The provided code snippet is a model of the hyperpolarization-activated cation current, commonly known as Ih or HCN (hyperpolarization-activated cyclic nucleotide-gated) current, in a computational neuroscience simulation. This current plays a crucial role in the electrical properties of neurons, contributing to the control of rhythmic activity, resting membrane potential, and responsiveness to synaptic input.

Biological Basis

Ih Current:

• Ion Channel Type: Ih is facilitated by HCN channels, which are permeable to both sodium (Na⁺) and potassium (K⁺) ions. However, it is the inward Na⁺ flow that predominantly drives the depolarizing effect of this current.
• Activation Properties: Unlike most cation channels, HCN channels activate upon membrane hyperpolarization rather than depolarization. This unusual feature enables HCN channels to participate in pacemaking and rhythmic oscillatory behavior in neuronal and cardiac cells.
• Voltage Dependence: The model accounts for the voltage-dependent properties of HCN channels. The rate equations (mAlpha and mBeta) described suggest that channel gating kinetics are influenced by the membrane potential (V), impacting how rapidly these channels open (mTau is the time constant). The steady-state activation variable mInf describes the probability of the HCN channel being open at a certain membrane voltage.

Parameters and Variables:

• gbar: This represents the maximum conductance of the Ih channels. It's a measure of how many channels are present and fully open at a given time.
• ehcn: The reversal potential (ehcn) reflects the ion selectivity of the HCN channels, typically around -45 mV, a value that reflects the mixed Na⁺ and K⁺ permeability.
• m: The state variable m represents the gating state of the channel, with mInf serving as its steady-state value and mTau as the time constant of approach to this steady state.

Functional Role

• Pacemaking and Rhythmicity: Ih is integral to the generation of rhythmic ion flow, aiding in the timing of pacemaking cells, such as in the heart and thalamus.
• Modulation of Excitability: By contributing to the resting membrane potential and counteracting hyperpolarization, Ih helps stabilize membrane potential and influence the rate of synaptic input changes, playing a regulatory role in neuronal excitability.
• Synaptic Integration: Ih modulates temporal summation of synaptic inputs and integrates synaptic signals over time, thereby influencing cognitive functions like learning and memory.

In summary, this code models the Ih (HCN) current, capturing its voltage-dependent behavior and biophysical properties relevant to neuronal signaling and excitability.