A neural geometry for forelimb proprioception in the cervical spinal cord

A neural geometry for forelimb proprioception in the cervical spinal cord | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results A neural geometry for forelimb proprioception in the cervical spinal cord View ORCID Profile Tejapratap Bollu , View ORCID Profile Martyn Goulding doi: https://doi.org/10.1101/2025.09.26.678887 Tejapratap Bollu 1 Molecular Neurobiology Laboratory,Salk Institute for Biological Studies; La Jolla , 92037, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Tejapratap Bollu For correspondence: tpbollu{at}gmail.com goulding{at}salk.edu Martyn Goulding 1 Molecular Neurobiology Laboratory,Salk Institute for Biological Studies; La Jolla , 92037, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Martyn Goulding For correspondence: tpbollu{at}gmail.com goulding{at}salk.edu Abstract Full Text Info/History Metrics Supplementary material Preview PDF Abstract Precise, real-time somatosensory feedback is essential for coordinated movement. While the anatomy and physiology of these sensory pathways is well described, their neural code and its construction remains unclear. Here we show that neurons in the cervical spinal cord generate a precise neural representation of the forelimb’s kinematic state using muscle and tendon sensory afferent inputs. We identify two classes of movement responsive neurons - the first encodes speed, position and direction of the limb, while the second exhibits precise firing at specific limb positions or grid-like firing patterns that tile space. Their composite population activity is constrained to a low dimensional manifold that is an ordered representation of the position and velocity of the limb. Ablating muscle and tendon sensory afferents, but not cutaneous sensory afferents, disrupts this neural manifold. Moreover, transient perturbations of muscle and tendon afferents in freely moving mice reaching to spatial targets cause end-point errors as predicted by the deficits in the neural code. Our findings demonstrate that spinal networks, one synapse from the periphery, perform the complex computations necessary to represent forelimb movement. Main Text How the nervous system generates a representation of the body in time and space is still, for the most part, poorly understood. Body representations are thought to emerge from proprioception( 1 , 2 ) - the sense that allows animals to perceive the position, movement, and force of their body parts - by integrating continuous sensory input from muscles, joints, and skin to construct an internal map of the body’s posture and configuration in space( 3 ). Neurophysiological descriptions of these representations have been largely limited to brain regions such as the somatosensory cortex( 4 – 8 ). However, it has been known for some time that fully-spinalized vertebrates can account for their body schema during goal directed movements( 9 – 11 ). Consequently, the spinal cord must have the ability to construct a complete representation of the limb’s kinematic state using only feedback from muscle, tendon and/or cutaneous mechanosensory receptors. The anatomical organization of muscle, tendon and cutaneous afferent inputs to the spinal cord suggests that it has the capacity to integrate information across various muscle groups and skin territories to build a kinematic representation of the body( 12 – 14 ). However, what is not known is the nature of these neural representations, and how different somatosensory modalities contribute to these representations. By performing high-density in vivo electrophysiological recordings from the cervical spinal cord while delivering precise motion stimuli to the forelimb, we have discovered that the spinal cord constructs an ordered low-dimensional representation of forelimb kinematics using information derived from muscle and tendon sensory afferents. The cervical spinal cord contains a precise representation of forelimb kinematics To identify and map neural responses to forelimb movement in the cervical spinal cord, we developed a motion control system that precisely moved the forelimb of an anesthetized mouse with micron-millisecond resolution ( Fig. 1A , left and Fig. S1A-D) while we systematically recorded stable high-density, single unit electrophysiological signals (Fig. S1E-G) at different mediolateral and dorsoventral locations of the ipsilateral cervical spinal cord ( Fig. 1B , left). We found that the kinematic information was predominantly localized to medial lamina IV and V ( Fig. 1B , right), where over half the neurons were modulated by movement (53%, 145/273). In contrast, the lateral dorsal horn had few movement modulated neurons (6.5%, 5/77). In the ventral zone encompassing medial lamina VII/lateral lamina VIII, a region known to contain premotor interneurons that receive muscle and tendon afferent input( 15 ), approximately a quarter of the recorded neurons responded to movement stimuli (19/80). We then examined the neural code represented by movement modulated neurons using two complementary motion stimuli patterns that emphasized either position or velocity, two major kinematic parameters that contribute to proprioception. First, we densely sampled the movement space by moving the limb in 64 directions at 40 mm/s ( Fig. 1A , middle). We then sampled the velocity space by moving the limb in 8 directions at 20 mm/s, 40 mm/s and 80 mm/s ( Fig. 1A , right). Download figure Open in new tab Fig. 1. Cervical spinal cord contains precise neural representations of forelimb kinematics. ( A ) Left, The forelimb of an anesthetized mouse was systematically moved by a precise motion control system (Fig. S1) to densely sample the spatial and temporal dynamics of movement. Middle, spatial histogram of 1,920 trials recorded from a single session. Right, the three minimum-jerk speed profiles used in the motion stimuli. (B) Left, a schematic for in vivo multielectrode array recordings of single unit neural activity from the cervical spinal cords of mice. Middle, neurons modulated by the motion stimulus were localized to the medial deep dorsal horn and the lamina VIII of the cervical spinal cord. (C) Unsupervised clustering of the peristimulus time histogram of modulated neurons reveals three distinct clusters: Gain-field, Sparse-coding and Cutaneous-responsive neurons. (D) Example raster, rate histogram and spatial firing fields for two example Gain-field neurons. Trials sorted and grouped by angle of movement stimulus. 10 trials per movement direction. Shaded region indicates duration of movement stimulus. (E) Temporal (Top) and directional (Bottom) fits of the rate histograms of example neurons in (d) to a gain-field model for position, speed and direction of motion stimulus. (F) r-squared values for fits of Gain-field neuron rate histograms to a gain-field model. (G) Preferred response directions of the Gain-field neurons are widely distributed. (H) Example raster, rate histogram and spatial firing fields for two example Sparse-coding neurons. Trials grouped as in (D). (I) The sizes of the spatial firing fields of Gain-field neurons have a fat-tailed distribution. (J) Spatially tiled neural responses of Sparse-coding have complete coverage of the stimulus space. By performing unsupervised clustering of the neural responses ( Fig. 1C , Methods), we found three major clusters. Cluster 1 exclusively contained neurons whose firing rates were jointly modulated by the direction, speed and position of the forelimb ( Fig. 1D , Fig. S2A). A gain-field rate model with a von Mises function for directional tuning explained >90% of the variance in firing rates of individual neurons ( Fig. 1E-F , Fig. S2B, Methods), thus we term these units ‘Gain-field’ neurons. These neurons were differentially sensitive to the speed and position components of the stimulus, with the speed/position ratio displaying a single peaked Gaussian distribution (Fig. S2D, Methods). The vast majority of Gain-field neurons were tuned to a single direction, i.e. were unimodal (∼84%), and the tuned direction was largely uniform ( Fig. 1G ). Some, however, were tuned to two directions (∼14%) and very few (<2%) were tuned to more than two directions (Fig. S2C,E). The width of the tuning direction of these neurons were relatively broad, with a median dispersion of ∼50 degrees (Fig. S2F). Cluster 2 neurons had firing fields at precise spatial locations, with some neurons firing a single spike with striking precision (∼5μm) across trials ( Fig. 1H left, Fig. S3A). A subpopulation of the neurons in this cluster fired in precise radial grids over the entire workspace ( Fig. 1H right, Fig. S3E). Neurons in this cluster lacked any baseline activity and typically had firing fields restricted to <10% of the workspace. We term these neurons ‘Sparse-coding’ ( Fig. 1H,I ). Most importantly, Sparse-coding neurons had precise representations that occupied varying spatial scales ( Fig. 1I , Fig. S3A-E), i.e. ‘Multiscale representations’ - a key feature for a basis-set that is computationally efficient and scale invariant( 16 ). To determine if the Sparse-coding neurons spatially tiled the workspace, we estimated their firing fields (Methods) and then overlaid them ( Fig. 1j ). Their composite neural activity provided good representation of the entire spatial workspace, with each location represented by ∼10% of the Sparse-coding neurons. Cluster 3 neurons exhibited relatively noisy and inconsistent responses to the movement stimulus (Fig. S4), and their firing rates were only weakly tuned to kinematics. We hypothesized that these neurons were responding to stimulation of skin and hair induced by the motion of the arm, a hypothesis that we subsequently tested and confirmed. We putatively term these ‘Cutaneous-responsive’ neurons. To rule out the possibility that these motion-specific responses were inherited from supraspinal structures, we recorded responses to the movement stimulus after making complete spinal transections at the C4 cervical segment that physically disconnected the brain from the spinal cord (Fig. S5A). Importantly, we saw similar numbers of both Gain-field and Sparse-coding neurons in the cervical cords of mice following the complete transection of the spinal cord (Fig. S5B,C), thereby demonstrating that these representations of forelimb movement in the spinal cord are constructed locally and are not inherited from the brain. Identification of a neural geometry for forelimb proprioception To understand how the neural population activity evolves over the trajectory of the movement and the relationship between the population response to movements in different directions, we used de-mixed principal component analysis( 17 ) (dPCA) on the smoothed firing rates of neurons where both the velocity and movement space were densely sampled (n = 431 neurons, Methods). dPCA is a dimensionality reduction method that can separate the population neural activity into components associated with specific variables, such as direction. 72% of the neural variance could be described by 4 dimensions (Fig. S6A). Surprisingly, although the dPCA algorithm did not have access to the values for the direction, speed or position of the movements, the neural population structure was an ordered representation in this low dimensional space ( Fig. 2A ) with a pinwheel structure that faithfully reflected the kinematic state of the forelimb (Supplemental Video 1). Specifically, we find that the first three condition dependent components correspond to the anterior/posterior position, medial/lateral position and the speed of the hand movements, respectively ( Fig. 2B ). This order was maintained in movements with different peak speeds (Fig. S6B,C). We then evaluated the relative contribution of each of the three identified neural clusters to the construction of this low dimensional manifold by performing dPCA on the individual clusters. This analysis showed that Gain-field and Sparse-coding neurons differentially contribute to the position and speed components, while the Cutaneous-responsive neurons have almost no ordered structure (Fig. S6D-F). These experiments demonstrate that this neural geometry cannot trivially arise from the activity of any movement-modulated neurons (such as the Cutaneous-responsive neurons), but requires the patterns of activity exhibited by Gain-field and Sparse-coding neurons. Download figure Open in new tab Fig. 2. Neural population code in the cervical spinal cord is an ordered representation of forelimb kinematics. (A) Left, three condition-independent demixed principal components (dPCs) of neural activity in the cervical spinal cord color coded by the direction of stimulus. Right, temporal dynamics of the same three dPCs. (B) The dPCs are strongly correlated to specific kinematic variables, such as anterior-posterior position (dPC1), medio-lateral position (dPC2) and speed (dPC4). (C) Example decoding of single trial kinematics from neural recordings in the cervical spinal cord using Linear (left), maximum-likelihood (MLE)(middle) and a long-short term memory (LSTM) recurrent artificial neural network (Right) models. (D) and (E) r-squared values (D) and the mean absolute error (E) for single trial decoding across the three model classes. Values are represented as Mean +/- SEM. The structure of the neural population response suggests that information about the kinematic state of the limb is wholly present in the spinal cord. To evaluate this possibility and identify the computations required to estimate the kinematic information, we built and validated decoders to extract the forelimb kinematic state from the neural population activity (Methods). We analyzed three classes of decoders that approximate biologically plausible computational mechanisms - linear models, maximum likelihood models (MLE), and long short-term memory recurrent neural networks ( Fig. 2C , Fig. S7, Methods). Linear models approximate feedforward neural circuits that compute using instantaneous firing rates of inputs( 18 ), MLE models approximate associative networks that rely on probabilistic priors( 19 ), and LSTMs model recurrent neural networks( 20 ) that enable computations incorporating temporal context. A compact LSTM network (8 hidden units) with access to information from ∼40 neurons was able to decode single trial kinematics with an accuracy of ∼50 um for position and ∼5 mm/s for speed ( Fig. 2D,E , Fig. S7E). In contrast, both the linear and MLE models performed significantly worse on single trials ( Fig. 2D,E , Fig. S7A-D). These analyses demonstrate that downstream neural circuits with compact memory and recurrent connectivity can compute forelimb kinematics with high precision from the neural population activity in the cervical spinal cord. The neural code for kinematic state requires activity of muscle and tendon afferents but not cutaneous afferents The spinal cord receives two major sources of mechanosensory information that have been implicated in estimating the kinematic state of the limb, mechanoreceptors embedded in muscles and tendons, and skin-derived cutaneous low-threshold mechanoreceptor (LTMR) afferents( 21 ). To identify which of these sensory pathways are required to construct the kinematic neural code we report here, we employed an intersectional genetic approach to selectively target and ablate them. Muscle and tendon afferents were targeted with Pirt::Cre ; PV FlpO ( 22 – 24 ) and cutaneous LTMRs with Pirt::Cre;MafA FlpO ( 25 ). Crossing