Abstract
Conduction delay and failure behaviors of action potentials with a high frequency along nerve fiber are related to the abnormal functions. For instance, upregulation of a hyperpolarization-activated cation current (Ih) is identified to reduce the conduction delay to recover the temporal encoding, and downregulation of the Ih current to enhance the conduction failure rate to ease the pain sensation, with the dynamic mechanisms remaining unclear. In the present paper, the dynamic mechanism is obtained in a chain network model with coupling strength (gc) and action potentials induced by periodic stimulations with a period (Ts). At first, as the action potentials exhibit a high frequency corresponding to a short Ts and the network has a small gc, i.e., a short and unrecovered afterpotential and a small coupling current, the conduction delay is reproduced. The conduction failure is reproduced for Ts shorter and gc smaller than those of the conduction delay, presenting a direct relationship between the two behaviors. Then, the conduction delay and failure are explained with the response time and current threshold of an action potential evoked from the unrecovered afterpotential. The prolonged response time for short Ts and small gc presents the cause for the conduction delay, and the enhanced threshold for shorter Ts and smaller gc presents the cause for the conduction failure. Furthermore, reduction of the delay and enhancement of the failure rate respectively induced by upregulation and downregulation of the Ih current are reproduced and explained. The positive Ih current induces Hopf bifurcation advanced and resting membrane potential elevated. Then, upregulation and downregulation of the Ih current induce the afterpotential elevated to shorten the response time and reduced to enhance the threshold, respectively. The results present nonlinear dynamics for the non-faithful conduction behaviors and dynamical mechanism for the modulation effect of the Ih current on the conduction delay and failure related to encoding and pain.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The data used in this study are available upon request from the corresponding author.
References
Arancibia-Cárcamo IL, Ford MC, Cossell L et al (2017) Node of Ranvier length as a potential regulator of myelinated axon conduction speed. Elife 6:e23329. https://doi.org/10.7554/eLife.23329
Ballo AW, Bucher D (2009) Complex intrinsic membrane properties and dopamine shape spiking activity in a motor axon. J Neurosci 29:5062–5074. https://doi.org/10.1523/JNEUROSCI.0716-09.2009
Ballo AW, Nadim F, Bucher D (2012) Dopamine modulation of Ih improves temporal fidelity of spike propagation in an unmyelinated axon. J Neurosci 32:5106–5119. https://doi.org/10.1523/JNEUROSCI.6320-11.2012
Bernard Healey SA, Scholtes I, Abrahams M et al (2021) Role of hyperpolarization-activated cyclic nucleotide-gated ion channels in neuropathic pain: a proof-of-concept study of ivabradine in patients with chronic peripheral neuropathic pain. Pain Reports 6:e967. https://doi.org/10.1097/PR9.0000000000000967
Bucher D, Goaillard JM (2011) Beyond faithful conduction: Short-term dynamics, neuromodulation, and long-term regulation of spike propagation in the axon. Prog Neurobiol 94:307–346. https://doi.org/10.1016/j.pneurobio.2011.06.001
Bukh AV, Shepelev IA, Elizarov EM et al (2023) Role of coupling delay in oscillatory activity in autonomous networks of excitable neurons with dissipation. Chaos 33:073114. https://doi.org/10.1063/5.0147883
Byczkowicz N, Eshra A, Montanaro J et al (2019) HCN channel-mediated neuromodulation can control action potential velocity and fidelity in central axons. Elife 8:e42766. https://doi.org/10.7554/eLife.42766
Cartwright R (2010) A guide to XPPAUT for researchers and students. Perspect Public Health 130:239–239. https://doi.org/10.1177/1757913910379198
Chaplan SR, Guo HQ, Lee DH et al (2003) Neuronal hyperpolarization-activated pacemaker channels drive neuropathic pain. J Neurosci 23:1169–1178. https://doi.org/10.1523/jneurosci.23-04-01169.2003
