firing of PC and is directly modulated by stimulation parameters (Figure 2). While lesions and tracing studies have long pointed to a role of the vermis in basic postural functions (Chambers and Sprague 1955a;1955b;[START_REF] Joyal | Effects of Midline and Lateral Cerebellar Lesions on Motor Coordination and Spatial Orientation[END_REF][START_REF] Manni | A Century of Cerebellar Somatotopy: A Debated Representation[END_REF], this is to our knowledge the first direct experimental evidence in the intact freely behaving animal of a vermal role in postural maintenance.

Anterior vermis involvement in anti-gravity postural maintenance

Previous studies had intended to assess the effects of optogenetic manipulation of PC activity in the dorsal vermis of the mouse [START_REF] Witter | Strength and Timing of Motor Responses Mediated by Rebound Firing in the Cerebellar Nuclei after Purkinje Cell Activation[END_REF][START_REF] Hoogland | Role of Synchronous Activation of Cerebellar Purkinje Cell Ensembles in Multi-Joint Movement Control[END_REF][START_REF] Heffley | Coordinated Cerebellar Climbing Fiber Activity Signals Learned Sensorimotor Predictions[END_REF]).

One of them described a behavioral response of the animal exclusively at the termination of PC stimulation, which was characterized by whole-body twitches [START_REF] Witter | Strength and Timing of Motor Responses Mediated by Rebound Firing in the Cerebellar Nuclei after Purkinje Cell Activation[END_REF]. We similarly observed a movement at stimulation termination, which not only involves a posture retrieval of the mouse but also a rebound movement graded by stimulation power (Figure 1H), which we further characterize as a rebound contraction in specific muscles (Figure 3E-G).

Witter et al. performed experiments in head-fixed animals, however, which most likely prevented the observation of the anti-gravity effect reported here. Interestingly, a subsequent report using head-fixed animals placed on a rotating disk [START_REF] Hoogland | Role of Synchronous Activation of Cerebellar Purkinje Cell Ensembles in Multi-Joint Movement Control[END_REF] pointed to an initiation of stepping around 200 ms after stimulation commenced. This timing arguably corresponds to the compensatory postural adjustment we observe in this study, which often manifests as a forward step. The same study reported a slow-down of stepping when the animal had already been walking, while in contrast we observed a continuation of the ongoing forward movement (Figure 2B). These observations can be reconciled if one accepts the plausible argument that in head-fixed animals [START_REF] Hoogland | Role of Synchronous Activation of Cerebellar Purkinje Cell Ensembles in Multi-Joint Movement Control[END_REF], the stimulation will cause a weakening of the forelimbs and thus reduce stepping without causing an imbalance of the body towards the front. In freely-moving animals (as in this report), reduced anti-gravity tone of the forelimb causes a downward movement of the head and a loss of equilibrium, leading to a strong maintenance reflex, hence a stepping forward. Thus, previous reports are consistent with our results but appear to have failed to uncover the direct effect of the stimulation, presumably because of the experimental constraints encountered in a head-fixed animal.

Compensatory postural reflex elicited by optogenetic stimulation

We identified a compensatory postural reflex following postural collapse of the animal body, which is associated with a sequence of muscle contractions. The first pair of muscles to contract (trapezius and splenius) are neck muscles whose role is to maintain the head of the animal up. The contraction of these muscles 100 ms after optogenetic stimulation commences matches a short slowing in the animal's barycenter drop in altitude (Figure 2D), indicating a first reflexive component. In contrast, the second set of muscles (pectoris and triceps) that contract 70 ms later are more likely involved in the subsequent compensatory step performed by the animal, which translates in strong correlations with this part of the movement. Moreover, the reliable contraction observed in these two muscles at stimulation termination (Figures 3G) indicates that they are likely the ones directly affected by the stimulation.

