Bifurcations for counterintuitive post-inhibitory rebound spike related to absence epilepsy and Parkinson disease
Xian-Jun Wang(王宪军)1, Hua-Guang Gu(古华光)2,†, Yan-Bing Jia(贾雁兵)3, Bo Lu(陆博)1, and Hui Zhou(周辉)1
1 School of Mathematics and Science, Henan Institute of Science and Technology, Xinxiang 453003, China; 2 School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China; 3 School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471000, China
Abstract Seizures are caused by increased neuronal firing activity resulting from reduced inhibitory effect and enhancement of inhibitory modulation to suppress this activity is used as a therapeutic tool. However, recent experiments have shown a counterintuitive phenomenon that inhibitory modulation does not suppress but elicit post-inhibitory rebound (PIR) spike along with seizure to challenge the therapeutic tool. The nonlinear mechanism to avoid the PIR spike can present theoretical guidance to seizure treatment. This paper focuses on identifying credible bifurcations that underlie PIR spike by modulating multiple parameters in multiple theoretical models. The study identifies a codimension-2 bifurcation called saddle-node homoclinic orbit (SNHOB), which is an intersection between saddle node bifurcation on invariant cycle (SNIC) and other two bifurcations. PIR spike cannot be evoked for the SNIC far from the SNHOB but induced for the SNIC close to the SNHOB, which extends the bifurcation condition for PIR spike from the well-known Hopf to SNIC. Especially, in a thalamic neuron model, increases of conductance of T-type Ca2+ (TCa) channel induce SNIC bifurcation approaching to the SNHOB to elicit PIR spikes, closely matching experimental results of the absence seizure or Parkinson diseases. Such results imply that, when inhibition is employed to relieve absence seizure and Parkinson diseases related to PIR spike, modulating SNIC to get far from the SNHOB to avoid PIR spike is the principle. The study also addresses the complex roles of TCa current and comprehensive relationships between PIR spike and nonlinear conceptions such as bifurcation types and shapes of threshold curve.
(Synapses: chemical and electrical (gap junctions))
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12072236, 11872276, and 11802086), the Postdoctoral Research Project of Henan Province, China (Grant No. 19030095), and the Science and Technology Development Program of Henan Province, China (Grant No. 212102210543).
Xian-Jun Wang(王宪军), Hua-Guang Gu(古华光), Yan-Bing Jia(贾雁兵), Bo Lu(陆博), and Hui Zhou(周辉) Bifurcations for counterintuitive post-inhibitory rebound spike related to absence epilepsy and Parkinson disease 2023 Chin. Phys. B 32 090502
[1] Izhikevich E M 2000 Int. J. Bifurcation Chaos10 1171 [2] Yan B, Panahi S, He S, et al. 2020 Nonlinear Dyn.101 521 [3] Yilmaz E, Ozer M, Baysal V, et al. 2020 Sci. Rep.6 30914 [4] Ma J 2023 J. Zhejiang Univ. Sci. A24 109 [5] Cao B, Gu H G and Li Y Y 2021 Chin. Phys. B30 050502 [6] Liu Y R and Liu S Q 2020 Nonlinear Dyn.101 531 [7] Wang J J, Yang Y, Gao Z W, et al. 2020 Chin. Phys. B29 058701 [8] Xu Y, Liu M H, Zhu Z G and Ma J 2020 Chin. Phys. B29 98704 [9] Valenti O, Cifelli P, Gill K M, et al. 2011 J. Neurosci.31 12330 [10] Badimon A, Strasburger H J, Ayata P, et al. 2020 Nature586 417 [11] Hesse J, Schleimer J H, Maier N, et al. 2022 Nat. Commun.13 3934 [12] Tang X, Jaenisch R and Sur M 2021 Nat. Rev. Neurosci.22 