### Biological Basis of the Computational Model The provided code is a simulation of a simplified neuronal model capturing both Type-1 and Type-2 neuronal excitability, based on adaptations of the Hodgkin-Huxley (HH) model. The HH model is a classic mathematical description of the electrical characteristics of excitable cells, such as neurons, and forms the foundation of this model. Below is a detailed breakdown of the key biological elements represented in the code: #### Neuronal Excitability Types - **Type-1 Excitability:** This is characterized by a continuous frequency response to increasing input current, usually leading to very low-frequency action potentials near the threshold current. In this model, Type-1 dynamics are configured when the `type21` variable is set to 1. The model parameters such as leak conductance (`gl`), leak reversal potential (`el`), and others are adjusted accordingly to represent this type. - **Type-2 Excitability:** Distinct from Type-1, Type-2 excitability shows a discontinuous jump to a higher firing frequency when threshold input is reached, typical of resonant neurons. The model switches to Type-2 dynamics when `type21` is set to 2, updating parameters such as `gl`, `el`, etc., to capture these dynamics. #### Ionic Currents and Gating Variables - **Ionic Currents:** - **Sodium Current (INa):** Modeled using a fast activation described by a steady-state activation variable `m_inf`. This current is crucial for the rapid depolarization phase of the action potential. The parameters `gna` and `ena` represent sodium conductance and reversal potential, respectively. - **Potassium Current (IK):** Modeled using a delayed rectifier channel with activation variable `n`. This current contributes to repolarization, driven by parameters `gk` (conductance) and `ek` (reversal potential). - **Gating Variables:** - **Activation and Inactivation Dynamics:** The model describes voltage-dependent activation (`m_inf`, `n_inf`) and time constants (`n_tau`) based on sigmoidal functions typical in biological systems. The dynamics capture how ion channels open and close in response to membrane voltage changes. - **Steady-State and Kinetics:** These are captured through expressions for `n_inf` and `n_tau`, defining how potassium channels transition between open and closed states. #### Model Parameters - Parameters such as `n0`, `v12`, `sl`, and others are used to adjust the channel kinetics and behavior, representing the ion channel's voltage sensitivity and time constants. - **Membrane Properties:** - The default parameters assume a neuronal membrane with specific properties like a specific capacitance (`1 uF/cm^2`) and a defined surface area (`1000 um^2`). #### Resting Potential and Input Resistance - **Resting Potential:** The initial conditions in the model move towards the observed resting potential of neurons, which is critical for maintaining the neuron's readiness to fire. - **Input Resistance:** The model accounts for how the neuron's input resistance (both for positive and negative currents) varies between Type-1 and Type-2 behaviors, affecting neuronal responsiveness. #### Action Potential Characteristics - **Threshold, Duration, and Height:** The model provides values for action potential threshold, duration, and height, matching observed data for physiological action potentials. - **After-Hyperpolarization (AHP):** After an action potential, neurons experience an AHP, which is represented in the model influencing subsequent firing behavior. ### Conclusion The code models essential features of neuronal excitability by simulating how ion channels regulate membrane potential and spike generation. It provides insight into how neurons with different excitability types can be described using variations of a common framework, helping bridge the gap between theoretical models and biological neurons.