The compensatory reflex may involve several extracerebellar brain regions at the spinal and brainstem levels, in particular in link with the vestibular system [START_REF] Horak | Postural Orientation and Equilibrium: What Do We Need to Know about Neural Control of Balance to Prevent Falls?[END_REF]). However, in particular for the muscles directly affected by the stimulation, the reflex could have a cerebellar origin. It is known that PCs can control their own afferent climbing fiber discharge with a minimal delay of 80-100 ms [START_REF] Chaumont | Clusters of Cerebellar Purkinje Cells Control Their Afferent Climbing Fiber Discharge[END_REF]. Therefore, we can expect a synchronous CF discharge in the stimulated PCs around the timing of reflex initiation, which would participate in the reported reflexive movement. Interestingly, we observed that muscle contractions were often prolonged during the whole stimulation duration (Figure 3B-C). This signals a prolonged compensation of the postural loss, which translates in a prolonged forward movement of the animal, in particular at long durations (Figure 1D). This compensation is nonetheless insufficient to outweigh the stimulation effect, since the barycenter altitude only recovers after stimulation termination (Figure 2D-E). Thus, the cerebellum does not decrease a specific drive associated to anti-gravity function but exerts a global gain function on muscle tone, which prevents these muscles from being properly used in the subsequent motor command generating the forward stepping during the optogenetic stimulation.

Influence of PC activation on muscle tone

Because the anterior vermis has been associated with the anterior axial part of the body (Chambers and Sprague 1955a;1955b), we targeted axial and proximal muscles in the neck region for our EMG recordings during optogenetic stimulations. Surprisingly, we did not observe any muscle relaxation in our EMG recordings (Figure 3B-C). While the affected muscles could belong to other body regions, such as the back or the belly of the animal, the specificity of the contraction at stimulus termination in two muscles strongly indicates that they could be amongst the ones controlled by the vermal lobule IV/V at midline. This hypothesis would fall in line with the known representation of the forelimbs in the vermis [START_REF] Heffley | Coordinated Cerebellar Climbing Fiber Activity Signals Learned Sensorimotor Predictions[END_REF][START_REF] Wagner | A Neural Circuit State Change Underlying Skilled Movements[END_REF]. The absence of muscle tone loss in our recordings could be explained by experimental limitations. In Figure 2I, we observe that the mouse barycenter decreased 1 mm 100 ms after stimulation commenced. We can thus calculate that the acceleration of the animal's body is around 0.1 m/s -2 , which roughly represents a hundredth of earth gravity (9.8m/s -2 ). Therefore only a few percent of muscle tone loss could be sufficient to trigger the observed effect. If these calculations are correct, the resulting EMG variation would be difficult to pick up in our recordings.

Cerebellar output activity during PC stimulation

Although we did not record the PC activity during our experiments, based on previous studies, we can confidently infer that our PC optogenetic stimulations elicit a graded DCN inhibition [START_REF] Chaumont | Clusters of Cerebellar Purkinje Cells Control Their Afferent Climbing Fiber Discharge[END_REF][START_REF] Witter | Strength and Timing of Motor Responses Mediated by Rebound Firing in the Cerebellar Nuclei after Purkinje Cell Activation[END_REF]). This assessment is non-trivial because strong PC stimulations have been shown to induce a depolarizing block in PC activity, which could result in net DCN disinhibition [START_REF] Chaumont | Clusters of Cerebellar Purkinje Cells Control Their Afferent Climbing Fiber Discharge[END_REF]. The stimulation power we report was measured directly at the fiber tip. Because a glass coverslip is positioned between the fiber and brain, we can extrapolate based on our fiber NA (0.22) and coverslip thickness (150 μm) that there is a 1.5-fold increase in the illuminated surface when the light reaches the brain. The irradiance is therefore divided by 1.5, which yields a range of 5-90 mW/mm² at the brain surface, which is similar to that used in the study characterizing the mouse line we used [START_REF] Chaumont | Clusters of Cerebellar Purkinje Cells Control Their Afferent Climbing Fiber Discharge[END_REF]. Moreover, even if at high power stimulations PCs directly below the fiber tip were to undergo a depolarizing block, the diffusion of light in living tissue with increasing power would recruit large numbers of PCs around the stimulation site and globally result in a net DCN inhibition [START_REF] Chaumont | Clusters of Cerebellar Purkinje Cells Control Their Afferent Climbing Fiber Discharge[END_REF]. Finally, the postural collapse we observed was consistent over the entire ranges of durations and powers assayed in our experiments. It is therefore most probable that, even at high intensities, we effectively inhibit the cerebellar output from the DCN instead of activating it.

