Dynamics of a random neural network with synaptic depression

Phase changes in neuronal postsynaptic spiking due to short term plasticity

In the brain, the postsynaptic response of a neuron to time-varying inputs is determined by the interaction of presynaptic spike times with the short-term dynamics of each synapse. For a neuron driven by stochastic synapses, synaptic depression results in a quite different postsynaptic response to a large population input depending on how correlated in time the spikes across individual synapses are. Here we show using both simulations and mathematical analysis that not only the rate but the phase of the postsynaptic response to a rhythmic population input varies as a function of synaptic dynamics and synaptic configuration. Resultant phase leads may compensate for transmission delays and be predictive of rhythmic changes. This could be particularly important for sensory processing and motor rhythm generation in the nervous system.

The synapses that connect neurons in the brain are far from being simple relay points that pass a signal from one neuron to another. There is now much evidence that long term changes in the strength of such connections, which determines the amplitude of the received signal, underpin learning and memory in the brain. However, signal amplitudes also fluctuate on fast time scales of milliseconds to seconds due to a variety of particular presynaptic mechanisms that regulate the release of neurotransmitter from the presynaptic terminal. Understanding the signal filtering properties of this short-term plasticity (STP) is a challenge and requires theoretical models. Aspects such as rate filtering and information transfer have been studied. Here we explore the effects of STP on the phase of a receiving neuron’s response to oscillating input and show that short-term depression can result in a frequency-dependent phase lead. This may be particularly important in the processing of rhythmic visual and auditory signals and producing rhythmic motor outputs.

Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model

We have studied neuronal synchronisation in a random network of adaptive exponential integrate-and-fire neurons. We study how spiking or bursting synchronous behaviour appears as a function of the coupling strength and the probability of connections, by constructing parameter spaces that identify these synchronous behaviours from measurements of the inter-spike interval and the calculation of the order parameter. Moreover, we verify the robustness of synchronisation by applying an external perturbation to each neuron. The simulations show that bursting synchronisation is more robust than spike synchronisation.

Review : Robustness and Self-regulation in the Production of Neural Activity by Developing Networks

Spontaneous activity is an important regulator of network development throughout the nervous system. Activity produced in different parts of the developing nervous system shares many features, which suggests that it does not depend on the detailed architecture of developing networks but rather on their common properties. Insights into the mechanisms responsible for generating spontaneous activity have come from recent studies of the spinal cord. Developing spinal networks are hyperexcitable and their immature syn apses are subject to activity-dependent synaptic depression. The conjunction of these properties, which may be common throughout the developing nervous system, is responsible for the spontaneous, episodic activity expressed by spinal networks. These properties endow developing spinal networks with an extremely robust mechanism for generating spontaneous activity that is resistant to major pharmacological and surgical per turbations. NEUROSCIENTIST 5:41-47, 1999

Short-Term Synaptic Plasticity at Interneuronal Synapses Could Sculpt Rhythmic Motor Patterns

The output of a neuronal network depends on the organization and functional properties of its component cells and synapses. While the characterization of synaptic properties has lagged cellular analyses, a potentially important aspect in rhythmically active networks is how network synapses affect, and are in turn affected by, network activity. This could lead to a potential circular interaction where short-term activity-dependent synaptic plasticity is both influenced by and influences the network output. The analysis of synaptic plasticity in the lamprey locomotor network was extended here to characterize the short-term plasticity of connections between network interneurons and to try and address its potential network role. Paired recordings from identified interneurons in quiescent networks showed synapse-specific synaptic properties and plasticity that supported the presence of two hemisegmental groups that could influence bursting: depression in an excitatory interneuron group, and facilitation in an inhibitory feedback circuit. The influence of activity-dependent synaptic plasticity on network activity was investigated experimentally by changing Ringer Ca(2+) levels, and in a simple computer model. A potential caveat of the experimental analyses was that changes in Ringer Ca(2+) (and compensatory adjustments in Mg(2+) in some cases) could alter several other cellular and synaptic properties. Several of these properties were tested, and while there was some variability, these were not usually significantly affected by the Ringer changes. The experimental analyses suggested that depression of excitatory inputs had the strongest influence on the patterning of network activity. The simulation supported a role for this effect, and also suggested that the inhibitory facilitating group could modulate the influence of the excitatory synaptic depression. Short-term activity-dependent synaptic plasticity has not generally been considered in spinal cord models. These results provide further evidence for short-term plasticity between locomotor network interneurons. As this plasticity could influence the patterning of the network output it should be considered as a potential functional component of spinal cord networks.

