In a paper published in Science in 1979, Stuart Newman and Harry Frisch presented a mathematical model, based on Alan Turing’s reaction-diffusion idea, to explain the patterning of the skeleton during chick limb development. Newman and Frisch proposed that the proximodistal sequence of skeletal elements results from spatial patterning of a cell surface protein following diffusion through the extracellular matrix. Their model provided an alternative to Lewis Wolpert’s positional information model, which was widely accepted at the time. Forty-six years after the paper was published, I spoke with Stuart Newman to find out about the origins of this paper, its impact on the field, and what we’ve learnt since about patterning during limb development.
Citation: Newman, S. A., & Frisch, H. L. (1979). Dynamics of skeletal pattern formation in developing chick limb. Science, 205(4407), 662-668.
Interview conducted online on 21 February 2025; Stuart Newman was in New York, USA and Hari Sridhar in Klosterneuburg, Austria.
Hari Sridhar: I’d like to start by asking you about your motivation to do the work presented in this paper, in relation to the research that you had done until then
Stuart Newman: Thank you for doing this. My graduate work was in theoretical chemistry at the University of Chicago. While I was a graduate student, my advisor—Stuart Rice (who died last year) —took an interest in theoretical biology. There was a new group in this area coming together at the University of Chicago. He knew some of the faculty, and he encouraged three of his students, including me, to look into the connection between theoretical chemistry and theoretical biology. Apart from me, they included my friends Leon Glass, who became a famous chaos theorist in biology, and Hugh Wilson, currently in York University in Toronto, who became a theoretical psychologist of perception. This all stemmed from our graduate work in theoretical chemistry. I did my Ph.D. work on an early dynamical systems theory approach to metabolism. It was really a new field—attractors, oscillations and so on. So, I became steeped in theoretical concepts of complex systems. Afterward, Stuart Rice seemed to lose interest in biology and didn’t actively pursue the subject.
This was in the late 1960s. I joined the department of theoretical biology as a postdoctoral fellow as I was finishing my Ph.D. and shared my time between Chicago and the University of Sussex, where the evolutionary theorist John Maynard Smith and the theoretical biologist Brian Goodwin had affiliations with the Chicago department. I spent half my time at Sussex and decided to learn some experimental biology there. I worked on the invertebrate Hydra, a specialty of Brian Goodwin’s colleague Gerry Webster. I was interested in pattern formation and was helped through the relevant biology by friends and colleagues in what was a very interactive environment. Jonathan Cooke, later a formulator of the clock-and-wavefront model for vertebrate somite formation, was a postdoc at the same time. Stuart Kauffman, a new assistant professor and my nominal supervisor at Chicago, a collaborator of Goodwin’s, was exploring Turing-type reaction-diffusion models for fruit-fly embryogenesis. Arthur Winfree, an exceptionally creative theoretical biologist working on oscillations, was also a new member the Chicago department, and I spent a lot of time speaking with him. The population geneticist Richard (Dick) Lewontin and the theoretical ecologist, Richard (Dick) Levins, who in later decades came to be known for their then-brewing, Marx-and-Engels-inspired dialectical (multiscale, non-reductionist, systems-based) approach to biology, were adjunct members of the department. So, I was taught by some of the new field’s major innovators.
At Sussex, Gerry Webster, who had been a student of Lewis Wolpert’s in London, taught me how to do microsurgical manipulations on Hydra. Lewis visited our department in Sussex and took an interest in my work on Hydra. I had made some findings that he was very sceptical of, so, he invited me to London. I worked alongside his technician, Amata Hornbruch, who confirmed my results.
Lewis was about 15 years my senior—and already becoming an important figure in the field because of his concept of positional information, which soon became a reigning theory in developmental biology. Its claims to universality in an area that had been a conceptual hodgepodge brought a lot of excitement to the field. I returned to the United States and after an intensive summer course in embryology at the Marine Biology Laboratory (MBL) in Woods Hole, Massachusetts, did a second postdoctoral fellowship at University of Pennsylvania. I joined Howard Holtzer’s lab, which was focused on cartilage and muscle development, with tissues partly derived from the chicken embryonic limb. I thought I could use some of the lab’s experimental techniques to test ideas about limb patterning. At the same time, Wolpert and his group were also working on limb development, applying his ideas of positional information to their experimental results. Positional information was an example of the “informationist” paradigm that arose in biology—particularly in developmental biology/developmental genetics—in the middle to late 1960s. The idea was that the genome was like a computer—the genes were basically hardware whose collective variations constituted physiological and developmental programs. The positional information model held that patterns were formed when cells with evolved programs detected different amounts of a concentration gradient of a distributed molecule. This led them to perform complex routines due to their computational abilities. As a putative universal mechanism of development, it was applied to the limb to explain how the digits and other skeletal elements could form. Early on, the application of positional information to the limb also included the notion that all the cell types—the muscle cells and the cartilage cells (which eventually were replaced by bone)—were specified from a common precursor population according to the same positional information gradient. That is, whether a cell made muscle or cartilage depended on the amount of gradient substance it was exposed to.
I was sceptical of these proposals. I understood from my graduate and postdoctoral work that dynamical systems could self-organize complex patterns. I remembered looking at the repeated patterns of ribs and bones of the vertebrae and limbs in the animal skeletons on display at the Natural History Museum in Chicago and thinking they looked like some kind of mathematical result. So, I started thinking about the limb in those terms, particularly because Stuart Kauffman (who had moved to Penn shortly after I did) had been working on wave patterns in development. In Holtzer’s U Penn lab, one of the things that I was able to do, from the spatio-temporal progression of the chicken embryonic limb development (the embryologist John Saunders having found in the late 1940s that establishment of the pattern occurred proximodistally over time; see Fig. 1 of Newman & Frisch, 1979) was to separate the undifferentiated cells that produced cartilage from those that produced muscle, showing unambiguously that they were of different lineages. These lineages were established quite early in development and already divergent by the time the unpatterned limb bud emerged from the body wall. You couldn’t tell the difference between the cells by looking at them, but they were irreversibly committed.