to R26 ds-tdT confirmed ≥90% of Pirt::Cre ; PV FlpO afferents co-expressed PV and TrkC, a marker of muscle/tendon afferents (Fig. S8 a-d). Pirt::Cre;MafA FlpO labeled ∼15% of DRG neurons (Fig. S8F) which were large-diameter, non-nociceptive, and excluded muscle/tendon afferents. These are a major subset of LTMR afferents. We selectively ablated either the cutaneous or muscle and tendon afferents using the Tau ds-DTR system( 26 ) while recording motion stimulus driven neural activity in the cervical spinal cord ( Fig. 3A-F , Methods). Ablating muscle and tendon afferents led to the complete absence of neurons displaying sparse responses and a near absence of neurons displaying gain-field responses ( Fig. 3H , right). Cutaneous-responsive neurons with low kinematic information formed the vast majority of residual neural responses. Conversely, mice lacking most of their LTMR afferents had their proportion of Cutaneous-responsive neurons nearly halved, while retaining Gain-field and Sparse-coding neurons ( Fig. 3I , right). Consistent with these results, the neural geometry for proprioception was entirely disrupted by muscle and tendon afferent ablations ( Fig. 3H , left), but was largely unaltered by ablation of LTMR afferents ( Fig. 3I , left). Taken together, these experiments demonstrate that the overwhelming majority of the kinematic state information of the limb is derived from muscle and tendon afferents, and that cutaneous afferents make little, if any, contribution to the construction of the neural geometry for forelimb kinematics in the cervical spinal cord. Download figure Open in new tab Fig. 3. Neural code for forelimb proprioception requires muscle afferents, but not cutaneous afferents. (A-C). Selective ablation of muscle afferents by an intersectional genetic strategy with a cross of Pirt::Cre, PV Flpo , Tau ds-DTR and R26 ds-tdT alleles. Representative images of cervical spinal cord and dorsal root ganglia with an infusion of saline (A) or diphtheria toxin (B). Quantification of the ablation efficiency across mice (D). (D-F). Selective ablation of a subset of cutaneous low threshold mechanosensory afferents by an intersectional genetic strategy with a cross of Pirt::Cre, MafA FlpO , Tau ds-DTR and R26 ds-tdT alleles. Representative images of cervical spinal cord and dorsal root ganglia with an infusion of saline (D) or diphtheria toxin (E). Quantification of the ablation efficiency across mice (F). (G-I). Ablation of muscle/tendon afferents and cutaneous LTMR afferents target distinct clusters of neural responses and differentially perturbs the neural geometry. (H) Ablation of muscle afferents collapses the neural geometry for proprioception (left) by specifically eliminating gain-field and sparse neural responses (right) compared to controls (G), whereas (I) ablation of cutaneous LTMRs only affects Cutaneous-responsive neurons but not gain-field or sparse neural responses, leaving the neural geometry for proprioception intact. Values in (C),(F) are represented as Mean+/-SD. **** denotes a p-value <0.0001 for a two-sided t-test on the means. n = 10 sections from at least 3 animals each. Reducing muscle and tendon afferent input perturbs end-point precision but not reach direction The control of voluntary movement is hypothesized to rely on three essential signals: feedforward commands, efference copies and sensory feedback( 27 ). Having identified the code for sensory feedback in the cervical spinal cord and its dependence on muscle/spindle afferents, we next asked how this sensory information is used during voluntary skilled movement. Perturbations of sensory information will enable us to identify the specific contributions of sensory feedback to voluntary movement that cannot be compensated by feedforward motor commands or their efference copies. To this end, we trained freely moving mice to use a joystick and make rapid directional reaches to spatial targets( 28 ) ( Fig. 4A , Methods). Trained mice made highly stereotyped reaching movements, with precise end-points. Ablating muscle and tendon afferents led to a progressive degradation in the reaching movements over the following three days, characterized by reduced speeds and increased variability in both reach direction and end-point precision (Fig. S9A-D). By day three, muscle and tendon afferent-ablated mice were unable to initiate reaching and made almost no movements (Fig. S9B). In contrast, the reaching behavior in controls was unaffected by DT administration (Fig. S9E-H). These data, in addition to previous reports( 29 , 30 ) demonstrate that sensory feedback is essential for both initiating and coordinating skilled movement. Download figure Open in new tab Fig. 4. Transient silencing of muscle and tendon afferents perturbs speed and end-point precision, but not direction of skilled forelimb movements. (A) Freely moving mice expressing the hM4D DREADD in the muscle/tendon afferents were trained to make rapid center-out reaches to spatial targets using a custom-built low torque joystick (Top). After training, mice were given intraperitoneal injections of either saline or clozapine-N-oxide (CNO). (B) 5 example trajectories from saline (top) and CNO (bottom) sessions. The grey circles represent the starting position and target. X is the end-point of the reach. (C) Log-scaled heat maps for all the trajectories from a saline session (top) and a CNO (bottom) session. Note the reduced of density at the target for the CNO session (arrows). (D-G) Effect of CNO induced silencing on kinematics. Peak distance (D), reach angle (E), peak speed (F) and (G) end-point distributions. Data from an example animal (left) and across all animals (right). **** denotes a p-value <0.0001 for a hierarchical bootstrap test on the medians, n = 9 animals. Given the limited insight these experiments provided regarding the use of information from muscle afferents in the control of skilled movement, we developed a subtler perturbation using DREADD-based chemogenetics. The intersection of Pirt::Cre, PV FlpO and R26 ds-tdT-hM4D/ds-tdT- hM4D was used to selectively express the Gi-coupled hM4D receptor in muscle and tendon afferents (Fig. S10A). We validated the effectiveness of the DREADD receptor electrophysiologically by recording motion stimulus-evoked neural activity in the cervical spinal cord from the same neurons prior to, and then again after, CNO-treatment (Fig. S10 B,C). CNO infusion reduced firing rates in the Gain-field neurons by ∼30% on average (Fig. S10 B,D). Although the firing rates were reduced, the Gain-field neurons maintained their directional tuning (Fig. S10 B). The reduction in firing rates of Gain-field neurons alters the position and speed components of the neural code, but not the direction. Sparse-coding neuron responses deteriorated more than those of Gain-field neurons, and were accompanied by a marked disruption of their firing fields (Fig. S10 C,E) removing precise positional feedback. The combined effect of the disruptions of the neural code across Gain-field and Sparse-coding neurons was a loss of precise speed and positional feedback, but not direction. If neural circuits controlling voluntary movements rely on these kinematic estimates for precision, then we would predict that sensory perturbations during reaching would impair components that require precise positional feedback as such end-point accuracy, while leaving the overall reach direction intact. To test this prediction, we trained Pirt::Cre; PV FlpO ; R26 ds-tdT-hM4D/ds-tdT-hM4D animals in the joystick reaching task and transiently silenced their muscle and tendon afferents. In control sessions with saline infusion, mice made a series of rapid and accurate reaches to targets ( Fig. 4B,C top). As predicted, activation