The Holliday junction theory of the Dreemurr and Holiday family conflict. This will be relevant in how the families resolve their tension and save Dess.
"A Holliday junction is a branched nucleic acid structure that contains four double-stranded arms joined. These arms may adopt one of several conformations depending on buffer salt concentrations and the sequence of nucleobases closest to the junction."
This kind of structure occurs during meiotic cell division in recombination, when homologous chromosomes nearly identical in sequence exchange genetic information. Every DNA molecule is composed of a two strands of nucleotides, sugar and phosphates. In recombination, the strands from your paternal and maternal chromosomes form this quadruplex structure. I believe that the Dreemurrs represent the paternal chromosome i.e. strands 2 and 3 (due to Asgore's involvement in investigating Dess' disappearance) and the Holidays represent the maternal chromosome i.e. strands 1 and 4 (due to Carols support of Asgore) in this structure. Furthermore, DNA strands are always antiparallel to each other, as in they run in opposite directions. This is seen in both marriages in that the spouses of each are opposing in their personalities and goals, causing wedges between them. DNA strands pair according to complementary base pairing (A-T and C-G). Here, the married couples pair with each other but also with only one person of the other marriage (Toriel with Asgore [strands 2 and 3] and with Rudy [strands 2 and 1], and Carol with Rudy [strands 1 and 4] and Asgore [strands 4 and 3]). Yes Asgore is friends with Rudy, but this is specifically in relation to their current motivations in solving(or accepting) Dess' disappearance.
The idea is that the Holidays and Dreemurrs are deeply intertwined families, and despite current tensions they form a unit between the parents (an earlier on, between the kids) - a quadruplex, if you will. As this all relates to the disappearance of December Holiday, we could call this intersection of conflicting desires the Holliday junction. The Holliday junction is resolved in one of two ways.
The resolution is either vertical (resulting in recombinant DNA strands) or horizontal (no recombinants). Essentially we either get strands that either generate new functions or strands that exchange segments but remain functionally the same. In the context of the Holidays and Dreemurrs, I believe this would mean that
1) Horizontal resolution, no recombinants -> The two families are unable to communicate and the junction is resolved by breaking off the ties between them, leaving them forever changed by each other but not newly adapted to the current situation, i.e. they fight and cut ties with each other. Potentially due to insufficient exchange of information, like miscommunication?
2) Vertical resolution, recombinants -> The two families successfully exchange important information to reach a resolution between each other. This may have to do with Asgore and Carol fully revealing their investigation and explaining about the Dark Worlds, assuming they know about them, leading Toriel and Rudy to understand and come to terms with their respective spouses behaviors. This is especially relevant as Holliday junctions are involved as a pathway for DNA repair.
The vertical resolution is of course preferable and narratively I can see it being the only way for them to save Dess. It's also possible that one happens in the normal route and one in the Weird route. It's too early to tell though.
