Topology selection by chaotic neurons of a pyloric central pattern generator

The pyloric Central Pattern Generator (CPG) in the lobster has an architecture in which every neuron receives at least one connection from another member of the CPG. We call this a "non-open" network topology. An "open" topology, where at least one neuron does not receive synapses from any other CPG member, is found neither in the pyloric nor in the gastric mill CPG. Here we investigate a possible reason for this topological structure using the ability to perform a biologically functional task as a measure of the efficacy of the network. When the CPG is composed of model neurons that exhibit regular membrane voltage oscillations, open topologies are as able to maximize this functionality as non-open topologies. When we replace these models by neurons which exhibit chaotic membrane voltage oscillations, the functional criterion selects non-open topologies. As isolated neurons from invertebrate CPGs are known in some cases to undergo chaotic oscillations, this suggests that there is a biological basis for the class of non-open network topologies that we observe.     

Background sodium current stabilizes bursting in respiratory pacemaker neurons

Endogenous pacemaker properties have been proposed to generate rhythmic activity underlying many behaviors including respiration. For pacemakers to generate regenerative bursting, background currents maintain their membrane potential (Vm) within a range where bi-stable properties are expressed, thereby stabilizing rhythmogenesis. We previously found that the baseline Vm of respiratory pacemakers is stabilized against hyperpolarizing shifts in their Vm. In response to prolonged hyperpolarizing current injection synaptically isolated respiratory pacemakers steadily depolarize and resume bursting, suggesting a stabilizing background current is involved. What is the ionic basis of this background current in respiratory pacemakers? Here we demonstrate that in low-[Na(+)](o) ACSF, synaptically isolated respiratory pacemakers hyperpolarized and remained outside the bursting window, but could burst upon depolarizing current injection. These data suggest that pacemakers possess a background sodium current that is necessary to bring their Vm into a bursting range. Low-[Na(+)](o) ACSF also abolished the depolarizing shift evoked during prolonged hyperpolarizing current injection, and bursting did not resume. This depolarizing shift persisted in the presence of I(h)-current blockers, but was abolished in tetrodotoxin. Although, under control conditions, the Vm of synaptically isolated respiratory pacemaker neurons was not significantly affected when [K(+)](o) was changed from 3 to 8 mM, the Vm is altered when [K(+)](o) was raised in low-[Na(+)](o) ACSF. Thus, current-clamp studies suggest that respiratory pacemaker neurons possess a background sodium current that maintains their membrane potential within a range where they express bursting, thereby stabilizing rhythmogenesis.     

Axonal contribution to subthreshold currents inaplysia bursting pacemaker neurons

The contribution of axonal activity to the ionic currents which generate bursting pacemaker activity was studied by using the two-electrode voltage-clamp technique in Aplysia bursting neuron somata in conjunction with intraaxonal voltage recordings. Depolarizing voltage-clamp pulses applied to bursting cell somata triggered axonal action potentials. The voltage-clamp current recording exhibited transient inward current "notches" corresponding to each of the axonal spikes. The addition of 50 microM tetrodotoxin (TTX) to the bathing medium blocked the fast axonal spikes and current notches, revealing a slower axonal spike which was blocked by the replacement of external Ca2+ with Co2+. The inward current evoked by applying a depolarizing voltage-clamp pulse in the soma is distorted by the occurrence of the axonal Ca2+ spike. Elimination of the axonal spike, by injecting hyperpolarizing current into the axon, changes both the time course and the magnitude of the inward current. The axonal Ca2+ spikes are followed by a series of Ca2+-dependent afterpotentials: a rapid postspike hyperpolarization, a depolarizing afterpotential (DAP) and, finally, a long-lasting postburst hyperpolarization. The long-lasting hyperpolarization is not blocked by 50 mM external tetraethyl ammonium, an effective blocker of Ca2+-activated K+ current [IK(Ca)], and does not appear to reverse at EK. Hence, the axonal long-lasting hyperpolarization may not be due to IK(Ca). Somatic voltage-clamp pulses in bursting neurons are followed by a slow inward tail current, which is sometimes coincident with a DAP in the axon. In some cells, the amplitude of the slow inward tail current is greatly reduced if axonal spikes and DAPs are prevented by hyperpolarization of the axon, while, in other cells, elimination of axonal activity has little effect. Therefore, the slow inward tail current is not necessarily an artifact of poor voltage-clamp control over the axonal membrane potential but probably results from the activation of an ionic conductance mechanism located partly in the axon and partly in the soma.     