of hM4D by infusion of CNO altered the trajectories of the reaching movements ( Fig. 4B,C bottom). Kinematic analyses of the resultant trajectories revealed that while the overall reach distance and direction were not significantly altered ( Fig. 4D,E ), they were slower ( Fig. 4F ) and exhibited substantial errors in the reach end-point ( Fig. 4G ), with these deficits being reversed in the following control session. The selective disruption of endpoint accuracy, without changes in distance or direction, satisfies a key behavioral prediction of impaired proprioceptive coding. Discussion Our study shows that neurons in the cervical spinal cord generate an ordered neural population code with a pinwheel structure that encodes a precise moment-by-moment estimate for kinematic state of the forelimb. This representation is constructed by two neuron classes with distinct firing patterns. It comprises of a gain-field rate code that encodes speed, direction and position and a sparse code that encodes specific spatial locations. Genetically targeted manipulations of sensory inputs show that muscle and tendon afferents, but not cutaneous afferents, are required to construct this neural code. Moreover, transient perturbations of muscle and tendon afferents perturb end-point accuracy in skilled movements. Our findings show that the spinal cord uses sensory information from muscle and tendon afferents to perform the complex computations required to estimate the kinematic state of the forelimb, which is required for skilled movement. The neurons responsive to the movement stimulus are largely located in medial lamina IV-V and lamina VII/VIII, where Gain-field, Sparse-coding and Cutaneous-responsive neurons are intermingled without any topographical bias. These regions, in addition to being densely innervated by muscle and tendon afferents, are also innervated by descending inputs from the motor and somatosensory cortex( 31 , 32 ). This suggests that the motion responsive neurons in these areas could be neural substrates for top-down modulation by supraspinal structures, either for gain-modulation or suppressing reafference( 33 – 36 ). The firing patterns we see for Gain-field neurons in the ‘preferred direction’ are similar to those observed in isolated muscle spindle Ia and II afferents in response to stretch( 37 , 38 ), indicating that Gain-field neurons maintain the temporal precision of the information transmitted from the muscle afferents. However, contrary to predictions made by computational models( 39 ) and prior observations in the lumbar spinal cord( 40 ), the directional tuning of these neurons is largely uniform for the entire workspace and not strongly biased along one or two axes. A uniform representation of reaching directions has previously been interpreted as a signature of higher-order computation( 39 ). Second, we don’t see distinct clusters of firing rate patterns that correspond to Ia, II and Ib afferents. Rather, the position/speed ratio forms a Gaussian distribution – suggesting that Gain-field neurons integrate proprioceptive information from all three afferent types before transmitting them to downstream structures. This is consistent with studies in the cat showing that many spinal interneurons receive convergent Group Ia, Ib and II afferent input( 41 , 42 ). Similar integration has been seen in the ventral nerve cords of flies( 43 ). Intriguingly, the firing patterns of these spinally computed Gain-field neurons are similar to those seen in the primate S1 cortex( 4 ), suggesting that kinematic representations in higher-order structures could be inherited from the spinal cord. On the other hand, the Sparse-coding neurons constitute an entirely novel class of neural responses for proprioception, with the sharp distinction in firing patterns between the Gain-field and Sparse neurons indicating that they are separate cell-types. Importantly, their relatively uniform tiling of the entire workspace provides a spatial code for the nervous system where the firing of a subset of these neurons can immediately clarify a limb’s spatial location. Rate codes and spike-timing codes have different properties and utility for information processing( 44 ). Rate codes are noise robust( 45 ) and are able to encode graded information by modifying firing rates, however they require integration over longer times scales (∼10 ms) or across many neurons. The firing patterns of Gain-field neurons are consistent with a rate code. Their persistent activity during and after moving the forelimb ( Fig. 1 ) is well suited for generating a neural population state that represents a specific movement context, e.g. posture. On the other hand, the information embedded in the Sparse-coding neurons is encoded near-instantaneously by the precise timing of a single spike( 46 ), that is consistent with a spike timing code. This however makes information from Sparse-coding neurons sensitive to noise and transient with no memory. We propose that the presence of these two complementary coding mechanisms in the spinal cord enables neural circuits in the central nervous system to leverage the benefits of both. The results of our behavioral experiments provide direct evidence for this hypothesis. Chemogenetic silencing disrupted firing patterns in Sparse-coding neurons while leaving the activity in Gain-field neurons largely intact. The behavioral consequence for this perturbation was a loss in end-point precision, without altering direction and distance. These results indicate that the temporal precision of Sparse-coding neurons is essential for accurate movements, and consequently delineates the differential contributions of Gain-field and Sparse-coding neurons. Modeling work on neural manifolds in motor control offers a complementary theoretical context for our results( 47 ). It is known that low-dimensional manifolds can emerge when recurrent neural networks (RNNs) are trained on realistic muscle patterns or kinematics( 20 ). These studies support our finding of an ordered spinal manifold, while also suggesting that manifold organization may be a general principle across the sensorimotor hierarchy, including the spinal cord. While these modeling studies provide a normative framework for how structured low-dimensional representations can arise from task demands or network optimization, they do not yet encompass the computational diversity, or the temporal precision exhibited by spinal Sparse-coding neurons. The combination of rate-based gain-field coding and sparse-coding observed here implies that future models will need to incorporate parallel, complementary population codes to capture the richness of biological proprioceptive processing. The simultaneous presence of these two dichotomous information streams suggests that the downstream neural circuits can leverage the benefits of both, thus enabling the central nervous system to generate context-aware, rapid, goal-directed movements. Materials and Methods Mouse Lines All experiments were carried out in accordance with NIH guidelines and were approved by the Salk Institute’s Institutional Animal Care and Use Committee. Mice used for electrophysiological experiments were over 16 weeks of age and housed in groups of up to 5 animals under a 12-h light/dark cycle till the day of the recordings. For behavioral experiments, mice of over 16 weeks of age were individually housed under a 12-h light/dark cycle for the duration of the study, and were tested during the dark phase. All the mouse lines used in this study have been previously described, including Pirt::Cre, PV FlpO , MafA FlpO , Ai65 (R26 FSF-LSL-tdTomato , referred to here as R26 ds-tdT ), Tau FSF-LSL-DTR and R26 FSF-LSL-hM4Di (referred to here as R26 ds-tdT-hM4D ). The Cre