The code provided is a computational model of the SK-type (small conductance) calcium-activated potassium current, specifically referencing the work by Kohler et al. from 1996. SK channels are a subset of potassium channels that are activated by intracellular calcium ions (Ca²⁺) and are critical for the regulation of neuronal excitability and the afterhyperpolarization (AHP) following action potentials. ### Biological Basis 1. **SK Channels**: These are small-conductance, calcium-activated potassium channels that mediate potassium ion (K⁺) conductance. They are not voltage-gated but are instead activated by the binding of intracellular Ca²⁺, linking the neural activity to calcium signaling. 2. **Calcium Sensitivity**: - **Calcium Dependency**: The model leverages a calcium-dependent gating mechanism, where the calcium ion concentration (`cal1i`) influences the gating variable `z`. This reflects the biological process where increased intracellular calcium activates SK channels. - **Z Gate**: In the model, `z` represents the activation state of the channel, varying between 0 (closed) and 1 (fully open), which is modulated by calcium concentration. The steady-state value of `z` (`zInf`) follows a calcium-binding kinetics captured mathematically. 3. **Potassium Conductance (gSK_E2)**: - The code sets a maximal conductance (`gSK_E2bar`) parameterizing the density of SK channels in the membrane. This conductance scales with the gating variable `z`, representing the calcium-activated opening of SK channels that allow K⁺ to flow out of the cell. This outward flow of K⁺ hyperpolarizes the neuron, contributing to the afterhyperpolarization phase following an action potential. 4. **Voltage Dependence**: - The driving force for the current through SK channels is determined by the difference between the membrane potential (`v`) and the reversal potential of K⁺ (`ek`). This current is modeled as `ik`, linking the electrical activity to ionic gradients. 5. **Rate Dynamics**: - The dynamic behavior of the channel opening (`z`) in response to calcium is described using a differential equation, where `zTau` modulates the time constant for the channel's response to changes in calcium. ### Conclusion This model serves to elucidate how SK channels integrate intracellular calcium signals and contribute to neuronal excitability and firing dynamics. By modeling the SK-type calcium-activated potassium current, the provided code enables simulation and analysis of the effects of these channels on neuronal function, specifically in terms of how they regulate action potential afterhyperpolarization and overall neuron firing patterns.