A study and model of the role of the Renshaw cell in regulating the transient firing rate of the motoneuron

 This study sought to investigate the role of the Renshaw cell with respect to transient motoneuron firing. By studying the cat motoneuron and Renshaw cell, several low-order lumped parameter models were developed that simulate the known characteristics of the injected input current vs. firing rate. The neuron models in the Renshaw cell inhibition configuration were tuned to fit experimental data from cat motoneurons. Models included both linear versions and those with sigmoidal nonlinearities. Results of the simulation indicate that the motoneuron itself provides the adaptation seen in its firing rate and that the Renshaw cell’s role is primarily to fine-tune the motoneuron’s adaptation process. Received: 23 July 1993/Accepted in revised form: 9 February 1994     

Stochastic properties of motoneuron activity and the effect of muscular length

The activity of single motor units contributing to small tonic isometric contractions in human muscle at different muscular lengths was analyzed. The form of motor unit firing patterns shows that the interspike intervals compose independent sequences with about a 10% coefficient of variation and have a gamma distribution. The variability and the distribution shape curves show that as the mean interval decreases the variance also decreases and the interval density function becomes more symmetric. More significant is the fact that the form of the firing pattern remains unchanged when a motor unit has the same mean interval but with the muscle at different lengths. Comparison of these facts with experimental data from neuron models and cat motoneurons indicates that in the human the only relevant input-output relationship in motoneurons is that the net excitation adjusts the firing rate.     

Coerulospinal enhancement of repetitive firing with correlative changes in postspike afterhyperpolarization of cat spinal motoneurons

The present study was aimed at determining if inputs from the locus coeruleus (LC) have any effect on repetitive firing of ventral horn motoneurons in cats. In hindlimb flexor and extensor motoneurons stimulated intrasomatically with current below the threshold for repetitive discharges, added LC-evoked excitatory post-synaptic potentials (EPSPs) were consistently found to produce repetitive firing, suggesting a lowering in the repetitive firing threshold attributable to excitatory LC inputs. With those extensor motoneurons showing episodic, self-sustained firing, LC-EPSPs introduced during the quiescent period were capable of starting a continuous discharge with rhythmic frequencies higher than the spontaneous activity. In some of these cells, intracellularly applied hyperpolarizing current was able to stop the spontaneous discharges. Subsequently, LC stimuli were found to reinitiate repetitive discharges, thus counteracting the ongoing suppression of the motoneurons. Quantitative analysis of the single-spike afterhyperpolarization (AHP) indicated a consistent reduction in its amplitude and time course (duration, time-to-peak, half-decay time) for flexor and extensor motoneurons in response to LC conditioning stimuli. Present results suggest an excitatory LC action on the repetitive discharges of cat motoneurons accompanied by a concurrent decrease in the amplitude and time course of the single-spike AHPs.     

Sex differences in rabbit masseter motoneuron firing behavior

To evaluate whether sex differences in the proportions of fibers of different phenotypes in the masseter muscle might be the result of differences in the behavior of their motoneurons, we studied the firing patterns of masseter motoneurons in adult male and female rabbits. Activity in individual motoneurons was determined from high spatial resolution EMG recordings made during cortically evoked rhythmic activation of the masticatory muscles. Although some motoneurons could be said to fire according to slow-tonic or fast-phasic patterns, most did not. In both sexes a substantial range of median firing rates and median firing durations was found. In adult males, masseter motoneurons fired more rapidly than those recorded from adult females. No significant sex differences in motoneuron firing duration were found. These results are consistent with the hypothesis that androgen-induced differences in rabbit masseter muscle fiber phenotype are a reflection of differences in motoneuron firing rate. Whether this effect of androgen is directly upon the motoneurons or is the result of a response of muscle fibers to androgen remains to be investigated.     

