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

The cerebellum is known to control the proper balance of isometric muscular contractions that maintain body posture. Current optogenetic manipulations of the cerebellar cortex output, however, have focused on ballistic body movements, examining movement initiation or perturbations. Here, by optogenetic stimulations of cerebellar Purkinje cells, the output of the cerebellar cortex, we evaluate body posture maintenance. By sequential analysis of body movement, we dissect the effect of optogenetic stimulation into a directly induced movement that is then followed by a compensatory reflex to regain body posture. We identify a module in the medial part of the anterior vermis which, through multiple muscle tone regulation, is involved in postural anti-gravity maintenance of the body. Moreover, we report an antero-posterior and medio-lateral functional segregation over the vermal lobules IV/V/VI. Taken together our results open new avenues for better understanding of the modular functional organization of the cerebellar cortex and its role in postural anti-gravity maintenance. Highlights Vermal Purkinje cell activation elicits a graded postural collapse in the standing mouse The collapse triggers a secondary composite postural reflex An identified cerebellar module is involved in postural anti-gravity tone maintenance The anti-gravity function is somatotopically organized within this module


INTRODUCTION
Posture is defined by the arrangement of body parts in space resulting from muscle contractions (Horak 2006).Mechanisms of postural control obviously operate during movements, but as well by giving anti-gravity support to the body during maintenance of static posture (Massion and Dufosse 1988;Horak and Macpherson 1996;Horak 2006).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;Joyal et al. 1996).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 (Heiney et al. 2014), whole limb motions (Lee et al. 2015), locomotor and rhythmic movement perturbations (Hoogland et al. 2015;Sarnaik and Raman 2018;Gao et al. 2018;Gaffield, Sauerbrei, and Christie 2022), or even whole-body twitches (Witter et al. 2013).Vermal stimulations, however, have thus far failed to reveal a tonic role of the cerebellum in anti-gravity postural control (Witter et al. 2013;Hoogland et al. 2015).
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 (Groenewegen and Voogd 1977;Groenewegen, Voogd, and Freedman 1979;Sugihara and Shinoda 2007;Sugihara 2011;Ruigrok 2011).How the DCN outputs relate functionally to this modular organization has been the subject of attention (Fujita, Kodama, and Du Lac 2020;Heiney, Wojaczynski, and Medina 2021;Wang et al. 2023).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 (Fujita, Kodama, and Du Lac 2020).The anterior vermis can be subdivided in several broad modules, which may correspond to the ones previously identified by axonal morphology (Voogd and Glickstein 1998), and zebrin immunolabeling (Hawkes, Colonnier, and Leclerc 1985;Sugihara 2011).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 (Andersson and Oscarsson 1978;Jörntell et al. 2000).Functional microzones have also been identified by large-scale imaging and correlation of CF discharge in the dorsal cerebellar vermis (Ozden et al. 2009;Mukamel, Nimmerjahn, and Schnitzer 2009;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 (Ruigrok et al. 2008;Ruigrok 2011).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 (Chaumont et al. 2013), we aimed at investigating the functional micro-organization of 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 lobules IV/V/VI.Together, our

EXPERIMENTAL PROCEDURES Mice
We used male and female mice heterozygous for L7-ChR2-eYFP of 6-16 weeks of age (Chaumont et al. 2013).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 2 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 then cemented on the skull (Superbond).Two arrows on the anterior and posterior borders of the implant were used to center it on the lambda-bregma axis.Centering was done by manipulating the head plate with micrometric precision (<10 µm) using a custom-made head plate holder.This step was essential to locate the stimulation sites relative to the known microzonal organization of the cerebellum.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 craniotomy while vacuumsucked 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 (See supplementary online data for figures and details of custom implant).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 EMG implantations, the surgery was performed right after 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 split in the anteroposterior orientation with soft tip tweezers and kept separated to allow for deeper muscle access.Each pair of electrodes were funneled 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 (Tysseling et al. 2013).A section of electrode wire (A/M systems, multi stranded stainless steel, Teflon insulated, #793200) was cut in length depending 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 excess wire.Then, approximately 0.5 mm of insulated material was stripped from 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 3D impressions were done with a Form 2 SLA 3D printer (Formlabs).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 lays on the bottom part and can slide on it over 3 mm, allowing 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 two parts could be aligned using corresponding landmarks at their surface.The top part could then be moved relative to the bottom implant with 10 µm precision using a micromanipulator, while the animal was held headfixed.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, allowing antero-posterior mapping.

