Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes

Ali Calim

doi:10.29130/dubited.1525920

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Farklı Uyartım Rejimlerinde Stokastik Hodgkin-Huxley Nöronunun Ateşleme Karakteristiğinin Sayısal İncelemesi

Abstract

Bu makale, önemli içsel nöronal gürültü kaynaklarından biri olan iyon kanal gürültüsünün, farklı uyartım rejimlerinde Hodgkin-Huxley nöronunun tepkisi üzerindeki etkisini araştırmaktadır. Sonuçlarımız, nöron dinamiklerine dc akımının dahil edilmesi durumunda, uyarılabilir nörondaki nöronal ateşlemelerin, arttırılan iyon kanalı gürültüsü nedeniyle artan ateşleme hızıyla ortaya çıktığını göstermektedir. Ateşleme hızı ve kanal gürültüsü arasındaki böyle bir ilişkiye rağmen, ortaya çıkan davranış hala spontane ve düzensizdir. Ancak, ateşleyen nörondaki nöronal ateşlemeler, orta düzeydeki kanal gürültüsü nedeniyle seker veya susar. Bu, ters stokastik rezonans fenomeni olarak bilinir. Böyle bir ateşleyen nöronun, sekme veya susma davranışının ortaya çıktığı gürültü seviyeleri etrafında, ilginç bir şekilde, oldukça düzensiz olduğunu ve bunun daha yüksek gürültü seviyelerine doğru da devam ettiği gösterilmiştir. Öte yandan, kanal gürültüsünün, öncelikli olarak eşik altı genliğe sahip periyodik bir sinyale verilen nöronal tepki üzerindeki etkisi incelenmiştir. Sinyal frekansının kanal gürültü yoğunluğuna ilişkin tepki hassasiyeti üzerinde önemli bir etkiye sahip olduğu gösterilmektedir, oysa dc akım girdisiyle karşılaştırıldığında ateşleme olasılığı ve düzenlilik artan gürültü nedeniyle yakın bir ilişki göstermektedir. Son olarak, eşik üstü periyodik uyartım durumunda iyon kanal gürültüsüne bağlı nöronal davranış analiz edilmiştir. Belirli bir kanal gürültüsü seviyesine kadar, gürültü artan sinyal frekanslarıyla doğrusal olmayan bir ilişkiye sahip olan ateşleme sayısını ciddi şekilde etkilememektedir. Nispeten yüksek gürültü yardımıyla yüksek frekans bölgelerinde ters stokastik rezonans etkisinin olduğu söylenebilir. Bir diğer ilginç bulgu ise kanal gürültüsünün belirli frekanslarda düzenliliği etkilememesidir, ki bu eşik üstü periyodik sinyal uygulandığında düzensiz tepki bölgesinin varlığını ortaya çıkarmaktadır.

Keywords

Kanal gürültüsü, ateşleme düzenliliği, ateşleme oranı, dc uyartım, periyodik girdi

Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes

Abstract

This paper investigates the influence of the ion channel noise, that is one of important internal neuronal noise sources, on the response of a Hodgkin-Huxley neuron in different stimulus regimes. Our results show that, in the case of dc current introduction into neuron dynamics, neuronal firings in excitable neuron emerge with growing firing rate due to increasing ion channel noise. Despite such a relationship between firing rate and channel noise, emergent behaviour is still spontaneous and irregular. However, neuronal firings in spiking neuron skip or terminate due to intermediate level of channel noise. This is known as inverse stochastic resonance phenomenon. We show that firing behaviour of such a spiking neuron is, interestingly, highly irregular around the revealed noise levels and this continues towards higher noise intensities. On the other hand, we examine the influence of channel noise on the neuronal response to a periodic signal primarily with subthreshold amplitude. We show that signal frequency has a significant effect on the response sensitivity related to channel noise intensity whereas, compared to dc current input, firing probability and regularity show a close relationship due to increasing noise. Finally, neuronal behaviour due to ion channel noise in the case of suprathreshold periodic forcing is analysed. Up to a certain level of channel noise, it does not seriously affect number of firings which has a nonlinear relationship with increasing signal frequencies. It is also possible to see inverse stochastic resonance effect at the high frequency regions with the help of relatively high noise. Another interesting finding is that channel noise does not affect the regularity at certain frequencies, yielding the presence of irregular response region at suprathreshold periodic inputs.

