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Effects of Autapse and Channel Blockage on Firing Regularity in a Biological Neuronal Network

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Effects of Autapse and Channel Blockage on Firing Regularity in a Biological Neuronal Network Rukiye UZUN and Mahmut OZER / IU-JEEE Vol. 17(1), (2017), 3069-3073 Effects of Autapse and Channel Blockage on Firing Regularity in a Biological Neuronal Network Rukiye UZUN1, Mahmut OZER 1 1Bulent Ecevit University, Zonguldak, Turkey [email protected], [email protected] Abstract: In this paper; the effects of autapse (a kind of self-synapse formed between the axon of the soma of a neuron and its own dendrites) and ion channel blockage on the firing regularity of a biological small-world neuronal network, consists of stochastic Hodgkin-Huxley neurons, are studied. In this study, it is assumed that all of the neurons on the network have a chemical autapse and a constant membrane area. Obtained results indicate that there are different effects of channel blockage and parameters of the autapse on the regularity of the network, thus on the temporal coherence of the network. It is found that the firing regularity of the network is decreased with the sodium channel blockage while increased with potassium channel blockage. Besides, it is determined that regularity of the network augments with the conductance of the autapse. Keywords: Autapse, channel blocking, ion channel noise, small-world neuronal netwoks. 1. Introduction investigated the effect of ion channel noise on dynamics of neuron in the presence of autapse based on a stochastic The nervous system, having a complex biologic Hodgkin-Huxley (HH) model. They found that autapse is structure, comprises of billions of nerve cells (neurons) reduced the spontaneous spiking activity of neuron at and synaptic connections between them [1]. In this characteristic frequencies by inducing bursting firing and complex structure, it is believed that the signal multimodal interspike interval distribution. Connelly [17] communication (i.e. information transmission) can be revealed that autapses augment the gamma oscillations of carried out by synaptic coupling [2, 3]. Synapses are interneurons, known as basket cells, in a Wang-Buzsáki essentially categorized in two different types: electrical model during the gamma oscillations. Wang et al [18] and chemical synapses [4]. However, several decades discovered that autapses causes to switch the dynamics of ago, neurobiologists found out that some neurons could electrical activity of Hindmarsh-Rose model among different be connected to itself which forms a time-delayed firing patterns (quiescent, periodic and chaotic). In another feedback mechanism on a cellular level [5-9]. These study, it is demonstrated that autapses can regulate the mode- self-synapses named as an autapse and were proposed locking behaviors of a HH model subjected to sinusoidal by Van der Loss and Glaser in 1972 [10]. Although stimulus, especially by autaptic delay time [19]. Recently, autapses have an unusual (odd) structure, they have been Yılmaz and Ozer [20] consider the weak signal detection observed commonly in various brain areas, such as performance of a stochastic HH model with regard to an neocortex, hippocampus and cerebellum etc. [4, 11-13, electrical autapse. They obtained that the detection Wang and Chen 2015, Wang et al 2016]. performance can be healed or deteriorated depending on Besides, it has been experimentally presented that autapses’ parameters. Similar studies concerning weak these type of synapses have significant effects on the signal detection performance have been realized on small- firing dynamics of neurons. For example, Bacci and world (SW) and scale-free (SF) neural networks by Yilmaz Huguenard (2006) showed that the autaptic connections et al and have been obtained analogous results [21, 22]. have a vital role on determining the precise spike timing Wang and Gong [23] have shown that both multiple of inhibitory interneurons in neocortex [14]. Rusin et al. coherence resonance (MCR) and synchronization transitions [15] demonstrated that usage of continuous time- are occurred because of autpases, in SW neuronal network. delayed feedback stimulation can arrange the Recently, Wang and Chen revealed that autapses provide an synchronization of spikes in cultured neurons. In opportunity to engineer the response of a HH model to addition to these experimental studies, there is also subthreshold stimulus [24]. Moreover, in this study, it is numerous studies that investigate the impacts of autapse revealed out that the detection of subthreshold stimulus is on firing dynamics of the neuron with computational increased due to autapse. More recently, the impacts of both neuronal models [16-25]. In this context, Li et al [16] electrical and chemical autapses on the temporal coherence Received on: 30.01.2017 Accepted on: 