Randall K. Powers

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.

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 motoneurones 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 motoneurones 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.

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.

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.

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 postspike 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.

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.

Intrinsic Properties of Motoneurons

The following is a brief review of the intrinsic properties of motoneurons that contribute to their recruitment and rate modulation. Our emphasis is on properties that may either accelerate or delay the onset of muscular fatigue. In general, intrinsic motoneuron properties are regulated in a way that minimizes energy expenditure. The correlation of recruitment threshold with motoneuron type ensures that the most fatigable motor units are reserved for the most forceful contractions. The variation in minimum firing rates arising from variations in AHP characteristics ensures that motoneurons begin to fire at rates that are matched to the force producing characteristics of their muscle units. Further, it is possible that spike-frequency adaptation contributes to optimization of the tension (force)-firing frequency (T-f) transform of individual motor units.

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 units 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.

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.