I'm currently reading Eric Baum's What is Thought. It presents an interesting comparison between the operation of DNA and Post production systems. These systems provide a set of regular expressions paired with corresponding substitutions. An example is the rewrite rule:
x B A B y -> x C B y
where x and y are variables.
When provided the string
A B A B C B C
the result of the substitution is
A C B C B C. (example from Baum)
These types of operations happen both at the levels of intron removal and protein synthesis. The more common (and easier to visualize) comparison is of DNA to a Turing Machine. Here the DNA (actually RNA) strand is the tape and the Ribosome is the read/write head.
Looking back, both comparisons were explored in Hofstadter's Godel, Escher, Bach: an Eternal Golden Braid and Metamagical Themas
UPDATE: In a later chapter Baum points out the Turing equalence (proven by Minsky, discussed by Wolfram and others) between Turing machines and Post production systems.