A variable-threshold motoneuron model that incorporates time- and voltage-dependent potassium and calcium conductances

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.

The Influence of Force Level and Motor Unit Coherence on Nonlinear Surface EMG Features Examined Using Model Simulation

Nonlinear features extracted from surface EMG signals have been previously used to infer information on coherent or synchronous activity in the underlying motor unit discharges. However, it has not yet been assessed how these features are affected by the density of the surface EMG signal, and whether changes in the level of muscle activation can influence the effective detection of correlated motor unit firing. To examine this, a motoneuron pool model receiving a beta-band modulated cortical input was used to generate correlated motor unit firing trains. These firing trains were convolved with motor unit action potentials generated from an anatomically accurate electrophysiological model of the first dorsal interosseous muscle. The sample entropy (SampEn) and percentage determinism (%DET) of recurrence quantification analysis were calculated from the composite surface EMG signals, for signals comprised of both correlated and uncorrelated motor unit firing trains. The results show that although both SampEn and %DET are influenced by motor unit coherence, they are differentially affected by muscle activation and motor unit distribution. The results also suggest that sample entropy may provide a more accurate assessment of the underlying motor unit coherence than percentage determinism, as it is less sensitive to factors unrelated to motor unit synchrony.

Synaptic control of the shape of the motoneuron pool input-output function

Although motoneurons have often been considered to be fairly linear transducers of synaptic input, recent evidence suggests that strong persistent inward currents (PICs) in motoneurons allow neuromodulatory and inhibitory synaptic inputs to induce large nonlinearities in the relation between the level of excitatory input and motor output. To try to estimate the possible extent of this nonlinearity, we developed a pool of model motoneurons designed to replicate the characteristics of motoneuron input-output properties measured in medial gastrocnemius motoneurons in the decerebrate cat with voltage-clamp and current-clamp techniques. We drove the model pool with a range of synaptic inputs consisting of various mixtures of excitation, inhibition, and neuromodulation. We then looked at the relation between excitatory drive and total pool output. Our results revealed that the PICs not only enhance gain but also induce a strong nonlinearity in the relation between the average firing rate of the motoneuron pool and the level of excitatory input. The relation between the total simulated force output and input was somewhat more linear because of higher force outputs in later-recruited units. We also found that the nonlinearity can be increased by increasing neuromodulatory input and/or balanced inhibitory input and minimized by a reciprocal, push-pull pattern of inhibition. We consider the possibility that a flexible input-output function may allow motor output to be tuned to match the widely varying demands of the normal motor repertoire.NEW & NOTEWORTHY Motoneuron activity is generally considered to reflect the level of excitatory drive. However, the activation of voltage-dependent intrinsic conductances can distort the relation between excitatory drive and the total output of a pool of motoneurons. Using a pool of realistic motoneuron models, we show that pool output can be a highly nonlinear function of synaptic input but linearity can be achieved through adjusting the time course of excitatory and inhibitory synaptic inputs.

Muscle fatigue increases beta-band coherence between the firing times of simultaneously active motor units in the first dorsal interosseous muscle

Synchronization between the firing times of simultaneously active motor units (MUs) is generally assumed to increase during fatiguing contractions. To date, however, estimates of MU synchronization have relied on indirect measures, derived from surface electromyographic (EMG) interference signals. This study used intramuscular coherence to investigate the correlation between MU discharges in the first dorsal interosseous muscle during and immediately following a submaximal fatiguing contraction, and after rest. Coherence between composite MU spike trains, derived from decomposed surface EMG, were examined in the delta (1-4 Hz), alpha (8-12 Hz), beta (15-30 Hz), and gamma (30-60 Hz) frequency band ranges. A significant increase in MU coherence was observed in the delta, alpha, and beta frequency bands postfatigue. In addition, wavelet coherence revealed a tendency for delta-, alpha-, and beta-band coherence to increase during the fatiguing contraction, with subjects exhibiting low initial coherence values displaying the greatest relative increase. This was accompanied by an increase in MU short-term synchronization and a decline in mean firing rate of the majority of MUs detected during the sustained contraction. A model of the motoneuron pool and surface EMG was used to investigate factors influencing the coherence estimate. Simulation results indicated that changes in motoneuron inhibition and firing rates alone could not directly account for increased beta-band coherence postfatigue. The observed increase is, therefore, more likely to arise from an increase in the strength of correlated inputs to MUs as the muscle fatigues.

Context-dependent coding in single neurons

The linear-nonlinear cascade model (LN model) has proven very useful in representing a neural system's encoding properties, but has proven less successful in reproducing the firing patterns of individual neurons whose behavior is strongly dependent on prior firing history. While the cell's behavior can still usefully be considered as feature detection acting on a fluctuating input, some of the coding capacity of the cell is taken up by the increased firing rate due to a constant "driving" direct current (DC) stimulus. Furthermore, both the DC input and the post-spike refractory period generate regular firing, reducing the spike-timing entropy available for encoding time-varying fluctuations. In this paper, we address these issues, focusing on the example of motoneurons in which an afterhyperpolarization (AHP) current plays a dominant role regularizing firing behavior. We explore the accuracy and generalizability of several alternative models for single neurons under changes in DC and variance of the stimulus input. We use a motoneuron simulation to compare coding models in neurons with and without the AHP current. Finally, we quantify the tradeoff between instantaneously encoding information about fluctuations and about the DC.

