Rhythmic activity within the heartbeat pattern generator of the medicinal leech is based on the alternating bursting of mutually inhibitory pairs of oscillator heart interneurons (half-center oscillators). Bicuculline methiodide has been shown to block mutual inhibition between these interneurons and to cause them to spike tonically while recorded intracellularly (Schmidt and Calabrese, 1992). Using extracellular recording techniques, we show here that oscillator and premotor heart interneurons continue to burst when pharmacologically isolated with bicuculline, although the bursting is not robust in some preparations. We propose that a nonspecific leak current introduced by the intracellular microelectrode suppresses endogenous bursting activity to account for the discrepancy with results using intracellular recording. A two-parameter bifurcation diagram (E(leak) vs g(leak)) of a mathematical model of a single heart interneuron shows a narrow stripe of parameter values where bursting occurs, separating large zones of tonic spiking and silence. A similar analysis performed for a half-center oscillator model outlined a much larger area of bursting. Bursting in the half-center oscillator model is also less sensitive to variation in the maximal conductances of voltage-gated currents than in the single-neuron model. Thus, in addition to ensuring appropriate bursting characteristics such as period, phase, and duty cycles, the half-center configuration enhances oscillation robustness, making them less susceptible to random or imposed changes in membrane parameters. Endogenous bursting, in turn, ensures appropriate bursting if the strength of mutual inhibition is weakened and limits the minimum period of the half-center oscillator to a period near that of the single neuron.

We study a continuous and reversible transition between periodic tonic spiking and bursting activities in a neuron model. It is described as the blue-sky catastrophe, which is a homoclinic bifurcation of a saddle-node periodic orbit of codimension one. This transition constitutes a biophysically plausible mechanism for the regulation of burst duration that increases with no bound like 1/square root alpha-alpha0 as the transition value alpha0 is approached.

The generation of rhythmic patterns by neuronal networks is a complex phenomenon, relying on the interaction of numerous intrinsic and synaptic currents, as well as modulatory agents. To investigate the functional contribution of an individual ionic current to rhythmic pattern generation in a network, we constructed a hybrid system composed of a silicon model neuron and a heart interneuron from the heartbeat timing network of the medicinal leech. When the model neuron and a heart interneuron are connected by inhibitory synapses, they produce rhythmic activity similar to that observed in the heartbeat network. We focused our studies on investigating the functional role of the hyperpolarization-activated inward current (I h ) on the rhythmic bursts produced by the network. By introducing changes in both the model and the heart interneuron, we showed that I h determines both the period of rhythmic bursts and the balance of activity between the two sides of the network, because the amount and the activation/deactivation time constant of I h determines the length of time that a neuron spends in the inhibited phase of its burst cycle. Moreover, we demonstrated that the model neuron is an effective replacement for a heart interneuron and that changes made in the model can accurately mimic similar changes made in the living system. Finally, we used a previously developed mathematical model (Hill et al. 2001) of two mutually inhibitory interneurons to corroborate these findings. Our results demonstrated that this hybrid system technique is advantageous for investigating neuronal properties that are inaccessible with traditional techniques.

The dynamics of different ionic currents shape the bursting activity of neurons and networks that control motor output. Despite being ubiquitous in all animal cells, the contribution of the Na+/K+ pump current to such bursting activity has not been well studied. We used monensin, a Na+/H+ antiporter, to examine the role of the pump on the bursting activity of oscillator heart interneurons in leeches. When we stimulated the pump with monensin, the period of these neurons decreased significantly, an effect that was prevented or reversed when the h-current was blocked by Cs+. The decreased period could also occur if the pump was inhibited with strophanthidin or K+-free saline. Our monensin results were reproduced in model, which explains the pump’s contributions to bursting activity based on Na+ dynamics. Our results indicate that a dynamically oscillating pump current that interacts with the h-current can regulate the bursting activity of neurons and networks.DOI: http://dx.doi.org/10.7554/eLife.19322.001

We have designed, fabricated, and tested an analog integrated-circuit architecture to implement the conductance-based dynamics that model the electrical activity of neurons. The dynamics of this architecture are in accordance with the Hodgkin-Huxley formalism, a widely exploited, biophysically plausible model of the dynamics of living neurons. Furthermore the architecture is modular and compact in size so that we can implement networks of silicon neurons, each of desired complexity, on a single integrated circuit. We present in this paper a six-conductance silicon-neuron implementation, and characterize it in relation to the Hodgkin-Huxley formalism. This silicon neuron incorporates both fast and slow ionic conductances, which are required to model complex oscillatory behaviors (spiking, bursting, subthreshold oscillations).

Neurons can demonstrate various types of activity; tonically spiking, bursting as well as silent neurons are frequently observed in electrophysiological experiments. The methods of qualitative theory of slow-fast systems applied to biophysically realistic neuron models can describe basic scenarios of how these regimes of activity can be generated and transitions between them can be made. Here we demonstrate that a bifurcation of a codimension one can explain a transition between tonic spiking behavior and bursting behavior. Namely, we argue that the Lukyanov-Shilnikov bifurcation of a saddle-node periodic orbit with noncentral homoclinics may initiate a bistability observed in a model of a leech heart interneuron under defined pharmacological conditions. This model can exhibit two coexisting types of oscillations: tonic spiking and bursting, depending on the initial state of the neuron model. Moreover, the neuron model also generates weakly chaotic bursts when a control parameter is close to the bifurcation values that correspond to homoclinic bifurcations of a saddle or a saddle-node periodic orbit.

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The origin of spike adding in bursting activity is studied in a reduced model of the leech heart interneuron. We show that, as the activation kinetics of the slow potassium current are shifted towards depolarized membrane potential values, the bursting phase accommodates incrementally more spikes into the train. This phenomenon is attested to be caused by the homoclinic bifurcations of a saddle periodic orbit setting the threshold between the tonic spiking and quiescent phases of the bursting. The fundamentals of the mechanism are revealed through the analysis of a family of the onto Poincaré return mappings.