I wonder what it says about me that my first reaction to seeing the figure containing the two artificial bases was 'They don't even have hydrogen bonds, what the hell is that shit?' I mean, look at it: If you have too many of these bases not hydrogen bonding, the DNA's going to fall apart.
Interesting observation. The lack of hydrogen bonds appears to have been a deliberate strategy on the designers' part to avoid "cross talk" between the artificial bases and the normal base pairs. Source
Oh, they use hydrophobicity to form bonds! Cool. Even so, too much of that is a lot less stable than hydrogen bonds. Van der Waals forces are much weaker. Hell, water may be relatively fluid and be held together by transient hydrogen bonds, but they're relatively disordered hydrogen bonds, the water molecules have too much energy to maintain them, and the water molecules can only maintain three (and don't have a covalent sugar-phosphate backbone, either). Ice has just little enough energy to be essentially a lattice of stably-hydrogen-bonded water molecules. It's solid. If you accumulate enough of these bases, the DNA will fall apart for another reason - it'll get mushy in these areas. Also, I'm not sure why they think they're going to get new amino acids out of these things. The transcription and translation machinery is made of some truly wacky molecules and I'm not confident they have the means to generate stuff that will faithfully make new amino acids in a replicable manner that is well-integrated in the rest of the organism's transcriptome and proteome.