Motor unit

Movement is accomplished by the controlled activation of motor unit populations. Our understanding of motor unit physiology has been derived from experimental work on the properties of single motor units and from computational studies that have integrated the experimental observations into the function of motor unit populations. The article provides brief descriptions of motor unit anatomy and muscle unit properties, with more substantial reviews of motoneuron properties, motor unit recruitment and rate modulation when humans perform voluntary contractions, and the function of an entire motor unit pool. The article emphasizes the advances in knowledge on the cellular and molecular mechanisms underlying the neuromodulation of motoneuron activity and attempts to explain the discharge characteristics of human motor units in terms of these principles. A major finding from this work has been the critical role of descending pathways from the brainstem in modulating the properties and activity of spinal motoneurons. Progress has been substantial, but significant gaps in knowledge remain.

Modulation of inhibitory strength and kinetics facilitates regulation of persistent inward currents and motoneuron excitability following spinal cord injury

Spasticity is commonly observed after chronic spinal cord injury (SCI) and many other central nervous system disorders (e.g., multiple sclerosis, stroke). SCI-induced spasticity has been associated with motoneuron hyperexcitability partly due to enhanced activation of intrinsic persistent inward currents (PICs). Disrupted spinal inhibitory mechanisms also have been implicated. Altered inhibition can result from complex changes in the strength, kinetics, and reversal potential (E(Cl(-))) of γ-aminobutyric acid A (GABA(A)) and glycine receptor currents. Development of optimal therapeutic strategies requires an understanding of the impact of these interacting factors on motoneuron excitability. We employed computational methods to study the effects of conductance, kinetics, and E(Cl(-)) of a dendritic inhibition on PIC activation and motoneuron discharge. A two-compartment motoneuron with enhanced PICs characteristic of SCI and receiving recurrent inhibition from Renshaw cells was utilized in these simulations. This dendritic inhibition regulated PIC onset and offset and exerted its strongest effects at motoneuron recruitment and in the secondary range of the current-frequency relationship during PIC activation. Increasing inhibitory conductance compensated for moderate depolarizing shifts in E(Cl(-)) by limiting PIC activation and self-sustained firing. Furthermore, GABA(A) currents exerted greater control on PIC activation than glycinergic currents, an effect attributable to their slower kinetics. These results suggest that modulation of the strength and kinetics of GABA(A) currents could provide treatment strategies for uncontrollable spasms.

Effects of persistent inward currents, accommodation, and adaptation on motor unit behavior: a simulation study

Motor neurons are often assumed to generate spikes in proportion to the excitatory synaptic input received. There are, however, many intrinsic properties of motor neurons that might affect this relationship, such as persistent inward currents (PICs), spike-threshold accommodation, or spike-frequency adaptation. These nonlinear properties have been investigated in reduced animal preparation but have not been well studied during natural motor behaviors because of the difficulty in characterizing synaptic input in intact animals. Therefore, we studied the influence of each of these intrinsic properties on spiking responses and muscle force using a population model of motor units that simulates voluntary contractions in human subjects. In particular, we focused on the difference in firing rate of low-threshold motor units when higher threshold motor units were recruited and subsequently derecruited, referred to as ΔF. Others have used ΔF to evaluate the extent of PIC activation during voluntary behavior. Our results showed that positive ΔF values could arise when any one of these nonlinear properties was included in the simulations. Therefore, a positive ΔF should not be considered as exclusive evidence for PIC activation. Furthermore, by systematically varying contraction duration and speed in our simulations, we identified a means that might be used experimentally to distinguish among PICs, accommodation, and adaptation as contributors to ΔF.

Estimates of EPSP amplitude based on changes in motoneuron discharge rate and probability

When motor units are discharging tonically, transient excitatory synaptic inputs produce an increase in the probability of spike occurrence and also increase the instantaneous discharge rate. Several researchers have proposed that these induced changes in discharge rate and probability can be used to estimate the amplitude of the underlying excitatory post-synaptic potential (EPSP). We tested two different methods of estimating EPSP amplitude by comparing the amplitude of simulated EPSPs with their effects on the discharge of rat hypoglossal motoneurons recorded in an in vitro brainstem slice preparation. The first estimation method (simplified-trajectory method) is based on the assumptions that the membrane potential trajectory between spikes can be approximated by a 10 mV post-spike hyperpolarization followed by a linear rise to the next spike and that EPSPs sum linearly with this trajectory. We hypothesized that this estimation method would not be accurate due to interspike variations in membrane conductance and firing threshold that are not included in the model and that an alternative method based on estimating the effective distance to threshold would provide more accurate estimates of EPSP amplitude. This second method (distance-to-threshold method) uses interspike interval statistics to estimate the effective distance to threshold throughout the interspike interval and incorporates this distance-to-threshold trajectory into a threshold-crossing model. We found that the first method systematically overestimated the amplitude of small (<5 mV) EPSPs and underestimated the amplitude of large (>5 mV EPSPs). For large EPSPs, the degree of underestimation increased with increasing background discharge rate. Estimates based on the second method were more accurate for small EPSPs than those based on the first model, but estimation errors were still large for large EPSPs. These errors were likely due to two factors: (1) the distance to threshold can only be directly estimated over a limited portion of the interspike interval and (2) the distance to threshold can be affected by the EPSP itself. Both methods provide the most accurate EPSP estimates for EPSP amplitudes less than 5 mV and moderate background discharge rates (~15 imp/s).

