(281d) Nonlinear and Collective Dynamics in Microbial Locomotion: Bifurcations, Bundles and Biomixing

Many bacteria propel themselves though their fluid environment by means of multiple rotating flagella that self-assemble to form bundles. At a larger scale, the fluid motion generated by an individual microbe as it swims affects the motions of its neighbors. Experimental observations indicate the presence of long-range correlations and enhanced transport in suspensions of bacteria -- these phenomena may be important in many aspects of bacterial dynamics including chemotaxis and development of biofilms. This talk describes progress toward understanding these two aspects of bacterial locomotion, which both turn out to display fascinating nonlinear dynamical phenomena.

We first describe theory and simulations of hydrodynamically interacting microorganisms, using very simple models of the individual organisms. In the dilute limit, simple arguments reveal the dependence of swimmer and tracer velocities and diffusivities on concentration. As concentration increases, we show that cases exist in which the swimming motion generates large-scale flows and dramatically enhanced transport in the fluid.  A physical argument supported by a mean field theory sheds light on the origin of these effects.

The second part of the talk focuses on the dynamics of the flagellar bundling process, using a mathematical model that incorporates the fluid motion generated by each flagellum as well as the finite flexibility of the flagella. The initial stage of bundling is driven purely by hydrodynamics, while the final state of the bundle is determined by a nontrivial and delicate balance between hydrodynamics and elasticity. As the flexibility of the flagella increases a regime is found where, depending on initial conditions, one finds bundles that are either tight, with the flagella in mechanical contact, or loose, with the flagella intertwined but not touching.  That is, multiple coexisting states of bundling are found. The parameter regime at which this multiplicity occurs is comparable to the parameters for a number of bacteria.