Postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents: A simulation study

Postinhibitory excitation is a transient overshoot of a neuron's baseline firing rate following an inhibitory stimulus and can be observed in vivo in human motoneurons. However, the biophysical origin of this phenomenon is still unknown and both reflex pathways and intrinsic motoneuron properties have been proposed. We hypothesized that postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents (h-currents). Using an electrical circuit model, we investigated how h-currents can modulate the postinhibitory response of motoneurons. Further, we analyzed the spike trains of human motor units from the tibialis anterior muscle during reciprocal inhibition. The simulations revealed that the activation of h-currents by an inhibitory postsynaptic potential can cause a short-term increase in a motoneuron's firing probability. This result suggests that the neuron can be excited by an inhibitory stimulus. In detail, the modulation of the firing probability depends on the time delay between the inhibitory stimulus and the previous action potential. Further, the postinhibitory excitation's strength correlates with the inhibitory stimulus's amplitude and is negatively correlated with the baseline firing rate as well as the level of input noise. Hallmarks of h-current activity, as identified from the modeling study, were found in 50% of the human motor units that showed postinhibitory excitation. This study suggests that h-currents can facilitate postinhibitory excitation and act as a modulatory system to increase motoneuron excitability after a strong inhibition.

A geometric approach to quantifying the neuromodulatory effects of persistent inward currents on individual motor unit discharge patterns

Objective.All motor commands flow through motoneurons, which entrain control of their innervated muscle fibers, forming a motor unit (MU). Owing to the high fidelity of action potentials within MUs, their discharge profiles detail the organization of ionotropic excitatory/inhibitory as well as metabotropic neuromodulatory commands to motoneurons. Neuromodulatory inputs (e.g. norepinephrine, serotonin) enhance motoneuron excitability and facilitate persistent inward currents (PICs). PICs introduce quantifiable properties in MU discharge profiles by augmenting depolarizing currents upon activation (i.e. PIC amplification) and facilitating discharge at lower levels of excitatory input than required for recruitment (i.e. PIC prolongation).Approach. Here, we introduce a novel geometric approach to estimate neuromodulatory and inhibitory contributions to MU discharge by exploiting discharge non-linearities introduced by PIC amplification during time-varying linear tasks. In specific, we quantify the deviation from linear discharge ('brace height') and the rate of change in discharge (i.e. acceleration slope, attenuation slope, angle). We further characterize these metrics on a simulated motoneuron pool with known excitatory, inhibitory, and neuromodulatory inputs and on human MUs (number of MUs; Tibialis Anterior: 1448, Medial Gastrocnemius: 2100, Soleus: 1062, First Dorsal Interosseus: 2296).Main results. In the simulated motor pool, we found brace height and attenuation slope to consistently indicate changes in neuromodulation and the pattern of inhibition (excitation-inhibition coupling), respectively, whereas the paired MU analysis (ΔF) was dependent on both neuromodulation and inhibition pattern. Furthermore, we provide estimates of these metrics in human MUs and show comparable variability in ΔFand brace height measures for MUs matched across multiple trials.Significance. Spanning both datasets, we found brace height quantification to provide an intuitive method for achieving graded estimates of neuromodulatory and inhibitory drive to individual MUs. This complements common techniques and provides an avenue for decoupling changes in the level of neuromodulatory and pattern of inhibitory motor commands.

Multimodal parameter spaces of a complex multi-channel neuron model

One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin-Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.

The effects of membrane potential oscillations on the excitability of rat hypoglossal motoneurons

Oscillations in membrane potential induced by synaptic inputs and intrinsic ion channel activity play a role in regulating neuronal excitability, but the precise mechanisms underlying their contributions remain largely unknown. Here we used electrophysiological and modeling approaches to investigate the effects of Gaussian white noise injected currents on the membrane properties and discharge characteristics of hypoglossal (HG) motoneurons in P16-21 day old rats. We found that the noise-induced membrane potential oscillations facilitated spike initiation by hyperpolarizing the cells’ voltage threshold by 3.1 ± 1.0 mV and reducing the recruitment current for the tonic discharges by 0.26 ± 0.1 nA, on average (n = 59). Further analysis revealed that the noise reduced both recruitment and decruitment currents by 0.26 ± 0.13 and 0.33 ± 0.1 nA, respectively, and prolonged the repetitive firing. The noise also increased the slopes of frequency-current (F-I) relationships by 1.1 ± 0.2 Hz/nA. To investigate the potential mechanisms underlying these findings, we constructed a series of HG motoneuron models based on their electrophysiological properties. The models consisted of five compartments endowed with transient sodium (NaT), delayed-rectify potassium [K(DR)], persistent sodium (NaP), calcium-activated potassium [K(AHP)], L-type calcium (CaL) and H-current channels. In general, all our experimental results could be well fitted by the models, however, a modification of standard Hodgkin-Huxley kinetics was required to reproduce the changes in the F-I relationships and the prolonged discharge firing. This modification, corresponding to the noise generated by the stochastic flicker of voltage-gated ion channels (channel flicker, CF), was an adjustable sinusoidal function added to kinetics of the channels that increased their sensitivity to subthreshold membrane potential oscillations. Models with CF added to NaP and CaL channels mimicked the noise-induced alterations of membrane properties, whereas models with CF added to NaT and K(DR) were particularly effective in reproducing the noise-induced changes for repetitive firing observed in the real motoneurons. Further analysis indicated that the modified channel kinetics enhanced NaP- and CaL-mediated inward currents thus increasing the excitability and output of HG motoneurons, whereas they produced relatively small changes in NaT and K(DR), thus balancing these two currents and triggering variability of repetitive firing. This study provided insight into the types of membrane channel mechanisms that might underlie oscillation-induced alterations of neuronal excitability and motor output in rat HG motoneurons.

Imbalanced Subthreshold Currents Following Sepsis and Chemotherapy: A Shared Mechanism Offering a New Therapeutic Target?

Both sepsis and treatment of cancer with chemotherapy are known to cause neurologic dysfunction. The primary defects seen in both groups of patients are neuropathy and encephalopathy; the underlying mechanisms are poorly understood. Analysis of preclinical models of these disparate conditions reveal similar defects in ion channel function contributing to peripheral neuropathy. The defects in ion channel function extend to the central nervous system where lower motoneurons are affected. In motoneurons the defect involves ion channels responsible for subthreshold currents that convert steady depolarization into repetitive firing. The inability to correctly translate depolarization into steady, repetitive firing has profound effects on motor function, and could be an important contributor to weakness and fatigue experienced by both groups of patients. The possibility that disruption of function, either instead of, or in addition to neurodegeneration, may underlie weakness and fatigue leads to a novel approach to therapy. Activation of serotonin (5HT) receptors in a rat model of sepsis restores the normal balance of subthreshold currents and normal motoneuron firing. If an imbalance of subthreshold currents also occurs in other central nervous system neurons, it could contribute to encephalopathy. We hypothesize that pharmacologically restoring the proper balance of subthreshold currents might provide effective therapy for both neuropathy and encephalopathy in patients recovering from sepsis or treatment with chemotherapy.

