Regents Professor A. T. Winfree

My lab is supported by the National Science Foundation in
The Department of Ecology and Evolutionary Biology of the

University of Arizona.
 

Postdoc and grad student positions
available on NSF funding

I have funding for research into topics related to chemical, cardiac, and neural excitable media. This web page gives some idea of the topics.  Especially notice the recent colston.ps.gz or colston.pdf manuscript (to appear in 2002) containing 13 pointed questions, and summer 2001 publication of The Geometry of Biological Time (several lines below) containing about 200 specific questions ripe for answering. The book flags them with a bold "Q" in the margins and a  text file lists them more succinctly. Continuity of student succession was interrupted by my long absence; currently the lab is again operating as a 1-man band.
 

Directions to my office, address, phone, etc.

winfree@email.arizona.edu

Resume and publications:

Daughter at Princeton

Son at Cal Tech

.

Teaching

Society of Amateur Scientists column, "Adventures in Discovery"

This is a literary experiment, not guaranteed to succeed. Fantasize a scientist marooned on a desert island. While awaiting rescue he tries to "keep in shape" by daily exercises in the spirit of Sherlock Holmes, but about Nature rather than about crimes.  Verisimilitude is acquired by proscribing involvement in things I initially know anything about. Follow-up articles may provide links to web sites and journal articles subsequently located, but just as in Tom Hanks' celebratory night-time beach scene in "Cast Away" no apologies are made about re-inventing fire. The aim of the exercise is to describe personal adventures in discovering things unfamiliar to me, regardless who else might have known them for ages, minimizing reliance on costly technology in order to maximize reliance on resourceful question-asking. The inspiration comes partly from David Jones as  "Daedalus" in Nature, partly from Jearl Walker's Flying Circus of Physics,  partly from Ivars Peterson's Mathland, and partly from C.L. Stong's Amateur Scientist in the early and Ian Stewart's Mathematical Recreations in the recent Scientific American.

Your feedback would be most welcome.

SAS01: 09 Nov 2001: Curved lines in the sky
SAS02: 16 Nov 2001: Magnitudes of bright lights in the sky, Part I
SAS03: 23 Nov 2001: and Part II
SAS04: 30 Nov 2001: Trouble at full moon
SAS05: 07 Dec 2001: Curved lines in the sky, interpretation
SAS06: 14 Dec 2001: Possible worlds of discovery
SAS07: 28 Dec 2001: Paleontologists discover transistor radio...
SAS08: 11 Jan 2002:  Mystery of the rainbow moon introduced
SAS09: 25 Jan 2002:  Mystery of the rainbow moon: crucial experiment in Tucson this afternoon
SAS10: 08 Feb 2002:  Topological phase angle paradox: Moon and Sun violate reason
SAS11: 22 Feb 2002:  "Reason" takes a lesson from Moon and Sun
SAS12: 08 Mar 2002:  "Reason" takes a lesson, concluded
SAS13: 22 Mar 2002:  Iron falls from the sky
SAS14: 05 Apr 2002:  Meteorites again, concluding
SAS15: 19 Apr 2002:  Vibrating the Brain
SAS16: 03 May 2002: Brain Vibrates by Itself
SAS17: 17 May 2002: An Accident with Audio Tape
SAS18: 31 May 2002: Time Successfully Reversed
 
 

2001 edition of Geometry of Biological Time

The printed book alludes to this web site on eight pages:

• page x: Y2KGBT Corrections and Updates
• p. 276: See below, "What is the ultimately simplest...?"
• p. 282: See below, "growth in spiral waves.."
• p. 323: Mines archive in Montreal not yet opened so far as I know
• p. 403: Documentation, scripts, source code, Makefile for doing optical tomography in C on a Linux system. This is all 1993-96 home-brew from scratch: procedures are non-standard but well debugged and documented, and quantitatively proved in control experiments. Manual describing construction and operation of the optical hardware needed.
• p. 474: Similar package for the Pascal Toolkit used to analyze motion of vortex filaments in 3d excitable media, of graduated vintage 1987- 1993, the main tool behind all this lab's computational experiments through 1995. This runs under DOS with EMM386 (currently exhumed and working on an old 486 DOS machine for collaborative experiments with Paul Sutcliffe.)
• p. 491: Floating point arithmetic puzzle, merely for (surprising) amusement
• p. 561: See two lines below, "Circadian body clocks.."
• 200 unanswered Questions flagged in the book's margins

