# Microscopic Swimmers

The behavior of bacteria undergoing topotaxis at the microscale is studied with the help of theoretical models and custom-made microstructures

##### Sub-Project 1:

Asymmetric funnels have been used as passive pumps to concentrate E. coli in nanofabricated devices (Austin 2007). Funnel geometry changes pump efficiency, which could be important when driving cell sorters (Whitesides 2008). The large set of funnel geometries that could be considered when designing pumps motivated us to derive a path-integral-like formula to predict the flux produced by arbitrary funnel geometries. We applied this equation to a two-dimensional wedge-shaped funnel. Model and experiment agree that the steady-state ratio between concentrations on two sides of a funnel open to $60^{\circ}$ is 3 when the aperture is one fifth the bacterial run length and 1 when the aperture is 16 times the run length, an example of how the run length here has a role loosely analogous to the wavelength in quantum mechanical path integrals.

##### Sub-Project 2:

The ballistic-like motion of self-propelled particles at low-Reynolds number can be exploited to influence their direction of motion. In particular, it has been demonstrated that by using the right topology (in this case a micro-fabricated array of funnel-like asymmetrical barriers), E.coli bacteria can be "pumped" between two adjacent regions (Galajda 2007, Wan 2008). We built upon this idea and developed a micro-habitat array in which chemotaxis and topotaxis -- nutrient - and topology-driven motion, respectively -- are in opposition, leading to an inherently unstable environment in which a bacterium is constantly pushed away from the fitness landscape's summit in a Sisyphean fashion. Surprisingly, we find that the bacterial population as a whole is able to overcome the rectifying array. An in-depth microscopic analysis of the swimmer's motion is used to quantify the strategies adopted by the bacteria.

Publications