Axon initial segment geometry in relation to motoneuron excitability

The axon initial segment (AIS) responsible for action potential initiation is a dynamic structure that varies and changes together with neuronal excitability. Like other neuron types, alpha motoneurons in the mammalian spinal cord express heterogeneity and plasticity in AIS geometry, including length (AIS_l) and distance from soma (AIS_d). The present study aimed to establish the relationship of AIS geometry with a measure of intrinsic excitability, rheobase current, that varies by 20-fold or more among normal motoneurons. We began by determining whether AIS length or distance differed for motoneurons in motor pools that exhibit different activity profiles. Motoneurons sampled from the medial gastrocnemius (MG) motor pool exhibited values for average AIS_d that were significantly greater than that for motoneurons from the soleus (SOL) motor pool, which is more readily recruited in low-level activities. Next, we tested whether AIS_d covaried with intrinsic excitability of individual motoneurons. In anesthetized rats, we measured rheobase current intracellularly from MG motoneurons in vivo before labeling them for immunohistochemical study of AIS structure. For 16 motoneurons sampled from the MG motor pool, this combinatory approach revealed that AIS_d, but not AIS_l, was significantly related to rheobase, as AIS tended to be located further from the soma on motoneurons that were less excitable. Although a causal relation with excitability seems unlikely, AIS_d falls among a constellation of properties related to the recruitability of motor units and their parent motoneurons.

Impact of parameter selection on estimates of motoneuron excitability using paired motor unit analysis

OBJECTIVE

Noninvasive estimation of motoneuron excitability in human motoneurons is achieved through a paired motor unit analysis (ΔF) that quantifies hysteresis in the instantaneous firing rates at motor unit recruitment and de-recruitment. The ΔF technique provides insight into the magnitude of neuromodulatory synaptic input and persistent inward currents (PICs). While the ΔF technique is commonly used for estimating motoneuron excitability during voluntary contractions, computational parameters used for the technique vary across studies. A systematic investigation into the relationship between these parameters and ΔF values is necessary.

APPROACH

We assessed the sensitivity of the ΔF technique with several criteria commonly used in selecting motor unit pairs for analysis and methods used for smoothing the instantaneous motor unit firing rates. Using high-density surface EMG and convolutive blind source separation, we obtained a large number of motor unit pairs (5409) from the triceps brachii of ten healthy individuals during triangular isometric contractions.

MAIN RESULTS

We found an exponential plateau relationship between ΔF and the recruitment time difference between the motor unit pairs and an exponential decay relationship between ΔF and the de-recruitment time difference between the motor unit pairs, with the plateaus occurring at approximately 1 s and 1.5 s, respectively. Reduction or removal of the minimum threshold for rate-rate correlation of the two units did not affect ΔF values or variance. Removing motor unit pairs in which the firing rate of the control unit was saturated had no significant effect on ΔF. Smoothing the filter selection had no substantial effect on ΔF values and ΔF variance; however, filter selection affected the minimum recruitment and de-recruitment time differences.

SIGNIFICANCE

Our results offer recommendations for standardized parameters for the ΔF approach and facilitate the interpretation of findings from studies that implement the ΔF analysis but use different computational parameters.

Nonlinear Input-Output Functions of Motoneurons

All movements are generated by the activation of motoneurons, and hence their input-output properties define the final step in processing of all motor commands. A major challenge to understanding this transformation has been the striking nonlinear behavior of motoneurons conferred by the activation of persistent inward currents (PICs) mediated by their voltage-gated Na+ and Ca2+ channels. In this review, we focus on the contribution that these PICs make to motoneuronal discharge and how the nonlinearities they engender impede the construction of a comprehensive model of motor control.

Robust and accurate decoding of motoneuron behaviour and prediction of the resulting force output

KEY POINTS

The spinal alpha motoneuron is the only cell in the human CNS whose discharge can be routinely recorded in humans. We have reengineered motor unit collection and decomposition approaches, originally developed in humans, to measure the neural drive to muscle and estimate muscle force generation in the in vivo cat model. Experimental, computational, and predictive approaches are used to demonstrate the validity of this approach across a wide range of modes to activate the motor pool. The utility of this approach is shown through the ability to track individual motor units across trials, allowing for better predictions of muscle force than the electromyography signal, and providing insights in to the stereotypical discharge characteristics in response to synaptic activation of the motor pool. This approach now allows for a direct link between the intracellular data of single motoneurons, the discharge properties of motoneuron populations, and muscle force generation in the same preparation.

ABSTRACT

The discharge of a spinal alpha motoneuron and the resulting contraction of its muscle fibres represents the functional quantum of the motor system. Recent advances in the recording and decomposition of the electromyographic signal allow for the identification of several tens of concurrently active motor units. These detailed population data provide the potential to achieve deep insights into the synaptic organization of motor commands. Yet most of our understanding of the synaptic input to motoneurons is derived from intracellular recordings in animal preparations. Thus, it is necessary to extend the new electrode and decomposition methods to recording of motor unit populations in these same preparations. To achieve this goal, we use high-density electrode arrays and decomposition techniques, analogous to those developed for humans, to record and decompose the activity of tens of concurrently active motor units in a hindlimb muscle in the in vivo cat. Our results showed that the decomposition method in this animal preparation was highly accurate, with conventional two-source validation providing rates of agreement equal to or superior to those found in humans. Multidimensional reconstruction of the motor unit action potential provides the ability to accurately track the same motor unit across multiple contractions. Additionally, correlational analyses demonstrate that the composite spike train provides better estimates of whole muscle force than conventional estimates obtained from the electromyographic signal. Lastly, stark differences are observed between the modes of activation, in particular tendon vibration produced quantal interspike intervals at integer multiples of the vibration period.

The potential for understanding the synaptic organization of human motor commands via the firing patterns of motoneurons

Motoneurons are unique in being the only neurons in the CNS whose firing patterns can be easily recorded in human subjects. This is because of the one-to-one relationship between the motoneuron and muscle cell behavior. It has long been appreciated that the connection of motoneurons to their muscle fibers allows their action potentials to be amplified and recorded, but only recently has it become possible to simultaneously record the firing pattern of many motoneurons via array electrodes placed on the skin. These firing patterns contain detailed information about the synaptic organization of motor commands to the motoneurons. This review focuses on parameters in these firing patterns that are directly linked to specific features of this organization. It is now well established that motor commands consist of three components, excitation, inhibition, and neuromodulation; the importance of the third component has become increasingly evident. Firing parameters linked to each of the three components are discussed, along with consideration of potential limitations in their utility for understanding the underlying organization of motor commands. Future work based on realistic computer simulations of motoneurons may allow quantitative "reverse engineering" of human motoneuron firing patterns to provide good estimates of the relative amplitudes and temporal patterns of all three components of motor commands.

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.

Contribution of intrinsic motoneuron properties to discharge hysteresis and its estimation based on paired motor unit recordings: a simulation study

Motoneuron activity is strongly influenced by the activation of persistent inward currents (PICs) mediated by voltage-gated sodium and calcium channels. However, the amount of PIC contribution to the activation of human motoneurons can only be estimated indirectly. Simultaneous recordings of pairs of motor units have been used to provide an estimate of the PIC contribution by using the firing rate of the lower threshold unit to provide an estimate of the common synaptic drive to both units, and the difference in firing rate (ΔF) of this lower threshold unit at recruitment and de-recruitment of the higher threshold unit to estimate the PIC contribution to activation of the higher threshold unit. It has recently been suggested that a number of factors other than PIC can contribute to ΔF values, including mechanisms underlying spike frequency adaptation and spike threshold accommodation. In the present study, we used a set of compartmental models representing a sample of 20 motoneurons with a range of thresholds to investigate how several different intrinsic motoneuron properties can potentially contribute to variations in ΔF values. We drove the models with linearly increasing and decreasing noisy conductance commands of different rate of rise and duration and determined the influence of different intrinsic mechanisms on discharge hysteresis (the difference in excitatory drive at recruitment and de-recruitment) and ΔF. Our results indicate that, although other factors can contribute, variations in discharge hysteresis and ΔF values primarily reflect the contribution of dendritic PICs to motoneuron activation.

