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.     

Slow voltage inactivation of Ca2+ currents and bursting mechanisms for the mouse pancreatic beta-cell

Summary Recent whole-cell electrophysiological data concerning the properties of the Ca²⁺ currents in mouse -cells are fitted by a two-current model of Ca²⁺ channel kinetics. When the -cell K⁺ currents are added to this model, only large modifications of the measured Ca²⁺ currents will reproduce the bursting pattern normally observed in mouse islets. However, when the measured Ca²⁺ currents are modified only slightly and used in conjunction with a K⁺ conductance that can be modulated dynamically by ATP concentration, reasonable bursting is obtained. Under these conditions it is the K-ATP conductance, rather than the slow voltage inactivation of the Ca²⁺ current, that determines the interburst interval. We find that this latter model can be reconciled with experiments that limit the possible periodic variation of the K-ATP conductance and with recent observations of intracellular Ca²⁺ bursting in isletsThis work was supported in part by NSF grant DIR-90-06104 and the Agricultural Experiment Station of the University of California. P.S. gratefully acknowledges financial support from an NRC Fellowship. We have benefited from numerous conversations with Drs. John Rinzel, Arthur Sherman, Daniel Cook, and Leslie Satin     

NF-κB-Chromatin Interactions Drive Diverse Phenotypes by Modulating Transcriptional Noise

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The effect of ATP-sensitive K+ channels on the electrical burst activity and insulin secretion in pancreatic β-cells

In recent years, the electrical burst activity of the insulin releasing pancreatic β-cells has attracted many experimentalists and theoreticians, largely because of its functional importance, but also because of the nonlinear nature of the burst activity. The ATP-sensitive K⁺ channels are believed to play an important role in electrical activity and insulin release. In this paper, we show by computer simulation how ATP and antidiabetic drugs can lengthen the plateau fraction of bursting and how these chemicals can increase the intracellular Ca²⁺ level in the pancreatic β-cell.     

Co-condensation between transcription factor and coactivator p300 modulates transcriptional bursting kinetics

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Spike bursts generated by the thermosensitive (cold) neuron from the antennal campaniform sensilla of the ground beetle Platynus assimilis

Responses of the antennal thermosensitive neuron of the ground beetle Platynus assimilis to warming from 20 to 50 °C were measured and analysed. During warming, neurons switched from regular spiking to bursting. ISI analysis showed that the number of spikes in the burst and spike frequency within the burst were temperature dependent and may precisely encode unfavourably or dangerously high temperatures in a graded manner. In contrast, regular spikes of the neuron encode moderate temperatures at 20-30 °C. The threshold temperature of spike bursting varied in different neurons from 25 to 47 °C. As a result, the number of bursting neurons increased with temperature increase. Therefore, in addition to the burst characteristics, the total number of bursting neurons may also contain useful information on external temperature. A relationship between the spike bursts and locomotor activity of the beetles was found which may have importance in behavioural thermoregulation of the species. At 44.4 ± 0.6 °C, first indications of partial paralysis (of the hind legs) were observed. We emphasize, that in contrast to various sensory systems studied, the thermoreceptor neuron of P. assimilis has a stable and continuous burst train, no temporal information is encoded in the timing of the bursts.     

Type I burst excitability

We introduce the concept of type I burst excitability, which is a generalization of the normal excitability that is well-known in cardiac and neural systems. We demonstrate this type of burst excitability in a specific model system, a pyramidal cell from the electrosensory lateral line lobe of the weakly electric fish Apteronotus leptorhynchus. As depolarizing current is increased, a saddle-node bifurcation of periodic orbits occurs, which separates tonic and burst activity. This bifurcation is responsible for the excitable nature of the system, and is the basis for the type I designation. We verify the existence of this transition from in vitro recordings of a number of actual pyramidal cells. A scaling relationship between the magnitude and duration of a current pulse required to induce a burst is derived. We also observe this type of burst excitability and the scaling relationships in a multicompartmental model that is driven by realistic stochastic synaptic inputs mimicking sensory input. We conclude by discussing the relevance of burst excitability to communication between weakly electric fish.     

Monoamine release by neurons of a primitive nervous system: an amperometric study

We measured monoamine release from dissociated neurons of the sea pansy Renilla koellikeri, a representative of the most evolutionarily ancient animals with nervous systems, by real-time monitoring of exocytosis using the amperometric method with carbon-fiber microelectrodes. Depolarization-induced, as well as spontaneously active, neurons exhibited calcium-dependent exocytotic events at both the soma and the terminal bulb of neuritic processes. All spontaneously active neurons exhibited a bursting activity pattern in which amplitudes of exocytotic events appeared to be distributed in a quantal-like fashion. Fast Fourier transform analysis of bursting activity in 20 such neurons revealed burst harmonics with a major frequency of 8 Hz and a dominant rate of 95 Hz for individual exocytotic events within bursts. The results suggest that exocytotic transmitter release is as ancient as neurons and that endogenously bursting neurons in the sea pansy are as complex as those of higher animals. In addition, the observation that both soma and neuritic terminals of the same neuron can release transmitter suggests that local release sites in these cnidarian neurons are not critical for nerve net function.