Chen H, Garcia-Gonzalez D, Jérusalem A (2019) Computational model of the mechanoelectrophysiological coupling in axons with application to neuromodulation. Phys Rev E 99:032406. https://doi.org/10.1103/PhysRevE.99.032406
Cho IH, Panzera LC, Chin M, Hoppa MB (2017) Sodium channel β2 subunits prevent action potential propagation failures at axonal branch points. J Neurosci 37:9519–9533. https://doi.org/10.1523/JNEUROSCI.0891-17.2017
Cross KP, Robertson RM (2016) Ionic mechanisms maintaining action potential conduction velocity at high firing frequencies in an unmyelinated axon. Physiol Rep 4:e12814. https://doi.org/10.14814/phy2.12814
Crotty P, Levy WB (2007) Effects of Na+ channel inactivation kinetics on metabolic energy costs of action potentials. Neurocomputing 70:1652–1656. https://doi.org/10.1016/j.neucom.2006.10.063
Dai S, Lu L, Wei Z et al (2022) Influence of temperature and noise on the propagation of subthreshold signal in feedforward neural network. Chaos, Solitons Fractals 164:112762. https://doi.org/10.1016/j.chaos.2022.112762
Dilley A, Richards N, Pulman KG, Bove GM (2013) Disruption of fast axonal transport in the rat induces behavioral changes consistent with neuropathic pain. J Pain 14:1437–1449. https://doi.org/10.1016/j.jpain.2013.07.005
Ding Q, Jia Y (2021) Effects of temperature and ion channel blocks on propagation of action potential in myelinated axons. Chaos 31:053102. https://doi.org/10.1063/5.0044874
Duan L, Liang W, Ji W, Xi H (2020) Bifurcation patterns of bursting within pre-bötzinger complex and their control. Int J Bifurc Chaos 30:2050192. https://doi.org/10.1142/S0218127420501928
Dutta DJ, Woo DH, Lee PR et al (2018) Regulation of myelin structure and conduction velocity by perinodal astrocytes. Proc Natl Acad Sci U S A 115:11832–11837. https://doi.org/10.1073/pnas.1811013115
Feng Z, Wang Z, Guo Z et al (2017) High frequency stimulation of afferent fibers generates asynchronous firing in the downstream neurons in hippocampus through partial block of axonal conduction. Brain Res 1661:67–78. https://doi.org/10.1016/j.brainres.2017.02.008
Freeman WJ (2000) Characteristics of the synchronization of brain activity imposed by finite conduction velocities of axons. Int J Bifurc Chaos 10:2307–2322. https://doi.org/10.1142/S0218127400001547
Freeman SA, Desmazières A, Fricker D et al (2016) Mechanisms of sodium channel clustering and its influence on axonal impulse conduction. Cell Mol Life Sci 73:723–735. https://doi.org/10.1007/s00018-015-2081-1
Gillespie MJ, Stein RB (1983) The relationship between axon diameter, myelin thickness and conduction velocity during atrophy of mammalian peripheral nerves. Brain Res 259:41–56. https://doi.org/10.1016/0006-8993(83)91065-X
Guan L, Jia B, Gu H (2019) A novel threshold across which the negative stimulation evokes action potential near a saddle-node bifurcation in a neuronal model with Ih current. Int J Bifurc Chaos 29:1950198. https://doi.org/10.1142/S0218127419501980
Guan L, Gu H, Zhao Z (2021) Dynamics of subthreshold and suprathreshold resonance modulated by hyperpolarization-activated cation current in a bursting neuron. Nonlinear Dyn 104:577–601. https://doi.org/10.1007/s11071-021-06230-8
Guo Y, Zhou P, Yao Z, Ma J (2021) Biophysical mechanism of signal encoding in an auditory neuron. Nonlinear Dyn 105:3603–3614. https://doi.org/10.1007/s11071-021-06770-z
Hamada MS, Popovic MA, Kole MHP (2017) Loss of saltation and presynaptic action potential failure in demyelinated axons. Front Cell Neurosci 11:45. https://doi.org/10.3389/fncel.2017.00045
Hodgkin AL (1954) A note on conduction velocity. J Physiol 125:221–224. https://doi.org/10.1113/jphysiol.1954.sp005152
Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544. https://doi.org/10.1113/jphysiol.1952.sp004764
Jansen LAR, Forster LA, Smith XL et al (2021) Changes in peripheral HCN2 channels during persistent inflammation. Channels 15:165–179. https://doi.org/10.1080/19336950.2020.1870086
Khurana S, Remme MWH, Rinzel J, Golding NL (2011) Dynamic interaction of Ih and IK-LVA during trains of synaptic potentials in principal neurons of the medial superior olive. J Neurosci 31:8936–8947. https://doi.org/10.1523/JNEUROSCI.1079-11.2011
