There is an aside to be made here about the inadequacy
of classic "information theory" to DNA. Yes, the sequence of DNA
base pairs can be construed as information. However, the classic
definition of information leaves out detailed analysis of who
it is that understands that information. Information is not
universally accessible. Given the long and fascinating history of
that culture, I regret that I cannot read Chinese. Nonetheless,
despite my regret, a page of written Chinese is of no use to me.
The way that information theory acknowledges this is to say that we
append to the information the program that will allow our universal
Turing machine to understand the message. But this presupposes that
the system in question can be adequately modeled by such a machine,
which is, in the case of a living cell, a highly suspect claim.
Such things as the recipe for cytoplasm and the
timing of RNA injection into a developing cell are information in
a certain sense, but it is a sense that is unavailable for
capture by the classic paradigm of information theory.