The Optimal Deployment of Antibiotics: Whether, How and When to Switch

Optimal control is a term used to describe the research that made much of the space-race possible. Neil Armstrong s moon landing was made possible by understanding how to manipulate a space rocket with minimal fuel expenditure. The idea behind this work is to take the same basic engineering science and to apply it by asking whether the evolution of resistance that blights antibiotic treatments can be somehow minimised by understanding how to deploy those antibiotics in an optimal way.

We can already do this, in theoretical terms, and we are able to create weird and wonderful ways of deploying antibiotic to a biological system in order to maximise its health. However, a lot of biological theory based on mathematical modeling has been proposed in the past that turned out to be plain wrong when the right experiments were done. This is especially true of population biology, the branch of biology that treats interacting populations of organisms such as microbes and other cells. Now, the mathematical modeling in this work is a mix of population biology, cell biology and genetics; while space researchers have Newton s laws to lean on, population biology has no intrinsic, physical laws. As a result, it is sometimes a feature of the field that theoretical concepts stick before they are truly tested. So, we want to test our theories to destruction to make sure they work in the lab before we eventually go on to try and persuade medical practitonners that cycling different antibiotics is a good thing to do. Certainly, it is better to cycle than to mix them into a single treatment, at least that s what our theories always say. This research will go a long way to proving that what works in theory, also works in the lab, and hopefully in practise too.

The fields of mathematical modeling and evolving microbial microcosms provides a success
story in how cellular and population-level theoretical modeling can come together to
provide new insights and theories of how the most populous organisms on the planet, and
indeed in our own bodies, microbes, evolve in time.

I am a member of two networks seeking to exploit this synergy, MEMMS
(http://www.mmems.org/) and DIMME (via http://www.nescent.org) where antibiotic
resistance is seen as one of the most important of all challenges and I propose that
appropriately targeted mathematics, when built around new experimental research, can make
a real difference to this field.

In their review Antibiotic cycling or rotation: a systematic review of the evidence of
efficacy , Antimicrobial Chemotherapy, 2005, Brown and Nathwani pose numerous questions
regarding the efficacy of cycling different antibiotics in an antimicrobial treatment. Is
the order of rotation critical? and What is the optimal duration of each cycle? They
indicate that the evidence is sparse as to whether one should cycle antibiotics, or mix
them in an ideal treatment.

Mathematical and microbial modelling can answer questions like these, provided the
correct experimental, theoretical and computational techniques are used. So, yes, indeed,
the order of rotation is critical, moreover periodic cycling or rotation will almost
never provide the best treatments. We can show that the deployment of antibiotics to
laboratory systems should be based on some form of non-periodic, cycling treatment but
this is ongoing research based on an analysis of large classes of stochastic models of
evolving bacterial microcosms in continuous culture.

The idea of this first, theoretical aspect of the project is not to minimise antibiotic
usage, rather it is directed at better understanding how one can ascribe a numerical
health state or measure to an ecosystem, such as that found in a mammalian gut, and
to then find a deployment protocol for the antibiotics to maximise that measure.

The second part of this research project is to use microbial models to test this very
robust theoretical conclusion that in turn provides a very clear structure for
experimental design based on choosing antibiotic switching times and deployment
concentrations. For this, I am seeking some funding to undertake experimental work and
conduct the experiments with a collaborator in a lab at Oxford University s Zoology
Department using the human pathogen Pseudomonas aeruginosa and two bacteriostatic
antibiotics.