Most membrane-less organelles (MLOs) formed by LLPS contain both nucleic acids and IDR-rich proteins. Currently while IDRs are well-recognized to drive LLPS, nucleic acids are thought to exert non-specific electrostatic/salt effects. TDP-43 functions by binding RNA/ssDNA and its LLPS was characterized without nucleic acids to be driven mainly by PLD-oligomerization, which may further transit into aggregation characteristic of various neurodegenerative diseases. Here by NMR, we discovered unexpectedly for TDP-43 PLD: 1) ssDNAs drive and then dissolve LLPS by multivalently and specifically binding Arg/Lys. 2) LLPS is driven by nucleic-acid-binding coupled with PLD-oligomerization. 3) ATP and nucleic acids universally interplay in modulating LLPS by competing for binding Arg/Lys. However, the unique hydrophobic region within PLD renders LLPS to exaggerate into aggregation. The study not only unveils the first residue-resolution mechanism of the nucleic-acid-driven LLPS of TDP-43 PLD, but also decodes a general principle that not just TDP-43 PLD, all Arg/Lys-containing IDRs are cryptic nucleic-acid-binding domains that may phase separate upon binding nucleic acids. Strikingly, ATP shares a common mechanism with nucleic acids in binding IDRs, thus emerging as a universal mediator for interactions between IDRs and nucleic acids, which may underlie previously-unrecognized roles of ATP at mM in physiology and pathology.