SpringerLink
Log in

Energy-efficient firing modes of chay neuron model in different bursting kinetics

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

The firing sequence of the neuron system that transmits information consumes a significant amount of energy, but it is unclear how the firing pattern of the neuron system determines its energy efficiency. The mode transformation and energy efficiency in different firing modes are investigated using the Chay neuron model. It has been found that when system parameters are tuned, the neurons show complex bursting kinetics. The period-n bursting state of the neuron carries high amounts of information while consuming less energy per unit of information, resulting in higher energy efficiency. In particular, the mixed discharge state, where the neuron is in several bursting states simultaneously, is more energy efficient, and appropriate electromagnetic inductioncan enhance the neuron’s energy efficiency. Furthermore, there are optimal system parameters that maximize the energy efficiency of firing modes, demonstrating that the neuron carries high amounts of information while consuming less energy per unit of information. The study helps to understand the energy mechanism of neural information propagation and provides an insight into the energy efficiency characteristic of neuron systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fu X, Yu Y. Reliable and efficient processing of sensory information at body temperature by rodent cortical neurons. Nonlinear Dyn, 2019, 98: 215–231

    Article  Google Scholar 

  2. Yue Y, Liu L, Liu Y, et al. Dynamical response, information transition and energy dependence in a neuron model driven by autapse. Nonlinear Dyn, 2017, 90: 2893–2902

    Article  Google Scholar 

  3. Yu L, Yu Y. Energy-efficient neural information processing in individual neurons and neuronal networks. J Neurosci Res, 2017, 95: 2253–2266

    Article  Google Scholar 

  4. Jha M K, Morrison B M. Glia-neuron energy metabolism in health and diseases: New insights into the role of nervous system metabolic transporters. Exp Neurol, 2018, 309: 23–31

    Article  Google Scholar 

  5. Lu L, Jia Y, Kirunda J B, et al. Effects of noise and synaptic weight on propagation of subthreshold excitatory postsynaptic current signal in a feed-forward neural network. Nonlinear Dyn, 2019, 95: 1673–1686

    Article  Google Scholar 

  6. Ge M, Jia Y, Lu L, et al. Propagation characteristics of weak signal in feedforward izhikevich neural networks. Nonlinear Dyn, 2020, 99: 2355–2367

    Article  Google Scholar 

  7. Wang R, Fan Y C, Wu Y. Spontaneous electromagnetic induction promotes the formation of economical neuronal network structure via self-organization process. Sci Rep, 2019, 9: 9698

    Article  Google Scholar 

  8. Xu Y, Guo Y, Ren G, et al. Dynamics and stochastic resonance in a thermosensitive neuron. Appl Math Comput, 2020, 385: 125427

    MathSciNet  MATH  Google Scholar 

  9. Yao Y, Ma J. Logical chaotic resonance in a bistable system. Int J Bifurcat Chaos, 2020, 30: 2050196

    Article  MathSciNet  MATH  Google Scholar 

  10. Yao Y, Ma J, Gui R, et al. Enhanced logical chaotic resonance. Chaos, 2021, 31: 023103

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhu Z, Ren G, Zhang X, et al. Effects of multiplicative-noise and coupling on synchronization in thermosensitive neural circuits. Chaos Soliton Fract, 2021, 151: 111203

    Article  MathSciNet  Google Scholar 

  12. Danziger Z, Grill W M. A neuron model of stochastic resonance using rectangular pulse trains. J Comput Neurosci, 2015, 38: 53–66

    Article  MathSciNet  MATH  Google Scholar 

  13. Vilar J M G, Rubí J M. Noise suppression by noise. Phys Rev Lett, 2001, 86: 950–953

    Article  Google Scholar 

  14. Shimokawa T, Pakdaman K, Sato S. Time-scale matching in the response of a leaky integrate-and-fire neuron model to periodic stimulus with additive noise. Phys Rev E, 1999, 59: 3427–3443

    Article  Google Scholar 

  15. Lu L, Jia Y, Ge M, et al. Inverse stochastic resonance in hodgkin-huxley neural system driven by gaussian and non-gaussian colored noises. Nonlinear Dyn, 2020, 100: 877–889

    Article  Google Scholar 

  16. Li Y, Wei Z, Zhang W, et al. Bogdanov-Takens singularity in the hindmarsh-rose neuron with time delay. Appl Math Comput, 2019, 354: 180–188

    MathSciNet  MATH  Google Scholar 

  17. Wang G, Yu D, Ding Q, et al. Effects of electric field on multiple vibrational resonances in hindmarsh-rose neuronal systems. Chaos Solitons Fractals, 2021, 150: 111210