Keywords

Channel noise, spiking regularity, firing rate, dc stimulus, periodic input

References

[1] E. Schneidman, I. Segev and N. Tishby, “Information capacity and robustness of stochastic neuron models,” in Advances in Neural Information Processing Systems 12, S. Solla, T. Leen and K. Müller, Eds., MIT Press, 1999, pp. 178–84.
[2] B. P. Bean, “The action potential in mammalian central neurons,” Nat. Rev. Neurosci., vol. 8, no. 6, pp. 451–65, 2007.
[3] Y. Zhang, Y. Xu, Z. Yao and J. Ma, “A feasible neuron for estimating the magnetic field effect,” Nonlinear Dyn., vol. 102, pp. 1849–67, 2020.
[4] K. M. Stiefel, B. Englitz and T. J. Sejnowski, “Origin of intrinsic irregular firing in cortical interneurons,” Proc. Natl. Acad. Sci., vol. 110, no. 19, pp. 7886–91, 2013.
[5] A. Bahramian, F. Parastesh, V.-T. Pham, T. Kapitaniak, S. Jafari and M. Perc, “Collective behavior in a two-layer neural network with time-varying chemical connections that are controlled by a Petri net,” Chaos, vol. 31, no. 3, pp. 033138, 2021.
[6] S. Majhi, B. K. Bera, D. Ghosh and M. Perc, “Chimera states in neural networks: a review,” Phys. Life Rev., vol. 28, pp. 100–21, 2019.
[7] A. Calim, J. J. Torres, M. Ozer and M. Uzuntarla, “Chimera states in hybrid coupled neuron populations,” Neural Netw., vol. 126, pp. 108–17, 2020.
[8] Y. Gallero-Salas et al., “Sensory and behavioral components of neocortical signal flow in discrimination tasks with short-term memory,” Neuron, vol. 109, no. 1, pp. 135-148, 2021.
[9] S. W. Kennerley and M. E. Walton, “Decision making and reward in frontal cortex: complementary evidence from neurophysiological and neuropsychological studies,” Behav. Neurosci., vol. 125, no. 3, pp. 297-317, 2011.
[10] A. Csemer et al., “Astrocyte‐ and NMDA receptor‐dependent slow inward currents differently contribute to synaptic plasticity in an age‐dependent manner in mouse and human neocortex,” Aging Cell, vol. 22, no. 9, pp. e13939, 2023.

