Phase synchronization and energy balance between neurons

Ying XIE; Zhao YAO; Jun MA

doi:10.1631/FITEE.2100563

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Phase synchronization and energy balance between neurons

Regular Papers | Updated：2022-09-29

- Phase synchronization and energy balance between neurons
- 神经元之间的相位同步和能量平衡
- Frontiers of Information Technology & Electronic Engineering Vol. 23, Issue 9, Pages: 1407-1420(2022)
- Affiliations：
  
  1.Department of Physics, Lanzhou University of Technology, Lanzhou730050, China
  2.School of Science, Chongqing University of Posts and Telecommunications, Chongqing430065, China
- Author bio：
  
  ‡Corresponding authors
- Funds：
- DOI：10.1631/FITEE.2100563
  CLC： TN710; O59
- Received：07 December 2021，
  
  Revised：2022-03-02，
  
  Accepted：12 January 2022，
  
  Published Online：12 April 2022，
  
  Published：23 September 2022
- Accepted：
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XIE Ying,YAO Zhao,MA Jun.Phase synchronization and energy balance between neurons[J].Frontiers of Information Technology & Electronic Engineering,2022,23(09):1407-1420.
DOI：

XIE Ying,YAO Zhao,MA Jun.Phase synchronization and energy balance between neurons[J].Frontiers of Information Technology & Electronic Engineering,2022,23(09):1407-1420. DOI： 10.1631/FITEE.2100563.

摘要

在一类简单的神经元电路不同支路嵌入光电管和热敏电阻来设计一种功能性神经元。通过光电管的光电流和流经热敏电阻的通道电流可以控制神经元电路的场能量。神经元的放电模态同时依赖于外界光照和温度。在不同的光照和温度刺激下，两个功能神经元存在能量差。因此，在场能量传递和交换过程中神经元之间开始建立突触连接并相互耦合。我们提出两种规则来讨论神经元之间突触耦合增强问题，神经元之间的能量差控制着神经元之间突触耦合强度的增长和突触电流变化，且神经元之间的同步有利于维持神经元之间的能量平衡。第一类规则类似于饱和增益法，即神经元在达到完全同步之前其突触耦合强度以恒定的增益周期性增长。第二类规则指出神经元突触耦合强度以恰当的增益呈现指数型增长，直到神经元之间达到能量平衡。两个不同的神经元在突触耦合增强的过程中可以实现相位同步。两个完全相同的神经元即使在噪声环境下，神经元耦合突触按照第二类规则增长强度依旧可以有效实现完全同步和能量平衡。此结果表明神经元突触更倾向于以指数型方式来增长其耦合强度。这些研究结果有助于揭示外界刺激如何唤醒和激活神经元之间的突触连接，进一步理解突触耦合电流时变的特性。潜在的生物物理机制在于外界差异性的刺激打破了神经元之间的能量平衡，因此突触耦合不断被增强来实现神经元之间能量动态平衡。这些研究结果为设计和训练智能神经元电路提供了思路，即通过设置梯度性能量分布来调控耦合通道。

Abstract

A functional neuron has been developed from a simple neural circuit by incorporating a phototube and a thermistor in different branch circuits. The physical field energy is controlled by the photocurrent across the phototube and the channel current across the thermistor. The firing mode of this neuron is controlled synchronously by external temperature and illumination. There is energy diversity when two functional neurons are exposed to different illumination and temperature conditions. As a result

synapse connections can be created and activated in an adaptive way when field energy is exchanged between neurons. We propose two kinds of criteria to discuss the enhancement of synapse connections to neurons. The energy diversity between neurons determines the increase of the coupling intensity and synaptic current for neurons

and the realization of synchronization is helpful in maintaining energy balance between neurons. The first criterion is similar to the saturation gain scheme in that the coupling intensity is increased with a constant step within a certain period until it reaches energy balance or complete synchronization. The second criterion is that the coupling intensity increases exponentially before reaching energy balance. When two neurons become non-identical

