Bifurcation diagram globally underpinning neuronal firing behaviors modified by SK conductance

doi:10.1088/1674-1056/23/2/028701

Abstract Neurons in the brain utilize various firing trains to encode the input signals they have received. Firing behavior of one single neuron is thoroughly explained by using a bifurcation diagram from polarized resting to firing, and then to depolarized resting. This explanation provides an important theoretical principle for understanding neuronal biophysical behaviors. This paper reports the novel experimental and modeling results of the modification of such a bifurcation diagram by adjusting small conductance potassium (SK) channel. In experiments, changes in excitability and depolarization block in nucleus accumbens shell and medium-spiny projection neurons are explored by increasing the intensity of injected current and blocking the SK channels by apamin. A shift of bifurcation points is observed. Then, a Hodgkin–Huxley type model including the main electrophysiological processes of such neurons is developed to reproduce the experimental results. The reduction of SK channel conductance also shifts the bifurcations, which is in consistence with experiment. A global bifurcation paradigm of this shift is obtained by adjusting two parameters, intensity of injected current and SK channel conductance. This work reveals the dynamics underpinning modulation of neuronal firing behaviors by biologically important ionic conductance. The results indicate that small ionic conductance other than that responsible for spike generation can modify bifurcation points and shift the bifurcation diagram and, thus, change neuronal excitability and adaptation.

Keywords: neuron Hopf bifurcation SK channel excitability

Received: 07 May 2013
Revised: 03 July 2013
Accepted manuscript online:

PACS:	87.19.L-	(Neuroscience)
	87.16.Vy	(Ion channels)
	87.19.ll	(Models of single neurons and networks)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 30900443) and the Fundamental Research Funds for the Central Universities, China (Grant Nos. GK201302052 and GK261001007).

Corresponding Authors: Qu Shi-Xian, Ren Wei
E-mail: sxqu@snnu.edu.cn;renwei@snnu.edu.cn

About author: 87.19.L-; 87.16.Vy; 87.19.ll; 05.45.-a

Cite this article:

Chen Meng-Jiao (陈梦娇), Ling Heng-Li (令恒莉), Liu Yi-Hui (刘一辉), Qu Shi-Xian (屈世显), Ren Wei (任维) Bifurcation diagram globally underpinning neuronal firing behaviors modified by SK conductance 2014 Chin. Phys. B 23 028701

[1]	Hille B 2001 Ion Channels of Excitable Membranes, 3rd edn. (Sunderland, MA: Sinauer Associates) p. 27
[2]	Izhikevich E M 2007 Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, 2nd edn. (Massachusetts, Cambridge: MIT Press) p. 118
[3]	Wu X B, Mo J, Yang M H, Zheng Q H, Gu H G and Ren W 2008 Chin. Phys. Lett. 25 2799
[4]	Yooer C F, Wei F, Xu J X and Zhang X H 2011 Chin. Phys. Lett. 28 030501
[5]	Li L, Gu H G, Yang M H, Liu Z Q and Ren W 2004 Int. J. Bifur. Chaos 14 1813
[6]	Men C, Wang J, Qin Y M, Wei X L, Che Y Q and Deng B 2011 Chin. Phys. B 20 128704
[7]	Xu J, Kang N, Jiang L, Nedergaard M and Kang J 2005 J. Neurosci. 25 1750
[8]	Jung S C and Hoffman D A 2009 Plos One 4 e6549
[9]	Mu P, Moyer J T, Ishikawa M, Zhang Y, Panksepp J, Sorg B A, Schlüter O M and Dong Y 2010 J. Neurosci. 30 3689
[10]	Wu X B, Shi M M, Ling H L, Wei C L, Liu Y H, Liu Z Q and Ren W 2013 Brain Res. Bull. 90 92
[11]	Shi M M, Wu X B, Wei C L, Yang M H, Liu Z Q and Ren W 2011 Neuroreport 22 762
[12]	Bianchi D, Marasco A, Limongiello A, Marchetti C, Marie H, Tirozzi B and Migliore M 2012 J. Comput. Neurosci. 33 207
[13]	Valenti O, Cifelli P, Gill K M and Grace A A 2011 J. Neurosci. 31 12330
[14]	Boye S M and Rompré P P 2000 J. Neurosci. 20 1229
[15]	Grace A A, Bunney B S, Moore H and Todd C L 1997 Trends Neurosci. 20 31
[16]	Dovzhenok A and Kuznetsov A S 2012 Plos One 7 e42811
[17]	Kasten M R, Rudy B and Anderson M P 2007 J. Physiol. 584 565
[18]	Alvina K and Khodakhah K 2008 J. Physiol. 586 2523
[19]	Canavier C C and Landry R S 2006 J. Neurophysiol. 96 2549
[20]	Kim J, Park B H, Lee J H, Park S K and Kim J H 2011 Biol. Psychiat. 69 1026
[21]	Wolf J A, Moyer J T, Lazarewicz M T, Contreras D, Benoit-Marand M, O’Donnell P and Finkel L H 2005 J. Neurosci. 25 9080
[22]	Chay T R, Fan Y S and Lee Y S 1995 Int. J. Bifur. Chaos 5 595
[23]	Fan Y S and Chay T R 1994 Biol. Cybern. 71 417
[24]	Chay T R 1985 Physica D 16 233
[25]	Kourrich S and Thomas M J 2009 J. Neurosci. 29 12275
[26]	Brebner K, Wong T P, Liu L, Liu Y, Campsall P, Gray S, Phelps L, Phillips A G and Wang Y T 2005 Science 310 1340
[27]	Kourrich S, Rothwell P E, Klug J R and Thomas M J 2007 J. Neurosci. 27 7921
[28]	Izhikevich E M 2003 IEEE Trans. Neural Netw. 14 1569
[29]	Wang Z L 2008 Acta Phys. Sin. 57 4771 (in Chinese)
[30]	Qin Y M, Wang J, Men C, Zhao J, Wei X L and Deng B 2012 Chin. Phys. B 21 078702