Modulation of motoneuron firing by recurrent inhibition in the adult rat in vivo

Recent reports show that synaptic inhibition can modulate postsynaptic spike timing without having strong effects on firing rate. Thus synaptic inhibition can achieve multiplicity in neural circuit operation through variable modulation of postsynaptic firing rate vs. timing. We tested this possibility for recurrent inhibition (RI) of spinal motoneurons. In in vivo electrophysiological studies of adult Wistar rats anesthetized by isoflurane, we examined repetitive firing of individual lumbosacral motoneurons recorded in current clamp and modulated by synchronous antidromic electrical stimulation of multiple motor axons and their centrally projecting collateral branches. Antidromic stimulation produced recurrent inhibitory postsynaptic potentials (RIPSPs) having properties similar to those detailed in the cat. Although synchronous RI produced marked short-term modulation of motoneuron spike timing and instantaneous firing rate, there was little or no suppression of average firing rate. The bias in firing modulation of timing over average rate was observed even for high-frequency RI stimulation (100 Hz), perhaps because of the brevity of RIPSPs, which were more than twofold shorter during motoneuron firing compared with rest. These findings demonstrate that RI in the mammalian spinal cord has the capacity to support and not impede heightened motor pool activity, possibly during rapid, forceful movements.

Soma size and Cav1.3 channel expression in vulnerable and resistant motoneuron populations of the SOD1G93A mouse model of ALS

Although the loss of motoneurons is an undisputed feature of amyotrophic lateral sclerosis (ALS) in man and in its animal models (SOD1 mutant mice), how the disease affects the size and excitability of motoneurons prior to their degeneration is not well understood. This study was designed to test the hypothesis that motoneurons in mutant SOD1^G93A mice exhibit an enlargement of soma size (i.e., cross‐sectional area) and an increase in Ca_v1.3 channel expression at postnatal day 30, well before the manifestation of physiological symptoms that typically occur at p90 (Chiu et al. 1995). We made measurements of spinal and hypoglossal motoneurons vulnerable to degeneration, as well as motoneurons in the oculomotor nucleus that are resistant to degeneration. Overall, we found that the somata of motoneurons in male SOD1^G93A mutants were larger than those in wild‐type transgenic males. When females were included in the two groups, significance was lost. Expression levels of the Ca_v1.3 channels were not differentiated by genotype, sex, or any interaction of the two. These results raise the intriguing possibility of an interaction between male sex steroid hormones and the SOD1 mutation in the etiopathogenesis of ALS.

This study was designed to test the hypothesis that motoneurons in mutant SOD1G93A mice exhibit an enlargement of soma size (i.e., cross‐sectional area) and an increase in Cav1.3 channel expression at postnatal day 30, well before the manifestation of physiological symptoms that typically occur at p90 (Chiu et al. 1995). We made measurements of spinal and hypoglossal motoneurons vulnerable to degeneration, as well as motoneurons in the oculomotor nucleus that are resistant to degeneration. Overall, we found that the somata of motoneurons in male SOD1G93A mutants were larger than those in wild‐type transgenic males. When females were included in the two groups, significance was lost. These results raise the intriguing possibility of an interaction between male sex steroid hormones and the SOD1 mutation in the etiopathogenesis of ALS.

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.

Changes in motoneuron afterhyperpolarization duration in stroke survivors

Hemispheric brain injury resulting from a stroke is often accompanied by muscle weakness in limbs contralateral to the lesion. In the present study, we investigated whether weakness in contralesional hand muscle in stroke survivors is partially attributable to alterations in motor unit activation, including alterations in firing rate modulation range. The afterhyperpolarization (AHP) potential of a motoneuron is a primary determinant of motoneuron firing rate. We examined differences in AHP duration in motoneurons innervating paretic and less impaired (contralateral) limb muscles of hemiparetic stroke survivors as well as in control subjects. A novel surface EMG (sEMG) electrode was used to record motor units from the first dorsal interosseous muscle. The sEMG data were subsequently decomposed to derive single-motor unit events, which were then utilized to produce interval (ISI) histograms of the motoneuron discharges. A modified version of interval death rate (IDR) analysis was used to estimate AHP duration. Results from data analyses performed on both arms of 11 stroke subjects and in 7 age-matched control subjects suggest that AHP duration is significantly longer for motor units innervating paretic muscle compared with units in contralateral muscles and in units of intact subjects. These results were supported by a coefficient of variation (CV) analysis showing that paretic motor unit discharges have a lower CV than either contralateral or control units. This study suggests that after stroke biophysical changes occur at the motoneuron level, potentially contributing to lower firing rates and potentially leading to less efficient force production in paretic muscles.

Disturbances of motor unit rate modulation are prevalent in muscles of spastic-paretic stroke survivors

Stroke survivors often exhibit abnormally low motor unit firing rates during voluntary muscle activation. Our purpose was to assess the prevalence of saturation in motor unit firing rates in the spastic-paretic biceps brachii muscle of stroke survivors. To achieve this objective, we recorded the incidence and duration of impaired lower- and higher-threshold motor unit firing rate modulation in spastic-paretic, contralateral, and healthy control muscle during increases in isometric force generated by the elbow flexor muscles. Impaired firing was considered to have occurred when firing rate became constant (i.e., saturated), despite increasing force. The duration of impaired firing rate modulation in the lower-threshold unit was longer for spastic-paretic (3.9 ± 2.2 s) than for contralateral (1.4 ± 0.9 s; P < 0.001) and control (1.1 ± 1.0 s; P = 0.005) muscles. The duration of impaired firing rate modulation in the higher-threshold unit was also longer for the spastic-paretic (1.7 ± 1.6 s) than contralateral (0.3 ± 0.3 s; P = 0.007) and control (0.1 ± 0.2 s; P = 0.009) muscles. This impaired firing rate of the lower-threshold unit arose, despite an increase in the overall descending command, as shown by the recruitment of the higher-threshold unit during the time that the lower-threshold unit was saturating, and by the continuous increase in averages of the rectified EMG of the biceps brachii muscle throughout the rising phase of the contraction. These results suggest that impairments in firing rate modulation are prevalent in motor units of spastic-paretic muscle, even when the overall descending command to the muscle is increasing.

Examination of afterhyperpolarization duration changes in motoneurons innervating paretic muscles in stroke survivors

The after hyperpolarization (AHP) of a motoneuron is a primary determinant of motoneuron firing rate. Any increase in its duration or amplitude could alter normal motor unit (MU) firing rate properties in stroke, and potentially impact muscle force generation. The objective of this preliminary study was to examine potential differences in afterhyperpolarization (AHP) duration of motoneurons innervating paretic and contralateral limb muscles of hemiparetic stroke survivors. A novel surface EMG (sEMG) electrode was used to record from the first dorsal interosseous muscle (FDI) of three hemiparetic stroke survivors. sEMG data was decomposed to derive single motor unit (SMU) events, which were subsequently utilized to produce interval (ISI) histograms of the motor unit discharge. Interval Death Rate (IDR) analysis was then used to transform ISI histograms into death rate plots. [1] The prescribed IDR analysis method [1] involves a final transformation of death rate plots into an estimated AHP time course. The present study uses a modified method of interpreting death rate plots in order to determine AHP duration. AHP durations from this analysis are similar to durations obtained from ISI variability analysis. [2] Results from three subjects indicate that on average, motor units on the paretic side have a longer AHP duration than the contralateral side, potentially contributing to lower firing rates, and to less efficient force production in paretic muscles.

