School of Mathematics

Robert Beardmore

Robert Beardmore abstract

Robert Beardmore, Biosciences, University of Exeter

As a mathematician trying to develop a quite narrow area within dynamics (singularDAEs - it’s a bit of a backwater), I’d always slightly envied Mathematical Biology from afar, with it’s large conferences and important questions ranging from embryo development to cancer progression. In the end temptation was too great and, having started to think about evolution and how rapid it can be, and how for example, the competitive exclusion principle seemed to make no sense, I started to read some evolutionary microbiology literature. Inspired by the work of many evolutionary biologists and seeing what ‘physicists’ were doing in systems biology, wetook the plunge, left the comfort of a maths department, and started a lab studying the evolution of simple (if there issuch a thing) microbial populations.

Now Tom Ferenci had published a paper in Science in 2005 providing genomic data showingthat the competitive exclusion principle does not seem to hold in E.coli populations, sowe began to think about modifications of the chemostat equations that would permitmultiple coexisting metabolic phenotypes: Tom suggested stable polymorphisms comefrom metabolic and physiological constraints, not only from the number of available extracellular resources.This gave us what we needed for the equations, but the modifications needed trade-offs to do anything interesting.

So we started to look for trade-offs, both in theory and in data, and found some evidencefor one that had been proposed between growth rate and growth yield (the faster you grow, the less efficient you are), although this turns out to be quite subtle and we still don’treally understand it. In the right environmental conditions faster growth can also be more efficient.

As growth rates can be manipulated using antibiotics, we started to play with them tooto try and somehow control the trade-offs. But on reading the antibiotics literature, much of it clinical, it became clear that some commonly-accepted statements made little sense in the contextof simple mathematical models: “random" antibiotic allocation in the ICU optimally selects against drug-resistance (really?!), taking the full antibiotic course mitigates resistance mutations (eventhough it must maintain selection pressure to resist), multi-drug combinations mitigate drug-resistance(yes, resistance may require multiple mutations but combinations can also increase selection pressure).

Questions like these are where we now tend to concentrate our efforts. Our most interesting recent result seems to be that the sequential-in-time deployment of two antibiotics can force a population to collapse, at low dosages and when a scalable multi-drug efflux pump is encoded in the chromosome,even though the populations will proliferate reasonably happily in high-dose combinations of the drugs.

Evolution in this system is very fast as the mutation rates are high: the efflux pump is ’scalable’ because it sitswithin a genomic region that is duplicated, triplicated even, when the drugs are used, a mutational event that seesa 10-20% increase in the length of the E.coli chromosome within two days, or so, because of the use of the drugs.

This is joint work with Hinrich Schulenburg, Ivana Gudelj, several post-docs and PhD students.