Cross-connections coordinate postural motoneuron activity in the crayfish abdomen

Intracellular recordings and dye injections were used to examine mutual coupling among slow abdominal postural motoneurons in the 4th abdominal ganglion in crayfish (Procambarus clarkii). Intracellular current injection into one motoneuron altered the spike firing rate of some of its synergists. Depending on the polarity of the injected current, the premotor effect on the synergists was excitatory or inhibitory. The magnitude of the effect was intensity dependent. No dye coupling was found among the motoneurons following injection of Lucifer yellow. The morphological basis of the coupling was examined by differential filling of motoneuron pairs, one with horseradish peroxidase and the other with Lucifer yellow. The stained motoneurons were simultaneously visualized under light microscopy to determine the proximity of their differently colored dendrites. It was thus possible to locate the site of the presumed monosynaptic contacts between them. Combined physiological and morphological evidence suggests that these neurons are mutually coupled, forming part of an integrative system for abdominal posture control in crayfish.     

Gain modulation from background synaptic input

Gain modulation is a prominent feature of neuronal activity recorded in behaving animals, but the mechanism by which it occurs is unknown. By introducing a barrage of excitatory and inhibitory synaptic conductances that mimics conditions encountered in vivo into pyramidal neurons in slices of rat somatosensory cortex, we show that the gain of a neuronal response to excitatory drive can be modulated by varying the level of "background" synaptic input. Simultaneously increasing both excitatory and inhibitory background firing rates in a balanced manner results in a divisive gain modulation of the neuronal response without appreciable signal-independent increases in firing rate or spike-train variability. These results suggest that, within active cortical circuits, the overall level of synaptic input to a neuron acts as a gain control signal that modulates responsiveness to excitatory drive.     

Computer simulation study of the relationship between the profile of excitatory postsynaptic potential and stimulus-correlated motoneuron firing

This paper shows the results of computer simulation of changes in motoneuron (MN) firing evoked by a repetitively applied synaptic volley that consists of a single excitatory postsynaptic potential (EPSP). Spike trains produced by the threshold-crossing MN model were analyzed as experimental results. Various output functions were applied for analysis; the most useful was a peristimulus time histogram, a special modification of a raster plot and a peristimulus time frequencygram (PSTF). It has been shown that all functions complement each other in distinguishing between the genuine results evoked by the excitatory volley and the secondary results of the EPSP-evoked synchronization. The EPSP rising edge was best reproduced by the PSTF. However, whereas the EPSP rise time could be estimated quite accurately, especially for high EPSP amplitudes at high MN firing rates, the EPSP amplitude estimate was also influenced by factors unrelated to the synaptic volley, such as the afterhyperpolarization duration of the MN or the amplitude of synaptic noise, which cannot be directly assessed in human experiments. Thus, the attempts to scale any estimate of the EPSP amplitude in millivolts appear to be useless. The decaying phase of the EPSP cannot be reproduced accurately by any of the functions. For the short EPSPs, it is extinguished by the generation of an action potential and a subsequent decrease in the MN excitability. For longer EPSPs, it is inseparable from the secondary effects of synchronization. Thus, the methods aimed at extracting information about long-lasting and complex postsynaptic potentials from stimulus-correlated MN firing, should be refined, and the theoretical considerations checked in computer simulations.     

A compartmental model of an external urethral sphincter motoneuron of Onuf's nucleus