and FlpO driver lines were maintained on a C57Bl/6 background, while the effector lines were maintained on a mixed background. In vivo Cervical Spinal Cord Electrophysiology Mice were deeply anaesthetized with isoflurane (4%). Fur was trimmed over the skull and the dorsal cervical area, and mice were placed in a stereotaxic frame (Kopf Instruments). A heating pad was used to prevent hypothermia. Isoflurane was delivered at 1-3% throughout surgery; this level was adjusted to maintain a constant surgical plane. Ophthalmic ointment was used to protect the eyes. Lidocaine diluted to 0.5% was injected subdermally along the incision line of the scalp and over the cervical spinal cord. The entire shaved area was disinfected by a two-stage betadine and alcohol scrub, repeated three times. The scalp was then removed with surgical scissors to expose the skull, which was thoroughly cleaned. The skull was then roughened with the scalpel to improve adhesion to the dental cement. A craniotomy was then made over visual cortex (−3.5 AP ± 3 ML), and a ground electrode soldered to a gold pin (A-M Systems) was then implanted into the craniotomy to a depth of 1mm. The ground pin and a headplate were secured to the skull with Metabond dental cement. After the Metabond hardened, a second incision was performed over the cervical vertebrae and the adherent fascia was gently removed from the underlying muscle. Muscle and connective tissue overlying the C4-C8 vertebrae were removed by blunt dissection until the vertebrae were seen. Tendons connecting to the dorsal surface of the vertebrae were disconnected and the facet joints were exposed. The vertebrae and the surrounding areas were cleaned with narrow cotton swabs such that any debris was cleared. The mice were then given a cocktail of urethane (1.5 g/kg, Sigma) and xylazine (1.2 g/kg, Sigma) for long term anesthesia during the recordings. The isoflurane anesthesia was gradually reduced to zero over the next few minutes. The mouse was then moved to the electrophysiology rig, placed on a heating pad and was then head-fixed on the rig by the headplate. Spinal clamps (Kopf) positioned at C4/C5 were then used to stabilize the spinal cord, and lift the vertebral column up such that the rib cage moved freely during respiration. The right forepaw/hand of the mouse was then attached to the top of the pSCARA manipulandum by applying a cyanoacrylate glue to the glabrous skin. A laminectomy was performed to expose the spinal cord. The dura was then gently removed with fine forceps and spring scissors. To prevent the cord from drying out, the cord was continuously irrigated with saline. Once the dura was removed, silicon electrodes were driven to the appropriate coordinates in the spinal cord and neural responses to movement stimuli were recorded. Recording sessions lasted between 6 to 8 hours. At the end of the recording session, the animal was either perfused and collected for histological analyses or euthanized by cervical dislocation. Extracellular recordings were made acutely using 64-channel silicon probes (ASSY-77 H10, Cambridge Neurotech). The 64-channel voltage signals were amplified, filtered and digitized (16 bit) on a headstage (Intan Technologies, RHD2164), recorded on a 512-channel Intan recording controller (sampled at 20 kHz), and stored for offline analysis. Extracellular voltage traces were first band pass filtered for 250Hz-7.5kHz. The data were then spike-sorted automatically with Kilosort2.5, and curated manually with Phy2. During manual curation, units containing low-amplitude spikes and/or non-physiological or inconsistent waveform shape were discarded and not included in further analyses. Neurons with fewer than 4 trials in any of the conditions tested were excluded for all analyses. Neural location was estimated from the array’s depth read out from the micromanipulator, and the position of the electrode contact where the neuron had the largest voltage magnitude. pSCARA Motion Control System and Movement Stimuli We built a robotic manipulandum based on the parallel selective compliance articulated robot assembly (pSCARA) designed for rodents 53 . The robot has two degrees of freedom, and was driven by two direct current motors (Maxon RE-max 21) and coupled with two high-resolution optical rotary encoders (Gurley Precision Instruments R120B). The motors were driven with dedicated DC driver boards (VNH5019 Pololu Inc.) and the current drawn was measured with hall-effect based (ACS724) high resolution current sensors (800mV/A). The control system was a single board real time i/o field programmable gate array (sbRIO-9637, NI). The sbRIO is an integrated system that contains a real-time controller and an FPGA. Similar to previously described systems we used a nested control system. The lowest level of the control a standard proportional-integrative-derivative (PID) feedback controller operating at 1 kHz was implemented on the FPGA to control the motors. The second level of control was implemented on the real time controller which performed kinematic transformations from the coordinates of the robot joints to Cartesian coordinates. The final level of control was on the interfaced personal computer running LabView which determined the stimulus type and was responsible for writing the acquired data to disk. We sampled the manipulandum’s kinematics at 1 kHz. We fine-tuned the PID values and validated the motion control system by the comparing the commanded kinematics to that executed by the motors when it was attached to a mouse forelimb (Fig. S1A-C). This robotic system allows for delivery of stimuli with arbitrary kinematics. We chose stimuli that mimicked center-out reaching movements with minimum-jerk dynamics 54 . The range of speeds (20-80 mm/s) was chosen to be consistent with those observed in previous behavioral studies. Electrophysiological Analysis For this study we recorded a total 1458 neurons from 21 mice. For each neuron, a peristimulus time histogram (PSTH) was constructed for each direction of the movement stimulus. The PSTH was constructed by including spikes from 50ms before the onset of the movement stimulus to 200 ms after the onset of movement stimulus, with time bins of 5ms. The PSTH was then filtered with a 25ms Gaussian window. To perform unsupervised clustering of the neural responses, we first constructed the feature vector by horizontally concatenating the PSTH for each stimulus direction in clockwise order, starting with the direction of the peak firing rate. This feature vector was then z-scored and then vertically concatenated to create a 2D matrix of size N x (D x T). Where N is the number of neurons, D is the number of stimulus directions and the T is length of the PSTH vector. For the analyses in Figure 1 , this was 431 x (64 x 50). UMAP dimensional reduction was then applied to this matrix to get the representation in Figure 1 . The UMAP transformation revealed three distinct clusters that could easily be identified with a simple watershed algorithm. For modelling the single neuron firing rates for the Gain-field neurons we tested two gain field models both of which took a similar form: Where, FR is the firing rate calculated as the PSTH, X is distance and ̇X is instantaneous speed of the hand. The gain-field models differ in dependence of the gain-function on angle. The cosine gain-functions have the form: The von Mises gain function has the form: θ is the movement angle and θ pd is the preferred direction. a,b, c, d,,f and θ pd are parameters to be fit. We fit the models using the ‘fminsearch’ function in MATLAB 2021b. Speed/Position ratios were calculated at the ratio of G speed and G dist estimated from the fit. Firing fields for neurons were calculated by generating a 2D spatial