Frequency response of spinal Renshaw cells activated by stochastic motor axon stimulation

Spatial and Temporal Arrangement of Recurrent Inhibition in the Primate Upper Limb

Renshaw cells mediate recurrent inhibition between motoneurons within the spinal cord. The function of this circuit is not clear; we previously suggested based on computational modeling that it may cancel oscillations in muscle activity around 10 Hz, thereby reducing physiological tremor. Such tremor is especially problematic for dexterous hand movements, yet knowledge of recurrent inhibitory function is sparse for the control of the primate upper limb, where no direct measurements have been made to date. In this study, we made intracellular penetrations into 89 motoneurons in the cervical enlargement of four terminally anesthetized female macaque monkeys, and recorded recurrent IPSPs in response to antidromic stimulation of motor axons. Recurrent inhibition was strongest to motoneurons innervating shoulder muscles and elbow extensors, weak to wrist and digit extensors, and almost absent to the intrinsic muscles of the hand. Recurrent inhibitory connections often spanned joints, for example from motoneurons innervating wrist and digit muscles to those controlling the shoulder and elbow. Wrist and digit flexor motoneurons sometimes inhibited the corresponding extensors, and vice versa. This complex connectivity presumably reflects the flexible usage of the primate upper limb. Using trains of stimuli to motor nerves timed as a Poisson process and coherence analysis, we also examined the temporal properties of recurrent inhibition. The recurrent feedback loop effectively carried frequencies up to 100 Hz, with a coherence peak around 20 Hz. The coherence phase validated predictions from our previous computational model, supporting the idea that recurrent inhibition may function to reduce tremor.

SIGNIFICANCE STATEMENT We present the first direct measurements of recurrent inhibition in primate upper limb motoneurons, revealing that it is more flexibly organized than previous observations in cat. Recurrent inhibitory connections were relatively common between motoneurons controlling muscles that act at different joints, and between flexors and extensors. As in the cat, connections were minimal for motoneurons innervating the most distal intrinsic hand muscles. Empirical data are consistent with previous modeling: temporal properties of the recurrent inhibitory feedback loop are compatible with a role in reducing physiological tremor by suppressing oscillations around 10 Hz.

Synaptic Connectivity between Renshaw Cells and Motoneurons in the Recurrent Inhibitory Circuit of the Spinal Cord

Renshaw cells represent a fundamental component of one of the first discovered neuronal circuits, but their function in motor control has not been established. They are the only central neurons that receive collateral projections from motor outputs, yet the efficacy of the excitatory synapses from single and converging motoneurons remains unknown. Here we present the results of dual whole-cell recordings from identified, synaptically connected Renshaw cell-motoneuron pairs in the mouse lumbar spinal cord. The responses from single Renshaw cells demonstrate that motoneuron synapses elicit large excitatory conductances with few or no failures. We show that the strong excitatory input from motoneurons results from a high probability of neurotransmitter release onto multiple postsynaptic contacts. Dual current-clamp recordings confirm that single motoneuron inputs were sufficient to depolarize the Renshaw cell beyond threshold for firing. Reciprocal connectivity was observed in approximately one-third of the paired recordings tested. Ventral root stimulation was used to evoke currents from Renshaw cells or motoneurons to characterize responses of single neurons to the activation of their corresponding presynaptic cell populations. Excitatory or inhibitory synaptic inputs in the recurrent inhibitory loop induced substantial effects on the excitability of respective postsynaptic cells. Quantal analysis estimates showed a large number of converging inputs from presynaptic motoneuron and Renshaw cell populations. The combination of considerable synaptic efficacy and extensive connectivity within the recurrent circuitry indicates a role of Renshaw cells in modulating motor outputs that may be considerably more important than has been previously supposed.

SIGNIFICANCE STATEMENT

We have recently shown that Renshaw cells mediate powerful shunt inhibition on motoneuron excitability. Here we complete a quantitative description of the recurrent circuit using recordings of excitatory synapses between identified motoneuron and Renshaw cell pairs. We show that the excitation is highly effective as a result of a high probability of neurotransmitter release onto multiple release sites and that efficient neurotransmission is maintained at physiologically relevant firing rates in motoneurons. Our results also show that both excitatory and inhibitory connections exhibit considerable convergence of inputs. Because evaluation of the determinants of synaptic strength and the extent of connectivity constitute fundamental parameters affecting the operation of the recurrent circuit, our findings are critical for informing any future models of motor control.

