The code provided is a computational model of neuronal activity based on the Hodgkin-Huxley-Schwabe (HHS) framework. It simulates a neuronal cell's response to Poisson-distributed stimuli, specifically focusing on the dynamics of action potentials (APs) under different conditions of ionic currents and stochastic perturbations. Here's a breakdown of the biological elements represented in the code: ### Biological Basis #### Ion Channels and Gating Variables 1. **Ion Channels:** - **Sodium (Na⁺) Channels:** The model includes terms representing sodium conductance (`gNa`) and the reversal potential for sodium (`VNa`). These channels are responsible for the rapid depolarization phase of action potentials. - **Potassium (K⁺) Channels:** Similarly, potassium conductance (`gK`) and its reversal potential (`VK`) are modeled. Potassium channels facilitate repolarization, restoring the membrane potential to its resting state after an action potential. - **Leak Channels:** The model includes a constant leak conductance (`gL`) and its reversal potential (`VL`), representing background ion flow maintaining a resting potential. 2. **Gating Variables:** - The HHS model uses gating variables (`m`, `h`, `n`, `s1`), which represent the probability of ion channel states. These variables follow stochastic dynamics, reflecting the probabilistic opening and closing of ion channels: - **`m`, `h`:** Control the activation and inactivation dynamics of sodium channels, respectively. - **`n`:** Governs the activation dynamics of potassium channels. - **`s1`:** Represents a slower inactivation mechanism, potentially related to slow sodium channel inactivation or other modulatory processes. #### Membrane Potential Dynamics - **Membrane Potential (`V`):** The model computes changes in membrane potential over time, taking into account the ionic currents flowing through the channel types described above. The change in voltage is influenced by both deterministic (conductance) and stochastic (noisy input) components, reflecting the impact of intrinsic cellular noise and external input variability. #### Stochasticity - The code introduces stochasticity into gating dynamics via a Langevin approach, adding random fluctuations to mimic biological noise. This stochastic model captures the variability observed in neuronal firing, which could arise from molecular fluctuations and synaptic noise. #### Slow Inactivation - The term `s1` introduces a mechanism of slow inactivation based on parameters like `amp`, `sigma`, and `Vhalf`, which may reflect modulatory processes affecting the sodium channel availability on a slower timescale. This aspect is significant in studying conditions like intermittent or repetitive firing patterns associated with excitability disorders. ### Simulation Context - **Poisson Stimulation:** The code operates with Poisson-distributed inter-stimulus intervals, representing a common model for synaptic inputs resulting from stochastic synaptic firing patterns seen in vivo. - **High-Fidelity Simulation:** The settings simulate prolonged neural activity (55 hours), allowing exploration of long-term dynamics and potential emergent behaviors under varied conditions, such as increased noise and different input frequencies. This code is effectively a detailed biophysical model of neuronal excitability, accommodating both ionic dynamics central to action potentials and the stochastic properties of biological systems that add to the complexity and richness of neuronal signaling.