Functional Information (again)

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Biological functional information as defined by Hazen and Szostak.
https://doi.org/10.1073/pnas.0701744104

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That looks like a very complicated paper. Could you summarize it for us, in your own words? TIA!

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Using Hazen and Szostak’s method, what is the measured information in this sequence?

ATAAGGAGAACGGAGTTGCCAAGGACGAAAGCGACTCTAGGTTCTAACCGTCGACTTTGGCGGAAAGGTTTCACTCAGGAAGCAGACACTGATTGACACGGTTTAGCAGAACGTTTGAGGATTAGGTCAAATTGAGTGGTTTAATATCGGTATGTCTGGGATTAAAATATAGTATAGTGCGCTGATCGGAGACGAATTAAAGACACGAGTTCCCAAAACCAGGCGGGCTCGCCACGACGGCTAATCCTGGTAGTTTACGTGAACAATGTTCTGAAGAAAATTTATGAAAGAAGGACCCGTCATCGCCTACAATTACCTACAACGGTCGACCATACCTTCGATTGTCGTGGCCACCCTCGGATTACACGGCAGAGGTGGTTGTGTTCCGATAGGCCAGCATATTATCCTAAGGCGTTACCCCAATCGTTTTCCGTCGGATTTGCTATAGCCCCTGAACGCTACATGCACGAAACCAAGTTATGTATGCACTGGGTCATCAATAGGACATAGCCTTGTAGTTAACATGTAGCCCGGCCGTATTAGTACAGTAGAGCCTTCACCGGCATTCTGTTTATTAAGTTATTTCTACAGCAAAACGATCATATGCAGATCCGCAGTGCGCGGTAGAGACACGTCCACCCGGCTGCTCTGTAATAGGGACTAAAAAAGTGATGATTATCATGAGTGCCCCGTTATGGTCGTGTTCGATCAGAGCGCTCTTACGAGCAGTCGTATGCTTTCTCGAATTCCGTGCGGTTAAGCGTGACAGTCCCAGTGAACCCACAAAACGTGATGGCAGTCCATGCGATCATACGCAAGAAGGATGGTCTCCAGACACCGGCGCACCAGTTTTCACGCCGAAAGCATAAACGAGGAGCACAAATGAGAGTGTTTGAACTGGACCTGTAGTTTCTCTACGAAGAACACCTTGAGCTGTTGCGTTGTTGCGCTGCCTAGATGCAGTGTCGCACGTATCACTTTTGCCTCAACGACTGCTGCT

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I’ll note that cryptographers make extensive use of random number generators. This seems to suggest that the output of a random number generator can be very functional, at least for cryptographic functions.

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I am not an expert on Information Theory, but the definition of “functional information” contained in this paper’s abstract seems to require a number of things:

  1. that “all possible configurations of the system” are known;

  2. that the “degree of function” of each of these configurations is known; and

  3. that this “degree of function” is scalar (i.e. it has a single dimension, it is not multi-dimensional).

I have to ask, for how complex a “system” is this definition feasible? Particularly if the system in question is a complex lifeform.

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Yep. The the information content of no known biological sequence is known, or knowable in practice, with the definition of functional information used in that paper. I have explained that to Bill at length in multiple threads on this forum:
https://discourse.peacefulscience.org/t/why-is-it-hard-to-estimate-functional-information/9117/2

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Contingency also plays a massive role. As gene products interact with one another and evolve with one another you can quickly create a very steep and local fitness peak. This can produce highly conserved sequences which can give the false impression that there is a very narrow window for a given function.

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I’d add to Tim’s comments that Hazen, Szostak and Carothers’s “functional information” calculates how much information-that-helps-function is in a particular sequence. We have to know the amount of function in each possible sequence. They were not in any way trying to make an argument that ordinary evolutionary processes could not result in that amount of information. When there are two sequences in a population, and one of them has a higher degree of FI than the other, and when that results in it having a higher fitness, then there will be natural selection to increase the frequency of that one. That is the simplest case where we can see natural selection acting to put more information (FI) into the population’s pool of genomes by increasing the average value of FI. So we can immediately see that there is no general principle that natural evolutionary processes cannot increase Functional Information. A few additional points:

  1. No, you do not have to run off to discussing gene duplication to see this. Calm down, change of gene frequencies can do it!
  2. If someone says “but I am talking about new information, this is not new information because the alleles are already there” then they are not talking about Functional Information, but rather Creationist Information, which is not affected by changes of gene frequency.
  3. If someone says “but I am talking not about these microevolutionary changes but about Really Big, Really Important New Body Plans” then they are not talking about Functional Information.

Here is a thread at The Skeptical Zone where I discuss assertions by “gpuccio” of limits on accumulation of FI , where after hundreds of comments it turns out he has no proof of his assertions but just thinks that natural selection is ineffective. (Oops, I erred: after over 2,000 comments)

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Hi Joe
Is there any reason that the DNA required to build a functioning animal would not fall under Hazen and Szostak’s definition?

A specification for a functioning animal could be generated and over time we hopefully will learn how DNA does this.

If the information content of the entire genome is not under Hazen and Szostak’s definition then is this something that should be defined?

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We do. Or some of us do, at least.

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What colewd is advocating is discovering all the properties of organisms with all possible past and future genomes. Good luck with that!

I repeat: there is no reason at all to believe that the increase of functional information by natural selective is in principle impossible. Change of gene frequencies can do that.

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Yes, exactly this.

I think it might be worthwhile to suggest to @colewd the following:

Bill, we’ll accept this definition of ‘Functional Information’ of being at least potentially useful, if you can calculate for us (with working) the FI of some lifeform under this definition.

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Functional Information in this paper does not attempt all of those things, but rather to examine a single function. That said, your comments are spot on.

We might imagine a more complex sort of information measure for multiple functions, but what we get is measure of relative information between two functions, or two sequences with similar function. We can talk about the difference in info or change in info, but it is always relative to some reference.

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It is a potentially useful definition if one restricts “function” to be something more easily measured. In the case of Hazen et al. It was activity of one enzyme.

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Yes, but this restriction would appear to disqualify this definition as a useful definition of “information” (as @John_Harshman requested) in the wider context of Evolution (the context @colewd in which was discussing information, that spurred this request).

That leaves us still in need of a definition of information that is useful beyond what is “easily measured” in the context of the “activity of one enzyme”.

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You could look at the functional information contained in the genes required to build an animal from a single cell. If you can estimate the information contained in a single gene then you can see what genes are critical by knockout experiments. If the information is in bits you simply add the bits of the necessary genes required to build the animal.

The reason to consider that selection does not increase information is the possibility that a change in gene frequency is simply changing the overall information and not increasing it. Survival probability can be improved by a loss of information (Behe). It can also be improved by a change in information that results in a new color or beak size.

How do you show that the information is increasing?

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I recommend you stop posting and proceed to spend all your time doing that. Good luck.

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You have just switched definitions of “Information”, which previously was tied to fitness. Now it’s tied to…what? Consider the possibility that a loss of information in a gene might be a gain of information in the organism, by the previous definition.

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Apparently, as Bill Shakespeare said, it

doth suffer a sea change, into something rich and strange
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Can I not then argue that survival also be improved by a loss of functionality?

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