The evolution of antimicrobial resistance presents a major, and growing, threat to our ability to effectively and economically treat bacterial infections. With few new antibiotics in the development pipeline, an important question is how best to use existing or newly deployed antibiotics, to which resistance is not yet prevalent, to conserve their efficacy. That is, in patients who were initially infected by an antibiotic-sensitive bacterial strain, we wish to dose antibiotics in a way that effectively clears the predominant sensitive bacteria, while avoiding the emergence of resistance.
Mathematical modelling is an important tool for understanding bacterial population dynamics and evolution during antibiotic treatment. Most models are deterministic (e.g. systems of non-linear ordinary differential equations). However, the occurrence of resistance mutations and subsequent outgrowth of a large resistant population from the initial mutant cell are stochastic processes that may occur at a variable time, or not at all. Predicting the probability that resistance emerges thus calls for stochastic mathematical models (e.g. birth-death processes).
Importantly, bacteria live in an ever-changing environment. Firstly, antibiotic treatment induces a time-varying concentration of antibiotic through dosing and degradation/excretion of antibiotics (pharmacokinetics). Secondly, bacteria continually shape their own environment by consuming nutrients, excreting by-products, and even absorbing or breaking down antibiotics. These processes can give rise to indirect competition and cooperation among bacteria (ecological effects). As the environment varies over time, so too do rates of bacterial cell division and death. Therefore, a resistant mutant arising earlier versus later may face a very different chance of survival. However, to date there has been limited consideration of temporal variation in stochastic models of resistance emergence.
The goal of this project is to develop a mathematical model of bacterial population dynamics in a time-varying environment and use this to explore antibiotic dosing strategies. Depending on student interest, the focus may be either on pharmacokinetics or on ecological aspects mediated by bacterial modification of their environment. This model would be studied with analytical, numerical, and/or stochastic simulation techniques. Potential questions include:
• How does the probability of a resistant mutant arising and establishing itself in the bacterial population change over the course of an infection?
• What is the optimal antibiotic dosing strategy to avoid emergence of resistance, within realistic constraints on tolerable doses? Are there trade-offs between clearing sensitive bacteria as fast as possible and minimizing the probability that resistance emerges?
• Could we manipulate bacterial competition or cooperation to improve treatment outcomes?
These findings could be linked to broader theory on “evolutionary rescue” of populations threatened by environmental change. Depending on time and student interest, key model predictions may also be tested experimentally.
This project would be well suited to a student with strong mathematical/quantitative skills (such as, but not limited to, a background in mathematics or physics) and keen interest in bacterial evolution. The student will have the opportunity to deepen their understanding of microbiology and evolutionary theory, to develop their skills in mathematical modelling and coding, and to gain wet lab skills if desired.
The project will be supervised by Dr. Helen Alexander (https://scholar.google.co.uk/citations?user=jRW2Z7QAAAAJ
) and Dr. Luke McNally (http://lukemcnally.wordpress.com/
). The student will have the opportunity to interact with lab members studying microbial evolution and ecology, diverse theoretical and experimental biologists in the Institute of Evolutionary Biology, mathematicians (e.g. through the Mathematical Biology Seminar series), and the broader network of researchers in Edinburgh studying antimicrobial resistance (https://www.ed.ac.uk/edinburgh-infectious-diseases/amr
). Informal enquiries to Helen Alexander are encouraged.
1. Brockhurst, M. A. et al. “Assessing evolutionary risks of resistance for new antimicrobial therapies”, Nat Ecol Evol (2019).
2. Alexander, H. K. et al. “Evolutionary rescue: linking theory for conservation and medicine”, Evol Appl 7:1161-1179 (2014).
3. Lipsitch, M. and Levin, B. R. “The population dynamics of antimicrobial chemotherapy”, Antimicrob Agents Chemother 41:363-373 (1997).