This article discusses a model of the electrical behavior of an external urethral sphincter motoneuron, based on morphological parameters like soma size, dendritic diameters and spatial dendritic configuration, and several electrical parameters. Because experimental data about the exact ion conductance mix of external urethral sphincter neurons is scarce, the gaps in knowledge about external urethral sphincter motoneurons were filled in with known data of alpha-motoneurons. The constructed compartmental model of motoneurons of Onuf's nucleus contains six voltage-dependent ionic conductances: a fast sodium and potassium conductance and an anomalous rectifier in the soma; a fast delayed rectifier type potassium conductance and a fast sodium conductance in the initial axon segment; an L-type calcium channel in the dendritic compartments. This paper considers the simulation of external urethral sphincter motoneuron responses to current injections that evoke bistable behavior. Simulations show self-sustained discharge following a depolarizing pulse through the microelectrode; the firing was subsequently terminated by a short hyperpolarizing pulse. This behavior is highly functional for neurons that have to exhibit prolonged activation during sphincter closure. In addition to these 'on' and 'off ' responses, we also observed a particular firing behavior in response to long-lasting triangular current pulses. When the depolarizing current was slowly increased and then decreased (triangular pulse) the firing frequency was higher during the descending phase than during the initial ascending phase.     

Neuronal firing properties and swimming motor patterns in young tadpoles of four amphibians: Xenopus, Rana, Bufo and Triturus

We have compared intrinsic firing properties of motoneurons with the way they fire during locomotion in young tadpoles of four species of amphibian. Xenopus motoneurons have the highest current threshold for spiking; most fire a single spike to depolarising current steps; all fire reliably once per cycle during fictive swimming. Xenopus motoneurons recorded with Cs⁺-filled microlelectrodes fire repetitively to current but still fire only once per swimming cycle. Rana, Bufo and Triturus motoneurons have lower current thresholds; most fire bursts of spikes to suprathreshold current but most do not fire reliably during swimming and most still fire only once (if at all) per cycle. We conclude that neuronal firing patterns during locomotion cannot reliably be predicted from intrinsic firing properties, and suggest the composition and form of the underlying synaptic input is more important. We also measured cycle period, ventral root burst duration, and longitudinal delay during fictive swimming. These basic swimming parameters range from relatively long in Rana to relatively short in Xenopus. By discounting differences in neuronal firing properties between the four species, we can start to relate differences in fictive swimming to differences in synaptic drive, particularly the strong electrotonic input seen only in Xenopus. Accepted: 27 January 1997     

Data processing in the cat motoneuron system: averaging functions and rate limitation

The variability in instantaneous frequency of cat motoneurons in response to various degrees of regularity and synchronization of input is used to examine several forms of data processing occurring in the cat motoneuron system. A theoretical basis is presented which distinguishes between spatial averaging and time averaging of information from muscle afferents and which suggests realizable experiments for assessing their relative strengths. The results of the experiments demonstrate spatial averaging to be a strong form of processing in the motoneuron system; time averaging is found to be much less so. Thus, temporal information is preserved to a greater extent by the motoneuron than is spatial information. Also, an inherent source of motoneuron variability is identified and linked with the process of rate limitation.     

Determination of the inter-spike times of neurons receiving randomly arriving post-synaptik potentials

Stein's model for a neuron receiving randomly arriving post-synaptic potentials is studied from an analytic viewpoint, using some recent results in the theory of first passage times for temporally homogeneous Markov processes. The case when the only input is excitatory can be treated exactly. It is shown that the moments of the firing time are guaranteed to be finite so that the differential-difference equation for the expectation (and higher moments) of the time for the membrane potential to first reach threshold from resting level can be written down. Analytic solutions are obtained in a number of cases with main emphasis on the case when the threshold is twice the epsp magnitude. An invariance principie is formulated wherein at a given mean input frequency and for a given decay parameter, the distribution of firing times depends only on the ratio of threshld to epsp magnitude. For the case where this ratio is two, the variation in the mean discharge rate is obtained as a function of mean input frequency. The results are compared with the experimental data for the Poisson monosynaptic excitation of cat motoneurons by Redmanet al. Agreement between theoretical and experimental values is excellent at input frequencies near 102 sec^-1, and theory underestimates the firing rate below that input frequency. Reasons for the discrepancy are discussed at length including the uncertainties in the neuronal parameters and the dependence of epsp magnitude on mean input frequency. The problem of including an inhibitory input process together with excitation is treated by an approximation procedure when the inhibition is considerably weaker than the excitation. At the input frequency investigated it is shown that when inhibition “half as weak” as the excitation occurs, the mean discharge frequency is approximately halved. In the final section a method of estimating neuronal parameters from the moments of the experimental inter-spike time distribution is outlined.     