Compartmental models of mammalian motoneurons of types S, FR and FF and their computer simulation

Mathematical models of motoneurons (MNs) of types S, FR and FF were developed based on cat MN data. Each of the three models has an initial segment, a soma and a dendritic tree. The initial segment and the soma include models of several types of ionic currents, including a calcium-dependent slow potassium current. The dendritic tree is modeled as a series association of several electrically passive cylinders. Afterhyperpolarization parameters, current to frequency relation and the responses to input current steps, ramps and sinusoids were used for model validation. The effects of sinusoidally varying synaptic inputs at different levels of the dendritic tree were studied by computer simulation. The corresponding frequency response functions resulted of lowpass type with cutoff frequencies from 10 to 40 Hz, for synapses occurring more distally or more proximally, respectively. The nonlinear effects caused by two sinusoidally varying synaptic conductances (at 7 and 11 Hz), acting at different dendritic segments, were quantified by spectral analysis of the current reaching the soma. The simulations pointed to two main nonlinear effects: (i) harmonics of the two input frequencies (e.g., 14 Hz) and (ii) intermodulation terms (e.g., 4 Hz). When the two synaptic inputs occurred on more distal dendritic compartments the nonlinear effects were more pronounced.

Direct control of firing rate gain by dendritic shunting inhibition

The firing rate gain of neurons, defined as the slope of the relation between input to a neuron and its firing rate, has received considerable attention in the past few years. This has been largely motivated by the many experimental demonstrations of behavior related gain changes in a variety of neural circuits of the CNS. A surprising result was that a prime candidate, shunting inhibition, apparently does not change the firing rate gain of neurons. However, in this paper, we show a physiologically plausible mechanism by which shunting inhibition in the dendritic tree does, in a simple and direct manner, modulate the firing gain of neurons. The effect is due to a strong attenuation of the dendritic current arriving at the soma by shunting dendritic inhibition. Increasing the dendritic inhibitory conductance enhances the attenuation of current flowing from the dendritic to the somatic compartment and thus reduces firing gain. This mechanism relies on known physiological and anatomical properties of CNS neurons and does not require special features such as tunable neural noise inputs. Gain control by the proposed mechanism may prove to be a ubiquitous feature of neural circuit operations and it is readily verifiable experimentally.

The afterhyperpolarization conductance exerts the same control over the gain and variability of motoneurone firing in anaesthetized cats

Does the afterhyperpolarization current control the gain and discharge variability of motoneurones according to the same law? We investigated this issue in lumbar motoneurones of anaesthetized cats. Using dynamic clamp, we measured the conductance, time constant and driving force of the AHP current in a sample of motoneurones and studied how the gain was correlated to these quantities. To study the action of the AHP on the discharge variability and to compare it to its action on the gain, we injected an artificial AHP-like current in motoneurones. This increased the natural AHP. In three motoneurones, we abolished most of the natural AHP with the calcium chelator BAPTA to investigate the condition where the discharge was essentially controlled by the artificial AHP. Our results demonstrate that both the gain and the coefficient of variation of the firing rate are inversely proportional to the magnitude and to the time constant of the artificial AHP conductance. This indicates that the AHP exerts the same control over the gain and the variability. This mechanism ensures that the variability of the discharge is modulated with the gain. This guarantees a great regularity of the discharge when the motoneurone is in a low excitability state and hence good control of the force produced.

A simulation study to examine the effect of common motoneuron inputs on correlated patterns of motor unit discharge

The influence of common oscillatory inputs to the motoneuron pool on correlated patterns of motor unit discharge was examined using model simulations. Motor unit synchronization, in-phase fluctuations in mean firing rates known as 'common drive', and the coefficient of variation of the muscle force were examined as the frequency and amplitude of common oscillatory inputs to the motoneuron pool were varied. The amount of synchronization, the peak correlation between mean firing rates and the coefficient of variation of the force varied with both the frequency and amplitude of the common input signal. Values for 'common drive' and the force coefficient of variation were highest for oscillatory inputs at frequencies less than 5 Hz, while synchronization reached a maximum when the frequency of the common input was close to the average motor unit firing rate. The frequency of the common input signal for which the highest levels of synchronization were observed increased as motoneuron firing rates increased in response to higher target force levels. The simulation results suggest that common low-frequency oscillations in motor unit firing rates and short-term synchronization result from oscillatory activity in different bands of the frequency spectrum of shared motoneuron inputs. The results also indicate that the amount of synchronization between motor unit discharges depends not only on the amplitude of the shared input signal, but also on its frequency in relation to the present firing rates of the individual motor units.

How Membrane Properties Shape the Discharge of Motoneurons: A Detailed Analytical Study

Electrophysiological experiments and modeling studies have shown that after hyperpolarization regulates the discharge of lumbar motoneurons in anesthetized cats and is an important determinant of their firing properties. However, it is still unclear how firing properties depend on slow after hyperpolarization, input conductance, and the fast currents responsible for spike generation. We study a single-compartment integrate-andfire model with a slow potassium conductance that exponentially decays between spikes. We show that this model is analytically solvable, and we investigate how passive and active membrane properties control the discharge. We show that the model exhibits three distinct firing ranges (primary, secondary, and high frequency), and we explain the origin of these three ranges. Explicit expressions are established for the gain of the steady-state current-frequency (I− f) curve in the primary range and for the gain of the I− f curve for the first interspike interval. They show how the gain is controlled by the maximal conductance and the kinetic parameters of the after hyperpolarization conductance. The gain also depends on the spike voltage threshold, and we compute how it is decreased by threshold accommodation (i.e., the increase of the threshold with the injected current). In contrast, the gain is not very sensitive to the input conductance. This implies that tonic synaptic activity shifts the current-frequency curve in its primary range, in agreement with experiments. Taking into account the absolute refractory period associated with spikes somewhat reduces the gain in the primary range. More importantly, it accounts for the approximately linear and steep secondary range observed in many motoneurons. In the nonphysiological high-frequency range, the behavior of the I− f curve is determined by the fast voltage-dependent currents, via the amplitude of the fast repolarization afterspike, the duration of the refractory period, and voltage threshold accommodation, if present.

