An output-null signature of inertial load in motor cortex

Kirk, Eric A.; Hope, Keenan T.; Sober, Samuel J.; Sauerbrei, Britton A.

doi:10.1038/s41467-024-51750-7

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Published: 24 August 2024

An output-null signature of inertial load in motor cortex

Eric A. Kirk¹,
Keenan T. Hope¹,
Samuel J. Sober² &
…
Britton A. Sauerbrei ORCID: orcid.org/0000-0003-3386-3243¹

Nature Communications volume 15, Article number: 7309 (2024) Cite this article

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Abstract

Coordinated movement requires the nervous system to continuously compensate for changes in mechanical load across different conditions. For voluntary movements like reaching, the motor cortex is a critical hub that generates commands to move the limbs and counteract loads. How does cortex contribute to load compensation when rhythmic movements are sequenced by a spinal pattern generator? Here, we address this question by manipulating the mass of the forelimb in unrestrained mice during locomotion. While load produces changes in motor output that are robust to inactivation of motor cortex, it also induces a profound shift in cortical dynamics. This shift is minimally affected by cerebellar perturbation and significantly larger than the load response in the spinal motoneuron population. This latent representation may enable motor cortex to generate appropriate commands when a voluntary movement must be integrated with an ongoing, spinally-generated rhythm.

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Introduction

The ability to perform the same movement repeatedly in a changing environment is a hallmark of skilled motor control. Inertial load is a key environmental variable which changes with the distribution of mass across the body and must be countered with appropriately-scaled motor commands. For example, raising a coffee cup to the lips when the cup is empty and full requires different patterns of muscle activity. Similarly, the motor output generated during walking in bare feet must be adjusted when heavy boots and a backpack are worn. Such adjustments pose a demanding challenge for neural control, which is distributed across multiple interacting systems, including the motor cortex, cerebellum, brainstem, spinal cord, and muscle receptors (Fig. 1a).

**Fig. 1: Mice rapidly adjust motor output following a change in forelimb load.**

In the context of voluntary movement, studies in nonhuman primates have demonstrated that the motor cortex drives the generation of forces to move the upper limb and to compensate for loads^1,2, and cortical neurons are modulated by force magnitude and direction^3,4,5,6. Furthermore, several observations suggest that load-related responses in the motor cortex might be driven, in part, by ascending cerebellar input. Cooling of the cerebellar dentate nucleus attenuates long-latency motor cortical responses to impulse torques during voluntary movement^7,8, though cortical activity during holding against a load is minimally affected by this manipulation⁹, and disruption of the cerebellar outflow with high-frequency electrical stimulation can partially suppress cortical activity in an isometric wrist task¹⁰. On the other hand, firing rates in cerebellar Purkinje cells closely resemble kinematics, but are altered only slightly with changes in force required to move the hand against viscous or elastic loads¹¹. In mice, the forelimb is approximately three orders of magnitude less massive than in primates, and inertial forces may be relatively less important in control. The mouse behavioral repertoire and manual dexterity are also more limited. Nonetheless, mice can be trained to perform precise reaching and grasping tasks. The forelimb regions of the sensorimotor cortex are not necessary for pulling a lever against a load¹², but are required for adaptation to a force applied to a pulled lever over dozens of trials¹³, and for the initiation and execution of reach-to-grasp movements^12,14,15,16.

The complexity and heterogeneity of the motor cortical population pose a significant challenge to understanding its role in control^17,18. For example, a neuron’s response to load during reaching cannot be accurately predicted from its load sensitivity during posture⁶, and directional tuning can change substantially between movement preparation and execution¹⁹ and throughout a reach¹⁷. A powerful emerging approach to this complexity focuses less on the information represented by individual neurons and more on the coordinated dynamics across the cortical population, how these dynamics are related to features of the task, and how they are generated by interactions across brain areas and with the sensory periphery^{15,20,21,22,23}. This approach has helped explain several perplexing features of cortical activity, such as the observation that large changes in firing rate can occur during motor preparation without evoking movement. As a movement is planned, cortical activity changes in directions, termed output-null dimensions, along which the net effect of cortical output on muscle activity is constant^24,25. These changes enable the cortical population state to be set to the appropriate initial condition from which activity can evolve during movement execution. More broadly, a growing body of work²⁶ has shown that output-null dynamics are a key mechanism for preparing movements^24,25, correcting errors online²⁷, and learning^28,29,30 without producing aberrant muscle activity.

Given the central role of motor cortical dynamics in voluntary limb movements, how might these dynamics contribute to load compensation in rhythmic movements which are coordinated by an intrinsic spinal network? In mammalian overground locomotion, a spinal central pattern generator (CPG) governs the basic pattern of flexor-extensor and left-right limb alternation, can operate independently of the brain and sensory feedback^31,32,33, and is controlled by networks in the midbrain and brainstem that determine locomotor initiation and speed^34,35,36. The motor cortex is not necessary for locomotion over a flat surface, but is required when precision demands are increased during steps over obstacles or across a horizontal ladder^{12,37,38,39,40}. Some adjustments for mechanical load are implemented by subcortical structures: in walking premammillary cats, for instance, loading of an ankle extensor tendon increases the activation of the corresponding muscle during stance, and can suppress the CPG when large forces are applied⁴¹. Nonetheless, the rhythmic, step-entrained activity of some cortical cells, including pyramidal tract neurons projecting to the spinal cord and brainstem, can be modulated by speed and by loading of the limb^42,43, suggesting that descending cortical signals may be important for the regulation of force during locomotion.

The present study aims to address three central questions. First, does the motor cortex drive compensation for changes in inertial load imposed on the limbs during locomotion, as it does in voluntary movement, or is this compensation instead implemented by subcortical structures? Second, how are such loads represented in motor cortical population activity, and does the representation depend on cerebellar input? Finally, how are cortical dynamics related to the output of the nervous system at the level of the spinal motoneuron population? We address these questions in unrestrained, chronically instrumented mice performing an adaptive locomotion task in which they must adjust motor output to compensate for a weight on the wrist. Our approach combines three-dimensional kinematic pose estimation, recordings from forelimb muscles, the motor cortex, spinally-innervated motor units, optogenetic perturbations, and computational approaches for modeling neural population data. We find that, although inactivation of the motor cortex does not attenuate load compensation, the dominant component of cortical population activity is a tonic shift imposed by the load, and is robust to optogenetic perturbation of the cerebellum. Furthermore, the geometric properties of cortical population activity in the task contrast strongly with those of the spinal motoneuron population. While cortical activity is significantly modulated by load, cerebellar perturbation, and animal speed, with cortical trajectories that maintain relatively low tangling across experimental conditions, consistent with noise-robust dynamics, the spinal motoneuron population is instead dominated by condition-invariant signals related to flexor-extensor alternation, and also exhibits higher trajectory tangling. We conclude that load-related dynamics in the motor cortex do not directly drive motor compensation during locomotion, but instead constitute a latent representation of changes to the limb mechanics, which may modulate cortical commands during voluntary gait modification or alter the gain of spinal reflexes to correct for unexpected perturbations.

Results

Adaptation of locomotor output to changes in inertial load

Unrestrained mice were trained to trot at ~20 cm/s on a motorized treadmill as their movements were captured with four synchronized high-speed cameras (Fig. 1b). Three-dimensional limb kinematics were measured from video using an automatic pose estimation pipeline^44,45, enabling extraction of fingertip position and velocity (Fig. 1c, lower: magenta and green traces) and segmentation of the session into swing and stance epochs (Fig. 1c, lower: green boxes). Electromyograms (EMG) were recorded from forelimb flexor (biceps brachii) and extensor (triceps brachii) muscles, rectified, and smoothed (Fig. 1c, lower: gray traces). At the beginning of each session, animals ran freely for 5–20 minutes. We then imposed an inertial load on one forelimb by attaching a 0.5 g weight to the wrist, increasing the moment of inertia of the radius-ulna about the elbow, and the animals ran for a second epoch of 5–10 min. This load, which increased the total mass of the forelimb by ~50%, induced a compensatory increase in elbow flexor muscle activity during swing and a corresponding suppression of extensor activity during stance (Fig. 1d). The compensation was consistent across step cycles (Fig. 1e) and sessions (Fig. 1f; signed rank test, p = 8.4e-6 for biceps, p = 7.1e-3 for triceps). Finger velocity was, on average, slightly higher in the loaded condition (Fig. 1f; p = 5.7e-4), consistent with modest overcompensation for the load. Furthermore, in contrast with adaptation to a split-belt treadmill, which unfolds over many successive steps and requires the cerebellum^46,47, this adaptation appeared to occur almost instantaneously after the load was applied (Fig. 1g).

Load compensation is robust to perturbation of the motor cortex and cerebellum

Adjustment of motor output in different tasks requires distinct contributions from motor cortex^43,48, cerebellum⁴⁹, and cerebellar inputs to cortex⁸. To determine whether the observed compensation for inertial load requires the motor cortex and cerebellum, we used an optogenetic approach to transiently inactivate each brain area during the task. Motor cortical perturbation experiments were performed in VGAT-ChR2-EYFP mice, which express the light-gated ion channel ChR2 selectively in inhibitory interneurons, enabling robust suppression of cortical output following illumination of the brain surface with blue light^15,50. An optical fiber was implanted over the forelimb motor cortex (Fig. 2a, left), and animals performed treadmill locomotion with and without a 0.5 g weight on the contralateral forelimb as laser stimulation was delivered intermittently to suppress motor cortical activity (473 nm, 40 Hz, 1 s stimulus duration, randomized 1–6 s delay between stimuli). While the load induced an increase in elbow flexor muscle activity during swing and a decrease in extensor activity during stance, cortical perturbation did not attenuate this compensation (Fig. 2a, center and right). We next tested the effects of cerebellar perturbation on motor output by implanting a fiber over the forelimb area of the pars intermedia ipsilateral to the loaded forelimb in L7Cre-2 x Ai32 mice (Fig. 2b, left), which express ChR2 selectively in Purkinje cells and allow suppression of cerebellar output during laser stimulation⁵¹. Cerebellar perturbation did not erase the adaptation of motor output to the load; on the contrary, it produced a modest flexor muscle enhancement and extensor attenuation (Fig. 2b, center and right and Supplementary Fig. 1c, d). To quantify the effects of load, optogenetic perturbation, and speed on motor output, we fit a linear model for each experimental session and examined the distribution of the resulting coefficients (Fig. 2c and Supplementary Fig. 1c, d; see Methods). The load had a significant positive effect on elbow flexor EMG and a negative effect on extensor EMG (sign rank test, q < 0.05), and step frequency had positive effects on both flexor and extensor EMG. The interaction terms between load and both optogenetic perturbations were centered at zero, indicating that these perturbations failed to erase the adaptation of motor output to changes in load. Overall, these results show that load compensation in the task does not require normal motor cortical or cerebellar output.