Optic fiber design
For Figures 1 to 3, commercial 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, connected to the rotary joint, consists of fourteen 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 2 , enabling the stimulation of 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 arena 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° enabling simultaneous collection of side and bottom views and 3-D analysis of the data (Machado et al. 2015).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, consisting 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 in the optical path to allow triggering of 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 animal's 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 acclimatize to 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 and the upper part of the implant was temporally removed so that the glass coverslip could be cleaned.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.Optogenetic stimulations consisted of single continuous illuminations.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 was randomly varied between trials, in the 7.5-120 mW/mm² and 50-1600 ms ranges, respectively.Tens of sessions could be performed with 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 a 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's 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 M OFF over the whole dataset.The different peak values and timings were defined as local maxima in a specific temporal window (between 0 and 250 ms for M ON peak, from 0 to 250 ms after stimulation termination for M OFF .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 M ON was defined as a M ON 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, 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 mouse barycenter altitude in a 100 ms time window preceding light stimulation (2.5 cm from the ground).Walking was defined with a threshold on the animal's speed in a 100 ms time window preceding light stimulation (>5 cm/s).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 moment of significant contraction during light stimulation.

Points of interest tracking and realignment along animal body axis
Specific animal body landmarks were tracked using the DeepLabCut software (Mathis et al. 2018).The base of the tail was tracked and used to realign the movie in the mouse-centered referential according to the following protocol.First, a subfield centered on the barycenter of the animal was extracted from the original bottom view recording.This reduced movie was processed by DeepLabCut software for tail tracking (Mathis et al. 2018).Then, the bottom view video was rotated to be aligned with the barycenter-tail body axis of the animal, so that in the resulting movie the mouse had a constant orientation.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.Resulting trajectories were smoothed using a gaussian filter (30 ms width).When computing the snout trajectory, a reliable detection threshold was set based on a confidence level returned by the algorithm (>0.8).

Statistics
All statistics were performed using 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 and 2, each condition included between 171 and 513 trials (n = 8 mice).In Figure 3, each condition included 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 includes between 132 and 392 trials (n = 8 mice).In Figure 4E-M

Optogenetic stimulation of anterior vermal Purkinje cells elicits 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 (Chaumont et al. 2013).We implanted these mice with a small-core optic fiber (200 µm), which enabled confined light stimulations of PCs in freely moving mice.Optogenetic stimulations consisted of single continuous illuminations, which could be varied in intensity and duration.To prevent learned anticipatory reflexive behavior, light pulses were randomized and delivered at random intervals (mean frequency 0.1 Hz).
Mice were introduced into a transparent glass arena where they could behave freely (Figure 1A), thus preventing potential confounding factors encountered in constrained animals.Animals were monitored from the side and the bottom at high frame rate (100 Hz) to facilitate precise 3D spatio-temporal movement analysis.When optogenetic stimulations were delivered 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 movements' 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 M OFF appeared to overlap.For 50 ms duration stimulations M OFF would fall within the M ON latency window.Indeed, a single movement occurred and with a shorter latency than normal M ON (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, M OFF is not a correction of M ON (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 it being 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 (Witter et al. 2013;Lee et al. 2015).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 M OFF and had a constant amplitude (Figure 1D and 1J).
Although M ON seemed to increase gradually and saturate with stimulation power (Figure 1G and 1K), closer examination of the response at sub-saturating stimulations powers (7,5 and 15 mW/mm²) revealed that the amplitude distribution of the response was bimodal (Figure 1L).The first mode consisted of near-zero amplitude events, corresponding to failures of the M ON component of the response, while the second mode consisted of full-blown responses with amplitudes similar to those observed at high stimulation power (Figure 1L).Hence, the apparent gradual increase in average M ON response actually reflects a gradual decrease of M ON failure probability (Figure 1M), while the non-failure amplitude remained statistically independent from stimulation power (Figure 1K, p = 0.67 between 15 mW/mm² and 120 mW/mm², Wilcoxon rank sum test).Thus, M ON, a full-blown response of constant amplitude, qualifies as a reflex movement.Movie inspection revealed that M ON corresponded to a forward movement (Figure 2B; xb) which often involved a forward step when the animal was standing on its four legs, but more rarely when the animal was sitting on its hindlimb in a regrouped position (Movie S2).The forward step seen in the standing posture is consistent with previous observations in head-fixed animals (Hoogland et al. 2015).
Previous optogenetic stimulation of vermal PCs performed in head-fixed animals was shown to evoke a movement exclusively when light stimulation terminated (Witter et al. 2013).While we also observe this in a freely moving animal, we additionally report the occurrence of a M ON .
The reflexive nature of M ON 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 .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).
Histograms of M ON peak amplitudes for two stimulation powers (stimulation duration = 400 ms).M. M ON failure probability plotted against stimulation power (computed for stimulations longer than 200 ms).

