Fractals are a fascinating type of pattern for mathematics nerds, with their repeating, artificial-looking structures. Now, scientists have discovered the first known fractal protein – and it seems to be an evolutionary accident.
Fractals are tricky to define, even for mathematicians, but generally speaking they’re geometric shapes that are made up of smaller structures that themselves resemble the whole. In practice, that means that if you zoom in on part of a fractal, you’ll see a similar structure – and if you zoom in on part of that part, you’ll see a similar structure, and so on essentially into infinity.
In nature, fractal features appear in things like snowflakes, lightning bolts, and river networks. Molecules might seem like a prime place you’d expect to find them, since they can arrange themselves into all kinds of intriguing shapes, but among all the existing catalogs of molecules, there has never been a regular fractal (those that match almost exactly across scales).
But now, scientists at Max Planck Institute and the Philipps University have found the first regular molecular fractal. It’s an enzyme used by a species of cyanobacteria to produce citrate, which was found to naturally assemble itself into a specific fractal pattern called the Sierpiński triangle.
Basically, start with a single equilateral triangle. Then punch out an inverted triangle from the center, so you have three smaller triangles that make up one larger triangle, with a triangular void in the center (a symbol that may look familiar to fans of The Legend of Zelda). Then punch out an inverted triangle from each of the smaller solid triangles, so you’ve got three of the second shape, or nine of the original shape, making up a larger triangle. You could potentially keep doing this forever, with each smaller triangle – and that’s the Sierpiński triangle fractal pattern.
“We stumbled on this structure completely by accident and almost couldn’t believe what we saw when we first took images of it using an electron microscope,” said Franziska Sendker, first author of the study. “The protein makes these beautiful triangles and as the fractal grows, we see these larger and larger triangular voids in the middle of them, which is totally unlike any protein assembly we’ve ever seen before.”
To figure out how this protein takes on such an intriguing structure, the researchers used electron microscopy to analyze it in more detail, and found that its self-assembly wasn’t symmetrical. Different protein chains were found to make slightly different interactions at various positions in the fractal, forming the striking structure.
So does this mathematical marvel serve a specific purpose in the bacterium’s biology? To find out, the team genetically altered the microbe so that the protein didn’t form the fractal structure, but the bacterium was still able to produce citrate just fine.
This inspired the researchers to investigate another possibility: that this structure is relatively easy to evolve, so it just happens by chance, and doesn’t need to have a specific purpose. They used an ancestral sequence reconstruction technique to trace back its possible evolution over millions of years, then biochemically produced those ancient proteins.
Perhaps surprisingly, they found that the fractal structure appeared fairly quickly, after only a few mutations. But it was soon lost in other cyanobacteria lineages, until it remained only in the one species it was recently found in.
“Although we can never be totally sure of the reasons why things happened in the past, this particular case does have all the trappings of a seemingly complex biological structure that just popped into existence for no good reason at all because it was simply very easy to evolve,” said Georg Hochberg, senior author of the study.
That might not be a particularly satisfying explanation for people looking for meaning in something that almost feels artificial, but on the plus side, it does suggest that there may be many more molecular fractals waiting to be discovered.
The research was published in the journal Nature.
Source: Max Planck Institute
