Travelling waves modulated by resonant currents in laterally-inhibited grids of leaky integrate-and-fire neurons

Travelling waves of neural activity are a biologically salient and analytically tractable dynamic of networks of neurons. They have been observed experimentally across the whole brain as well as at smaller scales, linked to functions as diverse as visual processing, motor coordination, and situating oneself in space. The simple analytical description of travelling waves have made them a popular lens through which to examine the dynamics of both neural field models and spiking neuronal networks, whether in isolation, considering the interactions of waves, or using their solutions as scaffolds for less tractable behaviours such as localised bumps of firing activity. This thesis investigates the role of slow voltage-gated ion channels in modulating the dynamics of travelling waves, using a laterally inhibited spiking network of leaky integrate-and-fire neurons to link the single-neuron and network scales explicitly. Voltage-gated ion channels such as HCN channels that operate on a timescale slower than neural spikes enable a variety of dynamics in single neurons such as subthreshold oscillations, resonant responses to input, and bistable tonic firing. The inclusion of these ion channels in our model introduces a variety of effects. We observe an increase in wave speed through interplay between the resonant ion channel and lateral inhibition, and see weakly-coupled waves form on scales linked to the natural frequency of the neuron. While some solutions are stabilised by stronger ion channels, subthreshold oscillations promote a multiplicity of grazing bifurcations, producing intermediate regions of solution existence in parameter space. Beyond bifurcations, we also note modulation of more complex behaviours such as stationary bumps. This points to a broader investigation of spiking dynamics modulated or permitted by multi-variable integrate-and-fire models. We also consider the utility of the spiking neuron network model for investigations of travelling waves in higher dimensions.<p></p>

Author dc:creator

• Henry Kerr (21041375)

• Neuroscience
• Dynamical Systems
• Computational Neuroscience
• Travelling waves
• Ion channels

Statement dc:rights

• All rights reserved
• Open Access after 2027-05-24

Identifier

10779/exe.32393907.v1

OAI identifier oai:identifier

oai:figshare.com:article/32393907