Energy dependence on modes of electric activities of neuron driven by different external mixed signals under electromagnetic induction

LuLu LU; Ya JIA; Ying XU; MengYan GE; LiJian YANG; Xuan ZHAN

doi:10.1007/s11431-017-9217-x

SCIENCE CHINA Technological Sciences

Download PDF

SCIENCE CHINA Technological Sciences, Volume 62, Issue 3: 427-440(2019) https://doi.org/10.1007/s11431-017-9217-x

Energy dependence on modes of electric activities of neuron driven by different external mixed signals under electromagnetic induction

LuLu LU, Ya JIA^*, Ying XU, MengYan GE, LiJian YANG, Xuan ZHAN

More info

ReceivedSep 28, 2017
AcceptedFeb 26, 2018
PublishedOct 19, 2018

Previous Table of Contents Next

Rating

Abstract

Energy supply and release play an important role in individual neuron and neural network. In this paper, the electrical activities and Hamilton energy of neuron are investigated when external mixed signals (i.e., the periodic stimulus current and the periodic electromagnetic field) are imposed on the neuron under the electromagnetic induction. As a result, the Hamilton energy is much dependent on the mode transition, the multiple electric activity modes and the numerical analysis of Hamilton energy are more complicated under various parameters. When the periodic high-low frequency electromagnetic radiation is imposed in neuron, it is found that the electrical activities are more complex, and the changing of energy is obvious. In addition, the response of electrical activity and Hamilton energy is much dependent on the changing of amplitude A, B when the external high-low frequency signal is imposed on the neuron, meanwhile, the energy of bursting state is lower than the one of spiking state. It can be used for investigation about the energy coding in the neuron even the neuron networks.

Funded by

the National Natural Science Foundation of China(Grant,Nos.,11474117,11775091)

Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11474117 and 11775091). The authors gratefully acknowledge Prof. Jun Ma from Lanzhou University of Technology for the constructive suggestions.

References

[1] Puls I, Jonnakuty C, LaMonte B H, et al. Mutant dynactin in motor neuron disease. Nat Genet, 2003, 33: 455-456 CrossRef PubMed Google Scholar

[2] Zhang P, Adams U, Yuan Z Q. Re-mention of an old neurodegenerative disease: Alzheimer’s disease. Chin Sci Bull, 2013, 58: 1731-1736 CrossRef ADS Google Scholar

[3] Hodgkin A L, Huxley A F. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J Physiol, 1952, 116: 449-472 CrossRef Google Scholar

[4] Fitzhugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys J, 1961, 1: 445-466 CrossRef ADS Google Scholar

[5] Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophys J, 1981, 35: 193-213 CrossRef ADS Google Scholar

[6] Hindmarsh J L, Rose R M. A model of the nerve impulse using two first-order differential equations. Nature, 1982, 296: 162-164 CrossRef ADS Google Scholar

[7] Fan D G, Wang Q Y. Synchronization and bursting transition of the coupled Hindmarsh-Rose systems with asymmetrical time-delays. Sci China Tech Sci, 2017, 60: 1019-1031 CrossRef Google Scholar

[8] Ando H, Suetani H, Kurths J, et al. Chaotic phase synchronization in bursting-neuron models driven by a weak periodic force. Phys Rev E, 2012, 86: 016205 CrossRef PubMed ADS arXiv Google Scholar

[9] Yang L, Jia Y, Yi M. The effects of electrical coupling on the temporal coding of neural signal in noisy Hodgkin-Huxley neuron ensemble. In: 2010 Sixth International Conference on Natural Computation (ICNC). Yantai: IEEE, 2010. 819–823. Google Scholar

[10] Ma J, Qin H, Song X, et al. Pattern selection in neuronal network driven by electric autapses with diversity in time delays. Int J Mod Phys B, 2015, 29: 1450239 CrossRef ADS Google Scholar

[11] Nordenfelt A, Used J, Sanjuán M A F. Bursting frequency versus phase synchronization in time-delayed neuron networks. Phys Rev E, 2013, 87: 052903 CrossRef PubMed ADS Google Scholar

[12] Han Q K, Sun X Y, Yang X G, et al. External synchronization of two dynamical systems with uncertain parameters. Sci China Tech Sci, 2010, 53: 731-740 CrossRef Google Scholar

[13] Qin H X, Ma J, Jin W Y, et al. Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci China Tech Sci, 2014, 57: 936-946 CrossRef Google Scholar

[14] Lu L, Jia Y, Liu W, et al. Mixed stimulus-induced mode selection in neural activity driven by high and low frequency current under electromagnetic radiation. Complexity, 2017, 2017: 7628537 CrossRef Google Scholar

