Arthur Taylor Winfree, a distinguished theoretical biologist whose discoveries repeatedly opened new lines of inquiry in physics, died of brain cancer on 5 November 2002 in Tucson, where he was Regents’ Professor at the University of Arizona.
Art was born on 15 May 1942 in St. Petersburg, Florida. As a boy fascinated by the mysteries of the living world, he decided somewhat paradoxically that the best strategy was to acquire the quantitative tools and training of a physicist. He majored in engineering physics at Cornell University and received his BS in 1965. His senior thesis gave another early hint of his unconventional way of thinking. Motivated by the phenomenon of circadian rhythms, Art devised a model based on an enormous collection of coupled, self-sustained oscillators. Those hypothetical oscillators were supposed to represent multiple cellular clocks whose collective behavior would be mirrored in an animal’s activity. Because no mathematical methods existed for analyzing large systems of nonlinear oscillators, Art built a gadget that he called the firefly machine, consisting of 71 flickering neon lamps, each coupled electrically to all the others. His hunch was that the aggregate output of that system, when plotted in the format used by circadian biologists, might suggest new ways of interpreting their data.
His experiments led to his first publication, in 1967, on the population dynamics of limit-cycle oscillators. Art discovered that, under appropriate conditions, such oscillator populations can spontaneously synchronize. As the variance of their natural frequencies is reduced, the oscillators remain incoherent until the dispersion falls below a certain threshold. Then synchrony breaks out cooperatively in a manner reminiscent of a second-order phase transition. In the years that followed, that novel nonequilibrium phase transition stimulated extensive theoretical research in nonlinear dynamics and statistical mechanics, most notably by Yoshiki Kuramoto and his colleagues.
Art received his PhD in biology from Princeton University in 1970 and worked in the lab of Colin Pittendrigh, an expert on circadian rhythms. Contrary to the prevailing dogma of the time (most vigorously espoused by his own adviser), Art demonstrated that biological clocks could be stopped by surprisingly mild stimuli. He predicted that result by ingenious topological reasoning about maps between circles, and then confirmed it experimentally in studies on fruitflies. In 1970, he showed that a brief pulse of light administered at just the right time in a fruitfly’s circadian cycle could nudge its biological clock to a “phase singularity” at which all phases of the cycle converge and the rhythm’s amplitude drops to zero. In the years since then, similar phase singularities have been documented for diverse kinds of biological oscillators, with possible medical implications for sudden infant death syndrome, cardiac arrhythmias, and other disorders involving abrupt termination of a biological rhythm.
Art held faculty positions as an assistant professor of theoretical biology at the University of Chicago (1969–72), and then as an associate professor (1972–79) and professor (1979–86) of biological sciences at Purdue University. From the late 1960s to the late 1980s, he focused his attention on the Belousov–Zhabotinsky (BZ) chemical reaction. In its quiescent form, the BZ reaction appears rusty red, but a sufficiently strong stimulus can trigger the propagation of a blue wave of oxidation, like a grassfire spreading across a prairie. As the wave travels, the liquid remains motionless; the pattern of chemical activity spreads by pure diffusion. Again using topological reasoning, Art convinced himself that a thin, two-dimensional layer of BZ reaction could not support a persistently rotating wave unless the medium had a hole in it. When he tried the experiment, he found otherwise. He wrote, “It came as a bewildering surprise, on October 10, 1970, to behold several perfectly stable spiral waves sedately rotating in a dish of this chemical reagent.” Since then, spiral waves analogous to the ones that Art discovered have been found in heart tissue (where they are associated with tachycardias and other arrhythmias, thus accounting for much of the applied interest in spiral waves); in aggregation patterns of slime mold (a key example in developmental biology); in surface catalysis; and in calcium waves in cells.
In the 1980s, he pioneered the study of scroll waves, the three-dimensional counterpart of spiral waves. He found that the ends of the scrolls typically join together to form closed rings that could be diversely linked, twisted, and knotted in a discrete set of ways quantized by a topological exclusion principle. Those structures represent the basic particlelike solutions of the field equations for excitable media. Aside from the fundamental importance of scroll waves, Art always believed they were likely to be important in cardiac arrhythmias, especially ventricular fibrillation.
In 1986, Art accepted a position as professor of ecology and evolutionary biology at the University of Arizona and, in 1989, was named a Regents’ Professor. He spent the final years of his career exploring the dynamics of scroll waves in supercomputer simulations, seeking the laws of motion for how they slither and writhe, and trying to understand their curious stability.
Art’s impact on diverse fields was recognized with several awards. In 1984, the John D. and Catherine T. MacArthur Foundation named him a MacArthur fellow for his work in theoretical biology. He received the Einthoven Award in cardiology in 1989 from the Einthoven Foundation and the Norbert Wiener Prize in Applied Mathematics in 2000 from the American Mathematical Society and the Society for Industrial and Applied Mathematics. His magnum opus was his 1980 monograph The Geometry of Biological Time (Springer-Verlag). Art’s sense of humor, irreverence, and creative spirit leap off every page of this masterpiece. In a section about the menstrual cycle, titled “Statistics (‘Am I Overdue?!’),” he plotted 15 years of data collected by his own mother. The book is aimed especially at students, with suggestions for which research problems are ripest. In many ways, it reads like a map for fortune hunters, a guide to future discoveries.
In his teaching as well, Art loved to help students develop their creativity. He taught a popular course called “The Art of Scientific Discovery,” and he was forever fascinated by puzzles and games. Art will be remembered for his playfulness, his honesty, and his contagious sense of wonder.
