Proxy bodies are composed of Amrita Cells. Re-L reads in episode 2 that the outer membrane of an Amrita cell is intensively activated when it nears other amrita cells, most likely due to a magnetic field radiated by all Proxies.
Though described as "immortal cells," Amrita Cells can be killed by FP Ray bullets (invented by Daedalus as an improvised weapon system against Proxies). As such, Amrita Cells are not truly immortal, though they quickly regenerate from conventional damage and are confirmed (in a brief snapshot of Daedalus' report in episode 2) to be capable of bypassing the Hayflick limit. FP Rays are the only known method by which a Proxy can be dispatched (with the exception of death at the hands of another Proxy), though FP Rays are not foolproof: Proxy One demonstrated that a Proxy can survive the dose of FP Rays by isolating and removing the infected area (having been shot in the arm by an FP Ray bullet, Proxy One survived by ripping off the arm and regenerating a new one). An infusion of Amrita Cells saved Re-l Mayer's life following her exposure to infectious or toxic elements outside Romdeau . Amrita Cells cannot live under blue sky (indicating that particular cyan wave lengths of light destroys them, same as the color of light emmitted from the FP bullets).
'Amrita' is a Sanskrit word meaning 'that which is immortal', and in Hindu mythology, it was the nectar drunk by the gods to give them their immortality.