In The Edge of Evolution, Michael Behe argued that resistance to the drug chloroquine was as complex a genetic change as evolution could ever achieve.


Unfortunately, this conclusion is based on flawed reasoning about the probabilities of multiple events in evolution.



At the heart of Behe's argument is the claim that the odds of getting two CCC's are the square of the odds for just one.


But that logic is mistaken, especially for protein-to-protein binding sites.


Behe overstates the specificity required for a protein binding site.


Click for Sean Carroll's review in Science magazine.


Edging towards Irrelevance:

Part 1
Part 2
Part 3
Part 4
Part 5

Click Here for a complete copy of this web posting in PDF format.


Rigging the Odds

Cells are filled with protein-to-protein binding sites, which play vital roles in signal transduction, gene expression, and biosynthetic pathways.  According to Behe, these sites are so specific that “generating a new protein-to-protein binding site is of the same order of difficulty or worse than the development of chloroquine resistance in the malarial parasite” (Behe, 2007, p. 135). In other words, roughly one in 1020 or worse.  He goes on:


“Now suppose that, in order to acquire some new, useful property, not just one but two new protein-binding sites had to develop.    So, if other things were equal, the likelihood of getting two new binding sites would be what we called in Chapter 3 a ‘double CCC’ — the square of a CCC, or one in ten to the fortieth power.  Since that’s more cells than likely have ever existed on earth, such an event would not be expected to have happened by Darwinian processes in the history of the world.  ..  And the great majority of proteins in the cell work in complexes of six or more. Far beyond that edge." (Behe, 2007, p. 135).


Pretty conclusive, eh? And even if 1020 isn’t the right number for a CCC, even if that probability is one in 1015 or 1010, once you string together three or four such binding sites the odds of “Darwinian processes” getting there vanish into nothingness. Sort of makes you wonder why mathematical biologists haven’t thought it before, doesn’t it?  Well, if they have, they’ve dismissed it at once, because such reasoning is built around a statistical trick. That trick is demanding a fixed set of particular, highly specific outcomes for a series of unrelated events.


Here’s how it works. Let’s accept Behe’s number of 1 in 1020 for the evolution of a complex mutation like his CCC. As he admits, CCC’s have arisen multiple times in the malaria parasite population since the drug was first introduced in 1947. In fact, resistance to the drug appeared in the late 1950s and early 1960s, within just 15 years of its widespread use. So it only took a decade and a half for one of Behe’s CCC’s to emerge in the parasite population. Now, suppose that another drug, equal in effectiveness to chloroquine, were to come into wide use. According to Behe, resistance to both drugs would require two CCCs, and the probability of double resistance arising would be a CCC squared. That’s 1 in 1020 x 1020 or one chance in 1 in 1040. According to Behe’s math, that’s such a large number that we can call it impossible:


“…throughout the course of history there would have been slightly fewer than 1040 cells, a bit less than we’d expect to need to get a double CCC. The conclusion, then, is that the odds are slightly against even one double CCC showing up by Darwinian processes in the entire course of life on earth.” (Behe, 2007, p. 63).


Wow! Not even once in the history of life on earth? Pretty impressive. But the math is wrong, and it’s easy to see why. Chloroquine resistance arose in just a decade and a half, and is now common in the gene pool of this widespread parasite. Introduce a new drug for which the odds of evolving resistance are also 1 in 1020, and we can expect that it will take just about as long, 15 years, to evolve resistance to the second drug. Once you get that first CCC established in a population, the odds of developing a second one are not CCC squared. Rather, they are still 1 in 1020. Behe gets his super-long odds by pretending that both CCCs have to arise at once, in the same cell, purely by chance. They don’t, and I pointed this out in my Nature review when Behe attempted to apply his reasoning to human genetics:


Behe, incredibly, thinks he has determined the odds of a mutation “of the same complexity” occurring in the human line. He hasn’t. What he has actually done is to determine the odds of these two exact mutations occurring simultaneously at precisely the same position in exactly the same gene in a single individual. He then leads his unsuspecting readers to believe that this spurious calculation is a hard and fast statistical barrier to the accumulation of enough variation to drive darwinian evolution.


It would be difficult to imagine a more breathtaking abuse of statistical genetics.


Interestingly, Behe’s kind of math would apply only in one very special situation, and that would be if both drugs were applied in similar doses at exactly the same time, so that the emergence of resistance to one would be useless without the simultaneous appearance of resistance to the other. That, in fact, is the reason that multiple drug therapy can be effective against HIV and other diseases. By manipulating the doses of several anti-viral drugs at once, it’s possible to prevent the emergence of resistant strains of the virus. But this situation only prevails under carefully designed therapeutic conditions. You might say, ironically, that it takes “intelligent design” to produce conditions favoring the long odds he demands, conditions that don’t exist in nature.


But that’s not the only problem with Behe’s math. When he turns his attention to protein binding sites, he uses the extremely tight and specific fit between antibody and antigen as his model. On that basis, he feels justified in telling his lay readers that “…one way to get a new binding site would be to change just five or six amino acids in a coherent patch in the right way” (Behe, 2007, p. 143).  Not surprisingly, the odds of getting “just” five or six specific, predetermined point mutations to occur together in a single genome are too long to be within the bounds of probability. But that’s because, just as before, Behe has stacked the statistical deck in a completely unrealistic manner. Sean Carroll was quick to point this out in his review of The Edge:


He insists, based on consideration of just one type of protein structure (the combining sites of antibodies), that five or six positions must change at once in order to make a good fit between proteins—and, therefore, good fits are impossible to evolve. An immense body of experimental data directly refutes this claim. There are dozens of well-studied families of cellular proteins (kinases, phosphatases, proteases, adaptor proteins, sumoylation enzymes, etc.) that recognize short linear peptide motifs in which only two or three amino acid residues are critical for functional activity [reviewed in (79)]. Thousands of such reversible interactions establish the protein networks that govern cellular physiology.


Needless to say, nothing in the PNAS study supports Behe’s mistaken view of how new protein binding sites must evolve. Behe insists that each such site must include five or six specific amino acids, which is not correct, and calculates his probabilities by insisting on predetermined results, which unrealistically stacks the deck. As Carroll wrote in his review:


Behe has quite a record of declaring what is impossible and of disregarding the scientific literature, and he has clearly not learned any lessons from some earlier gaffes.


What about those “earlier gaffes?”  They have been plenty of them, but some of the most telling have involved Joe Thornton’s groundbreaking work on protein evolution. That's what we'll look at next.


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