[15] Ge M, Jia Y, Xu Y, et al. Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation. Nonlinear Dyn, 2018, 91: 515-523 CrossRef Google Scholar

[16] Liao X, Li S, Chen G. Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain. Neural Netw, 2004, 17: 545-561 CrossRef PubMed Google Scholar

[17] Xie Y, Kang Y M, Liu Y, et al. Firing properties and synchronization rate in fractional-order Hindmarsh-Rose model neurons. Sci China Tech Sci, 2014, 57: 914-922 CrossRef Google Scholar

[18] Izhikevich E M. Which model to use for cortical spiking neurons?. IEEE Trans Neural Netw, 2004, 15: 1063-1070 CrossRef PubMed Google Scholar

[19] Gu H G, Chen S G. Potassium-induced bifurcations and chaos of firing patterns observed from biological experiment on a neural pacemaker. Sci China Tech Sci, 2014, 57: 864-871 CrossRef Google Scholar

[20] Laflaquiere A, Masson S L, Dupeyron D, et al. Analog circuits emulating biological neurons in real-time experiments. In: Proceedings of 19th International Conference (IEEE/EMBS). Chicago, 1997. 2035–2038. Google Scholar

[21] Gu H, Pan B, Chen G, et al. Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models. Nonlinear Dyn, 2014, 78: 391-407 CrossRef Google Scholar

[22] Wang H T, Chen Y. Firing dynamics of an autaptic neuron. Chin Phys B, 2015, 24: 128709 CrossRef ADS arXiv Google Scholar

[23] Tang J, Zhang J, Ma J, et al. Astrocyte calcium wave induces seizure-like behavior in neuron network. Sci China Tech Sci, 2017, 60: 1011-1018 CrossRef Google Scholar

[24] Wang Z H, Wang Q Y. Effect of the coordinated reset stimulations on controlling absence seizure. Sci China Tech Sci, 2017, 60: 985-994 CrossRef Google Scholar

[25] Zhang H H, Zheng Y H, Su J Z, et al. Seizures dynamics in a neural field model of cortical-thalamic circuitry. Sci China Tech Sci, 2017, 60: 974-984 CrossRef Google Scholar

[26] Li J J, Xie Y, Yu Y G, et al. A neglected GABAergic astrocyte: Calcium dynamics and involvement in seizure activity. Sci China Tech Sci, 2017, 60: 1003-1010 CrossRef Google Scholar

[27] Guo D Q, Xia C, Wu S D, et al. Stochastic fluctuations of permittivity coupling regulate seizure dynamics in partial epilepsy. Sci China Tech Sci, 2017, 60: 995-1002 CrossRef Google Scholar

[28] Yan C. A Neuron Model Based on Hamilton Principle and Energy Coding. Berlin, Heidelberg: Springer, 2012. 395–401. Google Scholar

[29] Nabi A, Mirzadeh M, Gibou F, et al. Minimum energy spike randomization for neurons. In: 2012 American Control Conference Fairmont Queen Elizabeth. Montreal: IEEE, 2012. 4751–4756. Google Scholar

[30] Ma J, Wu F, Jin W, et al. Calculation of Hamilton energy and control of dynamical systems with different types of attractors. Chaos, 2017, 27: 053108 CrossRef PubMed ADS Google Scholar

[31] Sarasola C, Torrealdea F J, D'Anjou A, et al. Energy balance in feedback synchronization of chaotic systems. Phys Rev E, 2004, 69: 011606 CrossRef PubMed ADS Google Scholar

[32] Lv M, Wang C, Ren G, et al. Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn, 2016, 85: 1479-1490 CrossRef Google Scholar

[33] Carpenter C J. Electromagnetic induction in terms of the Maxwell force instead of magnetic flux. IEE Proc-Sci Measurement Tech, 1999, 146: 182-193 CrossRef Google Scholar

[34] Bao B C, Liu Z, Xu J P. Steady periodic memristor oscillator with transient chaotic behaviours. Electron Lett, 2010, 46: 228 CrossRef Google Scholar

[35] Muthuswamy B. Implementing memristor based chaotic circuits. Int J Bifurcation Chaos, 2010, 20: 1335-1350 CrossRef ADS Google Scholar

[36] Harris J J, Jolivet R, Attwell D. Synaptic energy use and supply. Neuron, 2012, 75: 762-777 CrossRef PubMed Google Scholar

[37] Wang R, Zhang Z, Chen G. Energy coding and energy functions for local activities of the brain. Neurocomputing, 2009, 73: 139-150 CrossRef Google Scholar

[38] Torrealdea F J, Sarasola C, D'Anjou A, et al. Energy efficiency of information transmission by electrically coupled neurons. Biosystems, 2009, 97: 60-71 CrossRef PubMed Google Scholar

