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On irreducible complexity - Otangelo ("Rationalist") is clueless on the Falsification Principle

arg-fallbackName="Sparhafoc"/>
Maybe you should ask Ken Miller, why he did stop to reply to me at his Facebook timeline, when i challenged him not only on the Flagellum, but also on the locomotion mechanism of the Mycoplasma mobile....


I am not sure why that is relevant.

Ken Miller's credentials and publishing history speak for his knowledge, whereas all you've got is an internet obsession of tossing around mendacious quote-mines and blathering nonsense. Whether he replies to you on FB or not has fuck all bearing on anything, certainly not his credibility, and certainly not the fact of evolution.

But I can perhaps toss out a couple of suggestions as to why he might not be bothered to engage you: maybe he got sick of you lying? Maybe he can't be arsed with someone who keeps quote-mining? Maybe he's too busy to teach basic cellular biology to someone fundamentally hostile to the entire scientific process? Maybe he thought you were a dick.

I can come up with more plausible explanations if you like?
 
arg-fallbackName="Sparhafoc"/>
ROFL....

Ok. Just one example falsified is fine with me and I grant that the concept and hypothesis of IC would have to be reformulated .

The bacterial flagellum evolved from a bacterial secretory system, therefore the claim that it is irreducibly complex and consequently evidence of intelligent design is wrong - the contention is falsified.

But of course, you've got your cute little get out of jail free card: Ahh well, you say, so it was never a irreducibly complex system in the first place, and shuffle on to your next asinine assertion which involves no actual labour on your part other than formulating an assertion.
 
arg-fallbackName="Sparhafoc"/>
Yes, you got me...... i did not make the distinction in that case. My fault. Acknowledged.
But that does not mean that the framework of the ID hypothesis is not to draw a line. It does, and any inference to the nature of the designer is prohibited.

Once, a step further is done, it does not belong anymore to ID, but theology, religion, and philosophy.

There is more than ample evidence that I.D. is just Creationism repacked. And not just Creationism, but expressly American Evangelical Creationism.


For years, "intelligent design" (ID) proponents denied that ID is just a new label for creationism. However, it is now well-known that the first intelligent design "textbook," Of Pandas and People, is just a revised version of a classic "two-model' creationism vs. evolution book named Creation Biology. As Barbara Forrest showed during her testimony in Kitzmiller v. Dover, Pandas was remade into an intelligent design textbook in 1987, in a few months after the Supreme Court ruling against creation science in Edwards v. Aguillard came down.

The most striking example of the transition was discovered by Dr. Forrest as she compared the drafts of Creation Biology and Of Pandas and People. Not only had "creationism" and "creationist" literally been replaced, apparently via a word processor, with "intelligent design" and "design proponent" in passages that were otherwise unchanged, but she even found a transitional form between the two labels!

Maybe you never got the cdesign proponentsists memo? Or maybe you know full well that it's just fundamentalist Christian Creationism and you're lying to me and everyone else.

That would be par for the course with evangelizing Creationists.


The Wedge Strategy is a creationist political and social action plan authored by the Discovery Institute, the hub of the pseudoscientific intelligent design movement. The strategy was put forth in a Discovery Institute manifesto known as the Wedge Document. Its goal is to change American culture by shaping public policy to reflect politically conservative fundamentalist evangelical Protestant values. The wedge metaphor is attributed to Phillip E. Johnson and depicts a metal wedge splitting a log.

Intelligent design is the religious[1] belief that certain features of the universe and of living things are best explained by an intelligent cause, not a naturalistic process such as evolution by natural selection. Implicit in the intelligent design doctrine is a redefining of science and how it is conducted (see theistic science). Wedge strategy proponents are opposed to materialism,[2][3][4] naturalism,[3][5] and evolution,[6][7][8][9] and have made the removal of each from how science is conducted and taught an explicit goal.[10][11] The strategy was originally brought to the public's attention when the Wedge Document was leaked on the Web. The Wedge strategy forms the governing basis of a wide range of Discovery Institute intelligent design campaigns.


Full text of the Wedge Document in link below:


Discovery Institute's Center for the Renewal of Science and Culture seeks nothing less than the overthrow of materialism and its cultural legacies.

