From my understanding, both of those papers measure mutual information, not functional information.
You may want to check out my thread on catalytic antibodies:
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No, I am using the “testable hypothesis” approach.
You’ve got it backwards, Kirk. To be useful, your hypothesis needs to make empirical predictions that allow you no interpretive wiggle room. You’re supposed to be trying to falsify it, not keep it alive. If, after you bash it diligently and ruthlessly, it is still standing, then you’ve got something!
I really don’t get this idea that the hypothesis is the product.
I’m afraid that I would disagree and note that what you wrote makes no sense. I respectfully suggest that you consult my publication record to see that I do have a clue:
As you’ve presented it, cataloguing is all it is. There’s nothing mechanistic.
Why me?
I would rigorously test hypotheses regarding when the hypothetical design occurred.
I agree that you should stop doing that. 
It’s nonsensical. Absolutely nonsensical. Why the fork and knife should the “functional sequence complexity” of a protein depend on how many such similar proteins can be found in PFAM? What does that tell us? That just makes FSC a measure of a completely arbitrarily defined quality, partly constrained by historical circumstance (how many genomes have been sequenced and properly annotated, for example).
Why not count how many birds passed by your window in the last hour before, dividing it by the length of the protein in picometers, multiplied by the logarithm of it’s weight on Jupiter, and then have that be it’s “functional sequence complexity”? What is that a measure of? What does it tell us, other than you have created some nonsensical mathematical relationship to … look clever?
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Stealing this
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I can’t claim credit. Got it from The Good Place.
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The evolution of cancer can produce FI, quite a bit of it. So, therefore, we know intelligence is not the only source. I’m not sure, for that matter, you have even demonstrated intelligence can produce FI. See here: Computing the Functional Information in Cancer.
@Kirk what if the task you are undertaking is (logically or practically) impossible? What if it is like trying to make a perpetual motion machine? How would you know? Perhaps continuing to try is just waisting you effort. How would you be able to avoid that waiste?
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Rum he is measuring conservation of a site similar to the way gpuccio measures it. Does a particular site tolerate substitution.
@Rumraket is correct @colewd. FSC is not FI, and FSC is essentially an arbitrarily defined quantity. It is not the measure of how many functional sequences there are, nor is it a measure of how difficult it is to evolve something.
Are you saying that the paper Kirk posted should have called it FI instead of FSC?
I’m saying he measured an arbitrary quantity that he called FSC, and posited that it equaled FI despite overwhelming evidence to the contrary. FSC is not and never has been a measure of FI.
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So you believe that his method of measurement and calculation does not estimate FI?
That is correct.
I’ve also provided an alternative approach to computing the difficulty of evolvability, that does not suffer from the same problems as FSC (and, for that matter, FI).
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Is this in the cancer discussion?
Yes. The right measure is KL divergence, not delta entropy (which is what @Kirk uses for FSC). KL divergence measure how close new functions are to the starting point. Notice how @Agauger and Axe make their argument:
- Evolution of new protein functions requiires design IF…
- Function is exceedingly RARE in sequence space AND…
- Function is exceedingly ISOLATED in sequence space.
FSC, at best, only measures #2, the rarity of function in sequence space. (Note: It does not even accomplish this). It does not measure #3, how separated functions are in sequence space. Neither FI or FSC, even in principle, measure #3. Both #2 and #3 have to be true for the Axe-@agauger argument to work.
KL-divergence measures #3, which is a better way to measure how difficult it is to evolve a new function, and it is measured in bits too. So we can understand it as the amount of information required to evolve a new function. Using KL divergence, we find out that new functions require far less bits than @Kirk calculates, and we can demonstrate dramatic increases in functional information (as measured by KL-divergence) in natural systems (such as cancer). So less bits are required, and we have direct evidence that natural process can produce them.
The argument fails. I think @kirk is sincere and doing his best here, but it seems he is working towards a desired conclusion, regardless of the evidence. It looks very much like a quest for a perpetual motion machine to me.
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No, I’m saying he hasn’t measured a property of the protein at all. The relationship by which he defines FI, or FSC, or whatever you might want to call it, is fictional and arbitrary.
No conclusion about the protein’s origin or function can be reached from the data used to compute it’s “FSC”. Because it is computed from measures that aren’t actually measures of the proteins attributes, but things entirely unrelated to it. Like how many OTHER proteins with similar sequences that humans have decided to put into the PFAM database.
In other words, Kirk is essentially saying that we can infer something about the protein’s origin and history by, among other things, seeing how industrious human biochemists have been at sequencing and annotating genomes.
Clearly, CLEARLY we aren’t measuring a property of one my genes by considering how often biochemists have sequenced similar genes in other species and uploaded their sequences to PFAM. That should go without saying. That’s before we even begin to consider whether such a value (whatever it might be) should be multiplied, taken the square-root or base-2 log of, or divided by yet another measure.
It’s numerology. It looks fancy and technical, but it’s nonsense.
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I don’t know why they make the argument like this as there is lots of function in Axe’s experiment. The issue is does the ratio of function to total sequence space allow for the number of evolutionary experiments available. I understand you and Rum are questioning if the measurement has validity.
If an experiment shows function is rare does it matter if it is isolated? While this can show evolution inside a protein family is possible it does not show how a new protein family with very different sequences is formed.
Yes it does. Because if isn’t isolated, we can change from one function to another very easily. @Agauger and Axe know this, and go to lengths to argue that function is isolated because they know this is central to the argument.
That is a good question for you understand. Axe argues (approx) that function is 10^-77 rare, but comparable experiments that directly test this show that funciton is more like 10^-10 rare. Everyone agrees it is rare (10^-8 is rare), but there is a big different between those numbers. One is easy to evolve, and the other is more difficult (though not impossible!).
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Can you explain why natural selection would not be able to conserve sequence that is required for function? If functional information is simply sequence conservation then it is exceedingly obvious that natural selection can produce functional information.
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Can you explain the difference between rare and isolated? Want to make sure I’m grasping that correctly.
Functional information and sequence conservation are different things.