Nonlinear and ionic mechanisms for bursting patterns and subthreshold resonance in mesencephalic V neurons

i

This article has been updated. A Correction to this article was published on .

i

The Original Article was published on

i

The Original Article was published on

i

This article has been updated

i

This article was retracted on

i

This article has been updated

Abstract

The bursting and subthreshold resonance of mesencephalic trigeminal nucleus neurons play a critical role in bite force control and orofacial pain processing, yet their underlying dynamical mechanisms remain poorly understood. The nonlinear and ionic mechanisms are presented in the present paper. First, bifurcations from the resting state to bursting, modulated by persistent sodium current (I_NaP) and applied current (I_app), are obtained, including a Hopf bifurcation. Second, three typical bursting patterns are distinguished via codimension-2 bifurcations, and coexisting behaviors are acquired through fast/slow analysis. Modulated by I_NaP, the most common bursting pattern, similar to experimental observations, exhibits bursts interrupted by long quiescent states. In the fast subsystem, the limit cycle for the burst is far from the coexisting equilibrium for the quiescent state. Then, stochastic transitions between the two behaviors cannot be evoked, resulting in robustness to noise. Two other bursting patterns manifest transitions between bursts for a large limit cycle and subthreshold oscillation for a small limit cycle. Proximity between the two limit cycles allows noise to drive stochastic transitions, leading to noise-sensitive dynamics. The sensitivity is determined by the distance between the two cycles. Finally, subthreshold resonance evoked from the resting state is reproduced, which is mediated by potassium current. Enhanced I_NaP and I_app amplify the resonance amplitude and frequency by driving the resting state toward the Hopf bifurcation. The dynamics of bursting and resonance advance the understanding of sensorimotor processing and present potential targets for treating orofacial motor disorders.

Keywords

bursting / subthreshold resonance / bifurcation / coexistence / mesencephalic trigeminal neurons / persistent sodium current

CHANGE HISTORY

A Correction to this paper has been published:
https://doi.org

The Retraction Note was updated to reflect reception of statements of disagreement from all authors.

This article has been retracted.Please see the Retraction Notice for more detail:
https://doi.org

References

[1] J. Li, Y. Xie, Y. Yu, M. Du, R. Wang, Y. Wu, A neglected GABAergic astrocyte: Calcium dynamics and involvement in seizure activity, Sci. China Technol. Sci., 60 (2017), 1003-1010. https://doi.org/10.1007/s11431-016-9056-2

[2] Y. Cui, Y. Yang, Z. Ni, Y. Dong, G. Cai, A. Foncelle, et al., Astroglial Kir4.1 in the lateral habenula drives neuronal bursts in depression, Nature, 554 (2018), 323-327. https://doi.org/10.1038/nature25752

[3] H. Zhou, X. Wang, H. Gu, Y. Jia, Deep brain stimulation-induced two manners to eliminate bursting for Parkinson’s diseases: synaptic current and bifurcation mechanisms, Cognit. Neurodyn., 19 (2025), 78. https://doi.org/10.1007/s11571-025-10267-3

[4] M. L. Saggio, V. Jirsa, Bifurcations and bursting in the Epileptor, PLoS Comput. Biol., 20 (2024), e1011903. https://doi.org/10.1371/journal.pcbi.1011903

[5] Q. Xu, Y. Fang, H. Wu, H. Bao, N. Wang, Firing patterns and fast-slow dynamics in an N-type LAM-based FitzHugh-Nagumo circuit, Chaos, Solitons Fractals, 187 (2024), 115376. https://doi.org/10.1016/j.chaos.2024.115376

[6] Z. Wang, X. Wei, L. Duan, Regulatory mechanism of inhibitory interneurons with time-delay on epileptic seizures under sinusoidal sensory stimulation, Cognit. Neurodyn., 19 (2025), 37. https://doi.org/10.1007/s11571-025-10227-z

[7] X. Han, Q. Bi, P. Ji, J. Kurths, Fast-slow analysis for parametrically and externally excited systems with two slow rationally related excitation frequencies, Phys. Rev. E, 92 (2015), 012911. https://doi.org/10.1103/PhysRevE.92.012911

