Final answer:
ERK and eIF-4E are the two signaling molecules that activate mTOR during resistance exercise, leading to muscle hypertrophy and increased muscle strength and size.
Step-by-step explanation:
The two signaling molecules that directly activate the mechanistic target of rapamycin (mTOR) during resistance exercise are Extracellular signal-regulated kinases (ERK) and eIF-4E. ERK, a MAP kinase, becomes active when phosphorylated and in turn phosphorylates MNK1, which subsequently phosphorylates eIF-4E. This phosphorylated eIF-4E is an elongation initiation factor associated with mRNA, which when activated, allows for the initiation of protein synthesis. This pathway is critical for building muscle mass as it leads to hypertrophy, the enlargement of muscles, which is a common goal for athletes engaging in resistance exercise to increase muscle strength and size.