I am glad to see that you are acknowledging that recombination even by itself, is capable of generating information, even if the sequence fragments pre-exist in the genome of the B-cell.
But I find it rather odd that you’re suddenly interested in calculating just (I) instead of FI, functional information. You must by now recognize that you can’t actually calculate the FI for antibodies, because you have no idea what the total number of molecules of that length that meet the minimal threshold for function is. And for reasons explained in that post of mine you still have not acknowledged, Gpuccio’s method is incapable of providing any sensible estimate.
No, calculating FI has nothing to do with how the sequences is generated. It is simply a measure of the fraction of sequences that meet the minimum threshold for function, out of all possible sequences of equal length.
What you’re saying doesn’t make any sense, because that would render FI completely useless as a measure of functional information in evolving sequences, since all sequences evolve from other sequences(either by recombination, or mutation). So they are related to them, they can’t evolve “from an unrelated state”. They can change so much that they become so dissimilar we no longer can see any sign of them having been related through, but that isn’t necessary for there to be FI in the molecule.
How the sequences that meets the threshold, come into existence, whether by design, or by completely scrambling and overwriting some existing sequence, or even by a single substitution mutation, is irrelevant. In either case, the amount of FI exhibited by that sequence would be the same because the ratio of sequences that fall inside, to those outside the minimum threshold, would remain the same.
No, the real problem is that you don’t actually know how much FI is exhibited by any molecules and you have no way of even estimating it(Gpuccio’s was a commendable but ultimately flawed attempt to get at that). You could try to do it empirically, but for proteins of even small size (30-mers) the total sequence space becomes so large it becomes practically impossible to do thoroughly. So the design inference doesn’t actually work because you couldn’t ever be in a position to say with sufficient certainty that the molecule in question exhibits 500 bits or more.
In my view, the issue is not whether VDJ recombination and somatic hypermutation generates “high FI”(I don’t know what counts as high, is it 500 bits?). I don’t know whether it does that, the problem is that the design inference doesn’t work as long as it’s based on FI.