Respiratory pattern generator model using Ca++-induced Ca++ release in neurons shows both pacemaker and reciprocal network properties

There are two contradictory explanations for central respiratory rhythmogenesis. One suggests that respiratory rhythm emerges from interaction between inspiratory and expiratory neural semicenters that inhibit each other and thereby provide reciprocal rhythmic activity (Brown 1914). The other uses bursting pacemaker activity of individual neurons to produce the rhythm (Feldman and Cleland 1982). Hybrid models have been developed to reconcile these two seemingly conflicting mechanisms (Smith et al. 2000; Rybak et al. 2001). Here we report computer simulations that demonstrate a unified mechanism of the two types of oscillator. In the model, we use the interaction of Ca⁺⁺-dependent K⁺ channels (Mifflin et al. 1985) with Ca⁺⁺-induced Ca⁺⁺ release from intracellular stores (McPherson and Campbell 1993), which was recently revealed in neurons (Hernandez-Cruz et al. 1997; Mitra and Slaughter 2002a,b; Scornik et al. 2001). Our computations demonstrate that uncoupled neurons with these intracellular mechanisms show conditional pacemaker properties (Butera et al. 1999) when exposed to steady excitatory inputs. Adding weak inhibitory synapses (based on increased K⁺ conductivity) between two model neural pools surprisingly synchronizes the activity of both neural pools. As inhibitory synaptic connections between the two pools increase from zero to higher values, the model produces first dissociated pacemaker activity of individual neurons, then periodic synchronous bursts of all neurons (inspiratory and expiratory), and finally reciprocal rhythmic activity of the neural pools.     

A sodium leak current regulates pacemaker activity of adult central pattern generator neurons in Lymnaea stagnalis

The resting membrane potential of the pacemaker neurons is one of the essential mechanisms underlying rhythm generation. In this study, we described the biophysical properties of an uncharacterized channel (U-type channel) and investigated the role of the channel in the rhythmic activity of a respiratory pacemaker neuron and the respiratory behaviour in adult freshwater snail Lymnaea stagnalis. Our results show that the channel conducts an inward leak current carried by Na(+) (I(Leak-Na)). The I(Leak-Na) contributed to the resting membrane potential and was required for maintaining rhythmic action potential bursting activity of the identified pacemaker RPeD1 neurons. Partial knockdown of the U-type channel suppressed the aerial respiratory behaviour of the adult snail in vivo. These findings identified the Na(+) leak conductance via the U-type channel, likely a NALCN-like channel, as one of the fundamental mechanisms regulating rhythm activity of pacemaker neurons and respiratory behaviour in adult animals.     

Model predictions of the ionic mechanisms underlying the beating and bursting pacemaker characteristics of molluscan neurons

The general properties of the excitable membrane on molluscan pacemaker neurons can be described on the basis of a fair amount of experimental evidence available in the literature. The neuronal membrane exhibits under voltage clamp an initial inward current carried by both Na⁺ and Ca²⁺ ions, the time- and voltage-dependent characteristics of which are similar to that of other excitable structures. The conductance mechanism for the two ion species and the transport kinetics appear to be closely similar. The time course and amplitude of the delayed outward current carried by K⁺ ions shows a marked dependence on the membrane potential. Characteristic for the molluscan neurons is the existence of an additional fast transient outward current which is only activated by hyperpolarizing shifts from the membrane potential. A regular beating discharge over a wide range of frequencies can be predicted by making the assumption of a metabolically controlled driving of the Na⁺ conductance. Bursting pacemaker characteristics can be correctly simulated by the model if sinusoidal variations of an additional Na⁺ and Ca²⁺ conductances g _Na and g _Ca, and periodic variations of the K⁺ conductance g _K, governed by the known operation of a metabolic substrate cycle are introduced. The close approximation of experimentally observed impulse bursts requires that the actual inpulse-frequency and the amplitude of the after-spike hyperpolarization are determined by the temporal pattern of g _Na, while the spike amplitude is controlled by g _Na which (although of similar time course) is lagging in phase behing g _Na. The periodic changes in additional K⁺ conductance g _K, are responsible for burst termination and the changes in inter-burst interval, to the effect that spike doublets, triplets and multi-spike bursts can be simulated by a suitable choice for the time characteristics of g _K. The model makes use of the finding that the Ca²⁺ inflow associated with a spike discharge actually activates g _K, so that large postburst hyperpolarizations can be obtained in high-frequency bursts.Supported by the Deutsche Forschungsgemeinschaft (Grant Ch 25/1)     