The recurrent case for the Renshaw cell

Although Renshaw cells (RCs) were discovered over half a century ago, their precise role in recurrent inhibition and ability to modulate motoneuron excitability have yet to be established. Indirect measurements of recurrent inhibition have suggested only a weak modulatory effect but are limited by the lack of observed motoneuron responses to inputs from single RCs. Here we present dual recordings between connected RC-motoneuron pairs, performed on mouse spinal cord. Motoneuron responses demonstrated that Renshaw synapses elicit large inhibitory conductances and show short-term potentiation. Anatomical reconstruction, combined with a novel method of quantal analysis, showed that the strong inhibitory input from RCs results from the large number of synaptic contacts that they make onto individual motoneurons. We used the NEURON simulation environment to construct realistic electrotonic models, which showed that inhibitory conductances from Renshaw inputs exert considerable shunting effects in motoneurons and reduce the frequency of spikes generated by excitatory inputs. This was confirmed experimentally by showing that excitation of a single RC or selective activation of the recurrent inhibitory pathway to generate equivalent inhibitory conductances both suppress motoneuron firing. We conclude that recurrent inhibition is remarkably effective, in that a single action potential from one RC is sufficient to silence a motoneuron. Although our results may differ from previous indirect observations, they underline a need for a reevaluation of the role that RCs perform in one of the first neuronal circuits to be discovered.

Neuromuscular mechanisms and neural strategies in the control of time-varying muscle contractions

The organization of the neural input to motoneurons that underlies time-varying muscle force is assumed to depend on muscle transfer characteristics and neural strategies or control modes utilizing sensory signals. We jointly addressed these interlinked, but previously studied individually and partially, issues for sinusoidal (range 0.5–5.0 Hz) force-tracking contractions of a human finger muscle. Using spectral and correlation analyses of target signal, force signal, and motor unit (MU) discharges, we studied 1) patterns of such discharges, allowing inferences on the motoneuronal input; 2) transformation of MU population activity (EMG) into quasi-sinusoidal force; and 3) relation of force oscillation to target, carrying information on the input's organization. A broad view of force control mechanisms and strategies emerged. Specifically, synchronized MU and EMG modulations, reflecting a frequency-modulated motoneuronal input, accompanied the force variations. Gain and delay drops between EMG modulation and force oscillation, critical for the appropriate organization of this input, occurred with increasing target frequency. According to our analyses, gain compensation was achieved primarily through rhythmical activation/deactivation of higher-threshold MUs and secondarily through the adaptation of the input's strength expected during tracking tasks. However, the input's timing was not adapted to delay behaviors and seemed to depend on the control modes employed. Thus, for low-frequency targets, the force oscillation was highly coherent with, but led, a target, this timing error being compatible with predictive feedforward control partly based on the target's derivatives. In contrast, the force oscillation was weakly coherent, but in phase, with high-frequency targets, suggesting control mainly based on a target's rhythm.

Strategies for the control of voluntary movements with one mechanical degree of freedom

A theory is presented to explain how accurate, single-joint movements are controlled. The theory applies to movements across different distances, with different inertial loads, toward targets of different widths over a wide range of experimentally manipulated velocities. The theory is based on three propositions. (1) Movements are planned according to “strategies” of which there are at least two: a speed-insensitive (SI) and a speed-sensitive (SS) one. (2) These strategies can be equated with sets of rules for performing diverse movement tasks. The choice between SI and SS depends on whether movement speed and/or movement time (and hence appropriate muscle forces) must be constrained to meet task requirements. (3) The electromyogram can be interpreted as a low-pass filtered version of the controlling signal to the motoneuron pools. This controlling signal can be modelled as a rectangular excitation pulse in which modulation occurs in either pulse amplitude or pulse width. Movements to different distances and with loads are controlled by the SI strategy, which modulates pulse width. Movements in which speed must be explicitly regulated are controlled by the SS strategy, which modulates pulse amplitude. The distinction between the two movement strategies reconciles many apparent conflicts in the motor control literature.

