# Biological Basis of the Model Code The provided code models the SK-type calcium-activated potassium (K\(^+\)) current, which is a crucial component in regulating neuronal excitability. This model is based on the work referenced by Kohler et al., 1996, and it has been adopted from ModelDB, a repository for computational neuroscience models. ## Key Biological Concepts ### SK-type Calcium-Activated Potassium Channels - **Function**: SK channels belong to a family of potassium channels that are activated by the presence of intracellular calcium ions (Ca\(^{2+}\)). They are key regulators of the afterhyperpolarization (AHP) phase that follows neuronal action potentials. - **Calcium Dependence**: The gating of these channels is dependent on intracellular calcium concentrations. As calcium levels increase, these channels open more readily, contributing to potassium efflux, which in turn hyperpolarizes the neuron. ### Gating Variable (z) - **State Variable**: The model uses a gating variable `z` to represent the open probability of the SK channels. The value of `z` ranges from 0 to 1, where 0 indicates all channels are closed and 1 indicates all are open. - **Equilibrium and Dynamics**: `zInf` represents the steady-state value of the gating variable based on calcium concentration, while `zTau` is the time constant for reaching this steady-state. The dynamics of `z` are described using the equation \( z' = (zInf - z) / zTau \), governing how `z` approaches `zInf` over time. ### Conductance and Current - **Conductance**: `gSK_E2` represents the conductance of the SK channels, which is a product of the maximum conductance `gSK_E2bar` and the gating variable `z`. This reflects the calcium-dependence of channel conductance dynamics. - **Potassium Current**: The code computes the potassium current (`ik`) using Ohm’s law, defined by the product of the conductance and the driving force (difference between membrane potential `v` and equilibrium potential `ek` for potassium). This current plays a critical role in stabilizing membrane potential and modulating neuronal firing patterns. ## Calcium Dependency and Activation - **Calcium Activation**: The model uses a procedure `rates` to determine the relationship between calcium concentration and channel activation. The steady-state open probability (`zInf`) is defined by a sigmoidal function indicative of cooperative binding (Hill coefficient), showing that multiple calcium ions might be involved in channel activation. - **Threshold for Activation**: Notably, the code ensures a minimal threshold for calcium concentration to avoid mathematical inaccuracies, as channels have a minimal operational calcium level. Overall, this model replicates the biophysical behavior of SK channels in neurons by emphasizing the calcium-dependent gating mechanism and its influence on action potential dynamics and neuronal excitability.