How maths can help in neutralizing antibiotic resistance

This is a beautiful example of how one branch of science can help another one.

We all know that bacteria can evolve to develop resistance to antibiotics making them ineffective as time goes by. Medical professionals 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. This, however, doesn't work very efficiently making the bacteria win the games most often. 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, 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 published in PLoS ONE recently.

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"Rational Design of Antibiotic Treatment Plans: A Treatment Strategy for Managing Evolution and Reversing Resistance"
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.01...

Abstract of the paper:

The development of reliable methods for restoring susceptibility after antibiotic resistance arises has proven elusive. A greater understanding of the relationship between antibiotic administration and the evolution of resistance is key to overcoming this challenge. Here the researchers present a data-driven mathematical approach for developing antibiotic treatment plans that can reverse the evolution of antibiotic resistance determinants. They have generated adaptive landscapes for 16 genotypes of the TEM β-lactamase that vary from the wild type genotype “TEM-1” through all combinations of four amino acid substitutions. They also determined the growth rate of each genotype when treated with each of 15 β-lactam antibiotics. By using growth rates as a measure of fitness, the researchers computed the probability of each amino acid substitution in each β-lactam treatment using two different models named the Correlated Probability Model (CPM) and the Equal Probability Model (EPM). They then performed an exhaustive search through the 15 treatments for substitution paths leading from each of the 16 genotypes back to the wild type TEM-1. They identified optimized treatment paths that returned the highest probabilities of selecting for reversions of amino acid substitutions and returning TEM to the wild type state. For the CPM model, the optimized probabilities ranged between 0.6 and 1.0. For the EPM model, the optimized probabilities ranged between 0.38 and 1.0. For cyclical CPM treatment plans in which the starting and ending genotype was the wild type, the probabilities were between 0.62 and 0.7. Overall this study shows that there is promise for reversing the evolution of resistance through antibiotic treatment plans.

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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. It’s an interesting mathematical analysis based on laboratory-measured growth rates across multiple antimicrobial drugs. How it works in real world situation has to be seen. 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.
We are waiting with bated breaths to see the results in hospital environments and how scientists can get an upper hand over the little devils. Watch this space!

Here is an update...

Recently scientists have found that Combination Of Three Drugs Increases Effectiveness

They grew E coli bacteria in a laboratory and treated the samples with combinations of one, two and three antibiotics from a group of 14 drugs.The biologists studied how effectively every single possible combination of drugs worked to kill the bacteria. Some combinations killed 100% of the bacteria, including 94 of the 364 three-drug groupings tested.

According to Pamela Yeh from the University of California, Los Angeles (UCLA), the success rate might have been even greater if the researchers tested higher doses of the drugs. Elif Tekin, UCLA graduate student, helped create a sophisticated framework that enabled the scientists to determine when adding a third antibiotic was producing new effects that combinations of just two drugs could not achieve.“Three antibiotics can change the dynamic. Not many scientists realise that three-drug combinations can have really beneficial effects that they would not have predicted even by studying all pairs of the antibiotics together,“ she said.

Different classes of antibiotics use different mechanisms to fight bacteria. One class, which includes amoxicillin, kill bacteria by preventing them from making cell walls. Another disrupts their tightly coiled DNA. A third inhibits their ability to make proteins. But there had been little previous research indicating that combinations of three antibiotics might be more potent together than any two of them. “People tend to think that you don't need to understand interactions beyond pairs. We found that is not always so,“ said Van Savage, a UCLA associate professor.

The researchers combined techniques from biology and mathematics to determine which groups of antibiotics would be most effective.