Effects of spinal recurrent inhibition on motoneuron short-term synchronization

Spinal recurrent inhibition linking skeleto- motoneurons (alpha-MNs) via Renshaw cells (RCs) has been variously proposed to increase or decrease tendencies toward synchronous discharges between alpha-MNs. This controversy is not easy to settle experimentally in animal or human paradigms because RCs receive, in addition to excitatory input from alpha-MNs, many other modulating influences which may change their mode of operation. Computer simulations help to artificially isolate the recurrent inhibitory circuit and thus to study its effects on alpha-MN synchronization under conditions not achievable in natural experiments. We present here such a study which was designed to specifically test the following hypothesis. Since many alpha-MNs excite any particular Renshaw cell, which in turn inhibits many alpha-MNs, this convergence-divergence pattern establishes a random network whose random discharge patterns inject uncorrelated noise into alpha-MNs, and this noise counteracts any synchronization potentially arising from other sources, e.g., common inputs (Adam et al. in Biol Cybern 29:229-235, 1978). We investigated the short-term synchronization of alpha-MNs with two types of excitatory input signals to alpha-MNs (random and sinusoidally modulated random patterns). The main results showed that, while recurrent inhibitory inputs to different alpha-MNs were indeed different, recurrent inhibition (1) exerted rather small effects on the modulation of alpha-MN discharge, (2) tended to increase the short-term synchronization of alpha-MN discharge, and (3) did not generate secondary peaks in alpha-MN-alpha-MN cross-correlograms associated with alpha-MN rhythmicity.

Decorrelating actions of Renshaw interneurons on the firing of spinal motoneurons within a motor nucleus: a simulation study

A simulation of spinal motoneurons and Renshaw cells was constructed to examine possible functions of recurrent inhibition. Recurrent inhibitory feedback via Renshaw cells is known to be weak. In our model, consistent with this, motoneuron firing was only reduced by a few pulses per second. Our initial hypothesis was that Renshaw cells would suppress synchronous firings of motoneurons caused by shared, dynamic inputs. Each motoneuron received an identical pattern of noise in its input. Synchrony coefficients were defined as the average motoneuron population firing relative to the activity of selected reference motoneurons; positive coefficients resulted if the motoneuron population was particularly active at the same time the reference motoneuron was active. With or without recurrent inhibition, the motoneuron pools tended to show little if any synchronization. Recurrent inhibition was expected to reduce the synchrony even further. Instead, it reduced the variance of the synchrony coefficients, without a comparable effect on the average. This suggests-surprisingly-that both positive and negative correlations between motoneurons are suppressed by recurrent inhibition. In short, recurrent inhibition may operate as a negative feedback mechanism to decorrelate motoneurons linked by common inputs. A consequence of this decorrelation is the suppression of spectral activity that apparently arises from correlated motoneuron firings due to common excitatory drive. Without recurrent inhibition, the power spectrum of the total motoneuron pool firings showed a peak at a frequency corresponding to the largest measured firing rates of motoneurons in the pool. Recurrent inhibition either reduced or abolished this peak, presumably by minimizing the likelihood of correlated firing among pool elements. Renshaw cells may act to diminish physiological tremor, by removing oscillatory components from aggregate motoneuron activity. Recurrent inhibition also improved coherence between the aggregate motoneuron output and the common drive, at frequencies above the frequency of the "synchronous" peak. Sensitivity analyses demonstrated that the spectral effect became stronger as the duration of inhibitory synaptic conductance was shortened with either the magnitude or the spatial extent of the inhibitory conductances increased to maintain constant net inhibition. Overall, Renshaw inhibition appears to be a powerful way to adjust the dynamic behavior of a neuron population with minimal impact on its static gain.

