Shape, shear, search & strife; mathematical models of bacteria

This project aims to develop an integrated mathematical model to explore the early stages of bacterial biofilm formation. The project requires the development of new mathematical models that can correctly capture details of how bacteria move in fluid environments and colonize surfaces. Furthermore, recent experiments on surface-attached bacteria have identified new movement patterns that are not currently captured in existing mathematical models. We will, therefore, be undertaking mathematical research to tackle the important societal and economic challenge of biofilms. The resulting new mathematical models and techniques will also be of relevance to many other phenomena concerning active particles that can transition between existing in the bulk fluid and being attached to a surface.

Bacteria are among the most primitive forms of life. Yet, despite their relative simplicity and small size, bacteria can actively sense a remarkable diversity of different environmental signals, and use this information to direct their motility towards more favourable environments. This ability to move profoundly affects where we expect to find bacteria.

It is important to study biofilms because during bacterial infection the emergence of anti-microbial resistance frequently occurs within biofilms; and combatting bacterial infections in a major health challenge. Furthermore biofilms have impact beyond health: a study by the National Biofilm Innovation Centre estimated that biofilms act on a $4 trillion global industrial base operating across many sectors, including contamination of food and water supplies, disruption of oil and gas and biofouling in marine environments, and also benefitting waste-water treatment processes, biorefining and biotechnology.

Many factors affect how biofilms form. In this project we focus on the very early stages of biofilm formation where the behaviour of cells, in particular the way in which they move and compete with each other, can profoundly impact what happens in the later stages. By developing a mathematical framework, we will clarify the complexity of the problem, and be able to test biological hypothesis concerning how different bacterial species compete and colonize surfaces.

The ability of bacteria to swim and move up chemical gradients (chemotaxis) has been well-known for several decades. However we still cannot fully predict where the bacteria are, and how likely they are to encounter a surface, in flow environments such as the digestive tract or circulatory system. This is the challenge we address in our first objective (shape & shear). It has recently been discovered that some surface-attached bacteria can undergo chemotaxis, and our second objective (search) aims to develop a new model to explain the mechanisms for this and develop a model which can predict where bacteria will accumulate on a surface. Our final objective (strife) will investigate how bacterial strains with different growth and motility signatures compete, either indirectly through competition for resources, or directly for example through toxin production. By developing a mathematical model of this we can investigate the early spatial patterning of bacteria on a surface, which will impact the composition of resultant biofilms.

We will achieve direct societal impact through our proposed public outreach activities. Mathematics underpins all STEM activity, yet is often hidden and under-appreciated by the public, and the UK suffers from a major skills shortage in workers qualified in STEM fields. The project team will contribute to public engagement activities at the Universities of Liverpool and Manchester which both have strong mathematical sciences outreach teams that run events for schools and the local community (e.g. Science Jamboree, MathsBombe, FunMaths Roadshow). The project team will also present at local and national science events (e.g.#ScienceX, STEM for Britain, Big Bang Fair). Our project partner, the National Biofilm Innovation Centre (NBIC), will assist us in showcasing how mathematics underpins broader scientific research.

Our fundamental research which aims to model the distribution of bacteria as they adhere to surfaces and initiate biofilms has long-term potential economic and societal impact. We anticipate that our modelling framework will help in the design of smart materials and guide the development of interventions (e.g. biological or chemical) which control the formation of biofilms.

We shall work closely with NBIC to ensure our fundamental research is part of a pathway which, through industrial and non-academic collaborators, achieves impact. There are major societal health challenges associated with bacterial infection and ultimately the emergence of anti-microbial resistance fomented in biofilms. Furthermore, as detailed in our national importance section, biofilms have huge economic impact beyond health. By working closely with NBIC we will: (1) develop opportunities to showcase our research to industry; (2) increase our understanding of the applied challenges; and (3) develop new collaborations with industrial partners. To facilitate this cross-fertilisation of ideas, we will organise an international workshop on mathematical models of biofilms bringing together academics, clinicians, and industrial representatives.

This research will also provide a framework for the study of particles which transition between existing in the bulk fluid and being attached to a surface and so will be relevant to a range of particles beyond bacteria. We therefore anticipate long-term impact for other applications in the chemical engineering industry, for example in materials innovation.