Circadian body clocks and jet-lag

• gif images of shirt-pocket "do-it-yourself" travel calculator
• Transparent top layer = map of globe from south pole perspective, on which to note the airport you leave from
• Opaque bottom layer = map of globe from south pole perspective, on which to note the airport you go to.
• User Manual
• Java version by Petteri Kettunen
• Another write-up of the principles involved: a 1993 McGraw-Hill Encyclopedia of Science article.
• Yet another, also equivalent, comes from Chapter 19 of my new book, The Geometry of Biological Time (2001 edition, p562). The measured human phase resetting curve in response to a rather complicated dim light exposure is here supposed similar to the response to the intended single, short, more intense exposure. Horizontally old phase, and vertically new phase, are indicated from a 0 at personal dusk. The shading covers personal night (sleep, presumably in the dark) in both directions. Loci of fixed phase shift or longitude change are diagonal lines. For any needed shift, follow the corresponding diagonal to the curve and notice the time at home relative to the shaded block on the old phase axis and on the new phase axis time at destination relative to the shaded block when and where the exposure is taken that resets the clock from that old phase to that local new phase. (The numbers along the axes are in hours relative to core body temperature minimum, not useful in this context.) Notice that entrainment to the prior light/dark cycle (shading) so phased the clock that its hours of negligible phase shift (along the 0deg; diagonals) occur midday (in the prior environment, i.e., of personal habits of day light exposure at home), with modest advances occurring during personal morning (first hours of daylight exposure) and balancing delays during personal afternoon. The hour of +-12-hour resetting arrives slightly after the middle of darkness or personal midnight at home. Notice that in terms of time at destination, i.e., the time to which the clock is thus reset, the hours of substantial phase shifting all occur in daylight, when the job can be done, weather permitting. Modest advances are taken in the personal morning at destination after eastward flight, and delays after westward flight in the personal afternoon at destination, converging toward the middle of the personal light/dark cycle in the case of the largest advance/delays. (Adapted from Czeisler et al., Figure 5 in Science 244, 1328-1333.)
• All the foregoing are based on comprehensive theory that seems to cover animal and plant phase resetting experiments comprehensively, and on experimental data from human phase resetting by light, and they all give the same answers. Alternative recommendations on unknown grounds have appeared at a commercial site, and many more are available as digital calculators, books, and bags of vitamin pills for a price in airport bookshops. Many companies have formed to exploit general gullibility in this area; they can easily be found by web searches.

Some unpublished odds and ends of research:

• Physiological experiments on ventricular fibrillation (4/97)

 

 
 
 

A tall rack of CD's containing movies from April 1997 adventures with F.X.Witkowski at Edmonton require elaborate numerical processing to answer questions about the dynamics of fibrillation.The data are sequences of thousands of 12-bit 128x128 images of voltage-dependent fluorescence for 10 seconds at 1.2 msec intervals on 30 square cm of electrophysiologically normal dog epicardium. The heart is on Langendorff support without DAM (which we found to seriously alter the character of canine electrical dysrhythmias.) See Witkowski..Winfree in Nature 5 March 1998 ( Fig 3 ).

The key questions of interest at the moment are whether the onset of VF consists of rotors, and whether their mode of decay to something more complicated consists in mere rapid irregular 2d motion, or in 2d fragmentation of activation fronts driven at the short period of those few sources, or in something fundamentally 3d as forecast in my Science 1994 paper and in Fenton and Karma's computations based on rotational anisotropy of myocardium. Winfree & Witkowski (abstract for October 98 presentation at IEEE Biomedical Engineering meeting.) observe eruptions to the epicardial surface which suggest (mostly by their charcteristic period) 3d vortex filaments, but none have yet been directly observed during VF in normal hearts (unless Igor Efimov has succeeded 11/98). Text of 10-min Presentation
 

