The provided code is a computational model simulating the electrical activity of a neuron, specifically focusing on the impact of the hyperpolarization-activated current, often denoted as **Ih** (also known as the **H-current** or hyperpolarization-activated cyclic nucleotide-gated current). This current plays a critical role in the rhythmic activity and excitability of neurons. ### Key Biological Concepts 1. **Ih Current**: - The Ih current is a mixed cation current carried predominantly by sodium (Na+) and potassium (K+) ions. - It is activated by hyperpolarization (i.e., when the membrane potential becomes more negative than the resting potential). - In many neurons, including those in the heart and brain, Ih contributes to the pacemaker potentials, affecting rhythmic activity and influencing the overall excitability and timing of the neuronal firing. 2. **Biophysical Properties**: - The model uses parameters such as the maximal conductance for the H-current (`gh_max`) and its reversal potential (`Eh = -33.7 mV`), which is characteristic of the Ih current due to the ions involved. - The activation of the Ih current is modulated by a voltage-dependent component with half-activation (`Vh = -90.7 mV`) and a slope factor (`k = 12.5`), shaping the sigmoid-like activation curve crucial for the channel dynamics. 3. **Passive Membrane Properties**: - The model includes passive properties such as membrane capacitance (`Cm`) and leak conductance (`gL`), with `EL = -75 mV` as the leak reversal potential. These are vital for determining how the neuron's membrane potential changes in response to ionic currents. 4. **Membrane Voltage Dynamics**: - The model simulates the membrane potential (`Vm`) over time, considering the contributions of the Ih current and a leak current. This relates to the equation for membrane dynamics expressed as `Cm(dVm/dt) = -(Ih + Ileak) + Iapplied`. - In this context, `Iapplied` represents external currents such as injective currents (`Izap`), which may mimic synaptic inputs or experimental stimulations. 5. **Simulation Methodology**: - The simulation employs a straightforward approach using a forward Euler method to simulate the changes in membrane potential and ionic currents over discrete time steps, which are derived from the biological sampling frequency (`Fs`). In essence, this model attempts to represent the electrical behavior of neurons, particularly how the Ih current influences the neuron's response to applied stimuli and passive membrane properties. This type of model can be used to study the role of Ih in neuronal excitability and its role in various physiological and pathophysiological conditions.