Frequency-dependent amplification of stretch-evoked excitatory input in spinal motoneurons

Voltage-dependent calcium and sodium channels mediating persistent inward currents (PICs) amplify the effects of synaptic inputs on the membrane potential and firing rate of motoneurons. CaPIC channels are thought to be relatively slow, whereas the NaPIC channels have fast kinetics. These different characteristics influence how synaptic inputs with different frequency content are amplified; the slow kinetics of Ca channels suggest that they can only contribute to amplification of low frequency inputs (<5 Hz). To characterize frequency-dependent amplification of excitatory postsynaptic potentials (EPSPs), we measured the averaged stretch-evoked EPSPs in cat medial gastrocnemius motoneurons in decerebrate cats at different subthreshold levels of membrane potential. EPSPs were produced by muscle spindle afferents activated by stretching the homonymous and synergist muscles at frequencies of 5-50 Hz. We adjusted the stretch amplitudes at different frequencies to produce approximately the same peak-to-peak EPSP amplitude and quantified the amount of amplification by expressing the EPSP integral at different levels of depolarization as a percentage of that measured with the membrane hyperpolarized. Amplification was observed at all stretch frequencies but generally decreased with increasing stretch frequency. However, in many cells the amount of amplification was greater at 10 Hz than at 5 Hz. Fast amplification was generally reduced or absent when the lidocaine derivative QX-314 was included in the electrode solution, supporting a strong contribution from Na channels. These results suggest that NaPICs can combine with CaPICs to enhance motoneuron responses to modulations of synaptic drive over a physiologically significant range of frequencies.

Contribution of intrinsic properties and synaptic inputs to motoneuron discharge patterns: a simulation study

Motoneuron discharge patterns reflect the interaction of synaptic inputs with intrinsic conductances. Recent work has focused on the contribution of conductances mediating persistent inward currents (PICs), which amplify and prolong the effects of synaptic inputs on motoneuron discharge. Certain features of human motor unit discharge are thought to reflect a relatively stereotyped activation of PICs by excitatory synaptic inputs; these features include rate saturation and de-recruitment at a lower level of net excitation than that required for recruitment. However, PIC activation is also influenced by the pattern and spatial distribution of inhibitory inputs that are activated concurrently with excitatory inputs. To estimate the potential contributions of PIC activation and synaptic input patterns to motor unit discharge patterns, we examined the responses of a set of cable motoneuron models to different patterns of excitatory and inhibitory inputs. The models were first tuned to approximate the current- and voltage-clamp responses of low- and medium-threshold spinal motoneurons studied in decerebrate cats and then driven with different patterns of excitatory and inhibitory inputs. The responses of the models to excitatory inputs reproduced a number of features of human motor unit discharge. However, the pattern of rate modulation was strongly influenced by the temporal and spatial pattern of concurrent inhibitory inputs. Thus, even though PIC activation is likely to exert a strong influence on firing rate modulation, PIC activation in combination with different patterns of excitatory and inhibitory synaptic inputs can produce a wide variety of motor unit discharge patterns.

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).

Deciphering the contribution of intrinsic and synaptic currents to the effects of transient synaptic inputs on human motor unit discharge

The amplitude and time course of synaptic potentials in human motoneurons can be estimated in tonically discharging motor units by measuring stimulus-evoked changes in the rate and probability of motor unit action potentials. However, in spite of the fact that some of these techniques have been used for over 30 years, there is still no consensus on the best way to estimate the characteristics of synaptic potentials or on the accuracy of these estimates. In this review, we compare different techniques for estimating synaptic potentials from human motor unit discharge and also discuss relevant animal models in which estimated synaptic potentials can be compared to those directly measured from intracellular recordings. We also review the experimental evidence on how synaptic noise and intrinsic motoneuron properties influence their responses to synaptic inputs. Finally, we consider to what extent recordings of single motor unit discharge in humans can be used to distinguish the contribution of changes in synaptic inputs versus changes in intrinsic motoneuron properties to altered motoneuron responses following CNS injury.

Estimation of the contribution of intrinsic currents to motoneuron firing based on paired motoneuron discharge records in the decerebrate cat

Motoneuron activation is strongly influenced by persistent inward currents (PICs) flowing through voltage-sensitive channels. PIC characteristics and their contribution to the control of motoneuron firing rate have been extensively described in reduced animal preparations, but their contribution to rate modulation in human motoneurons is controversial. It has recently been proposed that the analysis of discharge records of a simultaneously recorded pair of motor units can be used to make quantitative estimates of the PIC contribution, based on the assumption that the firing rate of an early recruited (reporter) unit can be used as a measure of the synaptic drive to a later recruited (test) unit. If the test unit's discharge is augmented by PICs, less synaptic drive will be required to sustain discharge than required to initially recruit it, and the difference in reporter unit discharge (Delta F) at test recruitment and de-recruitment is a measure of the size of the PIC contribution. We applied this analysis to discharge records of pairs of motoneurons in the decerebrate cat preparation, in which motoneuron PICs have been well-characterized and are known to be prominent. Mean Delta F values were positive in 58/63 pairs, and were significantly greater than zero in 40/63 pairs, as would be expected based on PIC characteristics recorded in this preparation. However, several lines of evidence suggest that the Delta F value obtained in a particular motoneuron pair may depend on a number of factors other than the PIC contribution to firing rate.

Facilitation of somatic calcium channels can evoke prolonged tail currents in rat hypoglossal motoneurons

Voltage-dependent persistent inward currents (PICs) make an important contribution to the input-output properties of alpha motoneurons. PICs are thought to be mediated by membrane channels located primarily on the dendrites as evidenced by prolonged tail currents following the termination of a voltage step and by a clockwise hysteresis in the whole cell inward currents recorded in response to depolarizing then repolarizing voltage ramp commands. We report here, however, that voltage-clamp currents with these same features can be generated in isolated somatic membrane patches from rat hypoglossal motoneurons. Long-lasting (200-800 ms) tail currents after 1-s voltage-clamp pulses were observed in nucleated patches from 16 of 23 cells. Further, these somatic PICs display "facilitation" in response to conditioning depolarization as previously observed in whole cell recordings from intact neurons. Pharmacological tests suggest that the PICs were primarily mediated by Cav1 channels. Our results show that many of the features of persistent calcium currents recorded from intact motoneurons do not necessarily reflect a remote dendritic origin but can also be ascribed to the intrinsic properties of their Cav1 channels.

Black box revisited: a technique for estimating postsynaptic potentials in neurons

Our understanding of the operation of the brain depends on knowledge of its wiring. Currently, the wiring of the human brain is estimated by counting the number of neuron discharges that occur at specific times following a stimulus. There is now strong evidence that this approach generates significant errors. Recently, the accuracy of this 'count' method has been compared directly with an alternative 'rate' method in rat brain slices. The results confirmed that the count method generates significant errors that are minimized by the rate method, because the rate of discharge of a neuron accurately displays its excitability at the time of discharge. Therefore, it is now crucial that the rate method be used to reassess previous estimates of the characteristics of wiring in the brain.

