FLOCKS OF BIRDS FLY ACROSS THE SKY in shifting configurations. In the retina of an eye, millions of neurons ignite in ever-changing combinations, translating light into meaningful images. Yet both of these seemingly random behaviors have an underlying order that can be described by mathematics.
Like these cells and birds, when atoms and molecules come together they can display coordinated behaviors that are more than the sum of their parts. At a critical point, such as the boundary between liquid and gas, local interactions between molecules propagate through an entire material, changing its essential properties.
Princeton biophysicist William Bialek thinks criticality may also underlie collective behaviors in living organisms, and he’s using real-world data to test this hypothesis. Recently, Bialek and his colleagues have analyzed the flocking behaviors of birds, the genetic networks of fruit fly embryos and the activation patterns of salamander neurons.
“In physics, we use the same mathematical language to describe many seemingly different behaviors,” said Bialek, the John Archibald Wheeler/Battelle Professor in Physics and the Lewis-Sigler Institute for Integrative Genomics. “So we understand that the emergence of collective behavior from all the individual interactions has a kind of universality.”
To explore the possibility that this universality might extend to living systems, Bialek made use of a large dataset on the changing positions and velocities of thousands of individual birds in a flock of starlings. A group of Italian physicists used multiple cameras to record the birds and calculate their exact locations over time in three dimensions — “a technical triumph,” according to Bialek.
The researchers, including former Princeton postdoctoral fellows Thierry Mora and Aleksandra Walczak, analyzed the deviations of each bird from the flock’s average speed and direction of movement. They found not only that these variations were correlated between nearby birds, but also that the fluctuations from the average propagated through the group over long distances. This pattern of rapid, remote signal transmission echoes the changes that occur among molecules during a phase change from solid to liquid or liquid to gas. At a critical point, this could allow information to spread swiftly through the group, enabling the whole flock to nimbly change direction.
“The model you build just by keeping track of what each bird does relative to its neighbors predicts what happens throughout the entire flock,” Bialek said. “And it does so with an accuracy that is beyond what we had any reason to expect. It’s really a very precise prediction.”
Other biological examples of criticality play out on a microscopic scale. Bialek has an ongoing collaboration with Princeton’s Squibb Professor in Molecular Biology Eric Wieschaus, a Howard Hughes Medical Institute researcher and Nobel Prize winner, who has uncovered many of the genes involved in the embryonic development of the fruit fly — a model biological system.
Bialek has found signatures of criticality in gene activation patterns during the first few hours of fly embryo development. The synchronized actions of “gap genes” establish the fly’s 14-segment body plan. Mutations in these genes lead to gaps between segments, whose effects are reflected in the names of the genes: two examples are “hunchback” and “giant.”
Recently, Thomas Gregor, an assistant professor of physics and also a member of the Lewis-Sigler Institute, has developed experimental tools to precisely measure the activity of many gap genes at once, all along the halfmillimeter length of the fly embryo. These measurements allowed Bialek and physics graduate student Dmitry Krotov to test whether the patterns of gene activity across the embryo fit a model of criticality. Indeed, using data from 24 embryos, they found that fluctuations from the average level of gene activity at each point along the embryo were correlated between certain pairs of gap genes, which regulate one another’s activity like on/off switches. They mapped the locations of these switch points, which appear to act like signals that spread over long distances, just as changes in velocity are correlated in a flock of birds.
Bialek has also looked for signatures of criticality among the activation patterns in a patch of 160 nerve cells from a salamander retina, a model system for studying this light-sensing layer of the eye. In collaboration with Michael Berry, an associate professor of molecular biology and the Princeton Neuroscience Institute, Bialek and his colleagues showed how the coordinated activity of the neurons could be tuned to a critical state.
Bialek thinks critical systems may be common features of life that have repeatedly evolved in different organisms and at different levels — both molecular and behavioral. This could explain why, though systems of cells or groups of organisms could be organized in any number of possible ways, networks with similar properties continue to emerge.
“Is there anything special about the way nature has organized things in living systems?” Bialek wondered. He said much more work is necessary to claim criticality as a general biological principle. “But I do think we’re seeing in the data, somehow, signs of that specialness — things that it seems you can only get if the system has been set up in particular ways and not in others,” he said. “That I find very appealing.”
This work was supported in part by the National Science Foundation, the National Institutes of Health, the Howard Hughes Medical Institute, the W.M. Keck Foundation and the Swartz Foundation.
–By Molly Sharlach