The road to delta involved synergistic sequence changes which were independently and collectively advantageous, and resulted in measurable and pronounced optimization of function.
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Certainly, but that doesn’t change the fact that the FI associated with a given level of function in a given environment is invariant.
Nope, FI varies within a given environment. Some sequences will have a higher FI, while others will possess lower FIs. There is a gradient or distribution. As you already know, some PfCRT variants have lower CQ uptake activity, while others are effective extruders of CQ within a CQ-exposed environment. That’s the gradient.
Am I going to recommend that Behe corrects that part of the book? No, for he recommended this himself. However, he insisted that the correction would not matter a whit for the validity of his overall argument.
Here is the relevant passage from a piece called « How many ways to win at Sandwalk? » (see the link below)
There is a lot of chatter at Sandwalk deriding the idea of “simultaneous” mutations (which was not intended in my book The Edge of Evolution in the sense it is being taken there, and which at this point I would gladly replace with other words simply to avoid the distraction). Yet it matters not a whit for the prospects of Darwinian theory whether the pathway consists of two required mutations that are individually lethal to a cell and must occur strictly simultaneously (that is, in the exact same replication cycle), or whether it consists of several mutations each with moderately negative selection coefficients, or consists of, say, five required mutations that are individually neutral and segregating at some appreciable frequency in the population, or some other scenario or combination thereof. The bottom line for all of them is that the acquisition of chloroquine resistance is an event of statistical probability 1 in 1020.
It is the outlandish improbability of the pathway — not its particular features — that is the crux. It puts strong limits on what we can expect from Darwinian processes. And that is an important point for any biologist — whether in a medical field or not — to appreciate.
Everyone (@Michael_Okoko & @RonSewell) needs to track this back to the original comment:
Here, @Dan_Eastwood was speaking with respect to the functional information of a sequence, which can obviously change. The comment he was responding to was in reference to a function, but NOT a specific level of function. That is, at that point in time the discussion was on ‘x’, NOT ‘Ex’. In fact, all previous discussion had focused on the functional information of sequences.
Your decision to redirect to defined levels of function was an evasion. Specified levels of functionality are arbitrary until and unless you have evidence of binary states associated with particular thresholds, something so far not mentioned much less demonstrated.
As such, the only coherent question is ‘Can the functional information of a sequence for some function increase?’, and the obvious answer is ‘YES!!!’.
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You don’t understand what FI is. FI doesn’t caracterize a sequence but a function. In order to assess the FI of a function, you first have to define that function as well as the level of function.
You don’t understand what FI is. As I’ve just said, FI doesn’t caracterize a sequence but a defined function. So your question « can the FI of a sequence for some function increase? » makes no sense.
Oh, the irony.
FI characterizes sequences with respect to a specified function, but not a specified level of function. If you don’t understand why this is true, you need to reread your own reference.
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No, not as defined by Hazen & Szostak 2007. Here the FI is defined as -log2 of the fraction of all sequences that meet some arbitrarily defined minimal threshold for function. Once you have defined the minimal threshold, you can then proceed to try to estimate how many sequences out of all possible meet that threshold, and once you’ve done that you can take -log2 of that fraction to get the FI. But that means, in the context of the minimal threshold you’ve decided on, the FI is invariant. The fraction of all possible sequences that meet that threshold doesn’t change.
The only way to get from low FI to high FI is to change function, which would entail we also have to change what we think constitutes the minimal threshold for the new function. But that would then be how high FI functions evolve, from low FI functions. Select for simpler things like rudimentary folding(secondary structural elements) and/or binding activity, a low FI function, then once you have binding and/or stable secondary structural elements, select for catalysis, a higher FI function. That’s how they evolved abzymes for example.
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Which would be great, if such had been defined at the point in the conversation. But it wasn’t, they were just talking about sequences. Defined as such, changes in sequence change the FI of that sequence.
I’m pretty sure @Giltil referenced Hazen and Szostak 2007 and from there on out when speaking of FI was referring to the definition supplied in that paper. As far as I can tell from your exchange he’s been consistent on that.
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Congratulations for this nice explanation! Hope that it will help @CrisprCAS9, @Dan_Eastwood, @Michael_Okoko, @RonSewell to better understand what FI is.
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Thanks. Appreciate.
You’re welcome.
With Hazen you can either work forwards from a threshold or backwards from a sequence. That is, define an arbitrary level of function or determine a level of function from a particular sequence. In fact, the authors consistently refer to functional information with respect to sequences:
In this paper we consider the functional information of both symbolic systems
For example, the functional information of a ribozyme may be greater than zero with respect to its ability to catalyze one specific reaction
To quantify the functional information of any given configuration
Any analysis of the functional information of a specific functional sequence or object
And several others throughout.
I should add that another way to change FI is to change the minimal threshold. You can technically still define the FI with respect to the same function, but adjust the minimal threshold up and down, and this could then have the effect of changing the FI. There might be a much lower fraction of sequences capable of meeting some threshold set very high, but a much higher fraction capable of meeting a threshold set very low, and thus you could move from low to high FI as the threshold goes up.
I don’t see how you can calculate the FI for a particular sequence. What are going to take -log2 of?
There is a confusion here between ‘function’ and ‘degree of function’. FI requires a defined function, certainly. But defining this does not require defining anything else (" Functional information is defined only in the context of a specific function x."). As I said, you can then define your ‘Ex’ either by an arbitrary functional threshold or from an empirical determination of a sequence.
You can measure the degree of function of some sequence empirically, yes. But in order to then calculate how much FI it takes to implement that degree of function, you’d need to find out how many other sequences also meet that FI, so you can take the -log2 of the fraction of sequence space that are functionally equivalent or better sequences.
Thus you’re not obtaining the FI of a particular sequence, but of the function in relation to sequence space. I suppose you could then just say that because sequences with that level of function are so rare, then this sequence because it has that level of function, must have that much FI.
You could do it that way, but that would still require you have to find some way of estimating how many other sequences besides the one you have, that are also capable of meeting that level of function.
This, along with everything in the remaining sections, represents an identical problem to simply defining an arbitrary threshold. In which case every objection you present applies equally to applying FI to a sequence as to a threshold. If either one fails because of these objections, both fail equally.
In other words, if you can determine FI at all, then you can determine it for a sequence. And if you are determining it for a sequence (as they were at the start of this), then FI changes as the sequence changes.
And I’ll note again, the authors themselves repeatedly discuss functional information of sequences. So it’s odd to suggest that you can’t apply it to sequences, when the authors do so throughout the original work.