Contribution of Persistent Sodium Currents to Spike-Frequency Adaptation in Rat Hypoglossal Motoneurons

In response to constant current inputs, the firing rates of motoneurons typically show a continuous decline over time. The biophysical mechanisms underlying this process, called spike-frequency adaptation, are not well understood. Spike-frequency adaptation normally exhibits a rapid initial phase, followed by a slow, later phase that continues throughout the duration of firing. One possible mechanism mediating the later phase might be a reduction in the persistent sodium current ( INaP) that has been shown to diminish the capacity of cortical pyramidal neurons and spinal motoneurons to sustain repetitive firing. In this study, we used the anticonvulsant phenytoin to reduce the INaP of juvenile rat hypoglossal motoneurons recorded in brain stem slices, and we examined the consequences of a reduction in INaP on the magnitude and time course of spike-frequency adaptation. Adding phenytoin to the bathing solution (≥50 μM) generally produced a marked reduction in the persistent inward currents (PICs) recorded at the soma in response to slow, voltage-clamp triangular ramp commands (−70 to 0 mV and back). However, the same concentrations of phenytoin appeared to have no significant effect on spike-frequency adaptation even though the phenytoin often augmented the reduction in action potential amplitude that occurs during repetitive firing. The surprising finding that the reduction of a source of sustained inward current had no appreciable effect on the pattern of spike generation suggests that several types of membrane channels must act cooperatively to insure that these motoneurons can generate the sustained repetitive firing required for long-lasting motor behaviors.

Contributions of the input signal and prior activation history to the discharge behaviour of rat motoneurones

The principal computational operation of neurones is the transformation of synaptic inputs into spike train outputs. The probability of spike occurrence in neurones is determined by the time course and magnitude of the total current reaching the spike initiation zone. The features of this current that are most effective in evoking spikes can be determined by injecting a Gaussian current waveform into a neurone and using spike-triggered reverse correlation to calculate the average current trajectory (ACT) preceding spikes. The time course of this ACT (and the related first-order Wiener kernel) provides a general description of a neurone's response to dynamic stimuli. In many different neurones, the ACT is characterized by a shallow hyperpolarizing trough followed by a more rapid depolarizing peak immediately preceding the spike. The hyperpolarizing phase is thought to reflect an enhancement of excitability by partial removal of sodium inactivation. Alternatively, this feature could simply reflect the fact that interspike intervals that are longer than average can only occur when the current is lower than average toward the end of the interspike interval. Thus, the ACT calculated for the entire spike train displays an attenuated version of the hyperpolarizing trough associated with the long interspike intervals. This alternative explanation for the characteristic shape of the ACT implies that it depends upon the time since the previous spike, i.e. the ACT reflects both previous stimulus history and previous discharge history. The present study presents results based on recordings of noise-driven discharge in rat hypoglossal motoneurones that support this alternative explanation. First, we show that the hyperpolarizing trough is larger in ACTs calculated from spikes preceded by long interspike intervals, and minimal or absent in those based on short interspike intervals. Second, we show that the trough is present for ACTs calculated from the discharge of a threshold-crossing neurone model with a postspike afterhyperpolarization (AHP), but absent from those calculated from the discharge of a model without an AHP. We show that it is possible to represent noise-driven discharge using a two-component linear model that predicts discharge probability based on the sum of a feedback kernel and a stimulus kernel. The feedback kernel reflects the influence of prior discharge mediated by the AHP, and it increases in amplitude when AHP amplitude is increased by pharmacological manipulations. Finally, we show that the predictions of this model are virtually identical to those based on the first-order Wiener kernel. This suggests that the Wiener kernels derived from standard white-noise analysis of noise-driven discharge in neurones actually reflect the effects of both stimulus and discharge history.

Estimation of postsynaptic potentials in rat hypoglossal motoneurones: insights for human work

Classical techniques for estimating postsynaptic potentials in motoneurones include spike-triggered averages of rectified surface and multiunit electromyographic recordings (SEMG and MU-EMG), as well as the compilation of peristimulus time histograms (PSTH) based on the discharge of single motor units (SMU). These techniques rely on the probability of spike occurrence in relation to the stimulus and can be contaminated by count- and synchronization-related errors, arising from post-spike refractoriness and the discharge statistics of motoneurones. On the other hand, since these probability-based techniques are easy to use and require only inexpensive equipment, it is very likely that they will continue to be used in clinical and laboratory settings for the foreseeable future. One aim of the present study was to develop a modification of these probability-based analyses in order to provide a better estimate of the initial phase of postsynaptic potentials. An additional aim was to combine probability-based analyses with frequency-based analyses to provide a more reliable estimate of later phases of postsynaptic potentials. To achieve these aims, we have injected simple as well as complex current transients into regularly discharging hypoglossal motoneurones recorded in vitro from rat brainstem slices. We examined the discharge output of these cells using both probability- and frequency-based analyses to identify which of the two represented the profile of the postsynaptic potential more closely. This protocol was designed to obtain PSTHs of the responses of single motor units to repeated application of the same afferent input. We have also simulated multiunit responses to afferent input by replacing the times of spike occurrence in individual trials with a representation of either an intramuscular or surface-recording single motor unit waveform and summing many of these trials to obtain either a simulated SEMG or MU-EMG. We found that in a regularly discharging motoneurone, the rising phase of an EPSP moves the occurrence of spikes forward and hence induces a substantial peak in all probability-based records. This peak is followed immediately by a period of reduced activity ('silent period') due to the phase advancement of spikes that were to occur at this period. Similarly, the falling phase of an IPSP delays spikes so that they occur during the rising phase of the IPSP. During the delay, the probability-based analyses display gaps and during the occurrence of the delayed spikes they generate peaks. We found that all the probability-based analyses (SEMG, MU-EMG and PSTH) can be made useful for illustrating the underlying initial PSP by a special use of the cumulative sum (CUSUM) calculation. We have illustrated that, in most cases, the CUSUM of probability-based analyses can overcome the delay- or advance-related (i.e. the count-related) errors of the classical methods associated with the first PSP only. The probability-based records also induce secondary and tertiary peaks and troughs due to synchronization of the spikes in relation to the stimulus (i.e. the synchronization-related errors) by the first PSP to occur at fixed times from the stimulus. Special CUSUM analyses cannot overcome these synchronization-related errors. Frequency-based analysis (PSFreq) of individual and summed trials gave comparable and often better indications of the underlying PSPs than the probability-based analyses. When used in combination, these analyses compliment each other so that a more accurate estimation of the underlying PSP is possible. Since the correct identification of the connections in the central nervous system is of utmost importance in order to understand the operation of the system, we suggest that as well as the using the special CUSUM approach on probability-based records, researchers should seriously consider the use of frequency-based analyses in their indirect estimation of stimulus-induced compound synaptic potentials in human motoneurones.

Relative strengths and distributions of different sources of synaptic input to the motoneurone pool: implications for motor unit recruitment

Understanding how synaptic inputs from segmental and descending systems shape motor output from the spinal cord requires information on the relative magnitudes of the synaptic currents produced by the different systems and their patterns of distribution within a motoneurone pool. Equally important are quantitative descriptions of how different synaptic inputs are integrated when they are concurrently active and of how voltage- and ligand-gated conductances on the dendrites of motoneurones affect the transfer of synaptic currents to the soma. We have carried out a number of experimental studies of these inter-related problems on motoneurones in the cat spinal cord and have explored the implications of our findings with computer simulations utilizing a synthetic model of the cat medial gastrocnemius motoneurone pool. This paper provides a brief review of the principal results of our studies.

