Fitting bifurcation structure, not voltage traces: A biophysically inspired derivation of reduced neuron models exemplified by potassium dynamics

Abstract In conductance-based models, spiking-induced ion concentrations fluctuations can modify single neurons’ excitability. What are the consequences in networks? To study this, simple models capturing ion concentration dynamics realistically are needed. We propose a method to derive a phenomenological model capturing the coupled extracellular potassium and voltage dynamics from a given class I conductance-based model. Rather than fitting voltage traces, we fit the bifurcation structure of the target model, thereby capturing parameter heterogeneity and rich dynamics. The resulting model extends the quadratic integrate-and-fire model, with extracellular potassium accumulation altering voltage dynamics by increasing the reset voltage. We apply our systematic reduction procedure to the Wang-Buzsáki model. Its phenomenological version exhibits quantitatively comparable dynamics and replicates the reshaping of the phase-response curve associated with the transition from SNIC to HOM spikes at elevated potassium. To illustrate the derived model’s applicability, we explore how changes in potassium concentration influence synchronization in networks.