Stimulus-dependent synchronization in delayed-coupled neuronal networks

Abstract

Time delay is a general feature of all interactions. Although the effects of delayed interaction are often neglected when the intrinsic dynamics is much slower than the coupling delay, they can be crucial otherwise. We show that delayed coupled neuronal networks support transitions between synchronous and asynchronous states when the level of input to the network changes. The level of input determines the oscillation period of neurons and hence whether time-delayed connections are synchronizing or desynchronizing. We find that synchronizing connections lead to synchronous dynamics, whereas desynchronizing connections lead to out-of-phase oscillations in network motifs and to frustrated states with asynchronous dynamics in large networks. Since the impact of a neuronal network to downstream neurons increases when spikes are synchronous, networks with delayed connections can serve as gatekeeper layers mediating the firing transfer to other regions. This mechanism can regulate the opening and closing of communicating channels between cortical layers on demand.

Dendritic and Axonal Propagation Delays Determine Emergent Structures of Neuronal Networks with Plastic Synapses

“…5D. This is because the connectivity of the interconnected network does not support the retention of the π phase difference through all links68. Hence, in contrast to the inphase state, the antiphase state does not constitute a building block for the entire network.…”

“…This can be illustrated by considering a three-neuron loop around which the sum of phase differences should be multiples of 2 π and this is at odds with the presence of a π phase difference in all three links of the loop. Such a geometric constraint on the relative phase relations between neurons in systems of this kind leads to frustrated dynamics 68. In this case, the relative phase relations between neurons and consequently the changes in the network connectivity through STDP cannot be readily predicted by the analysis of two-neuron motif.…”

Quantifying axonal responses in patient-specific models of subthalamic deep brain stimulation

“…In turn, analyzing the network dynamics induced by DBS requires a different kind of model system that is designed to simulate the oscillatory activity of interconnected groups of neurons [Rubin and Terman, 2004; Hauptmann and Tass, 2007]. PAM results should represent the stimulation inputs to DBS network models, specifically driving activity in the various pathways at representative percentages [Hahn and McIntyre, 2010] and conduction delays [Esfahani et al, 2016]. We propose that integration of pathway activation results with dynamical network analysis has great potential to accelerate the clinical optimization of novel stimulation paradigms [Tass et al, 2012].…”

Modeling of time delay-induced multiple synchronization behavior of interneuronal networks with the Izhikevich neuron model

“…Modeling the dynamic behavior of a network has attracted much attention in recent years [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Gibson et al [6] showed by paired-cell recordings that while the same type of inhibitory neurons were strongly interconnected by electrical synapses, electrical synapses between different inhibitory cell types were rare.…”

“…Several works in the literature used only chemical synaptic currents in the investigation of the synchronization behavior of networks [2,[7][8][9][10]. In the wok by Kudela et al [2], a conductance-based model was used to study the networks of synaptically connected neurons generating action potentials.…”