What can be learned about motoneurone properties from studying firing patterns?

The discharge patterns of tonically-firing neurones are influenced by both the characteristics of their presynaptic input and their intrinsic properties. The regularity of the discharge of motoneurones is thought to reflect their prominent post-spike afterhyperpolarization (AHP). When a motoneurone fires at steady mean rate, the distribution of interspike intervals is determined by the amplitude and frequency content of the synaptic noise together with the decrease in excitability following a spike due to AHP. This paper considers how motoneurone discharge statistics can be used to estimate AHP trajectories as well as a motoneurone's sensitivity to excitatory input.

Persistent sodium and calcium currents in rat hypoglossal motoneurons

Voltage-dependent persistent inward currents are thought to make an important contribution to the input-output properties of alpha-motoneurons, influencing both the transfer of synaptic current to the soma and the effects of that current on repetitive discharge. Recent studies have paid particular attention to the contribution of L-type calcium channels, which are thought to be widely distributed on both the somatic and the dendritic membrane. However, the relative contribution of different channel subtypes as well as their somatodendritic distribution may vary among motoneurons of different species, developmental stages, and motoneuron pools. In this study, we have characterized persistent inward currents in juvenile (10- to 24-day-old) rat hypoglossal (HG) motoneurons. Whole-cell, voltage-clamp recordings were made from the somata of visualized rat HG motoneurons in 300-microm brain stem slices. Slow (10 s), triangular voltage-clamp commands from a holding potential of -70 to 0 mV and back elicited whole-cell currents that were dominated by outward, potassium currents, but often showed a region of negative slope resistance on the rising phase of the command. In the presence of potassium channel blockers (internal cesium and external 4-aminopyridine and tetraethylammonium), net inward currents were present on both the rising and falling phases of the voltage-clamp command. A portion of the inward current present on the ascending phase of the command was mediated by TTX-sensitive sodium channels, whereas calcium channels mediated the remainder of the current. We found roughly the same relative contributions of P-, N-, and L-type channels to the calcium currents recorded at the soma that had previously been found in neonatal rat HG motoneurons. In most cells, the somatic voltage thresholds for calcium current onset and offset were similar and the peak current was largest on the ascending phase of the clamp command. However, about one-third of the cells exhibited a substantial clockwise current hysteresis, i.e., inward currents were present at lower voltages on the descending phase of the clamp command. In the same cells, 1-s depolarizing voltage-clamp commands were followed by prolonged tail currents, consistent with a prominent contribution from dendritic channels. In contrast to previous reports on turtle and mouse motoneurons, blocking L-type calcium channels did not eliminate these presumed dendritic currents.

The effects of common input characteristics and discharge rate on synchronization in rat hypoglossal motoneurones

Synchronous discharges between a pair of concurrently active motoneurones are thought to arise from the spike-triggering effects of synaptic inputs shared by the pair. Although there are a number of quantitative indices that have been developed to estimate the strength of this common input, there is still some debate as to whether motoneurone discharge rate affects the values of these indices. The aim of the present study was to test the effects of motoneurone discharge rate on these synchronization indices using known common inputs. To achieve this aim we elicited repetitive discharge in rat hypoglossal motoneurones by combining a suprathreshold injected current step with superimposed noise to mimic the synaptic drive likely to occur during physiological activation. The amplitude of the current step was varied in different trials to achieve discharge rates from 5 to 22 Hz. We first examined the effect of discharge rate on the spike-triggering efficacy of individual EPSPs. Motoneurones were more responsive to large EPSPs delivered at a low rate when their background discharge rate was relatively low and the probability of the EPSPs evoking an extra spike decreased with increasing discharge rate. However, the opposite dependence was found for small, high-frequency EPSPs. We then compared the discharge records obtained in several trials in which the same EPSP train was applied repeatedly to the same cell firing at different background discharge rates. The effect of this 'common input' on motoneurone discharge probability was determined by compiling cross-correlation histograms (CCHists) between the discharges of the same cell at different times. The common inputs induced synchronous discharge that gave rise to large central peaks in the CCHists. The relationship between the discharge rate and the level of synchronization changed depending on the synchronization indices used and the amplitude of the common EPSPs. When large EPSPs were used as the common input, the normalized probability of synchronous spikes declined as the discharge rate increased, regardless of the method of normalization used. In contrast, when the common input was composed of a large number of small EPSPs, similar to that likely to occur during physiological activation of motoneurones, different synchronization indices exhibited a positive, a negative or no dependence on the background discharge rate. Indices based on normalizing the number of synchronous spikes by either the number of discharges in the lower frequency train (E), or by the total number of discharges in both trains (S) showed no dependence on background discharge rate and therefore may be the most suitable for quantifying motoneurone synchrony over a range of background discharge rates.

Effects of common excitatory and inhibitory inputs on motoneuron synchronization

We compared the effects of common excitatory and inhibitory inputs on motoneuron synchronization by simulating synaptic inputs with injected current transients. We elicited repetitive discharge in hypoglossal motoneurons recorded in slices of rat brain stem using a combination of a suprathreshold injected current step with superimposed noise to mimic the synaptic drive likely to occur during physiological activation. The effects of common inputs to motoneurons were simulated by the addition of a waveform composed of from 6 to 300 trains of current transients designed to mimic excitatory and/or inhibitory synaptic currents. We compared the discharge records obtained in several trials in which the same "common input" waveform was applied repeatedly in the presence of different background noise waveforms. The effects of the common input on motoneuron discharge probability and discharge rate were determined by compiling a cross-correlation histogram (CCHist) and a perispike frequencygram (PSFreq) between the discharges of the same cell at different times. Both excitatory and inhibitory common inputs induced synchronous discharge that was evident by a large central peak in the CCHist. The CCHists produced by common excitatory inputs were characterized by larger and narrower central peaks than those generated by common inhibitory inputs. The PSFreqs produced by common excitatory inputs indicated an increase in the discharge rate of motoneurons around time 0 that coincided with the narrow and large central peak in the CCHist. On the other hand, inhibitory inputs often generated very little, if any, change in the discharge rate around time 0 corresponding with the small and wide central peak in the CCHist. These results suggest that the CCHist indicates the effective strength of the net common input but not its sign. Although correlated changes in discharge rate are often quite different for net excitatory and inhibitory common input, except in some restricted conditions, the PSFreq analysis also cannot be used to unambiguously distinguish net excitation from net inhibition.

Relationship between simulated common synaptic input and discharge synchrony in cat spinal motoneurons

Synchronized discharge of individual motor units is commonly observed in the muscles of human subjects performing voluntary contractions. The amount of this synchronization is thought to reflect the extent to which motoneurons in the same and related pools share common synaptic input. However, the relationship between the proportion of shared synaptic input and the strength of synchronization has never been measured directly. In this study, we simulated common shared synaptic input to cat spinal motoneurons by driving their discharge with noisy, injected current waveforms. Each motoneuron was stimulated with a number of different injected current waveforms, and a given pair of waveforms were either completely different or else shared a variable percentage of common elements. Cross-correlation histograms were then compiled between the discharge of motoneurons stimulated with noise waveforms with variable degrees of similarity. The strength of synchronization increased with the amount of simulated "common" input in a nonlinear fashion. Moreover, even when motoneurons had >90% of their simulated synaptic inputs in common, only approximately 25-45% of their spikes were synchronized. We used a simple neuron model to explore how variations in neuron properties during repetitive discharge may lead to the low levels of synchronization we observed experimentally. We found that small variations in spike threshold and firing rate during repetitive discharge lead to large decreases in synchrony, particularly when neurons have a high degree of common input. Our results may aid in the interpretation of studies of motor unit synchrony in human hand muscles during voluntary contractions.