[1]	Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Chin. Phys. B, 2023, 32(3): 038701.
[2]	Epilepsy dynamics of an astrocyte-neuron model with ammonia intoxication Zhixuan Yuan(袁治轩), Mengmeng Du(独盟盟), Yangyang Yu(于羊羊), and Ying Wu(吴莹). Chin. Phys. B, 2023, 32(2): 020502.
[3]	Inhibitory effect induced by fractional Gaussian noise in neuronal system Zhi-Kun Li(李智坤) and Dong-Xi Li(李东喜). Chin. Phys. B, 2023, 32(1): 010203.
[4]	High-performance artificial neurons based on Ag/MXene/GST/Pt threshold switching memristors Xiao-Juan Lian(连晓娟), Jin-Ke Fu(付金科), Zhi-Xuan Gao(高志瑄),Shi-Pu Gu(顾世浦), and Lei Wang(王磊). Chin. Phys. B, 2023, 32(1): 017304.
[5]	Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse Zhi-Jun Li(李志军), Wen-Qiang Xie(谢文强), Jin-Fang Zeng(曾金芳), and Yi-Cheng Zeng(曾以成). Chin. Phys. B, 2023, 32(1): 010503.
[6]	Power-law statistics of synchronous transition in inhibitory neuronal networks Lei Tao(陶蕾) and Sheng-Jun Wang(王圣军). Chin. Phys. B, 2022, 31(8): 080505.
[7]	Effect of astrocyte on synchronization of thermosensitive neuron-astrocyte minimum system Yi-Xuan Shan(单仪萱), Hui-Lan Yang(杨惠兰), Hong-Bin Wang(王宏斌), Shuai Zhang(张帅), Ying Li(李颖), and Gui-Zhi Xu(徐桂芝). Chin. Phys. B, 2022, 31(8): 080507.
[8]	Negative self-feedback induced enhancement and transition of spiking activity for class-3 excitability Li Li(黎丽), Zhiguo Zhao(赵志国), and Huaguang Gu(古华光). Chin. Phys. B, 2022, 31(7): 070506.
[9]	The dynamics of a memristor-based Rulkov neuron with fractional-order difference Yan-Mei Lu(卢艳梅), Chun-Hua Wang(王春华), Quan-Li Deng(邓全利), and Cong Xu(徐聪). Chin. Phys. B, 2022, 31(6): 060502.
[10]	The transition from conservative to dissipative flows in class-B laser model with fold-Hopf bifurcation and coexisting attractors Yue Li(李月), Zengqiang Chen(陈增强), Mingfeng Yuan(袁明峰), and Shijian Cang(仓诗建). Chin. Phys. B, 2022, 31(6): 060503.
[11]	Memristor-based multi-synaptic spiking neuron circuit for spiking neural network Wenwu Jiang(蒋文武), Jie Li(李杰), Hongbo Liu(刘洪波), Xicong Qian(钱曦聪), Yuan Ge(葛源), Lidan Wang(王丽丹), and Shukai Duan(段书凯). Chin. Phys. B, 2022, 31(4): 040702.
[12]	Long range electromagnetic field nature of nerve signal propagation in myelinated axons Qing-Wei Zhai(翟卿伟), Kelvin J A Ooi(黄健安), Sheng-Yong Xu(许胜勇), and C K Ong(翁宗经). Chin. Phys. B, 2022, 31(3): 038701.
[13]	Explosive synchronization: From synthetic to real-world networks Atiyeh Bayani, Sajad Jafari, and Hamed Azarnoush. Chin. Phys. B, 2022, 31(2): 020504.
[14]	Switching plasticity in compensated ferrimagnetic multilayers for neuromorphic computing Weihao Li(李伟浩), Xiukai Lan(兰修凯), Xionghua Liu(刘雄华), Enze Zhang(张恩泽), Yongcheng Deng(邓永城), and Kaiyou Wang(王开友). Chin. Phys. B, 2022, 31(11): 117106.
[15]	Voltage-controllable magnetic skyrmion dynamics for spiking neuron device applications Ming-Min Zhu(朱明敏), Shu-Ting Cui(崔淑婷), Xiao-Fei Xu(徐晓飞), Sheng-Bin Shi(施胜宾), Di-Qing Nian(年迪青), Jing Luo(罗京), Yang Qiu(邱阳), Han Yang(杨浛), Guo-Liang Yu(郁国良), and Hao-Miao Zhou (周浩淼). Chin. Phys. B, 2022, 31(1): 018503.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Bifurcation diagram globally underpinning neuronal firing behaviors modified by SK conductance

Cite this article:

Online attention