神经元分岔景观中的简并性：不同参数集产生等价分岔序列
Degeneracy in neuronal bifurcation landscapes: Equivalent bifurcation sequences across distinct parameter sets
一个仅含三个可变电导的最小神经元模型显示，结构不同的电导参数配置会占据参数空间中结构化的区域，支持相同的分岔路径，从而产生爆发、癫痫样活动和去极化阻滞等等价活动模式。研究系统考察了细胞外钾浓度变化（代表生理与病理条件）如何重塑神经元动力学，并引入"韧性"（resilience）作为量化指标，衡量给定电导配置在外界离子变化下转入特定活动模式的阈值。结果表明，这些简并配置对细胞外扰动的敏感性各不相同：固定条件下的功能等价并不意味着同等的鲁棒性。简并性因此不只是多解共存，而是形成在环境调制下具有不同轨迹的结构化景观，为定量研究内在变异性如何影响神经元在不同动力学状态下的脆弱性与韧性提供了框架。
来源：PLOS Computational Biology · journals.plos.org
by Gianmarco Cafaro, Christophe Bernard, Meysam Hashemi, Damien Depannemaecker
Degeneracy, the capacity of structurally distinct systems to achieve similar functions, is a fundamental property of living organisms, enabling adaptability and resilience. Neurons can maintain stable activity patterns despite substantial variability in ion channel expression, highlighting how different intrinsic configurations can produce equivalent electrophysiological behaviors. Previous studies have shown that neuronal activity emerges from the interaction between intrinsic membrane properties and ionic concentration dynamics. However, how degeneracy is organized within the dynamical landscape of neurons and how different degenerate configurations respond to external perturbations remain poorly understood. Here, we investigate how distinct biophysical parameter sets generate equivalent bifurcation sequences and how their resilience changes under ionic modulation. Using a minimal neuron model with three variable conductances, we systematically explore how variations in extracellular potassium concentration, representing physiological and pathological conditions, reshape neuronal dynamics. We show that distinct conductance configurations occupy structured regions of parameter space that support the same bifurcation pathways, leading to equivalent activity regimes such as bursting, seizure-like activity, and depolarization block. However, these degenerate configurations exhibit different sensitivities to extracellular perturbations, revealing that functional equivalence under fixed conditions does not imply equivalent robustness. To quantify this effect, we introduce resilience as a measure of the threshold at which a given conductance configuration transitions into a specific activity regime under external ionic changes. Our results demonstrate that degeneracy extends beyond the coexistence of multiple solutions: degenerate configurations form structured landscapes with distinct trajectories under environmental modulation. This framework provides a quantitative approach to investigate how intrinsic variability influences neuronal vulnerability and resilience across different dynamical states.