The provided computational code models the electrophysiological properties of a neuron, focusing on action potential propagation along an axon. This model leverages the Hodgkin-Huxley framework, a widely-used biophysical model that describes how action potentials in neurons are initiated and propagated. ### Biological Basis - **Axonal Structure**: The axon is represented with a specific length (`L = 3131`) and segmentation (`nseg = 51`), reflecting the cable properties of neuronal axons. The axon diameter is variable, allowing the model to explore different conduction properties. - **Ionic Currents**: - **Na+ (Sodium) Channels**: Sodium channels are critical for the initiation of action potentials. The parameter `gmax_na` represents the maximum conductance of voltage-gated sodium channels. - **K+ (Potassium) Channels**: The model includes `kd` (delayed rectifier potassium channels) and `ka` (A-type potassium channels), both of which are involved in repolarization and afterhyperpolarization phases of action potentials. `gmax_kd` and `gmax_ka` represent their respective conductances. - **Leak Channels**: A `leak` current introduces a baseline level of ionic permeability, representing non-specific ion channels. `gmax_leak` determines the maximum leakage conductance. - **Na+/K+ Pump**: - The code includes a model for the sodium-potassium pump (`nadp`), a crucial membrane protein that maintains the ionic gradients across the cell membrane by exchanging three Na+ ions out for two K+ ions in. The `TotalPump_nadp` parameter indicates the density of this pump, modulated by `f_nak`, which can affect neuronal excitability by altering intracellular Na+ concentration (`nai_i_nadp`). - **Stimuli and Synaptic Input**: - An `Ipulse3` object enables simulation of direct current stimulation of the axon, representing the effect of synaptic input. - The burst parameters like `NPULSES` dictate the number of spikes per stimulus, mimicking the frequency and pattern of synaptic input a neuron might receive. - **Temperature and Frequency**: - The model considers different temperatures with `global_q10` to reflect physiological conditions. Typically, neuronal conduction velocity and channel kinetics are temperature-dependent. - Frequency-related parameters (`Freqmax`, `freq_spike`) allow exploration of neuronal activity at different firing rates, essential for understanding how neurons respond to high-frequency input. ### Recording Outputs - **Voltage and Ion Concentration**: - The model records voltage changes (`v_v0`, `v_v1`, `v_v2`) at different points along the axon, providing insights into how action potentials propagate. - Intracellular sodium concentration (`na_v0`, `na_v1`, `na_v2`) is also recorded, which is significant for observing the dynamics of ionic currents over time. Overall, the code simulates the dynamic processes of neuronal excitability and action potential propagation, focusing on sodium and potassium dynamics and the role of the sodium-potassium pump. By varying parameters such as axonal diameter and stimulation frequency, the model can explore how different factors influence neuronal function.