Mathematical Modelling

Predicting the re‐distribution of antibiotic molecules caused by inter‐species interactions in microbial communities

Drug efficacy measured using pure cultures is not maintained in the presence of neighbouring microbes. Using simple physical laws, I pinpoint the mechanism for this change to demonstrate that drug efficacy can be predictably manupulated, and suggest why microbes began to co-operate and form communities.

Plasmid carriage and the unorthodox use of Fisher's theorem in evolutionary biology

The link between fitness and reproduction rate is a central tenet in evolutionary biology: mutants reproducing faster than the dominant wild-type are favoured by selection, otherwise the mutation is lost. This link is given by Fisher's theorem under …

Canonical host-pathogen tradeoffs subverted by mutations with dual benefits

Tradeoffs between life history traits impact diverse biological phenomena, including the maintenance of biodiversity. We sought to study two canonical tradeoffs in a model host-parasite system consisting of bacteriophage lambda and _Escherichia …

Fluorescence photography of patterns and waves of bacterial adaptation at high antibiotic doses

Fisher suggested advantageous genes would spread through populations as a wave so we sought genetic waves in evolving populations, as follows. By fusing a fluorescent marker to a drug efflux protein (AcrB) whose expression provides _Escherichia coli_ …

Regulation of multi-drug efflux pump AcrAB-TolC

The abundance of AcrAB-TolC protein seldom correlates with the number copies of _acr_ operons in _Escherichia coli_. The regulation of this efflux pump is complex, so to understand this phenomenon I modelled its entire regulatory network.

The unconstrained evolution of fast and efficient antibiotic-resistant bacterial genomes

For decades it was hypothesised that the growth rate of populations and their size engage in a trade-off, but the data was always inconclusive. Using bacteria, we set off to underpin a physical mechanism for this trade-off, and then explain why it is not always found in the data.

Using a Sequential Regimen to Eliminate Bacteria at Sublethal Antibiotic Dosages

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Testing the optimality properties of a dual antibiotic treatment in a two-locus, two-allele model

Mathematically speaking, it is self-evident that the optimal control of complex, dynamical systems with many interacting components cannot be achieved with ‘non-responsive’ control strategies that are constant through time. Although there are notable …