Final answer:
Metabotropic channels do not allow for rapid EPSPs/PSPs, amplification of postsynaptic potentials, and activation of second messenger systems.
Step-by-step explanation:
The statement that metabotropic channels can allow for rapid EPSPs/PSPs, amplification of postsynaptic potentials, and activation of second messenger systems is False.
Metabotropic receptors are different from ionotropic receptors in that they do not directly open ion channels when the neurotransmitter binds to them. Instead, they cause metabolic changes in the cell through a complex of proteins and activate second messenger systems. This process is slower compared to the rapid changes brought about by ionotropic receptors.