The unexpected complexity of nothing

I don’t think I’ve covered anything theoretical in a while, so here’s an interesting modelling study that I’ve just come across in PNAS (Shah et al., 2015). It discusses a key point in evolutionary theory – that “mutations” and “fitness” don’t exist in a vacuum. More specifically, it investigates how mutations that have little effect on fitness at the time interact with other mutations in a protein under strong purifying selection. Lots of studies deal with the role of interactions (or epistasis) between mutations in adaptation and innovation, but apparently, the question is much less explored when selection is keeping things the way they are.

Shah et al.’s approach is a mixture of theory and empirical data. The protein they consider is perfectly real – it’s the amino acid-binding protein argT from the bacterium Salmonella typhimurium (yep, that salmonella), and it was chosen because its structure is well-known and relatively simple. In contrast, the mutations happen entirely on a computer, although the models used to calculate their fitness effects in a simulated population of bacteria were calibrated to match the real-world distribution of the effects of mutations under similar circumstances.

The most important of these circumstances is the fact that this protein is not actively adapting to anything. It is already well-adapted to its function, and there is nothing pushing it in a new direction. Nonetheless, mutations happen whether or not they are needed; what the authors wanted to know is whether the mutations that arise in this environment constrain the course of evolution.

The researchers took the real argT protein sequence and introduced changes. In each round, ten random mutations were proposed, only one of which made it into the next round. For each proposed mutation, they used a program designed to model protein structure to calculate the stability of the new protein. Proteins are long chains of amino acids twisted and folded into specific 3D shapes. The stability of these shapes is important because a protein that is too rigid or too floppy can’t bind the right molecules with the right strength (remember, the function of argT is to grab certain amino acids).

The simulations assumed that the real protein is pretty much optimally stable already, and either increased or decreased its stability would decrease its fitness*. Protein stability was converted to fitness in a way that a realistic percentage of mutations were neutral, kinda bad or plain lethal (you can’t have beneficial mutations here, since the original protein is assumed to be optimised for its function). Finally, the least bad mutation in each round was chosen to update the protein sequence. This procedure was repeated until the protein had accumulated 30 changes, and the whole process was replicated 100 times.

With a hundred new virtual proteins in hand, the really interesting part of the experiment could begin. The grand aim of this whole study was to examine mutations in their historical context. All mutations that were added to the original argT sequence were neutral or nearly neutral at the time of their introduction – but would they be neutral if they were introduced at an earlier point in the evolutionary sequence? And would they still be neutral, or rather, reversible, after a bunch of other mutations had accumulated on top of them?

As you may have guessed, the answer to both questions is no. Even though the final 100 proteins were pretty much as good as the original, and each of the mutations that made it through had close to zero effect on fitness at the time, taking mutations out of their context and sticking them into different backgrounds showed that their lack of effect was highly contingent on the history of that particular sequence.

The graph below summarises what happens if you take mutation 16 and either shift it to an earlier point, or take it out at a later point (a similar pattern holds no matter which mutation you start from). On the vertical axis is the fitness effect of the same mutation at different points relative to its effect at the time it actually occurred. The left side of the graph is consistently below zero – at any point before its “proper” time, mutation 16 would have been more deleterious. It only worked with all 15 previous mutations already in place.


On the right side – mutation 16’s future – fitness effects rise rapidly. The more new mutations are added, the more “beneficial” (or more precisely, irreversible) mutation 16 becomes. Even though it didn’t do much at the time, as soon as other mutations come to rely on it, you can’t take it out without royally screwing up the whole protein. The mutation has become entrenched, to use the authors’ terminology. This figure is an average of all 100 simulations; the results are pretty consistent.

Of course, there are some caveats. One of the most important is that in real populations, mutations are not necessarily fixed one at a time, and the way multiple co-existing mutations interact could be quite different from the way individual mutations affect subsequent individual mutations. Another big if is the accuracy of the software that calculates protein stability – getting from protein sequence to structure and physical/chemical properties is still notoriously difficult. In this study, considering only the first few mutations in each series (i.e. before the virtual protein diverged too far from the original with known properties) doesn’t change the main results, so the authors don’t think this is a major problem for their conclusions. There is also the fact that global protein stability, the variable used here to estimate fitness, is not the same thing as function (in this case, binding specific amino acids). However, the latter depends only on a tiny proportion of the larger structure, so global stability is probably a reasonable proxy.

It occurs to me that what Shah et al.’s study simulated is basically the evolution of irreducibly complex nothing. Here we have a protein that does the exact same thing its ancestor did (with the above caveat) despite having a rather different sequence. This utter lack of change evolved one tiny step at a time; each step dispensable, each step insignificant. Yet try to take out any of the earlier steps from the final product, and the whole edifice collapses.

Call me strange, but I find this… amusing.


*They actually repeated the entire experiment with an alternative assumption that increases in stability are neutral rather than deleterious, but they got very similar results, largely due to the fact that very few mutations actually increased the stability of argT.



Shah P et al. (2015) Contingency and entrenchment in protein evolution under purifying selection. PNAS 112:E3226–E3235


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