Temperature Induced Codimension-One and Codimension-Two Bifurcations in Hodgkin-Huxley Neurons

Temperature fluctuations can have detrimental effects on the firing pattern and electrical activity of biological neurons, eliciting diverse responses depending on the neuronal cell types and the underlying ion channels exhibited. Using the classical Hodgkin-Huxley (HH) model, we performed a comprehensive dynamical systems analysis to determine how temperature fluctuations alter neuronal excitability, spike morphology, and bifurcation structure. We first relied on experimentally-derived temperature coefficients, or Q10 values, associated with gating kinetics and conductances, and examined codimension-1 and codimension-2 bifurcations across a range of temperatures and standard HH parameters governing the intrinsic properties (firing frequency, spike amplitude, spike width, afterhyperpolarization (AHP), time-to-peak AHP, etc...) of the model HH neuron. Our analysis revealed that increasing temperature accelerates gating dynamics, leading to narrower and higher-frequency spikes but reduced amplitudes, and ultimately to a loss of sustained firing via temperature-induced depolarization block. We identified generalized Hopf (Bautin) bifurcations as critical boundaries beyond which the system becomes strictly monostable. Extending the model to independently scale sodium activation, sodium inactivation, and potassium activation kinetics showed that excitability is particularly sensitive to potassium gating dynamics. Our findings provide a quantitative framework for understanding temperature modulations of neuronal activity, highlighting how temperature reshapes the excitability landscape, unveiling the intricate interplays between the activation/inactivation kinetics of ion channels, and identifying key parameters governing temperature robustness in neuronal models.