Firing pattern of bursting neurons under sinusoidal drive in mean-field modeling

Bursting has been observed in many sensory neurons, and is thought to be important in neural signaling, sleep, and some disorders of the brain. Bursting neurons have been studied via various types of conductance-based models at the single-neuron level. Important features of bursting have been reproduced by this type of model, but it is not certain how well the behavior of populations of bursting neurons can be represented solely by that of individual neurons. To study bursting neurons at the population level, a conductance-based model is incorporated into a mean-field model to yield a mean-field bursting model. The responses of the model to sinusoidal inputs are studied, showing that neurons with various different initial states are capable of phase-locked or intermittent firing, depending on their baseline voltage. Furthermore, depending on this voltage, the bursting frequency either slaves to the original unperturbed bursting frequency or approaches a steady value when the external driving frequency increases. Finally, use of white noise perturbations shows that the bursting frequency of the neurons remains the same even under a more general external stimulus.     

Linking dynamical and functional properties of intrinsically bursting neurons

Several studies have shown that bursting neurons can encode information in the number of spikes per burst: As the stimulus varies, so does the length of individual bursts.Therepresented stimuli, however, vary substantially among different sensory modalities and different neurons.The goal of this paper is to determine which kind of stimulus features can be encoded in burst length, and how those features depend on the mathematical properties of the underlying dynamical system.We show that the initiation and termination of each burst is triggered by specific stimulus features whose temporal characteristsics are determined by the types of bifurcations that initiate and terminate firing in each burst. As only a few bifurcations are possible, only a restricted number of encoded features exists. Here we focus specifically on describing parabolic, square-wave and elliptic bursters. We find that parabolic bursters, whose firing is initiated and terminated by saddle-node bifurcations, behave as prototypical integrators: Firing is triggered by depolarizing stimuli, and lasts for as long as excitation is prolonged. Elliptic bursters, contrastingly, constitute prototypical resonators, since both the initiating and terminating bifurcations possess well-defined oscillation time scales. Firing is therefore triggered by stimulus stretches of matching frequency and terminated by a phase-inversion in the oscillation. The behavior of square-wave bursters is somewhat intermediate, since they are triggered by a fold bifurcation of cycles of well-defined frequency but are terminated by a homoclinic bifurcation lacking an oscillating time scale. These correspondences show that stimulus selectivity is determined by the type of bifurcations. By testing several neuron models, we also demonstrate that additional biological properties that do not modify the bifurcation structure play a minor role in stimulus encoding. Moreover, we show that burst-length variability (and thereby, the capacity to transmit information) depends on a trade-off between the variance of the external signal driving the cell and the strength of the slow internal currents modulating bursts. Thus, our work explicitly links the computational properties of bursting neurons to the mathematical properties of the underlying dynamical systems.     

Dynamic control of the central pattern generator for locomotion

We show that an ongoing locomotor pattern can be dynamically controlled by applying discrete pulses of electrical stimulation to the central pattern generator (CPG) for locomotion. Data are presented from a pair of experiments on biological (wetware) and electrical (hardware) models of the CPG demonstrating that stimulation causes brief deviations from the CPG’s limit cycle activity. The exact characteristics of the deviation depend strongly on the phase of stimulation. Applications of this work are illustrated by examples showing how locomotion can be controlled by using a feedback loop to monitor CPG activity and applying stimuli at the appropriate times to modulate motor output. Eventually, this approach could lead to development of a neuroprosthetic device for restoring locomotion after paralysis. R. J. Vogelstein and F. Tenore contributed equally to this work.     

Possible interaction between synaptic and pacemaker mechanisms of electrical activity in bursting neurons of Helix pomatia

Membrane hyperpolarization induced by short pulses of inward current, by stimulation of the anal nerve, which leads to the appearance of a long IPSP in the neuron, and developing during the appearance of spontaneous IPSPs in the neuron was investigated in neuron RPa1 ofHelix pomatia. Short-term hyperpolarization of the neuron membrane by an inward current (10 msec) led to the development of self-maintained (regenerative) membrane hyperpolarization lasting several seconds. The amplitude and duration of regenerative hyperpolarization increased with an increase in amplitude and duration of the pulse of inward current. The time course of IPSPs arising spontaneously in the neuron and in response to stimulation of the anal nerve was similar to that of regenerative hyperpolarization evoked by a pulse of inward current. It is suggested that regenerative hyperpolarization associated with activation of endogenous mechanisms of regulation of the bursting activity of the neuron may be due not only to short-term membrane hyperpolarization of the test neuron by the electric current, but also to hyperpolarization occurring during IPSP generation.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 13, No. 1, pp. 67–74, January–February, 1981.     