    Article  MathSciNet  MATH  Google Scholar 

  18. Lin H, Wang C. Influences of electromagnetic radiation distribution on chaotic dynamics of a neural network. Appl Math Comput, 2020, 369: 124840

    MathSciNet  MATH  Google Scholar 

  19. Izhikevich E M. Which model to use for cortical spiking neurons? IEEE Trans Neural Netw, 2004, 15: 1063–1070

    Article  Google Scholar 

  20. Steriade M, Nunez A, Amzica F. A novel slow (<1 Hz) oscillation of neocortical neurons in vivo: Depolarizing and hyperpolarizing components. J Neurosci, 1993, 13: 3252–3265

    Article  Google Scholar 

  21. Hunt D L, Lai C, Smith R D, et al. Multimodal in vivo brain electrophysiology with integrated glass microelectrodes. Nat Biomed Eng, 2019, 3: 741–753

    Article  Google Scholar 

  22. Barral J, Wang X J, Reyes A D. Propagation of temporal and rate signals in cultured multilayer networks. Nat Commun, 2019, 10: 3969

    Article  Google Scholar 

  23. Strong S P, Koberle R, de Ruyter van Steveninck R R, et al. Entropy and information in neural spike trains. Phys Rev Lett, 1998, 80: 197–200

    Article  Google Scholar 

  24. Jia Y, Gu H. Identifying nonlinear dynamics of brain functional networks of patients with schizophrenia by sample entropy. Nonlinear Dyn, 2019, 96: 2327–2340

    Article  Google Scholar 

  25. Zhu F, Wang R, Aihara K, et al. Energy-efficient firing patterns with sparse bursts in the chay neuron model. Nonlinear Dyn, 2020, 100: 2657–2672

    Article  Google Scholar 

  26. Zhou S L, Yu Y G. Synaptic EI balance underlies efficient neural coding. Front Neurosci, 2018, 12: 45–46

    Google Scholar 

  27. Zaks M A, Sailer X, Schimansky-Geier L, et al. Noise induced complexity: From subthreshold oscillations to spiking in coupled excitable systems. Chaos, 2005, 15: 026117

    Article  MathSciNet  MATH  Google Scholar 

  28. Trang-Anh N, Bartosz T, Olivier M, et al. Maximum-entropy models reveal the excitatory and inhibitory correlation structures in cortical neuronal activity. Phys Rev E, 2018, 98: 012402

    Article  Google Scholar 

  29. Yang H H, Amari S. Adaptive online learning algorithms for blind separation: Maximum entropy and minimum mutual information. Neural Comput, 1997, 9: 1457–1482

    Article  Google Scholar 

  30. Kamimura R. Mutual information maximization for improving and interpreting multi-layered neural networks. In: 2017 IEEE Symposium Series on Computational Intelligence (SSCI). Honolulu, 2017

  31. Xu L, Qi G, Ma J. Modeling of memristor-based hindmarsh-rose neuron and its dynamical analyses using energy method. Appl Math Model, 2022, 101: 503–516

    Article  MathSciNet  MATH  Google Scholar 

  32. Lu L L, Jia Y, Xu Y, et al. Energy dependence on modes of electric activities of neuron driven by different external mixed signals under electromagnetic induction. Sci China Tech Sci, 2019, 62: 427–440

    Article  Google Scholar 

  33. Zhou P, Hu X, Zhu Z, et al. What is the most suitable lyapunov function? Chaos Soliton Fract, 2021, 150: 111154

    Article  MathSciNet  MATH  Google Scholar 

  34. Wang Y, Xu X, Wang R. The place cell activity is information-efficient constrained by energy. Neural Networks, 2019, 116: 110–118

    Article  Google Scholar 

  35. Sengupta B, Stemmler M, Laughlin S B, et al. Action potential energy efficiency varies among neuron types in vertebrates and invertebrates. PLoS Comput Biol, 2010, 6: e1000840

    Article  MathSciNet  Google Scholar 

  36. Oh S, Shi Y, Del Valle J, et al. Energy-efficient Mott activation neuron for full-hardware implementation of neural networks. Nat Nanotechnol, 2021, 16: 680–687

    Article  Google Scholar 

  37. Yu L, Shen Z, Wang C, et al. Efficient coding and energy efficiency are promoted by balanced excitatory and inhibitory synaptic currents in neuronal network. Front Cell Neurosci, 2018, 12: doi: https://doi.org/10.3389/fncel.2018.00123

  38. Zhu F, Wang R, Pan X, et al. Energy expenditure computation of a single bursting neuron. Cogn Neurodyn, 2019, 13: 75–87

