Simulation of the bursting activity of neuron R15 in Aplysia: role of ionic currents, calcium balance, and modulatory transmitters

Modeling slowly bursting neurons via calcium store and voltage-independent calcium current

Recent experiments indicate that the calcium store (e.g., endoplasmic reticulum) is involved in electrical bursting and [Ca2+]i oscillation in bursting neuronal cells. In this paper, we formulate a mathematical model for bursting neurons, which includes Ca2+ in the intracellular Ca2+ stores and a voltage-independent calcium channel (VICC). This VICC is activated by a depletion of Ca2+ concentration in the store, [Ca2+]cs. In this model, [Ca2+]cs oscillates slowly, and this slow dynamic in turn gives rise to electrical bursting. The newly formulated model thus is radically different from existing models of bursting excitable cells, whose mechanism owes its origin to the ion channels in the plasma membrane and the [Ca2+]i dynamics. In addition, this model is capable of providing answers to some puzzling phenomena, which the previous models could not (e.g., why cAMP, glucagon, and caffeine have ability to change the burst periodicity). Using mag-fura-2 fluorescent dyes, it would be interesting to verify the prediction of the model that (1) [Ca2+]cs oscillates in bursting neurons such as Aplysia neuron and (2) the neurotransmitters and hormones that affect the adenylate cyclase pathway can influence this oscillation.

Modeling Hermissenda: I. Differential contributions of IA and IC to type-B cell plasticity

We developed a multicompartmental Hodgkin-Huxley model of the Hermissenda type-B photoreceptor and used it to address the relative contributions of reductions of two K+ currents, IA and IC, to changes in cellular excitability and synaptic strength that occur in these cells after associative learning. We found that reductions of [symbol: see text] C, the peak conductance of IC, substantially increased the firing frequency of the type-B cell during the plateau phase of a simulated light response, whereas reductions of [symbol: see text] A had only a modest contribution to the plateau frequency. This can be understood at least in part by the contributions of these currents to the light-induced (nonspiking) generator potential, the plateau of which was enhanced by [symbol: see text] C reductions, but not by [symbol: see text] A reductions. In contrast, however, reductions of [symbol: see text] A broadened the type-B cell action potential, increased Ca2+ influx, and increased the size of the postsynaptic potential produced in a type-A cell, whereas similar reductions of [symbol: see text] C had only negligible contributions to these measures. These results suggest that reductions of IA and IC play important but different roles in type-B cell plasticity.

Voltage gated calcium channels in molluscs: classification, Ca2+ dependent inactivation, modulation and functional roles

Molluscan neurons and muscle cells express transient (T-type like) and sustained LVA calcium channels, as well as transient and sustained HVA channels. In addition weakly voltage sensitive calcium channels are observed. In a number of cases toxin or dihydropyridine sensitivity justifies classification of the HVA currents in L, N or P-type categories. In many cases, however, pharmacological characterization is still preliminary. Characterization of novel toxins from molluscivorous Conus snails may facilitate classification of molluscan calcium channels. Molluscan preparations have been very useful to study calcium dependent inactivation of calcium channels. Proposed mechanisms explain calcium dependent inactivation through direct interaction of Ca2+ with the channel, through dephosphorylation by calcium dependent phosphatases or through calcium dependent disruption of connections with the cytoskeleton. Transmitter modulation operating through various second messenger mediated pathways is well documented. In general, phosphorylation through PKA, cGMP dependent PK or PKC facilitates the calcium channels, while putative direct G-protein action inhibits the channels. Ca2+ and cGMP may inhibit the channels through activation of phosphodiesterases or phosphatases. Detailed evidence has been provided on the role of sustained LVA channels in pacemaking and the generation of firing patterns, and on the role of HVA channels in the dynamic changes in action potentials during spiking, the regulation of the release of transmitters and hormones, and the regulation of growth cone behavior and neurite outgrowth. The accessibility of molluscan preparations (e.g. the squid giant synapse for excitation release studies, Helisoma B5 neuron for neurite and synapse formation) and the large body of knowledge on electrophysiological properties and functional connections of identified molluscan neurons (e.g. sensory neurons, R15, egg laying hormone producing cells, etc.) creates valuable opportunities to increase the insight into the functional roles of calcium channels.

Oscillation in motor pattern-generating networks

Oscillation in motor pattern generators is driven either by pacemaker neurons with inherent bursting properties or through network interactions. In a few examples in invertebrates and lower vertebrates, the mechanisms by which reciprocal inhibition combines with inherent membrane properties to produce network oscillation are beginning to emerge. A recently developed theoretical framework provides a context for understanding and comparing these findings.