The work at Penn and the earlier course at the MBL (under the direction of Eric Davidson, then a rising star in developmental biology) equipped me with the techniques of molecular developmental biology. By that time, I had met John Saunders who had recently moved to the biology department at the State University of New York at Albany, and the molecular biologist Corrado Baglioni, who was the department’s chair. Owing specifically to Saunders’ interest in my limb cell lineage work, the two of them recruited me there—my first academic position.
During that time (in 1976), there was a limb meeting in Glasgow. I wasn’t known in the limb field at all, but Saunders was a senior figure, and I was a kind of protégé of his, so he easily had me invited to that meeting, and I met and became known to others in the limb field. At Albany, I also met Harry Frisch, a professor of chemistry there and a remarkably creative and versatile scientist. He worked on many different systems—physical, chemical, biological, seeing mathematical relationships everywhere, with what seemed to be a magic touch in his approach to the natural world. Although I knew of him by reputation, he sought me out because he had learned that I had done my Ph.D. with his friend Stuart Rice. He was very impressed with my “provenance,” and that someone from this esteemed theoretical chemistry group was working on embryonic development. Though he was nearly two decades my senior, we became good friends. I introduced him to the problem of skeletal patterning in limb development. As mentioned, I had been familiar with the Turing reaction-diffusion mechanism from discussions with Stuart Kauffman during my postdoctoral work at Chicago and realized that you could apply the Turing model to all sorts of developmental systems. To many biologists, particularly those with training in anatomy, the limb’s digits are totally different from each other. The positional information model, for example, proposed that each finger is the expression of a different subprogram, and comes up in the right place at the right time because the limb bud cells are programmed to make each specific digit at a particular gradient value. The Turing mechanism, in contrast, forms a series of standing waves of a molecular factor. If you apply it to the limb, the implication is that all the fingers are basically the same. If the fingers turn out to be different, it’s a second-order phenomenon — the result of fine-tuning and customization concomitantly or at later stages of development. As a physical scientist looking at the limb, this became my starting point.
Harry and I worked closely together and came up with a model applying Turing’s idea to explain how the limb skeleton develops. Some contemporaneous work by James Tomasek, a Ph.D. student I was supervising at Albany, showed that a newly discovered protein of the extracellular matrix – fibronectin – appeared co-ordinately with the precartilage condensations that templated the skeletal elements. I suggested that that might be one of one of the components of our proposed mechanism.
Our objective was not simply to generate a single pattern, e.g., the three digits of the chicken forelimb, but the full sequence of transitions over developmental time from a single bone (the humerus of the forelimb) to two bones (the radius and ulna) and then the three digits (Fig. 1 of Newman & Frisch, 1979). (This is the proximodistal sequence identified by Saunders, mentioned above.)
While there were a few earlier papers, from Hans Meinhardt and Stuart Kauffman, that applied Turing’s idea to developmental systems, I think our paper was the first one that invoked actual molecules – it wasn’t purely abstract. We claimed that there was an experimental basis for a Turing-type mechanism, and these specific molecules might be involved. And it turned out that they were involved; fibronectin as well as the extracellular polysaccharide hyaluronan, which we proposed (with some experimental support) as a blocking agent that kept a reserve population of cells unresponsive to the inducing morphogens (diffusible developmental signalling molecules) until a given stage of development was reached.
However, the model that we published in Science was incomplete. It was what’s called a stationary-state model: a representation of what the patterns would look like after all the transient dynamics have settled. Because we didn’t know the identities of all the molecules in play there was not sufficient information for a detailed dynamical model. A component of such models, for example, should be self-activating, since symmetry breaking in the Turing mechanism depends one of the molecules inducing its own production, either by autocatalysis or positive feedback. We didn’t know what that might be, but we assumed its existence. Further (in the context of the limb system), the putative self-activating factor should induce the production of fibronectin, which is what causes the cells to stick together in condensations. We didn’t know what that might be either. But interestingly, about three or four years after our paper was published, some investigators described TGF-β, a protein unknown at the time that we wrote our paper, but which the paper essentially predicted. It’s a diffusible molecule that’s produced by mesenchymal cells, including those of the developing limb; it induces its own production, and it also induces the production of fibronectin. So, it was a key missing link in our model, anticipated by our paper. This bolstered my confidence that we were on the right track.
As a stationary-state treatment, our model required a lot of mathematical manipulation. You can see, in the Appendix to the paper, that the simple equilibrium formula (the paper’s Eq. 5) corresponds to a series of waves fitting into a box. It’s not the kind of analysis that the community of applied mathematicians involved in theoretical biology were doing, since the governing system (Eq. 1) was too underspecified to be dynamically informative. A more standard treatment would have been a completely specified system of equations, even an oversimplified one (a “toy model”) that would start with a homogeneous state and evolve to a heterogeneous one, with the “symmetry breaking” occurring in a mathematically explicit fashion. We didn’t do that.