**Fig. 2: Load adaptation is robust to cortical and cerebellar perturbation.**

Load and cerebellar perturbation modulate motor cortical activity

The finding that muscle activity was unaffected by cortical inactivation could be explained simply by a lack of cortical responsiveness to load. Alternatively, the motor cortex might track changes in limb mass by shifting its state along output-null dimensions—that is, dimensions which do not directly influence muscle activity. We note that because cortical inactivation not only failed to erase load-related changes in EMG, but had no detectable effect on locomotor performance, any cortical activity in the task should be confined to the null space. Furthermore, in the latter case, load-related activity in the cortex might be driven by input from the cerebellum, or by input from other sources. To distinguish between these explanations, we chronically implanted high-density silicon probes in the motor cortex of L7Cre-2 x Ai32 mice, along with an optical fiber over the contralateral forelimb area of the cerebellar pars intermedia (Fig. 3a). Mice then performed the adaptive locomotion task as we recorded limb kinematics and cortical spiking (n = 710 neurons, n = 2 mice) while intermittently perturbing the cerebellum by stimulating Purkinje cells (473 nm, 40 Hz, 1 s stimulus duration, randomized 1–6 s delay between stimuli). Most neurons were synchronized with the locomotor rhythm (n = 618/710, 87.0%, q < 0.05, Rayleigh test with Benjamini–Hochberg correction for multiple comparisons), consistent with studies in cats^37,43 and primates^52,53. The effects of load and cerebellar perturbation were highly diverse across neurons. Firing rates for some cells were modulated by load (neurons 1–3, Fig. 3b), by Purkinje cell stimulation (neuron 5), or by both (neuron 6), while effects were relatively modest for others (neuron 4). While the range of patterns observed in both animals was qualitatively similar, with many neurons exhibiting responses to load and cerebellar perturbation, the former were more numerous in one mouse, and the latter in the other (Supplementary Fig. 2). Overall, 47.7% of neurons exhibited changes related to load, 24.1% to Purkinje cell stimulation, and 10.6% to both, while interaction between load and Purkinje cell stimulation occurred in only 2.7% of cells (multi-way ANOVA for each neuron, q < 0.05). Among the load-sensitive neurons, 46.0% had higher firing rates in the load-on condition; among the neurons sensitive to Purkinje cell stimulation, 71.9% had a response of higher firing rates (Fig. 3c, d).

**Fig. 3: Load and cerebellar perturbation modulate motor cortical neuron activity.**

Cortical population dynamics in adaptive locomotion

Because the effects of load and cerebellar perturbation were heterogeneous across the sample of cortical cells, we next aimed to identify the coordinated, low-dimensional dynamics across the population. To extract a low-dimensional representation of cortical population dynamics in interpretable, task-relevant coordinates, we used demixed principal component analysis (dPCA; see Methods), which decomposes neural activity into dimensions related to specific experimental parameters while capturing most of the variance in the original firing rates⁵⁴. Because animals frequently modulated their speed on the treadmill by starting and stopping locomotion, potentially influencing cortical firing rates, we included speed as a pseudo-experimental variable, in addition to load and cerebellar perturbation. For each cortical neuron, the average step-aligned firing rate was measured in twenty conditions: load on/off (two levels) x Purkinje cell stimulation on/off (two levels) x animal speed (five levels). Next, we used dPCA to find a decoder matrix that mapped the firing rates for all neurons onto a 20-dimensional latent variable space. This model explained 92.9% of the total firing rate variance and yielded scores parameterized by step phase for each dimension and condition (Fig. 4a–c), and an encoder matrix that reconstructs the measured firing rates from these scores. We observed condition-invariant signals that were modulated by step phase, but did not differ strongly across experimental parameters (Fig. 4a, X-Y axes; Fig. 4b, first and second columns, first row). The first condition-invariant dimension was roughly sinusoidal, with a period of one stride and a peak near the swing-stance transition, while the second was qualitatively similar except for a phase shift, with a peak in mid-swing. Taken together, the condition-invariant components accounted for 28.8% of the explained variance in cortical firing rates. Animal speed had a moderate effect on cortical dynamics (18.9% of the variance), but this was distributed broadly across multiple dimensions (Fig. 4b, first column, second row; Fig, 4c). The largest speed component consisted of tonic shifts in activity, with little dependence on the step phase. Dynamics in this dimension and the top two condition-invariant dimensions, therefore, yielded stacked elliptical trajectories that translated continuously with movement speed (Fig. 4a, right), reminiscent of motor cortical dynamics in primates performing a rhythmic cycling task⁵⁵.

**Fig. 4: Load strongly modulates cortical population dynamics.**

The largest single component of cortical activity, however, was related almost purely to inertial load (Fig. 4a, left; Fig. 4b, third column, first row), accounting for 22.6% of the explained variance in firing rate. This component depended only weakly on step phase, and consisted of a tonic shift in activity between the load-on and load-off conditions, consistent with patterns observed in individual neurons (c.f. cells 1, 3, and 6 in Fig. 3b). Because inactivation of motor cortex had no effect on muscle activity (Fig. 2), we conclude that cortical activity in all measured conditions and dimensions - including the load-related dimensions - was confined to the output-null subspace. Because prior work has shown cortical compensation for load during voluntary upper limb movements can be influenced by ascending cerebellar drive^7,8, we next tested whether the load signals observed during locomotion were cerebellum-dependent by examining several consequences of cerebellar perturbation. First, the effect of Purkinje cell stimulation was concentrated primarily in a single dimension (11.8% of the variance; Fig. 4c) and, like the load effect, consisted of a tonic shift in activity (Fig. 4a, center; Fig. 4b, fourth column, first row). Second, the principal axes with the largest effects of load and cerebellar perturbation were not closely aligned (inner product −0.45; Fig. 4c, upper triangular matrix), though we failed to reject the null hypothesis that their relative orientations were random (p = 0.31, exact test based on beta distribution; Fig. 4c, lower triangular matrix). Third, the interaction between load and cerebellar perturbation was small, accounting for only 1.0% of firing rate variance (Fig. 4b, second column, second row; Fig. 4c). Fourth, activity in the top load-related dimension was not partitioned by cerebellar perturbation; instead, trajectories were tightly grouped within each load condition (Fig. 4a, left; Fig. 4b, third column, first row). Fifth, projection of firing rates aligned to the onset of cerebellar perturbation onto the top load dimension revealed a minimal response (Fig. 4d, upper), while projection onto the first Purkinje cell stimulation dimension produced a large signal that was sustained throughout the stimulus train (Fig. 4d, lower). Finally, an analysis of population activity using principal component analysis, which provides an orthonormal basis, revealed that the load and Purkinje cell stimulation induced nearly orthogonal shifts in neural trajectories (Supplementary Fig. 3a–d). Taken together, these observations support the hypothesis that the cortical representation of load in the adaptive locomotion task is independent of cerebellar input.

Effects of load and cerebellar perturbation on spinal motoneuron dynamics

Intuitively, it might be expected that a load representation in the cortical null space would be small relative to the changes in muscle activity required to move the limb against a load. Ideally, this intuition would be tested against recordings at cellular resolution from spinal motoneurons, which forward the ultimate results of central computations to muscles that actuate the body. In healthy motor units, muscle fiber action potentials are tightly locked to action potentials in the corresponding motoneuron, and motor unit potentials recorded in the muscle enable the measurement of motoneuron spike trains. Thus, we implanted flexible fine wire electrodes and high-density electrode arrays in the forelimb muscles, enabling us to record motor output at the resolution of individual spinally-innervated motor units in the adaptive locomotion task (Fig. 5a; n = 108 motor units, n = 27 sessions, n = 6 L7Cre-2 x Ai32 mice). Of the six animals, three were implanted with traditional fine wire EMG electrodes^12,56,57, and three were implanted with Myomatrix arrays⁵⁸ designed to record forelimb muscles in the mouse. This approach allowed a comparison of motor unit yield between the two electrode designs. As detailed in the Methods, mice were each implanted with either four twisted fine wire EMG electrodes or with a single Myomatrix array with four “threads”. In two mice, all four Myomatrix threads were implanted in target muscles, and in the third mouse, only two of the four threads were successfully implanted. Animals implanted with fine wire EMGs performed a total of 14 recording sessions yielding 35 motor units (mean 2.5, min-max 1–5, per session; n = 3 mice). Animals implanted with Myomatrix devices performed 13 recording sessions, yielding 73 motor units (mean 5.6, min-max 2–10, per session; n = 3 mice). These results indicate a significant increase in motor unit yield from Myomatrix electrode arrays compared to traditional fine wire methods (p < 0.01, two-sample KS-test).

**Fig. 5: Spinal motoneuron activity is influenced by load and cerebellar perturbation.**

Inertial load and cerebellar perturbation were applied as in the cortical recording experiments. Motor units were more strongly entrained to the locomotor rhythm (n = 108/108, q < 0.05, Rayleigh test) in comparison to cortical units, with flexor motor units activated during swing, and extensor motor units during stance (Fig. 5b). The firing rates of 50.9% of motor units were significantly modulated by load (n = 55/108; q < 0.05, multi-way ANOVA; Fig. 5c, d), 28.7% by Purkinje cell stimulation (n = 31/108), 20.4% by both load and stimulation (n = 22/108), and 7.4% by the interaction between load and stimulation (n = 8/108). Among the load-sensitive neurons, 38.2% had firing rate increases, while increases occurred in 71.0% of Purkinje cell stimulation-sensitive neurons. To identify coordinated activity patterns at the motor unit population level, we performed dPCA as for the cortical population, and projected firing rates onto twenty dPCA decoder dimensions, which explained 94.2% of the total firing rate variance. The dominant patterns revealed by dPCA consisted of robust, condition-invariant oscillations (Fig. 6a, X-Y axes; Fig. 6b, first two columns, first row), and overall, the condition-invariant signals accounted for 70.6% of the explained firing rate variance (Fig. 6c). The first two condition-invariant dimensions showed approximately sinusoidal oscillations with a period of one stride. Inertial load and Purkinje cell stimulation had modest effects, accounting for 7.4 and 4.6% of the variance, respectively (Fig. 6a, left and center; Fig. 6b, third and fourth columns, first row; Fig. 6c). In contrast with cortical activity patterns, the first load and Purkinje cell stimulation dimensions for the motor unit population exhibited a clear dependence on step phase, with maximal separation between conditions in mid-stance. Animal speed accounted for 12.8% of the firing rate variance, with continuous, tonic shifts in the first speed dimension (Fig. 6b, first column, second row). While these patterns yielded stacked, elliptical trajectories in the first two condition-invariant dimensions and the first speed dimension (Fig. 6a, right), roughly resembling the corresponding cortical dynamics (c.f. Fig. 4a, right), these spinal trajectories were less clearly separated across speed conditions in comparison to the cortex. The projection of motor unit firing rates aligned to Purkinje cell stimulation onto the dPCA axes revealed no effect on load dimensions, but a small, tonic modulation in the first two stimulation dimensions (Fig. 6d), though these were small in comparison to the corresponding cortical signal (c.f. Fig. 4d). Finally, an analysis of population activity using principal component analysis, which provides an orthonormal basis, revealed that the load and Purkinje cell stimulation induced smaller shifts in spinal trajectories (Supplementary Fig. 4a–d).