This isn't a document that is in the slightest bit scientific in nature - it's a political & social engineering agenda and a functional admission that science is inconsistent with their (and your) religious belief and that rather than let scientific knowledge inform their beliefs, they will be working to undermine all aspects of science in the social arena.

But then that's not new either considering that the modern evangelic Creationist movement's founder - Henry Morris - was quite clear in just how far he'd be willing to pervert the truth in order to prop up religious propaganda

No geologic difficulties, real or imagined, can be allowed to take precedence over the clear statements and necessary inferences of Scripture.

Biblical Cosmology and Modern Science (1970) p.32-33


Read that, read it again, and read it as many times as necessary. The hubris is disgusting. It's the hubris all 'scientific' Creationists possess.

Not only is he saying that hard, empirical evidence will never take precedence in Creationism, not only is he saying that the Bible is the last word in knowledge, not only is he thereby admitting that there is absolutely zero fucking science at the heart of Creationism, but the most arrogant thing of all is that he simply assumes with no justification that his exegesis, his interpretation of the writings in the Bible are to be considered gospel. People like him and you have no role to play in the modern world - the seeking after truth is a journey of humility and self-awareness, a willingness to acknowledge errors, to incorporate new information and amend previously held beliefs. If you can't do that, you fail at science, and frankly, you fail at religion too.

Ken Miller is not just a real scientist, unlike you and Morris, he's also an honest theist, and an all round better human being.
 
arg-fallbackName="Nesslig20"/>
HIV has undergone every possible combination of 4 mutations, so it's not surprising that it could find gains that require 2, 3, or 4 amino acids at the same time, if each amino acid change doesn't require too many mutations.
Again....then you admit that an IC system can evolve....at least one that requires "few changes"
But probably you don't even need to have them all at the same time though.
"HIV's acquisition of its ability to counteract human tetherin appears to be a stepwise evolutionary gain where mutations gradually improved the ability, since "chimeras within each region yielded intermediate phenotypes. In other words, each mutation made HIV increasingly better at counteracting tetherin. How can it be IC if it's a gradual path?
In other words, each step was advantageous to improve the mechanism.....
You got that quote from the secondary source that says
HIV's acquisition of its ability to counteract human tetherin appears to be a stepwise evolutionary gain where mutations gradually improved the ability, since "chimeras within each region yielded intermediate phenotypes."18 In other words, each mutation made HIV increasingly better at counteracting tetherin.
Here is what the original source says.
1611357044829.png

We found that although full-length SIVcpz Vpu was unable to counteract human Tetherin, substitution of the N-terminal transmembrane domain from HIV-1 Vpu for that of SIVcpz Vpu conferred the ability to counteract Tetherin (Fig. 5B). This was specific to the transmembrane domain of Vpu, since substitution of the cytoplasmic domain (α-helix) leading up to the β-TrCP binding motif (DSGxxS) was insufficient to rescue the restriction phenotype (data not shown). Two regions in the transmembrane domain of Vpu were necessary for Tetherin antagonism activity: amino acids 1 to 8 and amino acids 14 to 22. Replacement of either region alone was insufficient to counteract Tetherin [Fig. 5B, HIV(1-8) and HIV(14-22)]. Further chimeras within each region yielded intermediate phenotypes, suggesting that these regions harbored several minor determinants (data not shown). More importantly, SIVcpz Vpu was able to completely rescue the Tetherin restriction phenotype when it encoded both regions 1-8 and 14-22 from HIV (Fig. 5B).
As the paper says, since the "chimeras" do not represent single mutational steps, rather they represent replacing 2 sections within the trans membrane domain, each section involving 8 amino acid residues - thus 16 aa substitutions in total - requiring 16 nucleotide substitutions in total. When replacing each section at a time was insufficient to counter tetherin, both are required. However, the important line here says that "chimeras" within each of the two regions resulted in intermediate phenotype (although data is not show). It isn't exactly specified how many substitutions these chimeras constitute, but as the paper itself says, this suggested "that these regions harbored several minor determinants". So no, this alone doesn't say that "each mutation made HIV increasingly better at counteracting tetherin."...not at all.

The paper also goes further into the specific of how many changes are required:
Although none of the Vpu proteins of SIVcpz strains were identical to the consensus Vpu of HIV-1 group M, among several strains of SIVcpz (LB7, CAM5, EK505, and MB66) that include the closest relatives of HIV-1 group M (18), the SIVcpz strain LB7 would be predicted to require seven minimal adaptations within the two critical regions of Vpu (amino acids 1 to 8 and 14 to 22) in order to gain the ability to antagonize human Tetherin.
Seven minimal changes. Although a more recent paper goes even further, determining the minimal CRITICAL residues required.