Interplay between Subthreshold Oscillations and Depressing Synapses in Single Neurons

In this paper we analyze the interplay between the subthreshold oscillations of a single neuron conductance-based model and the short-term plasticity of a dynamic synapse with a depressing mechanism. In previous research, the computational properties of subthreshold oscillations and dynamic synapses have been studied separately. Our results show that dynamic synapses can influence different aspects of the dynamics of neuronal subthreshold oscillations. Factors such as maximum hyperpolarization level, oscillation amplitude and frequency or the resulting firing threshold are modulated by synaptic depression, which can even make subthreshold oscillations disappear. This influence reshapes the postsynaptic neuron’s resonant properties arising from subthreshold oscillations and leads to specific input/output relations. We also study the neuron’s response to another simultaneous input in the context of this modulation, and show a distinct contextual processing as a function of the depression, in particular for detection of signals through weak synapses. Intrinsic oscillations dynamics can be combined with the characteristic time scale of the modulatory input received by a dynamic synapse to build cost-effective cell/channel-specific information discrimination mechanisms, beyond simple resonances. In this regard, we discuss the functional implications of synaptic depression modulation on intrinsic subthreshold dynamics.

Riluzole-induced oscillations in spinal networks

We previously showed in dissociated cultures of fetal rat spinal cord that disinhibition-induced bursting is based on intrinsic spiking, network recruitment, and a network refractory period after the bursts. A persistent sodium current (I(NaP)) underlies intrinsic spiking, which, by recurrent excitation, generates the bursting activity. Although full blockade of I(NaP) with riluzole disrupts such bursting, the present study shows that partial blockade of I(NaP) with low doses of riluzole maintains bursting activity with unchanged burst rate and burst duration. More important, low doses of riluzole turned bursts composed of persistent activity into bursts composed of oscillatory activity at around 5 Hz. In a search for the mechanisms underlying the generation of such intraburst oscillations, we found that activity-dependent synaptic depression was not changed with low doses of riluzole. On the other hand, low doses of riluzole strongly increased spike-frequency adaptation and led to early depolarization block when bursts were simulated by injecting long current pulses into single neurons in the absence of fast synaptic transmission. Phenytoin is another I(NaP) blocker. When applied in doses that reduced intrinsic activity by 80-90%, as did low doses of riluzole, it had no effect either on spike-frequency adaptation or on depolarization block. Nor did phenytoin induce intraburst oscillations after disinhibition. A theoretical model incorporating a depolarization block mechanism could reproduce the generation of intraburst oscillations at the network level. From these findings we conclude that riluzole-induced intraburst oscillations are a network-driven phenomenon whose major accommodation mechanism is depolarization block arising from strong sodium channel inactivation.

Timing of network synchronization by refractory mechanisms

Even without active pacemaker mechanisms, temporally patterned synchronization of neural network activity can emerge spontaneously and is involved in neural development and information processing. Generation of spontaneous synchronization is thought to arise as an alternating sequence between a state of elevated excitation followed by a period of quiescence associated with neuronal and/or synaptic refractoriness. However, the cellular factors controlling recruitment and timing of synchronized events have remained difficult to specify, although the specific temporal pattern of spontaneous rhythmogenesis determines its impact on developmental processes. We studied spontaneous synchronization in a model of 600-1,000 integrate-and-fire neurons interconnected with a probability of 5-30%. One-third of neurons generated spontaneous discharges and provided a background of intrinsic activity to the network. The heterogeneity and random coupling of these neurons maintained this background activity asynchronous. Refractoriness was modeled either by use-dependent synaptic depression or by cellular afterhyperpolarization. In both cases, the recruitment of neurons into spontaneous synchronized discharges was determined by the interplay of refractory mechanisms with stochastic fluctuations in background activity. Subgroups of easily recruitable neurons served as amplifiers of these fluctuations, thereby initiating a cascade-like recruitment of neurons ("avalanche effect"). In contrast, timing depended on the precise implementation of neuronal refractoriness and synaptic connectivity. With synaptic depression, neuronal synchronization always occurred stochastically, whereas with cellular afterhyperpolarization, stochastic turned into periodic behavior with increasing synaptic strength. These results associate the type of refractory mechanism with the temporal statistics and the mechanism of synchronization, thereby providing a framework for differentiating between cellular mechanisms of spontaneous rhythmogenesis.