Relinquishing the aim of providing a full dynamical description paradoxically permitted us to introduce a different aspect of realism into the model. The model was three-dimensional, with the smooth paddle-shaped limb bud represented as a solid parallelepiped (Fig, 2 of Newman & Frisch, 1979). It had to be at least two-dimensional to represent the proximodistal (body-to-limb tip) dimension, which elongates during development, and the anteroposterior (thumb-to-little finger) dimension, along which the number of elements increases from 1 to 2 to 3 over the same period. There was no change in the character of the skeleton in the dorsoventral (back-to-front) of the limb during development, but we had experimental measurements for all these dimensions, so we used them. Even today, nearly a half century later, solving a system of partial differential equations in a three-dimensional domain of changing size would be computationally prohibitive, so the theoretically desirable “full model” for demonstrating the plausibility of reaction-diffusion-based limb development was never feasible. The sequence of stationary patterns with changing limb parameters seemed to us a good compromise.
Harry arranged a meeting with friends and colleagues of his at the Courant Institute of Mathematical Sciences at NYU. These were among the world’s premier applied mathematicians and theoretical biologists: Jerome Percus, Joseph Keller, Charles Peskin, and Stephen Childress. We presented our model to them and, notwithstanding our unorthodox mathematical approach, they agreed it was an accurate representation of the successive stationary endpoints of a Turing-based process. In their view, the importance of the model was the suitability of the formal treatment to the known properties of the limb’s cellular and molecular components.
Then, in 1983 a paper was published in the Journal of Embryology and Experimental Morphology (the journal that later became Development) by Oster, Murray and Harris. Harris was a tissue biologist and Murray and Oster were theoretical biologists. They used the same mathematics as we did in our paper, but they had a different physical model—rather than a chemical reaction-diffusion model, it was a tissue compression model that also generated periodic patterns. They neglected to cite our paper, however, and I telephoned Oster and asked how he could justify this. He replied that the mathematics was obvious. Any theorist looking at the limb would realize that you would have to use a wave equation to explain the pattern – it was a no-brainer. But in fact, it took until 1979 for anybody to apply this type of mathematics to it. So, now there were essentially two versions of our model in the literature, with the second presented as if it were a de novo concept.
The positional information idea was much more popular than either of the Turing-type models. There must have been two dozen papers in Science and Nature on positional information in the limb in the two decades that followed, and many more in the developmental biology journals. A parade of candidate molecules was proposed over the years for the positional information gradient that putatively specified both the locations and identities of the digits: retinoic acid, retinoid receptors, various Hox gene products, Sonic Hedgehog. Each time some positional information candidate was proposed, there was pushback. So, there were papers supporting, e.g., retinoic acid, and then there were papers opposing retinoic acid, and so on for the other candidates, for years and years. But in none of these papers—many of which were extensively cited and discussed—was there ever a mention of our 1979 paper, nor, in fact, of the 1983 paper of Oster and coworkers.
Limb research was burgeoning with the rise of developmental biology because limbs are an obvious and easy-to-visualize example of a developmental system. You can’t see the lungs or the liver, but you can see the limbs. And so, it became a paradigmatic system for developmental biologists. Anything that happened in the limb field got a lot of attention, News and Views pieces in Nature, and so forth. But the positional information framework maintained a grip on the field until as recently as a decade ago, when its disconfirmation became unavoidable. There have been biannual international meetings on the limb starting in the 1970s. One of the first was the one I attended in Glasgow in 1976. But after our 1979 paper appeared, I was never invited to speak at any of them, although our experimental and theoretical work on the model generated dozens of papers.
One person who was instrumental in keeping our paper from vanishing from the world of developmental biology was the biologist and historian Scott Gilbert. He wrote the most widely used textbook in the field, and beginning in the early 80s, and in every edition since (now it’s in its 13th) always cited our 1979 article. That kept it on the table and created the possibility for students to encounter it. However, among the hundreds of medical students or scores of graduate students I taught, who took a developmental biology course in college, I never spoke to one who knew about our model (though many knew about the positional information model, or its longest-lived version, the Shh gradient). It was squeezed out of the mainstream of research, but also of education. There was one group, in Japan, led by Takashi Miura, that took our model seriously. Their work began around 2000, two decades after the paper was published. They used it in both theoretical and experimental studies and established its plausibility in new contexts, such as mutant mice. As far as I can tell, that was it.
Then in 2012, a paper by James Sharpe and colleagues appeared in Science, in which they performed genetic manipulations of mouse embryos, and found that the only way they could account for their results was that certain Hox genes must be modulators of the rate factors in a Turing mechanism that generated the digits. By these means, and according to a Turing-type model they presented, you could change the number or the thickness of the digits by tuning the model’s parameters. They cited our ’79 paper, and after that others did as well. In my opinion, the long delay in accepting a Turing-type alternative to positional information for limb development was tied to the limb being the preferred system of the theory’s originator. In other developmental systems it was either considered and quickly rejected with accumulating evidence, or, as happened with the limb, integrated as a refining effect of physical processes of morphogenesis.
HS: You mentioned earlier that Lewis Wolpert didn’t believe some of your experimental results with Hydra. Tell us a little more about this.
SN: Hydra has two ends, a hypostome or “head,” and a basal disk, or “foot.” If you plug in tissue isolated from either end to the midsection of a different Hydra, it will induce outgrowth of the respective axial region, capped by a head in the first case, or a foot in the second. These inductive potentials are graded. The rate of regeneration of either end is slower the further from the end the animal is cut. Wolpert proposed that there was a single positional information gradient that was read by the hydra’s cells as “make hypostome” at the head end and “make basal disk” at the foot end. One of my experiments involved isolating hypostome and basal disk tissues, mashing them together and inserting the combination into the midsection of another Hydra. I found that the indictive effects cancelled each other out. So, the whole thing became more complicated than a single gradient determining positional information. Based on the older idea of the “inducer” due to Spemann and Mangold (originally demonstrated in Hydra by Ethel Browne decades before), I concluded that the Hydra has two different, antagonistic inducers, each of them forming the peak of its own gradient. It wasn’t one positional information gradient that was telling the cells what to do, but an interaction between inductive tissues.