phase synchronization can be controlled during the activation of synapse connections to neurons. For two identical neurons

the second criterion for taming synaptic intensity is effective for reaching complete synchronization and energy balance

even in the presence of noise. This indicates that a synapse connection may prefer to enhance its coupling intensity exponentially. These results are helpful in discovering why synapses are awaken and synaptic current becomes time-varying when any neurons are excited by external stimuli. The potential biophysical mechanism is that energy balance is broken and then synapse connections are activated to maintain an adaptive energy balance between the neurons. These results provide guidance for designing and training intelligent neural networks by taming the coupling channels with gradient energy distribution.

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references

An XL , Zhang L , 2018 . Dynamics analysis and Hamilton energy control of a generalized Lorenz system with hidden attractor . Nonl Dynam , 94 ( 4 ): 2995 - 3010 . https://doi.org/10.1007/s11071-018-4539-9 https://doi.org/10.1007/s11071-018-4539-9

Andreev A , Makarov V , Runnova A , et al. , 2017 . Coherent resonance in neuron ensemble with electrical couplings . Cybern Phys , 6 ( 3 ): 145 - 148 .

Ansariara M , Emadi S , Adami V , et al. , 2020 . Signs of memory in a plastic frustrated Kuramoto model of neurons . Nonl Dynam , 100 ( 4 ): 3685 - 3694 . https://doi.org/10.1007/s11071-020-05705-4 https://doi.org/10.1007/s11071-020-05705-4

Baysal V , Saraç Z , Yilmaz E , 2019 . Chaotic resonance in Hodgkin‍–‍Huxley neuron . Nonlinear Dyn , 97 ( 2 ): 1275 - 1285 . https://doi.org/10.1007/s11071-019-05047-w https://doi.org/10.1007/s11071-019-05047-w

Blankenburg S , Wu W , Lindner B , et al. , 2015 . Information filtering in resonant neurons . J Comput Neurosci , 39 ( 3 ): 349 - 370 . https://doi.org/10.1007/s10827-015-0580-6 https://doi.org/10.1007/s10827-015-0580-6

Breakspear M , Heitmann S , Daffertshofer A , 2010 . Generative models of cortical oscillations: neurobiological implications of the Kuramoto model . Front Human Neurosci , 4 : 190 . https://doi.org/10.3389/fnhum.2010.00190 https://doi.org/10.3389/fnhum.2010.00190

Cumin D , Unsworth CP , 2007 . Generalising the Kuramoto model for the study of neuronal synchronisation in the brain . Phys D , 226 ( 2 ): 181 - 196 . https://doi.org/10.1016/j.physd.2006.12.004 https://doi.org/10.1016/j.physd.2006.12.004

Daniels BC , Dissanayake STM , Trees BR , 2003 . Synchronization of coupled rotators: Josephson junction ladders and the locally coupled Kuramoto model . Phys Rev E , 67 ( 2 ): 026216 . https://doi.org/10.1103/PhysRevE.67.026216 https://doi.org/10.1103/PhysRevE.67.026216

Deng B , Wang J , Wei X , 2009 . Effect of chemical synapse on vibrational resonance in coupled neurons . Chaos , 19 : 013117 . https://doi.org/10.1063/1.3076396 https://doi.org/10.1063/1.3076396

Du MM , Li JJ , Yuan ZX , et al. , 2020 . Astrocyte and ions metabolism during epileptogenesis: a review for modeling studies . Chin Phys B , 29 ( 3 ): 038701 . https://doi.org/10.1088/1674-1056/ab6961 https://doi.org/10.1088/1674-1056/ab6961

Guo YT , Zhou P , Yao Z , et al. , 2021 . Biophysical mechanism of signal encoding in an auditory neuron . Nonl Dynam , 105 ( 4 ): 3603 - 3614 . https://doi.org/10.1007/s11071-021-06770-z https://doi.org/10.1007/s11071-021-06770-z