Short-term depression at primary afferent synapses in rat substantia gelatinosa region

Short-term synaptic depression is a widespread and predominant mechanism underlying the process of neural information. To study the short-term depression at primary afferent synapses between Adelta fibers and substantia gelatinosa (SG) neurons in the spinal cord, transverse spinal cord slices with dorsal root attached were made from young rats. With whole-cell voltage-clamp method, Adelta-fiber elicited excitatory post-synaptic currents (EPSCs) were recorded from SG neurons visualized by infrared microscope. Using the normalized peak amplitudes of EPSCs, the existence of short-term depression was examined at all six stimulus frequencies ranging from 0.5 to 20 Hz. Both paired-pulse and steady-state depressions became greater with the increasing stimulus frequency. External calcium concentration could significantly affect the degrees of paired-pulse and steady-state depressions, with paired-pulse depression more affected. Application of NMDA receptor antagonist had no significant effect on this depression. These results indicated that short-term synaptic depression exists at primary afferent neurotransmission in spinal cord and results from the presynaptic reduction in the number of quanta of transmitter released by impulses.

Convulsant and anticonvulsant effects on spontaneous CA3 population bursts

This paper analyzes the effects of a convulsant and an anticonvulsant manipulation on spontaneous bursts in CA3 pyramidal cells in the in vitro slice preparation under conditions of low (3.3 mM [K(+)](o)) and high (8.5 mM [K(+)](o)) burst probability. When burst probability was low, the anticonvulsant, pentobarbital, produced the anticipated effects: the burst duration decreased and interburst interval increased. However, when burst probability was high, both anticonvulsant and convulsant manipulations decreased the interburst interval and the burst duration. To reconcile these findings, we utilized a model in which CA3 burst duration is limited by activity-dependent depression of CA3 excitatory recurrent collateral synapses and the interburst interval is determined by the time required to recover from this depression. We defined the burst end threshold as the level of synaptic depression at which bursts terminate, and the burst start threshold as the level of synaptic depression at which burst initiation is possible. Synapses were considered to oscillate between these thresholds. When average burst duration and interburst interval data were fit using this model, the paradoxically similar effects of the convulsant and anticonvulsant manipulations could be quantitatively interpreted. The convulsant maneuver decreased both the burst start and end thresholds. The start threshold decreased more than the end threshold, so that the thresholds were closer together. This decreased the time needed to transition from one threshold to the other, i.e., the interburst interval and burst duration. The anticonvulsant manipulation primarily increased the burst end threshold. This also decreased the difference between thresholds, decreasing both interburst interval and burst duration. This model resolves the paradoxical proconvulsant effects of pentobarbital in the CA3 preparation and provides insights into the effects of anticonvulsants on epileptiform discharges in the human EEG.

Associative memory with dynamic synapses

We have examined a role of dynamic synapses in the stochastic Hopfield-like network behavior. Our results demonstrate an appearance of a novel phase characterized by quick transitions from one memory state to another. The network is able to retrieve memorized patterns corresponding to classical ferromagnetic states but switches between memorized patterns with an intermittent type of behavior. This phenomenon might reflect the flexibility of real neural systems and their readiness to receive and respond to novel and changing external stimuli.

Physiological effects of sustained blockade of excitatory synaptic transmission on spontaneously active developing neuronal networks--an inquiry into the reciprocal linkage between intrinsic biorhythms and neuroplasticity in early ontogeny