**Fig. 6: Spinal motoneuron dynamics are predominantly condition-invariant.**

Distinct dynamics in cortical and spinal motoneuron populations

Although neural dynamics in the cortical and spinal populations had several qualitative similarities, including the shape of trajectories in the leading condition-invariant and speed dimensions, several key differences were apparent. First, the condition-invariant dimensions had similar time-varying trajectories (Figs. 4b, 6b, first and second columns, first row), but the amount of firing rate variance explained was 2.4-fold larger in the spinal motoneuron population (70.6 and 28.8% in spinal and motor cortex, respectively). In this sense, the spinal population response primarily reflected the locomotor rhythm, while load, speed, and Purkinje cell stimulation imposed smaller modulations on this rhythm. In the motor cortex, however, the dominant signal was related to load, and components for both Purkinje cell stimulation and speed were also prominent. This larger balance of condition-invariant activity for spinal motor output in comparison with cortex in locomoting mice contrasts with findings in primates reaching multiple targets, which showed a much larger condition-invariant component in cortex⁵⁹, and in primates walking over obstacles⁵³. Second, load and Purkinje cell stimulation effects for the motor cortex consisted primarily of tonic shifts, whereas the corresponding effects on spinal motoneurons were modulated by step phase. Third, neural trajectories were more clearly separated at different speeds for the cortical than for the spinal population.

To determine how the geometry of neural trajectories changed across conditions, we next asked how a change in a given experimental variable (e.g., from load-off to load-on) reshaped the trajectories by turning, moving, or stretching them. In particular, for each neural population (motor cortex and spinal motoneurons) and variable (load, Purkinje cell stimulation, and speed), we used Procrustes analysis to identify the rotation, translation, and rescaling required to map trajectories in baseline conditions (load-off, stimulation-off, and lowest speed) to the corresponding trajectories in the complementary conditions (load-on, stimulation-on, and highest speed; see Methods). This produced a concise description of how each experimental manipulation altered neural trajectory geometry. Inertial load and Purkinje cell stimulation induced large vertical translation in the cortical trajectories (Fig. 7a, left and center), but produced largely rotational effects for spinal trajectories (Fig. 7b, left and center; Fig. 7c, left and center), resulting from the modulation by step phase in the latter case. For speed, both populations displayed a combination of rotation and translation, along with a slight increase in scale (Fig. 7a–c, right).

**Fig. 7: Distinct neural population geometries in the motor cortex and spinal motoneurons.**

We also observed that, while cortical trajectories were clearly separated across experimental conditions, spinal trajectories had greater overlap across conditions and time points. To quantify this finding, we computed a trajectory tangling index⁶⁰ (see Methods), which measures the extent to which nearby neural states have distinct derivatives. We found that trajectories in the motor cortex consistently exhibited lower tangling in comparison with the spinal motoneuron population (Fig. 7d). Highly tangled trajectories imply dynamics that are driven by external input, while low tangling may suggest more autonomous dynamics that are robust to noise. However, the motor cortex maintains relatively low tangling despite the presence of strong signals about the state of the limbs and throughout experimental manipulation of cerebellar inputs. Thus, low tangling might constitute a mark of noise robustness even in systems that depend strongly on inputs.

Discussion

In this study, we have identified a robust signature of limb inertial load in the mouse motor cortex during adaptive locomotion, which comprised the largest single component of cortical activity in the task. Because muscle activity during load compensation was unchanged by cortical inactivation, we conclude this load-related signal is not a motor command underlying the compensation, but is instead a latent, output-null representation (Fig. 8). Our finding that activity along the load dimension is minimally influenced by cerebellar perturbation further suggests it is not driven primarily by cerebellar projections through the ventrolateral thalamus, but likely reflects sensory signals ascending from the dorsal column nuclei via somatosensory cortex^61,62. Extensive work in cats and primates has shown that responses in the motor cortex can be driven by proprioceptive and cutaneous inputs^{63,64,65,66,67}, though the latter appears to be attenuated during active movements, including locomotion⁶⁸. In mice, signals broadly distributed across the cerebral cortex can reflect spontaneous movements, and these signals are likely generated, in part, from sensory feedback⁶⁹. In the locomoting mouse, however, it is possible that the load-related shift in the cortex may not reflect purely sensory information; given its relatively weak dependence on the locomotor phase, this shift could be a more abstract contextual signal from other cortical regions or neuromodulatory inputs, reflecting a reconfiguration of network dynamics⁷⁰.

**Fig. 8: Schematic illustrating key questions, experiments, and findings.**

We suggest two potential interpretations of our central finding. First, an output-null representation of load may support the generation of appropriately-scaled commands when a voluntary modification of gait that requires motor cortex must be integrated with the spinally-generated locomotor program. Studies in cats and mice have shown that unimpeded locomotion on a flat surface is relatively automatic, and can be largely handled by the spinal CPG, postural reflexes, and an input specifying speed. Our data indicate that compensation for an increase in inertial load is also handled by subcortical centers, and appears to be relatively automatic. However, when voluntary adjustments are required, as when an animal must traverse a barrier or precisely place its feet on the rungs of a ladder, the motor cortex becomes essential, and generates commands to alter gait^37,38,39,40. Such voluntary commands must also take into account changes to the limb mechanics: a leap over a hurdle in bare feet will require different commands than a leap in hiking boots, or while carrying a heavy backpack. Thus, we reason, the motor cortex should continually represent the parameters and state of the plant, including the mass distribution across the limbs, even when it is operating in an output-null regime, in order to subsequently generate appropriate commands when discrete, voluntary adjustments such as a step over an obstacle are required. The output-null shift in response to load we identify here is a candidate for such a cortical representation. A second possible interpretation is that the motor cortex may adjust the gain of spinal reflexes to regulate joint impedance⁷¹ and calibrate the motor response to unexpected perturbations, as has been found for rhythmic, voluntary upper limb movements⁷² and on a longer time scale during split-belt locomotor adaptation in humans⁷³.

How might subcortical centers use sensory feedback to adjust muscle activity in our task? Prior studies in cats suggest positive force feedback in the homonymous muscle mediated by Ib afferents enhances extensor activation during stance as the load is increased^41,74. It is possible we observe an analogous response for the flexors: the wrist weight may increase flexor tendon strain early in swing, inducing an increase in flexor activation and, subsequently, a suppression in the extensors. We expect future studies in mice will exploit the growing arsenal of tools for precise optogenetic manipulations to suppress specific classes of afferents⁷⁵ (e.g., tendon afferents and primary and secondary spindle afferents) to narrow down the circuits involved in load-compensatory responses. Viewed more broadly, our task exemplifies the general problem of adjusting periodic force profiles to counter mechanical constraints imposed by the environment. This problem is solved by neural control in humans to grip food during chewing⁷⁶, lungfish swimming in media of different viscosities⁷⁷, stick insects and cockroaches walking with variable load and substrate friction^78,79,80,81, and cats performing treadmill locomotion as the gravitational load is altered⁸². Despite their diversity, these adaptive motor programs share a strong reliance on sensory feedback, phase-dependent gating, a relatively automatic character, and implementation at lower levels of the motor hierarchy.

The motor cortical dynamics we observed share several key similarities with those reported in primates performing a voluntary cycling task^55,60,83. Neural trajectories in the primary and dorsal premotor cortex during cycling are periodic and elliptical in the dominant dimensions, and translate continuously along an axis approximately orthogonal to the plane of rotation with changing speed. These dynamics are consistent with a cortical rhythm generator that determines movement speed and phase while driving smaller, more complex, muscle-like output commands that control movement via corticospinal projections. In locomotion, by contrast, the rhythm is generated by an intrinsic spinal circuit, and oscillatory activity in the cortical condition-invariant dimensions likely reflects sensory feedback or an efference copy from the CPG. Thus, although the condition-invariant activity in mouse spinal motoneurons qualitatively resembles the cortical dynamics, it is unlikely they are driven by cortical commands. Indeed, we observed that the inactivation of the motor cortex had little effect on either the rhythmic flexor-extensor alternation or on the additional forelimb EMG changes imposed by load.

Another feature of primate cortical dynamics during cycling is the maintenance of significantly lower trajectory tangling in comparison with muscle activity. That is, nearby neural states have similar derivatives, so cortical trajectories tend to avoid crossing one another across different time points and conditions (see Methods). Because higher tangling is a signature of external forcing, low tangling is therefore consistent with strong internal dynamics in the primate cortical network during the task. Similarly, tangling is low in the spinal CPG for scratching in the turtle, which transforms a tonic stimulus into rhythmic output through local network interactions⁸⁴. In locomoting mice, we also observe lower levels of tangling in the motor cortex in comparison to the spinal motoneuron population, which must be driven by external inputs. This difference, however, is smaller than in the primate cycling task, consistent with a spinal rather than cortical locus of pattern generation, and with a greater role for inputs in driving cortical dynamics. In addition, cycling studies used both forward and backward rotations, which tended to increase tangling in muscle trajectories, while we tested locomotion in the forward direction only. Our alignment of neural activity to mouse step cycles might also attenuate tangling differences, as the duration of a step is relatively short - approximately 250 ms. Recent modeling and experimental work⁸⁴ has demonstrated rotational dynamics in the spinal CPG that can control the frequency and vigor of rhythmic movements while maintaining low trajectory tangling. In light of this finding, we expect tangling may arise primarily at the final stage of the motor system, in the spinal motoneuron population, and that load compensation might be achieved by increasing the rotation amplitude in the CPG network. Future studies could test this hypothesis in rodents by recording from the spinal interneuron population in freely moving animals, though this will require technically challenging experiments.