Functional characterization of caudal hypoglossal neurons by spectral patterns of neuronal discharges in the rat

This study evaluated the spectral characteristics of neuronal discharges in the caudal hypoglossal nucleus and their physiological relevance in adult, male Sprague Dawley rats which were anaesthetized and maintained with pentobarbital sodium. Based on auto-spectral analysis of extracellular single-neuron activity, three spectral patterns were identified in the spontaneous discharges of hypoglossal neurons. Neurons that exhibited a rhythmic pattern manifested a concentrated peak in the auto-spectrogram that corresponded to the mean discharge rate. A majority of hypoglossal neurons displayed the modulated pattern, which was manifested either as scattered power densities (wide-band modulated pattern) or with a peak frequency component that was different from the mean discharge rate (narrow-band modulated pattern). Neurons that exhibited a mixed pattern displayed both rhythmic and modulated spectral patterns. Cross-spectral analysis further revealed that respiratory modulation constituted a major physiological influence on caudal hypoglossal neurons. The respiratory modulated pattern, however, could be converted to a mixed pattern in the presence of a central dipsogen, angiotensin III. The results suggest that the spectral patterns of neuronal discharges in caudal hypoglossal neurons represent manifestations of multiple physiological information, including that regarding respiration and dipsogenesis, which is encoded in these neurons. It was also shown that this information may only be revealed by auto-spectral and cross-spectral analysis of neuronal discharge signals.

On the role of recurrent inhibitory feedback in motor control

This article reviews presumed roles of recurrent inhibition in motor control, that have been proposed over the past five decades. The discussion is structured in an order of increasing complexity. It starts out with the simplest and earliest circuit, that is recurrent self-inhibition of skeleto-motoneurons, and related functions. It soon becomes clear that in order to understand recurrent inhibition, we must look beyond the simple self-inhibitory CNS circuit. First, recurrent inhibition must be seen in the context of other neural circuits. Second, some quantitative features appear to be correlated with features of the neuromusculo-skeletal periphery. Third, the aspect of lateral inhibition between different members of a motoneuron pool as well as between different motoneuron pools points to the essential multiple input-multiple output structure of recurrent inhibition that again can be understood only by correlating it with features of the neuromusculo-skeletal periphery. Another extension results from the discovery that recurrent inhibition affects not only skeleto-motoneurons, but also gamma-motoneurons, Ia inhibitory interneurons mediating reciprocal inhibition between antagonist motoneurons, other Renshaw cells and cells of origin of the ventral spinocerebellar tract (VSCT). Then the view broadens again, investigating the potential role that recurrent inhibition plays in two far-ranging theories of motor control, the inverse-dynamics approach and the equilibrium-point hypothesis. Finally, the present author tries to formulate, in broad strokes, a personal functional interpretation of recurrent inhibition. All the functional considerations, right or wrong, should yield ideas for new experiments, and this then is the last objective of this review.

Signal transmission from motor axons to group Ia muscle spindle afferents: frequency responses and second-order non-linearities

Spinal recurrent inhibition via Renshaw cells and proprioceptive feedback via skeletal muscle and muscle spindle afferents have been hypothesized to constitute a compound feedback system [Windhorst (1989) Afferent Control of Posture and Locomotion; Windhorst (1993) Robots and Biological Systems--Towards a New Bionics]. To assess their detailed functions, it is necessary to know their dynamic characteristics. Previously we have extensively described the properties of signal transmission from motor axons to Renshaw cells using random motor axon stimulation and data analysis methods based thereupon. Using the same methods, we here compare these properties, in the cat, with those between motor axons and group Ia muscle spindle afferents in terms of frequency responses and nonlinear features. The frequency responses depend on the mean rate (carrier rate) of activation of motor axons and on the strength of coupling between motor units and spindles. In general, they are those of a second-order low-pass system with a cut-off at fairly low frequencies. This contrasts with the dynamics of motor axon-Renshaw cell couplings which are those of a much broader band-pass with its peak in the range of c. 2-15 Hz [Christakos (1987) Neuroscience 23, 613-623]. The second-order non-linearities in motor unit-muscle spindle signal lines are much more diverse than those in motor axon-Renshaw cell couplings. Although the average strength of response declines with mean stimulus rate in both subsystems, there is no systematic relationship between the amount of non-linearity and the average response in the former, whilst there is in the latter. The qualitative appearance of motor unit-muscle spindle non-linearities was complicated as was the average response to motor unit twitches. Thus, whilst Renshaw cells appear to dynamically reflect motor output rather faithfully, muscle spindles seem to signal local muscle fibre length changes and their dynamics. This would be consistent with the hypothesis that the two feedback pathways monitor different state variables determining the production of muscle force: neural input and length and its changes. Specifically, the dynamic properties of both subsystems may combine favourably to decrease the risk of instability (tremor) in the motoneuron-muscle spindle loop.