Spontaneous bioelectric activity (SBA) taking the form of extracellularly recorded spike trains (SBA) has been quantitatively analyzed in organotypic neonatal rat visual cortex explants at different ages in vitro, and the effects investigated of both short- and long-term pharmacological suppression of glutamatergic synaptic transmission. In the presence of APV, a selective NMDA receptor blocker, 1-2- (but not 3-)week-old cultures recovered their previous SBA levels in a matter of hours, although in imitation of the acute effect of the GABAergic inhibitor picrotoxin (PTX), bursts of action potentials were abnormally short and intense. Cultures treated either overnight or chronically for 1-3 weeks with APV, the AMPA/kainate receptor blocker DNQX, or a combination of the two were found to display very different abnormalities in their firing patterns. NMDA receptor blockade for 3 weeks produced the most severe deviations from control SBA, consisting of greatly prolonged and intensified burst firing with a strong tendency to be broken up into trains of shorter spike clusters. This pattern was most closely approximated by acute GABAergic disinhibition in cultures of the same age, but this latter treatment also differed in several respects from the chronic-APV effect. In 2-week-old explants, in contrast, it was the APV+DNQX treated group which showed the most exaggerated spike bursts. Functional maturation of neocortical networks, therefore, may specifically require NMDA receptor activation (not merely a high level of neuronal firing) which initially is driven by endogenous rather than afferent evoked bioelectric activity. Putative cellular mechanisms are discussed in the context of a thorough review of the extensive but scattered literature relating activity-dependent brain development to spontaneous neuronal firing patterns.

Mechanisms controlling bursting activity induced by disinhibition in spinal cord networks

Disinhibition reliably induces regular synchronous bursting in networks of spinal interneurons in culture as well as in the intact spinal cord. We have combined extracellular multisite recording using multielectrode arrays with whole cell recordings to investigate the mechanisms involved in bursting in organotypic and dissociated cultures from the spinal cords of embryonic rats. Network bursts induced depolarization and spikes in single neurons, which were mediated by recurrent excitation through glutamatergic synaptic transmission. When such transmission was blocked, bursting ceased. However, tonic spiking persisted in some of the neurons. In such neurons intrinsic spiking was suppressed following the bursts and reappeared in the intervals after several seconds. The suppression of intrinsic spiking could be reproduced when, in the absence of fast synaptic transmission, bursts were mimicked by the injection of current pulses. Intrinsic spiking was also suppressed by a slight hyperpolarization. An afterhyperpolarization following the bursts was found in roughly half of the neurons. These afterhyperpolarizations were combined with a decrease in excitability. No evidence for the involvement of synaptic depletion or receptor desensitization in bursting was found, because neither the rate nor the size of spontaneous excitatory postsynaptic currents were decreased following the bursts. Extracellular stimuli paced bursts at low frequencies, but failed to induce bursts when applied too soon after the last burst. Altogether these results suggest that bursting in spinal cultures is mainly based on intrinsic spiking in some neurons, recurrent excitation of the network and auto-regulation of neuronal excitability.

The generation of rhythmic activity in dissociated cultures of rat spinal cord

Locomotion in vertebrates is controlled by central pattern generators in the spinal cord. The roles of specific network architecture and neuronal properties in rhythm generation by such spinal networks are not fully understood. We have used multisite recording from dissociated cultures of embryonic rat spinal cord grown on multielectrode arrays to investigate the patterns of spontaneous activity in randomised spinal networks. We were able to induce similar patterns of rhythmic activity in dissociated cultures as in slice cultures, although not with the same reliability and not always with the same protocols. The most reliable rhythmic activity was induced when a partial disinhibition of the network was combined with an increase in neuronal excitability, suggesting that both recurrent synaptic excitation and neuronal excitability contribute to rhythmogenesis. During rhythmic activity, bursts started at several sites and propagated in variable ways. However, the predominant propagation patterns were independent of the protocol used to induce rhythmic activity. When synaptic transmission was blocked by CNQX, APV, strychnine and bicuculline, asynchronous low-rate activity persisted at approximately 50% of the electrodes and approximately 70% of the sites of burst initiation. Following the bursts, the activity in the interval was transiently suppressed below the level of intrinsic activity. The degree of suppression was proportional to the amount of activity in the preceding burst. From these findings we conclude that rhythmic activity in spinal cultures is controlled by the interplay of intrinsic neuronal activity and recurrent excitation in neuronal networks without the need for a specific architecture.

