Ghostbursting: A Novel Neuronal Burst Mechanism

Pyramidal cells in the electrosensory lateral line lobe (ELL) of weakly electric fish have been observed to produce high-frequency burst discharge with constant depolarizing current (Turner et al., 1994). We present a two-compartment model of an ELL pyramidal cell that produces burst discharges similar to those seen in experiments. The burst mechanism involves a slowly changing interaction between the somatic and dendritic action potentials. Burst termination occurs when the trajectory of the system is reinjected in phase space near the ghost of a saddle-node bifurcation of fixed points. The burst trajectory reinjection is studied using quasi-static bifurcation theory, that shows a period doubling transition in the fast subsystem as the cause of burst termination. As the applied depolarization is increased, the model exhibits first resting, then tonic firing, and finally chaotic bursting behavior, in contrast with many other burst models. The transition between tonic firing and burst firing is due to a saddle-node bifurcation of limit cycles. Analysis of this bifurcation shows that the route to chaos in these neurons is type I intermittency, and we present experimental analysis of ELL pyramidal cell burst trains that support this model prediction. By varying parameters in a way that changes the positions of both saddle-node bifurcations in parameter space, we produce a wide gallery of burst patterns, which span a significant range of burst time scales.     

Comparison of Coding Capabilities of Type I and Type II Neurons

We consider the dependence of information transfer by neurons on the Type I vs. Type II classification of their dynamics. Our computational study is based on Type I and II implementations of the Morris-Lecar model. It mainly concerns neurons, such as those in the auditory or electrosensory system, which encode band-limited amplitude modulations of a periodic carrier signal, and which fire at random cycles yet preferred phases of this carrier. We first show that the Morris-Lecar model with additive broadband noise ("synaptic noise") can exhibit such firing patterns with either Type I or II dynamics, with or without amplitude modulations of the carrier. We then compare the encoding of band-limited random amplitude modulations for both dynamical types. The comparison relies on a parameter calibration that closely matches firing rates for both models across a range of parameters. In the absence of synaptic noise, Type I performs slightly better than Type II, and its performance is optimal for perithreshold signals. However, Type II performs well over a slightly larger range of inputs, and this range lies mostly in the subthreshold region. Further, Type II performs marginally better than Type I when synaptic noise, which yields more realistic baseline firing patterns, is present in both models. These results are discussed in terms of the tuning and phase locking properties of the models with deterministic and stochastic inputs.     

Ionic and neuromodulatory regulation of burst discharge controls frequency tuning

Sensory neurons encode natural stimuli by changes in firing rate or by generating specific firing patterns, such as bursts. Many neural computations rely on the fact that neurons can be tuned to specific stimulus frequencies. It is thus important to understand the mechanisms underlying frequency tuning. In the electrosensory system of the weakly electric fish, Apteronotus leptorhynchus, the primary processing of behaviourally relevant sensory signals occurs in pyramidal neurons of the electrosensory lateral line lobe (ELL). These cells encode low frequency prey stimuli with bursts of spikes and high frequency communication signals with single spikes. We describe here how bursting in pyramidal neurons can be regulated by intrinsic conductances in a cell subtype specific fashion across the sensory maps found within the ELL, thereby regulating their frequency tuning. Further, the neuromodulatory regulation of such conductances within individual cells and the consequences to frequency tuning are highlighted. Such alterations in the tuning of the pyramidal neurons may allow weakly electric fish to preferentially select for certain stimuli under various behaviourally relevant circumstances.     