This was not what Lewis had been anticipating. He had hoped positional information would replace some of these classical concepts. And he was sceptical that these things could have antagonistic effects. And, you know, I was kind of a novice experimentally then, but I did the experiment many times and was pretty sure of my results. But Lewis’s technical assistant, Amata Hornbruch, was a real virtuoso, and he trusted everything she did. I showed her what I was doing, and she did it independently and got the same result. I published the paper on the antagonistic gradients in Hydra in the period between leaving England and arriving at the University of Pennsylvania. In that paper, I said that positional information can’t be the main explanation because of the inducer-inducer interaction.
HS: Did the lack of attention to the ’79 limb paper affect your desire to work on this subject? Did you feel like you should move away from the topic?
SN: Not at all. I felt like I was right and that there was no reason for me to step away from the problem. I just stayed with it. My students and I did experiments for 25 years addressing pattern formation in limb bud tissues, in vitro and in the embryo. I also formulated interpretive models in collaboration with a variety of talented physicists and mathematicians, simulating these phenomena in different ways, and ultimately filling in many of the biological and mathematical gaps of the ’79 paper. In our most recent papers, we’ve moved beyond our focus on the fibronectin stage of condensation formation. It’s still part of the process, but we found that it appears later in development than the point at which the primary pattern is established. The pattern of “proto-condensations” appears to be established by a set of proteins called galectins. They are widely studied in immunology and cancer biology, but not in development, because there’s a lot of redundancy in the galectin family in mammals, making mouse experiments hard to interpret. In birds, there are many fewer galectins. We’ve now published nearly a dozen papers that show that there’s a very deep evolutionary history of galectins in the patterning of the limb and the fin of earlier emerging fish, and we’ve done mathematical analyses of their interactions in the patterning process. The interaction between the two main galectins also constitutes a Turing-type system, but a very complicated one involving cell movement, i.e., biomechanics. It’s turned out to be very interesting. The galectin system eventually links up with the fibronectin-TGF-β system, which kicks in a little later in development. There’s a lot of over-determination and evolutionary “rewiring” in the development of the limb. During his Ph.D. studies, my former student Ramray Bhat did all the experimental work on galectins and contributed to the modelling. That was one of the most satisfying collaborations of my career. A friend from my time as a postdoc in theoretical biology at the University of Chicago, Vidyanand Nanjundiah, supervised Ramray in a research project at IISc Bangalore and suggested that he work with me as a graduate student. Now, Ramray himself is a professor at IISc, occupying the same lab that Vidya directed before his retirement.
HS: I want to go back to your collaboration with Harry Frisch and ask you a little bit more about what each of you brought to this paper. Were your roles complementary in any way?
SN: Our roles were complementary, but in unexpected ways. I came to Harry with the idea of using the Turing mechanism to study the limb. He, of course, knew about the Turing mechanism and he was very adept at devising models, but he kept on coming up with trigonometric solutions that exhibited patterns, but not the relevant ones, or with suitable symmetries. The model wasn’t giving us what we needed. But I pressed him. I said, can’t you work on it so that it generates sine waves, rather than more complicated trigonometric functions? And he finally came up with a version that generated sine waves in three dimensions and also conformed geometrically to the limb bud. It seemed miraculous! Even though I wasn’t the mathematician, I saw what formal properties we required, and he figured out how to get us there. The “correct” model also had unexpected biological implications. It opened the way to predictions about yet to be discovered factors.
You had asked me in your email about the “Saunders number”. John Saunders was the senior person in my department, and the internationally recognized “dean” of limb developmental biology. He was very encouraging about this work, although he did not think about things mathematically and didn’t fully understand the model. A dispersion relation is a mathematical expression for a wave equation (such as our model became when Harry set it up suitably) that relates wavelength, wavenumber and frequency to the dimensions of the spatial domain of a wave. Typically, ratios of parameters of the system and universal constants like π equate to a conserved quantity, which we called S, the “Saunders numbe”r. It was Harry Frisch, the theoretician, not me, the biologist. who thought of honouring the senior biologist in the field by coming up with that designation.
HS: How did you and Harry Frisch actually work together? Would you meet on a daily basis, to sit and do this together?
SN: I would go to his office and discuss it with him, working together on the blackboard. I drew pictures of the shape of the limb bud and progression of skeletal development and Harry wrote equations and solved them. We went back and forth like this for at least two weeks until we hit on a suitable system. Although we were seeking stationary patterns (for the reasons mentioned above) we were also describing a time-dependant developmental process. So, we needed to model a sequence of stationary states for which the transitions were driven by changes in biologically determined parameters, not mathematically determined instabilities. We also had an observer—it was my good fortune that Harry had a Hungarian postdoctoral fellow who had recently arrived from Paris, with a desk in the same office. That was Gabor Forgacs, who years later became one of my most important collaborators. Then, he was just listening to us and kept on saying, “I don’t know what you guys are talking about! Is biology really a science?” Gabor was a theoretical condensed matter physicist, and it was to Harry’s great credit and talent for multi-tasking that he could conduct his collaborations with Gabor and with me in the same periods, and sometimes, seemingly, simultaneously.
