You can learn a lot from a little slime mold.
For Nate Cira, assistant professor of biomedical engineering in Cornell Engineering, the tiny eukaryotic organism provided inspiration for modeling "traveling networks" - connected systems that move by rearranging their structure.
Understanding these networks could help explain the structures and movements of certain biological systems and human organizations, from protein units that reassemble themselves to corporations expanding their product lines.
The findings were published Feb. 26 in Nature Communications.
It all began with a game.
As a graduate student, Cira took a course with professor Ingmar H. Riedel-Kruse at Stanford University in which students played "biotic games" with simple organisms as a means to explore their biological processes.
The game in question put a slime mold organism in an "arena" of agar. The students then guided the mold's movements by depositing food, in the form of oatmeal droplets, via a robotic system. Cira noted that the mold moved in a curious manner, like a tree that crawls by extending some of its branches while simultaneously retracting others.
Long after the class ended, Cira, along with Riedel-Kruse, now at the University of Arizona, and a group of collaborators continued playing around with the organism's curious motion. Together they built a toy model of the organism to understand how it functioned, and they coined a term to describe it: a traveling network. While many types of networks have been studied and explicated in great detail - from neural and social networks to photonic nanostructures - Cira was surprised to find a lack of work on systems that move through space by rearranging their structures. Little did he know that studying every facet and feature of the model would become "a kind of long-running passion project, one of these things I kept bouncing along on the side, just uncovering fresh and interesting insights and things to explore," said Cira, whose main area of study is microfluidics. "It's almost more of a hobby than work in some way. But it turned into something quite beautiful in the end."
The model is essentially a graph of edges and nodes. Any node can have at most three edges, which gives it a tree-like shape. The structure can be manipulated to move by a few simple actions: the leaf, i.e., the tip of a branch, can grow; it can split to generate two new edges; or it can retract until it disappears.
"It's actually a very simple model," Cira said. "It only involves a few basic actions, and due to these dynamic rearrangements it travels over to some new area, much as the organism does."
The model in motion resembles the rudimentary screensavers of yesteryear, but there is nothing simple about explaining a structure that is constantly rearranging itself as it moves. Cira credited his collaborators' patience for an exhaustive treatment of the topic - work that stretched on for roughly a decade.
In order to characterize the traveling network's behavior, the team derived mathematical relationships and visualized network behaviors through simulation. The network's ability to self-organize to the point poised between growth and decay also enabled it to respond to small changes in its environment, which the researchers demonstrated by introducing digital oatmeal for the model to gobble up like Pac-Man.
"We tried to derive as much as we could, mathematically, about why does it have the fractal-like appearance of a tree? How much can we say about the characteristics of the motion? And what does that mean for systems like this?" said Cira, who drew inspiration from a range of physics disciplines, such as the study of polymers and earthquakes, to clarify the mechanisms at work.
Among the systems that fit the criteria of traveling networks, the researchers identified very different candidates: the actin cytoskeleton - a network of monomeric protein units that disassemble and reassemble, creating a branch-like structure that drives the movement of cells - and, on a more conceptual level, the Nokia Corporation.
"People often talk about companies branching out into new markets or cutting a product line," Cira said. "Nokia started out in paper and branched into rubber markets and then made electrical wires coated with rubber. That got them into electronics of all different sorts, phones, especially. And then eventually the iPhone came out and totally decimated their business in that sector."
At one point the researchers wondered if the concept could be applied to art as well. While the prospect of having a scientific theory that explains the development of Picasso or the chronic reinvention of David Bowie is certainly enticing, Cira found that type of progression increasingly difficult to quantify. But with less ineffable systems, such as the gene flow between interbreeding populations or communication among swarming robots, the traveling-network model could be a helpful framework for scientists, and a springboard for more complicated modeling.
"Whether or not that means they're going to use any of the math that we spent so much time deriving, it remains to be seen," Cira said. "And it remains to be determined whether this specific model is directly applicable to any system, but if our work is any indication, the study of connected dynamic systems that travel through space promises to be full of rich insights."
Co-authors include researchers from Stanford, Harvard University, University of New South Wales and University of California, Berkeley.