Our findings highlight a disassociation between the dominant patterns of motor cortical activity in a given task and the necessity of these patterns for generating motor output. Because many distinct descending and spinal pathways ultimately converge onto the same motoneurons, the problem of inferring the effects of cortical dynamics on muscle activity from simultaneous measurements of both is necessarily ill-posed. Furthermore, changes in cortical activity with experimental conditions or behavioral epochs may effectively cancel out at the motoneuronal level, enabling cortical computations to occur without influencing movement^24,25. An emerging body of evidence suggests the contribution of the motor cortex to forelimb movements can depend strongly on behavioral tasks and context. In the mouse, silencing the motor cortex has negligible effects on normal locomotion^12,40, moderately impairs skilled gait modification⁴⁰, and severely disrupts precise reach-to-grasp movements^14,15,16. Correlations between cortical neurons and the mapping between neural and muscle activity can change substantially between tasks^12,85, though work in the cat suggests this mapping is preserved between voluntary gait modification and reaching⁸⁶. In rats, lesions to the motor cortex impair learning of an interval timing task, but do not affect performance if delivered after the task has been learned⁸⁷, and the necessity of the motor cortex for a task can depend on the preceding training regimen⁸⁸. Meanwhile, studies of neural population dynamics in reaching primates have emphasized the significance of cortical dimensions that are decoupled from movement and contribute to internal computations during motor preparation^24,25, initiation^59,89, and learning^28,29. Our results build upon these findings by identifying a robust, latent representation of limb mechanics in motor cortical population activity during the adaptation of a rhythmic movement governed by a spinal CPG.

Methods

Experimental animals and behavioral task

All experiments and procedures were approved by the Institutional Animal Care and Use Committee at Case Western Reserve University, and in accordance with NIH guidelines. At the time of surgical implantation, all mice were 16–23 weeks old and weighed 24–33 g. Mice with higher body mass were selected for experiments, as they were better able to carry the implant payload on the head. A total of 12 adult mice were used for experiments, including four (male) VGAT-ChR2-EYFP line-8 strain mice (Jackson Laboratory; JAX stock #014548) and eight (six male and two female) L7Cre-2 x Ai32 strain mice (Jackson Laboratory; JAX stock #004146 and #024109). Hemizygous VGAT-ChR2-EYFP mice obtained from JAX were bred with C57Bl/6J mice to obtain experimental animals. Homozygous L7-Cre2 and homozygous Ai32 mice (both obtained from JAX) were bred to obtain experimental animals. Animals were healthy, individually housed under a 12-h light-dark cycle at 65–75 °F and 40–60% humidity, and had no prior treatment, drug, or altered diet exposure. After surgery, animals were cared for and studied for up to 3 months.

General surgical procedures

All mice were implanted with optical fibers for optogenetic perturbation, and with either (1) fine wire electrodes in forelimb muscles for electromyographic (EMG) recording, (2) Myomatrix arrays⁵⁸ for high-resolution recording from motor units, or (3) silicon probes in motor cortex for neural ensemble recording. The initial surgical procedures preceding the implantation of EMG or neural electrodes was similar across surgeries. Anesthesia was induced with isoflurane (1–5%, Kent Scientific), eye lubricant was applied, fur on top of the head and posterior neck was shaved, and the mouse was positioned in a stereotaxic apparatus (model 1900, KOPF instruments) on top of a heating pad.

Under sterile technique, the top of the head was cleansed with alternating swabs of 70% ethanol and iodine surgical scrub, lidocaine (10 mg/kg) was injected under the skin on the top of the skull, the skin was removed, the periosteum on top of the skull removed, and a custom-designed 3D-printed head post was attached with UV-cured dental cement (3 M RelyX Unicem 2). Then, optical fibers and chronic recording electrodes were surgically implanted (see below). Post-surgery, the minimum recovery period was 48 h, Meloxicam (5 mg/kg) was administered for pain management once per day, and the investigators monitored animal behavior, body mass, food, and water intake on a daily basis. The recovery period was extended an additional 24–48 h for some animals as necessary.

Adaptive locomotion task

After at least 2 days of recovery from surgery, mice were placed on a custom-built motor-driven treadmill (46 cm long by 8 cm wide) that was controlled at fixed speeds between 10–30 cm/s (Fig. 1b). The treadmill apparatus was enclosed in transparent acrylic, and belt speed monitored by a rotary encoder. Locomotion was motivated through negative reinforcement with airpuffs triggered by an infrared brake beam at the back of the treadmill belt. Mice were acclimated to the apparatus for up to three sessions, until they ran continuously without prompting. For the condition of unrestrained, load adaptive locomotion, one investigator briefly scruffed the mouse while another positioned a small weight (0.5 g) on the wrist, and at the conclusion of the load-on condition, the wrist weight was removed. The wrist weight was fabricated by gluing a steel ball bearing to a small zip-tie. For each animal, recording sessions were performed up to twice a day. Per session, mice ran between 5–20 min within the load-off and 5–10 min within the load-on conditions. Sessions started with the mouse running in the load-off condition that was followed by load-on, in a subset of sessions (n = 8) there was a final load-off condition that was performed. Each session was concluded based on mouse performance having at least 5 min of continuous locomotion per condition, or was ended due to mouse stress or reaching the 30 min time mark.

Videography

Four synchronized high-speed cameras (Blackfly, model BFS-U3-16S2C-CS, Teledyne FLIR; Vari-Focal IP/CCTV lens, model 12VM412ASIR, Tamron) were positioned around the treadmill, with two cameras recording from each side of the treadmill belt, acquiring approximately sagittal views of the locomoting mouse. Under infrared illumination of the field, each camera was positioned to record the complete length of the treadmill belt at a frame rate of 150 Hz and a region of interest of 1440 × 210 pixels, and was triggered by an external pulse generator using custom LabVIEW code (National Instruments). Images were acquired with the SpinView GUI (Spinnaker SDK software, Teledyne FLIR).

Pose estimation during locomotion

For tracking mouse pose (i.e., anatomical landmarks) across cameras during locomotion, DeepLabCut⁴⁴ was used. The position of 22 landmarks was tracked, including the nose, eye, fingertip, wrist, elbow, shoulder, toe, foot, ankle, knee, hip, and tail on each side of the body. Separate tracking models were developed for EMG and cortical electrodes due to differences in animal appearance between the implant types. In total, 1850 and 2002 labeled frames were used for training the EMG and cortical implant models, respectively. Next, Anipose⁴⁵ was used to triangulate the 3D pose from the 2D estimates in the four cameras. Briefly, the four cameras were calibrated using simultaneously acquired images of a ChArUco board, and the 3D pose was estimated by minimizing an objective that enforced small reprojection errors, temporal smoothness, and soft constraints on the length of rigid body segments.

The pose estimates obtained from Anipose were then transformed into a natural coordinate frame: (1) forward on treadmill, (2) right on treadmill, and (3) upward against gravity. Next, the forward coordinate was unrolled by adding the cumulative displacement of the treadmill computed from the rotary encoder. This resulted in a treadmill belt-centered coordinate frame, as though the mouse was progressing along an infinitely-long track: (1) forward on treadmill, relative to the unrolled position of the back of the belt at the start of the experiment, (2) right on treadmill, and (3) upward against gravity. Sessions were then segmented into swing and stance epochs by detecting threshold crossings of the forward finger velocity and upward finger position. For a step to be included, finger velocity during swing was required to be greater than 60% of the forward and 40% of the upward median values per session. Also, for the inclusion of each step cycle, the swing phase duration was required to be 60–400 ms. The identified swing and stance time points were used for the alignment of electrophysiological recordings. For each mouse and session, the quality of the pose estimates was assessed using Anipose quality metrics, visual inspection of trajectories, and comparison of the estimated pose with the raw videos.

Optogenetic perturbations

Optical fibers (catalog number FT200UMT, core diameter 200 μm, ThorLabs) were glued inside ceramic ferrules (catalog number CFLC230-10, ThorLabs) and positioned onto the skull over a thin layer of transparent dental cement (Optibond, Kerr), which enabled optical access to the brain^51,90. To enable transient perturbation of intermediate deep cerebellar nuclei, the optical fibers were placed bilaterally above the pars intermedia of cerebellar lobule V (bregma -6.75 mm, lateral 1.7 mm) of L7Cre-2 x Ai32 mice to stimulate Purkinje cells^91,92. Higher laser power levels (>8 mW) have been shown to suppress Purkinje cell firing⁹³, likely due to depolarization block; we therefore ensured that the minimum effective power was used in these mice. In separate experiments, to transiently inactivate the motor cortex, optical fibers were placed bilaterally above the forelimb area of the motor cortex (bregma +0.5 mm, lateral 1.7 mm) of VGAT-ChR2-EYFP mice to stimulate inhibitory interneurons^12,15,94. For both implant types, all stimulation during experiments was delivered unilaterally within each session.

Optogenetic perturbation with a 473 nm wavelength laser was delivered with sinusoidal waves at 40 Hz (Opto Engine LLC). The laser was triggered by an external pulse generator controlled with custom labVIEW software. For each mouse and genotype, laser power levels used during locomotion were calibrated to achieve a similar functional impact with the range of laser power based on prior investigations^{12,15,50,91,92}. In L7Cre-2 x Ai32 mice, optogenetic perturbation of the cerebellum at power levels greater than ~2 mW arrested mouse locomotion, and the forelimb musculature was unable to support the mouse during stance. Whereas in VGAT-ChR2-EYFP mice, higher power levels were well tolerated during locomotion. Therefore, the power for each genotype and animal was first calibrated based on measuring EMG responses to stimulation in the home cage.