Ionic current model of a hypoglossal motoneuron

We have developed a single-compartment, electrophysiological, hypoglossal motoneuron (HM) model based primarily on experimental data from neonatal rat HMs. The model is able to reproduce the fine features of the HM action potential: the fast afterhyperpolarization, the afterdepolarization, and the medium-duration afterhyperpolarization (mAHP). The model also reproduces the repetitive firing properties seen in neonatal HMs and replicates the neuron's response to pharmacological experiments. The model was used to study the role of specific ionic currents in HM firing and how variations in the densities of these currents may account for age-dependent changes in excitability seen in HMs. By varying the density of a fast inactivating calcium current, the model alternates between accelerating and adapting firing patterns. Modeling the age-dependent increase in H current density accounts for the decrease in mAHP duration observed experimentally, but does not fully account for the decrease in input resistance. An increase in the density of the voltage-dependent potassium currents and the H current is required to account for the decrease in input resistance. These changes also account for the age-dependent decrease in action potential duration.

Afterhyperpolarization-firing rate relation of turtle spinal neurons

This study addressed the afterhyperploarization-firing rate relationship of unanesthetized turtle spinal motoneurons and interneurons. The afterhyperploarization of their solitary action potential at rheobase was compared to that during the cells' minimum and maximum firing rates. Like previous mammalian findings, afterhyperpolarization duration and area at rheobase were 32 and 19% less for high- versus low-threshold motoneurons. Contrariwise, maximum firing rate was two times less for the high-threshold group. Other new findings were that for high- versus low-threshold interneurons, afterhyperpolarization duration and area were 25 and 95% less, and maximum firing rate 21% higher for the high-threshold group. For combined motoneurons versus interneurons, there were no differences in afterhyperpolarization duration and area at rheobase, whereas maximum firing rate was 265% higher for the interneurons. For high-threshold motoneurons alone, there were significant associations between minimum firing rate and afterhyperpolarization duration and area measured at rheobase. In summary, this study showed that (1) the afterhyperploarization values of both turtle spinal motoneurons and interneurons at rheobase provided little indication of their corresponding values at the cells' minimum and maximum firing states, and (2) the evolution of afterhyperploarization from rheobase to maximum firing state differed both qualitatively and quantitatively for motoneurons versus interneurons.

Quantification of the factors that influence discharge correlation in model motor neurons

The purpose of this study was to quantify the influence of intrinsic properties, active dendritic conductances, and background excitation and inhibition on measures of discharge correlation in the time and frequency domains with known levels and patterns of common synaptic input. The study involved a computer simulation of a population of neurons with a range of input resistances (0.54-3.7 MOmega) and surface areas (407,000-712,000 microm(2)). The neurons were simulated with no, moderate, or high levels of active dendritic conductances and were activated with either excitatory input only or excitatory and inhibitory inputs. The patterns of common input, either branched common input or common modulation, were tested with 0, 30, 60, and 90% common input. The results confirm previous findings of an exponential relation between the level of common input and indexes of synchronization; only when the common input comprised >/=60% of the total excitatory input was there a significant effect on discharge correlation. Synchronization was greatest in models that had passive dendrites. Active dendritic conductances caused the discharge rate of the neuron to saturate and decreased motor-unit synchronization. However, the addition of 10% background inhibitory input increased synchronization in these models. In contrast, common rhythmic modulation of inputs at 24 Hz usually decreased synchronization. Significant coherence at the modulated frequency occurred in the commonly modulated neurons when >/=60% of the inputs were modulated. Furthermore, active dendritic conductances decreased coherence. Branched common input caused high levels of coherence across a broad spectrum and when combined with active dendritic conductances caused significant frequency peaks in the 30- to 50-Hz band. In conclusion, the level of inhibitory input and active dendritic conductances interact with the amount of common input to determine time- and frequency-domain discharge correlation.

Input-output functions of mammalian motoneurons

Our intent in this review was to consider the relationship between the biophysical properties of motoneurons and the mechanisms by which they transduce the synaptic inputs they receive into changes in their firing rates. Our emphasis has been on experimental results obtained over the past twenty years, which have shown that motoneurons are just as complex and interesting as other central neurons. This work has shown that motoneurons are endowed with a rich complement of active dendritic conductances, and flexible control of both somatic and dendritic channels by endogenous neuromodulators. Although this new information requires some revision of the simple view of motoneuron input-output properties that was prevalent in the early 1980's (see sections 2.3 and 2.10), the basic aspects of synaptic transduction by motoneurons can still be captured by a relatively simple input-output model (see section 2.3, equations 1-3). It remains valid to describe motoneuron recruitment as a product of the total synaptic current delivered to the soma, the effective input resistance of the motoneuron and the somatic voltage threshold for spike initiation (equations 1 and 2). However, because of the presence of active channels activated in the subthreshold range, both the delivery of synaptic current and the effective input resistance depend upon membrane potential. In addition, activation of metabotropic receptors by achetylcholine, glutamate, noradrenaline, serotonin, substance P and thyrotropin releasing factor (TRH) can alter the properties of various voltage- and calcium-sensitive channels and thereby affect synaptic current delivery and input resistance. Once motoneurons are activated, their steady-state rate of repetitive discharge is linearly related to the amount of injected or synaptic current reaching the soma (equation 3). However, the slope of this relation, the minimum discharge rate and the threshold current for repetitive discharge are all subject to neuromodulatory control. There are still a number of unresolved issues concerning the control of motoneuron discharge by synaptic inputs. Under dynamic conditions, when synaptic input is rapidly changing, time- and activity-dependent changes in the state of ionic channels will alter both synaptic current delivery to the spike-generating conductances and the relation between synaptic current and discharge rate. There is at present no general quantitative expression for motoneuron input-output properties under dynamic conditions. Even under steady-state conditions, the biophysical mechanisms underlying the transfer of synaptic current from the dendrites to the soma are not well understood, due to the paucity of direct recordings from motoneuron dendrites. It seems likely that resolving these important issues will keep motoneuron afficiandoes well occupied during the next twenty years.

