Some biologists remain skeptical that Turing mechanisms are sufficient to account for these periodic patterns, particularly because there are other viable models, including one proposed by Lewis Wolpert, an emeritus developmental biologist at University College London. In Wolpert’s model, cells interpret their position in space based on how much of each morphogen there is, resulting in stripes, spots or digits. Furthermore, Wolpert said, “no one has yet identified the molecules that work for a Turing mechanism in development.”
That lack of experimental identification has been the most serious stumbling block for Turing advocates, but that has begun to change. Last year, Green and his colleagues identified two chemicals that behave as activator and inhibitor, giving rise to the regularly spaced ridges found in the roof of the mouth in mouse embryos. A protein called fibroblast growth factor (FGF) serves as the activator, and a gene variant dubbed Sonic hedgehog (Shh) acts as an inhibitor. When the researchers increased or decreased the activity of those chemicals, the pattern of ridges were affected just as Turing’s equations predicted.
Biology is messy and complicated, with many confounding factors, which makes it difficult to demonstrate experimentally that a pattern results from a Turing mechanism. So Green and his cohorts removed one of the ridges, thereby increasing the space between ridges. If there were no Turing mechanism, a replacement ridge would have formed. Instead, the researchers saw extra ridges pop up in a branching pattern to fill the space — a hallmark of Turing’s model.
Applicable to any number of systems, the Turing mechanism is almost too general. Researchers have identified Turing-like features in the distribution of species in ecological systems, such as the predator-prey model, in which the prey function as activators, seeking to reproduce and increase their numbers while the predators act as inhibitors, keeping the population in check. Neurons, too, can be described mathematically as activators or inhibitors, encouraging or dampening the firing of other, nearby neurons in the brain.
“If you have any two processes that act [as activator and inhibitor], you can always get periodic patterns out of them,” said Green, pointing to the ripples that form on sand dunes as an example. “Clearly there are no diffusing morphogens at work there. It’s just that the processes have a property you can represent using a diffusion function.”
Turing admitted as much in his original paper: “This model will be a simplification and an idealization, and consequently a falsification,” he wrote. That doesn’t necessarily mean the model is wrong, but it is challenging to move from identifying the behavior of a system that seems to follow a Turing mechanism to identifying the specific physical processes that act as activator and inhibitor. For example, experiments with zebra fish stripes have shown that they arise from a Turing mechanism, but rather than secreting chemicals that spread throughout the system, the fish has two kinds of cells that serve the same purpose as activators and inhibitors. The molecules most likely to play the activator/inhibitor roles can only be embedded in a cell membrane, not secreted. So for the mechanism to work, the cells must have contact with one another.
Granted, the Turing model has shortcomings. A Turing mechanism alone cannot account for scaling in nature’s patterns. Chicken eggs are a good example of scaling, in that they can be large, small or anything in between, but regardless of the size of a fertilized egg, if it hatches, the product will be a complete chick — not one that is missing crucial parts. “The question Turing fails to answer is: How do you get that scaling process?” Green said.