Gabor and I are close to the same age. We became very good friends, and our families became friends. And then about six years later, Dorothy Frenz, a student doing her Ph.D. with me after I moved to New York Medical College, discovered a very interesting effect that drove cells, and (as we eventually found) non-living cell-sized particles, through collagen gels. It had nothing to do with what I had been working on with Harry but was definitely a physical phenomenon. Since Gabor (who had by then joined the faculty of Clarkson University in upstate New York), was one of the few theoretical physicists I knew, I got in touch with him and described this problem. As he started taking an interest in it he became increasingly interested in biological physics And his whole career turned around, from being a theoretical particle physicist to being a tissue biologist, We wrote a whole bunch of papers on that the phenomenon that Dorothy Frenz and I called “matrix-driven translocation” This led to a lot of work on the physical assembly of collagen, which brought me to France working with other colleagues of Gabor’s, and so on. A whole new vein opened up in my career as well. I wrote a book with Gabor—a widely read textbook—Biological Physics of the Developing Embryo. All of this began with Gabor just sitting on the side, doing his own work and expressing puzzlement, while I was talking about the limb with Harry Frisch!
HS: I’d like to go over some of the people you mentioned in the Acknowledgements to get a sense of who they were and how they contributed to this paper. Some of these people, like Saunders, you’ve already spoken about. You thank some people from the Courant Institute. There’s J. Percus, J. Keller, C. Peskin and S. Childress.
SN: Jerome Percus was a pioneering statistical mechanics and condensed matter physicist. And a long-time collaborator of Harry’s. As a graduate student I had known of him as the co-formulator of the Percus-Yevick equation, which describes physical properties of liquids and other amorphous materials. When I was in England as a postdoctoral fellow with Brian Goodwin and Gerry Webster and visited Wolpert’s laboratory, I was surprised to find the famous theoretician Jerry Percus doing a sabbatical in Lewis’s group and working at a bench in the laboratory! This was in the early 70s, way before our limb paper. So, when Harry Frisch arranged our meeting at the Courant Institute, I had already met Jerry. The other three were applied mathematicians who had done modelling in biology, and they were probably the most important group of biomathematicians in the country at the time. I was gratified that they put their imprimatur on our paper.
A sequel to Jerry’s participation in the life of the paper occurred a few years later. When the Oster, Murray and Harris paper came out, and I shared among colleagues my annoyance at their appropriating our model, the authors had allies come to their defence. A 1986 paper published in the Journal of Theoretical Biology by a mathematical biologist named Hans Othmer suggested that our paper in Science was spurious because it didn’t lay out the full mathematical model that generated the patterns. Since it completely neglected our stated intention to only seek equilibrium patterns, Jerry Percus proposed that Harry and I join him in a response that laid out our approach in a mathematically rigorous fashion. However, by the time our rejoinder was published (also in J. Theor. Biol.) damage had been done among mathematical biologists, who subsequently avoided our model. But Jerry’s intervention was important in setting the record straight and cemented our approach beyond the text of the original paper and its explanatory footnote.
HS: Going down the list in the Acknowledgements, the next person you thank is J Tomasek.
SN: Jim Tomasek was a doctoral student with me at the time. As mentioned previously, he was the person that found that the protein fibronectin was present at sites of precartilage condensation as the limb developed. In the ‘79 paper, we cited Jim’s Ph.D. work.
HS: And then you thank N Seeman and S Greenstein for help with computer graphics.
SN: Yes. In those days—in the mid- to late 70s—people didn’t have their own computers! There was a separate department where you went if you had something that required computation, like running a program or drawing a picture. Nadrian (Ned) Seeman, a contemporary of mine and departmental colleague, was already becoming known for founding the field of “DNA origami”— he would construct nanomachines and other structures from DNA molecules, Unfortunately, he died not long ago. Ned’s work involved extensive computation. and he sent me to a staff member he was confident could produce a key figure for our paper, Steven Greenstein. I started working with Steve, describing what I wanted the picture to look like. It’s the figure with three panels, each showing a three-dimensional contour of sine waves of 1, 2 or 3 wavenumbers in one dimension and a wavenumber of 1 in the orthogonal dimension (see Fig. 5 of Newman & Frisch, 1979). This would represent the stationary fibronectin patterns in successive cross-sections of the parallelepiped-limb, directing the formation of the humerus, radius, and ulna, and three digits of schematic chicken wing. It’s something you could generate in 30 seconds now, but it took us about a week to do it. The proportions kept on coming out wrong. Steve knew how to program patterns, but it was not that straightforward to get them right.
We also acknowledged Ryland Loos. He was our exceptionally talented departmental staff artist. I could just give him sketches and photographs and he would turn them into beautiful line drawings. He hand-drew all the figures in the paper other than the computer generated one.
I was very happy with the paper and remain so. It took the work of many people with different skills. But without Harry Frisch it would have never happened.
HS: There’s one other name in the Acknowledgements: you thank L. Callahan for preparing the typescript.
SN: Linda Callahan was a secretary in my department. I was handwriting my manuscripts at the time, and she would type them. These typists, mostly women, were adept in reading the often-enigmatic scrawls of many faculty members. The way that you submitted papers to journals at the time was that you send a typescript to a journal by post. There was no email or web portals.
HS: You say you were supported by an NIH grant. Was the grant paying your salary, or was it for a particular project?
SN: My NIH grant was for an entirely different project. It paid part of my salary for my last few months at Albany (I left for New York Medical College in July 1979, a month before the paper appeared in Science). And we acknowledged Harry’s long-term support from the National Science Foundation (NSF).
You would get these grants to do what you had already done, and then you would start to do new things that weren’t specified in the grants! The NIH grant that I had wasn’t for theoretical work but experimental studies. I was working on limb cells in culture and learning things about their chromosomal proteins—which I eventually published on in other contexts. And Harry had a very general grant on mathematical modelling of complex systems in chemistry and biology. It was very rare, even later, for me to be able to get a grant to do the kind of work that led to the limb model. And after it was published, any NIH grant that I submitted to test the model or purse related ideas was invariably turned down. After a while, I participated in some large multi-site NSF grants in which I was the biologist working in collaboration with mathematicians and physicists on problems in developmental biology. Since they were reviewed by physics and mathematical biology panels they passed under the radar, since our model was considered plausible by theoreticians. Had they been reviewed by developmental biology panels, we would certainly have received very unpleasant comments about our crazy model that had nothing to do with positional information!
