Final answer:
During long-term potentiation at glutamate synapses, all events from options A to C occur, involving the opening of sodium and calcium channels, increased sensitivity to glutamate, and more glutamate release.
Step-by-step explanation:
During long-term potentiation at glutamate synapses, E) all of the above occurs. This includes A) sodium channels and calcium channels on the postsynaptic cell opening, B) the postsynaptic cell becoming more sensitive to glutamate, and C) the presynaptic cell releasing more glutamate. Specifically, during long-term potentiation (LTP), calcium entry through NMDA receptors initiates a cascade that causes the insertion of more AMPA receptors into the postsynaptic membrane. The presence of these added receptors increases the sensitivity of the neuron to glutamate, allowing for a greater excitatory postsynaptic potential (EPSP) when glutamate is released from the presynaptic cell.