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

Lead Research Organisation: Imperial College London
Department Name: Dept of Mathematics


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.

Technical Summary

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
( and DIMME (via 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


10 25 50
Description EPSRC C-DIP Award
Amount £83,702 (GBP)
Funding ID EP/I018263/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 01/2011 
End 01/2016
Description EPSRC Leadership Fellowship EP/I00503X/1 Bacteriophage and Antibiotic Resistance: a Mathematical and Imaging Approach
Amount £989,446 (GBP)
Funding ID EP/I00503X/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 01/2011 
End 01/2016
Title Cell Tracking 
Description We have used ImageJ to track individual cell lineages in growing colonies. Packages already exist for this purpose, we implemented one in ImageJ to improve the accuracy and reliability (reducing the need for human intervention). 
Type Of Material Data analysis technique 
Provided To Others? No  
Impact As a result of these algorithms, we have started a project with Martin Ackermann to track cells in growing colonies and to determine statistics on cell division times as a function of antibiotic concentration. We have a hypothesis that the MIC (minimal inhibitory concentration) is an illusory population-level, collective artefact and not recognised by individual cells. This, and similar analysis tools developed by us, will be used to probe this hypothesis using individual cells of E.coli and a C.crescentus system developed previously by Ackermann. 
Title Drug inhibition curves 
Description Microbial inhibition curves are classically fitted as Hill functions to optical density or CFU data. We developed a technique that produces a theoretical inhibition curve by fitting a mechanistic model to a drug-free environment and predicting inhibition curves from the mode of action of the drug. When this is done for multiple drugs we can predict the interaction of the drug pair (synergistic, antagonistic or otherwise) by knowing something of the way the drugs bind to their respective targets. During the 12-month project we performed this analysis for the drug erythromycin and doxycycline as inhibitors of E.coli in microtiter well plates, but we are extending the technique (without modification) to other pathogens, drugs and are modifying it for yeast/fluconazol. 
Type Of Material Data analysis technique 
Provided To Others? No  
Impact The technique described will be used to predict not only drug interactions, but to use theoretical techniques to deduce optimal drug combinations against a number of criteria for a culture lasting one-two weeks (50-100 microbial generations). While this remains future work, we have used these models to hypothesise that synergistic drug interactions select so strongly for multi-drug resistance that synergistic combinations are best deployed as sequential (non-combination) therapies. It is only the short duration of the Discipline Hopping award that has prevented us from performing the evolutionary experiments to test these hypotheses, having had to master the experimental techniques and develop new modelling techniques to both generate and analyse this dataset. However, this project will continue to completion and would not have been possible without the DH award. 
Title Imaging for Phage Binding Assays 
Description We have developed algorithms using the Java-based package ImageJ to analyse images of experimental assays (typically conducted on 96-well microtiter plates) to determine the adsorption properties of viral phage to bacteria. In collaboration with Justin Meyer and Richard Lenski, we have applied this tool to determine the adsorption matrix of around 100 E.coli B with mutations in lamB with respect to around 50 lambda virus mutants. This information is of importance in evolutionary ecology where it is believed that host-pathogen interaction genetics occur through mechanisms commonly called "gene-for-gene" or "matching alleles". This dataset shows this to be untrue for E.coli and lambda interactions. 
Type Of Material Data analysis technique 
Provided To Others? No  
Impact This has lead to an ongoing collaboration whereby lambda and Ecoli are to be co-evolved to understand whether their interaction genetics is sufficient to be able to predict their coevolution over 100-200 generations. We have predicted "patterns" of lamB polymorphism across different bacterial micro-environments (controlled by the supply of maltotriose) and we will soon conduct these experiments to relate our mathematical predictions to the biology. 
Description Ackermann - Microscopy for Cell Individuality 
Organisation ETH Zurich
Country Switzerland 
Sector Academic/University 
PI Contribution Undertaken image analyses (and written software) to track cells (sizes, pole locations) within growing colonies up to 100/1000 cells.
Collaborator Contribution Prof Martin Ackermann has offered to our group training in the use of confocal microscopy to study single-cell responses to antibiotics. This is a new collaboration aimed at understanding the response of individual cells to antibiotics in a growing, colony of bacteria.
Impact A collaboration between mathematicians and evolutionary microbiologists: 2-d cell-tracking software written by us has led to the production of datasets of cell sizes and division rates as a function of time and antibiotic concentration. This collaboration has led to me organising a forthcoming international meeting on the mathematical modelling of antimicrobials. For information on this meeting visit
Start Year 2008
Description Frink and Sandia Labs - fluids DFT 
Organisation Sandia Laboratories
Country United States 
Sector Private 
PI Contribution The development of algorithms to solve theoretical problems in soft condensed matter physics.
Collaborator Contribution Sandia have offered training in HPC computational methods to a PhD student (funded by EPSRC) to apply classical/fluids density functional theory to study problems in molecular biology relating to the action of antibiotics. They will provide 3, 3-month placements in Albuquerque with travel expenses of the student covered by Sandia.
Impact The collaboration (between mathematically-oriented scientists) was instrumental in two recent EPSRC awards totalling £1.1M of which one part was to have a PhD student use modern algorithms to study problems in the theory of adsorption.
Start Year 2009
Description Lenski/Mayer - Evolution of Phage Resistance 
Organisation University of Michigan
Department Department of Ecology and Evolutionary Biology
Country United States 
Sector Academic/University 
PI Contribution image analysis/processing creating a dataset from raw experimental images; predictive modelling (blending evolutionary genetics and system biology approaches) of the E.coli lamB receptor and its adaptation to the virus
Collaborator Contribution They have provided two experimental datasets concerning the adaptation of the lambda phage to the lamB maltoporin on E.coli: one concerns binding affinities of the virus to the host receptor, the other concerns co-adapation of host and virus in a 21-day experimental protocol.
Impact Collaboration between evolutionary biologists and mathematicians: the output consists of an ongoing collaboration highly likely to lead to a publication within 12 months on the prediction of evolution of a virus to its host, with the aim of understanding how the genetic diversity of responses is mediated by environmental conditions.
Start Year 2010
Description Schuelenberg - Evolution of Antibiotic Resistance 
Organisation University of Kiel
Department Department of Evolutionary Ecology and Genetics
Country Germany 
Sector Academic/University 
PI Contribution performed experimental tasks (design/data analysis/model development) provided training to UG students in mathematical modelling techniques
Collaborator Contribution They (with input on experimental design and data analysis tasks from my group) have provided a dataset on the adaptation of P. aeruginosa, E.coli and MRSA to a series of broad-spectrum antibiotics. This dataset has allowed us to develop mathematical models that can predict interactions between drugs (at the moment for rifampicin, erythromycin and doxycycline) from information on their modes of action. We are now applying these models (that blend evolutionary genetics and systems biological approaches) to produce hindcasts of robot-based evolutionary experiments. A number of future experimental collaborations are planned to build on this, including the use of robots (programmed by us) to improve the quality of the data. We plan to share a German PhD student (David Laehnemann, currently an UG member of the group) hosted by Kiel to manage the day-to-day operation of the work.
Impact An interdisciplinary interaction between mathematicians and evolutionary geneticists: the main current output (due to the sort length of the collaboration that is due entirely to MRC DH funding) is a dataset on the adaptation of various bacteria to antibiotics. We expect this to lead (within 12 months) to a number of high profile publications as the initial results (available as yet in preprint form) are highly promising: we can "predict" certain drug interactions from their individual modes of action.
Start Year 2009