He ZW , Yao CG , Liu S , et al. , 2021 . Transmission of pacemaker signal in a small world neuronal networks: temperature effects . Nonl Dynam , 106 ( 3 ): 2547 - 2557 . https://doi.org/10.1007/s11071-021-06907-0 https://doi.org/10.1007/s11071-021-06907-0

Herz AVM , Gollisch T , Machens CK , et al. , 2006 . Modeling single-neuron dynamics and computations: a balance of detail and abstraction . Science , 314 ( 5796 ): 80 - 85 . https://doi.org/10.1126/science.1127240 https://doi.org/10.1126/science.1127240

Leutcho GD , Khalaf AJM , Njitacke Tabekoueng Z , et al. , 2020 . A new oscillator with mega-stability and its Hamilton energy: infinite coexisting hidden and self-excited attractors . Chaos , 30 ( 3 ): 033112 . https://doi.org/10.1063/1.5142777 https://doi.org/10.1063/1.5142777

Lin HR , Wang CH , Sun YC , et al. , 2020 . Firing multistability in a locally active memristive neuron model . Nonl Dynam , 100 ( 4 ): 3667 - 3683 . https://doi.org/10.1007/s11071-020-05687-3 https://doi.org/10.1007/s11071-020-05687-3

Lin HR , Wang CH , Deng QL , et al. , 2021 . Review on chaotic dynamics of memristive neuron and neural network . Nonl Dynam , 106 ( 1 ): 959 - 973 . https://doi.org/10.1007/s11071-021-06853-x https://doi.org/10.1007/s11071-021-06853-x

Liu Y , Xu WJ , Ma J , et al. , 2020 . A new photosensitive neuron model and its dynamics . Front Inform Technol Electron Eng , 21 ( 9 ): 1387 - 1396 . https://doi.org/10.1631/FITEE.1900606 https://doi.org/10.1631/FITEE.1900606

Liu ZL , Wang CN , Zhang G , et al. , 2019 . Synchronization between neural circuits connected by hybrid synapse . Int J Mod Phys B , 33 ( 16 ): 1950170 . https://doi.org/10.1142/S0217979219501704 https://doi.org/10.1142/S0217979219501704

Liu ZL , Zhou P , Ma J , et al. , 2020 . Autonomic learning via saturation gain method, and synchronization between neurons . Chaos Soliton Fract , 131 : 109533 . https://doi.org/10.1016/j.chaos.2019.109533 https://doi.org/10.1016/j.chaos.2019.109533

Ma SY , Zhou P , Ma J , et al. , 2020 . Phase synchronization of memristive systems by using saturation gain method . Int J Mod Phys B , 34 ( 9 ): 2050074 . https://doi.org/10.1142/S0217979220500745 https://doi.org/10.1142/S0217979220500745

McDonnell MD , Iannella N , To MS , et al. , 2015 . A review of methods for identifying stochastic resonance in simulations of single neuron models . Netw Comput Neur Syst , 26 ( 2 ): 35 - 71 . https://doi.org/10.3109/0954898X.2014.990064 https://doi.org/10.3109/0954898X.2014.990064

Miller AC , Voelker LH , Shah AN , et al. , 2015 . Neurobeachin is required postsynaptically for electrical and chemical synapse formation . Curr Biol , 25 ( 1 ): 16 - 28 . https://doi.org/10.1016/j.cub.2014.10.071 https://doi.org/10.1016/j.cub.2014.10.071

Pereira T , Baptista MS , Kurths J , et al. , 2007 . Onset of phase synchronization in neurons with chemical synapse . Int J Bifurc Chaos , 17 ( 10 ): 3545 - 3549 . https://doi.org/10.1142/S0218127407019342 https://doi.org/10.1142/S0218127407019342

Rossant C , Goodman DFM , Fontaine B , et al. , 2011 . Fitting neuron models to spike trains . Front Neurosci , 5 : 9 . https://doi.org/10.3389/fnins.2011.00009 https://doi.org/10.3389/fnins.2011.00009

