# An Open Letter to Dr. Michael Behe (Part 6)

Dear Dr. Behe

Reflecting on your previous post, and the current one, I would like to note that both your mutation rates (10-4) and effective population size (109-1010) are too high. By a factor of around a hundred thousand.

The commonest estimates for HIV mutation rates are between 1x10-5 and 4x10-5, with 2.5x10-5 the most common. Well, what’s a half log unit between friends? More serious is your population size estimate. Here I’d like to introduce you to the concept of effective population size.

Your number is the total population of viruses. Now, not all members of a population reproduce. In population genetics, the effective population size is defined as the number of adults in a population contributing offspring to the next generation (yes, I know that viruses don’t have “adult” reproducing stages, bear with me for a moment). In a population of adults, some adults may not reproduce because there is a difference in the number of males to females. Some may not reproduce because disease or heredity renders them sterile, so the number off reproducing members will always be lower than the total population.

In considering mutational effects, and generating new mutations, you need to consider the effective population size, not the total population size. In HIV, this is important as viruses may replicate in immune cells that die or are cleared before the virus particles can become infective, or the HIV virus goes dormant. As well, there is a very high replicative failure rate in HIV, many copies of the virus are defective and cannot make copies of them selves, or infect other cells.

So what is the effective population size of HIV? It’s been estimated to be between 103 and 105 (depending on the kinds of assumption you make[1]). Even using the highest estimate, this is 10,000 to 100,000 times smaller than the figure you use. You can immediately see that your estimates of the number of mutations available to HIV are concomitantly smaller.

It’s not as if you could be unware of this, your own references show the the effective population sizes are smaller. For example the Rodrigo paper (PNAS, 1999, 96:10559-61 cited in 15, see page 290 of “Edge of Evolution”) where they say:

It has been estimated that the total number of HIV-infected cells in a human host is between 107 and 108 (6). However, only a portion of infected cells produce viable viral particles that go on to infect other cells. … [estimates of infected populations] place the value at around 103 infected cells

and then go on to give other estimates of up to 105 for HIV populations. Same goes for Althaus CL and Bonhoeffer (J Virol, (2005), 79:1313572-78, also listed under 15 in “Edge of Evolution”).

The viral population in an infected patient may indeed represent such a population limited in size, since current estimates of the effective population size range from 500 to 105.

They point to some evidence from the rise of resistance in HIV that is consistent with a low effective population compared to the total population.

Coffin MJ (Science, 1995, 267:483-89), is your source for the “each and every possible single-point mutation occurs” quote. This old paper uses the total population only, they do not account for the effective population. Well, it was an early report, and this incorrect use of the total population was pointed out in a subsequent comment (Levy JA, et al., Science. 1996 Feb 2;271(5249):670-1) noting that “most of these viruses are not infectious”. All evidence points to the fact that double point mutations are not occurring once per day as you claim (see also Seo T-K et al., 2002, cited in the references. Your viral replication rates over a humans lifetime seem to be a bit off as well)

So, your comments about the ability of HIV to explore all of its mutation space in the course of a single infection is basically incorrect. Also note that these estimates of effective population size are in contemporary populations, with highly evolved, very transmissible virus. When the YRKL Glogi binding sequence and the Vpu viroporin evolved, this was in a much more weakly infective and replicative virus (the high infectivity of modern HIV can be traced directly to these two mutations), in a much smaller population of humans. So the proto-HIV, which evolved these allegedly “unimpressive” binding sites, was even more restricted in its exploration of mutations than the modern one.

You also continue to use your “impressedness” as an indicator of the reality of binding sites. The haemoglobin S binding site isn’t particularly impressive, yet you use it as your own example. Mutations in the LTR which confer survival by generating new binding sites are no less impressive than your own example.

But again, this is irrelevant. Your claim is that it takes several simultaneous mutations to produce a protein-protein binding site. The probability that two (or three) given mutations will occur simultaneously is completely independent of the function of the two proteins binding together, or how impressed we are by the function. Whether the bound proteins make a molecular machine, or just glug together, the probabilities of a given two or three site simultaneous mutations is the same.

Not all new binding sites will make a flagellum, they are more likely to make something like the L-type calcium channel, where you have a core unit that functions okay in the absence of partner proteins, but works better when partner proteins bind to it (RAMPS and adrenomedullins are similar, and my beloved imidazoline binding site may turn out to be a RAMP-like protein interacting with the LPA receptor).

The main point is that binding sites are binding sites, no matter how impressed you are with them, and you claim is that binding sites pre se are very improbable to evolve. But it is clear from the Vpu example that they do evolve, and that they contribute significantly to the survival of the virus.

And that is just Vpu, there is also the LTR’s, evolution of CXCR4 binding and binding that leads to upregulation of TRAIL. And I haven’t exhaustively looked fro all possible examples of binding site evolution.

I do hope you will publish an erratum for your book.

Yours sincerely
A male featherless biped named Ian Musgrave
[1] See this book for a discussion of effective population size in HIV, and commonest HIV mutation rates. See also Seo T-K et al., (2002) Estimation of Effective Population Size of HIV-1 Within a Host: A Pseudomaximum-Likelihood Approach Genetics 160: 1283–1293
Update 20-11-2007 I’ve tided up some typos and taken the liberty of adding in a section dealing with the references from Dr. Behe’s book.