Abstract
We study the effects of synaptic plasticity on the determination of firing period and relative phases in a network of two oscillatory neurons coupled with reciprocal inhibition. We combine the phase response curves of the neurons with the short-term synaptic plasticity properties of the synapses to define Poincaré maps for the activity of an oscillatory network. Fixed points of these maps correspond to the phase-locked modes of the network. These maps allow us to analyze the dependence of the resulting network activity on the properties of network components. Using a combination of analysis and simulations, we show how various parameters of the model affect the existence and stability of phase-locked solutions. We find conditions on the synaptic plasticity profiles and the phase response curves of the neurons for the network to be able to maintain a constant firing period, while varying the phase of locking between the neurons or vice versa. A generalization to cobwebbing for two-dimensional maps is also discussed.
Highlights
The output of a neuronal network, determined in part by the relative spiking times of its individual neurons, depends on the coordinated activity of its neurons
In the analysis of an oscillatory network, the steady-state activity of the network can often be reduced to the study of a return map
The advantage of using maps is that it often allows the network dynamics to be understood by tracking empirically observable characteristics such as period and phase. We derive such a map for a two-cell network coupled with inhibitory synapses with the goal of understanding how short-term synaptic plasticity and other factors determine the network period and the relative activity phase of the two neurons
Summary
The output of a neuronal network, determined in part by the relative spiking times of its individual neurons, depends on the coordinated activity of its neurons. Individual neurons in a network can differ in their intrinsic properties, being silent, spiking or bursting; different neurons can have different responses to the synaptic inputs they receive, and the synaptic inputs themselves can differ widely These different characteristics all play a role in determining the resulting network activity. The main advance in our work is the derivation of tools for analyzing higherdimensional maps that incorporate the effects of synaptic plasticity and provide predictions on circumstances under which an oscillatory network of neurons will phaselock and at what period. We consider a network of two neurons, mutually coupled by inhibition in which the synaptic strength is frequency dependent In deriving these maps, we must track the phases of each cell, and the strength of each synapse. We show that the methods derived apply to networks that are heterogeneous either in the intrinsic properties of individual cells, in their synapses, or both
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