Improved neuronal models for studying neural networks

Previous neuronal models used for the study of neural networks are considered. Equations are developed for a model which includes: 1) a normalized range of firing rates with decreased sensitivity at large excitatory or large inhibitory input levels, 2) a single rate constant for the increase in firing rate following step changes in the input, 3) one or more rate constants, as required to fit experimental data for the adaptation of firing rates to maintained inputs. Computed responses compare well with the types of neuronal responses observed experimentally. Depending on the parameters, overdamped increases and decreases, damped oscillatory or maintained oscillatory changes in firing rate are observed to step changes in the input. The integrodifferential equations describing the neuronal models can be represented by a set of first-order differential equations. Steady-state solutions for these equations can be obtained for constant inputs, as well as the stability of the solutions to small perturbations. The linear frequency response function is derived for sufficiently small time-varying inputs. The linear responses are also compared with the computed solutions for larger non-linear responses.     

Generation of locomotion rhythms without inhibition in vertebrates: the search for pacemaker neurons

Locomotion rhythms are thought to be generated by neurons in the central-pattern-generator (CPG) circuit in the spinal cord. Synaptic connections in the CPG and pacemaker properties in certain CPG neurons, both may contribute to generation of the rhythms. In the half-center model proposed by Graham Brown a century ago, reciprocal inhibition plays a critical role. However, in all vertebrate preparations examined, rhythmic motor bursts can be induced when inhibition is blocked in the spinal cord. Without inhibition, neuronal pacemaker properties may become more important in generation of the rhythms. Pacemaker properties have been found in motoneurons and some premotor interneurons in different vertebrates and they can be dependent on N-Methyl-d-aspartate (NMDA) receptors (NMDAR) or rely on other ionic currents like persistent inward currents. In the swimming circuit of the hatchling Xenopus tadpole, there is substantial evidence that emergent network properties can give rise to swimming rhythms. During fictive swimming, excitatory interneurons (dINs) in the caudal hindbrain fire earliest on each swimming cycle and their spikes drive the firing of other CPG neurons. Regenerative dIN firing itself relies on reciprocal inhibition and background excitation. We now find that the activation of NMDARs can change dINs from firing singly at rest to current injection to firing repetitively at swimming frequencies. When action potentials are blocked, some intrinsic membrane potential oscillations at about 10 Hz are revealed, which may underlie repetitive dIN firing during NMDAR activation. In confirmation of this, dIN repetitive firing persists in NMDA when synaptic transmission is blocked by Cd(2+). When inhibition is blocked, only dINs and motoneurons are functional in the spinal circuit. We propose that the conditional intrinsic NMDAR-dependent pacemaker firing of dINs can drive the production of swimming-like rhythms without the participation of inhibitory neurotransmission.     

Neural spike generator entrainment by regularly spaced synaptic input

 It has been known for 30 years that the output of a repetitively firing neuron or pacemaker can be synchronized (locked) to regularly spaced inhibitory or excitatory postsynaptic input potentials. Conditions for stable locking have been determined mathematically, demonstrated in computer simulation, and locking has been observed in vivo. We have developed a neural spike generator circuit model which exhibits stable locking to externally derived simulated inhibitory or excitatory post-synaptic inputs. Conditions for stable 1 : 1 lock, in which pacemaker output frequency matches that of the periodic input, are derived. These take the form of expressions for stable delay and convergence factor which incorporate known or measurable parameters of the circuit model. The expressions have been evaluated and shown to compare satisfactorily with experimental observations of locking by our circuit model. Received: 28 March 1996 / Accepted in revised form: 18 February 1997     