[11] D. A. Ruff and M. R. Cohen, “Stimulus dependence of correlated variability across cortical areas,” J. Neurosci., vol. 36, no. 28, pp. 7546-7556, 2016.
[12] A. F. Meyer, R. S. Williamson, J. F. Linden and M. Sahani, “Models of neural stimulus-response functions: elaboration, estimation, and evaluation,” Front. Syst. Neurosci., vol. 10, pp. 109, 2017.
[13] D. Tang, J. Zylberberg, X. Jia and H. Choi, “Stimulus type shapes the topology of cellular functional networks in mouse visual cortex,” Nat. Commun., vol. 15, no. 1, pp. 5753, 2024.
[14] T. O’Leary, M. C. van Rossum and D. J. Wyllie, “Homeostasis of intrinsic excitability in hippocampal neurones: dynamics and mechanism of the response to chronic depolarization,” J. Physiol., vol. 588, no. 1, pp. 157-170, 2010.
[15] S. A. Alpizar, I. H. Cho and M. B. Hoppa, “Subcellular control of membrane excitability in the axon,” Curr. Opin. Neurobiol., vol. 57, pp. 117-125, 2019.
[16] J. A. Rosenkranz and D. Johnston, “Dopaminergic regulation of neural excitability through modulation of Ih in layer V entorhinal cortex,” J. Neurosci., vol. 26, no. 12, pp. 3229-3244, 2006.
[17] W. Gerstner, A. K. Kreiter, H. Markram and A. V. Herz, “Neural codes: firing rates and beyond,” Proc. Natl. Acad. Sci., vol. 94, no. 24, pp. 12740-12741, 1997.
[18] S. Panzeri, J. H. Macke, J. Gross and C. Kayser, “Neural population coding: combining insights from microscopic and mass signals,” Trends Cogn. Sci., vol. 19, no. 3, pp. 162-172, 2015.
[19] M. N. Shadlen and W. T. Newsome, “The variable discharge of cortical neurons: implications for connectivity, computation, and information coding,” J. Neurosci., vol. 18, no. 10, pp. 3870-3896, 1998.
[20] F. Li et al., “An artificial visual neuron with multiplexed rate and time-to-first-spike coding,” Nat. Commun., vol. 15, no. 1, pp. 3689, 2024.
[21] L. Gao, K. Kostlan, Y. Wang and X. Wang, “Distinct subthreshold mechanisms underlying rate-coding principles in primate auditory cortex,” Neuron, vol. 91, no. 4, pp. 905-919, 2016.
[22] C. P. Billimoria, R. A. DiCaprio, J. T. Birmingham, L. F. Abbott and E. Marder, “Neuromodulation of spike-timing precision in sensory neurons,” J. Neurosci., vol. 26, pp. 5910-5919, 2006.
[23] M. Bieler, K. Sieben, N. Cichon, S. Schildt, B. Röder and I. L. Hanganu-Opatz, “Rate and temporal coding convey multisensory information in primary sensory cortices,” eNeuro, vol. 4, no. 2, pp. e0037-17.2017, 2017.
[24] X. Wang, T. Lu, D. Bendor and E. Bartlett, “Neural coding of temporal information in auditory thalamus and cortex,” Neuroscience, vol. 154, no. 1, pp. 294-303, 2008.
[25] C. A. Navntoft and V. Adenis, “Does auditory cortex code temporal information from acoustic and cochlear implant stimulation in a similar way?,” J. Neurosci., vol. 38, no. 2, pp. 260-262, 2018.
[26] Y. Zuo, H. Safaai, G. Notaro, A. Mazzoni, S. Panzeri and M. E. Diamond, “Complementary contributions of spike timing and spike rate to perceptual decisions in rat S1 and S2 cortex,” Curr. Biol., vol. 25, no. 3, pp. 357-363, 2015.
[27] M. Ainsworth, S. Lee, M. O. Cunningham, R. D. Traub, N. J. Kopell and M. A. Whittington, “Rates and rhythms: a synergistic view of frequency and temporal coding in neural networks,” Neuron, vol. 75, no. 4, pp. 572-583, 2012.
[28] J. O'keefe and N. Burgess, “Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells,” Hippocampus, vol. 15, no. 7, pp. 853-866, 2005.
[29] S. K. Sudhakar, B. Torben-Nielsen and E. De Schutter, “Cerebellar nuclear neurons use time and rate coding to transmit Purkinje neuron pauses,” PLoS Comput. Biol., vol. 11, no. 12, pp. e1004641, 2015.
[30] L. Gammaitoni, P. Hänggi, P. Jung and F. Marchesoni, “Stochastic resonance,” Rev. Mod. Phys., vol. 70, no. 1, pp. 223, 1998.
[31] F. Moss, L. M. Ward and W. G. Sannita, “Stochastic resonance and sensory information processing: a tutorial and review of application,” Clin. Neurophysiol., vol. 115, no. 2, pp. 267-281, 2004.
[32] J. F. Mejias and J. J. Torres, “Emergence of resonances in neural systems: the interplay between adaptive threshold and short-term synaptic plasticity,” PLOS ONE, vol. 6, no. 3, pp. e17255, 2011.
[33] A. Torcini, S. Luccioli and T. Kreuz, “Coherent response of the Hodgkin–Huxley neuron in the high-input regime,” Neurocomputing, vol. 70, no. 10-12, pp. 1943-1948, 2007.
[34] D. Guo and C. Li, “Stochastic and coherence resonance in feed-forward-loop neural network motifs,” Phys. Rev. E, vol. 79, no. 5, pp. 051921, 2009.
[35] Q. Wang, M. Perc, Z. Duan and G. Chen, “Synchronization transitions on scale-free neural networks due to finite information transmission delays,” Phys. Rev. E, vol. 80, no. 2, pp. 026206, 2009.
