arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2001.04915q-bio.NC
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小DRG神经元9维模型的计算分析

Computational analysis of a 9D model for a small DRG neuron

Parul Verma, Achim Kienle, Dietrich Flockerzi, Doraiswami Ramkrishna

摘要:

背根神经节(DRG)小神经元是感受疼痛的主要伤害感受器。阐明其动力学对于理解和控制疼痛至关重要。为此,我们提出了一个小DRG神经元模型的数值分岔分析。模型为Hodgkin-Huxley型,有9个状态变量。它由Na $\mathrm{_v}$ 1.7和Na $\mathrm{_v}$ 1.8钠通道、渗漏通道、延迟整流钾通道和A型瞬时钾通道组成。该模型的动力学强烈依赖于电压门控离子通道的最大电导和外部电流,这可以通过实验来调整。我们发现,神经元动力学是最敏感的Na $\mathrm{_v}$ 1.8通道最大电导($\bar{g}_{1.8}$)。数值分岔分析表明,依赖于$\bar{g}_{1.8}$和外部电流,不同的参数区域可以被识别为稳定的稳态、动作电位的周期性放电、混合模式振荡(MMO)以及稳定的稳态和稳定的动作电位的周期性放电之间的双稳态。我们说明和讨论这些不同的制度之间的过渡。我们进一步分析了MMO的行为。在该区域内,分叉分析显示了一系列孤立的周期性解决方案分支,每个周期有一个大的动作电位和一些小幅度的峰值。更仔细的检查揭示了在这些周期性MMO分支之间的更复杂的级联MMO,形成Farey序列。最后,我们还发现了小的非周期振荡的解决方案窗口,这似乎是混乱的。这里发现的动力学模式作为不同参数的函数包含翻译的重要性,因为它们与疼痛感觉的关系,其强度是洞察控制疼痛的潜在来源。

英文摘要:

Small dorsal root ganglion (DRG) neurons are primary nociceptors which are responsible for sensing pain. Elucidation of their dynamics is essential for understanding and controlling pain. To this end, we present a numerical bifurcation analysis of a small DRG neuron model in this paper. The model is of Hodgkin-Huxley type and has 9 state variables. It consists of a Na$\mathrm{_v}$1.7 and a Na$\mathrm{_v}$1.8 sodium channel, a leak channel, a delayed rectifier potassium and an A-type transient potassium channel. The dynamics of this model strongly depends on the maximal conductances of the voltage-gated ion channels and the external current, which can be adjusted experimentally. We show that the neuron dynamics are most sensitive to the Na$\mathrm{_v}$1.8 channel maximal conductance ($\bar{g}_{1.8}$). Numerical bifurcation analysis shows that depending on $\bar{g}_{1.8}$ and the external current, different parameter regions can be identified with stable steady states, periodic firing of action potentials, mixed-mode oscillations (MMOs), and bistability between stable steady states and stable periodic firing of action potentials. We illustrate and discuss the transitions between these different regimes. We further analyze the behavior of MMOs. Within this region, bifurcation analysis shows a sequence of isolated periodic solution branches with one large action potential and a number of small amplitude peaks per period. A closer inspection reveals more complex concatenated MMOs in between these periodic MMOs branches, forming Farey sequences. Lastly, we also find small solution windows with aperiodic oscillations, which seem to be chaotic. The dynamical patterns found here as a function of different parameters contain information of translational importance as their relation to pain sensation and its intensity is a potential source of insight into controlling pain.

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