In molecular biology, a base pair is any of the pairs of nucleotides connecting the complementary strands of a molecule of DNA or RNA, that are held together by weak chemical bonds, which make up the "rungs" on a DNA "ladder" – known as the double helix.
In 2153, Doctor Phlox analyzed the genetic profile of the Xindi finger Jonathan Archer was given by the alien foreman of the trellium mining planet. From his analysis, he found that the DNA was "nearly identical to the tissue samples taken from the corpse found on Earth. Their base pair sequencing is far closer than, say, Humans and chimpanzees. Nearly identical, but not quite." Learning this, Archer suggested they were more "like Humans and Neanderthals." (ENT: "The Xindi")
While the USS Enterprise was in orbit of Terra 10 in 2269, it encountered the spiroid epsilon waves that were emanating from the planet. Upon further analysis, it was discovered that the waves tend to wind tight spiral molecules, such as dilithium or the double helix of DNA. Because there are limitations to how far DNA can compacted, they were able to calculate the limits to how much the crew was going to shrink. (TAS: "The Terratin Incident")
When the Drayans were given a tour of USS Voyager's sickbay in 2372, The Doctor explained that "we are fully equipped to provide a wide variety of treatments here, from removing a splinter to re-sequencing the base pairs in a strand of DNA." (VOY: "Innocence")
The Srivani possessed a form of sub-molecular technology, more advanced than anything developed by Starfleet. In 2374, Srivani scientists placed these microscopic genetic tags in the DNA of the some of Voyager's crew, which caused genetic mutations to several individuals. It was not until The Doctor discovered what appeared to be contaminant on Chakotay's base pair sequence, that he realized what the devices were. (VOY: "Scientific Method")
When Captain Kathryn Janeway attempted to "make conversation" with Crewman Mortimer Harren, in 2376, to get to know him better, such as asking about where he grew up, he explained to her that "I am a product of my nucleic acids. So if you're trying to understand me better, questions about my home planet are irrelevant." In response, Janeway humorously asked him, "how's your 13th chromosome? Missing a couple of base pairs in gene 178?" (VOY: "Good Shepherd")
In 2377, Icheb began tutoring Naomi Wildman in her study of genetics. Taking the creative approach, he had her learn by putting together a jigsaw puzzle featuring an image of a strand of DNA. After nearly completing the portion of the puzzle showing the DNA helix, Icheb congratulated Naomi for having "recognized the complementary base pair," she admitted to him that "actually, I just found two pieces that fit together." (VOY: "Shattered")