Home cage sessions (Supplementary Fig. 1a), in which the animals spent most of their time standing or quietly exploring the cage, involved stepwise power level adjustments of optogenetic perturbation and measurement of EMG. In L7Cre-2 x Ai32 mice, Purkinje cell stimulation (0.125-4 mW) induced suppression of forelimb flexor and extensor EMG, followed by a power-dependent rebound response after the termination of the stimulus. Therefore, laser power for behavioral sessions was adjusted within this range of effect, to a level that produced minimal rebound, and did not halt locomotion (0.25–2 mW). Similar home cage calibration sessions were separately performed in VGAT-ChR2-EYFP mice, with stepwise power level adjustments to confirm quiescent muscle activity during the stimulation of cortical inhibitory interneurons (1–12 mW). To maximize the effect of motor cortical perturbation during behavioral experiments, higher power levels were used (8–12 mW) and were not observed to halt locomotion. For home cage sessions, the stimulus duration was 0.25, 0.5, or 1 s, and interstimulus intervals were randomized and between 3–10 s. During locomotion, the stimulus duration was 1 s and interstimulus intervals were randomized between 1–6 s.

Electromyogram recordings

Electromyogram (EMG) recordings of gross muscle activity from the elbow flexors and extensors was made using fine-wire^12,56,57 electrodes, and recordings from single motor units were performed with both fine-wire electrodes and high-density Myomatrix arrays^58,95,96. For each mouse, we implanted a total of four muscle locations, targeting an elbow flexor and extensor muscle on each side. Fine-wire electrodes were made with four pairs of wires in a bipolar EMG configuration, following an established protocol⁵⁶. Each bipolar fine-wire electrode comprised two 0.001-inch diameter, seven-stranded braided steel wires (catalog number: 793200, A-M Systems) that were crimped into a 27 gauge needle, twisted, and knotted together. For recording contacts, ~0.5–1 mm of insulation was removed per wire between the knot and needle, made closer to the knot, and staggered with an inter-contact distance of ~2 mm. The open ends of the wire on the other side of the knot were soldered onto a 32-pin connector (Omnetics Nano, A79025, 36 pins, 4 guideposts), along with a gold pin cap for attachment to the ground (Mcmaster-Carr). Myomatrix electrodes (model number RF-4×8-BVS-5)⁵⁸ were used to only record EMG with single motor unit resolution, these electrodes had gold contacts that were plated with conductive polymer PEDOT to reduce the impedance to the measured range of 3–23 kOhm. Fine-wire electrodes were grounded with a gold pin soldered to a stainless steel wire placed through the skull and into the brain by performing a craniotomy with a dental drill ~4 mm rostral to the forelimb area of the motor cortex area. The dura was left intact, Kwik-sil (World Precision Instruments) was applied, and the pin was secured to the skull with dental cement. Myomatrix electrodes were grounded onto the skull and secured with dental cement.

For surgical implantation, the fur on the posterior neck, posterior shoulders, and both forelimbs above the elbow joint of the mouse was removed using depilatory cream prior to positioning within the stereotaxic apparatus. Electrodes were implanted only after the head post, optical fibers, and ground were secured. For each forelimb, lidocaine was injected under the skin, and a 2–3 cm incision of the skin was made between the elbow and shoulder joint, along the midline axis of the lateral head of the triceps brachii muscle, and was subsequently kept moist with saline. Each electrode was led under the skin from the posterior neck to be separately implanted in the long head of the biceps brachii or triceps brachii muscles. For targeting the biceps brachii muscle, the forelimb was abducted, the elbow extended, and the paw supinated, whereas for targeting the triceps brachii muscle, the elbow was flexed and the paw pronated. The skin was adjusted using forceps to provide an opening over the targeted muscle, and electrodes were inserted into the muscle belly from proximal to distal. The fine-wire electrodes were inserted with the attached crimped needle, after insertion, the needle and excess distal wire was cut and a distal knot was made. For Myomatrix electrodes, a suture knot was tied onto the distal polyimide hole of each thread, then, following the suture needle, was carefully pulled into the targeted muscle belly. One Myomatrix thread was inserted per muscle. For both the fine-wire and Myomatrix electrode implants, the incised skin was then flushed with saline and sutured. The connector was then secured to the head post with dental cement, and the inferior skin relative to the head post was hermetically sealed with skin adhesive (3 M Vetbond).

Despite targeting muscle long heads during implantations, we did not systematically differentiate EMG between the long and short head of the biceps brachii muscle, and likely EMG during locomotor swing comprised the synergist contribution from other elbow flexor muscles, including the brachialis and coracobrachialis. Likewise, we did not differentiate EMG between the heads of the triceps brachii muscle, and it remains possible that EMG during stance may have had a minor synergist contribution from the dorso-epitrochlearis brachii and anconeus muscles⁹⁷.

We implanted EMG electrodes in forelimb muscles bilaterally, because throughout the course of experiments the signal-to-noise would degrade and in some instances electrodes would be damaged, and these sessions were excluded. Therefore, the forelimb with better EMG signal-to-noise and minimal crosstalk from other muscles was used for experiments, determining on which side the wrist weight and optogenetic perturbations were applied. In VGAT-ChR2-EYFP mice, optogenetic silencing of the forelimb area of the motor cortex was linked to contralateral forelimb EMG and contralateral load. In L7Cre-2 x Ai32 mice, optogenetic silencing of deep cerebellar nuclei through the activation of Purkinje cells was linked to ipsilateral forelimb EMG, ipsilateral load, and contralateral cortical neuron recordings. Three (one female) L7Cre-2 x Ai32 and four VGAT-ChR2-EYFP mice were implanted with fine-wire electrodes, and three (one female) L7Cre-2 x Ai32 mice were implanted with Myomatrix electrodes. Recordings were amplified and bandpass filtered (0.01–10 kHz) using a differential amplifier and digitized (Intan RHD2216, 16-bit, 16 channel bipolar input recording headstage), and acquired at 30 kHz (Open Ephys acquisition board and software). At the conclusion of experiments on each mouse, the targeted muscles were verified post-euthanasia by dissection.

For subsequent analysis of step-aligned muscle activity, the gross EMG was high-pass filtered (200–250 Hz cutoff), rectified, and convolved with a Gaussian kernel (σ = 10 ms). To normalize the smoothed EMG signal, we first detected all peak events exceeding the 90th percentile of the full-time series. Then, the smoothed signal was divided by the median amplitude of these peaks.

Motor unit spike sorting

On many EMG recordings from fine-wire electrodes, single motor units were identified (e.g., the triceps unit in Fig. 1c, d). For these fine-wire recordings, the EMG was high-pass filtered on each channel (cutoff set between 200 and 1000 Hz, second-order Butterworth). Motor unit spike times were identified by voltage threshold and waveform template matching (Spike2 software, version 7, Cambridge Electronics Design). In the fine-wire electrodes implanted in the biceps brachii muscle, single motor units were sometimes recorded during the stance phase, possibly due to the small relative volume of elbow flexor to extensor muscle and that the cut-end of the electrode was closer to the distal aspect of the lateral triceps brachii.

For Myomatrix electrodes, each thread comprised four bipolar recording channels that were implanted into the same muscle that enabled correlated voltage and waveform analysis across channels. The EMG was high-pass filtered (400–500 Hz cutoff, Parks-Mclellan method), and motor unit waveforms and spike times were extracted using an existing method⁹⁸. Then, clusters were manually cut using peak-to-trough features from all channels on each thread, and unit quality was assessed by inspection of waveforms, autocorrelations, cross-correlations between units recorded on the same thread, and raw signals with unit spike times superimposed. Overall, we recorded 54 ipsilateral extensor units, 27 contralateral extensor units, 17 ipsilateral flexor units, and 10 contralateral flexor units.

Motor cortical recordings

Extracellular recordings in the forelimb area of the motor cortex^15,99 were made using chronically implanted high-density silicon probes (64 channel, 4-shank, 6 mm length E1 probe, Cambridge NeuroTech) secured to a manual micromanipulator (CN-01 V1, Cambridge NeuroTech). Probes were plated with the conductive polymer PEDOT to reduce the impedance to the measured range of 30–50 kOhm, and the tips were sharpened to ease insertion through the dura. The electrode was grounded with a gold pin soldered to a stainless steel wire placed through the skull and into the visual cortex. Surgical implantation of the probe occurred after the head post, optical fibers, and ground were secured to the skull. A craniotomy (dimensions ~1 × 2 mm) was performed with a dental drill to access the forelimb area of the motor cortex on the left side (bregma +0.5 mm, lateral 1.7 mm), care was taken to leave the dura intact, and cold saline was applied continuously to reduce swelling. The probe tip was inserted to a starting depth between 400–540 µm, silicone gel was applied (catalog number 3-4680, Dowsil, Dow), and the apparatus, including the amplifier, was secured to the head post, skull, and enclosed custom chamber using dental cement.

Two L7Cre-2 x Ai32 mice were implanted and recordings were amplified and bandpass filtered (0.01–10 kHz) using a differential amplifier and digitized (mini-amp-64, Cambridge NeuroTech) and acquired at 30 kHz (Open Ephys GUI). Each session, the electrophysiological signal-to-noise and spiking density across channels was assessed, to record from new neurons, and when signal quality degraded, the probe was moved 62.5–125 µm deeper every 1–3 days by adjusting the micromanipulator until the lowest recording channel hit white matter (~1–1.2 mm from the surface).

Motor cortex spike sorting

Single units in the motor cortex were identified using Kilosort 2.5^100,101,102 (https://github.com/MouseLand/Kilosort), and manually curated with the Phy GUI (https://github.com/cortex-lab/phy). Only well-isolated neurons were accepted based on spike waveforms, the presence of an absolute refractory period greater than 1 ms, the stability of spike amplitude over the session, and isolation of the cluster in feature space. Spike time cross-correlation was used to remove duplicated neurons.