Spatiotemporal characterization of rhythmic activity in rat spinal cord slice cultures

Rat spinal networks generate a spontaneous rhythmic output directed to motoneurons under conditions of increased excitation or of disinhibition. It is not known whether these differently induced rhythms are produced by a common rhythm generator. To investigate the generation and the propagation of rhythmic activity in spinal networks, recordings need to be made from many neurons simultaneously. Therefore extracellular multisite recording was performed in slice cultures of embryonic rat spinal cords grown on multielectrode arrays. In these organotypic cultures most of the spontaneous neural activity was nearly synchronized. Waves of activity spread from a source to most of the network within 35-85 ms and died out after a further 30-400 ms. Such activity waves induced the contraction of cocultured muscle fibres. Several activity waves could be grouped into aperiodic bursts. Disinhibition with bicuculline and strychnine or increased excitability with high K(+) or low Mg(2+) solutions could induce periodic bursting with bursts consisting of one or several activity waves. Whilst the duration and period of activity waves were similar for all protocols, the duration and period of bursts were longer during disinhibition than during increased excitation. The sources of bursting activity were mainly situated ventrally on both sides of the central fissure. The pathways of network recruitment from one source were variable between bursts, but they showed on average no systematic differences between the protocols. These spatiotemporal similarities under conditions of increased excitation and of disinhibition suggest a common spinal network for both types of rhythmic activity.

Post-Episode Depression of GABAergic Transmission in Spinal Neurons of the Chick Embryo

Whole cell recordings were obtained from ventral horn neurons in spontaneously active spinal cords isolated from the chick embryo [ embryonic days 10 to 11 ( E10–E11)] to examine the post-episode depression of GABAergic transmission. Spontaneous activity occurred as recurrent, rhythmic episodes approximately 60 s in duration with 10- to 15-min quiescent inter-episode intervals. Current-clamp recording revealed that episodes were followed by a transient hyperpolarization (7 ± 1.2 mV, mean ± SE), which dissipated as a slow (0.5–1 mV/min) depolarization until the next episode. Local application of bicuculline 8 min after an episode hyperpolarized spinal neurons by 6 ± 0.8 mV and increased their input resistance by 13%, suggesting the involvement of GABAergic transmission. Gramicidin perforated-patch recordings showed that the GABAa reversal potential was above rest potential ( E GABAa = −29 ± 3 mV) and allowed estimation of the physiological intracellular [Cl−] = 50 mM. In whole cell configuration (with physiological electrode [Cl−]), two distinct types of endogenous GABAergic currents ( I GABAa) were found during the inter-episode interval. The first comprised TTX-resistant, asynchronous miniature postsynaptic currents (mPSCs), an indicator of quantal GABA release (up to 42% of total mPSCs). The second (tonic I GABAa) was complimentary to the slow membrane depolarization and may arise from persistent activation of extrasynaptic GABAa receptors. We estimate that approximately 10 postsynaptic channels are activated by a single quantum of GABA release during an mPSC and that about 30 extrasynaptic GABAa channels are required for generation of the tonic I GABAa in ventral horn neurons. We investigated the post-episode depression of I GABAa by local application of GABA or isoguvacine (100 μM, for 10–30 s) applied before and after an episode at holding potentials ( V hold) −60 mV. The amplitude of the evoked I GABA was compared after clamping the cell during the episode at one of three different V hold: −60 mV, below E GABAa resulting in Cl− efflux; −30 mV, close to E GABAa with minimal Cl− flux; and 0 mV, above E GABAa resulting in Cl− influx during the episode. The amplitude of the evoked I GABA changed according to the direction of Cl− flux during the episode: at −60 mV a 41% decrease, at −30 mV a 4% reduction, and at 0 mV a 19% increase. These post-episode changes were accompanied by shifts of E GABAa of −10, −1.2, and +7 mV, respectively. We conclude that redistribution of intracellular [Cl−] during spontaneous episodes is likely to be an important postsynaptic mechanism involved in the post-episode depression of GABAergic transmission in chick embryo spinal neurons.

Population dynamics of spiking neurons: fast transients, asynchronous states, and locking

An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate-and-fire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay, and a bifurcation diagram is derived. The response of a population of noisy integrate-and-fire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized"locked"solutions is analyzed.

