Predicting the evolution of superbugs

In celebration of the recognition, Wahl presents the annual Bucke lecture on April 2 at 7:30 p.m. in Room 3250 of the 3M Building.

Wahl, from the Department of Applied Mathematics, says her investigations into the probability that a mutation could confer some benefit to a population started with some "beautiful mathematics from the 1920s-30s addressing these sorts of problems."

For a mathematician, biology can present so many interesting questions and possibilities.

"What's the probability that this gene gets off the ground once the mutation has happened? What's the probability that the mutation can spread through the population?"

"The mathematics that was done then (1920s and 1930s) was all for a constant population size and for a fixed generation time so everybody reproduces in the spring and then all of the surviving offspring reproduce again in the spring. The generation time is always one year long and then everybody has … the most basic discrete offspring distribution that mathematically you might think of using."

But that's not how real life works.

When it comes to bacteria and viruses, the reproduction strategies are vastly different from the model described above.

"The population size might fluctuate hugely, there's no season, so generation times are asynchronous as well as overlapping and they are also of different lengths," says Wahl.

"Especially for viral populations the virus has to first bump into a cell and infect it and then once it's in the infected cell, the generation time is roughly fixed, but that bumping in time can depend on a lot of factors so generation times vary a lot … randomly and then the offspring distribution for bacteria -- it's not a distribution which can be anywhere between zero and five offspring, it's two or one or zero. A lot of my work is taking these beautiful mathematical results and doing the same thing but trying to add some more realistic assumptions for microbes."

As an example of applying her work, Wahl points to modern drug treatment of AIDS.

"For HIV, just a single base pair mutation can confer tremendous resistance to a single drug, the drug can be 50 times less effective."

Now suppose the rate of the mutation is one in a million. At first that sounds like slim odds for a mutation. However, when you consider that an infected person can carry a virus load of millions upon millions, the odds of developing resistance doesn't seem that unlikely.

If, however, you started a drug regimen simultaneously with three drugs, then the odds of resistance decrease dramatically. As Wahl explains, when "triple-drug cocktails are prescribed for HIV, then you need three mutations simultaneously to be resistant to three different drugs."

In other words, if one mutation confers resistance at a rate of one in a million, then the chance of another mutation occurring at the same time for resistance to two drugs would be one in one thousand billion. The odds are even less for three mutations happening at the same time (the rate becomes a number with 18 zeroes after it).

Part of building a mathematical model of microbes depends on your starting point.

"We try to put in just the very most basic assumptions about the life history of the organism and that already complicates things so much, it's unbelievable… that's why it's research."

Following the Bucke Lecture, a complimentary reception will be held at Michael's, Room 3340, Somerville House.