Simulation of electric activity of neuron by setting up a reliable neuronal circuit driven by electric autapse

Ren Guo-Dong; Wu Gang; Ma Jun; Chen Yang

doi:10.7498/aps.64.058702

Abstract

Transition of electric activity of neuron can be induced by electric autapse, and its action potential is much sensitive to the stimuli from the electric autapse. Generally, the effect of electric autapse on membrane potential of neuron is often described by using time-delayed feedback in closed loop. Based on Pspice software, a class of electric circuit is designed with the electric autapse being taken into consideration, and a time-delayed circuit is used to detect the adjusting action of electric autapse on the action potential. Results are found as follows: (1) The neuronal electric circuit can produce quiescent state, spiking, bursting state under an external force besides the electric autapse circuit. (2) The transition of electric activity occurs between four different atates (quiescent, spiking, bursting state) by imposing a time-varying forcing current; its potential mechanism is that the electric circuit is associated with the memory, and the neuron can give different types of response to the same external forcing current. (3)When a strong external force is imposed, the outputs can show different type of electric activities due to an electric autapse, that is to say, self-adaption of gain in the autapse is useful for the neuron and thus different type of electric activities occurs, whose potential mechanism may be due to the effective feedback in the loop; so it is helpful to understand the synaptic plasticity.

Keywords:

Authors and contacts

1.
Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China
Funds: Project supported by the National Nautral Science of Foundation of China (Grant Nos. 11265008, 11372122).

References

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[26]	Gu H G, Jia B, Li Y Y, Chen G R 2013 Physica A 392 1361
[27]	Wang Q Y, Zheng Y H, Ma J 2013 Chaos Solitons & Fractals 56 19
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[39]	Wu X Y, Ma J, Yuan L H, Liu Y 2014 Nonlinear Dyn. 75 113
[40]	Wagemakers A, Sanjuán A F, Casado J M 2006 Int. J. Bifurcat. Chaos 16 3617
[41]	Dahasert N, Ozturk I, Kilic R 2012 Nonlinear Dyn. 70 2343
[42]	Rabinovich M, Huerta R, Bazhenov M, Kozlov A K, Abarbanel H D I 1998 Phys. Rev. E 58 6418
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[45]	Nowotny T, Rabinovich M I 2007 Phys. Rev. Lett. 98 128106
[46]	Sitt J D, Aliaga J 2007 Phys. Rev. E 76 051919
[47]	Kwon O, Kim K, Park S, Moon H T 2011 Phys. Rev. E 84 021911
[48]	Ayers J, Rulkov N, Knudsen D, Kim Y B, Volkovskii A, Selverston A 2010 Appl. Bionics. Biom. 7 57
[49]	Lee Y J, Lee J, Kim K K, Kim Y B, Ayers J 2007 Neurocomput . 71 284
[50]	Bekkers J M 2003 Curr. Biol. 13 R433
[51]	Bekkers J M 2002 Curr. Biol. 12 R648
[52]	Bekkers J M 2009 Curr. Biol. 19 R296
[53]	Herrmann C S, Klaus A 2004 Int. J. Bifurcat. Chaos 14 623
[54]	Wang H T, Ma J, Chen Y L, Chen Y 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 3242
[55]	Qin H X, Ma J, Jin W Y, Wang C N 2014 Sci. China Tech. Sci. 57 936
[56]	Chen J, Li C G 2011 Acta Phys. Sin. 60 050503 (in Chinese) [陈军, 李春光 2011 物理学报 60 050503]
[57]	L Y Y, Schmid G, Hänggi P, Schimansky-Geier L 2010 Phys. Rev. E 82 061907
[58]	Ma J, Ying H P, Liu Y, Li S R 2009 Chin. Phys. B 18 98