Shilnikov A , Cymbalyuk G , 2005 . Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe . Phys Rev Lett , 94 ( 4 ): 048101 . https://doi.org/10.1103/PhysRevLett.94.048101 https://doi.org/10.1103/PhysRevLett.94.048101

Shinomoto S , Kim H , Shimokawa T , et al. , 2009 . Relating neuronal firing patterns to functional differentiation of cerebral cortex . PLoS Comput Biol , 5 ( 7 ): e1000433 . https://doi.org/10.1371/journal.pcbi.1000433 https://doi.org/10.1371/journal.pcbi.1000433

Song XL , Wang HT , Chen Y , 2019 . Autapse-induced firing patterns transitions in the Morris–Lecar neuron model . Nonl Dynam , 96 ( 4 ): 2341 - 2350 . https://doi.org/10.1007/s11071-019-04925-7 https://doi.org/10.1007/s11071-019-04925-7

Szűcs A , 1998 . Applications of the spike density function in analysis of neuronal firing patterns . J Neurosci Methods , 81 ( 1-2 ): 159 - 167 . https://doi.org/10.1016/S0165-0270(98)00033-8 https://doi.org/10.1016/S0165-0270(98)00033-8

Tang J , Zhang J , Ma J , et al. , 2019 . Noise and delay sustained chimera state in small world neuronal network . Sci China Technol Sci , 62 ( 7 ): 1134 - 1140 . https://doi.org/10.1007/s11431-017-9282-x https://doi.org/10.1007/s11431-017-9282-x

Trees BR , Saranathan V , Stroud D , 2005 . Synchronization in disordered Josephson junction arrays: small-world connections and the Kuramoto model . Phys Rev E , 71 ( 1 ): 016215 . https://doi.org/10.1103/PhysRevE.71.016215 https://doi.org/10.1103/PhysRevE.71.016215

Ujfalussy BB , Makara JK , 2020 . Impact of functional synapse clusters on neuronal response selectivity . Nat Commun , 11 ( 1 ): 1413 . https://doi.org/10.1038/s41467-020-15147-6 https://doi.org/10.1038/s41467-020-15147-6

Uzuntarla M , Yilmaz E , Wagemakers A , et al. , 2015 . Vibrational resonance in a heterogeneous scale free network of neurons . Commun Nonl Sci Numer Simul , 22 ( 1-3 ): 367 - 374 . https://doi.org/10.1016/j.cnsns.2014.08.040 https://doi.org/10.1016/j.cnsns.2014.08.040

Uzuntarla M , Torres JJ , Calim A , et al. , 2019 . Synchronization-induced spike termination in networks of bistable neurons . Neur Netw , 110 : 131 - 140 . https://doi.org/10.1016/j.neunet.2018.11.007 https://doi.org/10.1016/j.neunet.2018.11.007

Wang XB , Xu C , Zheng ZG , 2021 . Phase transition and scaling in Kuramoto model with high-order coupling . Nonl Dynam , 103 ( 3 ): 2721 - 2732 . https://doi.org/10.1007/s11071-021-06268-8 https://doi.org/10.1007/s11071-021-06268-8

Wang ZH , Wang QY , 2019 . Stimulation strategies for absence seizures: targeted therapy of the focus in coupled thalamocortical model . Nonl Dynam , 96 ( 2 ): 1649 - 1663 . https://doi.org/10.1007/s11071-019-04876-z https://doi.org/10.1007/s11071-019-04876-z

Xie Y , Yao Z , Hu XK , et al. , 2021a . Enhance sensitivity to illumination and synchronization in light-dependent neurons . Chin Phys B , 30 ( 12 ): 120510 . https://doi.org/10.1088/1674-1056/ac1fdc https://doi.org/10.1088/1674-1056/ac1fdc