HS: What memories do you have of the writing of this paper? Do you remember how long it took, and how did you and Harry Frisch contribute to the writing?
SN: I basically wrote the paper, but all the mathematics (other than my pressing for solutions with the correct symmetry) were done by Harry. As the model took form, I commented on the emerging mathematical results. For example, we needed a gradient from the tip of the limb that would evolve in steepness, so that the linear dimension of the tip would change in size. I would tell Harry what variables and parameters we needed to make it biologically as complete as possible, and what the best estimates of their values or ranges were. All the equations were written and solved by him, and I would incorporate them into a biological framework.
I would do all the writing in the evenings. I worked late into the night and still do. It was all handwritten. I didn’t use a typewriter. I think it took about six weeks to write the paper.
HS: Was Science an obvious choice for this paper? Did you consider submitting it elsewhere?
SN: Well, Science was our first choice because it was the journal where it would get the most attention. We were lucky to have it accepted, and without a struggle. Stuart Kauffman had published a couple of theoretical papers in Science that paved the way for us. One of them was a Turing-type model of early Drosophila embryogenesis. Although this analysis was sidelined by subsequent genetic findings, it was conceptually compelling and led to Science’s editors being receptive to papers in theoretical developmental biology. I also recall that Leon Glass, then a rising theoretical biologist, whom I knew as a member of the Stuart Rice and Department of Theoretical Biology research groups on Chicago a decade before, told me he had been a reviewer of the paper. Both reviews were very positive. Finally, we were fortunate that the positional information model for the limb had not yet become entrenched internationally. If we had sent it to Nature, it would almost certainly have been rejected because the British groups were very thick with each other. There were few followers of Wolpert in the U.S. until a couple of years later, when almost every limb developmental biologist had converted to the positional information view. Two or three years later the paper wouldn’t have gotten into Science.
HS: In the paper, you make predictions about the likely molecular candidates—you call them ‘M’ and ‘I’. You have already spoken about ‘M’. What about the other molecule?
SN: Within the terms of the model, we needed two main molecules. We needed one whose concentration formed 3D sine waves and therefore served as the templates for the skeletal elements. That was ‘M,’ and we identified it with fibronectin. Fibronectin had that distribution and it appeared at the time that the limb elements were being established. And the mesenchymal cells, before they formed cartilage, formed tightly packed precartilage condensations. So, you needed something that could draw cells together, and fibronectin was known to do that. It was only about the mid-70s that it had been named and its properties (which were based on studies of several previously isolated proteins that were found to be the same) characterized.
The other factor, ‘I,’ was needed to control the size of the unorganized portion of the limb bud. Our equations were consistent with sine wave solutions with arbitrary numbers of peaks, What the actual solutions were at the stationary states were determined by a “control parameter.” The control parameter in our case was the length of the unpatterned limb tip. There were published studies (e.g.) that showed that the length of the undifferentiated portion of the limb tip decreased during development concomitantly with the elongation of the full limb bud. This change in the control parameter provided a “selection rule” for the number of skeletal elements. A polysaccharide called hyaluronic acid (or hyaluronan) is present in that region and had been experimentally shown to block differentiation and keep the zone labile. So, we hypothesized that the undifferentiated zone’s length was determined by a gradient of hyaluronan (see Fig. 3a of Newman & Frisch, 1979).
Those were the two molecules, and this partial characterization has held up. Fibronectin does anticipate the positioning of the skeletal elements and consolidates condensation. The apical ectodermal ridge (AER) is the tissue that controls the extent of the unpatterned tip, and it produces a molecule called fibroblast growth factor (FGF) whose role in limb development wasn’t discovered until several years later. If we knew about that, we would have included it in the model. FGF is known to induce hyaluronan, so the two factors may act in concert.
Anyway, the molecular biology has changed a lot since then. As I said, it’s the galectins that we now consider the primary patterning factors. Despite our evidence for this, it’s something that hasn’t been taken up by others in the field. Maybe it will take another 40 years!
HS: I’d like to ask you about the concluding lines in this paper, where you talk about some questions that remained open at that point in time. I’ll read out that section, and I would like you to tell me what you think of these lines now: “Many questions remain open. How, within our scheme, can one account for the anteroposterior and dorsoventral polarities that characterize the limb? Must these be introduced by an independent gradient-like system of specification, as suggested by Tickle and coworkers (50) and by Wilby and Ede (51), or can they be accommodated within our model by using more realistic chamber shapes, or even nonuniform circumferential boundary conditions for the system dynamics as might be implied by the clockface model of pattern regulation of French et al. (52)? Can the general scheme we have proposed be accommodated to systems such as the amphibian limb, which can regenerate in the adult form (53)? These theoretical questions, as well as experimental problems raised by our model, remain to be resolved.”
