The Caduceus (Kyrikeio) of Hermes as a universal symbol of medicine

The winged Hermes was the messenger of the gods in ancient Greek mythology. He always kept in his hand the Kyrikeio, which consisted of a staff which at the top had a bullet with wings and two snakes twined together. According to a Greek myth, two snakes were fighting each other, fell bloody and Hermes put in between the kyrikeio and they were wrapped around it, calmly and healed from their wounds. It was its first link as a symbol of Medicine. Around the 7^th century A.D. Hermes is also linked to alchemy thus taking the connection of the Caduceus to Medicine and Pharmacology even further. The way the two snakes are bonded to each other is the same as the graphic form of the genetic code or else DNA. Is it possible that the ancient Greeks by using the metaphor of Greek myths were trying to preserve the knowledge about the genetic code and its exact function in the human body, such as the transfer of hereditary properties (messages) among relatives, by paralleling it to the carrying, the divine messages to people, by Hermes?