Contrast adaptation and infomax in visual cortical neurons

In the primary visual cortex (V1) the contrast response function of many neurons saturates at high contrast and adapts depending on the visual stimulus. We propose that both effects - contrast saturation and adaptation - can be explained by a fast and a slow component in the synaptic dynamics. In our model the saturation is an effect of fast synaptic depression with a recovery time constant of about 200 ms. Fast synaptic depression leads to a contrast response function with a high gain for only a limited range of contrast values. Furthermore, we propose that slow adaptation of the transmitter release probability at the geniculocortical synapses is the underlying neural mechanism that accounts for contrast adaptation on a time scale of about 7 sec. For the functional role of contrast adaptation we make the hypothesis that it serves to achieve the best visual cortical representation of the geniculate input. This representation should maximize the mutual information between the cortical activity and the geniculocortical input by increasing the release probability in a low contrast environment. We derive an adaptation rule for the transmitter release probability based on this infomax principle. We show that changes in the transmitter release probability may compensate for changes in the variance of the geniculate inputs - an essential requirement for contrast adaptation. Also, we suggest that increasing the release probability in a low contrast environment is beneficial for signal extraction, because neurons remain sensitive only to an increase in the presynaptic activity if it is synchronous and, therefore, likely to be stimulus related. Our hypotheses are tested in numerical simulations of a network of integrate-and-fire neurons for one column of V1 using fast synaptic depression and slow synaptic adaptation. The simulations show that changing the synaptic release probability of the geniculocortical synapses is a better model for contrast adaptation than the adaptation of the synaptic weights: only in the case of changing the transmitter release probability does our model reproduce the experimental finding that the average membrane potential (DC component) adapts much more strongly than the stimulus modulated component (F1 component). In the case of changing the synaptic weights, however, the average membrane potential (DC) as well as the stimulus modulated component (F1 component) would adapt. Furthermore, changing the release probability at the recurrent cortical synapses cannot account for contrast adaptation, but could be responsible for establishing oscillatory activity often observed in recordings from visual cortical cells.

Tapping into spinal circuits to restore motor function

Motivated by the challenge of improving neuroprosthetic devices, the authors review current knowledge relating to harnessing the potential of spinal neural circuits, such as reflexes and pattern generators. If such spinal interneuronal circuits could be activated, they could provide the coordinated control of many muscles that is so complex to implement with a device that aims to address each participating muscle individually. The authors' goal is to identify candidate spinal circuits and areas of research that might open opportunities to effect control of human limbs through electrical activation of such circuits. David McCrea's discussion of the ways in which hindlimb reflexes in the cat modify motor activity may help in developing optimal strategies for functional neuromuscular stimulation (FNS), by using knowledge of how reflex actions can adapt to different conditions. Michael O'Donovan's discussion of the development of rhythmogenic networks in the chick embryo may provide clues to methods of generating rhythmic activity in the adult spinal cord. Serge Rossignol examines the spinal pattern generator for locomotion in cats, its trigger mechanisms, modulation and adaptation, and suggests how this knowledge can help guide therapeutic approaches in humans. Hugues Barbeau applies the work of Rossignol and others to locomotor training in human subjects who have suffered spinal cord injury (SCI) with incomplete motor function loss (IMFL). Michel Lemay and Warren Grill discuss some of the technical challenges that must be addressed by engineers to implement a neuroprosthesis using electrical stimulation of the spinal cord, particularly the control issues that would have to be resolved.

Implications of a neural network model of early sensori-motor development for the field of developmental neurology

This paper reports on a neural network model for early sensori-motor development and on the possible implications of this research for our understanding and, eventually, treatment of motor disorders like cerebral palsy. We recapitulate the results we published in detail in a series of papers [1-4]. The neural circuits in the model self-organize on the basis of rhythmic activity spontaneously generated in the model. This indicates the importance of endogenously generated activity in the developing brain. We also show that afferent feed-back from the mechanical part of the model is easily incorporated in the neural part of the model. In this way the model acquires reflex-related properties which have long been demonstrated in man. In the discussion we relate these experimental findings to the variability concept from developmental neurology and show how variable motor performance is important for motor learning. We also discuss possible implications of our modelling effort for movement disorders, specifically spastic cerebral palsy.

The origin of spontaneous activity in developing networks of the vertebrate nervous system

Spontaneous neuronal activity has been detected in many parts of the developing vertebrate nervous system. Recent studies suggest that this activity depends on properties that are probably shared by all developing networks. Of particular importance is the high excitability of recurrently connected, developing networks and the presence of activity-induced transient depression of network excitability. In the spinal cord, it has been proposed that the interaction of these properties gives rise to spontaneous, periodic activity.

