The soul was posited by the natural scientists of old to explain the unity of the matter in an organic body.
That is, how does the complicated mass of matter we call a body unify itself into a coherent single thing with everything working together in harmony in a certain nature. There is nothing in the individual parts that explains this. “Soul” is the “place filler” to describe that mystery.
Nobody knows how it works that is why its nothing directly to do with matter. Yet, like a poltergeist, its visible effects are obvious.
Some say the discovery of DNA replaces the need for soul nowadays.
Well, yes, to a large degree we no longer need to posit a poltergeist. The word soul probably applies well to DNA as well for it does most of what the soul was required to explain…only the “soul” now seems to be “material” rather than “spiritual” substance.
Thus far Aristotle would probably agree because he basically said animals had “material souls”.
The problem comes with humans who can “think”. This was considered a purely spiritual operation requiring a purely spiritual soul, not a material soul. DNA cannot substitute here.
However if computers can exhibit “memory” (which used to be considered a spiritual “faculty”) and even primitive thinking (e.g. abstraction of universals from matter) then perhaps the brain as matter can explain spiritual intellect also.
We just don’t know for sure.