峰峰间期逐渐增大的动力学机制

在3或4个轻度结扎受损的大鼠坐骨神经上加入5mmol／L EGTA的无钙灌流液的神经生理实验中,可以观察到一种在活动相峰峰间期逐渐增大的周期阵发放电现象。从非线性动力学角度分析该现象产生的动力学机制对于理解神经元复杂的放电行为具有重要意义。通过Hindmarsh-Rose神经元模型的分析,对该现象产生的一种可能的机制进行了揭示,即鞍结分岔和鞍点同宿分岔支配着这种阵发放电形式,而且后者对峰峰阃期逐渐的增大起着更重要的作用。     

Identifying type I excitability using dynamics of stochastic neural firing patterns

The stochastic firing patterns are simulated near saddle-node bifurcation on an invariant cycle corresponding to type I excitability in stochastic Morris–Lecar model. In absence of external periodic signal, the stochastic firing manifests continuous distribution in ISI histogram (ISIH), whose amplitude at first increases sharply and then decreases exponentially. In presence of the external periodic signal, stochastic firing patterns appear as two cases of integer multiple firing with multiple discrete peaks in ISIH. One manifests perfect exponential decay in all peaks and the other imperfect exponential decay except a lower first peak. These stochastic firing patterns simulated with or without external periodic signal can be demonstrated in the experiments on rat hippocampal CA1 pyramidal neurons. The exponential decay laws in the multiple peaks are also acquired using probability analysis method. The perfect decay law is determined by the independent characteristic within the firing while the imperfect decay law is from the inhibitory effect. In addition, the stochastic firing patterns corresponding to type I excitability are compared to those of type II excitability. The results not only reveal the dynamics of stochastic firing patterns with or without external signal corresponding to type I excitability, but also provide practical indicators to availably identify type I excitability.     

Biological effects of oscillating electric fields: Role of voltage-sensitive ion channels

An alternating component of potential across the membrane of an excitable cell may change the membrane conductance by interacting with the voltagesensing charged groups of the protein macromolecules that form voltage-sensitive ion channels. Because the probability that a voltage sensor is in a given state is a highly nonlinear function of the applied electric field, the average occupancy of a particular state will change in an oscillating electric field of sufficient magnitude. This “rectification” at the level of the voltage sensors could result in conformational changes (gating) that would modify channel conductance. A simplified two-state model is examined where the relaxation time of the voltage sensor is assumed to be considerably faster than the fastest changes of ionic conductance. Significant changes in the occupancy of voltage sensor states in response to an applied oscillating electric field are predicted by the model.     

The electric organ discharges of the gymnotiform fishes: I. Apteronotus leptorhynchus

We present high temporal and spatial resolution maps in 3-dimensions of the electric field vector generated by the weakly electric fish, Apteronotus leptorhynchus. The waveforms and harmonic composition of the electric organ discharge (EOD) are variable around the fish but highly stable over long times at any position. We examine the role of harmonics on the temporal and spatial characteristics of the EOD, such as the slew rate and rostral-to-caudal propagation. We also explore the radial symmetry of the fish's field. There are major differences in the direction of the electric field vector at the head and caudal body. In the caudal part of the fish, the electric field vector rotates during the EOD cycle. However, rostral of the pectoral fin, the field magnitude and sign oscillate while maintaining relatively constant orientation. We discuss possible functional ramifications of these electric field patterns to electrolocation, communication, and electrogenesis.Abbreviations EOD electric organ discharge - EO electric organ - RMS root mean square - ADC analog-to-digital converter     

Distribution of carotid body type I cells and other periadventitial type I cells in the carotid bifurcation regions of the rabbit

Summary The distribution of carotid body type I and periadventitial type I cells in the carotid bifurcation regions was investigated unilaterally in seven and bilaterally in two New Zealand White rabbits. Carotid body type I cells occurred in close proximity to the wall of the internal carotid artery immediately rostral to the carotid bifurcation, within a division of connective tissue with defineable but irregular borders. Caudally, and separate from the main mass of carotid body type I cells, isolated groups of periadventitial type I cells lay freely in the connective tissue around the internal carotid artery and alongside the carotid bifurcation and common carotid artery. A overall picture of the carotid body in the rabbit was reconstructed and the occurrence and significance of periadventitial type I cells discussed.The authors are indebted to Mr. Stephen Jones of the Department of Histopathology, St Bartholomew's Hospital, for expert assistance in the preparation of the material, and to Mr. A.J. Aldrich of the Department of Anatomy for photography. This work was supported by a grant from the Wellcome Trust to one of us (M. de B.D.)     

