What I read was a paper from Dan Weinreich called Darwinian Evolution Can Follow Only Very Few Mutational Paths to Fitter Proteins. In this paper they engineering 2^5 = 32 strains of E. coli with 5 different basepair substitutions in a gene that encodes resistance to a certain kind of antibiotics. Then they simply measured the fitness of each of the strains, and constructed a hypercube, like Sewall Wright suggested first in 1932 (before anyone knew anything about genes! he just called them allelomorphs). If you make a 5-cube, like Wright sketched:

If every mutation gives you a fitness boost (as the literature showed they individually do) you should be able to get from wildtype (far left) to 'fully mutated' (far right) in 120 different ways. This would be something called a Mt. Fuji landscape, with one peak. All paths go 'up' - which is essentially the null hypothesis that this paper was testing. At the time, I hadn't thought much about any other possible concepts -- being taught from the clinical oncology more-mutations-is-bad canon -- the more mutations a cancer has, the worse (more fit) it is. (n.b. we can talk a lot about different 'kinds' of mutations - like passengers vs drivers, some other time, and also there's the whole fact that mutational effects are likely context dependent -- but we'll get to that later). Anyways, this is where the hair on fire part came for me. After they measure all the corner's fitnesses, they found that

**only 18 paths**existed to get from left to right - and showed this figure:

There I sat, with my hair on fire, and a bap dangling out of my mouth. My world had changed forever. What they showed here was empirical proof that the theoretical possibility that some combinations of mutations (even if they are individually beneficial) can be deleterious! That means to two beneficial mutations could add up to a fitness penalty. This is something called epistasis (actually it's a special type called reciprocal sign epistasis, which you can read more about here). While this was known to other members of the scientific community, it was not to me, and this set of a bunch of thinking that led to the idea that Dan Nichol and I (and friends) explored in our 2015 paper Steering Evolution with Sequential Therapy to Prevent the Emergence of Bacterial Antibiotic Resistance. Here, we used a set of fitness landscapes that were measured in a similar way to the above description, but for a lot of drugs, that were published by Mira et al. together with a mathematical model that Dan came up with.

This model is a time homogeneous absorbing Markov chain model of evolution that requires assumptions about the population all being on a single corner of the hypercube at any given time (often referred to as Strong Selection Weak Mutation (SSWM)). Dan then calculated the probability of any given mutation from corner

*i*to corner

*j*($P_{ij}$) based on changes in fitness from one corner to the next, like this:

Using this, and some matrix multiplication, we came up with the cute idea that

**evolution doesn't (necessarily) commute**- that is, the evolutionary outcome could be quite different if you applied drug A and then B, as opposed to drug B and then A.

Given that many of the landscapes have more than one peak, there are also a number of situations in which evolution has to make a choice... it can go uphill in more than one direction. You can visualize this like a series of hills in which the population is 'walking up' them. Given that the population can't 'see ahead' but can only make decisions about going 'up' instead of 'down', you can imagine that a population could easily evolve to an optima that is not globally optimal. You can see an example below (in panel (a)) where a strain starting at the yellow circle would move uphill to the blue triangle and then have to choose 'left' or 'right'. (obviously the geometry of this is wrong, but it is the best we can do as humans to visualize)

**collateral sensitivity changing depending on evolutionary contingencies**.

This led us to want to

**do the experiments**. So, we continued our collaboration with Robert Bonomo at the Cleveland VA hospital, and performed 60 replicates of the same experiment - 60 what we now term

**evolutionary replicates**. Just showing the first 12, we see evidence for the different trajectories encoding different fitnesses through time, here:

Out of curiosity, we wondered how common it would be to get a different answer to the question: If I give one drug (drug A) and then another (drug B), how much variation could I see in collateral response. To answer this, we used another version of the mathematical model from our first paper (which you can download here, along with the data needed to redo our analysis). It turns out that there is

**wide**variability in collateral sensitivity (according to our mathematical model), so much that any one repeat of an evolution experiment could give you an opposite answer (could reveal collateral sensitivity) when the very next one could reveal cross-resistance.

This is sorta bad news... but to try to find the bright side, we propose using a new metric, which we call Collateral Sensitivity Likelihood (CSL), which is a measure of a sequence of drugs providing

**any**collateral sensitivity at all. This would make for safer recommendations -- where what you want is some method for clinicians to rationally choose a drug ordering that has a high probability of being better (or the opposite, a low probability of the drugs inducing resistance to one another).

So - from hair on fire to 5 years of research later, we finally were able to get this story out there. We published it last week, and you can read the whole paper, which is open access, here: Antibiotic collateral sensitivity is contingent on the repeatability of evolution. Lots more details and figures are available there...

In addition to making the code and phenotype data available (in the embedded github repo link), we also performed whole genome sequencing on 12 of the evolutionary replicates, and we uploaded those data to the NCBI Sequence Read Archive (SRA), and they are freely available through accession code PRJNA515080, or through this link. So, hurray for #openscience - we'd love any secondary analyses or ideas for future projects. Lots to think about.

If this research interests you, please check out our lab page to see what else we're up to. We're trying to apply evolutionary thinking, mathematical models and experimental evolution to cancer and pathogens to ease suffering.