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.

Amplification and linear summation of synaptic effects on motoneuron firing rate

The aim of this study was to measure the effects of synaptic input on motoneuron firing rate in an unanesthetized cat preparation, where activation of voltage-sensitive dendritic conductances may influence synaptic integration and repetitive firing. In anesthetized cats, the change in firing rate produced by a steady synaptic input is approximately equal to the product of the effective synaptic current measured at the resting potential (I(N)) and the slope of the linear relation between somatically injected current and motoneuron discharge rate (f-I slope). However, previous studies in the unanesthetized decerebrate cat indicate that firing rate modulation may be strongly influenced by voltage-dependent dendritic conductances. To quantify the effects of these conductances on motoneuron firing behavior, we injected suprathreshold current steps into medial gastrocnemius motoneurons of decerebrate cats and measured the changes in firing rate produced by superimposed excitatory synaptic input. In the same cells, we measured I(N) and the f-I slope to determine the predicted change in firing rate (Delta F = I(N) * f-I slope). In contrast to previous results in anesthetized cats, synaptically induced changes in motoneuron firing rate were greater-than-predicted. This enhanced effect indicates that additional inward current was present during repetitive firing. This additional inward current amplified the effective synaptic currents produced by two different excitatory sources, group Ia muscle spindle afferents and caudal cutaneous sural nerve afferents. There was a trend toward more prevalent amplification of the Ia input (14/16 cells) than the sural input (11/16 cells). However, in those cells where both inputs were amplified (10/16 cells), amplification was similar in magnitude for each source. When these two synaptic inputs were simultaneously activated, their combined effect was generally very close to the linear sum of their amplified individual effects. Linear summation is also observed in medial gastrocnemius motoneurons of anesthetized cats, where amplification is not present. This similarity suggests that amplification does not disturb the processes of synaptic integration. Linear summation of amplified input was evident for the two segmental inputs studied here. If these phenomena also hold for other synaptic sources, then the presence of active dendritic conductances underlying amplification might enable motoneurons to integrate multiple synaptic inputs and drive motoneuron firing rates throughout the entire physiological range in a relatively simple fashion.

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.

Summation of effective synaptic currents and firing rate modulation in cat spinal motoneurons

The aim of this study was to examine how cat spinal motoneurons integrate the synaptic currents generated by the concurrent activation of large groups of presynaptic neurons. We obtained intracellular recordings from cat triceps surae motoneurons and measured the effects of repetitive activity in different sets of presynaptic neurons produced by electrical stimulation of descending fibers or peripheral nerves and by longitudinal vibration of the triceps surae muscles (to activate primary muscle spindle Ia afferent fibers). We combined synaptic activation with subthreshold injected currents to obtain estimates of effective synaptic currents at the resting potential (I(Nrest)) and at the threshold for repetitive discharge (I(Nthresh)). We then superimposed synaptic activation on suprathreshold injected current steps to measure the synaptically evoked change in firing rate. We studied eight different pairs of synaptic inputs. When any two synaptic inputs were activated concurrently, both the effective synaptic currents (I(Nrest)) and the synaptically evoked changes in firing rate generally were equal to or slightly less than the linear sum of the effects produced by activating each input alone. However, there were several instances in which the summation was substantially less than linear. In some motoneurons, we induced a partial blockade of potassium channels by adding tetraethylammonium (TEA) or cesium to the electrolyte solution in the intracellular pipette. In these cells, persistent inward currents were evoked by depolarization that led to instances of substantially greater-than linear summation of injected and synaptic currents. Overall our results indicate that the spatial distribution of synaptic boutons on motoneurons acts to minimize electrical interactions between synaptic sites permitting near linear summation of synaptic currents. However, modulation of voltage-gated conductances on the soma and dendrites of the motoneuron can lead to marked nonlinearities in synaptic integration.

Effects of large excitatory and inhibitory inputs on motoneuron discharge rate and probability

We elicited repetitive discharge in hypoglossal motoneurons recorded in slices of rat brain stem using a combination of a suprathreshold injected current step with superimposed noise to mimic the synaptic drive likely to occur during physiological activation. The effects of repetitive en mass stimulation of afferent nerves were simulated by the further addition of trains of injected current transients of varying shapes and sizes. The effects of a given current transient on motoneuron discharge timing and discharge rate were measured by calculating a peristimulus time histogram (PSTH) and a peristimulus frequencygram (PSF). The amplitude and time course of the simulated postsynaptic potentials (PSPs) produced by the current transients were calculated by convolving the current transient with an estimate of the passive impulse response of the motoneuron. We then compared the shape of the injected current transient and the simulated PSP to the profiles of the PSTH and the PSF records. The PSTHs produced by excitatory PSPs (EPSPs) were characterized by a large, short-latency increase in firing probability that lasted slightly longer than the rising phase of the EPSP, followed by a reduced discharge probability during the falling phase of the EPSP. In contrast, the PSF analysis revealed a proportionate increase in discharge rate over the entire profile of the EPSP, even though relatively few spikes occurred during the falling phase. The PSTHs associated with inhibitory PSPs (IPSPs) indicated a reduction in discharge probability during the initial, hyperpolarizing phase of the IPSP, followed by an increase in the discharge probability during its subsequent repolarizing phase. Using the PSF analysis, the initial phase of the IPSP appeared as a large hole in the record where a very small number or no discharges occurred. The subsequent phase of the IPSP was associated with frequency values that were lower than the background values. The primary features of both PSTHs and PSFs can be used to estimate the relative amplitudes of the underlying EPSPs and IPSPs. However, PSTHs contain secondary peaks and troughs that are not directly related to the underlying PSP but instead reflect the regular recurrence of spikes following those affected by the PSP. The PSF analysis is more useful for indicating the total duration and the profile of the underlying PSP. The shape of the underlying PSP can be obtained directly from the PSF records because the discharge frequency of the spikes follow the PSPs very closely, especially for EPSPs.

Synaptic integration in spinal motoneurones

Spinal motoneurones receive thousands of presynaptic excitatory and inhibitory synaptic contacts distributed throughout their dendritic trees. Despite this extensive convergence, there have been very few studies of how synaptic inputs interact in mammalian motoneurones when they are activated concurrently. In the experiments reported here, we measured the effective synaptic currents and the changes in firing rate evoked in cat spinal motoneurones by concurrent repetitive activation of two separate sets of presynaptic neurons. We compared these effects to those predicted by a linear sum of the effects produced by activating each set of presynaptic neurons separately. We generally found that when two inputs were activated concurrently, both the effective synaptic currents and the synaptically-evoked changes in firing rate they produced in motoneurones were generally linear, or slightly less than the linear sum of the effects produced by activating each input alone. The results suggest that the spatial distribution synaptic terminals on the dendritic trees of motoneurones may help isolate synapses from one another, minimizing non-linear interactions.

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.

