Patterns and proofs

Superbugs vs maths: finding the path of least drug resistance

It’s mathematics against bugs. Vojta Kolencik

In a recently held poll, the Medical Research Council asked two questions. First, what medical advance from the past century has had the greatest impact? Responses ranged from MRI scanners and genome sequencing, but a good heap of the praise went to antibiotics. This is understandable, given how well drugs like penicillin have battered diseases like tuberculosis.

Second, what would the most important medical discovery be in the next 100 years? Although answers included cancer treatment, personalised medicine and tissue regeneration, some people had a different suggestion. They said we need new antibiotics.

Having developed one of the most useful medical treatments in history, we are now at risk of losing it. The problem is resistance: antibiotics put evolutionary pressure on pathogens, so those that are resistant to treatment can have an advantage over other strains.

One solution is to develop new drugs, which work against resistant strains. But keeping up with infections in this evolutionary arms race can be an expensive and difficult business. As a result, researchers have increasingly been looking at how we might extend the usefulness of existing drugs.

There are two important issues to address. What are the factors that drive pathogen resistance? And how can we reduce the risk of it happening? Because drug resistance is a dynamic process, with pathogens evolving within people and spreading between them, mathematical models can be a useful way to explore these questions.

The cost of mutation

When a pathogen – be it a bacterium or malaria parasite – picks up a mutation that helps it resist treatment, there is often a cost in the form of reduced reproductive fitness. So although the organism is now better at shrugging off drugs, it won’t be able to generate so many offspring.

Superbug: MRSA and a dead white blood cell. NIAID

Earlier this year, researchers at Princeton University found that the optimal balance between resistance and fitness costs can depend on location. Strains of the superbug MRSA that circulate in hospitals often have broader resistance to drugs than those found in the community, but they also have greater costs associated with mutation. Could the community-associated strain - whose reproductive ability seems to suffer less when developing resistance - therefore outcompete and replace the hospital strains?

Using a model of disease transmission, with people moving between hospital and the community, the group found that the two different strains could end up coexisting. This is because treatment rates are high in hospital, so highly resistant strains have the upper hand even if their reproductive capacity is poor, whereas treatment is less intense in the community, so strains that can generate lots of progeny have the advantage.

Extending drug lifespan

Treatment levels can also affect how quickly pathogens evolve to become resistant. The rate of this evolution depends on two things: how often resistance-conferring mutations actually appear and how much evolutionary pressure is placed on a new mutant strain.

The first process can be curbed by treating a patient. If the infection is briefer, there will be fewer pathogens, and hence a smaller chance that the crucial mutation will occur in one of them.

But researchers at Penn State and Queen’s University have argued that intense treatment can be a “double edged sword” when it comes to diseases like malaria. Although treatment reduces the chance of mutation, if a drug resistant parasite does appear, it will have a big advantage over its non-resistant peers. The researchers suggest that using drugs sparingly could therefore reduce the amount of evolutionary pressure on the parasite to develop resistance, and hence lengthen drug lifespan. They acknowledge that heavy treatment might sometimes be needed, but note that “we need to be very clear about when and why that is”.

New vs old

Although there is still much to understand in terms of increasing drug lifespan, most research efforts remain focused on finding new drugs. Biologists at Queen’s University are now looking at ways to compare the effectiveness of the two approaches.

In a recent study (available as a preprint), they used a simple mathematical model to explore two potential strategies: increasing the expected lifespan of a drug, or increasing the frequency at which new drugs appear. In both scenarios, they found same number of drugs are used before no effective treatment remains. However, their results imply that extending the lifespan of a drug creates a longer time period in which there is an effective treatment supply. In other words, slowing evolution might be more effective than boosting the discovery of new drugs.

The researchers do not dispute the importance of drug development, and point out that we should not necessarily focus on approach over the other. However, their results do add to growing suggestions that if we want to tackle the problem of drug resistance, we should put more emphasis on understanding - and controlling - pathogen evolution.