Quantification and statistical analysis

EMG analysis

To assess changes in behavior over individual experimental sessions, we first interpolated the smoothed biceps and triceps EMG and forward finger velocity between the start of swing and end of stance on each step cycle, and visualized the resulting curves as heatmaps (Fig. 1e). For optogenetic perturbation experiments, we averaged the step-aligned curves within each condition (load on/off, optogenetic perturbation on/off), and visualized the means using polar plots (Fig. 2a, b). Next, to obtain a compact representation of motor output on each step, we averaged the biceps (flexor) EMG during the swing epoch, the triceps (extensor) EMG during the stance epoch, and velocity (fingertip) over the entire step. Medians and bootstrapped confidence intervals for load-off and load-on conditions were visualized as scatterplots (Fig. 1f), and a difference between conditions (where each paired observation is a load-off and load-on median in one session) was assessed with a two-sided sign rank test. The trend in step-averaged EMG across each session was modeled using loess smoothing¹⁰³ (second-order, smoothing parameter α = 0.9; Fig. 1g). To estimate the effects of load, optogenetic perturbation, and speed on EMG and velocity, we fit one linear model for each session using ordinary least squares, where each observation corresponded to a single step. The dependent variables were biceps EMG, triceps EMG, and forward velocity, and the independent variables were step frequency (i.e., the inverse of the duration of each step), load, optogenetic perturbation, and interaction between the load and optogenetic perturbation. All variables were Z-scored to facilitate the comparison of effect sizes across variables and sessions. Coefficients and 95% confidence intervals were visualized using scatterplots and histograms (Fig. 2c and Supplementary Fig. 1c), and the sign of the coefficients assessed with a sign rank test with Benjamini–Hochberg correction (q < 0.05; Supplementary Fig. 1d). For coefficients related to optogenetic perturbation and its interaction with load, this test was applied separately to sessions using VGAT-ChR2-EYFP and L7Cre-2 x Ai32 mice.

Analysis of cortical neurons and spinal motoneurons

For each motor cortical neuron and spinally-innervated motor unit, firing rates over the full experimental session were computed using Gaussian smoothing (σ = 25 ms). Using the step cycle segmentation from kinematic data (described above), smoothed firing rate curves were extracted for each step using linear interpolation between the start of swing and end of stance, then averaged within each experimental condition to create peri-event time histograms (Figs. 3b; 5b). The effects of load and Purkinje cell stimulation as a function of the step phase were visualized by subtracting the Z-scored firing rates in the load-off, stim-off condition from the Z-scored firing rates in the load-on, stim-off (Fig. 3c), and load-off, stim-on conditions (Fig. 5c), respectively. Step-averaged firing rates were computed for each step by dividing the number of spikes by the step duration. Means and 95% confidence intervals for step-averaged rates were visualized with scatterplots (Figs. 3d; 5d) and analyzed with a multi-way ANOVA for each neuron. A Benjamini–Hochberg correction for multiple comparisons across neurons was applied. Scatterplots were implemented on log-log axes to transform a heavily skewed firing rate distribution across the sample of neurons into a more symmetric distribution (Supplementary Fig. 5).

Demixed principal component analysis

To identify the coordinated, low-dimensional dynamics in the motor cortical and spinal motoneuron populations, we used demixed principal component analysis (dPCA)⁵⁴, which decomposes measured firing rates into latent variables related to experimental parameters of interest, using a published Matlab package (https://github.com/machenslab/dPCA). Briefly, the average step-aligned firing rate for each unit (n = 710 for cortical neurons, n = 108 for spinal motoneurons) was measured in twenty different conditions in a factorial design: load on/off (two levels) × Purkinje cell stimulation on/off (two levels) × animal speed (five levels). Speed was included as it was relatively variable from stride to stride, exhibited nonstationarity in some sessions, and influenced firing rates (Supplementary Fig. 6). Firing rate was sampled at 100 evenly-spaced points across the step cycle, from the start of swing to the end of stance. For the speed factor, the forward speed of the animal’s nose at swing onset was partitioned into five bins with ~50% overlap using an equal count algorithm¹⁰³. This imposed the following marginalizations over parameters: (1) load, (2) speed, (3) Purkinje cell stimulation, (4) condition-invariant, (5) load/speed interaction, (6) load/Purkinje cell stimulation interaction, and (7) speed/Purkinje cell stimulation interaction. Next, we estimated the decoder and encoder matrices with twenty components and regularization parameter λ = 1e-5, and projected firing rates onto the decoder columns to obtain scores parameterized by step phase (Figs. 4a, b, 6a, b). The alignment between pairs of principal axes was assessed by computing the inner product (Fig. 4c, upper triangular; Fig. 6c, upper triangular), and by applying an exact test against the null hypothesis that the relative orientation of the axes is random with an alternative hypothesis that the axes are orthogonal. Under the null hypothesis, (x-1)/2 follows a beta distribution with α = β = (d-1)/2, where x is the inner product between axes and d = 20 is the dimension of the latent variable space. The probability the inner product x is within r of zero (i.e., that the axes are nearly orthogonal) under the null hypothesis is given by P(|x | <r) = B((1 + r)/2,(d-1)/2,(d-1)/2) − B((1-r)/2,(d-1)/2,(d-1)/2), where B is the beta cumulative distribution function. Thus, setting r as the absolute value of the measured inner product between two principal axes, we can calculate the probabilities shown in Figs. 4c, 6c (lower triangular).

Comparison of cortical neuron and spinal motoneuron trajectories

For each neural population (motor cortex and spinal motoneuron) and experimental parameter (load, Purkinje cell stimulation, and speed), we extracted neural trajectories in the leading component corresponding to that parameter and in the first two condition-invariant dimensions across all twenty conditions. We then used Procrustes analysis within each neural population and parameter to find the optimal transformations from trajectories in one set of conditions to those in another set. These mappings could include translation, rotation, and isotropic rescaling, but not reflection. For the load and Purkinje cell stimulation parameters, trajectories in load-off and stimulation-off conditions were mapped to the corresponding trajectories in load-on and stimulation-on conditions, respectively. For the speed parameter, trajectories in the lowest speed condition were mapped to trajectories in the highest speed condition. The resulting maps were visualized on a regular 3D grid by mapping each grid point to a second point in the direction of its image under the Procrustes transformation, with a scaling of 0.2 for the motor cortex and 0.4 for spinal motoneurons (Fig. 7a, b).

To further characterize the neural trajectories, we employed the concept of trajectory tangling. The intuition is that in an autonomous, noiseless system x’(t) = f(x(t)), the future trajectory is fully determined by the initial condition x(0). When inputs come into play, x’(t) = f(x(t)) + u(t), the same initial condition x(0) could diverge into distinct trajectories, depending on u(t). In this case, multiple observations of the system across trials or conditions will lead to intersecting, or “tangled,” trajectories at x(0). Thus, an observation of high trajectory tangling is taken to be evidence that inputs u(t) are driving the trajectories (under the assumption that the system is well-behaved - i.e., not chaotic). We note, however, that the converse does not hold: the periodically forced system x’(t) = (−sin(t),cos(t)) has no intrinsic dynamics, but generates minimally tangled trajectories. The analysis of trajectory tangling was performed as in previous studies⁶⁰. Briefly, neural trajectories in the full 20-dimensional latent variable space identified by dPCA were numerically differentiated along the time axis. Next, for each time point t* and condition c*, the following quantity was computed: max{t,c} ||Z’(t*,c*) - Z’(t,c)||/||Z(t*,c*) - Z(t,c)|| + ε, where Z(t,c) is the neural state in condition t at time c, and Z’(t,c) its derivative. The value of ε was set at 10% of the mean of the sum of squares of Z(t,c), concatenated across all conditions. This normalization was performed separately for the cortical and spinal populations.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

All data generated in this study have been deposited in the Dryad repository. The data were available under CC0 licensing at the following https://doi.org/10.5061/dryad.s7h44j1g4.

Code availability

All code supporting the findings in this study are packaged with the data on the Dryad repository at the following https://doi.org/10.5061/dryad.s7h44j1g4.