Multiple mechanisms of spike-frequency adaptation in motoneurones

Spike-frequency adaptation is the continuous decline in discharge rate in response to a constant stimulus. We have described three distinct phases of adaptation in rat hypoglossal motoneurones: initial, early and late. The initial phase of adaptation is over in one or two intervals, and is primarily due to summation of the calcium-activated potassium conductance underlying the medium duration afterhyperpolarization (mAHP). The biophysical mechanisms underlying the later phases of adaptation are not well understood. Two of the previously-proposed mechanisms for adaptation are an increase in outward current flowing through calcium-activated potassium channels and increasing outward current produced by the electrogenic sodium-potassium pump. We found that neither of these mechanisms are necessary for the expression of the early and late phases of adaptation. The magnitude of the initial phase of adaptation was reduced when the calcium in the external solution was replaced with manganese, but the magnitudes of the early and late phases were consistently increased under these conditions. Partial blockade of the sodium-potassium pump with ouabain had no significant effect on any of the three phases of adaptation. Our current working hypothesis is that the magnitude of late adaptation depends upon the interplay between slow inactivation of sodium currents, that tends to decrease discharge rate, and the slow activation or facilitation of a calcium current that tends to increase discharge rate. Adaptation is often associated with a progressive decrease in the peak amplitude and rate of rise of action potentials, and a computer model that incorporated slow inactivation of sodium channels reproduced this phenomenon. However, the time course of adaptation does not always parallel changes in spike shape, indicating that the progressive activation of another inward current might oppose the decline in frequency caused by slow sodium inactivation.

Distribution of effective synaptic currents in cat triceps surae motoneurons. VI. Contralateral pyramidal tract

We measured the effective synaptic currents (IN) produced by stimulating the contralateral pyramidal tract (PT) in triceps surae motoneurons of the cat. This is an oligosynaptic pathway in the cat that generates both excitation and inhibition in hindlimb motoneurons. We also determined the effect of the PT synaptic input on the discharge rate of some of the motoneurons by inducing repetitive firing with long, injected current pulses during which the PT stimulation was repeated. At resting potential, all but one triceps motoneuron received a net depolarizing effective synaptic current from the PT stimulation. The effective synaptic currents (IN) were much larger in putative type F motoneurons than in putative type S motoneurons [+4.6 +/- 2.9 (SD) nA for type F vs. 0.9 +/- 2.4 nA for putative type S]. When the values of IN at the threshold for repetitive firing were estimated, the distribution was markedly altered. More than 60% of the putative type S motoneurons received a net hyperpolarizing effective synaptic current from the pyramidal tract stimulation as did 33% of the putative type F motoneurons. This distribution pattern is very similar to that observed previously for the effective synaptic currents produced by stimulating the contralateral red nucleus. As would be expected from the wide range of IN values at threshold (-4.8 to +8.7 nA), the PT stimulation produced dramatically different effects on the discharge of different triceps motoneurons. The discharge rates of those motoneurons that received depolarizing effective synaptic currents at threshold were accelerated by PT stimulation (+1 to +8 imp/s), whereas the discharge rates of cells that received hyperpolarizing currents were retarded by the PT input (-2 to -7 imp/s). The change in firing rates produced by the PT stimulation was generally approximated by the product of the effective synaptic currents and the slopes of the motoneurons' frequency-current relations. Our findings indicate that the contralateral pyramidal tract may provide a powerful source of synaptic drive to some high-threshold motoneurons while concurrently inhibiting low-threshold cells. Thus this input system, like that from the contralateral red nucleus, can potentially alter the gain of the input-output function of the motoneuron pool as well as disrupt the normal hierarchy of recruitment thresholds.

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.

Effects of background noise on the response of rat and cat motoneurones to excitatory current transients

1. We studied the responses of rat hypoglossal motoneurones to excitatory current transients (ECTs) using a brainstem slice preparation. Steady, repetitive discharge at rates of 12-25 impulses s-1 was elicited from the motoneurones by injecting long (40 s) steps of constant current. Poisson trains of the ECTs were superimposed on these steps. The effects of additional synaptic noise was simulated by adding a zero-mean random process to the stimuli. 2. We measured the effects of the ECTs on motoneurone discharge probability by compiling peristimulus time histograms (PSTHs) between the times of occurrence of the ECTs and the motoneurone spikes. The ECTs produced modulation of motoneurone discharge similar to that produced by excitatory postsynaptic currents. 3. The addition of noise altered the pattern of the motoneurone response to the current transients: both the amplitude and the area of the PSTH peaks decreased as the power of the superimposed noise was increased. Noise tended to reduce the efficacy of the ECTs, particularly when the motoneurones were firing at lower frequencies. Although noise also increased the firing frequency of the motoneurones slightly, the effects of noise on ECT efficacy did not simply result from noise-induced changes in mean firing rate. 4. A modified version of the experimental protocol was performed in lumbar motoneurones of intact, pentobarbitone-anaesthetized cats. These recordings yielded results similar to those obtained in rat hypoglossal motoneurones in vitro. 5. Our results suggest that the presence of concurrent synaptic inputs reduces the efficacy of any one input. The implications of this change in efficacy and the possible underlying mechanisms are discussed.

Experimental evaluation of input-output models of motoneuron discharge

1. We measured the modulation of the background firing rate of cat spinal motoneurons produced by simulated, repetitive excitatory postsynaptic potentials (EPSPs) to test the accuracy of several proposed motoneuron input-output functions. Rhythmic discharge was elicited in the motoneurons by injecting suprathreshold current steps 1-1.5 s in duration. On alternate trials, trains of short (0.5-5 ms) current pulses were superimposed on the current steps to stimulate the effects of trains of individual EPSPs. The increase in firing rate (delta F) due to the addition of the pulses was calculated as the difference in motoneuron discharge rate between trials with and without the superimposed pulse trains. 2. In the same motoneurons, we were able to study the effects of changes in pulse frequency, duration, and amplitude, as well as changes in the background discharge rate. A sublinear relationship between pulse rate and delta F was observed, with delta F rising relatively steeply with increasing pulse frequency at low pulse rates and saturating at high pulse rates. A similarly shaped relation was observed between delta F and pulse duration. In contrast, delta F generally increased in a greater than linear fashion with increasing pulse amplitude. 3. In previous studies we demonstrated that when a relatively constant synaptic input is produced by high-frequency synaptic activity, delta F is approximately equal to the product of the net synaptic current reaching the soma and the slope of the motoneuron's steady-state frequency-current (f-I) relation. In the present study, this input-output function consistently underestimated the observed delta F, particularly for low input rates, indicating that the transient current pulses are more effective in modulating motoneuron discharge than an equivalent amount of constant current. 4. Other investigators have proposed input-output functions derived from the relation between synaptic potential amplitude and the magnitude of the peak of a cross correlogram compiled from the discharge of the pre- and postsynaptic neurons. These functions consistently overestimated the observed delta F, particularly for high pulse rates. This overestimation may result in part from the fact that the effects of a synaptic potential (or current pulse) on postsynaptic discharge probability also include a period of decreased firing probability. Moreover, the cross correlation function may depend on the arrival rate of synaptic potentials (or current pulses). 5. Another proposed input-output function based on a simple threshold-crossing model of the motoneuron with a fixed spike threshold predicts firing rates that were often close to the observed delta F. However, the model did not reproduce the observed relations between delta F and input pulse rate or pulse duration. 6. The deficiencies of the basic threshold-crossing model may arise from the fact that it does not incorporate variations in membrane conductance and firing threshold that occur in real motoneurons. A more complete motoneuron model that incorporates both of these features was able to replicate the observed delta Fs associated with changes in input pulse frequency and duration.