Relationship between the time course of the afterhyperpolarization and discharge variability in cat spinal motoneurones

1. We elicited repetitive discharges in cat spinal motoneurones by injecting noisy current waveforms through a microelectrode to study the relationship between the time course of the motoneurone's afterhyperpolarization (AHP) and the variability in its spike discharge. Interspike interval histograms were used to estimate the interval death rate, which is a measure of the instantaneous probability of spike occurrence as a function of the time since the preceding spike. It had been previously proposed that the death rate can be used to estimate the AHP trajectory. We tested the accuracy of this estimate by comparing the AHP trajectory predicted from discharge statistics to the measured AHP trajectory of the motoneurone. 2. The discharge statistics of noise-driven cat motoneurones shared a number of features with those previously reported for voluntarily activated human motoneurones. At low discharge rates, the interspike interval histograms were often positively skewed with an exponential tail. The standard deviation of the interspike intervals increased with the mean interval, and the plots of standard deviation versus the mean interspike interval generally showed an upward bend, the onset of which was related to the motoneurone's AHP duration. 3. The AHP trajectories predicted from the interval death rates were generally smaller in amplitude (i.e. less hyperpolarized) than the measured AHP trajectories. This discrepancy may result from the fact that spike threshold varies during the interspike interval, so that the distance to threshold at a given time depends upon both the membrane trajectory and the spike threshold trajectory. Nonetheless, since the interval death rate is likely to reflect the instantaneous distance to threshold during the interspike interval, it provides a functionally relevant measure of fluctuations in motoneurone excitability during repetitive discharge.

Synaptic control of motoneuronal excitability

Movement, the fundamental component of behavior and the principal extrinsic action of the brain, is produced when skeletal muscles contract and relax in response to patterns of action potentials generated by motoneurons. The processes that determine the firing behavior of motoneurons are therefore important in understanding the transformation of neural activity to motor behavior. Here, we review recent studies on the control of motoneuronal excitability, focusing on synaptic and cellular properties. We first present a background description of motoneurons: their development, anatomical organization, and membrane properties, both passive and active. We then describe the general anatomical organization of synaptic input to motoneurons, followed by a description of the major transmitter systems that affect motoneuronal excitability, including ligands, receptor distribution, pre- and postsynaptic actions, signal transduction, and functional role. Glutamate is the main excitatory, and GABA and glycine are the main inhibitory transmitters acting through ionotropic receptors. These amino acids signal the principal motor commands from peripheral, spinal, and supraspinal structures. Amines, such as serotonin and norepinephrine, and neuropeptides, as well as the glutamate and GABA acting at metabotropic receptors, modulate motoneuronal excitability through pre- and postsynaptic actions. Acting principally via second messenger systems, their actions converge on common effectors, e.g., leak K(+) current, cationic inward current, hyperpolarization-activated inward current, Ca(2+) channels, or presynaptic release processes. Together, these numerous inputs mediate and modify incoming motor commands, ultimately generating the coordinated firing patterns that underlie muscle contractions during motor behavior.

Dynamics of intrinsic electrophysiological properties in spinal cord neurones

The spinal cord is engaged in a wide variety of functions including generation of motor acts, coding of sensory information and autonomic control. The intrinsic electrophysiological properties of spinal neurones represent a fundamental building block of the spinal circuits executing these tasks. The intrinsic response properties of spinal neurones--determined by the particular set and distribution of voltage sensitive channels and their dynamic non-linear interactions--show a high degree of functional specialisation as reflected by the differences of intrinsic response patterns in different cell types. Specialised, cell specific electrophysiological phenotypes gradually differentiate during development and are continuously adjusted in the adult animal by metabotropic synaptic interactions and activity-dependent plasticity to meet a broad range of functional demands.

Voltage-activated K+ currents of hypoglossal motoneurons in a brain stem slice preparation from the neonatal rat

Whole cell, patch-clamp recordings were performed on motoneurons of the hypoglossus nucleus in a brain stem slice preparation from the neonatal rat brain. The aim was to investigate transient outward currents activated by membrane depolarization under voltage clamp conditions. In a Ca2+-free medium containing tetrodotoxin and Cs+, depolarizing voltage commands from a holding potential of -50 mV induced slow outward currents (Islow) with 34 +/- 6 ms (SE) onset time constant at 0 mV and minimal decline during a 1 s pulse depolarization. When the depolarizing command was preceded by a prepulse to -110 mV, the outward current became biphasic as it comprised a faster component (Ifast), which could be investigated in isolation by subtracting the two sets of records. Ifast showed rapid kinetics (9 +/- 4 ms 10-90% rise time and 70 +/- 20 ms decay time constant at 0 mV) and strong voltage-dependent inactivation (half inactivation was at -92.9 +/- 0.2 mV) from which it readily recovered with a biexponential timecourse (4.4 +/- 0.6 and 17 +/- 2 ms time constants at -110 mV membrane potential). Islow was selectively blocked by TEA (10-30 mM) while Ifast was preferentially depressed by 2-3 mM 4-aminopyridine. Analysis of tail current reversal indicated that both Islow and Ifast were predominantly due to K+ with minor permeability to Na+ (92/1 and 50/1, respectively). These results suggest that membrane depolarization activated distinct K+ conductances that, in view of their largely dissimilar kinetics, are likely to play a differential role in regulating the firing behavior of hypoglossal motoneurons.

