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Supplementary Notes Supplementary Note 1. Physiological analysis at lumbar levels and behavioural analysis at cervical levels. Several lines of evidence reinforce the idea that the basic anatomical and physiological organization of presynaptic inhibition of sensory input is conserved at cervical and lumbar levels of the spinal cord. We chose to characterize the physiological consequences of Gad2Cre neuron activation in lumbar spinal cord, at ages when spinal hemicord preparations are viable (<p15), and to evaluate the effect of cervical Gad2Cre neuron elimination on behaviour in adult mice for the reasons detailed below. 1. The aim of our physiological studies was to establish whether Gad2-marked neurons mediate classically

defined presynaptic inhibition. For this reason we chose to characterize the physiological consequences of Gad2Cre neuron activation in lumbar spinal cord, permitting a direct comparison of our in vitro findings in mouse with classical studies on presynaptic inhibition, performed in vivo in cat lumbar spinal cord. We observed a tight correspondence between our physiological data and the defining features of presynaptic inhibition described in these classical cat papers.

Moreover, there is reason to be confident that the basic functional organization of presynaptic inhibition does not differ between cervical and lumbar spinal segments. This issue was directly addressed during John C. Eccles and colleagues’ initial characterization of presynaptic inhibition, with the conclusion that “the mechanism of [presynaptic inhibition] in the cervical cord is the same as that in the lumbosacral cord”58. Specifically, in cervical spinal cord it has been shown that58,59:

i) There is no observable difference in the postsynaptic membrane properties of motor neurons in cervical and lumbar

spinal cord. ii) Cervical motor neurons, like their lumbar counterparts, receive direct, monosynaptic innervation from group Ia

afferent fibres of homonymous muscle groups, as well as disynaptic postsynaptic inhibition. iii) Presynaptic inhibition is recruited by activation of flexor afferents, as in lumbar cord. iv) Presynaptic inhibition in cervical cord has a prolonged time course, as in lumbar cord. v) The strength of presynaptic inhibition in cervical cord increases with the stimulus intensity (frequency, duration) of

the conditioning nerve, as in lumbar cord. vi) As in lumbar cord, group I afferents in cervical cord are responsible for the recruitment of presynaptic inhibitory

effects at sensory–motor synapses. vii) Primary afferent depolarization is produced by stimulation of forelimb sensory afferents, with the largest effects

being generated by stimulation of flexor nerves. This is consistent with observations in lumbar spinal cord.

In addition we show that the organization of Gad2-marked presynaptic inhibitory neurons and their contacts with proprioceptive afferent terminals is equivalent between cervical (Fig. 1g–i) and lumbar (Extended Data Fig. 1) segments at later ages, findings consistent with the original characterization of Gad2-marked interneurons in lumbar spinal cord7,15.

2. We chose to investigate the behavioural consequences of eliminating presynaptic inhibition in cervical spinal

cord for two main reasons. First, the most complete characterization of presynaptic inhibition as it relates to behavioural output to date has been carried out in the context of forelimb movements30. Second, we have found that high-resolution kinematic analysis of goal-directed forelimb movement is capable of extracting detailed quantitative features of motor behaviour31.

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Supplementary Note 2. Temperature dependence of GABAergic excitation of motor neurons. GABA released upon activation of Gad2Cre neurons depolarizes sensory neurons, due to high sensory intracellular Cl−, eliciting primary afferent depolarization (PAD). The basic issue addressed in these experiments derives from the fact that PAD recorded at a dorsal root does not resolve whether cutaneous and/or proprioceptive afferents were depolarized. In light of this it was important to establish that Gad2Cre neuronal photoactivation results in the depolarization of proprioceptive afferent terminals. To determine whether Gad2Cre neurons elicit PAD in proprioceptors, we exploited the direct innervation of motor neurons by proprioceptive, but not by cutaneous, afferents, inferring that only transmitter released from proprioceptors will have access to motor neurons. We showed that primary afferent depolarization generated at low temperatures is capable of eliciting a sensory action potential and subsequent sensory transmitter release (Fig. 2f and Extended Data Fig. 2). Our finding of a temperature-dependent excitatory input to motor neurons, triggered by activation of presynaptic inhibitory interneurons, is wholly consistent with prior work: 1. Dorsal root reflexes are most robust at lower temperatures60–62. 2. At low temperature, depolarization of sensory afferent terminals by presynaptic inhibitory interneurons excites motor