Xie Y , Zhu ZG , Zhang XF , et al. , 2021b . Control of firing mode in nonlinear neuron circuit driven by photocurrent . Acta Phys Sin , 70 ( 21 ): 210502 (in Chinese) . https://doi.org/10.7498/aps.70.20210676 https://doi.org/10.7498/aps.70.20210676

Xu L , Qi GY , Ma J , 2022 . Modeling of memristor-based Hindmarsh-Rose neuron and its dynamical analyses using energy method . Appl Math Model , 101 : 503 - 516 . https://doi.org/10.1016/j.apm.2021.09.003 https://doi.org/10.1016/j.apm.2021.09.003

Xu Y , Liu MH , Zhu ZG , et al. , 2020 . Dynamics and coherence resonance in a thermosensitive neuron driven by photocurrent . Chin Phys B , 29 ( 9 ): 098704 . https://doi.org/10.1088/1674-1056/ab9dee https://doi.org/10.1088/1674-1056/ab9dee

Yang CZ , Liu ZL , Wang QS , et al. , 2021 . Epilepsy as a dynamical disorder orchestrated by epileptogenic zone: a review . Nonl Dynam , 104 ( 8 ): 1901 - 1916 . https://doi.org/10.1007/s11071-021-06420-4 https://doi.org/10.1007/s11071-021-06420-4

Yang N , Ng YH , Pang ZP , et al. , 2011 . Induced neuronal cells: how to make and define a neuron . Cell Stem Cell , 9 ( 6 ): 517 - 525 . https://doi.org/10.1016/j.stem.2011.11.015 https://doi.org/10.1016/j.stem.2011.11.015

Yang XL , Li N , Sun ZK , 2019 . Extended analysis of stochastic resonance in a modular neuronal network at different scales . Nonl Dynam , 98 ( 2 ): 1029 - 1039 . https://doi.org/10.1007/s11071-019-05246-5 https://doi.org/10.1007/s11071-019-05246-5

Yao CG , Ma J , He ZW , et al. , 2019 . Transmission and detection of biharmonic envelope signal in a feed-forward multilayer neural network . Phys A , 523 : 797 - 806 . https://doi.org/10.1016/j.physa.2019.02.053 https://doi.org/10.1016/j.physa.2019.02.053

Zandi-Mehran N , Jafari S , Golpayegani SMRH , et al. , 2020 . Different synaptic connections evoke different firing patterns in neurons subject to an electromagnetic field . Nonl Dynam , 100 ( 2 ): 1809 - 1824 . https://doi.org/10.1007/s11071-020-05576-9 https://doi.org/10.1007/s11071-020-05576-9

Zhang XF , Wang CN , Ma J , et al. , 2020 . Control and synchronization in nonlinear circuits by using a thermistor . Mod Phys Lett B , 34 ( 25 ): 2050267 . https://doi.org/10.1142/S021798492050267X https://doi.org/10.1142/S021798492050267X

Zhang XF , Yao Z , Guo YY , et al. , 2021 . Target wave in the network coupled by thermistors . Chaos Sol Fract , 142 : 110455 . https://doi.org/10.1016/j.chaos.2020.110455 https://doi.org/10.1016/j.chaos.2020.110455

Zhang Y , Wang CN , Tang J , et al. , 2020 . Phase coupling synchronization of FHN neurons connected by a Josephson junction . Sci China Technol Sci , 63 ( 11 ): 2328 - 2338 . https://doi.org/10.1007/s11431-019-1547-5 https://doi.org/10.1007/s11431-019-1547-5

Zhou P , Hu XK , Zhu ZG , et al. , 2021 . What is the most suitable Lyapunov function? Chaos Sol Fract , 150 : 111154 . https://doi.org/10.1016/j.chaos.2021.111154 https://doi.org/10.1016/j.chaos.2021.111154

Zhou Q , Wei DQ , 2021 . Collective dynamics of neuronal network under synapse and field coupling . Nonl Dynam , 105 ( 1 ): 753 - 765 . https://doi.org/10.1007/s11071-021-06575-0 https://doi.org/10.1007/s11071-021-06575-0

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