Cited By

[1]	Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[2]	Rinzel J, Ermentrout G B 1989 Analysis of neuronal excitability and oscillations, C Koch and I. Segev (Eds.), Methods in neuronal Modeling: from synapses to Networks (MIT press, London)
[3]	Cronin J 1987 Mathematical Aspects of Hodgkin-Huxley Neural Theory (Cambridage University Press, Cambridge, UK)
[4]	Morris C, Lecar H 1981 Biophys. J. 35 193
[5]	Smith G D 2002 Comput. Cell Biol. 20 285
[6]	Sanjuán M A F, Ibarz B, Casado J M 2011 Phys. Rep. 501 1
[7]	Hindmarsh J L, Rose R M 1982 Nature 296 162
[8]	Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond. B 221 87
[9]	Gu H G 2013 Chaos 23 023126
[10]	Kunichika T, Hiroyuki K, Tetsuya Y, Aiharad K, Kawakamif H 2006 Neurocomput. 69 293
[11]	Shilnikov A 2012 Nonlinear Dyn. 68 305
[12]	Yang Z Q, Lu Q S 2008 Sci. China Ser. Phys. Mech. Astron. 51 687
[13]	Crotti P 2011 Analysis of coherence resonance near bifurcation points in the stochastic Class II Morris-Lecar model. Master thesis (University of Fribourg Switzerland)
[14]	Selverston A I, Rabinovich M I, Abarbanel H D I Elson R, Szcs A, Pinto R D, Huerta R, Varona P 2000 J. Physiol. (Paris) 94 357
[15]	Wang W, Chen G, Wang Z D 1997 Phys. Rev. E 56 3728
[16]	Wei D Q, Luo X S 2007 Commun. Theor. Phys. 48 759
[17]	Perc M 2007 Phys. Rev. E 76 066203
[18]	Perc M, Gosak M 2008 New J. Phys. 10 053008
[19]	Gosak M, Marhl M, Perc M 2009 Physica D 238 506
[20]	Kwon O, Jo H H, Moon H T 2005 Phys. Rev. E 72 066121
[21]	Yuan W J, Luo X S, Yang R H 2007 Chin. Phys. Lett. 24 835
[22]	Perc M 2009 Eur. Phys. J. B 69 147
[23]	Chik D T W, Wang Y Q, Wang Z D 2001 Phys. Rev. E 64 021913
[24]	Yu Y G, Wang W, Wang J F, Liu F 2001 Phys. Rev. E 63 021907
[25]	Zhang J Q, Wang C D, Wang M S, Huang S F 2011 Nerocomput. 74 2961
[26]	Gu H G, Jia B, Li Y Y, Chen G R 2013 Physica A 392 1361
[27]	Wang Q Y, Zheng Y H, Ma J 2013 Chaos Solitons & Fractals 56 19
[28]	Ma J, Wu Y, Wu N J, Guo H Y 2013 Sci. China Phys. .Mech. Astro. 56 952
[29]	H B L, Ma J, Tang J 2013 Plos One 8 69251
[30]	Li Y Y, Jia B, Gu H G 2012 Acta Phys. Sin. 61 070504 (in Chinese) [李玉叶, 贾冰, 古华光 2012 物理学报 61 070504]
[31]	Tang Z, Li Y Y, Xi L, Jia B, Gu H G 2012 Commun. Theor. Phys. 57 61
[32]	Liu S B, Wu Y, Li J J, Xie Y, Tan N 2013 Nonlinear. Dyn. 73 1055
[33]	Wu Y, Li J J, Liu S B, Pan J Z, Du M M, Lin P 2013 Cogn. Neurodyn. 7 431
[34]	Gu H G 2013 Plos One 8 81759
[35]	Gu H G, Pan B B, Xu J 2014 EPL 106 50003
[36]	Gu H G, Jia B, Chen G R 2013 Phys. Lett. A 377 718
[37]	Jia B, Gu H G 2012 Acta Phys. Sin. 61 240505 (in Chinese) [贾冰, 古华光 2012 物理学报 61 240505]
[38]	Knudsen Daniel P 2006 Creating functional neural control circuits incorporating both discrete-time, map based neuron and Hindmarsh-Rose electronic neurons (Honors Junior/Senior Projects) Paper 11
[39]	Wu X Y, Ma J, Yuan L H, Liu Y 2014 Nonlinear Dyn. 75 113
[40]	Wagemakers A, Sanjuán A F, Casado J M 2006 Int. J. Bifurcat. Chaos 16 3617
[41]	Dahasert N, Ozturk I, Kilic R 2012 Nonlinear Dyn. 70 2343
[42]	Rabinovich M, Huerta R, Bazhenov M, Kozlov A K, Abarbanel H D I 1998 Phys. Rev. E 58 6418
[43]	Mayer J, Schuster H G, Claussen J C 2006 Phys. Rev E. 73 031908
[44]	Li F, Liu Q R, Guo H Y et al. 2012 Nonlinear Dyn. 69 2169
[45]	Nowotny T, Rabinovich M I 2007 Phys. Rev. Lett. 98 128106
[46]	Sitt J D, Aliaga J 2007 Phys. Rev. E 76 051919
[47]	Kwon O, Kim K, Park S, Moon H T 2011 Phys. Rev. E 84 021911
[48]	Ayers J, Rulkov N, Knudsen D, Kim Y B, Volkovskii A, Selverston A 2010 Appl. Bionics. Biom. 7 57
[49]	Lee Y J, Lee J, Kim K K, Kim Y B, Ayers J 2007 Neurocomput . 71 284
[50]	Bekkers J M 2003 Curr. Biol. 13 R433
[51]	Bekkers J M 2002 Curr. Biol. 12 R648
[52]	Bekkers J M 2009 Curr. Biol. 19 R296
[53]	Herrmann C S, Klaus A 2004 Int. J. Bifurcat. Chaos 14 623
[54]	Wang H T, Ma J, Chen Y L, Chen Y 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 3242
[55]	Qin H X, Ma J, Jin W Y, Wang C N 2014 Sci. China Tech. Sci. 57 936
[56]	Chen J, Li C G 2011 Acta Phys. Sin. 60 050503 (in Chinese) [陈军, 李春光 2011 物理学报 60 050503]
[57]	L Y Y, Schmid G, Hänggi P, Schimansky-Geier L 2010 Phys. Rev. E 82 061907
[58]	Ma J, Ying H P, Liu Y, Li S R 2009 Chin. Phys. B 18 98

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Vol. 64, Issue 5 - 2015-03-05

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