References

Porter, R. & Lemon, R. Corticospinal Function and Voluntary Movement (Oxford Univ. Press, 1993).
Scott, S. H. Optimal feedback control and the neural basis of volitional motor control. Nat. Rev. Neurosci. 5, 532–546 (2004).
Article CAS PubMed Google Scholar
Evarts, E. V. Relation of pyramidal tract activity to force exerted during voluntary movement. J. Neurophysiol. 31, 14–27 (1968).
Article CAS PubMed Google Scholar
Kalaska, J. F., Cohen, D. A., Hyde, M. L. & Prud’homme, M. A comparison of movement direction-related versus load direction-related activity in primate motor cortex, using a two-dimensional reaching task. J. Neurosci. 9, 2080–2102 (1989).
Article CAS PubMed PubMed Central Google Scholar
Sergio, L. E. & Kalaska, J. F. Systematic changes in motor cortex cell activity with arm posture during directional isometric force generation. J. Neurophysiol. 89, 212–228 (2003).
Article PubMed Google Scholar
Kurtzer, I., Herter, T. M. & Scott, S. H. Random change in cortical load representation suggests distinct control of posture and movement. Nat. Neurosci. 8, 498–504 (2005).
Article CAS PubMed Google Scholar
Conrad, B., Matsunami, K., Meyer-Lohmann, J., Wiesendanger, M. & Brooks, V. B. Cortical load compensation during voluntary elbow movements. Brain Res. 71, 507–514 (1974).
Article CAS PubMed Google Scholar
Meyer-Lohmann, J., Conrad, B., Matsunami, K. & Brooks, V. B. Effects of dentate cooling on precentral unit activity following torque pulse injections into elbow movements. Brain Res. 94, 237–251 (1975).
Hore, J. & Flament, D. Changes in motor cortex neural discharge associated with the development of cerebellar limb ataxia. J. Neurophysiol. 60, 1285–1302 (1988).
Article CAS PubMed Google Scholar
Nashef, A., Cohen, O., Harel, R., Israel, Z. & Prut, Y. Reversible block of cerebellar outflow reveals cortical circuitry for motor coordination. Cell Rep. 27, 2608–2619.e4 (2019).
Article CAS PubMed Google Scholar
Pasalar, S., Roitman, A. V., Durfee, W. K. & Ebner, T. J. Force field effects on cerebellar Purkinje cell discharge with implications for internal models. Nat. Neurosci. 9, 1404–1411 (2006).
Article CAS PubMed Google Scholar
Miri, A. et al. Behaviorally selective engagement of short-latency effector pathways by motor cortex. Neuron 95, 683–696.e11 (2017).
Article CAS PubMed PubMed Central Google Scholar
Mathis, M. W., Mathis, A. & Uchida, N. Somatosensory cortex plays an essential role in forelimb motor adaptation in mice. Neuron 93, 1493–1503.e6 (2017).
Article CAS PubMed PubMed Central Google Scholar
Guo, J.-Z. et al. Cortex commands the performance of skilled movement. Elife 4, e10774 (2015).
Article PubMed PubMed Central Google Scholar
Sauerbrei, B. A. et al. Cortical pattern generation during dexterous movement is input-driven. Nature 577, 386–391 (2020).
Article CAS PubMed Google Scholar
Galiñanes, G. L., Bonardi, C. & Huber, D. Directional reaching for water as a cortex-dependent behavioral framework for mice. Cell Rep. 22, 2767–2783 (2018).
Article PubMed PubMed Central Google Scholar
Churchland, M. M. & Shenoy, K. V. Temporal complexity and heterogeneity of single-neuron activity in premotor and motor cortex. J. Neurophysiol. 97, 4235–4257 (2007).
Article PubMed Google Scholar
Scott, S. H. Inconvenient truths about neural processing in primary motor cortex. J. Physiol. 586, 1217–1224 (2008).
Article CAS PubMed PubMed Central Google Scholar
Crammond, D. J. & Kalaska, J. F. Prior information in motor and premotor cortex: activity during the delay period and effect on pre-movement activity. J. Neurophysiol. 84, 986–1005 (2000).
Article CAS PubMed Google Scholar
Churchland, M. M. et al. Neural population dynamics during reaching. Nature 487, 51–56 (2012).
Article ADS CAS PubMed PubMed Central Google Scholar
Shenoy, K. V., Sahani, M. & Churchland, M. M. Cortical control of arm movements: a dynamical systems perspective. Annu. Rev. Neurosci. 36, 337–359 (2013).
Article CAS PubMed Google Scholar
Vyas, S., Golub, M. D., Sussillo, D. & Shenoy, K. V. Computation through neural population dynamics. Annu. Rev. Neurosci. 43, 249–275 (2020).
Article CAS PubMed PubMed Central Google Scholar
Kalidindi, H. T. et al. Rotational dynamics in motor cortex are consistent with a feedback controller. Elife 10, e67256 (2021).
Kaufman, M. T., Churchland, M. M., Ryu, S. I. & Shenoy, K. V. Cortical activity in the null space: permitting preparation without movement. Nat. Neurosci. 17, 440–448 (2014).
Article CAS PubMed PubMed Central Google Scholar
Elsayed, G. F., Lara, A. H., Kaufman, M. T., Churchland, M. M. & Cunningham, J. P. Reorganization between preparatory and movement population responses in motor cortex. Nat. Commun. 7, 13239 (2016).
Article ADS CAS PubMed PubMed Central Google Scholar
Churchland, M. M. & Shenoy, K. V. Preparatory activity and the expansive null-space. Nat. Rev. Neurosci. 25, 213–236 (2024).
Article CAS PubMed Google Scholar
Stavisky, S. D., Kao, J. C., Ryu, S. I. & Shenoy, K. V. Motor cortical visuomotor feedback activity is initially isolated from downstream targets in output-null neural state space dimensions. Neuron 95, 195–208.e9 (2017).
Article CAS PubMed PubMed Central Google Scholar
Vyas, S. et al. Neural population dynamics underlying motor learning transfer. Neuron 97, 1177–1186.e3 (2018).
Article CAS PubMed PubMed Central Google Scholar
Sun, X. et al. Cortical preparatory activity indexes learned motor memories. Nature 602, 274–279 (2022).
Article ADS CAS PubMed PubMed Central Google Scholar
Vyas, S., O’Shea, D. J., Ryu, S. I. & Shenoy, K. V. Causal role of motor preparation during error-driven learning. Neuron 106, 329–339.e4 (2020).
Article CAS PubMed PubMed Central Google Scholar
Brown, T. G. On the nature of the fundamental activity of the nervous centres; together with an analysis of the conditioning of rhythmic activity in progression, and a theory of the evolution of function in the nervous system. J. Physiol. 48, 18–46 (1914).
Article CAS PubMed PubMed Central Google Scholar
Grillner, S. & Zangger, P. On the central generation of locomotion in the low spinal cat. Exp. Brain Res. 34, 241–261 (1979).
Article CAS PubMed Google Scholar
Kjaerulff, O. & Kiehn, O. Distribution of networks generating and coordinating locomotor activity in the neonatal rat spinal cord in vitro: a lesion study. J. Neurosci. 16, 5777–5794 (1996).
Article CAS PubMed PubMed Central Google Scholar
Shik, M. L. & Orlovsky, G. N. Neurophysiology of locomotor automatism. Physiol. Rev. 56, 465–501 (1976).
Article CAS PubMed Google Scholar
Capelli, P., Pivetta, C., Soledad Esposito, M. & Arber, S. Locomotor speed control circuits in the caudal brainstem. Nature 551, 373–377 (2017).
Article ADS CAS PubMed Google Scholar
Caggiano, V. et al. Midbrain circuits that set locomotor speed and gait selection. Nature 553, 455–460 (2018).
Article ADS CAS PubMed PubMed Central Google Scholar
Drew, T. Motor cortical activity during voluntary gait modifications in the cat. I. Cells related to the forelimbs. J. Neurophysiol. 70, 179–199 (1993).
Article CAS PubMed Google Scholar
Beloozerova, I. N. & Sirota, M. G. The role of the motor cortex in the control of accuracy of locomotor movements in the cat. J. Physiol. 461, 1–25 (1993).
Article CAS PubMed PubMed Central Google Scholar
Drew, T., Jiang, W., Kably, B. & Lavoie, S. Role of the motor cortex in the control of visually triggered gait modifications. Can. J. Physiol. Pharmacol. 74, 426–442 (1996).
CAS PubMed Google Scholar
Warren, R. A. et al. A rapid whisker-based decision underlying skilled locomotion in mice. Elife 10, e63596 (2021).
Duysens, J. & Pearson, K. G. Inhibition of flexor burst generation by loading ankle extensor muscles in walking cats. Brain Res. 187, 321–332 (1980).
Article CAS PubMed Google Scholar
Armstrong, D. M. & Drew, T. Discharges of pyramidal tract and other motor cortical neurones during locomotion in the cat. J. Physiol. 346, 471–495 (1984).
Article CAS PubMed PubMed Central Google Scholar
Beloozerova, I. N. & Sirota, M. G. The role of the motor cortex in the control of vigour of locomotor movements in the cat. J. Physiol. 461, 27–46 (1993).
Article CAS PubMed PubMed Central Google Scholar
Mathis, A. et al. DeepLabCut: markerless pose estimation of user-defined body parts with deep learning. Nat. Neurosci. 21, 1281–1289 (2018).
Article CAS PubMed Google Scholar
Karashchuk, P. et al. Anipose: a toolkit for robust markerless 3D pose estimation. Cell Rep. 36, 109730 (2021).
Article CAS PubMed PubMed Central Google Scholar
Morton, S. M. & Bastian, A. J. Cerebellar contributions to locomotor adaptations during splitbelt treadmill walking. J. Neurosci. 26, 9107–9116 (2006).
Article CAS PubMed PubMed Central Google Scholar
Darmohray, D. M., Jacobs, J. R., Marques, H. G. & Carey, M. R. Spatial and temporal locomotor learning in mouse cerebellum. Neuron 102, 217–231.e4 (2019).
Article CAS PubMed Google Scholar
Lawrence, D. G. & Kuypers, H. G. The functional organization of the motor system in the monkey. I. The effects of bilateral pyramidal lesions. Brain 91, 1–14 (1968).
Article CAS PubMed Google Scholar
Ilg, W., Giese, M. A., Gizewski, E. R., Schoch, B. & Timmann, D. The influence of focal cerebellar lesions on the control and adaptation of gait. Brain 131, 2913–2927 (2008).
Article CAS PubMed Google Scholar
Guo, Z. V. et al. Flow of cortical activity underlying a tactile decision in mice. Neuron 81, 179–194 (2014).
Article CAS PubMed Google Scholar
Gao, Z. et al. A cortico-cerebellar loop for motor planning. Nature 563, 113–116 (2018).
Article ADS CAS PubMed PubMed Central Google Scholar
Foster, J. D. et al. A freely-moving monkey treadmill model. J. Neural Eng. 11, 046020 (2014).
Article ADS PubMed Google Scholar
Xing, D., Truccolo, W. & Borton, D. A. Emergence of distinct neural subspaces in motor cortical dynamics during volitional adjustments of ongoing locomotion. J. Neurosci. 42, 9142–9157 (2022).
Article CAS PubMed PubMed Central Google Scholar
Kobak, D. et al. Demixed principal component analysis of neural population data. Elife 5, e10989 (2016).
Saxena, S., Russo, A. A., Cunningham, J. & Churchland, M. M. Motor cortex activity across movement speeds is predicted by network-level strategies for generating muscle activity. Elife 11, e67620 (2022).
Pearson, K. G., Acharya, H. & Fouad, K. A new electrode configuration for recording electromyographic activity in behaving mice. J. Neurosci. Methods 148, 36–42 (2005).
Article CAS PubMed Google Scholar
Akay, T., Acharya, H. J., Fouad, K. & Pearson, K. G. Behavioral and electromyographic characterization of mice lacking EphA4 receptors. J. Neurophysiol. 96, 642–651 (2006).
Article CAS PubMed Google Scholar
Chung, B. et al. Myomatrix arrays for high-definition muscle recording. eLife https://doi.org/10.7554/elife.88551.1 (2023).
Kaufman, M. T. et al. The largest response component in the motor cortex reflects movement timing but not movement type. eNeuro 3, ENEURO.0085-16.2016 (2016).
Russo, A. A. et al. Motor cortex embeds muscle-like commands in an untangled population response. Neuron 97, 953–966.e8 (2018).
Article CAS PubMed PubMed Central Google Scholar
Alonso, I. et al. Peripersonal encoding of forelimb proprioception in the mouse somatosensory cortex. Nat. Commun. 14, 1866 (2023).
Article ADS CAS PubMed PubMed Central Google Scholar
Conner, J. M. et al. Modulation of tactile feedback for the execution of dexterous movement. Science 374, 316–323 (2021).
Article ADS CAS PubMed PubMed Central Google Scholar
Adrian, E. D. & Moruzzi, G. Impulses in the pyramidal tract. J. Physiol. 97, 153–199 (1939).
Article CAS PubMed PubMed Central Google Scholar
Brooks, V. B., Rudomin, P. & Slayman, C. L. Peripheral receptive fields of neurons in the cat’s cerebral cortex. J. Neurophysiol. 24, 302–325 (1961).
Article Google Scholar
Armstrong, D. M. & Drew, T. Topographical localization in the motor cortex of the cat for somatic afferent responses and evoked movements. J. Physiol. 350, 33–54 (1984).
Article CAS PubMed PubMed Central Google Scholar
Lemon, R. N. & Porter, R. Afferent input to movement-related precentral neurones in conscious monkeys. Proc. R. Soc. Lond. B Biol. Sci. 194, 313–339 (1976).
Article ADS CAS PubMed Google Scholar
Picard, N. & Smith, A. M. Primary motor cortical responses to perturbations of prehension in the monkey. J. Neurophysiol. 68, 1882–1894 (1992).
Article CAS PubMed Google Scholar
Armstrong, D. M. & Drew, T. Locomotor-related neuronal discharges in cat motor cortex compared with peripheral receptive fields and evoked movements. J. Physiol. 346, 497–517 (1984).
Article CAS PubMed PubMed Central Google Scholar
Musall, S., Kaufman, M. T., Juavinett, A. L., Gluf, S. & Churchland, A. K. Single-trial neural dynamics are dominated by richly varied movements. Nat. Neurosci. 22, 1677–1686 (2019).
Article CAS PubMed PubMed Central Google Scholar
Harris-Warrick, R. M. & Marder, E. Modulation of neural networks for behavior. Annu. Rev. Neurosci. 14, 39–57 (1991).
Article CAS PubMed Google Scholar
Hogan, N. Adaptive control of mechanical impedance by coactivation of antagonist muscles. IEEE Trans. Autom. Contr. 29, 681–690 (1984).
Article Google Scholar
Dufresne, J. R., Soechting, J. F. & Terzuolo, C. A. Modulation of the myotatic reflex gain in man during intentional movements. Brain Res. 193, 67–84 (1980).
Article CAS PubMed Google Scholar
Refy, O. et al. Dynamic spinal reflex adaptation during locomotor adaptation. J. Neurophysiol. 130, 1008–1014 (2023).
Article PubMed Google Scholar
Gossard, J. P., Brownstone, R. M., Barajon, I. & Hultborn, H. Transmission in a locomotor-related group Ib pathway from hindlimb extensor muscles in the cat. Exp. Brain Res. 98, 213–228 (1994).
Article CAS PubMed Google Scholar
Santuz, A. & Zampieri, N. Making sense of proprioception. Trends Genet. 40, 20–23 (2024).
Article CAS PubMed Google Scholar
Türker, K. S., Brodin, P. & Miles, T. S. Reflex responses of motor units in human masseter muscle to mechanical stimulation of a tooth. Exp. Brain Res. 100, 307–315 (1994).
Article PubMed Google Scholar
Horner, A. M. & Jayne, B. C. The effects of viscosity on the axial motor pattern and kinematics of the African lungfish (Protopterus annectens) during lateral undulatory swimming. J. Exp. Biol. 211, 1612–1622 (2008).
Article PubMed Google Scholar
Pearson, K. G. Central programming and reflex control of walking in the cockroach. J. Exp. Biol. 56, 173–193 (1972).
Article Google Scholar
Zill, S., Moran, D. & Varela, F. G. The exoskeleton and insect proprioception: II. Reflex effects of tibial campaniform sensilla in the American cockroach, Periplaneta. Am. J. Exp. Biol. 94, 43–55 (1981).
Article Google Scholar
Epstein, S. & Graham, D. Behaviour and motor output of stick insects walking on a slippery surface: I. Forward walking. J. Exp. Biol. 105, 215–229 (1983).
Article Google Scholar
Dean, J. Control of leg protraction in the stick insect: a targeted movement showing compensation for externally applied forces. J. Comp. Physiol. A 155, 771–781 (1984).
Article Google Scholar
Orlovsky, G. N. The effect of different descending systems on flexor and extensor activity during locomotion. Brain Res. 40, 359–371 (1972).
Article CAS PubMed Google Scholar
Russo, A. A. et al. Neural trajectories in the supplementary motor area and motor cortex exhibit distinct geometries, compatible with different classes of computation. Neuron 107, 745–758.e6 (2020).
Article CAS PubMed PubMed Central Google Scholar
Lindén, H., Petersen, P. C., Vestergaard, M. & Berg, R. W. Movement is governed by rotational neural dynamics in spinal motor networks. Nature 610, 526–531 (2022).
Article ADS PubMed Google Scholar
Warriner, C. L., Fageiry, S., Saxena, S., Costa, R. M. & Miri, A. Motor cortical influence relies on task-specific activity covariation. Cell Rep. 40, 111427 (2022).
Article CAS PubMed PubMed Central Google Scholar
Yakovenko, S. & Drew, T. Similar motor cortical control mechanisms for precise limb control during reaching and locomotion. J. Neurosci. 35, 14476–14490 (2015).
Article CAS PubMed PubMed Central Google Scholar
Kawai, R. et al. Motor cortex is required for learning but not for executing a motor skill. Neuron 86, 800–812 (2015).
Article CAS PubMed PubMed Central Google Scholar
Mizes, K. G. C., Lindsey, J., Escola, G. S. & Ölveczky, B. P. Motor cortex is required for flexible but not automatic motor sequences. Preprint at bioRxiv https://doi.org/10.1101/2023.09.05.556348 (2023).
Afshar, A. et al. Single-trial neural correlates of arm movement preparation. Neuron 71, 555–564 (2011).
Article CAS PubMed PubMed Central Google Scholar
Li, N., Daie, K., Svoboda, K. & Druckmann, S. Robust neuronal dynamics in premotor cortex during motor planning. Nature 532, 459–464 (2016).
Article ADS CAS PubMed PubMed Central Google Scholar
Nguyen-Vu, T. D. B. et al. Cerebellar Purkinje cell activity drives motor learning. Nat. Neurosci. 16, 1734–1736 (2013).
Article CAS PubMed PubMed Central Google Scholar
Tsutsumi, S. et al. Purkinje cell activity determines the timing of sensory-evoked motor initiation. Cell Rep. 33, 108537 (2020).
Article CAS PubMed PubMed Central Google Scholar
Silva, N. T., Ramírez-Buriticá, J., Pritchett, D. L. & Carey, M. R. Climbing fibers provide essential instructive signals for associative learning. Nat. Neurosci. 27, 940–951 (2024).
Article CAS PubMed PubMed Central Google Scholar
Guo, Z. V. et al. Maintenance of persistent activity in a frontal thalamocortical loop. Nature 545, 181–186 (2017).
Article ADS CAS PubMed PubMed Central Google Scholar
Zia, M., Chung, B., Sober, S. & Bakir, M. S. Flexible multielectrode arrays with 2-D and 3-D contacts for in vivo electromyography recording. IEEE Trans. Compon. Packag. Manuf. Technol. 10, 197–202 (2020).
Article CAS Google Scholar
Lu, J. et al. High-performance flexible microelectrode array with PEDOT: PSS coated 3D micro-cones for electromyographic recording. In 2022 44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC) 5111–5114 (IEEE, 2022).
Mathewson, M. A., Chapman, M. A., Hentzen, E. R., Fridén, J. & Lieber, R. L. Anatomical, architectural, and biochemical diversity of the murine forelimb muscles. J. Anat. 221, 443–451 (2012).
Article PubMed PubMed Central Google Scholar
Marshall, N. J. et al. Flexible neural control of motor units. Nat. Neurosci. 25, 1492–1504 (2022).
Article CAS PubMed PubMed Central Google Scholar
Guo, J.-Z. et al. Disrupting cortico-cerebellar communication impairs dexterity. Elife 10, e65906 (2021).
Pachitariu, M., Steinmetz, N. A., Kadir, S. N., Carandini, M. & Harris, K. D. Fast and accurate spike sorting of high-channel count probes with KiloSort. Adv. Neural Inf. Process. Syst. 29 (2016).
Steinmetz, N. A. et al. Neuropixels 2.0: a miniaturized high-density probe for stable, long-term brain recordings. Science 372, eabf4588 (2021).
Article CAS PubMed PubMed Central Google Scholar
Pachitariu, M., Sridhar, S., Pennington, J. & Stringer, C. Spike Sorting with Kilosort4. Nat. Methods 21, 14–921 (2024).
Cleveland, W. S. Visualizing Data (Hobart Press, 1993).