Mechanisms of spontaneous activity in the developing spinal cord and their relevance to locomotion

The isolated lumbosacral cord of the chick embryo generates spontaneous episodes of rhythmic activity. Muscle nerve recordings show that the discharge of sartorius (flexor) and femorotibialis (extensor) motoneurons alternates even though the motoneurons are depolarized simultaneously during each cycle. The alternation occurs because sartorius motoneuron firing is shunted or voltage-clamped by its synaptic drive at the time of peak femorotibialis discharge. Ablation experiments have identified a region dorsomedial to the lateral motor column that may be required for the alternation of sartorius and femorotibialis motoneurons. This region overlaps the location of interneurons activated by ventral root stimulation. Wholecell recordings from interneurons receiving short latency ventral root input indicate that they fire at an appropriate time to contribute to the cyclical pause in firing of sartorius motoneurons. Spontaneous activity was modeled by the interaction of three variables: network activity and two activity-dependent forms of network depression. A "slow" depression which regulates the occurrence of episodes and a "fast" depression that controls cycling during an episode. The model successfully predicts several aspects of spinal network behavior including spontaneous rhythmic activity and the recovery of network activity following blockade of excitatory synaptic transmission.

Mechanisms of spontaneous activity in developing spinal networks

Developing networks of the chick spinal cord become spontaneously active early in development and remain so until hatching. Experiments using an isolated preparation of the spinal cord have begun to reveal the mechanisms responsible for this activity. Whole-cell and optical recordings have shown that spinal neurons receive a rhythmic, depolarizing synaptic drive and experience rhythmic elevations of intracellular calcium during spontaneous episodes. Activity is expressed throughout the neuraxis and can be produced by different parts of the cord and by the isolated brain stem, suggesting that it does not depend upon the details of network architecture. Two factors appear to be particularly important for the production of endogenous activity. The first is the predominantly excitatory nature of developing synaptic connections, and the second is the presence of prolonged activity-dependent depression of network excitability. The interaction between high excitability and depression results in an equilibrium in which episodes are expressed periodically by the network. The mechanism of the rhythmic bursting within an episode is not understood, but it may be due to a "fast" form of network depression. Spontaneous embryonic activity has been shown to play a role in neuron and muscle development, but is probably not involved in the initial formation of connections between spinal neurons. It may be important in refining the initial connections, but this possibility remains to be explored.

Pattern generation by two coupled time-discrete neural networks with synaptic depression

Numerous animal behaviors, such as locomotion in vertebrates, are produced by rhythmic contractions that alternate between two muscle groups. The neuronal networks generating such alternate rhythmic activity are generally thought to rely on pacemaker cells or well-designed circuits consisting of inhibitory and excitatory neurons. However, experiments in organotypic cultures of embryonic rat spinal cord have shown that neuronal networks with purely excitatory and random connections may oscillate due to their synaptic depression, even without pacemaker cells. In this theoretical study, we investigate what happens if two such networks are symmetrically coupled by a small number of excitatory connections. We discuss a time-discrete mean-field model describing the average activity and the average synaptic depression of the two networks. Depending on the parameter values of the depression, the oscillations will be in phase, antiphase, quasiperiodic, or phase trapped. We put forward the hypothesis that pattern generators may rely on activity-dependent tuning of synaptic depression.

Activity in sparsely connected excitatory neural networks: effect of connectivity

The Nucleus Tractus Solitarius (NTS) of the brainstem contains a neural circuit with only excitatory connections displaying a spontaneous activity involved in the control of respiration. A model of a network with random connections is presented and is used to investigate a possible mechanism of spontaneous activity generation consisting of the amplification of a low-background activity by the excitatory connections. First, the steady states of the network model and its ability to amplify the activity are studied. Then, a low-background activity is introduced, and dynamics of simulated networks are examined. Low-tonic, slow-phasic and fast-tonic activities are successively observed when the mean number K of connections per neuron increases. The transition between the two first types of activity is progressive whereas the transition from slow-phasic to fast-tonic activity is sharp. Simulation results show that activities of low frequency can be obtained with the proposed mechanism of spontaneous activity generation only if the network connectivity is low.