The provided code models neuronal electrical activity using a variant of the Morris-Lecar model, specifically adapted to incorporate additional ion channel types. The Morris-Lecar model is a simplified representation of excitable membrane dynamics, often used to study the electrical characteristics of neurons. Here’s a detailed explanation of the biological basis depicted in the code:

Biological Basis

1. Membrane Potential Dynamics:

   • The code simulates the changes in membrane potential over time due to various ionic currents. Membrane potential (V) describes the voltage difference across the neuronal membrane, which is crucial for action potential generation and propagation.

2. Ionic Currents:

   • Fast Sodium Current (INa): Modeled with parameters gNa and ENa, this current is rapid and depolarizing, playing a key role in action potential initiation.
   • Delayed Rectifier Potassium Current (IK): Represented by gK and EK, this current helps in repolarization of the membrane after an action potential, counteracting the depolarization caused by sodium inflow.
   • A-Type Potassium Current (IgA): A transient potassium current included via the Connor-Stevens framework, characterized by gating variables a and b. This current can modulate action potential firing frequency and shape.
   • Low-Threshold Potassium Current (Igsub): A slow, subthreshold potassium current modeled by z, important for setting the neuronal excitability threshold.
   • After-Hyperpolarization Potassium Current (Igahp): Though not extensively used in simulations here, this current may contribute to the neuron's refractory period by hyperpolarizing the membrane after an action potential.

3. Leak Current:

   • The leak current (Il), defined by gl and El, represents the passive movement of ions across the membrane, contributing to the resting membrane potential.

4. Gating Variables:

   • Gating variables (w, z, a, b, q) embody the probabilistic opening and closing of ion channels. Each channel type has specific steady-state functions (_inf) and time constants (tau) affecting the rate dynamics.
   • For example, w_inf and tau_w define the steady and dynamic properties of the delayed rectifier potassium channel.

5. Activation and Inactivation:

   • The model includes steady-state activation and inactivation properties for ion channels, denoted by variables like m_inf, w_inf, a_inf, and respective time constants, which dictate how channels respond to changes in membrane voltage.

6. Heaviside Function:

   • A helper function, heav, represents the Heaviside step function, used for model components that depend on threshold behavior (e.g., gating kinetics).

Integration and Simulation

The code employs the Euler method for numerical integration, simulating the evolution of membrane potential and ionic currents over time under specified conditions (e.g., stimulus current i_stim). It calculates the resultant membrane potential dynamics and the number of action potentials (numAPs), reflecting how the neuron integrates inputs to generate output.

Summary

This model extends the classic Morris-Lecar framework to include additional complexities of real neurons, such as a variety of potassium channels, to better understand their role in neuronal excitability and firing patterns. These adaptations provide insights into the intricate interplay of ionic movements that underpin neuronal signaling.