A comparison of human motoneuron data to simulated data using cat motoneuron models

The response of repetitively firing human motoneurons to a composite excitatory input was evaluated. It was clearly shown that the response of the motoneurons to the transient input decreased with an increase in the background firing rate of the cell. The current model of repetitively firing human motoneurons could not account for this experimental result. Therefore, a compartmental modelling approach was used to simulate the repetitive firing properties of anaesthetised cat motoneurons under current clamp conditions. The modelled motoneurons were used in simulations similar to the experimental paradigms where the response to a composite excitatory input was evaluated at different background firing rates. The motoneuron models also showed a decrease in response to the excitatory input at faster background firing rates. The results suggest that human motoneurons are more comparable to motoneurons in the anaesthetised cat preparation than formerly thought. The results also demonstrate that the apparent efficacy of a synaptic input may be modulated by changes in background firing rate of the postsynaptic neuron.

Functional identification of the input-output transforms of mammalian motoneurones

We studied the responses of rat hypoglossal and cat lumbar motoneurones to a variety of excitatory and inhibitory injected current transients during repetitive discharge. The amplitudes and time courses of the transients were comparable to those of the synaptic currents underlying postsynaptic potentials (PSPs) recorded in these cells. Poisson trains of these current transients were combined with an additional independent, high frequency random waveform to approximate band-limited white noise. The composite, white noise waveform was then superimposed on long duration suprathreshold current steps. We used the responses of the motoneurones to the white noise stimulus to derive zero-, first- and second-order Wiener kernels, which provide a quantitative description of the relation between injected current and discharge probability. The convolution integral computed for an injected current waveform and the first-order Wiener kernel provides the best linear prediction of the associated peristimulus time histogram (PSTH). This linear model provided good matches to most of the PSTHs compiled between the times of occurrence of individual current transients and motoneurone discharges. However, for the largest amplitude current transients, a significant improvement in the PSTH match was often achieved by expanding the model to include the convolution of the second-order Wiener kernel with the input. The overall transformation of current inputs into firing rate could be approximated by a second-order Wiener Model, i.e., a cascade of a dynamic, linear filter followed by a static non-linearity. At a given mean firing rate, the non-linear component of the motoneurone's response could be described by the square of the linear component multiplied by a constant coefficient. The amplitude of the response of the linear component increased with the average firing rate, whereas the value of the multiplicative coefficient in the nonlinear component decreased. As a result, the overall transform could be predicted from the mean firing rate and the linear impulse response, yielding a relatively simple, general description of the motoneurone's input-output function.

Computer simulation of post-spike facilitation in spike-triggered averages of rectified EMG

When the spikes of a motor cortical cell are used to compile a spike-triggered average (STA) of rectified electromyographic (EMG) activity, a post-spike facilitation (PSF) is sometimes seen. This is generally thought to be indicative of direct corticomotoneuronal (CM) connections. However, it has been claimed that a PSF could be caused by synchronization between CM and non-CM cells. This study investigates the generation of PSF using a computer model. A population of cortical cells was simulated, some of which made CM connections to a pool of 103 motoneurons. Motoneurons were simulated using a biophysically realistic model. A subpopulation of the cortical cells was synchronized together. After a motoneuron discharge, a motor unit action potential was generated; these were summed to produce an EMG output. Realistic values were used for the corticospinal and peripheral nerve conduction velocity distribution, for slowing of impulse conduction in CM terminal axons, and for the amount of cortical synchrony. STA of the rectified EMG from all cortical neurons showed PSF; however, these were qualitatively different for CM versus non-CM cells. Using an epoch analysis to determine reliability in a quantitative manner, it was shown that the onset latency of PSF did not distinguish the two classes of cells after 10,000 spikes because of high noise in the averages. The time of the PSF peak and the peak width at half-maximum (PWHM) could separate CM from synchrony effects. However, only PWHM was robust against changes in motor unit action-potential shape and duration and against changes in the width of cortical synchrony. The amplitude of PSF from a CM cell could be doubled by the presence of synchrony. It is proposed that, if a PSF has PWHM < 7 ms, this reliably indicates that the trigger is a CM cell projecting to the muscle whose EMG is averaged. In an analysis of experimental data where macaque motor cortical cells facilitated hand and forearm muscle EMG, 74% of PSFs fulfilled this criterion. The PWHM criterion could be applied to other STA studies in which it is important to exclude the effects of synchrony.

Compartmental model of vertebrate motoneurons for Ca2+-dependent spiking and plateau potentials under pharmacological treatment

