Art Winfree

Ecology and Evolutionary Biology

Housed in BioScience West in the Ecology and Evolutionary Biology Dept is the laboratory of A.T. Winfree

Here are ten projects currently in hand, all of which present mathematical problems at all levels of sophistication:

• Using blue light to force a new chemical gel to 3-dimensional initial conditions likely to evolve into linked and knotted vortex rings such as I demonstrated numerically by integrating the equations of reaction and diffusion in Nature 371, 233 (1994).
• Trying to check the notion that such rings prove stable not because of the putative laws of filament motion described by analytical theories, but rather because their topology compels the "slapping" of segments of filament by wavefronts from other segments.
• Modeling the parameter gradients in the thick membranes used by experimentalists to measure spiral wave periods and wavelengths in chemically excitable media. The experimental results are presented as contradicting 2-dimensional theory, but I think the results are actually 3-dimensional. If I am wrong, then there is a major contradiction between theory and experiment in this area.
• Cataloging the dimensionless ratio of spiral wavelength times speed/ diffusion coefficient, across 12 orders of magnitude of experimental observations of spiral waves in diverse physical, chemical, and biological systems. It seems curiously uniform. If this is really true, we have something fundamental to learn.
• Modeling a new gas-phase excitable medium based on phosphorescence.
• Checking the result from extensive numerical solutions of partial differential equations of reaction and diffusion, that the period of the spiral wave gravitates to the tangent from the origin to the curve describing the propagation speed of periodic wavetrains.
• Characterizing the complex motions (discovered here) of the spiral wave tip, called "hyper-meander". Computations show an exceedingly curious complex frequency spectrum.
• Comparing theory based on meander and hyper-meander to observations in heart muscle during fibrillation, for the intervals between successive arrivals of an activation front at an arbitrary electrode site. This uses data from experiments unforeseen when this present proposal was written. F.X.Witkowski and I did these experiments on dog hearts in 1994.
• From the same experimental data, comparing visible activation patterns on the epicardial surface against expectation according to the 3-dimensional theory of fibrillation that I published in Science 266, 1003 (1994).
• Attempting a derivation of the AC electrical threshold for inducing fibrillation in the heart. I did this successfully for DC shocks several years ago, but did not know how to think about the physiological impact of AC electricity until recently.

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