Periodic Reporting for period 4 - PhyMeBa (The Physical Mechanics of Swimming Bacteria)
Reporting period: 2021-03-01 to 2022-08-31
Bacteria play a critical role in the life of higher organisms. Their behaviour is constrained by the physical properties of their habitat, first and foremost the presence of a surrounding fluid. Most bacteria are motile, and most motile bacteria swim in fluids using slender helical appendages called flagella rotated by specialised rotary motors and joined using a short hook. While many bacteria have only one flagellum, most well-studied pathogenic bacteria possess multiple flagella. Why have some bacteria evolved to use many flagella when others survive with one? In order to answer this question, one needs to understand quantitatively how multiple flagella provide a fitness advantage to a cell exploring its environment. The principal difficulty in deriving rigorous models for swimming bacteria lies in the nonlinear nature of the underlying external physics, which involves nonlocal hydrodynamic interactions between flagella, short-range steric and electrostatic interactions, and elastic deformations of the flagella, which not only bend and twist but also undergo conformational changes. In this project, we develop novel theoretical modelling of the configurations and regimes relevant to swimming bacteria with multiple flagella with a focus on the mechanical forces at play. The project will provide first-principle understanding of the external forces at play in an important process in biology and will help answer a number of outstanding physical questions on the behaviour of swimming bacteria and the interactions with their environment.
During this reporting period we have: (1) developed mathematical methods to compute the interactions between the flagella of swimming bacteria, (2) characterised the impact of the geometry of flagella on their propulsive ability, (3) explored the role of shape-change of flagella due to its flexibility on the generation of hydrodynamic forces and flows, (4) developed new mathematical approaches to capture the interactions of bacteria and their flagella with complex microstructure in the fluid, (5) have shown that swimming bacteria interacting hydrodynamically can be subject to instabilities, (6) characterised the diffusive dynamics of bodies with asymmetric shapes, such as those of bacteria, (7) provided an accurate theoretical prediction for the value of the bacterial motor torque, (8) developed novel theoretical models for the bundling and unbundling of bacterial flagella, (9) captured theoretically the role of the flagellar hook on the stability of swimming bacteria, (10) developed a statistical method to measure the distribution of swimming speeds for swimming microorganisms, (11) modelled the stochastic motion of active particles and bacteria, (12) modelled the hydrodynamics of bacterial viruses, (13) developed models to capture the chemical aspects of micro-scale locomotion, and (14) started new experimental collaborations to understand the dynamics of magnetotactic bacteria and the buckling of flagellar filaments.
Beyond the current state of the art, expected results until the end of the project include primarily the synchronisation of bacterial flagella interacting through the fluid and first-principle mathematical models of the run-and-tumble dynamics of bacteria.