histogram quantifying the number of spikes that occurred in each spatial bin over all the trials. The 2D histogram had a bin size of 200μm x 200μm. The firing fields were then normalized to the 99 th percentile of number of spikes in a bin. To estimate the tiling of space, firing field maps were z-scored and were binarized. Significant bins (zscore > 1.65) were given the value 1 and others were assigned 0. This binarized firing field of each cell was then overlaid and normalized by the total number of neurons to calculate the tiling shown in Fig. 1J . For the dPCA analyses the design matrix was constructed as N x D x S x T. Where N is the number of neurons, D is the number of stimulus directions, S is the different speeds and the T is length of the PSTH vector. For the analyses in Figure 2 , this was 138 x (64 x 3 x 50). The dPCA decomposition was performed using the code made available by the original study 23 . For Fig. S6B-C, the neural data for the independent conditions are projected into the dPCA space estimated on the full dataset. For Fig. S6D-F, the dPCA was calculated independently for each of the ‘Clusters’ and the combined neural activity was plotted in the top 3 condition-independent dimensions identified for each dPCA calculation. Neural Decoders To estimate limb kinematics from neural activity we used three classes of models: Linear models, maximum likelihood models and recurrent neural networks. The linear models took the form of Where, X(t) is the x,y position of the hand kinematics at time t, W is the learned weights, FR is either the binned or the binned and smoothed firing rate of the neurons, and e is the estimation error. For cross-validation of the models, W was calculated by using half the trials to calculate the FR and then performing a pseudoinverse. The model was then tested on the mean FR estimated from the held out trials, the mean absolute error and the r-squared for the cross validation was calculated on these predictions. For single trial predictions, all the trials except one were used to calculate the mean FR and estimate W. The model was then tested on the remaining trial, and the mean absolute error and r-squared were calculated from this test. The linear models performed poorly on binned neural data (Fig. S7A, top), although their performance improved with smoothed firing rates (Fig. S7B, top). These models were sensitive to the number of neurons used to make the kinematic predictions (Fig. S7A,B) and showed improvement with larger neural populations. However, the single trial decoding errors with the full population of neurons were still substantial (∼800 um) and provided poor estimates of the moment-by-moment kinematics ( Fig. 2C-E and Fig. S7A,B bottom). The maximum likelihood models (MLE) used probabilistic priors of the ensemble neural activity to estimate the kinematics in the current moment. To validate the models we used half the trials to generate kinematics priors for neural firing patterns (FR train ), and then other half to generate spike probabilities (FR test ). As in the linear models, we evaluated these probabilities for both binned and binned+smoothed data. For decoding, we find the closest match of the FR test vector to the FR train vector in each time step. The kinematics of the most similar FR train vector is then determined as the decoded kinematic state, this can be formalized as: Similar to linear models, the maximum likelihood models showed improved prediction of the kinematics with smoothed firing rates and larger neural populations (Fig. S7C,D), and had substantially improved performance compared to the linear models ( Fig. 2C-E and Fig. S7C,D bottom). For the recurrent neural network models, we used the LSTM architecture. LSTM cells were implemented as described in the original literature 55 . We only needed one LSTM layer to estimate kinematics with high accuracy. Network size was varied by changing the number of hidden units in the layer. Networks were trained till the validation loss plateaued (typically 200 epochs). To generate training data for the LSTM networks, we created a single trial pseudopopulation data set. We did this by first randomly selecting a subset of neurons, and for then for each neuron randomly selecting one trial for each direction. One trial was held out for each neuron and each condition, and wasn’t used in the training dataset. We repeated this ∼1000 times to get a training dataset. This led to a dataset of N x D x FR x 1000, where N is the number of neurons used for the training set, D is the number of stimulus directions (typically 64, but varied for experiment in Fig. S7G) and FR is the spike count for that neuron in that trial, binned with 5ms. The test set was created similarly by using the held out data, the test set always had the dimensions N x D x FR x 1. Since LSTM networks have a large set of parameters that can lead to ‘memorizing’ the data, we undertook a series of validations to confirm that the network was learning a transformation. First, we tested the kinematic predictions on stimulus directions that were held out of the training data. If the LSTM was trained on at least ¼ of the stimuli, its predictions were entirely unimpaired (Fig. S7G). Additionally, an LSTM should perform very well on shuffled data if it is simply memorizing the data, but very poorly if it is learning a transformation. We found that LSTM networks performed poorly on shuffled data (Fig. S7G). The bin width for all models was 5ms and the firing rate vectors were smoothed with a 25ms wide Gaussian window. Immunohistochemistry Mice were anesthetized by a single intraperitoneal (i.p.) injection (10 ml/g body weight) of solution containing 10 mg/ml ketamine and 1 mg/ml xylazine immediately prior to perfusion with 20 mL of 4% paraformaldehyde in PBS. Spinal cords and DRGs were dissected and post fixed for 1 hr at room temperature (RT), then rinsed 3 times in PBS and cryoprotected in 30% sucrose-PBS overnight at 4C. Spinal cords were embedded in OCT (Tissue-Tek) and cryosectioned at 40μm using a Leica CM3050 cryostat, DRGs were similarly cyrosectioned at 14μm. Sections were dried at RT and stored at -20C. Before staining OCT was removed with a 15 min PBS wash. Slides with sections were then incubated in Blocking Solution (PBS, 10% donkey serum and 0.3% Triton X-100) for 1-2 hr at RT and then incubated with the primary antibody diluted in the antibody solution (PBS, 1% donkey serum and 0.3% Triton X-100) overnight at 4C. Sections were then washed 3 times (15 min each) in PBT (PBS and 0.1% Triton X-100) before being incubated for 2 hr at RT with antibody solution containing donkey-raised fluorophore-conjugated secondary antibodies (1:1000; Jackson Laboratories). Sections were again washed 3 times (15 min each) in PBT before being mounted with Aqua-Poly/Mount (Polysciences). A Zeiss LSM700 or an LSM900 confocal microscope was used to capture images. ImageJ software was used to count neurons, the Cell Count plug-in was used to analyze co-localization. Neuronal Ablation Neuronal ablations for the experiments related to Fig. 3 were performed by two i.p. injections of diphtheria toxin (DT, 50 ng/gram of weight; List Biological Laboratories) three days apart in animals >16 weeks of age. Electrophysiological experiments for recording movement responsive neurons were then performed soon after (<3 weeks). For the behavioral experiments the animals received a single i.p. injection with the same total dose (100 ng/gram of weight) Drug Administration Clozapine-N-oxide (Sigma) was dissolved in DMSO and then diluted with 0.9% sterile saline such that the concentration of DMSO did not exceed 1% of the injected solutions. For experiments related to the electrophysiological validation of the chemogenetic