Externally forced oscillatory and excitable systems
We use a time-dependent chemical reaction-diffusion system called the Belouzov-Zhabotinsky reaction to investigate resonant behavior in spatially extended oscillatory and excitable systems exposed to periodic perturbation. This project is one of the first thorough studies of resonance phenomena in spatially extended systems, see Nature, 388, 655-657 (1997) and PRL, 84, 4240 (2000) , and was begun at the University of Texas at Austin. We continue this work here at Duke University, exploring the effects of multiple-frequency forcing and spatial forcing. Excitability is a dynamical response to stimulation found in biological systems such as the brain, fertilized frog eggs, and the heart. We use the excitable chemistry of this system to investigate mechanisms of signal propagation and pattern formation in excitable systems.
Neuron-Glia Interactions & Signaling
Recent work has shown that glial cells support both local and long-distance reaction-diffusion mediated calcium waves . These waves can be initiated by nearby neuronal activity and may affect synaptic transmission through nonlinear feedback. Propagation of fast (1 m/s) neuron action potentials and slow (10 microns/s) glial waves in rat hippocampal cell cultures cause intracellular chemical changes which are simultaneously recorded using fluorescence microscopy and calcium sensitive dyes. We quantitatively investigate the spatio-temporal patterns of calcium activity supported by the system due to the separation of time scales and rich physical connectivity between the fast neuronal activity and the slow reaction-diffusion waves.
 Araque, A., Parpura, V., Sanzgiri, R. P., and Haydon, P.G. (1999) Tripartite Synapses: Glia, the unacknowledged partner. Trends Neurosci. 22: 208-215.
Spatio-temporal E. coli populations under inhomogeneous growth conditions
A naturally occurring growth condition in which bacterial colony dynamics are dominated by external forces is one that is spatially inhomogeneous and in which there is a second, convective transport mechanism for the food or the bacteria in the system, in addition to the relatively slow transport mechanism of diffusion. Such conditions may dominate in a wide range of bacterial and viral behavior, from contamination of ground water flows to bacterial distributions in the body which have relevance to gene therapy and in understanding the transition from localized to systemic infection. We investigate UV sensitive E. coli living in a one-dimensional channel under a varying spatio-temporal UV light pattern. The UV light causes fatal mutation in the bacterial population. Extinction or survival of the E. coli depends on the light-pattern intensity and drift velocity. We search for abrupt qualitative changes in the colony's dynamics as a control parameter is changed, an indication that a bifurcation has occured. Numerical simulations of a reaction-diffusion model describing the system are conducted to help guide and interpret experiments.