    Article  Google Scholar 

  39. Bélanger M, Allaman I, Magistretti P J. Brain energy metabolism: Focus on astrocyte-neuron metabolic cooperation. Cell Metab, 2011, 14: 724–738

    Article  Google Scholar 

  40. Usha K, Subha P A. Collective dynamics and energy aspects of starcoupled hindmarsh-rose neuron model with electrical, chemical and field couplings. Nonlinear Dyn, 2019, 96: 2115–2124

    Article  MATH  Google Scholar 

  41. Du M, Li J, Wang R, et al. The influence of potassium concentration on epileptic seizures in a coupled neuronal model in the hippocampus. Cogn Neurodyn, 2016, 10: 405–414

    Article  Google Scholar 

  42. Li J, Tang J, Ma J, et al. Dynamic transition of neuronal firing induced by abnormal astrocytic glutamate oscillation. Sci Rep, 2016, 6: 32343

    Article  Google Scholar 

  43. Zare M, Zafarkhah E S, Anzabi-Nezhad N. An area and energy efficient LIF neuron model with spike frequency adaptation mechanism. Neurocomputing, 2021, 465: 350–358

    Article  Google Scholar 

  44. Das B, Schulze J, Ganguly U. Ultra-low energy LIF neuron using Si NIPIN diode for spiking neural networks. IEEE Electron Device Lett, 2018, 39: 1832–1835

    Article  Google Scholar 

  45. Peng Z X, Wang J P, Zhan Y, et al. A high-accuracy and energy-efficient CORDIC based izhikevich neuron. In: 2021 19th IEEE International New Circuits and Systems Conference (NEWCAS). Toulon, 2021

  46. He Z Z, Fan D L. A tunable magnetic skyrmion neuron cluster for energy efficient artificial neural network. In: Design, Automation & Test in Europe Conference & Exhibition (DATE). Lausanne, 2017

  47. Cruz-Albrecht J M, Yung M W, Srinivasa N. Energy-efficient neuron, synapse and STDP integrated circuits. IEEE Trans Biomed Circuits Syst, 2012, 6: 246–256

    Article  Google Scholar 

  48. Dienel G A, Rothman D L. Reevaluation of astrocyte-neuron energy metabolism with astrocyte volume fraction correction: Impact on cellular glucose oxidation rates, glutamate-glutamine cycle energetics, glycogen levels and utilization rates vs. Exercising muscle, and Na+/K+ pum** rates. Neurochem Res, 2020, 45: 2607–2630

    Article  Google Scholar 

  49. Alle H, Roth A, Geiger J R P. Energy-efficient action potentials in hippocampal mossy fibers. Science, 2009, 325: 1405–1408

    Article  Google Scholar 

  50. Litt B, Esteller R, Echauz J, et al. Epileptic seizures may begin hours in advance of clinical onset. Neuron, 2001, 30: 51–64

    Article  Google Scholar 

  51. Zhu Z, Wang R, Zhu F. The energy coding of a structural neural network based on the hodgkin-huxley model. Front Neurosci, 2018, 12: 122–137

    Article  Google Scholar 

  52. Wang Q, Ma X, Wang H. Information processing and energy efficiency of temperature-sensitive morris-lecar neuron. Biosystems, 2020, 197: 104215

    Article  Google Scholar 

  53. Wu K J, Yu C, Wang D C. The dynamics behaviors of Chay neuron model under different parameters. Concurr Comp Pract Exper, 2019, 31: e4836

    Google Scholar 

  54. Wu F, Wang C, ** W, et al. Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise. Physica A, 2017, 469: 81–88

    Article  MathSciNet  MATH  Google Scholar 

  55. Moujahid A, d’Anjou A, Torrealdea F J, et al. Energy and information in hodgkin-huxley neurons. Phys Rev E, 2011, 83: 031912

    Article  MathSciNet  Google Scholar 

  56. Carter B C, Bean B P. Sodium entry during action potentials of mammalian neurons: Incomplete inactivation and reduced metabolic efficiency in fast-spiking neurons. Neuron, 2009, 64: 898–909

    Article  Google Scholar 

  57. Denève S, Machens C K. Efficient codes and balanced networks. Nat Neurosci, 2016, 19: 375–382

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

    LuLu Lu, Ming Yi & **aoQian Liu

Authors
  1. LuLu Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ming Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. **aoQian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to LuLu Lu.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 11675060) and the China Postdoctoral Science Foundation (Grant No. 2021M703011).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, L., Yi, M. & Liu, X. Energy-efficient firing modes of chay neuron model in different bursting kinetics. Sci. China Technol. Sci. 65, 1661–1674 (2022). https://doi.org/10.1007/s11431-021-2066-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-021-2066-7

Keywords

Search

Navigation