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Acknowledgements

We thank Andrew Pruszynski and Jonathan Michaels for the discussions and Alex Sohn for the design of the motorized treadmill. This work made use of the High-Performance Computing Resource in the Core Facility for Advanced Research Computing at Case Western Reserve University. Line drawings of the mouse brain and body were obtained from SciDraw.io under a CC BY 4.0 license. The drawings were created by Ethan Tyler, Lex Kravitz, and Emmett Thompson, were edited by the authors to display the design of specific experiments, and are archived at https://zenodo.org/records/3925915 and https://zenodo.org/records/3925987. Research reported in this publication was supported by Case Western Reserve University, by the National Institute of Neurological Disorders and Stroke of the National Institutes of Health under award numbers R01NS129576 (PI: B.A.S.), R01NS109237 (PI: S.J.S.), R01NS084844 (PI: S.J.S.), R01EB022872 (PI: S.J.S.) and U24NS126936 (PI: S.J.S.), and by the McKnight Foundation (PI: S.J.S.), Kavli Foundation (PI: S.J.S.), Azrieli Foundation (PI: S.J.S.), and the Simons-Emory International Consortium on Motor Control (PI: S.J.S.). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. E.A.K. was supported by a Postdoctoral Fellowship from the Natural Sciences and Engineering Research Council of Canada.

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Department of Neurosciences, Case Western Reserve University School of Medicine, Cleveland, OH, USA
Eric A. Kirk, Keenan T. Hope & Britton A. Sauerbrei
Department of Biology, Emory University, Atlanta, GA, USA
Samuel J. Sober

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Eric A. Kirk
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Britton A. Sauerbrei
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E.A.K. and B.A.S. designed the study. E.A.K. performed the experiments. K.T.H. assisted with behavioral procedures and designed the cortical recording chamber. E.A.K. and B.A.S. analyzed the data, interpreted the results, and wrote the paper. S.J.S. contributed the Myomatrix electrode arrays, compared the performance of fine-wire electrodes and Myomatrix arrays, and wrote the relevant text in the Results. E.A.K., S.J.S., and B.A.S. edited and revised the manuscript. B.A.S. supervised the project.

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Correspondence to Britton A. Sauerbrei.

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Kirk, E.A., Hope, K.T., Sober, S.J. et al. An output-null signature of inertial load in motor cortex. Nat Commun 15, 7309 (2024). https://doi.org/10.1038/s41467-024-51750-7

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Received: 07 December 2023
Accepted: 15 August 2024
Published: 24 August 2024
DOI: https://doi.org/10.1038/s41467-024-51750-7