Continuing the discussion from A Ubiquitin Response to Gpuccio:
It is worth working out this math for broader understanding.
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This Art’s assertion. Having molecules bind on a single protein substrate is clearly event A and event B happening. The math here is very straight forward.
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His math depends on very large populations and limited protein structures. This is a limited view of species diversity.
His assumption that 10^20 proteins arrive every day is suspect as this assumes that 10^11 is a typical probability. The Lenski experiment over 30 years and large populations did not produce a new protein sequence de novo.
If you have to evolve a protein with 2 binding molecules and the probability is 10^11 of each protein binding then the probability of binding 2 molecules is 10 ^11 times 10^11 or 10^22…
This combinatorial mathematical problem extends to exons. How do we evolve a DNA sequence separated by exons and introns where exons typically have 150 nucleotides and their can be 10 or more per gene, If you use his number of 10^9 for each exon being matched how in the world can this structure evolve?
How does one determine this? This goes to how one detects a new protein.
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How do you know this? How and where did they test for new protein sequences?
My assumption is if a beneficial functional protein surfaced we would know about it. The announcement of consuming citrate was due to a gene duplication that activated a transport gene was announced.
Your point is right that a protein sequence could have evolved and it might not have been detected.
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Worse yet, it would not be detected without quite a bit of effort, and even then it might be missed. Even after identifying it, as you’ve seen, Behe would just dismiss it as imossible, therefore it must have been designed.
Do you have any evidence that Behe has taken a position like this?
Yes! You posted your personal correspondence with him on Turf13
I believe he said it would be very difficult for a Darwinian mechanism to explain. Please correct me if my old memory is failing 
Depends on how it was beneficial. The mutations that permitted aerobic growth on citrate were found because of the marked increase in cell densities. That was because bacteria were able to utilize an additional carbon source and keep replicating to a higher population count. I can say from experience that the first reaction to seeing the cultures would be: “Nuts! I either made the media wrong or there’s contamination in the cultures” (That’s because I’ve made those mistakes 
). It was a very startling change and confirmed to not be the results of an experimental mistake. Other beneficial changes could be harder to identify.
Lenski noted that beneficial mutations (point and/or rearrangements) arose all the time in the experiment. That is, when he ran competition experiments between generation numbers he found those that out-competed others. The population was a continuously changing set of genomes and competitive landscape. This shifting and turnover occurred all the time over the course of the work. Some mutations his group was able to map, but most of the generations are not characterized.
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“Very difficult” doesn’t appear to be a problem because in the case of Turf13 it was evolutionary mechanisms that gave rise to the protein.
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