[36] Q. Wang, G. Chen and M. Perc, “Synchronous bursts on scale-free neural networks with attractive and repulsive coupling,” PLOS ONE, vol. 6, no. 1, pp. e15851, 2011.
[37] A. B. Neiman, T. A. Yakusheva and D. F. Russell, “Noise-induced transition to bursting in responses of paddlefish electroreceptor afferents,” J. Neurophysiol., vol. 98, no. 5, pp. 2795-2806, 2007.
[38] D. Hansel and H. Sompolinsky, “Synchronization and computation in a chaotic neural network,” Phys. Rev. Lett., vol. 68, no. 5, pp. 718, 1992.
[39] B. A. Dosher and Z. L. Lu, “Perceptual learning reflects external noise filtering and internal noise reduction through channel reweighting,” Proc. Natl. Acad. Sci., vol. 95, no. 23, pp. 13988-93, 1998.
[40] J. Grenzebach and E. Romanus, “Quantifying the effect of noise on cognitive processes: a review of psychophysiological correlates of workload,” Noise Health, vol. 24, no. 115, pp. 199-214, 2022.
[41] H. Yu, R. R. Dhingra, T. E. Dick and R. F. Galán, “Effects of ion channel noise on neural circuits: an application to the respiratory pattern generator to investigate breathing variability,” J. Neurophysiol., vol. 117, no. 1, pp. 230-242, 2017.
[42] A. Manwani and C. Koch, “Detecting and estimating signals in noisy cable structures, I: Neural noise sources,” Neural Comput., vol. 11, no. 8, pp. 1797-1829, 1999.
[42] D. Guo, M. Perc, T. Liu and D. Yao, “Functional importance of noise in neural information processing,” EPL, vol. 124, no. 5, pp. 50001, 2018.
[44] J. A. White, R. Klink, A. Alonso and A. R. Kay, “Noise from voltage-gated ion channels may influence neural dynamics in the entorhinal cortex,” J. Neurophysiol., vol. 80, no. 1, pp. 262-269, 1998.
[45] Z. Jiang, D. Wang, H. Shang and Y. Chen, “Effect of potassium channel noise on nerve discharge based on the Chay model,” Technology and Health Care, vol. 28, no. S1, pp. 371-381, 2020.
[46] B. Moezzi, N. Iannella and M. D. McDonnell, “Ion channel noise can explain firing correlation in auditory nerves,” J. Comput. Neurosci., vol. 41, pp. 193-206, 2016.
[47] H. Yu, R. F. Galán, J. Wang, Y. Cao and J. Liu, “Stochastic resonance, coherence resonance, and spike timing reliability of Hodgkin–Huxley neurons with ion-channel noise,” Phys. A: Stat. Mech. Appl., vol. 471, pp. 263-275, 2017.
[48] M. Ozer, M. Perc and M. Uzuntarla, “Stochastic resonance on Newman–Watts networks of Hodgkin–Huxley neurons with local periodic driving,” Phys. Lett. A, vol. 373, no. 10, pp. 964-968, 2009.
[49] A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Physiol., vol. 117, no. 4, pp. 500-544, 1952.
[50] R. F. Fox, “Stochastic versions of the Hodgkin-Huxley equations,” Biophys. J., vol. 72, no. 5, pp. 2068-2074, 1997.
[51] M. Ozer, M. Perc and M. Uzuntarla, “Controlling the spontaneous spiking regularity via channel blocking on Newman-Watts networks of Hodgkin-Huxley neurons,” EPL, vol. 86, no. 4, pp. 40008, 2009.
[52] K. M. Stiefel, B. Englitz and T. J. Sejnowski, “Origin of intrinsic irregular firing in cortical interneurons,” Proc. Natl. Acad. Sci., vol. 110, no. 19, pp. 7886-7891, 2013.
[53] E. V. Pankratova, A. V. Polovinkin and E. Mosekilde, “Resonant activation in a stochastic Hodgkin-Huxley model: interplay between noise and suprathreshold driving effects,” EPJ B, vol. 45, pp. 391-397, 2005.
[54] V. Baysal, Z. Saraç and E. Yilmaz, “Chaotic resonance in Hodgkin–Huxley neuron,” Nonlinear Dyn., vol. 97, pp. 1275-1285, 2019.
[55] A. Calim and V. Baysal, “Chaotic resonance in an astrocyte-coupled excitable neuron,” Chaos Soliton Fract., vol. 176, pp. 114105, 2023.
[56] H. Yang, G. Xu and H. Wang, “Effects of magnetic fields on stochastic resonance in Hodgkin-Huxley neural network driven by Gaussian noise and non-Gaussian noise,” Cogn. Neurodyn., vol. 16, no. 3, pp. 707-717, 2022.
[57] K. Wu and J. Li, “Effects of high-low frequency electromagnetic radiation on vibrational resonance in Hodgkin–Huxley neural system,” J. Phys. A, vol. 57, no. 14, pp. 145702, 2024.
[58] V. Koren, G. Bondanelli and S. Panzeri, “Computational methods to study information processing in neural circuits,” Comput. Struct. Biotechnol. J., vol. 21, pp. 910-922, 2023.
[59] M. Perc and M. Marhl, “Amplification of information transfer in excitable systems that reside in a steady state near a bifurcation point to complex oscillatory behavior,” Phys. Rev. E, vol. 71, no. 2, pp. 026229, 2005.
[60] E. V. Pankratova, V. N. Belykh and E. Mosekilde, “Role of the driving frequency in a randomly perturbed Hodgkin-Huxley neuron with suprathreshold forcing,” EPJ B, vol. 53, pp. 529-536, 2006.