Attentional modulation of firing rate and synchrony in a model cortical network

The response of a neuron in the visual cortex to stimuli of different contrast placed in its receptive field is commonly characterized using the contrast response curve. When attention is directed into the receptive field of a V4 neuron, its contrast response curve is shifted to lower contrast values (Reynolds et al., 2000). The neuron will thus be able to respond to weaker stimuli than it responded to without attention. Attention also increases the coherence between neurons responding to the same stimulus (Fries et al., 2001). We studied how the firing rate and synchrony of a densely interconnected cortical network varied with contrast and how they were modulated by attention. The changes in contrast and attention were modeled as changes in driving current to the network neurons. We found that an increased driving current to the excitatory neurons increased the overall firing rate of the network, whereas variation of the driving current to inhibitory neurons modulated the synchrony of the network. We explain the synchrony modulation in terms of a locking phenomenon during which the ratio of excitatory to inhibitory firing rates is approximately constant for a range of driving current values. We explored the hypothesis that contrast is represented primarily as a drive to the excitatory neurons, whereas attention corresponds to a reduction in driving current to the inhibitory neurons. Using this hypothesis, the model reproduces the following experimental observations: (1) the firing rate of the excitatory neurons increases with contrast; (2) for high contrast stimuli, the firing rate saturates and the network synchronizes; (3) attention shifts the contrast response curve to lower contrast values; (4) attention leads to stronger synchronization that starts at a lower value of the contrast compared with the attend-away condition. In addition, it predicts that attention increases the delay between the inhibitory and excitatory synchronous volleys produced by the network, allowing the stimulus to recruit more downstream neurons. Action Editor: David Golomb     

Synchronization and sensitivity enhancement of the Hodgkin-Huxley neurons due to inhibitory inputs

Recent experimental results imply that inhibitory postsynaptic potentials can play a functional role in realizing synchronization of neuronal firing in the brain. In order to examine the relation between inhibition and synchronous firing of neurons theoretically, we analyze possible effects of synchronization and sensitivity enhancement caused by inhibitory inputs to neurons with a biologically realistic model of the Hodgkin-Huxley equations. The result shows that, after an inhibitory spike, the firing probability of a single postsynaptic neuron exposed to random excitatory background activity oscillates with time. The oscillation of the firing probability can be related to synchronous firing of neurons receiving an inhibitory spike simultaneously. Further, we show that when an inhibitory spike input precedes an excitatory spike input, the presence of such preceding inhibition raises the firing probability peak of the neuron after the excitatory input. The result indicates that an inhibitory spike input can enhance the sensitivity of the postsynaptic neuron to the following excitatory spike input. Two neural network models based on these effects on postsynaptic neurons caused by inhibitory inputs are proposed to demonstrate possible mechanisms of detecting particular spatiotemporal spike patterns. Received: 15 April 1999 /Accepted in revised form: 25 November 1999     

Relationship between the discharge rate of a firing motoneuron and the effectiveness of excitatory la afferent volleys in man

The H-reflex was evoked after producing regular unit firing in the flexor carpi ulnaris set up by moderate voluntary isometric muscular contraction. The firing index was used to quantify the effectiveness of the monosynaptic afferent signal traveling to the firing motoneuron. An analysis was made of the 3.3–16.0 spikes/sec firing range characteristic of naturally occurring muscular contraction. Effectiveness of afferent signals for motor units in the "fast" muscles under study were found to depend on motoneuronal background firing rate; the former declined as the latter rose, as previously discovered during research into "slow" soleus muscle units [2]. Afferent signals were most effective for motoneurons belonging to the "fast" muscles over the entire range of firing rates. It was found from analyzing afferent signal efficacy in relation to its point of occurrence within the interspike interval that variations in motoneuronal excitability within this interval are the reason for this relationship.Institute for Research into Information Transmission, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 19, No. 5, pp. 595–600, September–October, 1987.