• What is the ultimately simplest indispensible foundation principle underlying Efimov's surprising discovery of         "Virtual Electrode Induced Phase Singularities" ? Until Nov 98 I thought it was the inequality of electrical anisotropies in cardiac muscle. This enables a single shock from a single point-like electrode to induce a pattern of positive and negative polarizations in the neighborhood, from which rotor pairs arise even in the absence of any pre-existing gradient of refractoriness. This is so utterly different from all schemes familiar to me for creating phase singularities that I was intrigued to find the elemental difference from my schemes. It turned out to be the patterned stimulus imprint. Even in uniform FitzHugh-Nagumo model excitable media without any anisotropy, let alone unequal dual anisotropies, rotor pairs can arise if a suitably patterned stimulus is imposed on uniformly quiescent medium, much to my surprise. See for yourself by running, for example, these equations with these initial conditions in a square of medium 40 space units on a side. If you prefer to trust me, here is a snapshot of the initial state at time 0.6 time units on a scale of rotor period = 11.1 time units (time unit thus about 10 msec, if cardiac rotors are intended) and another after 57 time units, about 5 rotations. The white line traces one of the two wave tips. The twin rotors are stable and moving apart. The whole square is about 2 wave spacings apart, comparable to the heart of a dog or pig bearing rotor and spiral wave. The initial shock created adjacent puddles of positive and negative polarization, as a point shock will do in unequally anisotropic bidomains. In a monodomain like this simple model, a bipolar pair of opposite shocks less than a cm apart would serve the same purpose. This phenomenon cannot happen if only one or the other of the local state variables is affected by the shock, nor if both diffuse equally. The stimulus used affected both membrane potential and refractoriness, and only the former is free to diffuse.

    See my commentary in the March 2000 issue of the Journal of Cardiac Electrophysiology (paper #156). And note that because the caricature presented is deliberately carried to the greatest possible simplification, it loses the more complex kinetics that gives cardiac action potentials their long depolarized plateau. That is when Efimov shocks a broad uniform expanse of tissue. According to Lindblom et al. (2000) in the same issue, rotors may arise at the ends of a segment of activation front propagating inside a disk of shock-repolarized tissue, when the refractory outside abruptly regains excitability. Oppositely, the numerical shock here is given to a broad expanse of quiescence and its rotors arise at the ends of a segment of activation front propagating outside a disk of shock-excited refractory tissue, when the inside abruptly regains excitability.
 
• A gas-phase excitable medium operating in 2 or 3 dimensions (4/98)

By melting a thin layer of yellow phosphorus to cover the bottom of a plastic flask, leaving it some hours to consume all oxygen in the overlying air, and allowing fresh oxygen to diffuse into the flask through a long thin capillary tube, one obtains a volume of dilute P₄ and O₂ capable of reacting in a way that propagates like combustion. However the temperature rise in this "cold flame" is negligible: it does not cause convective disturbances. And it consumes only a small fraction of the local reactants, so after a refractory period, another such excitation can pass through the same volume. Meanwhile both are replenished by diffusion at some tenths of a cm²/sec. Propagation at about 1 cm/sec is observed in 3d with dark-adapted eyes or with a Gen II image intensifier; typical re-entry period is less than a second.

Misc unpublished notes; e.g., for seminar presentations

• About "Consciousness", mid-1987 text file
• Same thing as published: a PDF file
• Sunday morning sermon 4/94 at Tucson Consciousness symposium
• Biological growth in spiral waves
• Arizona/LosAlamos Days seminar 25 Jan 97: Tomography Experiments
• I made this into an exercise in "gizmo-ology" (pdf) (alternative ps.gz version), the making of sophisticated things from random junk, with help of a few undergrads. Work out marvelously.
• Comment/question about using the phenomenology of orgasm as an unexploited window into the mechanisms of consciousness, as part of UA course "Science, Mind, and Society" Spring 1999.
• Comment/question about special relativity and biological time and about general relativity. as part of UA course "Science, Mind, and Society" Springs 1999 and 2000.
• Comment/question about biological pattern formation as part of UA course "Science, Mind, and Society" Springs 1999 and 2000.
• During Fall 00 semester on sabbatical leave I was free to give seminars; here are 2000-2001 presentations in PowerPoint. These are served as interactive HTML and as (big) zip files. I present them unedited, in the spirit of newsreel documentation of past events. I know some errors in them, and would be grateful for your corrections of others.[Note 1/1/2002: none ever received]
• Postscript summary or PDF of unsolved question "what dynamics stabilize 3d organizing centers in excitable media?"
• History of Science (a joke): Leonardo da Vinci (a page here scanned from his notebooks) evidently foresaw not only helicopters and submarines, but even laptop computers

 

 
 
 
 
 




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"This material is partly based upon work supported by the National Science Foundation under Grant No. 9974334. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation."


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