Abstract
Contemporary simulators for networks of point and few-compartment model neurons come with a plethora of ready-to-use neuron and synapse models and support complex network topologies. Recent technological advancements have broadened the spectrum of application further to the efficient simulation of brain-scale networks on supercomputers. In distributed network simulations the amount of spike data that accrues per millisecond and process is typically low, such that a common optimization strategy is to communicate spikes at relatively long intervals, where the upper limit is given by the shortest synaptic transmission delay in the network. This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions. Here, we present a numerical algorithm based on a waveform-relaxation technique which allows for network simulations with gap junctions in a way that is compatible with the delayed communication strategy. Using a reference implementation in the NEST simulator, we demonstrate that the algorithm and the required data structures can be smoothly integrated with existing code such that they complement the infrastructure for spiking connections. To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers. Finally, we discuss limitations of the novel technology.
Highlights
Electrical synapses, or gap junctions, were classically regarded as a primitive form of neural signaling that play roles mostly in invertebrate neural circuits
First we investigate the pair of neurons coupled by a gap junction, which was already presented in the introduction to demonstrate the problems of the single-step method in contrast to the advanced integration schemes introduced in the present work
The approach discloses the general behavior of the methods and provides access to the single-neuron integration error not measurable in recurrent networks with chaotic dynamics
Summary
Electrical synapses, or gap junctions, were classically regarded as a primitive form of neural signaling that play roles mostly in invertebrate neural circuits. The functional roles of gap junctions in network behavior are still not fully understood but they are widely believed to be crucial for synchronization and generation of rhythmic activity. Recent results suggest that their contribution to synchronization is versatile, as it depends on the intrinsic currents and morphology of the neurons as well as their interaction with inhibitory synapses (Hansel et al, 2012). A classification of this diversity of synchronization behaviors is addressed by the study of phase response curves (PRCs) (Mancilla et al, 2007; Coombes and Zachariou, 2009; Hansel et al, 2012), which describe a neuronal oscillator by its phase response to a perturbation. Other prominent works study more specific functional roles of gap junctions and combine the detailed simulation of small networks with experiments (Vervaeke et al, 2012)
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