On May 10, 2018 my mentor and friend Garry Odell died after a half-year struggle to slow an advancing liver cancer just long enough for those closest to him to get used to his unavoidable departure. In a remarkable life – although it surely must have contained sadness and frustration and disappointment too, as all lives must – Garry was to so many students, colleagues, and friends the very most alive, lucent, and fascinated being we have known. He embodied the atheist’s faith that intelligent life is the device by which the Universe knows itself, and when he left us, we abruptly knew ourselves a little less well.

Over four decades, Garry’s published works were perhaps few, but all deeply insightful. Many became profoundly influential to cell and developmental biology and to ecology. The first paper of Garry’s that I read was co-written with Bruce Edgar, when Bruce was a graduate student with Gerold Schubiger and Garry had newly moved to the University of Washington’s Zoology department. Only a few years into the dawn of modern developmental genetics, Bruce and Garry expressed a vision of regulatory gene function that eventually became mainstream: instead of branching cascades or Turing mechanisms, they offered an experimentally-grounded dynamical system accounting for amplification of coarsely-specified patterns into sharp, stable domains (1). This early, simple model described mutual cross-regulation between genes whose products compete, nucleus by nucleus within a shared cytoplasm, to define cell state and hence one aspect of a regular coordinate system in the fly embryo. Expressed in straightforward differential equations using terms familiar to anyone with a passing exposure to biochemical kinetics, this vision of gene networks as entangled circuit elements slowly became second nature in modern molecular biology. When I found their paper I was working on mesoderm induction in frog embryos, and it was just the point in history where all of us in developmental biology were finding ourselves with just enough genes and signals active in the same place at the same time, that the sequential cascades began to curve into networks that abruptly came to defy human intuition. As Garry might have said, modeling gene networks as dynamical systems may have flaws, but it’s a big step up from a word-salad.

The next of Garry’s papers I came across was a collaboration with Charles Peskin and George Oster to theoretically substantiate the Brownian ratchet as a general means by which living matter might harvest thermal energy to accomplish directed motion (2). As the authors pointed out, the notion of molecular motors as thermal ratchets had been in the air for a long time, at least since Huxley. Likewise the claim that polymerization alone, without a motor, could push sufficiently to deform cell surfaces or propel loads; or even that binding could do the equivalent kind of work. The value to modern cell biology of this step – transforming the Brownian ratchet from a straw man with the vague odor of sleight-of-hand, to a credible hypothesis specific enough to relate to real data – would be hard to overstate. As Peskin et al. explained, if polymerization of a single filament could push, polymerization of several together could push more, and account not just for filopodia and acrosomes but the intracellular pathogen Listeria and, by extension, the lamellipod as well; or for any number of analogous circumstances from kinetochores to protein channels to membrane vesicle formation and on and on.

The paper of Garry’s that I’ve read most recently was his 30-year-old work with Peter Karieva deriving, from biologically-measurable traits, a model for “preytaxis” by swarms of predators (3). In an experimentally-tractable simple ecosystem (goldenrod, aphids, and ladybugs) that could be rendered nearly one-dimensional, they showed that a simple set of rules – principally, that ladybugs go straight but turn more frequently in proportion to their satiation – explains how, even without the means to detect prey from afar (let alone measure a gradient of prey), predators congregate where prey density is greatest. Moreover, this model accounts for the observed effect of predator congregation in suppressing further prey outbreaks within a neighborhood – that is, the ladybug-aphid system shares an essential similarity with classic activator-inhibitor models of pattern formation. The paper has two incidental aspects worth noting. First, it is so clearly and considerately explained that it is practically a tutorial. Second, it turns out to predict real-world outcomes that all gardeners should note: don’t heed the standard advice of master gardeners everywhere to pull that one aphid-infested Fava plant, because the Karieva/Odell model shows that this apparent pest source actually sustains effective control.

These highlights might surprise readers more familiar with Garry’s touchstone collaborations with George Oster and company on morphogenesis, his later papers with me, Eli Meir, and others on genetic networks, or his work with Victoria Foe, Ed Munro, Jon Alberts and others on cytoskeletal mechanics in cells and embryos. Garry was as generous with his time and talents – from mathematics to just plain figuring out how to do things – as he was eagerly curious, and his unpublished contributions to the work of numerous students and colleagues vastly outweigh the visible products he left behind. By analogy to the Erdös number, I suggest mathematical biologists devise an Odell number: to suitably measure his influence, it would have to be a complex number, the real part reflecting works that made it into print (with or without his name on them) and the imaginary part reflecting those many efforts which engaged his and others’ sustained effort deeply enough to have shaped their world-view, even if somehow no one ever got around to writing a paper about it. Furthermore, reflecting Garry’s deep commitments to physical realism, each component would increase not by mere increment but through a saturating response like n/(1+n), and collaborative distance would be modeled by diffusion. Like many of Garry’s models, armed with a suitable recipe for the Odell number it would be difficult to intuit the outcome from the start but the ingredients would make mechanistic sense.

