The provided code models the SK (small conductance calcium-activated potassium) channel in neurons, as described in the work of Aradi and Holmes (1999). Here is a biological overview based on the code: ### Biological Basis #### **Ion Channels and Gating** - **SK Channels:** SK channels are a type of potassium ion (K+) channel that is activated by intracellular calcium ions (Ca²⁺). They contribute to the regulation of neuronal excitability and are involved in the afterhyperpolarization phase following an action potential. - **Calcium Dependency:** The activation of these channels is tightly linked to the concentration of intracellular calcium (Ca²⁺), which influences the channel's gating variable `q`. In this model, calcium influx through the cell's calcium current (`ica`) modifies intracellular calcium concentration (`ca_i`), affecting the SK channels' open state probability. #### **Ionic Currents** - **Calcium Current (`ica`):** The model reads the calcium current to determine how much calcium enters the cell. This current is crucial, as it directly influences SK channel activation. - **Potassium Current (`ik`):** The model writes to the potassium current (`ik`) based on the open state of the SK channels (regulated by `q`) and the electrochemical potential difference for potassium (represented by `ek`, the reversal potential for K+ ions). #### **Equations of State** - **Calcium Dynamics (`ca_i`):** The model uses a differential equation to describe changes in intracellular calcium concentration. This considers both the influx of calcium (scaled by `cascale` and `ica`) and a decay term to a resting calcium concentration (`ca0`), with a characteristic time constant (`sstau`). - **Gating Variable (`q`):** The open probability of the SK channel is modeled by `q`, which is influenced by both `alphaq` and `betaq` functions. These functions depend on the transformed calcium concentration to determine the rates of channel opening and closing. #### **Calcium-Binding and Permeability** - **Calcium Binding:** Intracellular calcium elevation leads to the activation of SK channels through a bi-phasic response, characterized by `q`. This involves calcium binding to the channel's calmodulin or other calcium sensors, triggering channel opening. - **Conductance (`gsk`):** The conductance of the SK channels is modulated by `q^2`, which simulates the cooperative effect of calcium binding sites on channel opening. ### Conclusion In summary, the code effectively captures the dynamics of SK channels by modeling their dependence on intracellular calcium levels, which impact neuronal activity and signaling. The SK channel plays a vital role in modulating neuronal firing patterns and synaptic responses, making this model crucial for understanding how these channels influence neural computations.