[8] L. Duan, X. Chen, L. Xia, Z. Wang, Dynamics and control of mixed bursting in nonlinear pre-Bötzinger complex systems, Nonlinear Dyn., 112 (2024), 8539-8556. https://doi.org/10.1007/s11071-024-09473-8

[9] J. E. Rubin, J. A. Hayes, J. L. Mendenhall, C. A. Del Negro, Calcium-activated nonspecific cation current and synaptic depression promote network-dependent burst oscillations, PNAS, 106 (2009), 2939-2944. https://doi.org/10.1073/pnas.0808776106

[10] X. Ding, C. Feng, N. Wang, A. Liu, Q. Xu, Fast-slow dynamics in a memristive ion channel-based bionic circuit, Cognit. Neurodyn., 18 (2024), 3901-3913. https://doi.org/10.1007/s11571-024-10168-z

[11] D. Feng, Y. Chen, Q. Ji, Contribution of a Ca²⁺-activated K⁺ channel to neuronal bursting activities in the Chay model , Electron. Res. Arch., 31 (2023), 7544-7555. https://doi.org/10.3934/era.2023380

[12] K. Ma, H. Gu, Z. Zhao, Fast-slow variable dissection with two slow variables: a case study on bifurcations underlying bursting for seizure and spreading depression, Int. J. Bifurcation Chaos, 31 (2021), 2150096. https://doi.org/10.1142/s0218127421500966

[13] Q. Zhu, M. Li, F. Han, Hopf bifurcation control of the ML neuron model with Hc bifurcation type, Electron. Res. Arch., 30 (2022), 615-632. https://doi.org/10.3934/era.2022032

[14] Q. Xu, X. Tan, D. Zhu, H. Bao, Y. Hu, B. Bao, Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit, Chaos, Solitons Fractals, 141 (2020), 110353. https://doi.org/10.1016/j.chaos.2020.110353

[15] Y. Liu, S. Liu, Canard-induced mixed-mode oscillations and bifurcation analysis in a reduced 3D pyramidal cell model, Nonlinear Dyn., 101 (2020), 531-567. https://doi.org/10.1007/s11071-020-05801-5

[16] Y. Xie, Y. Kang, Y. Liu, Y. Wu, Firing properties and synchronization rate in fractional-order Hindmarsh-Rose model neurons, Sci. China Technol. Sci., 57 (2014), 914-922. https://doi.org/10.1007/s11431-014-5531-3

[17] L. Guan, H. Gu, X. Zhang, Dynamics of antiphase bursting modulated by the inhibitory synaptic and hyperpolarization-activated cation currents, Front. Comput. Neurosci., 18 (2024), 1303925. https://doi.org/10.3389/fncom.2024.1303925

[18] M. Xing, Z. Yang, Y. Chen, Bursting types and bifurcation analysis of the temperature-sensitive Purkinje neuron, Nonlinear Dyn., 111 (2022), 1819-1834. https://doi.org/10.1007/s11071-022-07917-2

[19] Q. Wen, S. Liu, B. Lu, Firing patterns and bifurcation analysis of neurons under electromagnetic induction, Electron. Res. Arch., 29 (2021), 3205-3226. https://doi.org/10.3934/era.2021034

[20] H. Wang, Q. Wang, Q. Lu, Bursting oscillations, bifurcation and synchronization in neuronal systems, Chaos, Solitons Fractals, 44 (2011), 667-675. https://doi.org/10.1016/j.chaos.2011.06.000

[21] S. Venugopal, S. Seki, D. H. Terman, A. Pantazis, R. Olcese, M. Wiedau-Pazos, et al., Resurgent Na⁺ current offers noise modulation in bursting neurons , PLoS Comput. Biol., 15 (2019), e1007154. https://doi.org/10.1371/journal.pcbi.1007154

[22] L. Guan, H. Gu, Y. Jia, Multiple coherence resonances evoked from bursting and the underlying bifurcation mechanism, Nonlinear Dyn., 100 (2020), 3645-3666. https://doi.org/10.1007/s11071-020-05717-0

