Temperature-Induced Bifurcations and Timescale Warping in the Hodgkin-Huxley Model: Dynamical Systems Insights into Temperature Modulation of Neuronal Excitability and Action Potential Morphology

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. Author SummaryNeurons communicate using brief electrical signals called action potentials, which are generated through the coordinated activity of the cocktail of ion channels that are expressed on the cell membrane. These electrical signals are sensitive to temperature; changes in heat can alter how quickly ion channels open and close, and even whether neurons can keep firing at all. While it is known that temperature can affect brain function, the precise ways it changes the fundamental electrical properties of neurons have not been fully mapped. In this study, we used the well-known Hodgkin-Huxley mathematical model of a neuron to explore how varying temperature changes its firing patterns. We applied tools from dynamical systems theory, such as bifurcation analysis, to identify the precise points where the neuron switches between active firing, silent resting, and mixed "bistable" states. We also discovered that certain ion channel properties, especially those controlling potassium flow, are particularly important in determining a neurons temperature sensitivity. Our results provide a detailed roadmap for understanding how temperature affects neural activity, with implications for biology, medicine, and the design of temperature-robust neural models.