Dissection and reduction of a modeled bursting neuron

An 11-variable Hodgkin-Huxley type model of a bursting neuron was investigated using numerical bifurcation analysis and computer simulations. The results were applied to develop a reduced model of the underlying subthreshold oscillations (slow-wave) in membrane potential. Two different low-order models were developed: one 3-variable model, which mimicked the slow-wave of the full model in the absence of action potentials and a second 4-variable model, which included expressions accounting for the perturbational effects of action potentials on the slow-wave. The 4-variable model predicted more accurately the activity mode (bursting, beating, or silence) in response to application of extrinsic stimulus current or modulatory agents. The 4-variable model also possessed a phase-response curve that was very similar to that of the original 11-variable model. The results suggest that low-order models of bursting cells that do not consider the effects of action potentials may erroneously predict modes of activity and transient responses of the full model on which the reductions are based. These results also show that it is possible to develop low-order models that retain many of the characteristics of the activity of the higher-order system.     

The electric image in weakly electric fish: I. A data-based model of waveform generation inGymnotus carapo

Understanding how electrosensory images are generated and perceived in actively electrolocating fish requires the study of the characteristics of fish bodies as electric sources. This paper presents a model ofGymnotus carapo based on measurements of the electromotive force generated by the electric organ and the impedance of the passive tissues. A good agreement between simulated and experimentally recorded transcutaneous currents was obtained. Passive structures participate in the transformation of the electromotive force pattern into transcutaneous current profiles. These spatial filtering properties of the fish's body were investigated using the model. The shape of the transcutaneous current profiles depends on tissue resistance and on the geometry and size of the fish. Skin impedance was mainly resistive. The effect of skin resistance on the spatial filtering properties of the fish's body was theoretically analyzed.The model results show that generators in the abdominal and central regions produce most of the currents through the head. This suggests that the electric organ discharge (EOD), generated in the abdominal and central regions is critical for active electrolocation. In addition, the well-synchronized EOD components generated all along the fish produce large potentials in the far field. These components are probably involved in long-distance electrocommunication.Preliminary results of this work were published as a symposium abstract.     

Monopolar electric discharges of the catfish <Emphasis Type="Italic">Parasilurus asotus</Emphasis> (Siluridae,Siluriformes)

Electric discharges in the catfish Parasilurus asotus are registered for the first time. The discharges are monopolar pulses of a 50–300 ms duration which corresponds to the frequency characteristics of ampoules of electroreceptors in these catfish. Electric generation is discovered only upon the aggressive-defensive behavior of not less than two species. In solitary fish no discharges were observed neither at prolonged continuous registration (longer than 24 h each) nor at mechanical stimulation. The hypothesis is discussed of a potential mechanism of active (under use of their own electric discharges) monitoring of water conductivity with a relative sensitivity on the order of 0.0002%. This hypothesis may be applied to an explanation of anomalous group behavior of these catfish before earthquakes.     

Time coding in the midbrain of mormyrid electric fish. I. Physiology and anatomy of cells in the nucleus exterolateralis pars anterior

In mormyrid electric fish, species-specific electric organ discharge waveforms are thought to be analyzed by the Knollenorgan electroreceptor subsystem. The midbrain anterior and posterior exterolateral nuclei (ELa and ELp) are thought to be the sites of this analysis. This paper is an electrophysiological study of the properties of the neurons in ELa. We recorded intracellularly from three classes of cells within ELa: the afferent axons from the nucleus of the electrosensory lateral line lobe (NELL), the large interstitial cells of ELa and an unidentified cell type. The large cells and the NELL axons were identified by intracellular injection of biocytin and are physiologically similar. Cells in ELa responded to square pulse stimuli with one or more time-locked action potentials with 2.8–3.0 ms latency. Both large cells and NELL axons arborized extensively in ELa and contacted numerous small cells. Based on the pattern of arborizations, we constructed a counter- current flow model of temporal coding by the small cells of ELa. We postulate that individual small cells are not selectively tuned for specific stimulus durations, but rather, the firing patterns of groups of small cells must be analyzed by neurons further up in the sensory hierarchy to determine the stimulus duration. Accepted: 25 June 1997     

Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons

We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh–Rose neurons. For modeling complex synaptic connectivity, we consider the Watts–Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the J–D plane (J: synaptic inhibition strength and D: noise intensity). As the rewiring probability p is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the J–D plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.     

Alteration of the action potential of tissue cultured neuronal cells by growth in the presence of a polyunsaturated fatty acid

The effects of alterations in membrane phospholipid fatty acid composition on the excitability of neuroblastoma × glioma hybrid cells, clone NG108-15, were examined using intracellular recording techniques. Cells were grown in the presence of arachidonate (20:4) added to the culture medium as a complex with bovine serum albumin. Exposure of the cells to 20:4 for 3–21 days produced a 40% decrease in the maximum rate of rise of the action potential (dV/dt) with a small change in its amplitude. The resting membrane potential and passive properties of the cells were unaffected. An effect of 20:4 was not observed until 24 hr after treatment and increased over the next 2 days. The phospholipid content of 20:4 and its metabolite 22:4 increased from 6.9% to 25.3% of total fatty acids during approximately the same time span. It is concluded that the action potential dV/dt can be altered by changes in membrane lipid composition.     

Fish <Emphasis Type="Italic">ES</Emphasis> Cells and Applications to Biotechnology

ES cells provide a promising tool for the generation of transgenic animals with site-directed mutations. When ES cells colonize germ cells in chimeras, transgenic animals with modified phenotypes are generated and used either for functional genomics studies or for improving productivity in commercial settings. Although the ES cell approach has been limited to mice, there is strong interest for developing the technology in fish. We describe the step-by-step procedure for developing ES cells in fish. Key aspects include avoiding cell differentiation, specific in vitro traits of pluripotency, and, most importantly, testing for production of chimeric animals as the main evidence of pluripotency. The entire process focuses on two model species, zebrafish and medaka, in which most work has been done. The achievements attained in these species, as well as their applicability to other commercial fish, are discussed. Because of the difficulties relating to germ line competence, mostly of long-term fish ES cells, alternative cell-based approaches such as primordial germ cells and nuclear transfer need to be considered. Although progress to date has been slow, there are promising achievements in homologous recombination and alternative avenues yet to be explored that can bring ES technology in fish to fruition.     

Bifurcation, Bursting, and Spike Frequency Adaptation

Many neural systems display adaptive properties that occur on timescales that are slower than the time scales associated withrepetitive firing of action potentials or bursting oscillations. Spike frequency adaptation is the name givento processes thatreduce the frequency of rhythmic tonic firing of action potentials,sometimes leading to the termination of spiking and the cell becomingquiescent. This article examines these processes mathematically,within the context of singularly perturbed dynamical systems.We place emphasis on the lengths of successive interspikeintervals during adaptation. Two different bifurcation mechanisms insingularly perturbed systems that correspond to the termination offiring are distinguished by the rate at which interspike intervalsslow near the termination of firing. We compare theoreticalpredictions to measurement of spike frequency adaptation in a modelof the LP cell of the lobster stomatogastric ganglion.     