[23] H. Hua, H. Gu, Y. Jia, B. Lu, The nonlinear mechanisms underlying the various stochastic dynamics evoked from different bursting patterns in a neuronal model, Commun. Nonlinear Sci. Numer. Simul., 110 (2022), 106370. https://doi.org/10.1016/j.cnsns.2022.106370

[24] B. Hutcheon, Y. Yarom, Resonance, oscillation and the intrinsic frequency preferences of neurons, Trends Neurosci., 23 (2000), 216-222. https://doi.org/10.1016/S0166-2236(00)01547-2

[25] R. Wang, H. Gu, X. Zhang, Dynamics of interaction between IH and IKLT currents to mediate double resonances of medial superior olive neurons related to sound localization, Cognit. Neurodyn., 18 (2023), 715-740. https://doi.org/10.1007/s11571-023-10024-6

[26] A. I. Tissone, V. B. Vidal, M. S. Nadal, G. Mato, Y. Amarillo, Differential contribution of the subthreshold operating currents I_T, I_h, and I_Kir to the resonance of thalamocortical neurons , J. Neurophysiol., 126 (2021), 561-574. https://doi.org/10.1152/jn.00147.2021

[27] D. Ulrich, Subthreshold delta‐frequency resonance in thalamic reticular neurons, Eur. J. Neurosci., 40 (2014), 2600-2607. https://doi.org/10.1111/ejn.12630

[28] R. Narayanan, D. Johnston, Long-term potentiation in rat hippocampal neurons is accompanied by spatially widespread changes in intrinsic oscillatory dynamics and excitability, Neuron, 56 (2007), 1061-1075. https://doi.org/10.1016/j.neuron.2007.10.033

[29] B. Hutcheon, R. M. Miura, E. Puil, Subthreshold membrane resonance in neocortical neurons, J. Neurophysiol., 76 (1996), 683-697. https://doi.org/10.1152/jn.1996.76.2.683

[30] M. W. H. Remme, R. Donato, J. Mikiel-Hunter, J. A. Ballestero, S. Foster, J. Rinzel, et al., Subthreshold resonance properties contribute to the efficient coding of auditory spatial cues, PNAS, 111 (2014), E2339-E2348. https://doi.org/10.1073/pnas.1316216111

[31] J. Vera, K. Lippmann, Post-stroke epileptogenesis is associated with altered intrinsic properties of hippocampal pyramidal neurons leading to increased theta resonance, Neurobiol. Dis., 156 (2021), 105425. https://doi.org/10.1016/j.nbd.2021.105425

[32] B. E. Kalmbach, A. Buchin, B. Long, J. Close, A. Nandi, J. A. Miller, et al., h-channels contribute to divergent intrinsic membrane properties of supragranular pyramidal neurons in human versus mouse cerebral cortex, Neuron, 100 (2018), 1194-1208. https://doi.org/10.1016/j.neuron.2018.10.012

[33] D. M. Fox, H. A. Tseng, T. G. Smolinski, H. G. Rotstein, F. Nadim, Mechanisms of generation of membrane potential resonance in a neuron with multiple resonant ionic currents, PLoS Comput. Biol., 13 (2017), e1005565. https://doi.org/10.1371/journal.pcbi.1005565

[34] J. Mikiel-Hunte, V. Kotak, J. Rinzel, High-frequency resonance in the gerbil medial superior olive, PLoS Comput. Biol., 12 (2016), e1005166. https://doi.org/10.1371/journal.pcbi.1005166

[35] H. Hu, K. Vervaeke, J. F. Storm, Two forms of electrical resonance at theta frequencies, generated by M-current, h-current and persistent Na⁺ current in rat hippocampal pyramidal cells , J. Physiol., 545 (2002), 783-805. https://doi.org/10.1113/jphysiol.2002.029249

[36] N. Binini, F. Talpo, P. Spaiardi, C. Maniezzi, M. Pedrazzoli, F. Raffin, et al., Membrane resonance in pyramidal and GABAergic neurons of the mouse perirhinal cortex, Front. Cell. Neurosci., 15 (2021), 703407. https://doi.org/10.3389/fncel.2021.703407

