Solution Manifold in the Electrophysiological Parameter Space of GPe Subtypes: Inverse Leak–HCN Conductance Correlations

Two primary neuronal subtypes summarize the dynamics of the external segment of the globus pallidus (GPe) with differentanatomical, electrophysiological, and functional properties: prototypical and arkypallidal neurons. Acknowledging these diversesubpopulations has altered comprehension of the GPe, demonstrating its variability and importance in typical and atypical states.In this study, we analyzed, using the Hodgkin-Huxley like model, the dynamics of these two GPe neuron subtypes, scanningconductance values for two ion channels: the leak (gleak) and the HCN (gHCN). We identified, through parameter space gleak vs.gHCN, values of intrinsic electrophysiological responses for each neuronal subtype, such as firing rate, sag-ratio, and troughpotential. With this, we developed a method for intersecting parameter spaces, which finds a subset of electrophysiologicalresults.Finally, from this subset of results, we extracted the linear inverse correlation between gleak and gHCN, establishing alow-dimensional range as a valid solutions manifold. This manifold maintains physiological excitability through compensatorychanges in ion channel expression, corresponding to the experimental observations. Our study highlights how conductanceimbalances can induce dysfunctional dynamics in basal ganglia circuits. This analysis provides an important starting pointfor future research into neurodegenerative diseases where alterations in intrinsic conductance regulation are likely to have asignificant impact.