The provided code leverages a computational approach to model the biophysical properties of a neuron using the Hodgkin-Huxley (HH) model. Here, the code simulates neuronal excitability by focusing on key ionic currents that are fundamental to action potential generation and propagation in neurons.

Biological Basis

Neuron Model

The model adopts the Hodgkin-Huxley framework to simulate the electrical characteristics of a segment of an axon. The HH model, established by Hodgkin and Huxley in 1952, accurately describes the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon.

Key Ionic Currents

The code implements two primary ionic currents:

1. Sodium Current (I_Na):

   • Controlled by the parameters gnabar_hhs (maximum conductance for Na+) and scaled by gna_f, this simulates how sodium ions contribute to depolarization during an action potential.
   • The sodium current is described by the gating variables m and h, where m represents the activation and h the inactivation of sodium channels.

2. Potassium Current (I_K):

   • The parameter gkbar_hhs sets the maximum conductance for potassium ions, crucial for repolarizing the membrane and restoring the resting potential following an action potential.
   • The gating variable n controls the activation of potassium channels.

Leak Current

The model also includes a leak current, specified by the conductance gl_hhy and reversal potential el_hhy, which represents a constant passive current that stabilizes the resting membrane potential.

Simulation Details

• Membrane Properties: The axon is modeled with a diameter (diam=1) and specific capacitance (cm=1), typical of neuronal membranes.
• Stimulation Protocol: A series of stimuli (2000 in total) are applied to the model neuron to observe responses, likely aiming to investigate abnormal spiking patterns under varied conditions.

Gating Variables

The code records the gating variables m, h, and n over time, which are central in determining the state of sodium and potassium channels and therefore the generation and propagation of action potentials.

Conclusion

This simulation serves as a fundamental exploration of neuronal electrical activity, focusing specifically on how changes in ionic conductance can lead to differences in neuronal excitability and action potential dynamics. It provides valuable insights into the biological processes governing neural behavior and is a pivotal tool in understanding conditions associated with abnormal neuronal spiking.