SN: The dorsoventral dimension is the axis defining the back vs. the front of the limb. If you think about the back of one of your finger bones versus the front, there are subtle distinctions that are likely mediated by quantitative and possibly qualitative differences in molecules that come into play when these elements are formed. The digits are not simple cylinders. The anterior to posterior differences across the limb bud that distinguish the thumb and the other fingers from one another, were most compelling for the positional information proponents, since in their view each digit was separately programmed or encoded in the genome. After our paper came out there was burst of research activity on the Hox genes and the proteins specified by them. These are modulators which are present in varying amounts and combinations throughout the bodies of vertebrates and most other animals and control or influence the development of regional differences. So, while the vertebrae in your neck, the ones in your back, and those closer to the pelvis are all formed by the same process but due to Hox gene gradients, Hox protein abundances differ across regions. Those proteins – transcription factors – serve to fine-tune the formation of those units. To summarize, tissues or tissue modules that are formed by the same mechanism, primarily, become customized secondarily. It’s similar to cars going down an assembly line all being made the same way, but then they might wind up being different colours or having different interiors.
For a long time, in line with positional information theory, the Hox proteins of the developing limb were thought of as components of the positional gradient that determined the digits directly eliciting their individualized formation, rather than as customizers of collectively generated (e.g., by a Turing-type mechanism) digits. This view influenced how new problems were approached. For example, in comparing the limbs of therapod dinosaurs with those of birds, a controversy arose as to whether the avian limb contained digits corresponding to 1-3 of dinosaurs, as predicted by trends in the fossil record, or digits 2-4, as suggested by the developmental anatomy of extant species. The “frameshift” model postulated there was a shift over evolution in the relationship between the capacity of limb bud tissue to form condensations and the positional information gradient. This led to digits of a certain identity in one species forming in different positions in a derived species. It seems clear that theorizing this evolutionary transition would have benefited from considering digit position and digit identity independently, as postulated by the Turing model. But this didn’t happen. The frameshift hypothesis generated numerous papers, but none discussed periodic pre-patterning mechanisms. The idea was eventually disconfirmed, with the putative evidence assimilated into a hybrid model in which digit identity is established independently of a periodic pre-skeleton template. Sidelining the Turing model distorted limb development research.
HS: What do you see as the place of this paper and the message of this paper in our understanding of evo-devo today? What might be a reason for somebody to read this paper today?
SN: At the time that this paper was written, physics wasn’t an important component of developmental biology. There was some mathematical modelling of patterns and forms, but it was a very marginal enterprise. One reason was that there wasn’t much interaction between theorists and experimentalists. The theoretical mindset was: “Consider the interaction between (unnamed) variables X and Y. This explains your observations.” And the experimentalists’ position was: “Physics is always there, but the genes are the only difference makers in development,” or more assertively: “The genes constitute computer programs that direct the behaviour of the embryo’s cells.” Our paper attempted to make a connection between the most recent molecular and cell biological findings in limb developmental biology and advanced theoretical concepts that explicitly disavowed computationism. Nowadays, experimental papers on pattern formation generally won’t be published in the major developmental biology journals unless they have a mathematical model in their supplementary information section. The whole field has changed. And I think that our paper was close to the beginning of this transition. It helped initiate a convergence of physical modelling and experimental developmental biology.
The kinds of theory that existed in developmental biology in the 1960s and early 70s – mainly computationist and informationist – has largely subsided. What has been learned about genes and their regulation in the past 50 years, and recognition of phenomena like developmental system drift (the conservation of structure and function despite extensive change in involved genes and developmental pathways) are inimical to the notion of computer-like genetic programs. The default now is to look for self-organization in development and physical models of development and not assume that the embryo or its cells are computers. The latter concept held on for longer than it should have because of positional information. Positional information was something easy to understand—cells are computers, we don’t need to be concerned with how they became computers – it was evolution. All these little computers needed were simple universal gradients to instruct them to act in a species-specific spatiotemporal fashion.
You didn’t really need to have any training in physics or mathematics courses to understand this. Now, developmental biologists need to collaborate with physicists and mathematicians to understand the relevant self-organizing processes and the complex tissue behaviors that have evolved in their context. Although embryos clearly establish regional differences in certain structures via Hox gene expression and other factors, and these are sometimes reused in different regions, the idea of positional information as the universal code of development quickly became discarded in a lot of different areas of developmental biology. So, regarding the formation of somites along the backbone, very quickly people started to look at oscillatory models and physical models instead of positional information. In the limb, it held on decades longer than it might have because the positional information originators were also working on the limb. So, there were generations of students and postdocs who were committed to looking at it from positional information viewpoints. No one looks at the stripes of a zebra, or the arrangement of hair follicles on the skin, and says that’s positional information. They say that it’s some kind of Turing-type reaction-diffusion mechanism, though the molecular and mechanical components, and their relationships, are often obscure and different between species. But in the limb, even with its discrete, periodically arranged digits, most investigators ignored the Turing model for more than 30 years. So, while our model helped to dispel the computational and cybernetic idea of development, and to bring together experiment and theory, it also happened that the people with the most popular informationist theory were working on this same system and they weren’t ready to let go of it.
HS: This is my final question, and I want to zoom out a bit from the paper. As you know, this is a project about foundational papers in evo-devo. Although this paper preceded the formal beginning of the field, it has had a big influence on it. I wanted to ask you whether you think of yourself as an evo-devo biologist and, if you do, at what point in your career did you start to think of yourself in this way?
SN: That was primarily due to Gerd [Müller]. I wasn’t thinking much about evolution when Harry and I wrote the ‘79 paper. I was just thinking about development. But there was a colleague at Albany, Helen Ghiradella, who noted the evolutionary implications: if this is the way the limb develops, it’s probably the way the limb got started. And I then also began thinking about the evolutionary side of development.