290 [13] Arinyo-I-Prats A, Moreno-Spiegelberg P, Matias M A, et al. 2021 Phys. Rev. E104 L052203 [14] Fan D G, Zheng Y H, Yang Z C, et al. 2020 Appl. Math. Mech. Engl. Ed.41 1287 [15] Du M M, Li J J, Chen L, et al. 2018 PLoS Comput. Biol.14 e1005877 [16] Kim J, Kim Y, Nakajima R, et al. 2017 Neuron95 1181 [17] Park C, Rubchinsky L L and Ahn R 2021 Chaos31 113121 [18] Wang X J, Gu H G and Lu B 2021 ERA29 2987 [19] Li L, Zhao Z G and Gu H G 2022 Chin. Phys. B31 070506 [20] Lu A C, Lee C K, Kleiman-Weiner M, et al. 2020 eLife9 e59548 [21] Ferrante M, Shay C F, Tsuno Y, et al. 2017 Cerebral Cortex27 2111 [22] Guan L N, Jia B and Gu H G 2019 Internat. J. Bifur. Chaos29 1950198 [23] Goaillard J, Taylor A, Pulver S, et al. 2010 J. Neurosci.30 4687 [24] Felix A, Fridberger A, Leijon S, et al. 2011 J. Neurosci.31 12566 [25] Villalobos C A and Basso M A 2022 Cell Reports39 110699 [26] Nejad M M, Rotter S and Schmidt R 2021 Eur. J. Neurosci.54 4295 [27] Yang Y, Cui Y, Sang K, et al. 2018 Nature554 317 [28] Howe W M and Kenny P J 2018 Nature554 304 [29] Kim D, Song I, Keum S, et al. 2001 Neuron31 35 [30] Sessolo M, IMarcon I, Bovetti S, et al. 2015 J. Neurosci.35 9544 [31] Chang M, Dian J A, Dufour S, et al. 2018 Neurobiology of Disease109 102 [32] Cheong E, Zheng Y, Lee K, et al. 2009 PNAS106 21912 [33] Ellender T J, Raimondo J V, Irkle A, et al. 2014 J. Neurosci.34 15208 [34] de Curtis M and Avanzini G 2001 Prog. Neurobiol.63 541 [35] Cammarota M, Losi G, Chiavegato A, et al. 2013 J. Physiol.591 807 [36] Schevon C, Weiss S, McKhann G, et al. 2012 Nat Commun.3 1060 [37] Ledri M, Madsen M G, Nikitidou L, et al. 2014 J. Neurosci.34 3364 [38] Zhao J Y, Yu Y and Wang Q Y 2022 Chaos, Solitons and Fractals164 112720 [39] Tikidji-Hamburyan R A, Martinez J J, White J A, et al. 2015 J. Neurosci.35 15262 [40] Li Y Y, Gu H G, Jia B, et al. 2021 Sci. China Technol. Sci.64 1459 [41] Lu B, Gu H G, Wang X J, et al. 2021 Chaos, Solitons and Fractals145 110817 [42] Yang Y X, Gu H G, Li Y Y, et al. 2023 Nonlinear Dyn.111 7751 [43] Wu F Q, Gu H G and Li Y Y 2019 Commun. Nonlinear Sci. Numer. Simul.79 104924 [44] Yao C G, He Z W, Nakano T, et al. 2019 Nonlinear Dyn.97 1425 [45] Ding X L, Jia B and Li Y Y 2019 Acta Phys. Sin.68 180502 (in Chinese) [46] Wang X J and Gu H G 2022 ERA30 459 [47] Wang X J, Gu H G, Li Y Y, et al. 2022 Mod. Phys. Lett. B36 2250082 [48] Zeberg H, Blomberg C and Arhem P 2010 PLoS Comput. Biol.6 e1000753 [49] Liu C M, Liu X L and Liu S Q 2014 Biol. Cybern.108 75 [50] Nigam A, Hargus N J, Barker B S, et al. 2019 Epilepsy Res.154 132 [51] Stephenson-Jones M, Yu K, Ahrens S, et al. 2016 Nature539 289 [52] McGregor M M and Nelson A B 2001 Neuron101 1042 [53] Wang Z H and Duan L X 2022 Nonlinear Dyn.108 191 [54] Njap F, Claussen J C, Moser A, et al. 2012 Cogn. Neurodynamics6 333 [55] Gerstner W, Kistler W M, Naud R, et al. 2014 Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition (Cambridge University Press) [56] Zhu T, Wei S and Wang Y 2022 J. Pain Res.15 2029 [57] Morris C and Lecar H 1981 J. Biophys.35 193 [58] Rinzel J, Terman D, Wang X J, et al. 1998 Science279 1351 [59] Rubin J E and Terman D 2004 J. Comput. Neuronsci.16 211 [60] Dhooge A, Govaerts W and Kuznetsov Y A 2003 ACM Trans. Math Softw29 141 [61] Ermentrout B 2002 Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students (Philadelphia: SIAM Press)
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