neurons63, a precedent and impetus for our findings (Extended Data Fig. 2b). 3. This motor neuron excitation is the result of presynaptic inhibitory depolarization of the sensory afferent terminal,

generating an action potential within the sensory afferent and consequent glutamate release21. 4. In the isolated neonatal mouse spinal cord, dorsal root reflexes are accompanied by activation of ventral roots,

presumably via this same mechanism64. 5. Our dorsal root recordings at 24–26 ºC reveal that Gad2Cre neuron photoactivation elicits an antidromic spike (Fig. 2f,

lower arrow). Moreover, simultaneous recording from the ventral root reveals spiking ~0.7 ms after the antidromic spike in the dorsal root (Extended Data Fig. 2a–c), consistent with accepted synaptic delays at sensory–motor synapses65.

6. The motor neuron EPSP we observe in response to Gad2Cre neuron photoactivation exhibits strict temperature dependence, i.e. is present at low temperature and absent at increased temperatures (Extended Data Fig. 2e), consistent with prior analyses63.

7. Pharmacological analysis demonstrates that this form of motor neuron activation is dependent on GABA released from Gad2Cre neurons as well as glutamate released from sensory afferents (Extended Data Fig. 2f, g).

Supplementary Note 3. The long-lasting nature of presynaptic inhibition. The prolonged time course of presynaptic inhibition is one of its most salient and distinguishing features, evident from the early characterization of presynaptic inhibition by Eccles and colleagues in cat spinal cord4. Our data bear striking resemblance to these classical studies (Extended Data Fig. 4). There are two basic hypotheses that could explain why presynaptic inhibition might elicit a long-lasting reduction in sensory-evoked EPSC amplitude. The first is that primary afferent depolarization, the physiological correlate of presynaptic inhibition, is known to have a markedly slow decay, particularly following repeated high frequency activation66,67. We have replicated these observations in the mouse, showing that sustained photoactivation of Gad2Cre neurons results in a prolonged primary afferent depolarization (data not shown). The second potential explanation is based on the finding that a component of presynaptic inhibition is mediated by GABA-B receptors, whose metabotropic actions are of considerably longer duration than those of GABA-A receptors68. We note that the long duration of PAD occurs even following a single 1 ms photoactivation pulse, resulting in at most two spikes in GABApre neurons. Thus this long time course occurs without sustained spiking in GABApre neurons, suggesting that asynchronous release of GABA from GABApre neurons may in part be responsible for the prolonged time course of PAD and presynaptic inhibition69.


