The provided code models the **persistent sodium current (NaP)**, a specific type of ionic current prevalent in neurons. This model is drawn from previous work by Rubin and Cleland (2006) for olfactory bulb neurons, with adaptations from the hippocampal neuron models of Fransen et al. (2004). ### Biological Basis #### Role of Persistent Sodium Current (NaP) 1. **Functionality**: The NaP is a non-inactivating current that plays a critical role in modulating neuronal excitability and repetitive firing. Unlike the transient sodium current, which inactivates quickly, the NaP maintains a prolonged depolarizing influence on the neuron's membrane potential. 2. **Location**: This current is observed in various types of neurons across different regions of the brain, including the hippocampus and olfactory bulb, as implied by the source studies of the code. 3. **Contribution to Neural Behavior**: The NaP is involved in subthreshold (below action potential threshold) activities, allowing neurons to fire in response to smaller input signals. It can also contribute to the plateau potentials and after-depolarization phenomena, influencing bursting and rhythmic oscillatory behaviors within neuronal networks. #### Key Aspects of the Model 1. **Ionic Conductance**: The code specifies `gbar`, which represents the maximal conductance of the NaP channels—reflecting the density of ion channels on the neural membrane. 2. **Ion Selection**: The `USEION na` statement indicates that this model involves sodium ions, consistent with persistent sodium currents, which rely on Na+ influx. 3. **Gating Variables**: The model uses `m` and `h` as gating variables. These represent the activation (`m`) and inactivation (`h`) states of the sodium channel. The deterministic state equations (`m'` and `h'`) describe how these gating variables change over time, influencing the overall current `ina`. 4. **Voltage Dependency**: The code captures how the gating variables change with membrane voltage (`v`). This voltage dependency is essential for modeling how the NaP contributes to the neurons' response to synaptic inputs and varying membrane potentials. 5. **Rate Equations and Functions**: `minf`, `mtau`, `hinf`, and `htau` define how quickly and to what extent the gating variables reach their steady state (infinity values) and how quickly they transition (`tau` values), based on empirical data adapted from previous studies. This determines the kinetics of channel opening/closing. Overall, this model encapsulates the critical dynamics of the persistent sodium current's contribution to neuronal electrophysiological properties, emphasizing the mechanisms regulating sodium ion flow through NaP channels and their role in sustaining prolonged excitatory activity in neurons.