There is a 2007 article in The New York Times, where Dennis Overbye discusses “genomic SETI”. Overbye was inspired by Japanese researchers who, shortly before, managed to embed the famous formula “E=mc2” and the year of its publication “1905” into bacterial genome (though, in fact, embedding non-biological information into genomes was performed as early as in 1986 and 1988, to name a few). Dennis Overbye hypothesizes that some kind of a message might already reside in DNA of terrestrial organisms, if life on Earth was seeded by a preceding galactic civilization, as proposed by Francis Crick and Leslie Orgel (though, again, Crick and Orgel proposed that Earth was seeded with living cells, not with DNA, as Overbye writes; seeding DNA makes no sense – it will simply decay outside the cell).
Overbye comes to the conclusion that there are two disadvantages to genomic SETI. The first one is that DNA mutates:
The sad truth is, as others will tell you, this is a bit like writing love letters in the sand. “I don’t buy it,” said Seth Shostak, an astronomer at the SETI Institute in Mountain View, Calif., pointing out that DNA is famously mutable. “Just ask Chuck Darwin,” he added in an e-mail message.
Apart from that it’s not clear what Darwin has to do with that (he had no idea about DNA, not to mention its mutability and role in heredity), this seems reasonable. Even though DNA is now considered to be the most reliable information storage that can safely keep information for tens and hundreds of thousands of years, it is still not that durable as needed for messaging in cosmic seeding, where intact message must be replicated with DNA for billions of years until intelligent beings (if any) evolve. This does not imply that it is definitely impossible to use DNA as billion-years storage; but no one knows how to do that.
The second problem is more subtle:
Gill Bejerano, a geneticist at the University of California, … pointed out that the problem with raising this question is that people who look will see messages in the genome even if they aren’t there — the way people have claimed in recent years to have found secret codes in the Bible.
Well, in this opinion the search for a message in genome is just that – take a genome and search for anything interesting. That’s not the way science works. You have first to develop the methodology for data analysis, based on the initial assumption(s). Without this component, any science will reduce to numerology and Bible codes. Of course, there still might be false positives, and typically all researchers tend to see patterns in data that seem to confirm their hypotheses, but this happens normally in any research.
At all events, both problems essentially dissolve if one turns from genomes to the genetic code. First, unlike DNA, the genetic code does not mutate (a few minor variations notwithstanding). Second, unlike genomes which are huge and diverse, the genetic code is small and universal. You simply don’t have much freedom here to see a lot of messages that are not actually there.