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Supplementary Note 4. Modelling of the limb as a damped harmonic oscillator. We modelled a simplified joint under the control of flexor and extensor torques, subject to gain-modulated sensory feedback. The basic principle of the limb model is that joint angle relates to torque as specified by Newton’s second law in its angular form, subject to a drag term, and scaled in time by a muscle time constant. Sensory feedback activates muscle torque in response to changes in joint angle, the efficacy of which is set by a gain factor. We considered a single joint extension under conditions of constant low (GABApre extant) or high (GABApre deleted) feedback gain values. When feedback gain is low, in the presence of presynaptic inhibition, joint extension evokes a feedback-driven flexor torque, which the low gain ensures has a limited effect on joint angle (Fig. 6a, c). In the high gain condition, the initial feedback-generated flexor torque induces changes in joint angle of sufficient magnitude to evoke subsequent cycles of flexor and extensor torques (Fig. 6b, d). To relate the behaviour of the simulated joint to post-DT reaching movements, we fit the model to the values that capture post-DT reaches: the oscillation frequency of ~20 Hz and the oscillation decay time of ~77 ms. To do this we took advantage of the linear nature of the model, representing it as a five dimensional system of linear first order equations with three free parameters, and solving for its eigenmodes to examine their behaviour as a function of the three model parameters. The parameters that describe the model are: the sensory gain h, which specifies the efficacy with which changes in joint angle induce flexor or extensor torques; the muscle time constant τm, by which all temporal processes in the model are scaled and which defines the rapidity with which the joint angle responds to applied torque; and a drag term k, which defines the rate at which the joint comes to rest in the absence of applied torque. The model has three non-oscillatory eigenmodes, which decay, and one oscillatory eigenmode, whose oscillations dominate the behaviour of the model. We used the complex eigenvalue corresponding to the oscillatory eigenmode (λ1) to generate expressions for the frequency of oscillation (fosc) and oscillatory decay time constant (τosc) of the model. These equations depend explicitly on the muscle time constant parameter, and so to create a parameter-free term that both describes the model’s oscillatory eigenmode and is comparable to our experimentally-derived data, we considered the product of the frequency of oscillation and the decay time of the model. This term, which we call ncycle, is equal to the product of fosc and τosc, and is independent of the choice of muscle time constant parameter, corresponding to the number of oscillatory cycles within a single decay time constant. This strategy permitted us to compare our experimentally-derived post-DT oscillation parameters of frequency and decay to the model, across the whole parameter space of the model. We first considered how ncycle varied as a function of the feedback gain parameter, with the aim of identifying which feedback gain of the model captures the oscillatory behaviour of post-DT reaches. We found that as gain increases, the value of ncycle approaches infinity, with a vertical asymptote at a critical gain level, which we set to 1. We found that the experimentally-derived value of ncycle, (19.5 ± 1.1 s−1) (0.077 ± 0.007 s) = 1.51 ± 0.16, corresponded to a feedback gain of 0.61 ± 0.04, roughly 60% of the critical gain (Extended Data Fig. 8a). We noted that this value did not vary significantly across a wide range of values of the drag parameter k, changing by <2% across a 100-fold range of k values. We therefore have derived a value of gain such that the value of ncycle in our model matches our experimental data. To simulate joint extension in the absence of subtractive scaling (representing postsynaptic inhibition) we added a

constant value to the sensory feedback such that s = hτmdθdt+C . The added constant C represents the added

feedback that would emerge in the absence of a tonic subtractive postsynaptic inhibitory term. Joint extension under these conditions is represented as the green line in Fig. 6c. After fitting the model parameters to post-DT reaching data, we explored how frequency and decay time of oscillations vary across the full range of subcritical feedback gains, using the time constant parameter calculated



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as described above. We found that as feedback gain increases, the frequency and the oscillation decay time of oscillation also increase. At low gain values, around 10% of the critical gain, the oscillation decay and frequency are low, such that any oscillations decay well before the first oscillatory cycle is complete. This provides a potential explanation of why, at low gain values consistent with intact presynaptic inhibition, reaching movements are smooth and uncontaminated by oscillation (Fig. 6c). At high gain values, around 60% of the critical gain, when oscillations dominate, the relationship between frequency and gain and decay time and gain is relatively flat (Fig. 6e, f), providing a possible explanation for the striking consistency in oscillatory frequency and decay time that we observe across animals. More generally, the fact that the model so effectively captures the quantifiable parameters associated with the reaching behaviour that we observe following GABApre elimination is a strong argument in favour of the view that post-DT reaches exhibit the core features of under-damped oscillation, with pre-DT reaches characterized by critically or near-critically damped oscillation. Elements of forelimb movement, then, can be likened to a damped harmonic oscillator, in which oscillations are critically damped during normal conditions, but under damped following the loss of GABApre-mediated gain control. Supplementary Note 5. Modelling monosynaptic and polysynaptic oscillatory pathways. We note that the success of modelling feedback-driven oscillation makes no assumptions about the direct nature of connectivity or the temporal delay incurred by the sensory–motor loop(s) recruited by unchecked proprioceptive feedback.

1. A broad range of feedback delays, representing typical monosynaptic and polysynaptic feedback loop

latencies, generates similar oscillation profiles. Notably, we find that introduction of feedback delay does not change the overall character of the model: we still observe oscillatory behaviour as feedback gain increases. What does change is the value of the critical gain (the gain level above which oscillations do not decay): as the delay increases, the value of the critical gain decreases (Extended Data Fig. 8c). Yet scaling these curves by their corresponding critical gain values reveals equivalent oscillatory lifetimes (Extended Data Fig. 8d). These findings provide further support for the idea that a modest change in the gain of sensory feedback is sufficient to result in the emergence of marked oscillatory behaviour.

