How the Tiger Really Got His Stripes

Imagine grasshoppers distributed evenly across a dry field. As the temperature rises, the grasshoppers start to sweat. The field catches fire in a few spots and starts to spread. But the perspiration of the hoppers (profuse!) inhibits the fire’s growth. What kind of burn pattern will appear in the field? If the grasshoppers sweat more, or less, or if the fire spreads faster, or slower—how will that alter the burn pattern? This visualization was proposed by James D. Murray, a prominent scholar in the field of mathematical biology, in a paper in 2012. The point of it was to give people a sense of Turing patterns, a concept worked out by the mathematician Alan Turing, in 1952, to describe how a pattern can arise from an initially homogenous state. Turing patterns offer insight into (among other things) the patterns we find on animals, whether it’s the splotches on giraffes, the dot-and-line motifs on whale sharks, or the stripes on tigers. Those stripes appear where pigment-producing melanocyte cells are turned “on,” analogous to the burned sections of the field; the factors that turn these melanocytes on, or off, are analogous to the fire and the sweat. For decades, Turing patterns were one of the few tools we had to think about nature’s perplexingly marvellous motifs. But, recently, owing to researchers in widely different fields, that has changed.

To understand this work, it’s helpful to know what Turing was really trying to do. He had already imagined the “universal machine” that prefigured modern computing, proposed a test for determining whether a machine could be considered intelligent, and cracked the Nazis’ Enigma code. Now he was thinking about Holstein Friesian cows and about the way that a small group of cells could somehow “know” how to grow into the cows’ characteristic black splotches—or into the five-fold symmetric pattern of a starfish body, or the spirals of a pinecone. Turing disliked the near-mystical thinking around the origin of such designs. He didn’t believe in God and didn’t like the prevalent arguments that only the presence of a divine hand could explain such beauty and complexity. To counter that thinking, he said that he wanted to develop a “mathematical theory of embryology,” one that would puzzle out how a small sphere of cells could go on to assemble themselves into extensive and elaborate patterns of which they were only a tiny, unknowing, unthinking part. He thought about a simple system with an activator (like Murray’s fire) and an inhibitor (like the grasshopper sweat), in which the activator stimulates the production of its own inhibitor. After working overnight on equations representing such systems, Turing would corner colleagues the next day with printouts, asking, Do these look like cow splotches to you? What about these? In August, 1952, this thinking culminated in the publication of “The Chemical Basis of Morphogenesis,” the last paper Turing published before dying from biting into a cyanide-laced apple. Turing used potassium cyanide in his home laboratory to electroplate spoons with gold, so it’s unclear whether his death was intentional. Of his final paper, Turing said that it “does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts.”

Ben Alessio and Ankur Gupta weren’t thinking about stripes or spots when they started the work that has since clarified the field. Alessio was working in Gupta’s chemical and biological engineering lab at the University of Colorado Boulder. (Alessio is now a graduate student at Stanford, studying how ice flows.) “It’s a little bit backward how we ran into this problem,” Alessio told me. “We were studying diffusiophoresis.”

Gupta broke this seven-syllable word apart, to make it more approachable: “There’s diffusion”—like what ink does in water—“and there’s phoresis”—which refers to the movement of a particle. Together, the word refers to “a big particle that is dragged by smaller particles around it, so the larger particle’s motion is in response to the diffusion of the smaller particle,” Gupta said. A good example of this is soapy laundry: as the relatively small soap particles diffuse through water, they bring with them relatively large dirt particles. Diffusiophoretic systems can be used to purify water without a filter, and might prove useful in altering how a medicine gets distributed in a body.

Alessio had mathematical inclinations, so Gupta suggested that he familiarize himself with Basilisk, a software program for running mathematical simulations. One of the examples in the Basilisk tutorial involved Turing patterns. “Honestly it was the first time I had heard of them,” Alessio said. “I had no idea Turing had done work in biophysics.”

They modelled a reaction-diffusion system (like the sweating-grasshoppers example) that also had a diffusiophoretic element. (Imagine some tasty seed in the field that grasshoppers roam to eat, altering their distribution.) A hexagonal pattern emerged. This was a classic Turing pattern—but with one notable difference. Just as ink diffuses in a cloudy way, Turing patterns, which are based on diffusion models, tend to have blurred boundaries. When Alessio and Gupta added diffusiophoresis to the standard reaction-diffusion models of Turing, the resultant patterning was sharpened, with each element more distinct. “It was like they were made with a pencil rather than a paintbrush,” Alessio said.

But this was just in mathematical simulations. “We wanted to find an experimental model to compare it to,” Gupta said. This wasn’t easy. Then Alessio visited the Birch Aquarium, in San Diego. The aquarium is home to little blue penguins and weedy sea dragons and leopard sharks. It is also home to the rare Australian ornate boxfish, whose body is a shimmery purple with thin orange lines that form hexagons on its sides. When Alessio saw the fish, it looked to him like the sharpened Turing patterns he and Gupta were studying. “It was uncanny,” Alessio said. He sent a photo to Gupta, who responded by saying that he’d found their next paper. Gupta said of the work that followed from that fortuitous fish sighting, “We are not debating the Turing-pattern mechanism” as a way of understanding how a sharp pattern like that of the boxfish might emerge. “We are adding a small feature to it, to crisp it up.” It is not unusual for biological systems to have small particles that “carry” larger particles around; in fish, for example, small proteins move chromatophores—pigment-containing cells—around. Gupta and Alessio’s work offers detail on how diffusiophoresis may underlie the formation of such natural patterns.

