Bacteriophage and Antibiotic Resistance: a Mathematical and Imaging Approach

There is general agreement that medical science is facing a problem of grave importance with implications for the future of human health.Due to the evolution and spread of antibiotic resistant bacteria and the increasing difficulty of synthesising new antibiotic products,we need to find new ways of treating bacterial infections. As we embark upon the design of synthetictherapies that exploit engineered bacteria and their viral bacteriophages, we need to better understand how to use the antimicrobial agents in our possession.Locating 'the optimal antibiotic treatment' may be a distant goal, but researchers have recently begun to consider new ways in whichantibiotics should be combined to minimise the evolution of resistance to antibiotics. This is the focus of the proposal: how do wego beyond pharmacokinetic measures of efficacy to find new rationales for the optimal treatment?An approach to this question must encompass different fields. We need tools from systems biology thattell us how to model the behaviour of the complex processes within a single cell, but we also need modelsdescribing how antibiotics inhibit those cellular processes and lead to death in bacteria: the systems biology of antibiotics. To test theory we need empirical work, for if we claim that a combination of different antibiotics makes a potent cocktail, we should then test the veracity of this claim in the lab.The experimental paradigm for the type of research questions tackled in the proposal are 'experimental microbial systems', evolving microcosms that can be created in vitro and their evolution observed and repeated. Indeed, the evolution of antibiotic resistance can be so rapid that it may be observed in experiments lasting a handful of days. The utility of this empirical device is the rapidity with which hypotheses can be tested, we will soon see whether ideas created in theory have any validity in practise.But how do we derive such theoretical predictions? By taking mathematical models of experimental systems and asking fora form of 'controllability'. That is, we first ask whether a particular outcome can be achieved within the mathematical model. This outcome might mean, for example, using antibiotics to removal a bacterium from its host by minimising its density while, at the same time, preventing that bacterium from evolving antibiotic resistance; we claim that this kind of problem fits nicely into a systems and control approach.Despite very rapid advances in genomic technologies, biological systems are notoriously hard to model and data can be sparse so we will need to work hard to control them. However, a fundemental feature of the work we propose is the principle of generality that may help see beyond data. The idea, a common mathematical technique, is to look for principles that identify different systems as having identical structures that can be dealt with abstractly using mathematical tools. For example, are there any principles common to the best antibiotic cocktails when treating both E.coli or Pseudomonas infections? Are treatments that cycle different antibiotics in time always better than ones that mix antibiotics into a single cocktail? Is the particular antibiotic protein target within the cell important? Mathematics can help elucidate general problems like these.As some of these problems are difficult and ambitious, more feasible goals are presented. For example, can we use imaging to watch bacterial colonies grow in different antibiotic media and predict and measure the potency of different cocktails? This kind of experiment is novel in itself and will provide a foundation for more theoretical parts of the work.In short, with a combination of tools from mathematics, biology and physics our aim is to understand what the optimalantibiotic treatments are in simple systems and to understand whether those treatments remain optimal for more complex biological systems.

Who will benefit from this research? While there are several academic beneficiaries of this work, it is certainly my desire to create a project that looks beyond academic boundaries, indeed Laura Frink is a gifted researcher who is also president of a company (Colder Insights) and has a base at a US governmental research facility (Sandia). I recently took the decision to participate in a research based on a ten-year clinical trials dataset (Hyvet) for a project unrelated to this proposal with the specific goal of gaining a better understanding of the working methodologies of medical research practitioners. There is a large skill set required to undertake the proposed research and it is essential to engage with researchers from other disciplines in order to gain those skills and to improve them when necessary. It is perhaps a surprising assertion but the medical literature on antibiotic resistance contains a plethora of problems that can be 'mathematised' and reformulated as theoretical modeling problems. The now-classical question of Niederman dating from 1997 that concerns whether the theory of 'antibiotic crop rotation' provides a basis for reducing the prevalence of drug-resistant infections in ICU units and hospitals is a good example of this. It can even be formulated as a problem in the theory of optimal control and readily solved in that context. However, I do recognise that communication between research communities from medicine to evolutionary biology to theory and back is difficult and potentially risky, for example it can slow down standard measures of academic success like publication numbers, but the subsequent long-term reward is potentially high and very worthwhile. How will they benefit from this research? As a department of mathematicians, biomathematicians and physicists at Imperial College we have a culture of engaging to the best of our ability with the applied sciences relevant to our largely theoretical work, it is almost expected as part of the departmental ethos. To illustrate this, in January 2009 I helped organize an EPSRC-funded conference (via our network MMEMS) that took place in Imperial's Mathematics Department on the epidemiology of antibiotic resistance where Hajo Grundman, Megan Murray and Randy Singer were among the invited speakers and Sebastian Bonhoefer attended the conference. Later that year we organized a meeting on classical density functional theory where Bob Evans, Jim Henderson, Matthias Schmidt and Laurie Frink were invited and George Jackson and Andy Parry attended. In short, both as an individual and as a group we endeavour at all times to ensure that leading researchers from applied fields visit the department and play a role in the cross-disciplinary research process. I believe that developing research links across disciplines in this manner will ensure that theoretical work can impact upon the wider community. While it would be churlish to claim that all research ideas naturally crystallise into a rationale for the design of a clinical trials, although it can happen, I will communicate the relevant results as widely as possible. This will lead to publishing in the journals of different fields, but also to laboratory visits and attendance at conferences dedicated to those fields. For example, I am currently in discussions with an editor of PLoS Biology to re-work a paper that gives a mathematical perspective on the antibiotic resistance question, to communicate properly with the intended audience this paper cannot contain any mathematics, however it is based on a good deal of mathematical and simulation work. By publishing in journals such as this I do expect to be able to reach biological communities and to have my work evaluated by them.