Gap junctions and emergent rhythms

Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic neural network models, which are event based, any model with gap junctions must necessarily involve a single neuron model that can represent the shape of an action potential. Indeed, not only do neurons communicating via gaps feel super-threshold spikes, but they also experience, and respond to, sub-threshold voltage signals. In this chapter we show that the so-called absolute integrate-and-fire model is ideally suited to such studies. At the single neuron level voltage traces for the model may be obtained in closed form, and are shown to mimic those of fast-spiking inhibitory neurons. Interestingly in the presence of a slow spike adaptation current the model is shown to support periodic bursting oscillations. For both tonic and bursting modes the phase response curve can be calculated in closed form. At the network level we focus on global gap junction coupling and show how to analyze the asynchronous firing state in large networks. Importantly, we are able to determine the emergence of non-trivial network rhythms due to strong coupling instabilities. To illustrate the use of our theoretical techniques (particularly the phase-density formalism used to determine stability) we focus on a spike adaptation induced transition from asynchronous tonic activity to synchronous bursting in a gap-junction coupled network

Gap junctions and emergent rhythms

Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic neural network models, which are event based, any model with gap junctions must necessarily involve a single neuron model that can represent the shape of an action potential. Indeed, not only do neurons communicating via gaps feel super-threshold spikes, but they also experience, and respond to, sub-threshold voltage signals. In this chapter we show that the so-called absolute integrate-and-fire model is ideally suited to such studies. At the single neuron level voltage traces for the model may be obtained in closed form, and are shown to mimic those of fast-spiking inhibitory neurons. Interestingly in the presence of a slow spike adaptation current the model is shown to support periodic bursting oscillations. For both tonic and bursting modes the phase response curve can be calculated in closed form. At the network level we focus on global gap junction coupling and show how to analyze the asynchronous firing state in large networks. Importantly, we are able to determine the emergence of non-trivial network rhythms due to strong coupling instabilities. To illustrate the use of our theoretical techniques (particularly the phase-density formalism used to determine stability) we focus on a spike adaptation induced transition from asynchronous tonic activity to synchronous bursting in a gap-junction coupled network

Regulation of rhythmic activity in the stomatogastric ganglion of decapod crustaceans

Neuronal networks produce reliable functional output throughout the lifespan of an animal despite ceaseless molecular turnover and a constantly changing environment. The cellular and molecular mechanisms underlying the ability of these networks to maintain functional stability remain poorly understood. Central pattern generating circuits produce a stable, predictable rhythm, making them ideal candidates for studying mechanisms of activity maintenance. By identifying and characterizing the regulators of activity in small neuronal circuits, we not only obtain a clearer understanding of how neural activity is generated, but also arm ourselves with knowledge that may eventually be used to improve medical care for patients whose normal nervous system activity has been disrupted through trauma or disease. We utilize the pattern-generating pyloric circuit in the crustacean stomatogastric nervous system to investigate the general scientific question: How are specific aspects of rhythmic activity regulated in a small neuronal network? The first aim of this thesis poses this question in the context of a single neuron. We used a single-compartment model neuron database to investigate whether co-regulation of ionic conductances supports the maintenance of spike phase in rhythmically bursting “pacemaker” neurons. The second aim of the project extends the question to a network context. Through a combination of computational and electrophysiology studies, we investigated how the intrinsic membrane conductances of the pacemaker neuron influence its response to synaptic input within the framework of the Phase Resetting Curve (PRC). The third aim of the project further extends the question to a systems-level context. We examined how ambient temperatures affect the stability of the pyloric rhythm in the intact, behaving animal. The results of this work have furthered our understanding of the principles underlying the long-term stability of neuronal network function.Ph.D

Firmas neuronales y multicódigos en neuronas con comportamiento en ráfagas

Tesis doctoral inédita. Universidad Autónoma de Madrid, Escuela Politécnica Superior, junio de 200