Interestingly, before I became involved in evo-devo, “evo-devo” took an interest in our limb model. In late 1981, I was contacted by a science writer at Newsweek magazine to arrange an interview at my New York Medical College laboratory. The interview appeared in the January 11, 1982, cover story “How Life Begins: Biology’s New Frontier,” which dealt with new trends – including experimental and conceptual approaches – in developmental biology, spurred by the controversies around abortion and in vitro fertilization. I asked one of the reporters (possibly Sharon Begley, who co-wrote the story) how our paper came to their attention and they said it was Pere Alberch, a young Spanish biologist who was then an assistant professor at Harvard. I had not heard of Pere, but now, three decades after his untimely death at 43, he is recognized, as the seminal figure in the establishment of evo-devo.
While Brian Goodwin and I never published anything together arising my time as a research fellow in Sussex in the early 1970s. he had an enormous influence on me. And he was always interested in evolution, eventually becoming one of the early evo-devo people. I also became close friends with Dick Lewontin at Sussex, where he was coincidentally doing a sabbatical during the time I was there, and had an interesting encounter about my nascent views of evolution with John Maynard Smith: I would always kind of take pot shots at adaptationist models during informal discussion and seminars. And Maynard Smith said, you know, you really don’t seem to believe what we’re saying. He said, “I can’t tell whether you don’t understand it or whether you really have serious disagreements with it.” It took doing a sabbatical in Australia in 1989, a decade after the Science paper, where I wrote a review article with the physical biochemist Wayne Comper on “generic” physical mechanisms of morphogenesis and pattern formation (Turing-type mechanisms and additional mesoscale physical effects that can organize tissues during development), and then encountering Gerd and his work a half-dozen years later, that I figured out the answer to Maynard Smith’s question, and found myself on a new track as an evolutionary developmental biologist.
In 1994, I submitted a paper to the Journal of Evolutionary Biology that brought together many different things I had been thinking about, including the limb model and the framework developed with Wayne Comper, on physical models in developmental biology, and how they might relate to evolution. I had never met Gerd, but he was the handling editor of that paper. With great insight into what I was trying to do, he picked two reviewers who were very receptive to my approach (as he was, since he was doing conceptual and experimental work in a complementary vein). The reviews were signed, and the reviewers were John Tyler Bonner and David Wake, two senior scientists whose work (on, respectively, social amoebae and anatomical homoplasy) anticipated the themes of evo-devo. My paper, by someone unknown to the field, would never have gotten into an evolutionary biology journal if it didn’t have an editor who understood it, and in those days there would have been very few. Then, about a year later, Gerd and I met in Chicago at a conference on vertebrate morphology and we really hit it off. I started visiting the KLI after that, and we began writing things together. Gerd has been one of my most important collaborators and dearest friends. He brought me into evolutionary biology and was instrumental in my arriving at the perspective that has compelled my work since then.
HS: What was the motivation for the paper you submitted to the Journal of Evolutionary Biology?
SN: Basically, I started considering physics as not a distinct factor from genetics, but in interaction with it the origination and development of form. If classic genes work in concert with chemistry, e.g., in bacterial sugar utilization or human metabolism, why not think about morphogenesis as gene products mobilizing the physics of materials? At the time the paper was written it wasn’t really clear how this happened phylogenetically – I was just speculating – but by the late 90s the set of unexpectedly conserved animal “developmental toolkit” genes were described, and it became clear that the products of those genes mobilized distinct physical forces and effects. Everything began to click into place. This implied that the origination of the animal body plans, and different animal phyla were, in many ways, predictable consequences of the inherencies of multicellular matter. Gerd and I published a paper in the Journal of Experimental Zoology Part B (one of the early evo-devo journals) titled “Epigenetic mechanisms of character origination” which was the first presentation of this idea in the “post-toolkit” era. This perspective was key to the work I later did with Ramray Bhat when he was a graduate student with me. I previously mentioned Ramray with respect to the galectin limb experiments and theory, but he also worked closely with me on the idea of “dynamical patterning modules,” associations between specific toolkit gene products and the physical effects they mobilize. By the first decade of the new century I had become a committed evo-devoist.
HS: This is really my final question. You said that when you were in John Maynard Smith’s department you were taking pot shots at adaptationist explanations. I was wondering about that because you said you were not so interested in evolutionary biology at that point in time, but were you already sceptical of these kinds of explanations?
SN: Yes, they just didn’t add up to me. Even when I read Darwin, I just wasn’t convinced! As I mentioned, I knew Richard Lewontin at Chicago and at Sussex. He was at odds intellectually with my main senior colleague there, Brian Goodwin, who was New Agey where Lewontin was Marxist (particularly from Dick’s side; Brian was much more tolerant of other’s views). But I resonated and found inspiration in both for a view of life that wasn’t merely a product of randomness and opportunism (i.e., adaptationism). (My predisposition to this way of thinking was reinforced by having read Edmund Sinnott’s Cell and Psyche: The Biology of Purpose and Rachel Carson’s The Sea Around Us – both from 1950 – as a teenager.)
Although Dick’s famous “Spandrels” paper with Stephen Jay Gould didn’t come out until 1979 (the same year as our limb model), his reservations were in evidence seven years before when we were at Sussex. By the time I met Gerd, his 1990 paper on ontogenetic side effects had appeared, and connected the notion of nonadaptive novelties to developmental processes (which were not considered in the Spandrels paper). This really connected with my own thinking. Since then, with the rise of evo-devo, adaptationism has been in retreat in evolutionary theory.
But how can novel forms (and functions) help set the direction of evolution when they arise by physical and developmental inherencies and other non-selected effects? This question, which stems from Lewontin’s (and Kropotkin’s before him) notion of organisms as subjects, not just objects of evolution, has led me to a new chapter in my career (which feels like the culminating one), which centers on organismal agency as a main driving force of evolution. A recent publication in The Quarterly Review of Biology, written with a group of long-standing and newer colleagues in biology, philosophy, and the physical and mathematical sciences, is directly concerned with this question.
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