Complementarity of spike- and rate-based dynamics of neural systems.
Relationships between spiking-neuron and rate-based approaches to the dynamics of neural assemblies are explored by analyzing a model system that can be treated by both methods, with the rate-based method further averaged over multiple neurons to give a neural-field approach. The system consists of a chain of neurons, each with simple spiking dynamics that has a known rate-based equivalent. The neurons are linked by propagating activity that is described in terms of a spatial interaction strength with temporal delays that reflect distances between neurons; feedback via a separate delay loop is also included because such loops also exist in real brains. These interactions are described using a spatiotemporal coupling function that can carry either spikes or rates to provide coupling between neurons. Numerical simulation of corresponding spike- and rate-based methods with these compatible couplings then allows direct comparison between the dynamics arising from these approaches. The rate-based dynamics can reproduce two different forms of oscillation that are present in the spike-based model: spiking rates of individual neurons and network-induced modulations of spiking rate that occur if network interactions are sufficiently strong. Depending on conditions either mode of oscillation can dominate the spike-based dynamics and in some situations, particularly when the ratio of the frequencies of these two modes is integer or half-integer, the two can both be present and interact with each other.
School of Engineering, University of Waikato, Hamilton, New Zealand. mtwilson@waikato.ac.nz
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Wilson
P A
PA
Robinson
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B
O'Neill
D A
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Steyn-Ross
D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D019295:Computational Biology; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*