Fractal pattern identified at molecular scale in nature for first time

By Alex Wilkins

Illustration of the citrate synthase enzyme assembling into triangular fractal structures Courtesy of Franziska L. Sendker

A bacterium has evolved an enzyme that assembles in a fractal structure, a mathematical pattern that repeats itself at smaller scales.

Fractal patterns are found throughout nature on large, macroscopic scales, like in romanesco broccoli or fern plants, but until now they have never been identified at the molecular scale.

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Georg Hochberg at the Max Planck Institute for Terrestrial Microbiology in Marburg, Germany, and his colleagues discovered the molecular fractal in an enzyme used by the cyanobacterium Synechococcus elongatus. The enzyme, citrate synthase, is used by a wide variety of organisms as part of the Krebs cycle, a series of chemical reactions that generate energy. But in S. elongatus, the enzyme can take the unusual form of a triangle containing ever-smaller triangular gaps – known as a Sierpiński triangle.

Electron microscope image of a triangular fractal structure made up of enzyme monomers Courtesy of Franziska L. Sendker

The citrate synthase consists of a single building block, or monomer, that can assemble into different shapes, some of which help break down molecules in the Krebs cycle. Using an electron microscope, Hochberg and his team found that in S. elongatus, the monomers can assemble into a triangular form containing six monomers, which can itself combine with two others to form an 18-monomer shape. This can then combine with two more to form a 54-monomer shape, which is again triangular and resembles a Sierpiński triangle.

By comparing the fractal enzyme to genetic sequences from other bacteria, the team also traced its evolutionary history. “It popped into existence very suddenly and was then almost immediately lost again by a few different versions of bacteria, and only stuck around in this one cyanobacterium, which makes our discovery of it almost more bizarre, because our chances of finding it were basically near zero,” says Hochberg.

Although the researchers suspect the fractal shape may have given the bacterium some evolutionary advantage, they couldn’t find any obvious effect caused by removing the enzyme in lab experiments. “The cyanobacteria does not seem to care at all if it’s there or not,” says team member Franziska Sendker, also at the Max Planck Institute for Terrestrial Microbiology.

“Perhaps there might actually be more of these complex, fractal-like shapes around in nature, just because people haven’t really looked for them,” says Ard Louis at the University of Oxford. “Fractals are simple, algorithmically. They should be relatively easy to evolve. Even if they are not adaptive, they may very well exist in a wider range of protein complexes.”

It would be interesting to see if the two-dimensional triangular structure might be combined into three-dimensional shapes like a tetrahedron, says Nico Bruns at the Technical University of Darmstadt in Germany. “It would make a nano-size container with defined edges with an interior and exterior, and then you’re in the realm of protein cages and capsules that you can use to encapsulate and release products and other molecules of interest.”

Journal reference:

Nature DOI: 10.1038/s41586-024-07287-2