Left-handed DNA does seem to exist in rare circumstances and is thought to be regulatory in how DNA is managed. The structure isn’t just a mirror image of right-handed DNA. Because the subunits that make up DNA are chiral (have a handedness of their own) the structure of left-handed DNA (called Z DNA) is radically different.
RNA can sometimes also be left handed in how it folds into structures.
Note: It’s a particular pet peeve of mine when pretty cartoons and drawings of DNA get the handedness wrong.
Two off the top of my head:
DNA in eukaryotes exists in a structure called chromatin which is basically DNA wrapped around proteins called histones. The turn of DNA has been shown to be important for determining positions of Histones on the DNA sequence.
Additionally all biological macromolecules are “chiral” which basically means they have a handedness to their bonds. Proteins and nucleic acids (which are chiral) that interact with DNA are shaped to interact with the right handed helix
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