There is actually a company looking to take this idea to court: http://www.nature.com/news/bioengineers-look-beyond-patents-...
"Last year, the company petitioned for US copyright protection of the DNA sequence for a fluorescent green protein, without success, but has launched an appeal. Its plan, says Christopher Holman, a law professor at the University of Missouri–Kansas City who is working with DNA2.0, is to pursue the appeal until the issue is heard in court."
It took a similar case to make software copyrightable: http://en.wikipedia.org/wiki/Software_copyright#History_in_t...