在大鼠受损坐骨神经上由藜芦碱诱发的抛物线簇放电

在大鼠受损坐骨神经上加入 5 μmol L藜芦碱溶液 ,观察到了抛物线簇放电的现象。根据Plant模型 ,发生抛物线簇放电的前提条件必须有两个慢变量所支配的慢振荡过程。结合实验模型 ,从离子通道活动的角度揭示了抛物线簇放电发生的生物物理机制。由藜芦碱诱发的慢变钠内流和钙依赖钾外流被认为是引发实验所观察到的抛物线簇放电的两个慢变量。进而阐明了藜芦碱引起这一放电形式所起的作用 ,即抑制钠通道失活引发慢变钠内流。这种利用非线性动力学理论的分析方法可能会为分析药物的药物动力学提供一种新的途径。     

Pyramidal-cell plasticity in weakly electric fish: a mechanism for attenuating responses to reafferent electrosensory inputs

Recordings within the posterior eminentia granularis of the weakly electric fish, Apteronotus leptorhynchus, revealed multiple types of proprioceptive units responsive to changes in the position of the animal's trunk and tail. Intracellular labelling showed that the proprioceptor recordings were made from axons that ramify extensively within the EGp. The location of the somata giving rise to these axons is presently unknown. Electroreceptor afferent responses to electric organ discharge amplitude modulations caused by movement of the animal's tail were compared to responses caused by electronically generated AMs of similar amplitude and time course. These did not differ. Electrosensory lateral line lobe pyramidal cells responded significantly less to electric organ discharge amplitude modulations caused by changing the animal's posture as compared to electronically produced AMs, suggesting that central mechanisms attenuate pyramidal cell responses to reafferent electrosensory inputs. Experiments in which the pattern of reafferent input associated with changes in posture was altered revealed that the pyramidal cells learn, over a time course of several minutes, to reject new patterns of input. Both proprioceptive input and descending electrosensory input to the posterior eminentia granularis are involved in generating the observed plastic changes in pyramidal cell responsiveness.Abbreviations AM amplitude modulation - EGp posterior eminentia granularis - ELL electrosensory lateral line lobe - EOD electric organ discharge - HRP horseradish peroxidase - LTD long-term depression - LTP long-term potentiation     

Gap junctions in excitable cells

Gap junction channels are an integral part of the conduction or propagation of an action potential from cell to cell. Gap junctions have rather unique gating and permeability properties which permit the movement of molecules from cell to cell. These molecules may not be directly linked to action potentials but can alter nonjunctional processes within cells, which in turn can affect conduction velocity. The data described in this review reveal that, for the majority of excitable cells, there are two limiting factors, with respect to gap junctions, that affect the conduction/propagation of action potentials. These are (1) the total number of channels and (2) the selective permeability of the channels. Interestingly, voltage dependence and the time course of voltage inactivation (kinetics) are not rate limiting steps under normal physiological conditions for any of the connexins studied so far. Only specialized rectifying electrical synapses utilize strong voltage dependence and rapid kinetics to permit or deny the continued propagation of an action potential.     

Time coding in the midbrain of mormyrid electric fish. II. Stimulus selectivity in the nucleus exterolateralis pars posterior

The anterior and posterior exterolateral nuclei (ELa and ELp) of the mormyrid midbrain are thought to play a critical role in the temporal analysis of the electric discharge waveforms of other individuals. The peripheral electroreceptors receiving electric organ discharges (EODs) of other fish project through the brainstem to ELa via a rapid conducting pathway. EODs, composed of brief, but stereotyped waveforms are encoded as a temporal pattern of spikes. From previous work, we know that phase locking is precise in ELa. Here it is shown that evoked potentials recorded from ELp show a similar high degree of phase locking, although the evoked potentials last much longer. Single-unit recordings in ELp reveal two distinct populations of neurons in ELp: type I cells are responsive to voltage step functions, and not tuned for stimulus duration; type II cells are tuned to a specific range of stimulus durations. Type II cells are less responsive than type I cells, tend to respond with bursts of action potentials rather than with single spikes, have a longer latency, show weaker time locking to stimuli, and are more sensitive to stimulus polarity and amplitude. The stimulus selectivity of type II cells may arise from convergence of type I cell inputs. Despite the loss of rapid conduction between ELa and ELp, analysis of temporal features of waveforms evidently continues in ELp, perhaps through a system of labeled lines. Accepted: 25 June 1997