Biological Pattern Formation

Reaction-diffusion phenomena are ubiquitous in biology, from the propagation of electrical impulses in the heart to population dynamics on the scale of kilometers. In this module, two examples of systems that constitute excitable media and display spiral waves will be studied: populations of the amoebae Dictyostelium discoideum and the Beluosov Zhabotinski (BZ) reaction.

A much-studied organism within developmental biology and also more recently within the physics community interested in pattern formation, populations of Dictyostelium form spectacular rotating spiral waves of cyclic AMP as a prelude toward aggregation into multicellular structures in response to starvation. These waves can be visualized by dark-field techniques (left) through their effect on cell shape and hence light scattering, and varying simple experimental control parameters results in an important competition between spirals and targets controlled by pacemaker cells.

In the BZ reaction (right), a purely non-living system, analogous patterns form through classical activator-inhibitor dynamics. In both cases, the primary experimental quantity of interest is the dispersion relation for the spirals, in comparison with theoretical results.

Bioconvection

The influence of individual cellular swimming on large-scale pattern formation will be examined in the context of bioconvection, in which the upward swimming of cells in a thin layer of fluid leads to an unstable density stratification and overturning flows. This phenomenon will serve as well to introduce students to the principles of hydrodynamic stability theory. Large numbers of the bacterium Bacillus subtilus (left) in a layer of water organize into distinctive, quasi-periodic patterns, not unlike those seen in thermal convection or other pattern-forming systems. This self-organization is a result of the interplay of the tendency of the bacteria to swim up towards oxygen in the upper layer and of gravity acting on the bacteria, which are less bouoyant than water. This results in convection rolls, with plumes of bacteria rising to the oxygen-rich layer of water, and then descending in plumes alongside the rising ones.