From: HAZEN ROBERT M, GRIFFIN PATRICK L, CAROTHERS JAMES M, et al. Functional Information and the Emergence of Biocomplexity. In: National Academy of Sciences; Avise JC, Ayala FJ, editors. In the Light of Evolution: Volume I: Adaptation and Complex Design. Washington (DC): National Academies Press (US); 2007. 2. https://www.ncbi.nlm.nih.gov/books/NBK254300/

Accordingly, we define “functional information,” I(Ex), as a measure of system complexity. For a given system and function, x (e.g., a folded RNA sequence that binds to GTP), and degree of function, Ex (e.g., the RNA–GTP binding energy), I(Ex) = −log2[F(Ex)], where F(Ex) is the fraction of all possible configurations of the system that possess a degree of function > Ex.

It’s not about the replacement of single amino acids at a time in the peptide.

For a peptide with a.a. length of ‘n’

“Et” = total number of all possible peptides = n^20

“Ex” = Number of all possible 'n-length peptides capable of performing the specified function ‘x’

“Q” = Number of all possible single a.a. replacements for a single peptide capable of performing the specified function ‘x’

Note that:
FI = -log2(Ex/Et)

‘Ex’ is not ‘Q’. Nobody has calculated Ex. They are only searching 20n sequences for activity when actually, there are n^20 sequences possible. They only calculated ‘Q’, which only considers a microscopic fraction of Et. To be specific they’re off by a factor of (1/20)n^19 total sequences…

With incorrect assumptions and mathematical errors, yes they are attempting to declare their number shuffling = FI. I agree that is their attempt. The errors however, make it an erroneous attempt.

Yes. I’ve partly explained it here. Computing the Functional Information in Cancer - #15 by swamidass. They have to take into account (1) the ability of common decent to create MI, and (2) alternate ways of arriving at the same function, and (3) the effect of purifying selection, and so on. Everyone of these factors biases their results upwards.

Yes. I’ve partly explained it here. Swamidass: Computing the Functional Information in Cancer . They have to take into account (1) the ability of common decent to create MI, and (2) alternate ways of arriving at the same function, and (3) the effect of purifying selection, and so on. Everyone of these factors biases their results upwards.

How do you establish functional information is increasing in cancer or is it assumed?

How do you establish that common descent can create FI or are you assuming this?

Bear in mind that Joshua, like Joe Felsenstein, is being generous. They are accepting the concept of “Functional Information” at face value. The allowed assumption is that genotype maps to phenotype. This is too generous for me.

To elaborate a little, mathematics is a modelling tool. But to come to some conclusion about reality, your mathematical model has to match reality to some extent, otherwise you need to modify or discard your model. You can’t expect reality to conform to your model.

If you want to make a criticism of a mathematical model you have to directly access that model and make specific comments. This is what Josh is doing with Eric H. Both models have strengths and weaknesses and are the beginning of measuring functional information.

Apples and oranges. Duston’s and Puccio’s models are based on empirical measurement and not just a math proof. It is also too early to tell on Eric’s model.