Four amino acid residues in the TMD are critical for anti-tetherin activity of N-Vpus​

To map the amino acid changes necessary for anti-tetherin activity in the TMD of N-Vpus, we analyzed eight different YBF30 and EK505 Vpu mutants (Figure 4A). The results revealed that four TMD amino acid substitutions (E15A, V19A, I25L and V26L) were sufficient to render the SIVcpz Vpu active against human tetherin, while the reciprocal changes disrupted the effect of the YBF30 Vpu on virus release (Figure 4B). These included two residues in the AxxxAxxxA motif, known to be important for helix-helix interactions [30], as well as two additional changes (LL) in the membrane-proximal hinge region (Figure 4C). Notably, these residues, which are highly conserved among N-Vpus (Figure 5A), overlap only partly with the A14, A18 and W22 residues previously shown to be important for the anti-tetherin activity of group M Vpus [34]. Thus, distinct adaptive changes in the TMD of SIVcpz Vpus seem to restore their interaction with human tetherin. Interestingly, none of the TMD mutations in the YBF30 and EK505 Vpus affected modulation of CD4, CD1d or NTB-A (Figure 4A). Thus, the changes in N-Vpus that conferred anti-tetherin activity are not responsible for the loss of the other Vpu functions.
It does say that the interaction for sufficient antagonism involves more sites than these, it is just that these four residues are critical ones, requiring at a minimum four mutations. Or three to achieve a "low" interaction, if you look closely at the figure. So, not only does this not support your statement that "each mutation made HIV increasingly better at counteracting tetherin." It refutes it. Stating that at least several are required for it to work.
The principle of evolutionary continuity, succinctly formulated by Albert Lehninger in his Biochemistry textbook. An adaptation that does not increase the fitness is no longer selected for and eventually gets lost in the evolution (in the current view, only those adaptations that effectively decrease the fitness end up getting lost). Hence, any evolutionary scenario has to invoke – at each and every step – only such intermediate states that are functionally useful (or at least not harmful).
So, IC systems, which have no intermediates that improve "fitness" along the way can still evolve nonetheless, as long as the intermediates are neutral and don't decrease the fitness. In addition to multiple (near) simultanious mutations, intermadiates can still persists by neutral drift, providing another way how the IC system discussed above evolved.
In the end, this is NOT an example of an irreducibly complex system at all as said before.
That's manifestly false as I have demonstrated.
The system lost, and then (re)gained its function.
We already went over this. NO! The Vpu could not antagonise human tetherin...especially not in the specific way it does. Also, even if it was regained, it wouldn't affect its status as an IC system that evolved.

About the rest of your post, I have covered in another thread on this forum.
I also collaborated with Jackson Wheat and Ration alMind on making videos on this exact topic.

[skip to 24:09]


The more comprehensive one
[skip to 14:06]
 
arg-fallbackName="he_who_is_nobody"/>
I am not sure why that is relevant.

Ken Miller's credentials and publishing history speak for his knowledge, whereas all you've got is an internet obsession of tossing around mendacious quote-mines and blathering nonsense. Whether he replies to you on FB or not has fuck all bearing on anything, certainly not his credibility, and certainly not the fact of evolution.

But I can perhaps toss out a couple of suggestions as to why he might not be bothered to engage you: maybe he got sick of you lying? Maybe he can't be arsed with someone who keeps quote-mining? Maybe he's too busy to teach basic cellular biology to someone fundamentally hostile to the entire scientific process? Maybe he thought you were a dick.

I can come up with more plausible explanations if you like?
It is always amusing to see a creationist (and all reality denier) challenge a scientist like this as if they are actually accomplishing something. As if a scientist not wanting to waste time with someone so obviously delusional means anything besides the fact that the scientists had better things to do. Imagine if some random person challenges LeBron James or Seth Curry to a game of one-on-one, and they laughed at them and walked off. Is the random person really better than the NBA professionals because the real players did not want to waste their time?
 
arg-fallbackName="Sparhafoc"/>
Comparing worldviews - there are basically just two

When you think in binaries, everything seems binary.

