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Adrian Fessel et. al.

# A Slimy Insight Into Treating Cancer

Smarty-pants slime molds can solve mazes and produce diagrams similar to the Tokyo rail system—and now, scientists suggest, they may also be able to help treat cancer. Biophysicists in Germany and Singapore suggest that mathematical models based on slime mold behavior might lead to new ways to starve tumors of blood.

The slime mold *Physarum polycephalum*, usually found growing inside rotting logs, forages for food by extending a network of thin tendrils from its edge. Once the mold has found food, such as a piece of decaying vegetation or a microorganism, it grows over it and secretes digestive enzymes. *P. polycephalum* then constructs an elaborate network of interconnections between food sources, allowing it to shuttle nutrients around.

In 2010, mathematical biologist Toshiyuki Nakagaki, now at the Future University Hakodate in Japan, and his colleagues observed how this networking behavior might translate to efficient city planning; they placed the mold in a laboratory culture that also contained a scale model of the region around Tokyo, with food sources representing population centers. The slime mold's tendrils, they found, produced interconnections strikingly similar to the layout of the Tokyo railway system.

But it's the mold's early growth, even before it forms those elaborate foraging networks, which might hold clues to understanding how tumors supply themselves with blood. Slime molds start as a collection of isolated spores; as they grow outward, the spores meet and fuse into islands. The islands send out tendrils that eventually meet other islands; when they meet, they fuse again, ultimately forming a large, single-celled organism that can now transport fluid throughout itself. There's a mathematical term for this: The point at which separate networks, each with its own transport system, become interconnected enough to allow a fluid or some other substance to move freely between them is called the "percolation transition."

To construct a mathematical model of the percolation transition, Adrian Fessel, Hans-Günther Döbereiner, and colleagues at the University of Bremen in Germany and the Mechanobiology Institute, Singapore studied the way that slime molds grow in the laboratory. Understanding how those connections form and when that transition occurs may have a practical application, Döbereiner says. To survive and grow, tumors need a blood supply; many highly invasive tumors can construct a completely new vascular system from tumor stem cells which grow, meet, and fuse before connecting to the healthy tissue's blood supply. Since the process of connection is mathematically identical to the percolation transition in the slime mold, a mathematical model of the latter should be equally valid for both, he says.

As the mold tendrils grew toward each other and joined up, the researchers used network diagrams (like subway maps) to track the connections between tendrils. They recorded how many connections radiated out from each node to get a measurement of "interconnectedness," similar to the number of subway lines that serve a particular station. Writing in *Physical Review Letters, *the scientists found that the transition from multiple mold islands to an interconnected network—the percolation transition—always occurred when the nodes and lines fell into one particular, peculiar pattern. Regardless of how many overall nodes there were, what mattered was how many of them had exactly three emerging lines, how many had one emerging line, and how many nodes remained completely isolated. For one particular ratio of those three numbers, percolation transition always happened.

"The results are very interesting and novel," says Nakagaki, who was not involved in the present work, "and the analysis by means of a standard technique of percolation is clear and beautiful."

Starving tumors of blood is a key way to attack cancers, so Döbereiner hopes that the researchers' insight into vascular network formation may one day lead to ways to inhibit the development of tumors' blood supplies and curb their growth. To demonstrate their model's applicability to vascular growth, the researchers showed that they could reproduce the results of a 2003 laboratory study conducted by other researchers into the growth of vascular networks using their slime mold-derived mathematical model.

Although reproducing that 2003 study is a useful demonstration that their model is applicable beyond slime molds, Döbereiner points out that from a mathematical standpoint, such a demonstration is somewhat redundant. The two situations—slime mold growth and vascular network growth—are mathematically equivalent, he says, and so a model that works for one is required to work for the other. "Even if we hadn't done that experiment [with the vascular network] … there is mathematically no way out!"