The direct effect of the stimulation is a postural collapse
In order to better characterize animal movement kinematics, we segmented the mouse, recording simultaneously the body from side and bottom cameras, and extracted 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 barycenter (Zb) altitude, 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 M ON 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 and 2E, R = 0.998, p= 4.2e-6), 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 and 2H).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 (R = 0.972, p = 5e-4, 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 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 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 of the forelimbs involved in body support (triceps and pectoris), and extracted their muscle tone from the recorded signal by computing the EMG envelope (Figure 3A, see Experimental Procedures).During optogenetic stimulation, we observed that 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 stimulation commenced.Therefore, we considered these muscle contractions a signature of mouse postural reflex.As expected, contractions of these muscles were also observed at posture retrieval (Figure 3B and 3C).
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 pectoris begins to contract, and finally triceps (183 ± 45 ms for triceps, p = 6.4e-36 between the two muscle pairs of trapezius & splenius versus pectoris & triceps).On a trial-totrial basis trapezius and triceps contractions were highly correlated to the amplitude of the M ON- REFLEX (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 pectoris and splenius respectively).This 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 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 1.58 ± 0.6, 1.33 ± 0.20 mV for triceps and pectoris respectively).In contrast, we did not see a similar rebound in the two neck muscles (Figure 3G, rebound values -0.41 ± 0.35 mV, 0.27 ± 0.45 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.That said, other muscles, which were not recorded in our experiments, are likely to be affected as well by the optogenetic stimulations.
It is striking, however, that of the four muscles recorded, only the two extensors, which counteract gravity, appear to be directly affected.

Optogenetic mapping of the anterior cerebellar vermal output
We next set out to map the output of the anterior vermis.For this, we 3D-printed an implant for mounting a custom optic fiber array (fourteen cores of 50 µm aligned in 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 PCs (Figure 4A) at different medio-lateral 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 = 8 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 (Hawkes, Colonnier, and Leclerc 1985;Sugihara et al. 2009;Voogd 2011;Fujita, Kodama, and Du Lac 2020).
In order to assess the existence of functional subregions within the responding medial region of the vermis (six locations: lobules V and VI, medial or 400 µm left and right), 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 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 = 4 mice).Comparing these body maps for different stimulation locations, we found that the mouse movement was lateralized in both lobule IV/V and VI, the mouse body falling ipsilateral to the side of stimulation (Figure 4D).This was confirmed by 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).In contrast, negligible lateral displacement of the animal body was seen for midline stimulations (Figure 4D-F, 0.19 ± 0.58 mm and -0.25 ± 0.74 mm ΔYb body vertical displacement in lobule IV/V and VI respectively).As expected, a global collapse of the body barycenter was observed at all six locations tested within the responsive medial region (Figure 4G, bottom panels).
The mouse's snout is a good proxy of head movement (Figure 4E, see Experimental Procedures).The Y coordinate of the snout reported a lateralization of the stimulation effect (Figure 4H and I, 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 which was greater for medial stimulations, as 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).While stimulations in lobule IV/V produced a snout altitude decrease (Figure 4L), stimulations in lobule VI evoked an increase in the snout altitude during the stimulation (Figure 4L and M, 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 in both cases (Figure 4G).This result suggests that stimulation in lobule VI produces an additional contraction of the dorsal neck muscles.Overall, our results indicate 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 PCs, and that this collapse 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;Joyal et al. 1996;Manni and Petrosini 2004), 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 (Witter et al. 2013;Hoogland et al. 2015;Heffley et al. 2018).
One of them described a behavioral response of the animal exclusively at the termination of PC stimulation, which was characterized by whole-body twitches (Witter et al. 2013).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 (Hoogland et al. 2015) pointed to an initiation of stepping around 200 ms after stimulation commenced.This timing arguably corresponds to the compensatory postural adjustment we observed in our analysis, 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 can be reconciled if one accepts the plausible argument that in head-fixed animals (Hoogland et al. 2015), 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 our experimental paradigm), 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 fittingly strongly correlates with this part of the movement.Moreover, the steadfast 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 involved with the vestibular system (Horak 2006).For the muscles directly affected by the stimulation, however, 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 (Chaumont et al. 2013).Therefore, we can reasonably consider 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 maintained during the entire stimulation duration (Figure 3B-C), indicating prolonged compensation of the postural loss, seen as prolonged forward movement of the animal (Figure 1D).Nonetheless, since the barycenter altitude only recovers after stimulation termination, such compensation appears insufficient to overpower the stimulation effect, (Figure 2D-E).Thus, rather than decreasing a specific drive associated with anti-gravity maintenance, the cerebellum exerts a global gain of function on muscle tone, which precludes these muscles from being used in the subsequent motor commands and results in the forward stepping motion seen 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, these recordings did not reveal any muscle relaxation (Figure 3B-C).While the muscles affected during these stimulations could be in other body regions, such as the back or the belly of the animal, the specificity of the contraction at stimulus termination in these two muscles strongly implies that they are amongst the ones controlled by vermal lobule IV/V at the midline.Moreover, this hypothesis is in accordance with the known representation of the forelimbs in the vermis (Heffley et al. 2018;Wagner et al. 2021).Thus, 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 1mm 100ms after stimulation commenced.We can 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 signal 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 DCN inhibition that is graded (Chaumont et al. 2013;Witter et al. 2013).This assessment is important because strong PC stimulations have been shown to induce a depolarizing block in PC activity, which could result in net DCN disinhibition (Chaumont et al. 2013).The stimulation powers we report were measured directly at the fiber tip.Because we also utilize a glass coverslip 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 (Chaumont et al. 2013).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 (Chaumont et al. 2013).Finally, the postural collapse we observed was consistent over the entire range 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 disinhibiting it.