Kiziltan E, Dalkilic N, Guney FB, Pehlivan F (2007) Conduction velocity distribution: Early diagnostic tool for peripheral neuropathies. Int J Neurosci 117:203–213. https://doi.org/10.1080/00207450600582496
Kueh D, Barnett WH, Cymbalyuk GS, Calabrese RL (2016) Na+/K+ pump interacts with the Ih-current to control bursting activity in central pattern generator neurons of leeches. Elife 5:e19322. https://doi.org/10.7554/eLife.19322
Lesnick TG, Papapetropoulos S, Mash DC et al (2007) A genomic pathway approach to a complex disease: axon guidance and parkinson disease. PLoS Genet 3:0984–0995. https://doi.org/10.1371/journal.pgen.0030098
Lezmy J, Arancibia-Cárcamo IL, Quintela-López T et al (2021) Astrocyte Ca2+-evoked ATP release regulates myelinated axon excitability and conduction speed. Science 374:eabh2858. https://doi.org/10.1126/science.abh2858
Li JJ, Xie Y, Yu YG et al (2017) A neglected GABAergic astrocyte: Calcium dynamics and involvement in seizure activity. Sci China Technol Sci 60:1003–1010. https://doi.org/10.1007/s11431-016-9056-2
Li T, Wu Y, Yang L et al (2023) Neuronal morphology and network properties modulate signal propagation in multi-layer feedforward network. Chaos, Solitons Fractals 172:113554. https://doi.org/10.1016/j.chaos.2023.113554
Lyu W, Li S, Chen Z, Bi Q (2023) Bursting dynamics in a singular vector field with codimension three triple zero bifurcation. Mathematics 11:2486. https://doi.org/10.3390/math11112486
Ma J (2023) Biophysical neurons, energy, and synapse controllability: a review. J Zhejiang Univ Sci A 24:109–129. https://doi.org/10.1631/jzus.A2200469
Mao H, Wang X, Chen W et al (2019) Use of in vivo single-fiber recording and intact dorsal root ganglion with attached sciatic nerve to examine the mechanism of conduction failure. J vis Exp 150:e59234. https://doi.org/10.3791/59234
Panzeri S, Brunel N, Logothetis NK, Kayser C (2010) Sensory neural codes using multiplexed temporal scales. Trends Neurosci 33:111–120. https://doi.org/10.1016/j.tins.2009.12.001
Ratas I, Pyragas K (2012) Effect of high-frequency stimulation on nerve pulse propagation in the FitzHugh-Nagumo model. Nonlinear Dyn 67:2899–2908. https://doi.org/10.1007/s11071-011-0197-x
Roth FC, Hu H (2020) An axon-specific expression of HCN channels catalyzes fast action potential signaling in GABAergic interneurons. Nat Commun 11:2248. https://doi.org/10.1038/s41467-020-15791-y
Shimba K, Kotani K, Jimbo Y (2021) Microfabricated device to record axonal conduction under pharmacological treatment for functional evaluation of axon ion channel. IEEE Trans Biomed Eng 68:3574–3581. https://doi.org/10.1109/TBME.2021.3078473
Song X, Wang H, Chen Y, Lai Y (2019) Emergence of an optimal temperature in action-potential propagation through myelinated axons. Phys Rev E 100:032416. https://doi.org/10.1103/PhysRevE.100.032416
Song J, Liu S, Lin H (2022) Model-based quantitative optimization of deep brain stimulation and prediction of Parkinson’s states. Neuroscience 498:105–124. https://doi.org/10.1016/j.neuroscience.2022.05.019
Sun W, Miao B, Wang XC et al (2012) Reduced conduction failure of the main axon of polymodal nociceptive C-fibres contributes to painful diabetic neuropathy in rats. Brain 135:359–375. https://doi.org/10.1093/brain/awr345
Takagi D, Okamoto Y, Ohba T et al (2020) Comparative study of hyperpolarization-activated currents in pulmonary vein cardiomyocytes isolated from rat, guinea pig, and rabbit. J Physiol Sci 70:6. https://doi.org/10.1186/s12576-020-00736-3
Wang X, Wang S, Wang W et al (2016a) A novel intrinsic analgesic mechanism: the enhancement of the conduction failure along polymodal nociceptive C-fibers. Pain 157:2235–2247. https://doi.org/10.1097/j.pain.0000000000000632
Wang X, Wang S, Zhang M et al (2016b) Α-dendrotoxin-sensitive Kv1 channels contribute to conduction failure of polymodal nociceptive C-fibers from rat coccygeal nerve. J Neurophysiol 115:947–957. https://doi.org/10.1152/jn.00786.2014
