Final answer:
Under parasympathetic control, cAMP decreases, leading to decreased HCN channel activity, resulting in the slowing of the heart rate.
Step-by-step explanation:
The question asks how cAMP gating of Hyperpolarization-Activated Cyclic Nucleotide-Gated (HCN) channels changes under parasympathetic nervous system control. Under the influence of the parasympathetic nervous system, which is involved in 'rest and digest' responses, there is a decrease in cAMP in the heart. This decrease in cAMP leads to decreased HCN channel activity, as cAMP is known to positively influence these channels, enhancing their open probability and therefore increasing cardiac pacemaker activity. When the parasympathetic system releases acetylcholine (ACh), it activates muscarinic receptors, which can lead to the opening of potassium channels and slowing of the heart rate through hyperpolarization of the cardiac cells. Thus, the correct answer regarding the changes in HCN channel activity under parasympathetic control is that cAMP decreases, resulting in decreased HCN channel activity (b).