[39] Song X L, Jin W Y, Ma J. Energy dependence on the electric activities of a neuron. Chin Phys B, 2015, 24: 128710 CrossRef ADS Google Scholar

Click to view Download high-quality image

Figure 1
Distribution of the different states in the two-parameter phase space k-I under different external stimulus currents I_ext=I+Acos(ωt)+Bcos(Nωt). A=0.15, B=0.1, ω=0.01, N=10.
Click to view Download high-quality image

Figure 2
Evolution of action potential and energy function with time are calculated by changing the external mixed signal at A=0.15, B=0.1, ω=0.01, N=10. (a₁)–(d₁) I=1.4; (a₂)–(d₂) I=1.9. The period current is imposed on the neuron from t=1000 time units.
Click to view Download high-quality image

Figure 3
Power spectrum of the time series for four different parameters. (a) N=0.1; (b) N=1.0; (c) N=10; (d) N=100. The external stimulus currents is I_ext=I+Acos(ωt)+Bcos(Nωt), A=0.15, B=0.1, ω=0.01, I=1.6.
Click to view Download high-quality image

Figure 4
Evolution of action potential and energy function with time are calculated by changing the external mixed signal at A=0.15, B=0.1, ω=0.01, I=1.8. (a₁)–(d₁) N=0.1; (a₂)–(d₂) N=1; (a₃)–(d₃) N=10; (a₄)–(d₄) N=100.
Click to view Download high-quality image

Figure 5
Evolution of action potential and energy function with time are calculated by changing the external mixed signal at A=0.15, B=0.1, N=10, I=1.8. (a₁)–(d₁) ω=0.01; (a₂)–(d₂) ω=0.1; (a₃)–(d₃) ω=1.0.
Click to view Download high-quality image

Figure 6
Evolution of action potential and energy function with time are calculated by changing the external mixed signal at A=0.15, N=10, ω=0.01, I=1.8. (a₁)–(d₁) B=0.2; (a₂)–(d₂) B=0.5; (a₃)–(d₃) B=1.0.
Click to view Download high-quality image

Figure 7
Evolution of action potential and energy function with time are calculated by changing the external mixed signal at B=0.1, ω=0.01, N=10, I=1.8. (a₁)–(d₁) A=0.3; (a₂)–(d₂) A=0.7; (a₃)–(d₃) A=1.0.
Click to view Download high-quality image

Figure 8
Distribution of the different states in the two-parameter phase space k-I under the different periodic electromagnetic radiation φ_ext=Acos(ωt)+Bcos(Nωt). A=0.1, B=0.2, ω=0.01, N=10.
Click to view Download high-quality image

Figure 9
Evolution of action potential and energy function with time are calculated by changing the periodic electromagnetic radiation at A=0.1, B=0.2, ω=0.01, N=10. (a₁)–(d₁) I=1.4; (a₂)–(d₂) I=1.8. The period electromagnetic radiation is imposed on the neuron from t=1000 time units.
Click to view Download high-quality image

Figure 10
Power spectrum of the time series for four different parameters. (a) N=0.1; (b) N=1.0; (c) N=10; (d) N=100. The periodic electromagnetic radiation is φ_ext=Acos(ωt)+Bcos(Nωt), A=0.1, B=0.2, ω=0.01, I=1.4.
Click to view Download high-quality image

Figure 11
Evolution of action potential and energy function with time are calculated by changing the periodic electromagnetic radiation at A=0.1, B=0.2, ω=0.01, I=1.4. (a₁)–(d₁) N=0.1; (a₂)–(d₂) N=1; (a₃)–(d₃) N=10; (a₄)–(d₄) N=100.
Click to view Download high-quality image

Figure 12
Evolution of action potential and energy function with time are calculated by changing the periodic electromagnetic radiation at A=0.1, B=0.2, N=10, I=1.4. (a₁)–(d₁) ω=0.01; (a₂)–(d₂) ω=0.1.
Click to view Download high-quality image

Figure 13
Evolution of action potential and energy function with time are calculated by changing the periodic electromagnetic radiation at A=0.1, N=10, ω=0.01, I=1.4. (a₁)–(d₁) B=0.3; (a₂)–(d₂) B=0.5; (a₃)–(d₃) B=0.9.
Click to view Download high-quality image

Figure 14
Evolution of action potential and energy function with time are calculated by changing the periodic electromagnetic radiation at B=0.2, ω=0.01, N=10, I=1.4. (a₁)–(d₁) A=0.3; (a₂)–(d₂) A=0.7; (a₃)–(d₃) A=1.0.