Delay-Induced Multistability and Loop Formation in Neuronal Networks with Spike-Timing-Dependent Plasticity

Mojtaba Madadi Asl,Alireza Valizadeh,Peter A Tass

doi:10.1038/s41598-018-30565-9

Abstract

Spike-timing-dependent plasticity (STDP) adjusts synaptic strengths according to the precise timing of pre- and postsynaptic spike pairs. Theoretical and computational studies have revealed that STDP may contribute to the emergence of a variety of structural and dynamical states in plastic neuronal populations. In this manuscript, we show that by incorporating dendritic and axonal propagation delays in recurrent networks of oscillatory neurons, the asymptotic connectivity displays multistability, where different structures emerge depending on the initial distribution of the synaptic strengths. In particular, we show that the standard deviation of the initial distribution of synaptic weights, besides its mean, determines the main properties of the emergent structural connectivity such as the mean final synaptic weight, the number of two-neuron loops and the symmetry of the final structure. We also show that the firing rates of the neurons affect the evolution of the network, and a more symmetric configuration of the synapses emerges at higher firing rates. We justify the network results based on a two-neuron framework and show how the results translate to large recurrent networks.

Highlights

It is possible to stabilize strong bidirectional connections by employing variations of STDP22 or by considering independent noise[31] in the plastic neuronal networks
Spike-timing-dependent plasticity (STDP) is conventionally known as a mechanism which generically breaks the structural symmetry of neuronal networks and underlies the formation of feedforward networks[4,19,24,25,56]
This result in recurrent networks contradicts the experimental observations in cortical circuits where bidirectional connections are frequent[26,27,28,29,30]

Summary

Introduction

It is possible to stabilize strong bidirectional connections by employing variations of STDP22 or by considering independent noise[31] in the plastic neuronal networks. As shown recently, by taking into account dendritic and axonal propagation delays, the conventional pair-based additive STDP may lead to the emergence of different connectivity patterns including both unidirectional and bidirectional connections, or decoupled neurons[32]. The presence of dendritic and axonal propagation delays can regulate the emergent structures of STDP-driven plastic neuronal populations[20,32]. This leads to a more symmetric final structure when the neurons are firing at higher rates All of these nontrivial phenomena are only seen when the propagation delays are incorporated in the formulation of the model: Without propagation delays, any initial preparation ends up with unidirectional connections regardless of the firing rate of the neurons and the initial weights of the synapses

Methods

Results

Conclusion