What motivated Garry Odell throughout his scientific work is stated most clearly and directly in one of the few papers he ever wrote alone, which describes a cytogel model of shuttle streaming in the plasmodial slime mold Physarum (4). This paper puzzles me greatly because, having co-written several manuscripts with Garry, at least a couple of which were never published, and having closely witnessed the fates of many others, I know well the kinds of barriers that reviewers and editors tended to erect, seemingly instinctively, to defend posterity against Garry’s writing. I don’t know the history of the Physarum paper, but because those who knew him can so clearly hear Garry’s living voice rising from the page, I cannot help but assume its publication transpired from a complete collapse of the usual editorial process. I can do no better than quote from it directly:

“Intuitive discussions, however compelling the prose… are flimsy and should never be taken seriously unless rigorous mathematical solutions have actually been computed. The kind of verbal reasoning given [here] to explain why the system oscillates could be subverted to explain instead why oscillations are impossible. The mathematical model presented in this paper comprises a dynamical system, i.e. a system of differential equations asserting that the time rate of change of the state of the system is a function of the present state of the system … [this kind of model] has a (stubborn) mind of its own and cannot be made to conform to prose forecasts of its behaviour or the most fervent hopes of its inventors. This perverse feature, at least, dynamical system models share with biological cells.”

And a little further on:

“The quest… is to understand the self organization process by which myriad identical proteins, transcribed directly from genetic sequence code, interact with each other to ignite an upward spiral of complexity amplification. … Even very simple interaction rules iterated by many sub-units of an organism (for example cells, proteins or organelles), can produce collective results of astonishing complexity. Mathematics [is] a language invented to facilitate the precise expression of such rules, together with the logical deduction of their consequences. In the quest to understand the dynamics of development, mathematics as a language is much more potent than ordinary language.”

Decades before there were departments of “Systems Biology”, these passages foresee and succinctly express both premise and promise of a field that he showed the way into.

Garry’s early work relied (necessarily) on relatively simple models and, where possible, matched analytical to numerical solutions. By the time I knew him, however, he was ambivalent about similar efforts and urged his students to eschew elegance and intuitive simplification while seeking a workable balance between realism and computational tractability. A native computer programmer who could proceed smoothly from emitting English to spoken C from either the front of a classroom or a log on the beach, Garry eagerly embraced Java and object-oriented programming when it came along and thereafter focused himself on crafting individual-based simulations as the apotheosis of the vision expressed in the excerpts above. That approach emphatically does not mean giving up hope of results that appeal to human intuition: on the contrary, Garry eagerly watched the simulations he crafted – for example, of microtubules and motors (5) – as keenly as any ethologist, and experimented on them to infer their intrinsic causes. He met with true and eager delight the never-ending stream of emergent rebuttals to his own or others’ predictions, and even the mundane challenges that arose as models took shape. This feeling was inarguably one with his own gladness to be alive and conscious. Take as a closing thought his reaction to the tricky challenge of figuring out, in code, if and when two virtual objects collide in a three-dimensional space: “just another one of the terrific things we get for free, just by being real!”

Works discussed here:

1. Edgar, B. A., Odell, G. M., & Schubiger, G. (1989). A genetic switch, based on negative regulation, sharpens stripes in Drosophila embryos. Genesis, 10(3), 124-142.
2. Peskin, C. S., Odell, G. M., & Oster, G. F. (1993). Cellular motions and thermal fluctuations: the Brownian ratchet. Biophysical journal, 65(1), 316-324.
3. Kareiva, P., & Odell, G. (1987). Swarms of predators exhibit” preytaxis” if individual predators use area-restricted search. The American Naturalist, 130(2), 233-270.
4. Odell, G. M. (1984). A mathematically modelled cytogel cortex exhibits periodic Ca++-modulated contraction cycles seen in Physarum shuttle streaming. Development, 83(Supplement), 261-287.
5. Odell, G. M., & Foe, V. E. (2008). An agent-based model contrasts opposite effects of dynamic and stable microtubules on cleavage furrow positioning. The Journal of cell biology, 183(3), 471-483.