2. The model predicts that simultaneous recruitment of multiple feedback loops of different delays (for example, 1 ms, 3 ms and 5 ms) still elicits an oscillation with a dominant peak frequency (Extended Data Fig. 8f–h), as exhibited in our behavioural data. With this finding it is possible to accommodate the reality that diverse proprioceptive target pathways are deregulated simultaneously by the loss of GABApre neurons and presynaptic inhibition.

3. Our modelling analysis also makes a case that the deregulation of short delay proprioceptive feedback loops is likely to underlie oscillations during reaching in GABApre-deficient mice. Modelling with realistic muscle time constants11 (Supplementary Note 4) reveals that oscillation frequencies decrease as temporal delays increase (Extended Data Fig. 8e, h). Thus for long latency feedback loops to generate 20 Hz oscillation, muscle time constants must become increasingly brief.

Supplementary Discussion GABApre neurons as a specialized gain control system. Theoretical analyses coupled with experiment suggest that presynaptic inhibition provides a specialized means of sensory gain control, and activation of postsynaptic inhibition is not an effective gain scaling mechanism. Thus the loss of postsynaptic inhibition should not, and does not, result in limb oscillations.



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To explore this issue we have used the sensory–motor feedback model to compare directly the impact of divisive (presynaptic) and subtractive (commonly achieved by postsynaptic inhibition) normalization on joint velocity oscillation. Loss of presynaptic inhibition is predicted to trigger limb oscillation (Fig. 6b, d). Addition of a postsynaptic inhibitory term into the model reveals no evidence for oscillation upon elimination of postsynaptic inhibition (Fig. 6c, green line and Supplementary Note 4). Thus loss of presynaptic, but not postsynaptic, inhibition is predicted to trigger limb oscillation in the model. This analysis also suggests that oscillations produced by selective elimination of presynaptic inhibition cannot be compensated by the remaining intact postsynaptic inhibitory system, consistent with our experimental observations (Fig. 5). In addition we cite below a number of studies, both theoretical and experimental, that further indicate the specificity of the behavioural disruption after GABApre ablation: 1. A large body of theoretical work shows that presynaptic inhibition is divisive, whereas postsynaptic inhibition

is typically subtractive unless synapses are placed at specific locations along a dendrite70,71, and thus, perturbation of postsynaptic inhibition alone will not result in a change in gain72. This theoretical work is supported by experiments coupled with modelling that establish that divisive gain changes occur only when postsynaptic inhibition is noisy and balanced by excitation73.

2. In the context of a computational model of the monosynaptic stretch reflex, gain changes can only be

achieved using presynaptic, and not postsynaptic, inhibition12,13. 3. Experimental approaches have shown that the slope of the f–I curve of motor neurons cannot be altered even

with very strong postsynaptic inhibition74. 4. Activation of recurrent Renshaw cell inhibition, a postsynaptic inhibitory mechanism, does not achieve

divisive changes in gain at sensory–motor synapses75. 5. Strychnine application to the spinal cord blocks glycinergic inhibition, yet leaves GABAergic inhibition, and

thus presynaptic inhibition, intact. This perturbation exerts a synchronizing action on flexor and extensor motor pools45, the opposite of the alternating behaviour that we observe. Moreover, strychnine has a blunt effect on motor behaviour, rendering mice unable to walk45, whereas Gad2Cre-ablated mice perform a horizontal ladder locomotion task normally (Fig. 4f). In addition, paw velocity at reach initiation, digit abduction during grasping and left-right paw alternation in the ladder task are all unaffected by GABApre ablation (Fig. 4f, Fig. 5d, e, Extended Data Table 1 and Supplementary Videos 3, 4), further indicating that the behavioural deficits we observe are far more specific than those seen after a more pervasive loss of inhibition.

6. Elimination of V1 inhibitory interneurons deletes a specific subset of postsynaptic inhibitory interneurons.

This ablation affects locomotor speed apparently without producing oscillation44. 7. We also note that elimination of presynaptic inhibition produces a behavioural perturbation quite distinct from

that observed after other motor circuit disruptions. For example, selective elimination of V2a neurons, a cardinal excitatory premotor interneuron subclass in the ventral spinal cord, perturbs forelimb movement in an entirely different manner than GABApre ablation, resulting in dysmetric reaching with no indication of limb oscillation31. These disparate behavioural phenotypes were elicited using the same genetic-toxin approach, applied to the same spinal segments, and were evaluated with the same behavioural kinematic assay — a



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demonstration that distinct motor circuit interventions do indeed produce specific and different motor behavioural disruptions.

