I have been looking at the book The Evolution of Biological Information, by Christoph Adami. I have criticized his definition of information, invocation of Maxwell’s demon, and attempts to show an increase of information along the line of descent. Today, let’s look at his analysis of HIV evolution in response to antiviral drugs.
Section 3.3 of the book is titled “Information Loss and Gain in HIV Evolution.” The story he tells is that, first, the introduction of an inhibitor targeting HIV’s protease causes a decrease in information. Recall that in his model, the genome has information about the environment. When the environment changes, such as by introducing the inhibitor, the information in the genome is no longer accurate and thus no longer information. As such, the quantity of information in the genome decreases. Secondly, as HIV adapts to the protease inhibitor, it is accumulating information about the environment. The genome now “knows” that there is an inhibitor in the environment.
Analyzing HIV Genomes
He supports his story by analyzing HIV genomes. Firstly, HIV genomes taken from patients undergoing the inhibitor treatment show an increase in entropy and thus, in his definition, a decrease in information. Secondly, over time there is a “small but steady increase of information” for the HIV for those being treated.
But the story has a big problem. The people being treated for HIV are not an independent population. Rather, they are a stream of new people predominantly infected by the wild type HIV. This means that the data is not measuring how HIV is evolving over the years in response to the inhibitor. What is actually being measured is how HIV responds to changing treatment protocols over the years.
Furthermore, Adami measures the two parts of his argument differently. Throughout the book, Adami typically uses the simplifying assumption that each position in a sequence is independent of the others. This assumption is not strictly true, but it allows calculation of an approximation to the sequence entropy. He uses this technique to show that, when subjected to the inhibitor, sequence entropy increases, thus demonstrating a decrease in information.
Not the Results He Expected
However, when Adami applied this to look at how the information level has changed over time, he did not get the results he expected. Rather than showing an increase in information over time, it showed a decrease. In this case, Adami blamed his approximation and adopts a more sophisticated one. He adds a term considering pairwise dependency between sites, where two sites show a pairwise correlation. This, he hopes, will get him a more accurate estimate of the sequence entropy and thus the information.
However, something is clearly wrong. He is considering 76 positions, which means that his maximum information should be 76 mers, where mer is the maximum information for one position. However, outside of one outlier, his figure showing total information varies from around 74 mers to 80 mers. His calculation has these sequences either just below or above their maximum theoretical information capacity. This cannot be correct.
To understand the problem, consider what happens if three positions are correlated. The first position will correlate with the second, the second position will be correlated with the third, and the third position will correlate with the first. Adami’s method adds up all of these correlations. But they are not independent correlations and thus adding them is a mistake and leads to overcounting.
Higher-Order Correlations
The problem is that his method does not take higher-order correlations into account. He notes that he does not have the data to estimate with any reliability. He says that, instead, “we therefore have to hope that this contribution is small.”
We have good reason to believe that the contribution will not be small. In the case of developing resistance, mutations that produce resistance are often damaging. They have to be compensated for by other mutations. But there are typically many different compensating mutations that could occur. This produces correlations among a large number of sites.
What Adami’s results actually show is that when HIV is subjected to the protease inhibitors, the sequence variability increases. There are a number of different ways that the virus can attempt to escape the protease’s effect. This results in a more diverse population. This is increasingly true as newer approaches to fighting HIV are developed.
As such, Adami’s story does not make sense because he’s not looking at the progress of evolution but at the progress of approaches to fighting HIV. He changes his method of estimating the information content of genomes between the two parts of his story. His second is flawed and produces non-sensical results. At the end, all his results show is that under the effects of the inhibitors, HIV increases sequence variability and that’s due to the variety of ways to develop resistance.