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<p>Bursting modulated by multiple slow variables, mixed-mode bursting containing multiple phases, and counterintuitive bursting induced by various external stimulations, are three difficult questions for nonlinear dynamics in the nervous system. Interestingly, experiments on seizure and migraine show a bursting involving in all three questions, with very complex dynamics studied in the present paper. At first, commonly, strong positive/excitatory stimulations can enhance the resting state to the mixed-mode bursting (MMB) with four phases including a high membrane potential phase in a theoretical model, corresponding to type I migraine. Counterintuitively, strong negative/inhibitory stimulations, which are expected to play a role opposite to that of positive/excitatory stimulations in suppressing the resting state, can also induce an identical MMB, corresponding to type III migraine. Secondly, the counterintuitive MMB is well explained with a novel negative threshold. Different from the well-known positive threshold for the MMB induced by positive effect, strong inhibitory stimulation induces the counterintuitive MMB via passage through the novel negative threshold. Then, multiple measures to reduce the inhibitory synaptic current from the interneuron to effectively eliminate the counterintuitive bursting are acquired. Finally, since the bursting is modulated by two slow variables, two-parameter bifurcations underlying the transition between the four phases are obtained, containing the saddle homoclinic orbit (SH), supercritical Hopf, and saddle-node (SN) bifurcation curves. For the MMB induced by positive and negative effects, the resting state phase transits to the burst phase via different routines to run across the SN curve, whereas transits to the high membrane potential phase, to the small oscillation phase, and back to the resting state phase via the same routine to pass through the Hopf, Hopf, and SH curves, respectively. Then, the results present an overall understanding of the nonlinear dynamics of the MMB and counterintuitive phenomenon for the inhibitory effect, and potential measures to modulate the bursting to treat brain diseases such as type I/III migraines.</p>

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Opposite stimulations can induce a same mixed-mode neuronal bursting containing four phases: underlying two-parameter bifurcations and threshold

  • 期刊论文

  • 发表日期：

    2025年6月7日

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  • Hongtao Hua,
  • Huaguang Gu,
  • Yanbing Jia,
  • Yuye Li

摘要

Bursting modulated by multiple slow variables, mixed-mode bursting containing multiple phases, and counterintuitive bursting induced by various external stimulations, are three difficult questions for nonlinear dynamics in the nervous system. Interestingly, experiments on seizure and migraine show a bursting involving in all three questions, with very complex dynamics studied in the present paper. At first, commonly, strong positive/excitatory stimulations can enhance the resting state to the mixed-mode bursting (MMB) with four phases including a high membrane potential phase in a theoretical model, corresponding to type I migraine. Counterintuitively, strong negative/inhibitory stimulations, which are expected to play a role opposite to that of positive/excitatory stimulations in suppressing the resting state, can also induce an identical MMB, corresponding to type III migraine. Secondly, the counterintuitive MMB is well explained with a novel negative threshold. Different from the well-known positive threshold for the MMB induced by positive effect, strong inhibitory stimulation induces the counterintuitive MMB via passage through the novel negative threshold. Then, multiple measures to reduce the inhibitory synaptic current from the interneuron to effectively eliminate the counterintuitive bursting are acquired. Finally, since the bursting is modulated by two slow variables, two-parameter bifurcations underlying the transition between the four phases are obtained, containing the saddle homoclinic orbit (SH), supercritical Hopf, and saddle-node (SN) bifurcation curves. For the MMB induced by positive and negative effects, the resting state phase transits to the burst phase via different routines to run across the SN curve, whereas transits to the high membrane potential phase, to the small oscillation phase, and back to the resting state phase via the same routine to pass through the Hopf, Hopf, and SH curves, respectively. Then, the results present an overall understanding of the nonlinear dynamics of the MMB and counterintuitive phenomenon for the inhibitory effect, and potential measures to modulate the bursting to treat brain diseases such as type I/III migraines.