Meaning of “cognate genes encode the basic biological functions of proteins”
The sentence quoted accidentally misuses the word ‘cognate’ because in attempting to appear profound it has become overweight and off-balance. Notice the sentence also contains the meaningless nonsense of “real-time dynamics”, and in the rest of the paper the word ‘cognate’ is (fortunately) nowhere to be found.

What does the author mean? His review is on proteomics, and he wishes to emphasize the importance of post-translation modification of proteins. He needs to refer to the unmodified form of proteins, and so he associates them with the information in their genes, which is limited to the unmodified amino acids. The word ‘cognate’ in plain English has the meaning of ‘related’ or ‘corresponding’, so the author would appear to be using it to imply the relationship between particular genes and the individual proteins that they encode. What he may have meant to say is:


  “Whereas genes encode the basic biological functions of their
  cognate proteins…”


This would have been linguistically correct, although the word ‘cognate’, in my opinion is unnecessary as it adds nothing to the sentence.

You can find a biological definition of cognate on GenScript:


  cognate 
  
  A term borrowed from linguistics, signifying a correspondence;
  e.g. a receptor and its cognate ligand, a tRNA and its cognate amino
  acid.


These two examples are of the most common uses of ‘cognate’ in molecular biology — that for tRNA can be found on the Wikipedia page for aminoacyl tRNA synthetase. A quick search brought up few examples of ‘cognate proteins’ or ‘cognate genes’, and in these cases I found the word was used to refer to similar genes or proteins in different organisms or strains.