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What Fractals Can Teach Us About Cancer

A new study describes fractal patterns emerging on the surfaces of single cancer cells.

A crucial difference between healthy cells and cancerous cells may be the presence of fractal patterns. This is according to new observations courtesy of researchers at Tufts University and Clarkson University, who have been examining the surfaces of cervical epithelial cells at nanoscale resolutions using atomic force microscopy.

These cancer fractals are a new, never-seen-before observation at single-cell resolutions, and their presence hardly seems to be a coincidence. They may even point the way toward a better, deeper understanding of what cancer even is: chaos. That is, cancer is the name given to a cell (and then tissue) that's gone off the rails, in a sense, where its complex machinery has become unbalanced and, indeed, chaotic in a scientific sense.

Previous studies had already found traces of fractal patterns in the biochemistry and mechanics of cancerous tissue, but never before on the surfaces of single, isolated cancer cells. And this is where cancer really becomes cancer—on the surfaces of cells—as it drives metastasis, e.g. when cancer cells leave their primary tumor homes and travel elsewhere in the body to set up shop, forming secondary tumors.

Read more: "Five Ways that Fractals Aren't Just for Nature Anymore"

Recall that a fractal is basically an endless pattern. As you zoom in on it, the pattern continues to repeat at every new scale. We can say that they are "infinitely complex," the very signatures of chaos itself. And so fractals are everywhere in nature, from coastlines (famously) to seashells to tropical storms to the large-scale structure of the universe.

Image:  I Sokolov et al​

"When talking about the nature of cancer, it is plausible to consider two different views," the researchers write in the New Journal of Physics. "[Either] cancer is a deterministic switch no matter how it is induced, or cancer is a chaotic imbalance of biochemical reactions, a sort of side effect of cellular complexity, which was overseen by evolution. In this work we show some evidence that the picture seems to be more complicated."

The fractal patterns seen here only arose at the stage in which cancer cells transition from the "immortal" premalignant stage to the properly cancerous stage. As cancer cells continue to divide, simple fractals give way to "multifractality," which is pretty much what it sounds like. This marks a transition period, where suddenly cells become aggressively disorganized and nondeterministic before the cancer again becomes organized and deterministic, albeit according to cancer organization and not healthy cell organization.

So, both views are right, sort of. Cancer is organization born from chaos.

"This result will be useful for the development of models describing cancer development and progression," the Tufts researchers conclude. "It may also bring a new means of attack on cancer, for example, by searching the points of instability that influence chaotic development the most. Biologists could start identifying those instabilities in the pathways connected to formation of the pericellular coating."

"Besides the fundamental interest," they continue, "the obtained results could be used to measure the degree of possible progression towards cancer."