Final answer:
A channel causing a negative ion to enter a postsynaptic cell initiates a hyperpolarizing graded potential, which may prevent action potential generation by making the inside of the cell more negative.
Step-by-step explanation:
When a channel opens on a postsynaptic membrane that causes a negative ion to enter the cell, this leads to a graded potential known as hyperpolarization.
Hyperpolarization occurs when the postsynaptic membrane becomes more negative relative to the outside, which can inhibit the generation of an action potential by increasing the difference between the membrane potential and the threshold potential.
This is facilitated through ligand-gated or voltage-gated ion channels regulated by chemicals, which upon binding to neurotransmitters or changes in voltage, allow ions to flow into or out of the neuron, respectively. Voltage-gated ion channels are particularly important in the propagation of action potentials, whereas ligand-gated channels are typically involved in generating graded potentials at the synapse.