Kolmogorov complexity can only be defined for a specified programming language, in which it is the shortest possible program that can be written to produce the string.
Er, no. I don't have my copy of Li and Vitanyi to hand for the direct citations, but this isn't the right definition. Kolmogorov complexity is not defined for languages, but for specific Universal Turing Machines (and since any one UTM can implement any other in a constant-length program), K-complexity is universal for any string to within that constant.
As such, it's a property of the string, not of the computing environment.
I could define a programming language in which Pi is compressed to 1 bit, if I define 1 as "the rather simple algorithm for Pi" and 0 as "NOT the rather simple algorithm for Pi".
You could; but the Kolmogorov complexity of Pi in this programming language would not simply be 1, but 1
plus the length of the UTM that compiles and executes that program. Or perhaps shorter, if there is a more direct representation.
Therefore the Kolmogorov Complexity of any given data set depends on the language used to describe it. It is not some absolute metaphysical quantity.
Competely and totally wrong.
It's quite reasonable, then, to use Kolmogorov complexity as a measure of the information contained in a digital biological system, as long as it does something recognizably Turing-like or that can be implemented as a Turing machine. DNA transcription and replication can, so it's reasonable to talk about the K-complexity of a given piece of DNA or a given protein that results directly from transcription. Of course, when you start getting into the non-digital processes (for example, enzymes working on (analog) proteins instead of on (digital) RNA), the model breaks down.
The real problem here is not that Kolmogorov complexity is inecessarily nappropriate, but that the units upon which this argument is based are inappropriate. FIrst, a "gene" is not a "bit"; far from it. A typical gene will contain hundreds or thousands of base pairs,
each of which contains (naively) two bits of information. The second is, of course, that the TM upon which biology "runs" also contains information -- human body temperature, for example, is relatively fixed and the development process can rely on it. This is why mammals like humans have shorter genomes than reptiles; mammals don't need to deal with a sudden
in utero "cold snap" -- and any assessment of K-complexity has to be able to take this information into account as well.
Good luck.