[dekhn]

This system isn't really turing complete, but existing biology provides everything required to make a computer which is Turing complete (assuming non-infinite tape size).

True programmatic biology is still very underdeveloped. I have seen logic gates, memory, and state machines all implemented, but I don't think anybody has built somethign with a straightforward instruction set, program counter, addressable RAM, and registers that was useful enough to justify advanced research.