Final answer:
Under sympathetic control, cAMP levels are increased, enhancing HCN channel activity through a cascade involving β-Adrenergic receptors, Gs proteins, and adenyl cyclase.
Step-by-step explanation:
Under sympathetic nervous system control, cAMP levels increase, leading to enhanced HCN channel activity. This is because β-Adrenergic receptors are stimulated by the sympathetic neurotransmitters such as norepinephrine (NE) and epinephrine, which are linked to Gs proteins that activate adenyl cyclase, increasing intracellular concentrations of cAMP. The rise in cAMP activates Protein Kinase A (PKA), which then phosphorylates and enhances the opening of Hyperpolarization-Activated Cyclic Nucleotide-Gated (HCN) channels, allowing for the increased flow of positive ions and leading to a facilitation of the cardiac rhythm.