Biological Basis of the H-current Model Using Na Ions

The provided code models the H-current, a hyperpolarization-activated current in neurons. This current plays a pivotal role in setting the resting membrane potential, regulating neuronal excitability, and contributing to rhythmic oscillatory activity in the brain, such as in thalamocortical and hippocampal neurons.

Key Biological Features

Ion Selectivity

• Ions Involved: The code explicitly uses sodium ions (Na^+) to modulate the H-current (USEION na READ ena WRITE ina). Normally, H-currents are associated with both sodium (Na^+) and potassium (K^+) permeability, but this model focuses on Na^+ ions to study their contribution to the current dynamics.

Conductance (g)

• The conductance of this current is modeled as a product of a maximum conductance (gbar) and the gating variable (n) which represents the opening probability of the channel. Conductance changes dictate the ionic flow across the membrane, influencing membrane potential.

Activation Dynamics

• Voltage Dependency: The H-current is activated by hyperpolarization (i.e., a more negative membrane potential):
  • vhalf: This parameter represents the half-activation voltage, showing the voltage at which 50% of channels are open.
  • K: Represents the slope factor for the voltage dependence, determining how steeply the channels transition between closed and open states with changes in membrane potential.
• Gating Variable (n): Represents the probability that the channel is open.
  • The model computes ninf as the steady-state activation function, determining the fraction of open channels as a function of membrane voltage (v).
  • The differential equation n' = (ninf - n)/taun signifies the time evolution of n towards its steady state, ninf, at a rate characterized by taun.

Time Constant (taun)

• Time Dynamics:
  • The taun parameter, or activation time constant, defines how quickly the channels respond to changes in membrane potential, which varies with voltage. It modulates the kinetics of the H-current, being explicitly faster for depolarized potentials (above -30 mV).

Reversal Potential

• Reversal Potential (eh): Set at -10 mV, it reflects the equilibrium potential for the combined Na^+ flux associated with the H-current. It indicates the potential where there is no net flow through these channels.

This model captures essential features of H-current dynamics within the physiological voltage range, focusing on Na^+ ions. This can be useful for investigating roles of H-currents in electrical behavior of neurons, especially in tuning rhythmicity and excitability regulated by Na^+ permeability.