Spatial specificity of the stimulation
Our optogenetic mapping of the vermis relies on spatial specificity of PC excitation.In order to best limit 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 increased 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:  = 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 (Chaumont et al. 2013;Gysbrechts et al. 2016;Yona et al. 2016), 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 2 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.Based on previous experiments, we can affirm that PCs more than 200 µm from the stimulation site are very unlikely to be affected (Chaumont et al. 2013).Thus, our custom optic fiber array may, in theory, allow to stimulate at the microzonal scale.Indeed, the observed lateralization of the postural collapse argues for a degree of spatial specificity in our stimulations, and the ipsilateral effect on the animal's body is consistent with the known cerebellar projections to spinal cord motoneurons (Teune et al. 2000).However, we were not able to distinguish, in the behavioral output, transitions between microzones inside the responding region.This may be due to the lack of medio-lateral spatial sharpness at the edge of the light stimulation area, which entails a gradual transition from a putative microzone to the next.

Functional organization of the vermal output
The olivary input to PCs is organized in translobular parasagittal bands of CF projections with specific receptive fields (Andersson and Oscarsson 1978), but parallel fibers (PF) distribute sensori-motor information to PCs in the medio-lateral direction (Heck, Thach, and Keating 2007).A long-standing hypothesis, as identified for eyelid closure, ocular saccades and for limb movement (Hesslow 1994;Mostofi et al. 2010;Heiney et al. 2014;Herzfeld et al. 2015;Heffley et al. 2018;Sedaghat-Nejad et al. 2022), 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 (Mukamel, Nimmerjahn, and Schnitzer 2009;Kostadinov, Beau, Pozo, et al. 2019;Tsutsumi et al. 2019;2020).This intersectional domain hypothesis is, however, consistent with the known PC-DCN convergence pattern (R. Apps and Garwicz 2000;Voogd 2011) and the known organization of the DCN (Heiney, Wojaczynski, and Medina 2021).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 Apps et al. 2018), and a recently genetically identified posturo-motor module (Fujita, Kodama, and Du Lac 2020).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 region of posterior lobule VI stimulation, which may overlap with an output module involved in orienting head and eye movement (Fujita, Kodama, and Du Lac 2020), evoked an upward movement of the head.
In conclusion, our results establish for the first time a functional microzonal organization of vermal PC output, and pave the way for future studies aiming at dissecting further functional cerebellar output in other paradigms.

Figure 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

Figure 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 linear regressions.K. Slope of the linear regressions from J plotted against stimulation power.

Figure 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 and pectoris, 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% distribution limits respectively.E. Evolution of the EMG envelope of the triceps muscle with stimulation power (400 ms stimulations, n = 3 mice).F. Evolution of the EMG envelope of the triceps muscle with stimulation duration (30mW/mm² stimulations, n = 3 mice).G. Relative muscle contractions for the muscles recorded in B following light termination.Same representation as in D (400 ms 30 mW/mm² stimulations).

Figure 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 = 8 mice, 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 (six locations: lobules V and VI, medial or 400 µm left and right, n = 4 mice, 30 mW/mm² 400 ms stimulations).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.