Of course, that's just an expression of ignorance.
 
arg-fallbackName="Nesslig20"/>
Have we talked about the Muller Two Step yet?


Imagine having your idea falsified decades before you conceive of it... and not even bothering to familiarise yourself with the available literature prior to making specious claims. That's religion masquerading as science for you.
Yeah, that is another thing I should've pointed out.

Behe's reasoning behind the IC argument is that something can only evolve by adding just one part at each step, and each step being an improvement in some way, often in regards to the SAME function that the system has at the end.

However, there are far more ways for systems to evolve. Systems can change functions (excaptation) as they become more complex. Also some steps could have been neutral, and multiple parts could have been addes at the same time in one step by combining subsystems each functional on its own with multiple components (co-option), and...as you point out...some steps can involve the removal of a scaffold as showin in the Muller Two step process:
1. Add a part
2. Make it necessary (remove the scaffold).

This is how bridges and arches are often made, and even natural bridges/arches, when at the end the scaffold is no longer necessary, and thus can be removed. But then the system is supporting itself and can no longer afford to lose more of its components.

Behe's reasoning is just flawed, even if we don't examine the systems themselves.
 
arg-fallbackName="rationalist"/>
See FIGURE 4A


The paper says "the results revealed that four TMD amino acid substitutions (E15A, V19A, I25L and V26L) were sufficient to render the SIVcpz Vpu active against human tetherin". So they are changing amino acids at positions 15, 19, 25, and 26 in that diagram.

Blue is chimp SIV and yellow is human HIV. they mix and match the pieces.

- is no anti-tetherin activity
(+) is a little bit
+ is some
++ is a lot.

In the first column under "release". Note how they never test amino acids 25 and 26 separately. Also note how they never test position 15 separately from either position 19 or position 25-26. Since they didn't test every path, they can't say it is or isn't gradual. Also note that some of the paths they tested were gradual. We go from - to (+) to + to ++. This is on the evolution of HIV-1 group N's anti tetherin activity.

That paper is inconclusive about whether all four amino acids had to change at the same time.
 
arg-fallbackName="rationalist"/>
Yeah, that is another thing I should've pointed out.

Behe's reasoning behind the IC argument is that something can only evolve by adding just one part at each step, and each step being an improvement in some way, often in regards to the SAME function that the system has at the end.

However, there are far more ways for systems to evolve. Systems can change functions (excaptation) as they become more complex. Also some steps could have been neutral, and multiple parts could have been addes at the same time in one step by combining subsystems each functional on its own with multiple components (co-option), and...as you point out...some steps can involve the removal of a scaffold as showin in the Muller Two step process:
1. Add a part
2. Make it necessary (remove the scaffold).

This is how bridges and arches are often made, and even natural bridges/arches, when at the end the scaffold is no longer necessary, and thus can be removed. But then the system is supporting itself and can no longer afford to lose more of its components.

Behe's reasoning is just flawed, even if we don't examine the systems themselves.
1. In biology, there are many complex elementary components necessary to build large integrated macromolecular systems like multi-protein complexes (RNA polymerase), 3D printers (the ribosome), organelles (mitochondria), etc., where their making requires complex multistep enzyme-catalyzed biosynthesis pathways. These elementary components are only useful in the completion of that much larger system. Not rarely, these biosynthetic pathways produce intermediate products, that left without further processing, are either a) nonfunctional, or b) harmful and kill the cell (for example, Reactive Oxygen Species (ROS), in the biosynthesis pathway of Chlorophyll b.
2. A minimal amount of prescribed, pre-programmed, instructional complex information stored in genes is required to instruct the making of a) functional elementary components and b) the assembly instructions to integrate them into complex macromolecular systems. Natural selection would not fix an allele variant that would instruct the making of an intermediate, nonfunctional, or harmful elementary component, and play no role in guiding its evolution. Foreknowledge is required to get a complex biological system through implementing a biosemiotic information system (which is irreducibly complex), directing the making of functional elementary components, and assembly into the entire complex integrated system.
3. Therefore, the origin of biological systems based on biosemiotic instructions are best explained by a brilliant, super-powerful mind with foresight and intent, and not undirected evolutionary pressures.
 
arg-fallbackName="Sparhafoc"/>
3. Therefore, the origin of biological systems based on biosemiotic instructions are best explained by a brilliant, super-powerful mind with foresight and intent, and not undirected evolutionary pressures.

