# Hyperpolarization-Activated Current (Ih) Model ## Biological Basis The code models the hyperpolarization-activated current, often referred to as Ih or the "anomalous rectifier". This current is a mixed cationic (Na⁺/K⁺) channel, primarily observed in thalamic relay neurons among other neuronal types. Ih plays a critical role in controlling neuronal excitability and the rhythmic oscillatory activity seen in certain types of neurons. ### Key Biological Aspects 1. **Voltage Dependence**: - The activation of Ih is dependent on the membrane voltage, primarily activated by hyperpolarization (more negative membrane potentials). - The document mentions specific kinetics related to the voltage dependency, derived from experimental data on thalamic neurons. 2. **Ion Channel Conductance**: - The code uses parameters like `ghbar`, representing the maximal conductance of the Ih channels, essential for modeling the flow of Na⁺ and K⁺ ions across the membrane. 3. **Calcium Regulation**: - Intracellular Ca²⁺ modulates the Ih current indirectly. This regulation is modeled by assuming that calcium influences the production of cAMP, which subsequently binds to the open state of the Ih channel, enhancing its activity. - Luthi and McCormick provided insights into this indirect calcium regulation via cAMP, which the model simulates. 4. **Binding Sites and State Transitions**: - The Ih channel model includes various gating states and transitions affected by both voltage and intracellular signals. - There are distinct states for closed and open channels (`c1` and `o1`), with additional states to account for calcium-bound configurations, representing the complex dynamics of protein interactions involved in Ih modulation. - Parameters like `nca` and `nexp` denote the number of binding sites for calcium on the second messenger and Ih channels, respectively, reflecting biochemical interaction details. 5. **Activation and Kinetics**: - The steady state of activation for the Ih channels (`h_inf`) is modeled using sigmoidal functions dependent on voltage, simulating the biological process of conformational changes leading to channel openings. - The time constant (`tau_s`) for these transitions includes temperature dependencies, modeled by adjusting with a Q10 factor, denoting sensitivity to changes in temperature. 6. **Experimental Foundations**: - The model and its parameters are grounded in experimental studies of Ih currents, such as McCormick & Pape’s work, and are further refined based on additional research outlined in the code comments. ### Conclusion The code represents a computational model of the Ih channel capturing its complex regulation through both voltage and biochemical interactions, predominantly calcium-mediated, albeit indirectly through cAMP. Its design aims to reflect the physiological properties observed in thalamic neurons, providing insights into the role of Ih in neural excitability and rhythmicity.