[1] Murphy began his career as a neuroscientist and professor at Harvard Medical School, where he taught from 1974 to 1986.
In 1992, Murphy was named Director of the Montreal Neurological Institute at McGill University,[2] where he expanded the faculty by 20 members and led an effort to establish the Brain Tumour Research Centre.
[3] In 2000, Murphy became the president and CEO of the Salk Institute for Biological Studies, where he remained until 2007.
[1][5] His primary research was in neurotrophins, a protein produced by brain cells and the peripheral nervous system.
He was married to Elaine (née Finnegan) Murphy, with whom he had three children: Jane, Mark, and Alison.