In contrast to the limited response properties observed under normal experimental conditions, spinal motoneurons generate complex firing patterns, such as Ca2+-dependent regenerative spiking and plateaus, in the presence of certain neurotransmitters and ion-channel blockers. We have developed a quantitative motoneuron model, based on turtle motoneuron data, toinvestigate the roles of specific ionic currents and the effects of their soma and dendritic distribution in generating these complex firing patterns. In addition, the model is used to explore the effects of multiple ion channel blockers and neurotransmitters that are known to modulate motoneuron firing patterns. To represent the distribution of ionic currents across the soma and dendrites, the model contains two compartments. The soma compartment, representing the soma and proximal dendrites, contains Hodgkin-Huxley-like sodium (INa) and delayed rectifier K+ (IK-dr) currents, an N-like Ca2+ current (ICa-N), and a calcium-dependent K+ current [IK(Ca)]. The dendritic compartment, representing the lumped distal dendrites, contains, in addition to ICa-N and IK(Ca) as in the soma, a persistent L-like calcium current (ICa-L). We determined kinetic parameters for INa, IK-dr, ICa-N, and IK(Ca) in order to reproduce normal action-potential firing observed in turtle spinal motoneurons, including fast and slow afterhyperpolarizations (AHPs) and a linear steady-state frequency-current relation. With this parameter set as default, a sequence of pharmacological manipulations were systematically simulated. A small reduction of IK-dr [mimicking the experimental effect of tetraethylammonium (TEA) in low concentration] enhanced the slow AHP and caused calcium spiking (mediated by ICa-N) when INa was blocked. Firing patterns observed experimentally in high TEA [and tetrodotoxin (TTX)], namely calcium spikes riding on a calcium plateau, were reproduced only when both IK-dr and IK(Ca) were reduced. Dendritic plateau potentials, mediated by ICa-L, were reliably unmasked when IK(Ca) was reduced, mimicking the experimental effect of the bee venom apamin. The effect of 5-HT, which experimentally induces the ability to generate calcium-dependent plateau potentials but not calcium spiking, was reproduced in the model by reducing IK(Ca) alone. The plateau threshold current level, however, was reduced substantially if a simultaneous increase in ICa-L was simulated, suggesting that serotonin (5-HT) induces plateau potentials by regulating more than one conductance. The onset of the plateau potential showed significant delays in response to near-threshold, depolarizing current steps. In addition, the delay times were sensitive to the current step amplitude. The delay and its sensitivity were explained by examining the model's behavior near the threshold for plateau onset. This modeling study thus accurately accounts for the basic firing behavior of vertebrate motoneurons as well as a range of complex firing patterns invoked by ion-channel blockers and 5-HT. In addition, our computational results support the hypothesis that the electroresponsiveness of motoneurons depends on a nonuniform distribution of ionic conductances, and they predict modulatory effects of 5-HT and properties of plateau activation that have yet to be tested experimentally.

Contribution of outward currents to spike-frequency adaptation in hypoglossal motoneurons of the rat

Contribution of outward currents to spike-frequency adaptation in hypoglossal motoneurons of the rat. J. Neurophysiol. 78: 2246-2253, 1997. Spike-frequency adaptation has been attributed to the actions of several different membrane currents. In this study, we assess the contributions of two of these currents: the net outward current generated by the electrogenic Na+-K+ pump and the outward current that flows through Ca2+-activated K+ channels. In recordings made from hypoglossal motoneurons in slices of rat brain stem, we found that bath application of a 4-20 microM ouabain solution produced a partial block of Na+-K+ pump activity as evidenced by a marked reduction in the postdischarge hyperpolarization that follows a period of sustained discharge. However, we observed no significant change in either the initial, early, or late phases of spike-frequency adaptation in the presence of ouabain. Adaptation also has been related to increases in the duration and magnitude of the medium-duration afterhyperpolarization (mAHP) mediated by Ca2+-activated K+ channels. When we replaced the 2 mM Ca2+ in the bathing solution with Mn2+, there was a significant decrease in the amplitude of the mAHP after a spike. The decrease in mAHP amplitude resulted in a decrease in the magnitude of the initial phase of spike-frequency adaptation as has been reported previously by others. However, quite unexpectedly we also found that reducing the mAHP resulted in a dramatic increase in the magnitude of both the early and late phases of adaptation. These changes could be reversed by restoring the normal Ca2+ concentration in the bath. Our results with ouabain indicate that the Na+-K+ pump plays little, if any, role in the three phases of adaptation in rat hypoglossal motoneurons. Our results with Ca2+ channel blockade support the hypothesis that initial adaptation is, in part, controlled by conductances underlying the mAHP. However, our failure to eliminate initial adaptation completely by blocking Ca2+ channels suggests that other membrane mechanisms also contribute. Finally, the increase in both the early and late phases of adaptation in the presence of Mn2+ block of Ca2+ channels lends further support to the hypothesis that the initial and later (i.e., early and late) phases of spike-frequency adaptation are mediated by different cellular mechanisms.

Functional identification of the input-output transforms of motoneurones in the rat and cat

1. We studied the responses of rat hypoglossal and cat lumbar motoneurones to a variety of excitatory and inhibitory injected current transients during repetitive discharge. The amplitudes and time courses of the transients were comparable to those of the synaptic currents underlying unitary and small compound postsynaptic potentials (PSPs) recorded in these cells. Poisson trains of ten of these excitatory and ten inhibitory current transients were combined with an additional independent, high-frequency random waveform to approximate band limited white noise. The white noise waveform was then superimposed on long duration (39 s) suprathreshold current steps. 2. We measured the effects of each of the current transients on motoneurone discharge by compiling peristimulus time histograms (PSTHs) between the times of occurrence of individual current transients and motoneurone discharges. We estimated the changes in membrane potential associated with each current transient by approximating the passive response of the motoneurone with a simple resistance-capacitance circuit. The relations between the features of these simulated PSPs and those of the PSTHs were similar to those reported previously for real PSPs: the short-latency PSTH peak (or trough) was generally longer than the initial phase of the PSP derivative, but shorter than the time course of the PSP itself. Linear models of the PSP to PSTH transform based on the PSP time course, the time derivative of the PSP, or a linear combination of the two parameters could not reproduce the full range of PSTH profiles observed. 3. We also used the responses of the motoneurones to the white noise stimulus to derive zero-, first- and second-order Wiener kernels, which provide a quantitative description of the relation between injected current and discharge probability. The convolution integral computed for an injected current waveform and the first-order Wiener kernel should provide the best linear prediction of the associated PSTH. This linear model provided good matches to the PSTHs associated with a wide range of current transients. However, for the largest amplitude current transients, a significant improvement in the PSTH match was often achieved by expanding the model to include the convolution of the second-order Wiener kernel with the input. 4. The overall transformation of current inputs into firing rate could be approximated by a second-order Wiener model, i.e. a cascade of a dynamic, linear filter followed by a static non-linearity. At a given mean firing rate, the non-linear component of the response of the motoneurone could be described by the square of the linear component multiplied by a constant coefficient. The amplitude of the response of the linear component increased with the average firing rate, whereas the value of the multiplicative coefficient in the non-linear component decreased. As a result, the overall transform could be predicted from the mean firing rate and the linear impulse response, yielding a relatively simple, general description of the motoneurone input-output function.

