Final answer:
Acetylcholine can have an inhibitory effect when it binds to muscarinic receptors that increase potassium permeability, leading to hyperpolarization of the cell.
Step-by-step explanation:
The student asks in which case the neurotransmitter acetylcholine could have an inhibitory effect on its target cell. The possible scenarios include binding to an excitatory receptor, increasing potassium permeability, decreasing sodium permeability, and enhancing calcium influx. The correct scenario for acetylcholine to have an inhibitory effect on the target cell would be increasing potassium permeability, as this would lead to hyperpolarization of the cell, making it less likely to fire an action potential.
When acetylcholine binds to the muscarinic receptor, if it causes an increase in concentration of K+ ions (potassium) leaving the cell, it can cause the target cell to become hyperpolarized. This hyperpolarization is an effect opposite to depolarization of the membrane, which is typically associated with excitation of a cell. Thus, when neurotransmitters like acetylcholine lead to an increase in K+ ions leaving the cell, it results in an inhibitory postsynaptic potential (IPSP).