As an evolutionary developmental biologist, Ricardo Mallarino said he has “always been fascinated by the question of how a single cell, through a series of very elaborate developmental processes, becomes a fully formed complex organism.” And, furthermore, how variations of the same developmental processes give rise to so many different species. Humans, mice, and flies all have nearly the same genes regulating the path from cell to sentient being. These curiosities very much overlap with Turing’s, so it’s not surprising that Mallarino’s work has also helped illuminate the mysteries of animal patterning. Mallarino is interested in the how of the phenomenon, in part because it can be ascertained with more certainty than the why.

Pattern formation in fish and in mammals is quite different; Mallarino wanted to study the subject in mammals, but cheetahs and zebras don’t make great lab specimens. Carsten Schradin, a colleague working in behavioral ecology at the University of Zurich, was studying a mouse species that is exceptional, in that the males care for the young. “Even among mammals, paternal care is very rare—it’s seen almost exclusively in primates,” Mallarino told me. “If you give a conventional male lab mouse a pup, it will immediately attack and kill it.” But this is not the case with the African striped mouse. “In these guys, the males will bring it back to the nest, lick it, hug it, keep it warm,” he said. That was compelling in and of itself, but what drew Mallarino to it was another feature: the stripes on the mouse’s back. In addition, this was a mouse species that hadn’t been bred for generations in labs, whose genetics were still essentially wild.

The dorsal skin of the African striped mouse, where the stripes are formed, has cell progenitors that have the potential to make hair light or dark. Rather than a blended distribution of light and dark, the progenitors form stripes. “We wanted to know when and how the cell decides which path to take,” Mallarino said. His group looked at cells very early in embryogenesis, before hair is formed, and found that “it was like a children’s coloring book.” The instructions for what color an individual hair should be appeared to have been laid out beforehand. Mallarino’s lab worked to identify genes in the striped mouse which might shape the early patterning.

Matthew Johnson, then a postdoctoral fellow working in Mallarino’s lab, was interested in applying mathematical modelling to the striped-mouse work. Using Turing patterns, he examined how the stripe pattern of the striped mouse could emerge if there were essentially an activator and an inhibitor of hair-follicle distribution, and the two regulated each other—Turing’s classic process. You have to be wary with mathematical modelling, Mallarino said, “because if you add enough parameters, you can generate pretty much whatever you want to see.” But he views modelling as a great way to generate testable hypotheses. “And we found something surprising,” he said. There was a set of genes that they had identified but whose role they didn’t understand. Further experiments predicted that they might underlie the patterning. With genome editing—CRISPR—they bred mice with one of those genes knocked out; just as their mathematical model predicted, the width of the stripes had changed.

Then they followed their curiosity a step further. Merlijn Staps, then a graduate student working with Mallarino, visited the holdings of the American Museum of Natural History. “He basically opened every drawer to see all the specimens of different rodent species that had stripes,” Mallarino said. The goal was to catalogue the diversity of patterns. “Tweaking the mathematical model we had been using allowed you to explain pretty close to every single pattern of stripes out there,” Mallarino said. The reaction-diffusion model they had worked out for the striped mouse could generate the patterns for ninety species of striped rodents. “That was very reassuring to us,” he said.

There was just one outlier. “The thirteen-lined ground squirrel,” Mallarino said. “That told us that the mechanism producing that pattern must be fundamentally different.” They have since begun to study the species. “It’s been super challenging,” he said. “It’s a mess.”

The “why” of animal patterns remains a puzzle. “There are several stories that are currently dominant in the thinking of biologists,” Mallarino explained, with each seeming more or less convincing depending on the species. Camouflage is the explanation with which people are probably the most familiar. Another well-known line of thinking is sexual selection—that certain patterns are especially attractive to potential mates. “This might be true for zebras,” Mallarino said. “But many species of rodents have poor vision. They rely more on olfaction.”

Another idea is thermoregulation, though a 2018 study challenged the notion that stripes help zebras maintain a cooler temperature than single-colored horses and cattle can. “Another one that came out recently is that it sort of helps with avoiding the bites of flies,” he said. “That was a pretty amusing paper.” Some horses were covered with striped cloth—they were visually turned into zebras—and researchers counted how many flies landed. “Far fewer flies landed on the striped horses,” he said.

As for Mallarino’s African striped mice, there are clues to why such stripes evolved in this species. For example, striped rodents are almost always diurnal and tend to have aerial predators, while strictly nocturnal rodents don’t have stripes. “I think the bottom line is that there are different hypotheses and it’s very hard to test them well,” Mallarino said. “And it really depends on the species.”

Attempts at understanding, however, still hold our attention. “You can lie around on the bare ground and look like a heap of pebbles,” the newly spotted leopard is told, in one of Rudyard Kipling’s “Just So Stories.” “You can lie out on the naked rocks and look like a piece of pudding-stone. You can lie out on a leafy branch and look like sunshine sifting through the leaves; and you can lie right across the center of a path and look like nothing in particular. Think of that and purr!” ♦