silencing (R26 ds- tdT-hM4D ) mice were give i.p. injections of saline before movement stimuli were delivered. After the saline responses were acquired, animals were injected with CNO (3 mg/kg). Approximately 10-20 minutes after the CNO injection, the second set of movement stimuli were delivered. For the behavioral experiments in Fig. 4 , animals were given saline on day 1, CNO on day 2 and saline again on day 3. Joystick Center-out Reach Task We trained mice to use a joystick to make center out reaches to specified targets in an automated home cage training system 34 . Individually housed mice were trained to enter a nose port, grab a fixed post with their left forelimb, and then grasp the joystick with their right forelimb. The mice were then trained to make rapid reaching movements to a spatial target 4 mm out from the center. All mice learn to reach to the target within 10 days of training. After the animals were consistently reaching out to a target, we started restricting the amount of time mice spend in home cage to 3 hours. Since the only source of water for these mice is through this task, the animals had to perform enough successful trials to meet their water needs within this time frame. After 3 days of training with the time restriction, we collect three more days of baseline trajectories. For the neuronal ablation experiments, on the fourth day mice received an injection of DT. The mice were then tested with the same time restriction for three more days. For the hM4D experiments, mice were given an i.p. injection and placed into the home cage 10 minutes after the injection. Mice given saline on the fourth day, CNO on the fifth day and saline again on the sixth day. The time restriction was necessary to make appropriate comparisons between saline and CNO trials since CNO’s potency is time dependent with maximal effects limited to within a few hours of the infusion. Analysis of Joystick Trajectories Trajectories were acquired at 1 kHz and low-pass filtered at 50 Hz with an 8-pole Butterworth filter in software. The reach direction was defined as the angle at which the target distance was transected by the trajectory. Velocity was calculated as a one sample difference of the filtered position vector. To make sure that we were specifically analyzing trajectories that were attributable to right forelimb movement with the animal in a consistent posture, only the trajectories that were contacted after the nose poke and fixed-post contact were considered valid trials eligible for reward. If the mouse exited the nose poke, lost contact with the fixed post or the joystick, the trial was immediately failed. The mouse also failed the trial if it reached in the wrong direction. There were no cues for failed or successful rewards (except the water delivery apparatus). However, a blue LED masking light roughly at eye level to the mouse was turned on at joystick contact. The mouse had to re-contact the joystick to start a new trial after both successful and failed trials. A reaching movement typically consists of initial reach segments followed by corrective segments. To identify the initial reach end-point points of the reaching movements we decomposed complex trajectories into submovements, where submovement boundaries were defined by temporally coincident minima of velocity and radius of curvature. The end-point of the first reach segment to cross the 1 mm distance from the center was defined as the initial reach end-point. Statistical Analysis All statistical analyses were performed in Matlab 2021b. Neurons were considered modulated by the movement stimulus if the number of spikes after movement onset were significantly different than baseline in any of the stimulus directions. Significance was assessed by performing a t-test for the mean number of spikes before and after the stimulus, with a p<0.01. Statistical analyses for measures of kinematics were performed using a hierarchical bootstrap for mice, sessions and trials. We used a two-tailed t-test for assessing difference in mean cell counts of histological analyses. Author Contributions Conceptualization: TB, MDG Methodology: TB Investigation: TB Writing – original draft: TB Writing – review and editing: TB, MDG Competing interests Authors declare that they have no competing interests. Data and materials availability All data, code, and materials used in the analysis will be made available by TB on reasonable request. Download figure Open in new tab Fig. S1. Stable in vivo electrophysiological recordings from the cervical spinal cord while delivering precise motion stimuli to the forelimb. (A) Schematic of a mouse forelimb attached to a parallel selective compliance assembly robot arm. (B) Example temporal profiles of the robot’s speed and position. The comparison of commanded (dashed black line) between and observed (blue line) kinematics illustrates the precision of the robot. (C) Quantification of the accuracy and precision of the robot’s position relative to the commanded position. Values are represented as Mean and standard deviation. (D) Same as (C), for speed. (E) Example filtered and whitened electrophysiological traces for a single channel as a movement stimulus was delivered to the mouse forelimb. Ten trials were recorded ∼ 5 mins apart from each other. Note the minimal effect of movement stimuli on the electrophysiology and the temporal stability of the neural spike amplitudes. (F) Quantification of the noise induced by the delivery of movement stimulus to the forelimb, represented as mean +/- standard deviation. (G) Estimated drift of the neural spikes over a ∼6 hour recording session. Red line is the median, solid blue lines are the 25-75 th percentiles, and whiskers are 1.5 times the interquartile range. Download figure Open in new tab Fig. S2. Firing rates of ‘Cluster 1’ neurons are modulated by speed, position and direction of movement stimuli. ( A ). Rasters and rate histograms of two example neurons across different speeds and directions. (B). Fits of the firing rates of the example neurons in (A) to a linear gain-field model where firing rates are dependent on speed, direction and position. Compared to cosine tuning, the flexibility in the tuning width of von Mises models enables better fits in the ‘Gain-field’ neural population. (C). Gain-field neurons can be differentially sensitive to speed (left) and position (right). A few Gain-field neurons were tuned to multiple movement directions (right). (D). The relative sensitivity to position and speed of Gain-field neurons is normally distributed. (E). The vast majority of Gain-field neurons have single peaked directional tuning. (F). Tuning widths for individual Gain-field neurons. Download figure Open in new tab Fig. S3. Firing patterns of sparse-coding neurons have multi-scale coverage of the kinematic state space. (A-E) . Rasters (top) and spatial firing fields (bottom) of five example neurons from Cluster 2, i.e. Sparse-coding neurons. The examples illustrate the range of spatial firing specificity observed in this cluster. Download figure Open in new tab Fig. S4. Firing rate modulation of Cluster 3 neurons in response to movement stimuli is inconsistent and spatially unstructured. (A-E) . Rasters (top), rate histograms (middle) and spatial firing fields (bottom) of five example neurons from Cluster 3, the Cutaneous-responsive cluster. The examples illustrate that although the neural firing rates of these neurons is significantly modulated by movement stimuli, the responses are inconsistent across trials and unstructured in space Download figure Open in new tab Fig. S5. Neural code for forelimb proprioception in the spinal cord persists after a complete transection between the spinal cord and the brain. (A). Image of