Mathematical modelling of microbial motility

Microbial life pervades our planet, and many species evolved the ability to propel themselves in their quest to colonise new environments. Understanding their movement patterns may have far-reaching implications such as the possibility of harnessing their motility to power microscopic machines, or using them to transport and mix microscopic cargo. Such insight will also shed light on crucial ecological processes, like the distribution of algae in the ocean or devise strategies to either accelerate or stop the colonisation of surfaces by all kinds of microorganisms.

This thesis aims to advance the field of the physical and mathematical understanding of microbial motility by developing comprehensive models that incorporate both physical and biological factors to explore the behaviour of different classes of microorganisms. Existing models are refined, new ones developed, and new techniques are applied to analyse their behaviour.

Within the scope of this thesis, models for three distinct systems are developed and meticulously analysed. Firstly, the behaviour of an isolated microswimmer in complex confinement is explored. We leverage tools of nonequilibrium physics to build a description of microbial motility based on probability flux loops uncovering patterns hidden in the system. A comprehensive comparison between model predictions and experimental observations confirms a quantitative agreement in the emerging fluxes. Secondly, we investigate the collective self-organisation of filamentous cyanobacteria that adhere to surfaces and frequently glide over one another. This behaviour enables pattern formation not observed in other classes of active matter. A novel approach to describe this kind of motion is introduced and their collective dynamics are explored. Comparisons with experiments reveal an intriguing connection between the properties of individual filaments and emerging structures. We predict that the balance of active motion and curvature fluctuations determines the length scale of the pattern. Lastly, motivated by the “paradox of the plankton”, that questions how many species of phytoplankton can seemingly occupy the same ecological niche, a model for phytoplankton in oceanic turbulence is devised, coupling the motion and interactions of active particles to a turbulent field.

Through the application of fundamental physical principles, and by the development, refinement, and analysis of these models, this thesis aims to expand our understanding of microbial motility, shedding light on fundamental aspects of microbial behaviour in diverse environments. The findings presented in this work may have implications for applications ranging from designing motility-powered microscopic devices to unravelling ecological processes in marine ecosystems.