Pigment-dispersing hormone-immunoreactive neurons in the cockroach Leucophaea maderae share properties with circadian pacemaker neurons

Neurons immunoreactive with antisera against the crustacean peptide -pigment dispersing hormone fullfill several anatomical criteria proposed for circadian pacemakers in the brain of the cockroach Leucophaea maderae. These include position of somata, projections to the lamina and midbrain and possible coupling pathways between the two pacemakers through commissural fibers. In behavioral experiments combined with lesion studies and immunocytochemical investigations we examined whether the presence of pigment-dispersing hormone-immunoreactive arborizations in the midbrain of the cockroach correlates with the presence of circadian locomotor activity. No rhythm was detected after severing both optic stalks in any animal for at least 12 days. Within the same time pigment-dispersing hormone-immunoreactive fibers in the midbrain disappeared. Two to seven weeks after the operation some of the cockroaches regained circadian locomotor activity, while others remained arrhythmic. In all cockroaches which regained rhythmic behavior pigment-dispersing hormone-immunoreactive fibers had regenerated and had largely found their original targets within the brain. In all arrhythmic cockroaches either none or very little regeneration had occurred. The period of the regained circadian activity inversely correlated with the number of regenerated immunoreactive commissural fibers. These data provide further evidence for the involvement of pigment-dispersing hormone-immunoreactive neurons in circadian clocks of orthopteroid insects.Abbreviations DD constant darkness - PDH pigment-dispersing hormone - PDHLI pigmentdispersing hormone-like immunoreactivity - PDFL a pigment-dispersing factor containing cells in the lamina - PDFMe pigment-dispersing factor containing cells in the medulla - QV quantification value     

On the definition of central pattern generator and its sensory control

A central pattern generator (CPG) is defined here as a neural network responsible for the production of the timing cues of a rhythmic motor output pattern in the isolated CNS. For the intact animal, model considerations show that this term is neither clearly delimited from the concept of a reflex chain nor from the concept of a pattern generator with functional principles different from those of the CPG. Therefore, it cannot be concluded from the existence of a CPG in the isolated nervous system that this CPG also provides the decisive timing cues in the intact animal. Consequences for the study of the neural basis of rhythmic movements are shown.     

Responses of a bursting pacemaker to excitation reveal spatial segregation between bursting and spiking mechanisms

Central pattern generators (CPGs) frequently include bursting neurons that serve as pacemakers for rhythm generation. Phase resetting curves (PRCs) can provide insight into mechanisms underlying phase locking in such circuits. PRCs were constructed for a pacemaker bursting complex in the pyloric circuit in the stomatogastric ganglion of the lobster and crab. This complex is comprised of the Anterior Burster (AB) neuron and two Pyloric Dilator (PD) neurons that are all electrically coupled. Artificial excitatory synaptic conductance pulses of different strengths and durations were injected into one of the AB or PD somata using the Dynamic Clamp. Previously, we characterized the inhibitory PRCs by assuming a single slow process that enabled synaptic inputs to trigger switches between an up state in which spiking occurs and a down state in which it does not. Excitation produced five different PRC shapes, which could not be explained with such a simple model. A separate dendritic compartment was required to separate the mechanism that generates the up and down phases of the bursting envelope (1) from synaptic inputs applied at the soma, (2) from axonal spike generation and (3) from a slow process with a slower time scale than burst generation. This study reveals that due to the nonlinear properties and compartmentalization of ionic channels, the response to excitation is more complex than inhibition.     

Low dimensional model of bursting neurons

A computationally efficient, biophysically-based model of neuronal behavior is presented; it incorporates ion channel dynamics in its two fast ion channels while preserving simplicity by representing only one slow ion current. The model equations are shown to provide a wide array of physiological dynamics in terms of spiking patterns, bursting, subthreshold oscillations, and chaotic firing. Despite its simplicity, the model is capable of simulating an extensive range of spiking patterns. Several common neuronal behaviors observed in vivo are demonstrated by varying model parameters. These behaviors are classified into dynamical classes using phase diagrams whose boundaries in parameter space prove to be accurately delineated by linear stability analysis. This simple model is suitable for use in large scale simulations involving neural field theory or neuronal networks.     

