New Mathematics Could Neutralize Pathogens That Resist Antibiotics

A “time machine” algorithm, backed by experimental data, reveals how to cycle drugs to reverse resistance

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A new algorithm that deciphers how bacteria genes gain resistance to antibiotics could help improve drug cycling regimes.

Bacteria that make us sick are bad enough, but many of them also continually evolve in ways that help them develop , making our medications less effective or even moot. Doctors try to reduce the evolution by cycling through various drugs over time, hoping that as resistance develops to one, the increased use of a new drug or the widespread reuse of an old drug will catch some of the bugs off guard.

The plans for cycling drugs are not that scientific, however, and don’t always work efficiently, allowing bacteria to continue to develop resistance. Now a new algorithm that deciphers how bacteria genes create resistance in the first place could greatly improve such a plan. The “time machine” software, developed by biologists and mathematicians, could help reverse resistant mutations and render the bacteria vulnerable to drugs again.

Miriam Barlow, a biologist from the University of California, Merced, first hit on the idea while trying to predict how antibiotic resistance would evolve several years ago. But she lacked the experimental data or the mathematics to quantify it. “We were pushing evolution forward, trying to predict how antibiotic resistance would evolve, and we saw a lot of trade-offs,” Barlow says. Introducing an antibiotic might lead to bacteria developing resistance but it might also lead to them losing resistance to some other medication. So Barlow partnered with mathematicians, including Kristina Crona from American University in Washington, D.C., and tried to figure out a series of steps to make those losses of resistance as likely as possible. Their work was May 6.

The researchers took as a starting point TEM-1, a protein stemming from an extremely common gene that confers resistance to penicillin. They considered four possible independent mutations that can occur in the gene, all of which confer resistance to new antibiotics, and they selected a range of 15 commonly used and studied antibiotics. They then measured the growth rates of bacteria, as each mutation was exposed to each of the antibiotics, which let them work out the probability that the overall population of would gain or lose a mutation to adapt.

In this way the researchers could directly model possible changes to drug-resistant genes. “At every single place in the genome we can say either the mutation happened here or it did not,” Crona says. The researchers were able to sketch a network of different mutation combinations and figure out the probabilities of moving from one to the other, given certain antibiotics. They called the software for finding the path back to TEM-1, created by their collaborator, mathematician Bernd Sturmfels of the University of California, Berkeley, the “Time Machine.” Although in the real world a bacterium would not revert to its exact, prior genetic form once it had evolved, this mathematical goal revealed the best genetic targets for slowing resistance.

In models of genes, researchers charted which antibiotics would encourage which of four genetic mutations in E.coli bacteria and the likelihood of each. Each mutation is represented by a “1,” so each combination is a four-digit number. Using a particular sequence of antibiotics can lead back to the wild type, 0000. 

The researchers were surprised to find that most mutations didn’t need a long chain of antibiotics to revert to TEM-1. They also found they could revert most mutations with about a 60 percent probability, which is more efficient than current antibiotic cycling schemes. And they found that they could reach a high level of reliability with just a few antibiotics in the cycle.

Direct network modeling like this is becoming more common in biology as researchers learn how to distill problems into the correct mathematical formats. But mathematicians are still learning the best ways to navigate and optimize networks of connections that can grow in complexity. And as with any model system, real-world work must be done. “It’s an interesting mathematical analysis based on laboratory-measured growth rates across multiple antimicrobial drugs, which is all novel,” says Joshua Plotkin, who investigates mathematical biology at the University of Pennsylvania and was not involved with this project. But he adds that researchers still need to pinpoint how long the cycles should last and the necessary dosages as well as looking into how the system adapts to more antibiotics and more complex mutations. The bacterial populations’ interactions in a clinic filled with people will be far more complex than one mutation per test tube.

To that end, Barlow’s group is currently setting up an experiment that will simulate the cross-pollination of different bacterial populations, which happens in places such as hospitals where multiple patients are exposed to one another. The same mathematical process they used can also incorporate new mutations and antibiotics found in hospitals—mutations that can apply to many different bacteria, not just . “We need more mathematicians working on this,” says Jonathan Iredell, an infectious disease physician from University of Sydney in Australia. “It indicates a way forward as we are desperate to find some positive remedies to what is basically an evolutionary and ecological problem.”

Robert Beardmore, a mathematical bioscientist at University of Exeter who, along with Iredell, did not take part in the study, describes this work as trying to find the signal in the noise of bacterial resistance development. Future lab work will reveal whether the interactions the team found are strong enough to define what happens in more complex scenarios. “At the heart of what everybody wants to know is how predictable is evolution—and if it’s predictable, can we reverse it?” he says. “It’s really hard, but you’ve got to try something.”

“We're talking about managing evolution, trying to steer evolution,” Crona adds. “And that's very new.”

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