Otherwise known as 'wild assertion that may fly in religious apologetics, but fails abysmally at even an elementary level of science'.

Dispute that?

So point to the super-powerful mind you assert is responsible.

Cannot?

Ok, then I assert the actual best explanation, far superior to yours, is teeny weeny little pink gremlins who have developed ether-powered technology which can tinker with the settings of the universe to effect outcomes desired by teeny weeny little pink gremlin tribal chiefs.

Coincidentally, these teeny weeny little pink gremlins are from an alternative universe we cannot detect; in our universe, they are immaterial, existing only as pure thought; their technology is forever beyond not only our understanding but is also completely undetectable to our senses and any technology we can hope to develop; teeny weeny little pink gremlins tribal chiefs love us and are very concerned about what we do with our whangers, but they're pretty much ok with us enslaving other humans because they're also capricious little fucks.

Prove me wrong.

Then go and learn what 'falsifiable' means and why you can't expect to be taken seriously in science when making unfalsifiable claims.
 
arg-fallbackName="Nesslig20"/>
Otangelo....like...really? Nothing you just put in there addresses anything that I said. Again, you're in bot-mode, showing no sign of comprehension of the points being made and you just put out a load of nonsense (probably copy pasted as well) that doesn't respond to the argument.
1. In biology, there are many complex elementary components necessary to build large integrated macromolecular systems like multi-protein complexes (RNA polymerase), 3D printers (the ribosome),
Ribosomes are not 3D printers, like not even remotely analogous. Don't be silly. I know you like to push these flawed analogies, but this makes no sense.
organelles (mitochondria), etc., where their making requires complex multistep enzyme-catalyzed biosynthesis pathways. These elementary components are only useful in the completion of that much larger system.
We know that mitochondria were once free-living bacteria. That has been pretty much established. So that is one example of a component that used to exist independently, but came part of an interdependent system. You not understanding how interdependency can arise is not an argument other than an argument for your ignorance.
Not rarely, these biosynthetic pathways produce intermediate products, that left without further processing, are either a) nonfunctional, or b) harmful and kill the cell (for example, Reactive Oxygen Species (ROS), in the biosynthesis pathway of Chlorophyll b.
ROS are, while in large amounts harmful, they are vital signaling molecules that the cell uses. They also function in the immune systems of various organisms, from plants to animals. They are by no means non-functional nor only harmfull.

About the biosynthesis of chlorophyl, even the intermediates have biochemical activity on their own and thus they could be functional. For example, the precursor Protoporphyrin IX (which is also a precursor of the heme in our blood).
1611531070725.png
Also you have had this conversation before. Of course, you are not the type to learn from your mistakes.
Screen Shot 2021-01-25 at 12.17.50.png
The problem you have is one that I have pointed out at the beginning. "Systems can change functions (excaptation) as they become more complex." Here, you mistake is thinking that the sole reason the intermediates are there is to build the end-products, but they could have had a function all by themselves and later they were used as an intermediate for the making of another product.
2. A minimal amount of prescribed, pre-programmed, instructional complex information stored in genes is required to instruct the making of a) functional elementary components and b) the assembly instructions to integrate them into complex macromolecular systems.
Not always. Genetic control does influence a lot of biological processes, sure, but other process are driven by self-organization, self-assembly and stochastic processes that induce noise and variability into the system, which are not "pre-programmed" in the genome.