Analysis of an autonomous phase model for neuronal parabolic bursting

An understanding of the nonlinear dynamics of bursting is fundamental in unraveling structure-function relations in nerve and secretory tissue. Bursting is characterized by alternations between phases of rapid spiking and slowly varying potential. A simple phase model is developed to study endogenous parabolic bursting, a class of burst activity observed experimentally in excitable membrane. The phase model is motivated by Rinzel and Lee's dissection of a model for neuronal parabolic bursting (J. Math. Biol 25, 653-675 (1987)). Rapid spiking is represented canonically by a one-variable phase equation that is coupled bi-directionally to a two-variable slow system. The model is analyzed in the slow-variable phase plane, using quasi steady-state assumptions and formal averaging. We derive a reduced system to explore where the full model exhibits bursting, steady-states, continuous and modulated spiking. The relative speed of activation and inactivation of the slow variables strongly influences the burst pattern as well as other dynamics. We find conditions of the bistability of solutions between continuous spiking and bursting. Although the phase model is simple, we demonstrate that it captures many dynamical features of more complex biophysical models.

Topological and phenomenological classification of bursting oscillations

We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (in Mathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the phenomenological character of different types of bursting, addressing the issue of how well the bursting can be characterized given the limited amount of information often available in experimental settings.

Analysis of the effects of modulatory agents on a modeled bursting neuron: dynamic interactions between voltage and calcium dependent systems

In a computational model of the bursting neuron R15, we have implemented proposed mechanisms for the modulation of two ionic currents (IR and ISI) that play key roles in regulating its spontaneous electrical activity. The model was sufficient to simulate a wide range of endogenous activity in the presence of various concentrations of serotonin (5-HT) or dopamine (DA). The model was also sufficient to simulate the responses of the neuron to extrinsic current pulses and the ways in which those responses were altered by 5-HT or DA. The results suggest that the actions of modulatory agents and second messengers on this neuron, and presumably other neurons, cannot be understood on the basis of their direct effects alone. It is also necessary to take into account the indirect effects of these agents on other unmodulated ion channels. These indirect effects occur through the dynamic interactions of voltage-dependent and calcium-dependent processes.

A new class of noninactivating K+ channels from aplysia capable of contributing to the resting potential and firing patterns of neurons

From the nervous system of Aplysia, we have cloned a new class of noninactivating K+ channels (aKv5.1) that are activated at low voltage and are capable of contributing to the resting potential and firing patterns of neurons. Expression of aKv5.1 in Aplysia neuron R15 revealed that aKv5.1 exerts an unusual control over cell excitability; it increased the resting potential by more than 20 mV and abolished the spontaneous bursting activity of the cell. In its ability to suppress the endogenous rhythm of R15, aKv5.1 differs in its actions from transient, inactivating K+ channels such as aKv1.1a, an Aplysia homolog of Shaker. aKv1.1a shortens the duration of the spike and increases the afterpotential, but does not suppress bursting. Thus, by expressing different classes of K+ channels, it is possible to redesign, in specific ways, the signaling capabilities of specific, identified neurons.

How neurons may compute: the case of insect sexual pheromone discrimination

Recognition of pheromone scent by male insects probably depends on analyzing the blend's composition in terms of relative concentrations of major and minor molecular components. Based on anatomical, physiological and behavioral data concerning certain moth species and the cockroach, we propose a simple, biologically plausible neural circuit which is able to perform this task reliably. The model employs oscillations as a detecting device. This principle is easily generalized to other systems. As a computational device, ratio detection may find applications in a variety of biological situations, e.g. in the olfactory system of all animals.

Reduced-system analysis of the effects of serotonin on a molluscan burster neuron

The mathematical model described in Bertram (1993) is used to carry out a detailed examination of the manner in which the neurotransmitter serotonin modifies the voltage waveform generated endogenously by burster neuron R15 of Aplysia. This analysis makes use of a reduced system of equations, taking advantage of the slow rate of change of a pair of system variables relative to the others. Such analysis also yields information concerning the sensitivity of the neuron to brief+ synaptic perturbations.

