Facts on eastern piece of DNA (4)

I believe the answer is:

gene

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'piece of dna' is the definition.
'gene' can be an answer for 'dna' (thesaurus). I'm unsure of the 'piece of' bit.

'facts on eastern' is the wordplay.
'facts' becomes 'gen'.
'on' means one lot of letters go next to another.
'eastern' becomes 'e'.
'gen'+'e'='GENE'

Can you help me to learn more?

(Other definitions for gene that I've seen before include "and 16 Down: Rockabilly singer" , "Part of DNA" , "What makes us different" , "Bodily factor controlling heredity" , "DNA unit" .)

I've seen this clue in The Mirror.

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