Details

Primary Language

English

Subjects

Machine Learning (Other)

Journal Section

Research Article

Authors

Ali Calim ^*
0000-0002-3681-6787
Türkiye

Publication Date

January 30, 2025

Submission Date

July 31, 2024

Acceptance Date

September 20, 2024

Published in Issue

Year 2025 Volume: 13 Number: 1

DOI

https://doi.org/10.29130/dubited.1525920

IZ

https://izlik.org/JA36HE96JY

APA

Calim, A. (2025). Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes. Duzce University Journal of Science and Technology, 13(1), 171-185. https://doi.org/10.29130/dubited.1525920

AMA

1.Calim A. Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes. DUBİTED. 2025;13(1):171-185. doi:10.29130/dubited.1525920

Chicago

Calim, Ali. 2025. “Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes”. Duzce University Journal of Science and Technology 13 (1): 171-85. https://doi.org/10.29130/dubited.1525920.

EndNote

Calim A (January 1, 2025) Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes. Duzce University Journal of Science and Technology 13 1 171–185.

IEEE

[1]A. Calim, “Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes”, DUBİTED, vol. 13, no. 1, pp. 171–185, Jan. 2025, doi: 10.29130/dubited.1525920.

ISNAD

Calim, Ali. “Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes”. Duzce University Journal of Science and Technology 13/1 (January 1, 2025): 171-185. https://doi.org/10.29130/dubited.1525920.

JAMA

1.Calim A. Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes. DUBİTED. 2025;13:171–185.

MLA

Calim, Ali. “Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes”. Duzce University Journal of Science and Technology, vol. 13, no. 1, Jan. 2025, pp. 171-85, doi:10.29130/dubited.1525920.

Vancouver

1.Ali Calim. Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes. DUBİTED. 2025 Jan. 1;13(1):171-85. doi:10.29130/dubited.1525920

Farklı Uyartım Rejimlerinde Stokastik Hodgkin-Huxley Nöronunun Ateşleme Karakteristiğinin Sayısal İncelemesi

Abstract

Keywords

Numerical Investigation of Firing Characteristic of Stochastic Hodgkin-Huxley Neuron under Different Forcing Regimes

Abstract

Keywords

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Details

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Published in Issue

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