Generation of periodic and chaotic bursting in an excitable cell model

There are interesting oscillatory phenomena associated with excitable cells that require theoretical insight. Some of these phenomena are: the threshold low amplitude oscillations before bursting in neuronal cells, the damped burst observed in muscle cells, the period-adding bifurcations without chaos in pancreatic beta-cells, chaotic bursting and beating in neurons, and inverse period-doubling bifurcation in heart cells. The three variable model formulated by Chay provides a mathematical description of how excitable cells generate bursting action potentials. This model contains a slow dynamic variable which forms a basis for the underlying wave, a fast dynamic variable which causes spiking, and the membrane potential which is a dependent variable. In this paper, we use the Chay model to explain these oscillatory phenomena. The Poincaré return map approach is used to construct bifurcation diagrams with the 'slow' conductance (i.e., gK, C) as the bifurcation parameter. These diagrams show that the system makes a transition from repetitive spiking to chaotic bursting as parameter gK, C is varied. Depending on the time kinetic constant of the fast variable (lambda n), however, the transition between burstings via period-adding bifurcation can occur even without chaos. Damped bursting is present in the Chay model over a certain range of gK, C and lambda n. In addition, a threshold sinusoidal oscillation was observed at certain values of gK, C before triggering action potentials. Probably this explains why the neuronal cells exhibit low-amplitude oscillations before bursting.

Activation and modulation of calcium-activated non-selective cation channels from embryonic chick sensory neurons

We have shown that calcium-activated non-selective (CAN) channels from embryonic chick sensory neurons are permeable to both Na+ and K+ and are not blocked by TTX, TEA, or 4-AP. These neuronal CAN channels are activated by sub-micromolar cytoplasmic Ca2+ with negative cooperativity. The effect of Ca2+ is to decrease the closed times of the channel with little effect on the time the channel remains open. Isolated neuronal CAN channels can be phosphorylated by cAMP-dependent protein kinase (PKA). The effect of phosphorylation is to shorten channel open time and to minimize the effect of Ca2+ on channel closed time.

An ionic current model for neurons in the rat medial nucleus tractus solitarii receiving sensory afferent input

1. Neurons from a horizontal slice of adult rat brainstem were examined using intracellular recording techniques. Investigations were restricted to a region within the nucleus tractus solitarii, medial to the solitary tract and centred on the obex (mNTS). Previous work has shown this restricted area of the NTS to contain the greatest concentration of aortic afferent baroreceptor terminal fields. Electrical stimulation of the tract elicited short-latency excitatory postsynaptic potentials in all neurons. 2. mNTS neurons were spontaneously active with firing frequencies ranging between 1 and 10 Hz, at resting potentials of -65 to -45 mV. These neurons did not exhibit spontaneous bursting activity. 3. Depolarizing current injection immediately evoked a finite, high-frequency spike discharge which rapidly declined to a lower steady-state level (i.e. spike frequency adaptation, SFA). Increasing depolarizations produced a marked increase in the peak instantaneous frequency but a much smaller increase in the steady-state firing level. 4. Conditioning with a hyperpolarizing prepulse resulted in a prolonged delay of up to 600 ms before the first action potential (i.e. delayed excitation, DE) with an attendant decrease in peak discharge rates. DE was modulated by both the magnitude and duration of the prestimulus hyperpolarization, as well as the magnitude of the depolarizing stimulus. Tetrodotoxin (TTX) eliminated spike discharge but had little effect on the ramp-like membrane depolarization characteristic of DE. 5. We have developed a mathematical model for mNTS neurons to facilitate our understanding of the interplay between the underlying ionic currents. It consists of a comprehensive membrane model of the Hodgkin-Huxley type coupled with a fluid compartment model describing cytoplasmic [Ca2+]i homeostasis. 6. The model suggests that (a) SFA is caused by an increase in [Ca2+]i which activates the outward K+ current, IK,Ca, and (b) DE results from the competitive interaction between the injected depolarizing current and the hyperpolarization-activated transient outward K+ currents, IA and ID. 7. We conclude that our ionic current model is capable of providing biophysical explanations for a number of phenomena associated with brainstem neurons, either during spontaneous activity or in response to patterned injections of current. This model is a potentially useful adjunct for on-going research into the central mechanisms involved in the regulation of both blood pressure and ventilation.

Neuromodulation

The ability of the nervous system to respond to the environment and to learn depends upon the tuning of neuronal electrical activity, loosely called neuromodulation. The substrates for electrical activity and, therefore, neuromodulation are ion channels which may be either synaptic or extrasynaptic. Neuromodulation is dynamic and most frequently involves neurotransmitters and hormones acting via G-protein-coupled pathways.