Spatial specificity of the stimulation

Our optogenetic mapping of the vermis relies on spatial specificity of PC excitation. In order to minimize the extent of the stimulated area, we used a custom optic fiber linear array composed of small-core 50 µm optic fibers, positioned over the vermis in a parasagittal orientation (Figure 4A). It must be noted, however, that beam divergence through the cranial window as well as diffusion inside brain tissue likely increase the extent of the stimulated area. Given the numerical aperture of the optic fiber (NA = 0.22), the glass index (1.5) and the glass window thickness (150 µm), we can expect a divergence through the thickness of the cranial window of: 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 2 * 150 * tan (asin � 0.22 1.5 �)

This gives a beam expansion of ~45 µm in diameter through the glass window, which results in a ~100 µm width of illuminated area at the cortical surface. Previous studies investigating light diffusion in cerebellar tissues have shown that the diffusion process is predominantly axial [START_REF] Chaumont | Clusters of Cerebellar Purkinje Cells Control Their Afferent Climbing Fiber Discharge[END_REF][START_REF] Gysbrechts | Light Distribution and Thermal Effects in the Rat Brain under Optogenetic Stimulation[END_REF][START_REF] Yona | Realistic Numerical and Analytical Modeling of Light Scattering in Brain Tissue for Optogenetic Applications[END_REF], with a 1% isoline located laterally at ~75 µm from the origin for a 50 µm core optic fiber and at 400 µm in depth.

Therefore, we can make the conservative assumption that our stimulation covers a surface of ~1000*150 µm of cerebellar cortical tissue, which is in the range of the known extent of cerebellar microzones (Kostadinov, Beau, Pozo, et al. 2019) and would correspond to roughly 250 PCs. Thus, our custom optic fiber array allows us to stimulate the vermal PC output at the microzonal scale. Based on previous experiments, we can affirm that PCs more than 200 µm from the stimulation site are very unlikely to be affected [START_REF] Chaumont | Clusters of Cerebellar Purkinje Cells Control Their Afferent Climbing Fiber Discharge[END_REF]. Moreover, the observed lateralization of the postural collapse argues for a degree of spatial specificity in our stimulations, and the ipsilateral effect on the animal body is consistent with the known cerebellar projections to spinal cord motoneurons [START_REF] Teune | Topography of Cerebellar Nuclear Projections to the Brain Stem in the Rat[END_REF].

Functional organization of the vermal output

The olivary input to PCs is organized in translobular parasagittal bands of CF projections with specific receptive fields [START_REF] Andersson | Climbing Fiber Microzones in Cerebellar Vermis and Their Projection to Different Groups of Cells in the Lateral Vestibular Nucleus[END_REF], but parallel fibers (PF) distribute sensori-motor information to PCs in the medio-lateral direction [START_REF] Heck | On-Beam Synchrony in the Cerebellum as the Mechanism for the Timing and Coordination of Movement[END_REF]. A long-standing hypothesis, as identified for eyelid closure, ocular saccades and for limb movement [START_REF] Hesslow | Correspondence between Climbing Fibre Input and Motor Output in Eyeblink-Related Areas in Cat Cerebellar Cortex[END_REF][START_REF] Mostofi | Electrophysiological Localization of Eyeblink-Related Microzones in Rabbit Cerebellar Cortex[END_REF][START_REF] Heiney | Precise Control of Movement Kinematics by Optogenetic Inhibition of Purkinje Cell Activity[END_REF][START_REF] Herzfeld | Encoding of Action by the Purkinje Cells of the Cerebellum[END_REF][START_REF] Heffley | Coordinated Cerebellar Climbing Fiber Activity Signals Learned Sensorimotor Predictions[END_REF][START_REF] Sedaghat-Nejad | Synchronous Spiking of Cerebellar Purkinje Cells during Control of Movements[END_REF], posits that the functional unit of the cerebellar cortex, controlling a specific motor function, consists of a small intersectional domain of PCs sharing common CF and PF information. In addition, microzones of correlated CF activity have been identified in relation to various other tasks but direct control of a specific motor output by the corresponding PCs has not been demonstrated in these cases [START_REF] Mukamel | Automated Analysis of Cellular Signals from Large-Scale Calcium Imaging Data[END_REF]Kostadinov, Beau, Pozo, et al. 2019;[START_REF] Tsutsumi | Modular Organization of Cerebellar Climbing Fiber Inputs during Goal-Directed Behavior[END_REF]2020). This intersectional domain hypothesis is, however, consistent with the known PC-DCN convergence pattern (R. [START_REF] Apps | Precise Matching of Olivo-Cortical Divergence and Cortico-Nuclear Convergence between Somatotopically Corresponding Areas in the Medial C1 and Medial C3 Zones of the Paravermal Cerebellum: Cerebellar Olivo-Cortico-Nuclear Connections[END_REF][START_REF] Voogd | Cerebellar Zones: A Personal History[END_REF]) and the known organization of the DCN [START_REF] Heiney | Action-Based Organization of a Cerebellar Module Specialized for Predictive Control of Multiple Body Parts[END_REF]. In this study, we used an optic fiber with a custom longitudinal small-core array to map the cerebellar output within a specific lobule with fine medial-lateral resolution. The postural function we identified was found to be encoded at the scale of a large vermal zone, roughly corresponding to the A zone of the cerebellar cortex (Richard [START_REF] Apps | Cerebellar Modules and Their Role as Operational Cerebellar Processing Units[END_REF]) and a posturo-motor module identified genetically [START_REF] Fujita | Modular Output Circuits of the Fastigial Nucleus for Diverse Motor and Nonmotor Functions of the Cerebellar Vermis[END_REF]. We show through refined movement analysis that neighboring stimulation sites within this module are associated with different motor outcomes that are putatively related to muscle groups directly controlled by PCs at each stimulation location. This patterning is both medio-lateral and antero-posterior, in agreement with the intersectional domain hypothesis.

