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.