14.03.2017 3070 Rukiye UZUN and Mahmut OZER / IU-JEEE Vol. 17(1), (2017), 3069-3073 of a single HH model and SF neuronal network is a simplified neuron model can be described by two different analyzed by Yilmaz et al [25]. They obtained that the forms. One is linear coupling (i.e. electrical) and the other is dynamics of neuron or network change nonlinear coupling (i.e. chemical). In this study we use prominently with the proper choice of autaptic chemical autaptic current which is given by the following parameters. two equations [21,23,41]: Nonetheless, it is well known that neuronal- information processing operates under diverse noise ( ) 퐼푎푢푡푖 = −푎푢푡[푉푖(푡) − 푉푠푦푛]푆 푡 − 휏 ; (2a) sources, which has therapeutic influences contrary to 푆푖(푡 − 휏) = 1/ {1 + exp[−푘(푉푖(푡 − 휏) − 휃]} (2b) expectations [26]. The most important noise source in neural systems is originated in voltage-gated ion Here gaut is the autaptic intensity and τ is the delay time channels due to their random transitions between which is taken as 10 ms throughout the study. Vsyn represents conducting and non-conducting states [27]. The strength the autaptic reversal potential and its value varies depending of channel noise is related with the numbers of ion on whether the autapse is excitatory (Vsyn=2 mV) or channels on membrane, thus membrane area. But, its inhibitory (Vsyn=-2 mV). We assumed that all neurons have real effect on neuron’s dynamics is determined by the excitatory chemical autapse with the same autaptic number of active ion channels participating in the parameters. The other parameters’ values, in equation (2), is generation of spikes [28]. Therefore, addressing impacts set as k=8, θ=-0.25. More interpretations of all parameters of the number of active ion channels is important in Eq. 2 can be found at Ref. [41]. especially to uncover the role of specific ion channel In equation (1), GNa, GK and GL denote sodium, noise on neuronal spiking activity. Experimental studies potassium and leakage ion channel conductance, indicate that some neurotoxins such as respectively. In the model, the leakage conductance is -2 tetraetylammonium (TEA) ve tetratoxin (TTX) can alter constant, GL=0.3mScm , whereas the others dynamically the properties of ion channels [29]. For a given change as follows [30, 34, 37, 38]: membrane, by a fine-tuned addition of these toxins a certain portion of potassium- and sodium ion channels 푚푎푥 3 푚푎푥 4 퐺푁푎(푚푖, ℎ푖) = χ푁푎푚 ℎ푖, 퐺퐾(푛푖) = χ퐾푛 (3) could be disabled or blocked and hence the number of 푁푎 푖 퐾 푖 active (working) ion channels can be reduced. There are max -2 max -2 where gNa =120mScm and gK =36mScm is the also plenty of studies based on different computational maximal conductance of the corresponding ion channel. χi neuron models, where the impacts of changing the i=(Na, K) is a scaling factor, which equals to the ratio of number of particular ion channels on firing dynamics of active (non-blocked) i-type ion channel numbers to total i- a single neuron or neuronal networks’ is examined [30- type ion channel number within a given membrane size [30, 38]. In these studies, it is uncovered that channel 31]. This factor is confined to unit interval and i-type ion blocking has crucial impacts on firing dynamics. channel blocking level gets higher as the factor approaches In this study, different from the above studies, we zero. In equation (3); ni, mi and hi are dimensionless variables investigate how the firing dynamics of Newman-Watts that represent for the potassium ion channel activation, SW neuronal network, consisting of stochastic HH sodium ion channel activation and inactivation, respectively. neurons, change in the presence of both ion channel The dynamics of these variables is described by the blocking and autapse. For this aim, we assume that all following Langevin equation for a finite membrane size [42]: neurons on the network have a chemical autapse and are exposed to same ratio of ion channel blocking. 푑푥 푖 = 훼 (푉)(1 − 푥 ) − 훽 (푉)푥 + 휉 (푡), 푑푡 푥푖 푖 푥푖 푖 푥푖 2. Model and Method 푥푖 = 푚, 푛, ℎ (4) Time evolution of membrane potentials of Newman- Here αxi and βxi are the voltage-dependent opening and Watss network of HH neurons in the presence of closing rates of xi. ζxi(t) is the zero mean Gaussian white chemical autapse is given as follows [16, 21-23, 25]: noises whose auto-correlation functions given as follows [42]: 푑푉 퐶 푖 = −퐺 (푚 , ℎ )(푉 − 푉 ) − 퐺 (푛 )(푉 − 푚 푑푡 푁푎 푖 푖 푖 푁푎 퐾 푖 푖 ′ 2훼푥훽푥 ′ 〈휉푥(푡)휉푥(푡 )〉 = 훿(푡 − 푡 ) (5a) 푉 ) − 퐺 (푉 − 푉 ) + ∑ 휀 (푉 (푡) − 푉 (푡)) + 퐼 (1) 푁푗χ푗(훼푥+훽푥) 퐾 퐿 푖 퐿 푖푗 푗 푖 푎푢푡푖 푁 = 휌 푆; 푗 = 푁푎, 퐾; 푥 = 푚, 푛, ℎ (5b) 푗 푗 Here C is the membrane capacitance per unit area, V m i where S denotes the membrane size, N and ρ are the total denotes the membrane potential of neuron i=1,...,N (N j j number and density of corresponding ion channel, shows the network size) in mV, and V =50mV, V =- Na K respectively [30, 31].
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