electrophysiological recordings from the C7-C8 segment of cervical spinal cord after a complete transection at the C4-C5 segment. (B). Rasters and rate histograms of four example ‘Gain-field’ neurons recorded from the cervical spinal cord after transection. (C). Rasters and spatial firing fields of four example ‘Sparse-coding’ neurons recorded from the cervical spinal cord after transection. Download figure Open in new tab Fig. S6. Neural geometry for proprioception in the cervical spinal cord is consistent across different peak speeds, and is constructed by the Gain-field and Sparse-coding neurons. (A). The first five demixed principal components (dPCs) can describe ∼80% of the variance in neural activity in the cervical spinal cord evoked by a movement stimulus (top). dPCs were labelled by the relative contributions of the direction and speed conditions to the variance (bottom). (B-C). The structure of the neural geometry is invariant to speed. The dynamics of the neural population when the average limb speed was 20 mm/s (B) and 80 mm/s (C) maintains the ordered representation of speed and direction. (D-F). Neural clusters contribute differentially to the construction of the neural geometry. The Gain-field (D) and Sparse-coding neurons (E) contribute to the position and speed components, while the Cutaneous-responsive neurons (F) do not form an ordered structure. Download figure Open in new tab Fig. S7. Linear, maximum-likelihood and recurrent neural network models can estimate moment-by-moment kinematics of the forelimb from neural responses in the cervical spinal cord. (A-B). Cross validation (top) and single trial predictions (bottom) of hand kinematics from binned (A) and smoothed (B) neural data when using a linear model on different fractions of the neural population. (C-D). Plotted as in (A-B), but for maximum-likelihood estimate (MLE) models. (E). Plotted as in (A) but for long-short term memory recurrent neural network models. (F). Increasing LSTM network size beyond 8 hidden units has a minimal effect in increasing model accuracy. (G). LSTM networks can robustly estimate hand kinematics in trials with stimuli they were not trained on. (H). LSTM network performs poorly when the identity of the trials is shuffled, demonstrating that this network is not overfitting and memorizing neural patterns for individual trials. Values are plotted as mean +/- standard deviation. Download figure Open in new tab Fig. S8. An intersectional strategy to selectively target muscle, tendon and cutaneous afferents. (A-D). Immunohistological validation of the intersectional genetics strategy to specifically target muscle afferents. Representative images of the cervical spinal cord (A) and a cervical dorsal root ganglion (B) from a Pirt::Cre; PV Flpo ; R26 ds-tdT animal (10 days postnatal). This intersection doesn’t target any neurons in the central nervous system, and captures ∼90% of the muscle afferents (D) which are identified by co-expression of TrkC and PV. (E-H). Immunohistological validation of the intersectional genetics strategy to specifically target cutaneous LTMRs. Representative images of the cervical spinal cord (E) and a cervical dorsal root ganglion (F) from a Pirt::Cre; MafA::FlpO; R26 ds-tdT animal (10 days postnatal). This intersection shows no overlap with muscle afferents in the spinal projections patterns (E) and has no overlap with the muscle afferents in the DRG (H). Values are plotted as mean +/- standard deviation. Download figure Open in new tab Fig. S9. Ablating muscle and tendon afferents blocks the ability to initiate skilled forelimb movements in freely moving mice. (A) Heat maps of forelimb reach trajectories in a representative Pirt::Cre; PV FlpO ; Tau ds-DTR ; R26 ds-tdT mouse injected with diphtheria toxin (DT) to selective ablate muscle afferents. Forelimb trajectories get progressively disorganized after the day of injection and the animal stops performs the task by day 3. (B). Pirt::Cre; PV FlpO ; Tau ds-DTR ; R26 ds-tdT injected with DT lose the ability to perform the task by day 3. (C-D). Muscle afferent ablation progressively slows down reaching movements across animals. Example distribution of peak reach speed across days in an example animal (C) and means across animals (D). (E-H). Plotted as (A-D) for control animals missing either the Cre or FlpO allele and injected with DT. The spatial structure of the trajectories and the speeds were unaltered by infusion of DT. Values are plotted as median +/- interquartile range. **** denotes a p value<0.0001 for a hierarchical bootstrap test on the medians n = 4 animals. Download figure Open in new tab Fig. S10. Electrophysiological validation of silencing muscle afferents with hM4D. (A). An intersectional strategy to express the DREADD Gi receptor hM4D in muscle afferents. Example images from the dorsal root ganglion of a Pirt::Cre; PV FlpO ; R26 ds-tdT-hM4D/ds-tdT-hM4D mouse. (B). Raster, rate histogram and spatial firing field for an example Gain-field neuron before (left) and after (right) the infusion of CNO in a Pirt::Cre; PV FlpO ; R26 ds-tdT-hM4D/ds-tdT-hM4D mouse. Note that while the tuning direction is maintained, the peak firing rate is reduced by ∼50% (C). Plotted as (B), but for an example Sparse-coding neuron. Note that the infusion of CNO completely disrupted the spatial firing field of this neuron. (D). Peak firing rates in Gain-field neurons are reduced by an infusion of CNO (E). Plotted as in (D), but for Sparse-coding neurons Acknowledgments We thank Graziana Gatto for advice on selection of mouse models in the early planning stages of this work. We thank Eiman Azim, Ruidong Chen, Joe Fetcho, Jesse Goldberg, Kee Wui Huang, Mayank Mehta and Akira Nagamori for feedback and comments on the manuscript. Funding : National Institutes of Health grant R35NS111643 (MDG), Helen Hay Whitney Foundation (TB) Funder Information Declared Helen Hay Whitney Foundation, https://ror.org/037ebw447 , Fellowship National Institutes of Health, https://ror.org/01cwqze88 , R35NS111643 References 1. ↵ J. C. Tuthill , E. Azim , Proprioception . Curr. Biol . 28 , R194 – R203 ( 2018 ). OpenUrl CrossRef PubMed 2. ↵ M. Goulding , T. Bollu , A. Büschges , Sensory feedback and the dynamic control of movement . Annu. Rev. Neurosci . 48 ( 2025 ). 3. ↵ U. Proske , S. C. Gandevia , The proprioceptive senses: their roles in signaling body shape, body position and movement, and muscle force . 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Share A neural geometry for forelimb proprioception in the cervical spinal cord Tejapratap Bollu , Martyn Goulding bioRxiv 2025.09.26.678887; doi: https://doi.org/10.1101/2025.09.26.678887 Share This Article: Copy Citation Tools A neural geometry for forelimb proprioception in the cervical spinal cord Tejapratap Bollu , Martyn Goulding bioRxiv 2025.09.26.678887; doi: https://doi.org/10.1101/2025.09.26.678887 Citation Manager Formats BibTeX Bookends EasyBib EndNote (tagged) EndNote 8 (xml) Medlars Mendeley Papers RefWorks Tagged Ref Manager RIS Zotero Tweet Widget Facebook Like Google Plus One Subject Area Neuroscience Subject Areas All Articles Animal Behavior and Cognition (7633) Biochemistry (17680) Bioengineering (13889) Bioinformatics (41927) Biophysics (21445) Cancer Biology (18585) Cell Biology (25491) Clinical Trials (138) Developmental Biology (13373) Ecology (19897) Epidemiology (2067) Evolutionary Biology (24308) Genetics (15606) Genomics (22494) Immunology (17736) Microbiology (40385) Molecular Biology (17175) Neuroscience (88583) Paleontology (666) Pathology (2830) Pharmacology and Toxicology (4822) Physiology (7641) Plant Biology (15149) Scientific Communication and Education (2045) Synthetic Biology (4293) Systems Biology (9822) Zoology (2271)