Galinsky Vitaly L, Frank Lawrence R
Center for Scientific Computation in Imaging, University of California at San Diego, La Jolla, CA, United States.
Center for Functional MRI, University of California at San Diego, La Jolla, CA, United States.
Front Cell Neurosci. 2025 Apr 25;19:1467466. doi: 10.3389/fncel.2025.1467466. eCollection 2025.
An alternative to the standard Hodgkin-Huxley model for the action potential in axons is presented. It is based on our recently developed theory of electric field wave propagation in anisotropic and inhomogeneous brain tissues, which has been shown to explain a broad range of observed coherent synchronous brain electrical processes. We demonstrate that this theory also explains the spiking behavior of single neurons, thereby bridging the gap between the fundamental element of brain electrical activity-the neuron-and large-scale coherent synchronous electrical activity. We demonstrate that our recently developed theory of electric field wave propagation in anisotropic and inhomogeneous brain tissues, which has been shown to explain a broad range of observed coherent synchronous brain electrical processes, also applies to the spiking behavior of single neurons, thus bridging the gap between the fundamental element of brain electrical activity (the neuron) and large-scale coherent synchronous electrical activity. Our analysis indicates that a non-linear system with several small parameters can mathematically describe the membrane interface of the axonal cellular system. This enables the rigorous derivation of an accurate yet simpler non-linear model through the formal small-parameter expansion. The resulting action potential model exhibits a smooth, continuous transition from the linear wave oscillatory regime to the non-linear spiking regime, as well as a critical transition to a non-oscillatory regime. These transitions occur with changes in the criticality parameter and include several different bifurcation types, representative of the various experimentally detected neuron types. This new theory addresses the limitations of the Hodgkin-Huxley model, including its inability to explain extracellular spiking, efficient brain synchronization, saltatory conduction along myelinated axons, and various other observed coherent macroscopic brain electrical phenomena. We also demonstrate that our approach recovers the standard cable axon theory, utilizing the relatively simple assumptions of piece-wise homogeneity and isotropy. However, the diffusion process described by the cable equation is not capable of supporting action potential propagation across a wide range of experimentally reported axon parameters.
本文提出了一种替代轴突动作电位标准霍奇金-赫胥黎模型的模型。它基于我们最近开发的关于各向异性和非均匀脑组织中电场波传播的理论，该理论已被证明能够解释广泛观察到的相干同步脑电过程。我们证明，该理论还能解释单个神经元的放电行为，从而弥合了脑电活动的基本元素——神经元——与大规模相干同步电活动之间的差距。我们证明，我们最近开发的关于各向异性和非均匀脑组织中电场波传播的理论，已被证明能够解释广泛观察到的相干同步脑电过程，该理论也适用于单个神经元的放电行为，从而弥合了脑电活动的基本元素（神经元）与大规模相干同步电活动之间的差距。我们的分析表明，一个具有几个小参数的非线性系统可以在数学上描述轴突细胞系统的膜界面。这使得通过形式上的小参数展开能够严格推导出一个准确但更简单的非线性模型。由此产生的动作电位模型表现出从线性波振荡状态到非线性放电状态的平滑、连续过渡，以及到非振荡状态的临界过渡。这些过渡随着临界参数的变化而发生，包括几种不同的分岔类型，代表了各种实验检测到的神经元类型。这一新理论解决了霍奇金-赫胥黎模型的局限性，包括其无法解释细胞外放电、有效的脑同步、沿有髓轴突的跳跃传导以及其他各种观察到的相干宏观脑电现象。我们还证明，我们的方法利用相对简单的分段均匀性和各向同性假设恢复了标准的电缆轴突理论。然而，电缆方程描述的扩散过程无法支持在广泛的实验报告轴突参数范围内的动作电位传播。
