Autapse-Induced Spiral Wave in Network of Neurons under Noise

Abstract

Autapse plays an important role in regulating the electric activity of neuron by feedbacking time-delayed current on the membrane of neuron. Autapses are considered in a local area of regular network of neurons to investigate the development of spatiotemporal pattern, and emergence of spiral wave is observed while it fails to grow up and occupy the network completely. It is found that spiral wave can be induced to occupy more area in the network under optimized noise on the network with periodical or no-flux boundary condition being used. The developed spiral wave with self-sustained property can regulate the collective behaviors of neurons as a pacemaker. To detect the collective behaviors, a statistical factor of synchronization is calculated to investigate the emergence of ordered state in the network. The network keeps ordered state when self-sustained spiral wave is formed under noise and autapse in local area of network, and it independent of the selection of periodical or no-flux boundary condition. The developed stable spiral wave could be helpful for memory due to the distinct self-sustained property.

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“…Experimental studies reveal that autapse is quite common, contrary to expectations (Lübke et al 1996, Bekkers 1998, Bacci and Huguenard 2006, Branco and Staras 2009, Flight 2009, Rusin et al 2011. Besides these experimental studies, numerical studies have shown that autaptic connections play important roles on the spiking dynamics of the neurons (Bacci and Huguenard 2006, Li et al 2010, Qin et al 2014, Yilmaz and Ozer 2015, Yilmaz et al 2015a, Yilmaz et al 2015b, Wang and Chen 2016, Wang and Gong 2016, Yilmaz et al 2016, Uzun and Ozer 2017a, Uzun and Ozer 2017b, Uzun et al 2017. For example, Li et al (2010) demonstrated that, at certain characteristic frequencies, the spiking dynamics of a single neuron are weakened by the delayed feedback which manifests itself by the occurrence of bursting firings and multimodal interspike interval distributions.…”

“…We reported that at different ion channel blocking levels, the spiking dynamics of the neuron do not change for too small coupling strength whether it increases after a certain coupling strength' value. Apart from these studies performed at single neuron level, there are also many studies conducted at neuronal networks modelled with different network structures in the literature (Qin et al 2014, Yilmaz et al 2015a, Yilmaz et al 2015b, Wang and Gong 2016, Uzun and Ozer 2017b, Uzun et al 2017.…”

Effects of autapse and channel blockage on firing regularity in a biological neuronal network

“…In this complex structure, it is believed that the signal communication (i.e. information transmission) can be carried out by synaptic coupling [2,3]. Synapses are essentially categorized in two different types: electrical and chemical synapses [4].…”

Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems

“…Further, time-delay occurred within the systems are ubiquitous in several real situations. In particular, intrinsic time-delay can be found in neuronal models, where neurons are connected to autapse (a self-synapse or a specialized connection between a neuron and itself), which can be described by time-delayed feedback in closed loop [48][49][50]. In addition, intrinsic time-delay can also observed in ecology, epidemics, physiology, physics, economics, engineering and control systems, [1] which inevitably require delay for a complete description of the dynamical system (note that an intrinsic delay is different from connection delays which arise between different systems due to finite signal propagation time).…”