A Central pattern generator to control a pyloric-based system

A central pattern generator (CPG) is built to control a mechanical device (plant) inspired by the pyloric chamber of the lobster. Conductance-based models are used to construct the neurons of the CPG. The plant has an associated function that measures the amount of food flowing through it per unit of time. We search for the best set of solutions that give a high positive flow of food in the maximization function. The plant is symmetric and the model neurons are identical to avoid any bias in the space of solutions. We find that the solution is not unique and that three neurons are sufficient to produce positive flow. We propose an effective principle for CPGs (effective on-off connectivity) and a few predictions to be corroborated in the pyloric system of the lobster.     

Travelling wave patterns in a model of the spinal pattern generator using spiking neurons

The aim of this study is to produce travelling waves in a planar net of artificial spiking neurons. Provided that the parameters of the waves – frequency, wavelength and orientation – can be sufficiently controlled, such a network can serve as a model of the spinal pattern generator for swimming and terrestrial quadruped locomotion. A previous implementation using non-spiking, sigmoid neurons lacked the physiological plausibility that can only be attained using more realistic spiking neurons. Simulations were conducted using three types of spiking neuronal models. First, leaky integrate-and-fire neurons were used. Second, we introduced a phenomenological bursting neuron. And third, a canonical model neuron was implemented which could reproduce the full dynamics of the Hodgkin–Huxley neuron. The conditions necessary to produce appropriate travelling waves corresponded largely to the known anatomy and physiology of the spinal cord. Especially important features for the generation of travelling waves were the topology of the local connections – so-called off-centre connectivity – the availability of dynamic synapses and, to some extent, the availability of bursting cell types. The latter were necessary to produce stable waves at the low frequencies observed in quadruped locomotion. In general, the phenomenon of travelling waves was very robust and largely independent of the network parameters and emulated cell types.     

Modular neuromuscular control of human locomotion by central pattern generator

The central pattern generators (CPG) in the spinal cord are thought to be responsible for producing the rhythmic motor patterns during rhythmic activities. For locomotor tasks, this involves much complexity, due to a redundant system of muscle actuators with a large number of highly nonlinear muscles. This study proposes a reduced neural control strategy for the CPG, based on modular organization of the co-active muscles, i.e., muscle synergies. Four synergies were extracted from the EMG data of the major leg muscles of two subjects, during two gait trials each, using non-negative matrix factorization algorithm. A Matsuoka׳s four-neuron CPG model with mutual inhibition, was utilized to generate the rhythmic activation patterns of the muscle synergies, using the hip flexion angle and foot contact force information from the sensory afferents as inputs. The model parameters were tuned using the experimental data of one gait trial, which resulted in a good fitting accuracy (RMSEs between 0.0491 and 0.1399) between the simulation and experimental synergy activations. The model׳s performance was then assessed by comparing its predictions for the activation patterns of the individual leg muscles during locomotion with the relevant EMG data. Results indicated that the characteristic features of the complex activation patterns of the muscles were well reproduced by the model for different gait trials and subjects. In general, the CPG- and muscle synergy-based model was promising in view of its simple architecture, yet extensive potentials for neuromuscular control, e.g., resolving redundancies, distributed and fast control, and modulation of locomotion by simple control signals.     

Light affects the branching pattern of peptidergic circadian pacemaker neurons in the brain of the cockroach Leucophaea maderae

Pigment-dispersing factor-immunoreactive neurons anterior to the accessory medulla (aPDFMes) in the optic lobes of insects are circadian pacemaker neurons in cockroaches and fruit flies. The authors examined whether any of the aPDFMes of the cockroach Leucophaea maderae are sensitive to changes in period and photoperiod of light/dark (LD) cycles as a prerequisite to adapt to changes in external rhythms. Cockroaches were raised in LD cycles of 11:11, 13:13, 12:12, 6:18, or 18:6 h, and the brains of the adults were examined with immunocytochemistry employing antisera against PDF and orcokinin. Indeed, in 11:11 LD cycles, only the number of medium-sized aPDFMes specifically decreased, while it increased in 13:13. In addition, 18:6 LD cycles increased the number of large- and medium-sized aPDFMes, as well as the posterior pPDFMes, while 6:18 LD cycles only decreased the number of medium-sized aPDFMes. Furthermore, PDF-immunoreactive fibers in the anterior optic commissure and orcokinin-immunoreactive fibers in both the anterior and posterior optic commissures were affected by different lengths of light cycles. Thus, apparently different groups of the PDFMes, most of all the medium-sized aPDFMes, which colocalize orcokinin, respond to changes in period and photoperiod and could possibly allow for the adjustment to different photoperiods.