Splice/WMG

Dren is an attempt to create The Seether.
Let's see, she is not born like other girls, she may not look like other girls, and it's pretty clear that she's hard to dispatch ("Can't fight the Seether!")

Dren looks like Mewtwo.
She does! Which follows that she might have been an attempt to create a living "Pokemorph". Poor thing. Nobody deserves that kind of life.
 * Not really. Mewtwo's structure is more feline (Though bipedial and somewhat humanoid), he's (Mewtwo is technically an "it" but it's easier just to call it a "he") got fur, a pair of cat-like ears (Yes, those are his ears, he only has three fingers on each hand on two toes on each foot, and he has that weird tube-thing on the back of his head. Dren, on the other hand, is more humanoid in structure, has no fur, has four fingers on each hand and four/five toes on each foot, and doesn't have a tube-thingy on the back of her head. Not to mention that unlike Mewtwo, Dren's tail has a stinger and that Dren has wings...which Mewtwo lacks. They look NOTHING alike.

Insanity is genetic within Elsa's family.
Think about it. Her mother was clearly crazy, Elsa, as Clive noted, is rather fucked up herself, particularly noted when she, and the fact that she. And well, let's not even get into.
 * You really don't need genes to perpetuate a cycle of abuse. Elsa's horribly bipolar treatment of Dren was enough, along with the poor creature's advanced growth ensured an incredibly imbalanced psyche well on their own.

Dren's human DNA came from Elsa's mom.
It was all part of her sick freudian thing. She wanted to have some revenge on her mother, that's shy she remade her as a "lesser" humanoid creature and why she wanted to raise her. On the other hand she did love her mother and/or Dren which was what drove her to act caring at times. She transferred her love/hate for her mother to poor Dren.
 * I'm pretty sure Dren's human DNA came from Elsa herself. When Clive looks at Dren all made up, he recognizes Elsa in her.

Elsa is a Farscape fan
And the naming of Dren was totally passive-aggressive.

Dren was an attempt to create a human-Xenomorph hybrid.
It's never really clear what Dren's non-human half is, as it matches no earthly creature. But what if it's something not of this Earth?

Both Dren and the Xenomorphs possess stinger-tails, very humanoid anatomy, and Ugly Cute baby forms. Dren's inhuman behavior could be the result of her Xenomorph thought processes conflicting with her more human brain, and her might be the fault of a "conflict" between the human genetic code for there to be a sex and the Xenomorph genetic code to possess no gender.
 * Couple of problems: First, to my knowledge Xenomorphs are not amphibians and obviously humans aren't, but Dren is. Second, they show early on, she's not human and something else, she's a mix of human and a whole bunch of different animals, plus Elsa says none of he componants are preditory, which rather rules of Xenomorphs.
 * Also Xenomorphs don't have stingers, they have chitinous blades on their tails, rather like a Stegosaurus' Thagomizer. (Early designs included stingers, but the final design was a blade that later films enlarged.)

There's at least one other hybrid out there.
Dren turns into a male briefly after having sex with Clive. Why did she take so much longer to change than Ginger? She didn't need her female aspects anymore because she had already reproduced. Dren developed as a fetus very rapidly, and this trait went on to her and Clive's offspring (Okay so it took several days in Dren's case, but her and Clive's child would have wildly different DNA, so who knows). She gave birth to it in the tank briefly before Clive and Elsa found her in deteriorating condition. After everything was over, by the time anybody checked the tank, it had taken off into the woods.