Dynamic behaviour of alpha-motoneurons subjected to recurrent inhibition and reflex feedback via muscle spindles

The dynamic transfer characteristics of mammalian spinal skeleto-motoneurons are determined by intrinsic properties and various sorts of feedback. Here, recurrent inhibition via Renshaw cells and reflex feedback via muscle units and muscle spindle (in particular Ia) afferents, in the cat, are considered. The dynamic properties of the motor axon-Renshaw cell and the motor unit-spindle afferent subsystems were experimentally determined by stimulating motor axons with pseudo-random patterns of electrical pulses at two mean rates (low: 9.5-13 pulses/s; high: 20-23 pulses/s) and recording discharges of the two output elements. Spectral analysis yielded frequency responses to which transfer functions were fitted. These transfer functions in conjunction with those previously derived for alpha-motoneurons were used to study the stability and input-output characteristics of motoneurons with regard to two issues: stability and input-output relations of the combined (recurrent plus reflex) system as compared with each subsystem alone, with (i) each feedback path consisting of a single loop at some moderate level of force production, and (ii) each pathway consisting of two loops related to two motoneuron subpopulations active at a higher level of recruitment. It is shown that Renshaw cells have frequency characteristics well suited to contribute to the stabilization of the reflex loop. They can do so at low gains of recurrent inhibition.

Frequency characteristics and nonlinear features of responses of cat dorsal horn neurons to random stimulation of cutaneous afferents

The system between cutaneous (suralis) afferents and dorsal horn neurons was studied for comparison with studies previously performed on the motor axon-Renshaw cell system, using the same methods. In anaesthetized or decerebrated cats, 27 dorsal horn neurons of segments L5 to S1 were recorded extracellularly in depths of 1-2.3 mm from cord dorsum. Cutaneous afferents in branches of the ipsilateral suralis nerve were stimulated with sequences of randomly occurring electrical pulses at two levels of mean rate. The responses of the dorsal horn neurons to the stimuli were evaluated in the frequency and time domain. Calculation of coherence, gain and phase functions (via spectral analysis) showed that the frequency response depended on the precise pattern on cell discharge and could vary from broad-band to low-pass or occasionally band-pass characteristics. There were minor differences in these characteristics with those of Renshaw cells. A special type of nonlinear analysis, using conditional peristimulus-time histograms, showed that the responses to test stimuli were facilitated, depressed or both by conditioning stimuli occurring some tens to a few hundred milliseconds before. Early and late response components could be conditioned individually and differently. Exponential fits to such conditioning curves yielded two time constants for depression (means of 21 and 94 ms) and one for facilitation (14 ms). Similar conditioning effects and time constants were previously found for the motor axon-Renshaw cell system although a few differences were apparent. By analogy, it is suggested that part of the long-lasting conditioning effects (with long time constants) are probably due to presynaptic mechanisms.(ABSTRACT TRUNCATED AT 250 WORDS)

A method to estimate the effects of parallel inputs on neuronal discharge probability

We here present a method to study the interaction of parallel neural input channels regarding their effects on a neurone. In particular, the method allows to disclose the effects of oligosynaptic pathways that may exist in parallel to direct monosynaptic connections to the cell. Two (or more) inputs (nerves) are stimulated with random patterns of stimuli. The response of the cell to these patterns is evaluated by the computation of peristimulus-time histograms (PSTHs). One of the two stimulus trains is selected as the one to yield reference events for the PSTH computation. From this stimulus train are selected those stimuli as reference events which are preceded, at defined mean intervals, by stimuli in the same or a parallel channel. These "conditioning" stimuli are determined (1) separately from each single stimulus train and (2) concomitantly from the two trains as events occurring simultaneously in both. The effects exerted by these various conditioning events on the effects of the "test" pulses on the cell response yield insights into the interactions between the two (or more) inputs. These methods are demonstrated on spinal Renshaw cells activated by independent random stimulation of two muscle nerves and on dorsal horn neurones responding to cutaneous nerve stimulation.

