Modelling motility and chemical communication of bacteria and microrobots

Robots have fascinated the public for centuries. Spurred by rapid developments in micro- and nanotechnology, there is great interest in exploring the use of microrobots for targetted drug delivery and minimally invasive surgery. Two important aspects of functionality are motility and control (of chemical or mechanical activity). In this seminar, Prof. Shum discusses models and simulations of these aspects separately. Incorporating motility and control into a larger multiscale and multiphysics model in future work will lead to the possibility of modelling more advanced behaviour of robots, such as stimulus-triggered swarm aggregation and coordinated release of a drug.
The swimming of flagellated bacteria is modelled to understand one possible propulsion mechanism. The equations of fluid flow around a cell body and rotating flagellum are solved numerically with a boundary element method, producing trajectories of these swimmers in the presence of various obstacles. It is shown that hydrodynamic interactions between the swimmer and solid surfaces greatly influences the motion of the swimmer; design of microrobots must, therefore, take these eects into account. Furthermore, it will be evident that the eects of elastic deformations can be important. In particular, Prof. Shum will discuss elastic instabilities of the flexible connection between the body and a single rigid flagellar filament. Clearly, it will be important to extend the model to more closely resemble E. coli and other bacteria that swim with a bundle of several intertwined filaments. This poses a significant numerical challenge due to the slenderness of the filaments and near-contact between filaments.
In the second part of this talk, Prof. Shum will introduce and analyze a model for a colony of immobile microrobots, or cells, that communicate by producing and releasing diusible chemical species into the surrounding fluid. To specify the concentration-dependent rates of production of three chemical species, a chemical regulatory network, known as the repressilator, is imposed. This network could be considered as a simplification of a larger biochemical network controlling protein synthesis in biological cells. It is known that the repressilator network can exhibit oscillations.
Starting from a system of partial dierential equations for the chemical concentrations in three spatial dimensions, coarse-grained models are considered, and it is shown that the occurrence of chemical oscillations depends on the spacing between cells and the total number of cells in a colony. Hence, this chemical feedback leads to a form of "quorum sensing" of the cells. That is, the colony is able to determine its size and density, and qualitatively change its behaviour accordingly.