From the paper: Is the cell really a machine? Emphasis mine.
I have argued in this paper that molecular biology is currently undergoing a fundamental shift in its theoretical conceptualization of the cell. The conventional mechanical, reductionistic, and deterministic view is gradually giving way to an understanding of the cell that emphasizes its fluidity, plasticity, and stochasticity. Faced with the formidable task of interpreting the vast and ever-growing amount of experimental data that continues to get published, explanatory appeals to engineering notions of design, programs, and circuits are increasingly being replaced by recourses to the physical principles of non-equilibrium thermodynamics and complexity theory. Cells are empirically revealing themselves to be inherently dynamic, self-organizing systems that respond stochastically and nonlinearly to environmental stimuli.
The inescapable conclusion that follows from the analysis I have presented is that the cell can no longer be unproblematically conceptualized as a machine5. Over the course of the paper, it has become apparent that cells lack all four characteristic properties of machines that were identified in the introduction. First, once the crucial role that self-organization plays in shaping the cellular architecture is acknowledged, it is difficult to uphold the idea that the spatiotemporal arrangement of the parts of a cell obeys a predetermined blueprint or design, as it does in a machine. Second, the conformational flexibility of most cellular constituents and the functional promiscuity they exhibit shows that a cell’s operation is not as tightly constrained by its structural configuration as it is in a machine. Third, whereas a machine performs its function by precisely following a predefined sequence of steps, a cell can arrive at a particular end in a variety of ways: it can recruit different kinds of molecules to the same function— or the same kind of molecule to different functions—depending on the conditions it finds itself in. And fourth, a cell cannot be broken down into parts without jeopardizing its structural integrity in the way that every machine can. Cellular components form deeply intertwined, everchanging networks of interactions that cannot be individually dissected without sacrificing the organization of the whole. “Cells are not engineered systems of discrete, interacting computational components, naturally yielding to compositional analysis” (Melham, 2013, p. 134), which is why they cannot be fully explained reductionistically; and neither do they operate deterministically, which is why their behaviour cannot be perfectly predicted.

Natural selection would not fix an allele variant that would instruct the making of an intermediate, nonfunctional,
Another point that I made addresses this: "some steps could have been neutral". Evolution isn't just natural selction. Don't forget about genetic drift.
or harmful elementary component, and play no role in guiding its evolution. Foreknowledge is required to get a complex biological system through implementing a biosemiotic information system (which is irreducibly complex),
Which we have determined, and you have admitted several times, is not a barrier in and of itself to evolution.
directing the making of functional elementary components, and assembly into the entire complex integrated system.
3. Therefore, the origin of biological systems based on biosemiotic instructions are best explained by a brilliant, super-powerful mind with foresight and intent, and not undirected evolutionary pressures.
Unfounded conclusion, unsupported by the things you have said previously, even if I granted everything you have said before. Sparhafoc pretty much nailed it why this is a complete non-sequitur.

Yes, biology is very complicated, and it is quite apparent that you understand very little about it. The fact that biology is complicated, and even granting for the sake of argument that no scientific explanation exists for any system in biology....this doesn't give any credence to "intelligent design". None whatsoever.

About this:
See FIGURE 4A


The paper says "the results revealed that four TMD amino acid substitutions (E15A, V19A, I25L and V26L) were sufficient to render the SIVcpz Vpu active against human tetherin". So they are changing amino acids at positions 15, 19, 25, and 26 in that diagram.

Blue is chimp SIV and yellow is human HIV. they mix and match the pieces.

- is no anti-tetherin activity
(+) is a little bit
+ is some
++ is a lot.

In the first column under "release". Note how they never test amino acids 25 and 26 separately.
This figure
1614614592313.png
Amino acid 25 and 26 don't need to be tested separately. If you look at the most bottom recombinant, where 25 and 26 are the only critical residues present, there is no anti-tetherin activity. So looking at one substitution at a time would be redundant.
Also note how they never test position 15 separately from either position 19 or position 25-26.
The same with 15 and 19. Looking at EK505 AxxxAxxxA. Substitutions at 15 and 19, together with the non-critical position of 11, also aren't sufficient to establish even mild anti-tetherin activity. And again, looking at them individually would be redundant.

You have a point with 15, 25 and 26. Which also what I noted before:
It does say that the interaction for sufficient antagonism involves more sites than these, it is just that these four residues are critical ones, requiring at a minimum four mutations. Or three to achieve a "low" interaction, if you look closely at the figure.
So yeah, at a minimum, three substitutions (15, 25 and 26) are needed for at least "low" interaction. For the same degree of interaction, all four are needed.
Since they didn't test every path, they can't say it is or isn't gradual.
That's not at all the case. They have determined that some substitutions, even together, don't increase interaction.
Also note that some of the paths they tested were gradual. We go from - to (+) to + to ++. This is on the evolution of HIV-1 group N's anti tetherin activity.
Yeah, they are "gradual" if you talk about steps in terms of involving multiple substitutions. Of course, each substitution is a step in its own right so, no.
That paper is inconclusive about whether all four amino acids had to change at the same time.
At least three together are needed to establish at least some level of interaction. That is conclusive.
 
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