The relationship between coherence and nonlinear characteristics in Renshaw cell responses to random motor axon stimulation

Cat spinal Renshaw cells were activated by stimulating muscle nerves or ventral roots with random (pseudo-Poisson) patterns of brief electrical stimuli. This input pattern is optimal for a comparative study in both the frequency- and time-domain. The frequency-dependent variable of particular interest in this study was the coherence as a measure of the degree to which signal transmission is linear and noise-free; it was estimated via spectral analysis. Time-domain analysis consisted of calculating peri-stimulus time histograms in order to estimate the amount of nonlinearity in the cell responses to pairs of stimuli. The main result was that the amount of nonlinearity measured in this way did not profoundly depress the coherence. Two types of peri-stimulus time histogram were calculated: the "conventional" peri-stimulus time histogram (as a reference) computed with respect to all the stimuli in a train, and the "conditional" peri-stimulus time histogram computed with respect to the second in pairs of stimuli which were separated from each other by varied intervals delta. The latter type of peri-stimulus time histogram showed that Renshaw cell responses to stimuli were conditioned by preceding stimuli, which could facilitate (at small delta s) and/or more often depress (up to several hundreds of milliseconds) the subsequent responses in a nonlinear manner. The objective of this study was to test the hypothesis that nonlinear characteristics contribute significantly to depress the coherence from its optimal value (1).(ABSTRACT TRUNCATED AT 250 WORDS)

Early and late components in cat Renshaw cell responses to random stimulation of motor axons: their differential sensitivity to preceding activation

Lumbosacral Renshaw cells were activated by random stimulation of motor axons in muscle nerves or ventral roots. The stimulus patterns had mean rates of 9.5-13 or 20-23 pulses per second. The Renshaw cell responses were evaluated by two kinds of peristimulus-time histograms. "Conventional" peristimulus-time histograms were calculated by averaging the cell discharge with respect to all the stimuli in a train. "Conditional" peristimulus-time histograms were determined by averaging the cell discharge with respect to the second ("test") stimulus in pairs of stimuli which were separated by varied intervals. The effects of the conditioning stimuli were evaluated after correcting for the effect of linear superposition of the conditioning and test stimuli. The conventional peristimulus-time histograms showed an excitatory response which often consisted of two distinct components: a narrow and high "early" peak and a broad and low "late" elevation of firing probability. The early and late excitatory components were conditioned in different ways. Whereas the late component was virtually always depressed, the early component showed three patterns: (1) uniform depression; (2) uniform facilitation; (3) a mixture of depression and facilitation. Frequency responses (coherence and gain estimates) were also calculated separately for the cell discharges underlying either the early or the late components. The estimates for the "late spikes" showed a stronger decline with increasing frequency than those for the "early spikes". The origin of the different conditioning effects probably lies in a combination of pre and postsynaptic factors. They may play a role in tremor mechanisms.

Relations between time-and frequency-domain measures of signal transmission from cutaneous afferents to dorsal horn neurons

In pentobarbitone-anesthetized cats, the spike sequences of dorsal horn neurons were recorded in response to random stimulation of branches of the suralis nerve. Combined frequency- and time-domain analysis was performed on the stimulus and spike trains. Coherence function estimates computed by spectral analysis were compared with peristimulus time histograms (PSTHs). The cell responses were divided into 4 main types: PSTHs with a single high and narrow peak were associated with broad-range high coherence; PSTHs with two (or sometimes 3) distinct peaks concurred with a coherence which was high a low frequencies, low at intermediate ones and higher again at high frequencies; broad unstructured PSTH peaks of varying height concurred with coherence declining from high values at low frequencies to lower values at higher ones; and small and broad PSTH peaks were associated with generally low coherence. Thus, the variation of coherence with frequency depends on the precise pattern of cell discharge.