Interestingly, our posterior stimulation of lobule VI, which may overlap with an output module involved in head and eye orienting movement [START_REF] Fujita | Modular Output Circuits of the Fastigial Nucleus for Diverse Motor and Nonmotor Functions of the Cerebellar Vermis[END_REF], evoked an upward movement of the head.

Our results therefore establish for the first time a functional microzonal organization of the vermal PC output, and pave the way for future studies aiming at dissecting further the cerebellar functional output in other paradigms.

Figure 1

 1 Figure 1 Optogenetic stimulations of the anterior vermal Purkinje cells elicit a movement sequence. A. The implanted mice were introduced in a transparent rectangular glass arena with a mirror below at 45° angle. Two high-speed cameras captured side and bottom views at 100 Hz. B. Two consecutive frames of the animal side view. Movement was defined as the number of pixels whose values significantly changed between the two frames (light blue areas). C. Normalized pixel difference around the optogenetic stimulation for three different behavioral states (see Experimental Procedures). Curves represent mean ± SEM (n = 8 mice, 30 mW/mm² 400 ms stimulations). D. Evolution of the mouse movement with the stimulation duration (n = 8 mice, 50 trials for each mouse and each condition).Curves represent mean ± SEM. MOFF peak timing plotted against stimulation duration (30 mW/mm² stimulations, R = 0.999, y = 1.02x + 126 ms). Bars represent mean ± SEM. F. MON peak timing plotted against stimulation duration (30 mW/mm² stimulations, n = 8 mice). G. Evolution of the mouse movement with the stimulation power (n = 8 mice, 400 ms stimulations). Curves represent mean ± SEM. H. MOFF peak amplitude plotted against the stimulation power (400 ms stimulations). I. MOFF peak amplitude plotted against stimulation duration (30 mW/mm² stimulations). J. MON peak amplitude plotted against stimulation duration (30 mW/mm² stimulations). K. Raw and non-failure (see Experimental Procedures) MON peak amplitude against stimulation power (computed for stimulations longer than 200 ms). L. Histograms of MON peak amplitudes for two stimulation powers (stimulation duration = 400 ms). M. MON failure probability plotted against stimulation power (computed for stimulations longer than 200 ms).

Figure 2

 2 Figure 2 The direct effect of the stimulation is a postural collapse. A. The barycenter of the mouse body was computed from two camera views. B. Individual and mean barycenter trajectories (gray and black traces respectively) following a 30 mW/mm² 400 ms optogenetic PC stimulation at the lobule IV/V midline (n = 63 trials). C. Time course of the Z coordinate of the body barycenter around the optogenetic stimulation for three different behavioral states (see Experimental Procedures). Curves represent mean ± SEM (n = 8 animals, 30 mW/mm² 400 ms stimulations). D. Time course of ΔZb for different stimulation durations (n = 8 mice). Curves represent mean ± SEM. E. Start of posture retrieval plotted against stimulation duration (R = 0.998, y = 1.01x + 168 ms). Data are mean ± SEM. F. ΔZbmax plotted against stimulation duration. G. Time course of ΔZb for different stimulation powers (n = 8 mice). Curves represent mean ± SEM. H. ΔZbmax plotted against stimulation power. I. Zb speed at stimulation onset (from 25 to 125 ms following stimulation onset) plotted against stimulation power (R = 0.972, y = -6.62e-3x -0.160). J. ΔZbmax plotted against Zb0 (before light stimulation) for individual trials and different stimulation powers (400 ms stimulations). Lines represent the linear regression. K. Slope of the linear regressions from J plotted against stimulation power.

