I would note that the bits calculated in this cited essay cannot be equated with bits derived from either BLAST analyses or the equation for FI that has been given above. They are quite completely different, and the calculation in the essay simply does not provide a bit-based estimate of probabilistic resources.
@gpuccio gpuccio, have you ever considered trying to derive expressions that would formalize the relationships between the different information calculations you have presented here? I believe this is possible for the BLAST-FI usages, and a clever mathematical biologist could probably do something similar for the metric you describe in the cited essay. I believe this could be a valuable addition to this field, as it were, and would address a lot of the concerns and confusion that you may see here, or have encountered before.