 controlled through the concentration of chemical signalers, called morphogens. He derived equations showing that interactions between morphogens that activate and inhibit one another’s gene expression could set up standing waves of morphogen concentration, and control embryonic patterning. With just four variables—production and degradation rates, diffusion rate, and interaction strength—Turing could reproduce biologically plausible, self-directed pattern formation.
His prediction of a chemical system of information management was proven true decades later with the first discovery of a morphogen in fruit flies, called bicoid (though his equations proved to be too simple). Cells in a fruit fly embryo with high bicoid concentration become the fly’s head, and those with lower concentration become its body. What is remarkable, however, is how quickly and accurately these cells differentiate. In 2007, a team led by Princeton biophysicist Thomas Gregor measured the concentration gradient and diffusion rate of bicoid in fruit fly embryos. They estimated that it would take around two hours for embryonic cells to measure the morphogen concentration with enough precision for adjacent cells to mature differently (measurement precision increases with measurement time). But this is nearly the entirety of the fruit fly’s developmental period, from fertilization to cellularization. The embryo was developing faster and more precisely than should have been possible.
Gregor proposed that multiple cells could be sharing information with each other using a second signaling chemical: One candidate is a morphogen called hunchback. This would allow them to compute a spatial average of bicoid concentrations, rather than relying entirely on individual readings. The averaging process would be less susceptible to variation and noise, and would allow the required pattern accuracy to be achieved in about three minutes, rather than two hours.
The process is not just ingenious, but efficient. To find out how efficient, physicist William Bialek used nucleus-by-nucleus measurements of morphogens in fruit-fly embryos to study how closely hunchback concentrations followed changes in bicoid concentrations. He found that the fidelity of this information transfer was 90 percent of the theoretical maximum.
A video interview with the author, Kelly Clancy.
When an embryo develops into an adult, it confronts a new information processing challenge. Its body must learn how to sample and integrate both external and internal information. Odorant molecules signal a predator, prompting a rodent to flee. The setting sun triggers melatonin release, causing a cascade of effects throughout the body, inducing sleep. Internal chemoreceptors measure high carbon dioxide levels, causing an athlete to breathe faster. Information from microscopic measurements, sampled by disparate sensors, must be integrated and used to make macroscopic decisions that are efficiently communicated back out to relevant body parts.
Here, too, nature has discovered an optimal solution, whose details can be read in the shapes of our anatomical structures. One of the earliest observations of a mathematical relation in biology was that almost every living creature in every ecosystem on the planet, spanning more than 20 orders of magnitude in size from uni- to multi-cellular, has features that scale with the mass of the organism, including heart rate, life span, aorta size, tree trunk size, and metabolic rate. This is called allometric scaling.
A rule of thumb common in the halls of Intel was programmed into our bodies eons ago.
Strangely, the relationship between these features and an organism’s mass usually follows a power law. That means, for example, that metabolic rate depends on the organism’s mass, raised to some constant power. Even stranger, the constant for the majority of these features is some multiple of one fourth. Physicist Geoffrey West has argued that this scaling results from the ubiquity of fractal-like networks within organisms. Fractals are structures that have similar structure at