Pulse shape and voltage-dependent synchronization in spiking neuron networks

Abstract

Pulse-coupled spiking neural networks are a powerful tool to gain mechanistic insights into how neurons self-organize to produce coherent collective behavior. These networks use simple spiking neuron models, such as the $\theta$-neuron or the quadratic integrate-and-fire (QIF) neuron, that replicate the essential features of real neural dynamics. Interactions between neurons are modeled with infinitely narrow pulses, or spikes, rather than the more complex dynamics of real synapses. To make these networks biologically more plausible, it has been proposed that they must also account for the finite width of the pulses, which can have a significant impact on the network dynamics. However, the derivation and interpretation of these pulses is contradictory and the impact of the pulse shape on the network dynamics is largely unexplored. Here, I take a comprehensive approach to pulse-coupling in networks of QIF and $\theta$-neurons. I argue that narrow pulses activate voltage-dependent synaptic conductances and show how to implement them in QIF neurons such that their effect can last through the phase after the spike. Using an exact low-dimensional description for networks of globally coupled spiking neurons, I prove for instantaneous interactions that collective oscillations emerge due to an effective coupling through the mean voltage. I analyze the impact of the pulse shape by means of a family of smooth pulse functions with arbitrary finite width and symmetric or asymmetric shapes. For symmetric pulses, the resulting voltage-coupling is not very effective in synchronizing neurons, but pulses that are slightly skewed to the phase after the spike readily generate collective oscillations. The results unveil a voltage-dependent spike synchronization mechanism in neural networks, which is facilitated by pulses of finite width and complementary to traditional synaptic transmission.

arXiv comment65 pages, 11 figures

References in corpus (36)

• Macroscopic description for networks of spiking neurons
• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators
• Low-dimensional dynamics of populations of pulse-coupled oscillators
• Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks
• Transition from asynchronous to oscillatory dynamics in balanced spiking networks with instantaneous synapses
• Stability of the splay state in pulse--coupled networks
• From quasiperiodic partial synchronization to collective chaos in populations of inhibitory neurons with delay
• Macroscopic phase resetting-curves determine oscillatory coherence and signal transfer in inter-coupled neural circuits
• Exact mean-field theory explains the dual role of electrical synapses in collective synchronization
• Exact neural mass model for synaptic-based working memory
• Dynamics of a large system of spiking neurons with synaptic delay
• An exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks
• Spatiotemporal dynamics and reliable computations in recurrent spiking neural networks
• Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons
• How effective delays shape oscillatory dynamics in neuronal networks
• Coherent oscillations in balanced neural networks driven by endogenous fluctuations
• Exact finite-dimensional description for networks of globally coupled spiking neurons
• Synchronization scenarios in the Winfree model of coupled oscillators
• Modeling the Network Dynamics of Pulse-Coupled Neurons
• Moving bumps in theta neuron networks
• Population spiking and bursting in next generation neural masses with spike-frequency adaptation
• Automated point-neuron simplification of data-driven microcircuit models
• Dynamics of a population of oscillatory and excitable elements
• Macroscopic Dynamics of Neural Networks with Heterogeneous Spiking Thresholds
• Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling
• Hierarchy of exact low-dimensional reductions for populations of coupled oscillators
• Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity
• Average activity of excitatory and inhibitory neural populations
• Exact finite-dimensional reduction for a population of noisy oscillators and its link to Ott-Antonsen and Watanabe-Strogatz theories
• Comparison between an exact and a heuristic neural mass model with second order synapses
• On the interpretation of Dirac $\delta$ pulses in differential equations for phase oscillators
• Collective dynamics in the presence of finite-width pulses
• The effects of within-neuron degree correlations in networks of spiking neurons
• Cross-scale excitability in networks of synaptically-coupled quadratic integrate-and-fire neurons
• Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons

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• Low-dimensional model for adaptive networks of spiking neurons
• Synaptic shot-noise triggers fast and slow global oscillations in balanced neural networks
• Two-phase quadratic integrate-and-fire neurons: Exact low-dimensional description for ensembles of finite-voltage neurons
• The interplay of common noise and finite pulses on biological neurons