.....The snake is related to sciences associated with poison and death, such as toxicology and toxinology, and it also implies a metaphysical idea. It is connected with the underworld, not only because it crawls on the ground, but because it can bring death, connecting the upper with the underground world. The ability of the snake to shed its skin has been associated with the circle of life, and the renaissance spirit also, ever since early Hellenic antiquity.

Consequently, as a symbol of the modern medical profession, toxicology and toxinology, the snake twisted around a stick or the snake beside a pharmapeutic cup, which also implies the use of medicines or even poison, has its roots in the ancient Mediterranean area as proven by the archeological data combined with literary references. Its benevolent as well as its poisonous properties could be paralleled by the similar properties of medicines.

https://pubmed.ncbi.nlm.nih.gov/11003127/