[37] H. G. Rotstein, F. Nadim, Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents, J. Comput. Neurosci., 37 (2013), 9-28. https://doi.org/10.1007/s10827-013-0483-3

[38] Z. Zhao, L. Li, H. Gu, Dynamical mechanism of hyperpolarization-activated non-specific cation current induced resonance and spike-timing precision in a neuronal model, Front. Cell. Neurosci., 12 (2018), 62. https://doi.org/10.3389/fncel.2018.00062

[39] L. Guan, H. Gu, Z. Zhao, Dynamics of subthreshold and suprathreshold resonance modulated by hyperpolarization-activated cation current in a bursting neuron, Nonlinear Dyn., 104 (2021), 577-601. https://doi.org/10.1007/s11071-021-06230-8

[40] K. B. Corbin, F. Harrison, Function of mesencephalic root of fifth cranial nerve, J. Neurophysiol., 3 (1940), 423-435. https://doi.org/10.1152/jn.1940.3.5.423

[41] W. Zhang, M. Kobayashi, M. Moritani, Y. Masuda, J. Dong, T. Yagi, et al., An involvement of trigeminal mesencephalic neurons in regulation of occlusal vertical dimension in the guinea pig, J. Dent. Res., 82 (2003), 565-569. https://doi.org/10.1177/154405910308200715

[42] Y. Zhao, Y. Liu, J. Wang, Q. Li, Z. Zhang, T. Tu, et al., Activation of the mesencephalic trigeminal nucleus contributes to masseter hyperactivity induced by chronic restraint stress, Front. Cell. Neurosci., 16 (2022), 841133. https://doi.org/10.3389/fncel.2022.841133

[43] G. J. Lavigne, S. Khoury, S. Abe, T. Yamaguchi, K. Raphael, Bruxism physiology and pathology: an overview for clinicians, J. Oral Rehabil., 35 (2008), 476-494. https://doi.org/10.1111/j.1365-2842.2008.01881.x

[44] N. Wu, A. Enomoto, S. Tanaka, C. F. Hsiao, D. Q. Nykamp, E. Izhikevich, et al., Persistent sodium currents in mesencephalic V neurons participate in burst generation and control of membrane excitability, J. Neurophysiol., 93 (2005), 2710-2722. https://doi.org/10.1152/jn.00636.2004

[45] A. Bergmann, D. Edelhoff, O. Schubert, K. J. Erdelt, J. M. P. Duc, Effect of treatment with a full-occlusion biofeedback splint on sleep bruxism and TMD pain: a randomized controlled clinical trial, Clin. Oral Invest., 24 (2020), 4005-4018. https://doi.org/10.1007/s00784-020-03270-z

[46] J. Xing, S. Hu, J. Yang, Electrophysiological features of neurons in the mesencephalic trigeminal nuclei, Neurosignals, 22 (2015), 79-91. https://doi.org/10.1159/000369822

[47] N. Wu, C. F. Hsiao, S. H. Chandler, Membrane resonance and subthreshold membrane oscillations in mesencephalic V neurons: participants in burst generation, J. Neurosci., 21 (2001), 3729-3739. https://doi.org/10.1523/JNEUROSCI.21-11-03729.2001

[48] S. Seki, T. Yamamoto, K. Quinn, I. Spigelman, A. Pantazis, R. Olcese, et al., Circuit-specific early impairment of proprioceptive sensory neurons in the SOD1G93A mouse model for ALS, J. Neurosci., 39 (2019), 8798-8815. https://doi.org/10.1523/jneurosci.1214-19.2019

[49] M. La Rosa, M. I. Rabinovich, R. Huerta, H. D. I. Abarbanel, L. Fortuna, Slow regularization through chaotic oscillation transfer in an unidirectional chain of Hindmarsh-Rose models, Phys. Lett. A, 266 (2000), 88-93. https://doi.org/10.1016/S0375-9601(00)00015-3