Thus presynaptic inhibition is uniquely poised to regulate sensory gain scaling14. Moreover, as GABApre neurons are genetically programed to establish presynaptic, but not postsynaptic, contacts in the ventral spinal cord7,76, our findings identify the cellular substrate of an evolutionarily conserved and genetically hardwired gain control system — a solution for the need to rescale the broad dynamic range of sensory feedback to the operating regime of central motor circuits. Dynamic gain control during behaviour. Several lines of evidence speak to the importance of high sensory gain during certain stages of movement, and low sensory gain at others: 1. The gain of sensory feedback is modulated phasically during locomotion. During the stance phase the gain of

sensory feedback is high, but is dramatically reduced during swing phase13. Presynaptic inhibition is the hypothesized mechanism behind this dynamic regulation of sensory gain12,77. Moreover, primary afferent depolarization, one hypothesized mechanistic substrate of presynaptic inhibition, is modulated in a phase-dependent manner during fictive locomotion9, supporting the view that presynaptic inhibition dynamically modulates sensory gain during locomotion.

2. In the context of voluntary movement, there is evidence to suggest that presynaptic inhibition serves to

regulate sensory gain dynamically as a function of a given muscle’s role in the movement. The gain of sensory feedback is high from a muscle undergoing a voluntary contraction, presumably due to reduced presynaptic inhibitory action, but is suppressed via presynaptic inhibition for non-contracting synergist muscles49.

3. Current theories of motor control assert that effective and rapid correction of ongoing motor plans requires the

comparison of sensory feedback signals with predictions generated by an internal model78. It is thought that the supraspinal systems likely involved in rapid motor correction require high sensory gain, as long as sensory delays are compensated appropriately79. This is in contrast to local spinal circuits, which likely require the gain in short-latency spinal feedback loops to be kept low, a task for which presynaptic inhibition is well equipped.

4. We emphasize that the firing rate of sensory feedback scales the strength of presynaptic inhibition4.

Optogenetic activation of Gad2Cre neurons scales sensory feedback strength as a function of stimulation frequency, duration and time (Extended Data Fig. 4), in correspondence with classical observations in the cat4. These data demonstrate the capacity for GABApre neurons to regulate sensory gain dynamically.

Thus presynaptic inhibition by Gad2Cre neurons is likely to provide a means with which to constrain sensory gain when necessary, while permitting high sensory gain in a task-specific manner. Supplementary References 58. Schmidt, R. F. & Willis, W. D. Intracellular recording from motoneurons of the cervical spinal cord of the cat.

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59. Schmidt, R. F. & Willis, W. D. Depolarization of central terminals of afferent fibers in the cervical spinal cord of the cat. Journal of Neurophysiology 26, 44-60 (1963).



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61. Brooks, C. M., Koizumi, K. & Malcolm, J. L. Effects of changes in temperature on reactions of spinal cord. Journal of Neurophysiology 18, 205-216 (1955).

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69. Hefft, S. & Jonas, P. Asynchronous GABA release generates long-lasting inhibition at a hippocampal interneuron–principal neuron synapse. Nature Neuroscience 8, 1319-1328 (2005).

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71. Lovett-Barron, M. et al. Regulation of neuronal input transformations by tunable dendritic inhibition. Nature Neuroscience 15, 423-430- S421-423 (2012).

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73. Chance, F. S., Abbott, L. F. & Reyes, A. D. Gain modulation from background synaptic input. Neuron 35, 773-782 (2002).

74. Granit, R., Kernell, D. & Lamarre, Y. Algebraical summation in synaptic activation of motoneurones firing within the primary range to injected currents. Journal of Physiology 187, 379-399 (1966).

75. Capaday, C. & Stein, R. B. The effects of postsynaptic inhibition on the monosynaptic reflex of the cat at different levels of motoneuron pool activity. Experimental Brain Research 77 (1989).

76. Ashrafi, S. et al. Neuronal IG/caspr recognition promotes the formation of axoaxonic synapses in mouse spinal cord. Neuron 81, 120-129 (2014).

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