Biological Fluid Dynamics

One of the areas of biology in which applied mathematics has made a number of important contributions concerns the swimming of microorganisms. In the world of Stokes flow relevant to motile bacteria, where motion is primarily geometrical rather than dynamical in origin, self-propulsion by rotating helical flagella or waving elastic flagella is a central subject.

The experiments in this module are designed to introduce students to the elementary properties of viscous flows as they relate primarily to self-locomotion. Following the classic work of Taylor, and later Purcell, the essential features of slender-body hydrodynamics will be revealed through the gravity-driven settling dynamics of rods, helices, and the like.

Dynamics of Chemotaxis

The chemotactic response of individual cells to external chemical gradients is a phenomenon which involves not only complex biochemical pathways but also the physics of diffusion and propulsion. As classic experimental work on E. coli (right) has revealed, regulation of the flagellar motors leads to swimming motion that involves "runs" and "tumbles." As a consequence, cells execute a random (or biased random) walk.

In this experimental module students will track the motion of individual bacterial cells to determine the statistics of runs and tumbles, and verify that the long-time behavior of such a system is diffusive. This will allow the biology students to see the connection between microscopic behavior and macroscopic descriptions (such as a diffusion equation), and gives the students from physics and mathematics backgrounds the opportunity to understand the biology behind a diffusive contribution to a partial differential equation governing bacterial pattern formation.