Wang X, Yu Y, Han F, Wang Q (2023) Dynamical mechanism of parkinsonian beta oscillation in a heterogenous subthalamopallidal network. Nonlinear Dyn 111:10505–10527. https://doi.org/10.1007/s11071-023-08381-2
Waxman SG (1977) Conduction in myelinated, unmyelinated, and demyelinated fibers. Arch Neurol 34:585–589. https://doi.org/10.1001/archneur.1977.00500220019003
Waxman SG (2006) Axonal conduction and injury in multiple sclerosis: The role of sodium channels. Nat Rev Neurosci 7:932–941. https://doi.org/10.1038/nrn2023
Weng X, Smith T, Sathish J, Djouhri L (2012) Chronic inflammatory pain is associated with increased excitability and hyperpolarization-activated current (Ih) in C- but not Aδ-nociceptors. Pain 153:900–914. https://doi.org/10.1016/j.pain.2012.01.019
Wimmer VC, Reid CA, So EYW et al (2010) Axon initial segment dysfunction in epilepsy. J Physiol 588:1829–1840. https://doi.org/10.1113/jphysiol.2010.188417
Xing M, Yang Z, Chen Y (2023) Bursting types and bifurcation analysis of the temperature-sensitive Purkinje neuron. Nonlinear Dyn 111:1819–1834. https://doi.org/10.1007/s11071-022-07917-2
Yang C, Liu Z, Wang Q et al (2021) Epileptic seizures in a heterogeneous excitatory network with short-term plasticity. Cogn Neurodyn 15:43–51. https://doi.org/10.1007/s11571-020-09582-w
Yao C, Yao Y, Qian Y, Xu X (2022) Temperature-controlled propagation of spikes in neuronal networks. Chaos, Solitons Fractals 164:112667. https://doi.org/10.1016/j.chaos.2022.112667
Zang Y, Marder E (2021) Interactions among diameter, myelination, and the Na/K pump affect axonal resilience to high-frequency spiking. Proc Natl Acad Sci U S A 118:e2105795118. https://doi.org/10.1073/pnas.2105795118
Zang Y, Marder E (2023) Neuronal morphology enhances robustness to perturbations of channel densities. Proc Natl Acad Sci 120:e2219049120. https://doi.org/10.1073/pnas.2219049120
Zang Y, Marder E, Marom S (2022) Sodium channel slow inactivation normalizes firing in axons with uneven conductance distributions. BioRxiv 33:1818–1824. https://doi.org/10.1016/j.cub.2023.03.043
Zhang X, Gu H (2019) Influence of hopf bifurcation dynamics on conduction failure of action potentials along nerve C-fiber. Int J Bifurc Chaos 29:1950093. https://doi.org/10.1142/S0218127419500937
Zhang Y, Bucher D, Nadim F (2017) Ionic mechanisms underlying history-dependence of conduction delay in an unmyelinated axon. Elife 6:e25382. https://doi.org/10.7554/eLife.25382
Zhang M, Guo H, Ma Y et al (2019a) Acupoint sensitization is associated with increased excitability and hyperpolarization-activated current (Ih) in C- but not Aδ-type neurons. Neuroscience 404:499–509. https://doi.org/10.1016/j.neuroscience.2019.02.028
Zhang X, Gu H, Guan L (2019b) Stochastic dynamics of conduction failure of action potential along nerve fiber with Hopf bifurcation. Sci China Technol Sci 62:1502–1511. https://doi.org/10.1007/s11431-018-9515-4
Zhang X, Gu H, Wu F (2019c) Memristor reduces conduction failure of action potentials along axon with Hopf bifurcation. Eur Phys J Spec Top 228:2053–2063. https://doi.org/10.1140/epjst/e2019-900004-2
Zhang X, Gu H, Ma K (2020) Dynamical mechanism for conduction failure behavior of action potentials related to pain information transmission. Neurocomputing 387:293–308. https://doi.org/10.1016/j.neucom.2019.12.114
Zhu ZR, Tang XW, Wang WT et al (2009) Conduction failures in rabbit saphenous nerve unmyelinated fibers. Neurosignals 17:181–195. https://doi.org/10.1159/000209279
Acknowledgements
This work was sponsored by the National Natural Science Foundation of China (Grant Numbers: 12072236 and 12202147) and Nature Science Foundation of Henan province (Grant Number: 212300410196)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors indicate no conflicts of interest related to the content of this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Lu, M., Gu, H. & Zhang, X. The influence of hyperpolarization-activated cation current on conduction delay and failure of action potentials along axon related to abnormal functions. Cogn Neurodyn (2024). https://doi.org/10.1007/s11571-024-10103-2
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11571-024-10103-2