Degeneracy in neuronal bifurcation landscapes: equivalent bifurcation sequences across distinct parameter sets

Abstract

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 wide variability in ion channel expression, highlighting how distinct internal configurations can yield equivalent electrophysiological behaviors. However, it remains unclear how degeneracy manifests in the context of bifurcations, the critical transitions between activity regimes that underlie phenomena such as different firing patterns, seizures and depolarization block. Here, we investigate how different biophysical parameter sets can lead to equivalent bifurcation sequences. Using a minimal neuron model with three variable conductances, we systematically explore how changes in extracellular potassium--mimicking physiological and pathological conditions--affect neuronal dynamics. Our results reveal that neurons with distinct intrinsic properties can traverse the same bifurcation pathways, entering regimes of bursting, seizure-like activity, and depolarization block. Yet, the specific parameter set determines the sensitivity and thresholds for these transitions. This work clarifies how degeneracy extends to the dynamical landscape of neurons, with implications for understanding resilience and vulnerability in neural circuits. 1 Author SummaryBiophysical models expressed through differential equations can reproduce the dynamics of biological systems with varying levels of detail. By changing model parameters, simulations can capture the natural variability that allows biological systems to achieve the same behavior through different mechanisms. This property, called degeneracy, underlies the robustness of living systems to internal and external perturbations. In this work, we identify dis-tinct behaviors in single-neuron models and link them to electrophysiological patterns observed under elevated extracellular potassium during epileptic events. These patterns correspond to specific classes of spontaneous bursting activity within the framework of nonlinear dynamics. We show that different combinations of conductance parameters, at a fixed extracellular potassium level, can generate the same class of patterns, defining degeneracy groups. Finally, we assess the robustness of these groups by analyzing how they respond to changes in extracellular potassium. Our findings provide a basis for studying variability and resilience in the dynamics of more complex neuronal systems.