It was surprising to me as a practising mathematician, after my first ‘professional’ contact with bacteria, just how poorly understood antibiotic resistance is. For example, we are told by doctors to complete the full course to prevent antibiotic resistance, but the science behind such a statement, long since medical textbook, seems to be lacking. And it’s not just me that thinks so: L. B. Rice. Bacteria by the book: Response. Science, 322:853–854, 2008. Only relatively recently do we see this dogma challenged with explicit clinical reviews of optimal treatment duration for a range of infections, such as R. Pugh, C. Grant, R. P. Cooke, and G. Dempsey. Short-course versus prolonged-course antibiotic therapy for hospital-acquired pneumonia in critically ill adults. Cochrane Database Syst Rev, (10):CD007577, 2011.

In this talk I’ll give an overview of my personal and highly biased (and naive) perspective of how mathematical theory has been used, tested, destroyed, misused, oversold and, ultimately, successfully applied to the science of how we use antibiotics. This ranges from clinically trialled predictions of how to manage drugs in hospital-wide settings to how we interpret bacterial growth data from disk diffusion tests that are performed daily in every hospital globally.

Of interest to me is clinically-relevant drug efflux, in particular the efflux pump, AcrABZ-TolC, that was recently implicated in the death of a patient where resistance evolved de novo in Salmonella during treatment (J. M. A. Blair et al. Acrb drug-binding pocket substitution confers clinically relevant resistance and altered substrate specificity. Proceedings of the National Academy of Sciences, 112(11):3511–3516, 2015). Adaptation in the acr operon was rapid and genomic changes in the Salmonella were observed from the first day of treatment, overnight!

We use acr as a model for resistance in the lab and have data to show that doxycycline-treated E.coli
populations can also gain acr mutations overnight and, moreover, subsequent rounds of doxy treatment see E.coli cleave the entire DLP12 prophage from its chromosome, with an interesting consequence. These genomic changes, plus one or two others, create an Ecoli “uber-mutant” within 96h that grows more quickly to greater population densities than its ancestor whether, or not, the antibiotic is present; so much for rK constraints during selection for Ab resistance! (Although no-one seems to believe the ecologists’ rK theory anyway, anymore.)

Plus: why do microbiologists spend up to £30,000 on spectrophotometers when we can make them for £50?