Biological Physics of Collective Motion: Circular Milling in Symsagittifera roscoffensis and Related Questions of Self-Organisation
Collective motion, a phenomenon resulting from the interactions of many individuals, occurs across the natural world across all length scales, from the flocking of birds to the swirling of Bacillus subtilis bacteria. Understanding these phenomena is critical to understanding how the organism thrives in its chosen ecological niche. In this dissertation, we aim to identify the physical processes behind these phenomena, integrating experimental studies with accompanying theoretical models for organisms in a wide range of different taxa, and thus elucidate how they give the organism a competitive advantage in their ecosystem. Circular Milling in Symsagittifera roscoffensis. It has been observed that the plant-animal worm Symsagittifera roscoffensis exhibits circular milling behaviour, a stunning manifestation of collective motion, both naturally in rivulets on intertidal sand and in a shallow layer of sea water in a Petri dish. In the first part of this dissertation, we investigate this phenomenon, through experiment and theory, from a fluid dynamical viewpoint, focusing on the effect that an established circular mill has on the surrounding fluid. The induced fluid velocity field allows nutrient circulation as well as providing an efficient method of dispersal of waste products away from the main body of worms. A series of novel mathematical models are analyzed to understand how the flow field produced by a single worm contributes to the total flow field generated by a circular mill, in light of the particular boundary conditions that hold for flow in a Petri dish. In particular, a model that treats a circular mill as a rigid rotating disc that generates a Stokes flow is shown to capture basic experimental results very well, both in terms of the mill centre orbit direction but also the predicted streamlines. Utilising this understanding, we shed light on the fluid dynamical stability of circular mills. Secondary circular mills form around stagnation points of the flow. The resulting system evolves to one of two kinds of stable states; namely a single mill with no nearby stagnation points or a set of linked mills where each mill centre is located in the stagnation region of another mill. Although in real life the geometry of the arena is more complicated than the circular model, the same principle remains, namely that stagnation points of the flow occur near a mill when that mill is close to a boundary. This allows the worm population to passively organise towards the arena centre without needing to know the exact extent of the domain. Typically the arena centre will be less shaded and more resource rich. Bacterial Biofilms under Confinement. A significant topic of research into the collective motion of organisms is investigating communities with a highly organised social structure. In the second part of this dissertation, we theoretically model how surface-bound communities of bacteria, called biofilms, grow. A biofilm gives the individual cells, embedded in an extracellular matrix network, a range of competitive advantages e.g. increased resistance to chemical attack. We show that for biofilms which grow in confined micro-spaces, the elasticity of the extracellular matrix produced by the bacteria is a key competitive trait upon which natural selection can act. Understanding the competitive traits underpinning biofilm growth is critical when trying to stop their spread in applications such as infectious diseases where bacterial cells increase their resistance to antibiotics up to a thousand fold just by virtue of being in a biofilm or in horticulture where pathogens colonise the xylem, causing wide-spread devastation in many different types of plants. Modelling Tissue Swelling. We model how a thin layer of tissue swells, using hydrogel as a proxy for tissue. Hydrogels are polymeric gels containing a hydrophilic crosslinked polymer matrix swollen by water. On small timescales, they behave like an incompressible elastic solid, whilst on longer timescales they behave like elastic compressible solids, reacting to changing environmental conditions by deforming, swelling or shrinking. We consider one of the simplest possible systems, namely the swelling of a thin hydrogel layer by a single water drop, leading to a rapidly spreading blister in the hydrogel. Using a linear poro-elastic framework, we develop a non-linear diffusion equation to describe the evolution of the blister height profile. This reduced theoretical model agrees very well with experiments using commercially available hydrogel. This strong agreement is exciting because this modelling framework is much simpler than the existing frameworks employed to model hydrogel in the literature, most of which utilise complicated non-linear models. This simplicity allows theoretical progress to be made when the tissue layer is a part of a more complicated and thus more realistic system e.g. modelling a biofilm growing on the tissue layer.
Biological Physics, Fluid Dynamics, Collective Motion, Active Matter
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