Computer simulation of the responses of human motoneurons to composite 1A EPSPS: effects of background firing rate

Two compartmental models of spinal alpha motoneurons were constructed to explore the relationship between background firing rate and response to an excitatory input. The results of these simulations were compared with previous results obtained from human motoneurons and discussed in relation to the current model for repetitively firing human motoneurons. The morphologies and cable parameters of the models were based on two type-identified cat motoneurons previously reported in the literature. Each model included five voltage-dependent channels that were modeled using Hodgkin-Huxley formalism. These included fast Na+ and K+ channels in the initial segment and fast Na+ and K+ channels as well as a slow K+ channel in the soma compartment. The density and rate factors for the slow K+ channel were varied until the models could reproduce single spike AHP parameters for type-identified motoneurons in the cat. Excitatory synaptic conductances were distributed along the equivalent dendrites with the same density described for la synapses from muscle spindles to type-identified cat motoneurons. Simultaneous activation of all synapses on the dendrite resulted in a large compound excitatory postsynaptic potential (EPSP). Brief depolarizing pulses injected into a compartment of the equivalent dendrite resulted in pulse potentials (PPs), which resembled the compound EPSPs. The effects of compound EPSPs and PPs on firing probability of the two motoneuron models were examined during rhythmic firing. Peristimulus time histograms, constructed between the stimulus and the spikes of the model motoneuron, showed excitatory peaks whose integrated time course approximated the time course of the underlying EPSP or PP as has been shown in cat motoneurons. The excitatory peaks were quantified in terms of response probability, and the relationship between background firing rate and response probability was explored. As in real human motoneurons, the models exhibited an inverse relationship between response probability and background firing rate. The biophysical properties responsible for the relationship between response probability and firing rate included the shapes of the membrane voltage trajectories between spikes and nonlinear changes in PP amplitude during the interspike interval at different firing rates. The results from these simulations suggest that the relationship between response probability and background firing rate is an intrinsic feature of motoneurons. The similarity of the results from the models, which were based on the properties of cat motoneurons, and those from human motoneurons suggests that the biophysical properties governing rhythmic firing in human motoneurons are similar to those of the cat.

A minimal, compartmental model for a dendritic origin of bistability of motoneuron firing patterns

Various nonlinear regenerative responses, including plateau potentials and bistable repetitive firing modes, have been observed in motoneurons under certain conditions. Our simulation results support the hypothesis that these responses are due to plateau-generating currents in the dendrites, consistent with a major role for a noninactivating calcium L-type current as suggested by experiments. Bistability as observed in the soma of low- and higher-frequency spiking or, under TTX, of near resting and depolarized plateau potentials, occurs because the dendrites can be in a near resting or depolarized stable steady state. We formulate and study a two-compartment minimal model of a motoneuron that segregates currents for fast spiking into a soma-like compartment and currents responsible for plateau potentials into a dendrite-like compartment. Current flows between compartments through a coupling conductance, mimicking electrotonic spread. We use bifurcation techniques to illuminate how the coupling strength affects somatic behavior. We look closely at the case of weak coupling strength to gain insight into the development of bistable patterns. Robust somatic bistability depends on the electrical separation since it occurs only for weak to moderate coupling conductance. We also illustrate that hysteresis of the two spiking states is a natural consequence of the plateau behavior in the dendrite compartment.

Responses of human motoneurons to Ia inputs: effects of background firing rate

The effects of synchronous Ia volleys on the firing probability of repetitively firing human motoneurons were examined at fast and slow firing rates. Ia afferents of either the median or the posterior tibial nerve were stimulated, while single motor unit activity was recorded from the homonymous muscles. Motoneuron responses to the Ia inputs were quantified by measurement of the magnitude of the short latency excitatory peak in peristimulus time histograms (PSTHs). When the stimuli were given at random with respect to the times of motor unit spikes, the magnitude of the PSTH peak (response probability) was significantly lower at a faster firing rate. In the "triggered" mode of stimulation, stimuli were given at various known times during the interspike interval. In this mode the response probability to the input increased monotonically as the stimuli were delivered progressively later during the interspike interval. The response probability at a fixed delay with respect to the triggering spike was higher at the faster firing rate. The results obtained with the two modes of stimulation are not in contradiction and both may be explained by the nature of membrane voltage trajectories and ionic conductances during the interspike interval described for repetitively firing cat motoneurons.

How different afferent inputs control motoneuron discharge and the output of the motoneuron pool

In theory, there are at least two distinct mechanisms by which afferent inputs could alter motoneuron discharge and shape the output of a motoneuron pool: either by delivering synaptic current to the motoneurons' somata ('classic' synaptic transduction); or by altering the motoneurons' voltage-sensitive conductances (neuromodulation). Recent work has confirmed the operation of both of these mechanisms. It has been shown that the effect of a 'classic' synaptic input on motoneuron firing rate is predicted by the product of the effective synaptic current and the slope of the motoneuron's frequency-current relation. It has also been shown that neuromodulators can alter both the slope of a motoneuron's frequency-current relation and its threshold for repetitive firing. It is argued here, however, that when two or more sources of synaptic input are activated concurrently, the distinction between these two mechanisms is blurred. Computer simulations of motoneuron and motor pool behavior have proved extremely useful in understanding these processes.