Take it to the limit (one more time)

The postdoc who's been working on the perl simulation of USS evolution now has everything working, including the equilibrium test that I said I would post about but didn't. I'll have to describe this test later (or maybe she will) because here I want to comment on a different issue.

One problem with simulating biological processes is that they need to be very unrealistic, otherwise they can't be made to work at all. One of the unrealistic features of our USS simulation is the need to use unrealistically high mutation rates, as much as a million times higher than real mutation rates. It's possible to simulate lower mutation rates, but each simulation would take years to run, rather than minutes or hours.

It's tempting to think that the most realistic simulations will be the most informative, but that's far from universally true. In most models the effects of changing variables, and the interactions between variables, are at least as important as the absolute values of the variables. In our USS model, we want to understand how changing each of the following affects the equilibrium numbers of perfect and imperfect USS sequences:

1. the mutation rate;
   
2. the strength of the uptake bias;
3. the ratio of mutation rate to uptake bias.

The most realistic simulations would use very low mutation rates, and they'd take a lllooonnngg time to run. But we may be able to identify the patterns of change by doing simulations with much higher rates.

For convenience we could start with a mutation rate and uptake bias that let the simulation reach equilibrium in 20 minutes, and test higher and lower rates, keeping the bias constant. Does a higher rate mean more USS or fewer? How big is the effect of a 2-fold change in rate? A 4-fold change? A 10-fold change? What happens to the imperfect USS? Next we can keep the rate constant and vary the bias. Does a 2-fold higher bias give more USS? How many more? What about a 2-fold lower bias? What happens if we change both mutation rate and uptake bias, keeping the ratio constant?

Such experiments can suggest the fundamental properties of the system even though they use very unrealistic values. Once this is done, there are several more directions to go.

First, we don't need to just assume that the properties we've found are likely to hold at more realistic values of rate and bias. Once we understand what happens when mutation rates are unrealistically high, we can think clearly about whether this should change when mutation rates are much lower. We can test our thinking by making a prediction of what we should see in runs with lower mutations rates, and then doing a few runs that test our predictions. If we have also tracked how long each simulation took to reach equilibrium, we'll be able to predict how long these more realistic runs should take, letting us decide whether they're practical or not.

Second, we can devise new tests based on our observations. For example, we should start with simple simulations where cells have no bias towards imperfect USS. But once we understand the properties of these simulations, we can introduce this extra bias and see what happens. Better, we can first predict what we think should happen, then test our predictions. These predictions and tests can be done at high mutation rates so they run fast. Once the results are in, we can consider whether we expect the same effects at low mutation rates, and test key predictions.

Once we're fairly sure of the results, we can work on polishing the paper that will report them. And because paper-polishing takes a long time, we can have a few key simulations running at very low mutations rates while we do this. The final paper will either report that the very low rates gave the expected result, or consider why they didn't.