Understanding how often cells develop mutations: Harder than it seems

Cells divide. But how often those divisions result in mutations to the cell’s DNA is fundamental to a number of problems in biology, from infectious diseases to cancer. When the cells in question are bacteria, the mutation rate—which is how often, on average, mutations occur—becomes vitally important to a wide array of issues related to human well-being.

“Perhaps the most important example of the mutation rate in public health research is antibiotic resistance,” said Qi Zheng, PhD, associate professor in the Department of Epidemiology at Biostatistics at the Texas A&M School of Public Health, who studies mutation rates.

Contrary to the common belief, antibiotic resistance is not someone’s own cells becoming somehow immune to the antibiotics used to fight infections. Instead, it is the bacteria themselves that are sometimes able to acquire an uncanny ability to survive the barrage of the very agent designed to kill them, and when they do, they are able to pass that resistant gene on easily—because they have a survival advantage when exposed to an antibiotic.

What is unclear and often misunderstood, is how to measure the rate at which the bacteria are able to acquire beneficial (for them) mutations. This is an important number, because it can indicate which types of bacteria are more likely to become resistant. “For example, if you wanted to find out if a strain is more prone to developing resistance than another strain, you’d have to measure the mutation rates of both strains,” Zheng said. “Unfortunately, that’s not easy: Even textbooks are struggling with a precise definition of the mutation rate.” He published an article earlier this year in the Bulletin of Mathematical Biology that tried to explain what was wrong with the existing definitions and how they can be improved.

Zheng’s interest in this area stemmed from a rather cryptic note he received nearly 20 years ago, asking for a copy of one of his articles but including a short postscript suggesting that he read two recent papers about what is called the Luria-Delbrück distribution. “I was totally unfamiliar with their work, so I spent a lot of time researching it and trying to figure out why someone I’d never met was directing me to this research,” Zheng said. He went back to look at a seemingly undecipherable seminal 1949 paper. After months of work, he realized that there was a problem with some of the earlier research.

Two forms of the mutation rate, which Zheng dubbed the p-form and the u-form in his paper, are in use. Although they are two sides of the same coin, the precise relation between the two forms had been elusive for the past 74 years. As a result, incorrect formulas relating the two forms were common in the literature. “This caused considerable confusion among researchers and educators, and baffled biology students,” Zheng said. In addition to elucidating the precise mathematical relation between the two forms of the mutation rate, his paper explains the distinct roles that the two forms play in scientific research: While the p-form is suited for cellular level research, the u-form is appropriate for population-level investigations.

“As soon as I understood the mathematical nature of the problem, I realized the implications were enormous,” Zheng said. “If a cell develops a way to resist penicillin, for example, its mutation rate—in other words, the probability that the cell begets a resistant daughter cell when it divides—will help predict how virulent the strain will be.”

Zheng also created a software package that can help microbiologists determine mutation rates. “I hope that biologists will be better able to explore and report mutation rates in future endeavors,” he said.