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Ion gradient-driven bifurcations of a multi-scale neuronal model

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  • Chesebro, Anthony G.
  • Mujica-Parodi, Lilianne R.
  • Weistuch, Corey

Abstract

Metabolic limitations within the brain frequently arise in the context of aging and disease. As the largest consumers of energy within the brain, ion pumps that maintain the neuronal membrane potential are the most affected when energy supply becomes limited. To characterize the effects of such limitations, we analyze the ion gradients present in a conductance-based (Morris–Lecar) neural mass model. We show the existence and locations of Neimark–Sacker and period-doubling bifurcations in the sodium, calcium, and potassium reversal potentials and demonstrate that these bifurcations form physiologically relevant bounds of ion gradient variability. Within these bounds, we show how depolarization of the gradients causes decreased neural activity. We also show that the depolarization of ion gradients decreases inter-regional coherence, causing a shift in the critical point at which the coupling occurs and thereby inducing loss of synchrony between regions. In this way, we show that the Larter-Breakspear model captures ion gradient variability present at the microscale level and propagates these changes to the macroscale effects such as those observed in human neuroimaging studies.

Suggested Citation

  • Chesebro, Anthony G. & Mujica-Parodi, Lilianne R. & Weistuch, Corey, 2023. "Ion gradient-driven bifurcations of a multi-scale neuronal model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077923000218
    DOI: 10.1016/j.chaos.2023.113120
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    References listed on IDEAS

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    1. Jing, Zhujun & Yang, Jianping & Feng, Wei, 2006. "Bifurcation and chaos in neural excitable system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 197-215.
    2. Achouri, Houssem & Aouiti, Chaouki & Hamed, Bassem Ben, 2022. "Codimension two bifurcation in a coupled FitzHugh–Nagumo system with multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. James A. Roberts & Leonardo L. Gollo & Romesh G. Abeysuriya & Gloria Roberts & Philip B. Mitchell & Mark W. Woolrich & Michael Breakspear, 2019. "Metastable brain waves," Nature Communications, Nature, vol. 10(1), pages 1-17, December.
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    Cited by:

    1. Yu, Xihong & Bao, Han & Chen, Mo & Bao, Bocheng, 2023. "Energy balance via memristor synapse in Morris-Lecar two-neuron network with FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    2. Shao, Yan & Wu, Fuqiang & Wang, Qingyun, 2024. "Dynamics and stability of neural systems with indirect interactions involved energy levels," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    3. Hu, Jingting & Bao, Han & Xu, Quan & Chen, Mo & Bao, Bocheng, 2024. "Synchronization generations and transitions in two map-based neurons coupled with locally active memristor," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).

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