The provided code is a computational model that represents the sodium (Na) ion channel dynamics specific to the neuronal axon. Sodium channels are crucial for the generation and propagation of action potentials in neurons. Here are the key biological aspects modeled in the code:
Ion Conductance: The model explicitly uses sodium (Na) ion channels, as indicated by the USEION na statement. The sodium ion equilibrium potential, ena, is exploited to calculate the sodium current, ina, using the Hodgkin-Huxley conductance-based formalism.
Gating Variables: The model uses gating variables m (activation) and h (inactivation) to simulate the opening and closing dynamics of the sodium channels. These variables are time-dependent and voltage-dependent, reflecting the transition between channel states.
Activation and Inactivation:
tha, qa, Ra, and Rb govern the activation of the channel (m). The voltage dependence (midpoint tha and slope qa) and rate constants (Ra for opening and Rb for closing) are designed to fit observed biophysical properties of axonal Na channels.thi1, thi2, Rd, and Rg. These control the dynamics of inactivation (h), similar to how the activation is modeled, but addressing the time scale and voltage dependence of channel inactivation.q10 parameter adjusts the rates of channel kinetics to account for temperature variations. This reflects the biological reality that channel dynamics can vary significantly with temperature changes in neurons.Maximal Conductance: The parameter gbar represents the maximal conductance of the sodium channels when fully open. This is a crucial determinant of how much Na current will flow in response to a given voltage change.
Threshold Shifts: The parameter sh allows adjustments to the voltage-dependence of activation and inactivation, simulating conditions where the threshold for channel opening is shifted, which could happen under certain physiological or pathological conditions.
Steady-State Functions: minf and hinf are steady-state values of the gating variables, representing the proportion of channels in the open state (for m) or the non-inactivated state (for h) at a given voltage.
Time Constants: mtau and htau define the time constants for reaching steady-state in activation and inactivation, respectively. These are crucial for modeling the temporal dynamics of channel opening and closing during an action potential.
trates procedure calculates the transition rates depending on the membrane potential v, using a helper function trap0 to handle cases where voltage approaches the activation or inactivation thresholds.Overall, this code captures the essential features of axonal sodium channels' biophysical properties using simplified mathematical representations, helping researchers simulate neuronal function under various conditions.