Figure 3

 3 Figure 3 Body muscles involvement during PC optogenetic activation. A. (Top) Mice were implanted with EMG electrodes in several body muscles (see Experimental Procedures for details). (Bottom) Raw EMG traces were temporally filtered and processed to compute the envelope of the signal (see Experimental Procedures). B. Example raster of the EMG envelope around optogenetic PC activation for the triceps muscle (30 mW/mm² 400 ms stimulations). White bars represent 5 trials. C. Average time-course of the EMG envelope for the recorded body muscles (30 mW/mm², 400 ms stimulations, n = 2 mice for the trapezius, 4 mice for the splenius, 3 mice for the triceps). Data are mean ± SEM. D. (Left) Normalized envelopes of the recorded body muscles around stimulation onset. (Right) Muscle contraction onset timing for the body muscles recorded in B. Plain dots represent the median, shaded boxes the 25-75% and colored lines the 5-95% distributions limits respectively. E. Relative muscle contractions for the muscles recorded in B following light termination. Same representation as in D (400 ms 30 mW/mm² stimulations). F. Evolution of the EMG envelope of the triceps muscle with stimulation power (400 ms stimulations, n = 3 mice). G. Evolution of the EMG envelope of the triceps muscle with stimulation duration (30mW/mm² stimulations, n = 3 mice).

Figure 4

 4 Figure 4 Optogenetic mapping of the anterior vermal output. A. (Left) Custom implant used to map the cerebellar vermis. The implant is composed of a top part which can slide on a bottom fixed part. (Middle) The implant is designed to position a custom linear fiber array over the cerebellar cortex. Moving the array allows sequential stimulation of sagittal PC bands with high spatial specificity. B. Time course of ΔZb for different medio-lateral locations over the vermal lobule IV/V. The coordinate 0 refers to the midline. The fiber was moved in the rightward direction. Curves are mean ± SEM (n = 4 mice, 50 trials per mouse, 30 mW/mm² 400 ms stimulations). C. ΔZbmax plotted against the medio-lateral location of the optic fiber array. Data are mean ± SEM. D. Average cumulative differential movie between 0 and 100 ms after stimulation commenced for different fiber locations. E. After a realignment of the mouse body along the tail-body barycenter axis, the snout of the animal was tracked with both camera views using the DeepLabCut software (see Experimental Procedures). F. Time course of the differential ΔYb coordinate of the animal segmented body barycenter for different medio-lateral locations in the lobules IV/V and VI. G. Same as F but for ΔZb. H. Same as F but for ΔYsnout. I. ΔYsnout at stimulation termination for the different fiber locations. Plain black dots represent the median, shaded boxes the 25-75% and colored lines the 5-95% distributions limits respectively. J. Same as F but for ΔXsnout. K. ΔXsnout 150 ms after light stimulation commenced for the different fiber locations. L. Same as F but for ΔZsnout. M. Same as H but for ΔZsnout.

ACKNOWLEDGEMENTS

We would like to thank Yvon Cabirou and Gerard Paresys for custom mechanical production and EMG amplifier. We also acknowledge the assistance of the IBENS Fablab (Fédération pour la Recherche sur le Cerveau -Rotary International France 2018) and Victor Llobet in 3D printing procedures. We thank Caroline Mailes-Hamon, the IBENS PFL2 platform and IBENS animal facility. We also thank Astou Tangara and the IBENS Imaging platform for assistance in experimental setup assembly. We thank Laurent Gallais for production of custom laser-cut coverslips.

FUNDING

This project was supported by AMX scholarship from École polytechnique (A.G.), Labex Memolife scholarship (A.G.), the ANR (GluBrain3A ANR 17-CE-16-0014 and FucPoc ANR 20-CE16-0026) and a QLife supporting program (DION-2021).

DATA AND CODE STATEMENT

Data shown in figures, example raw recordings and MATLAB codes used to analyze the raw data and generate the figures are available at: https://figshare.com/projects/MATLAB_codes_and_data_for_Optogenetic_mapping_of_the_p ostural_function_in_the_cerebellar_anterior_vermis/180511

AUTHOR CONTRIBUTION STATEMENT