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In this work they find that formaldehyde crosslinking happens by formation of a methylol adduct (due to nucleophilic attack by N or S in case of proteins) in protein which then attacks the DNA or vice-versa. The final crosslink is by a methylene bridge
Formaldehyde can react to amino groups in nucleotides and proteins and form a schiff's base, but i dont have a clue how this is involved in crosslinking