Scientists find a naturally occurring molecule that forms a fractal

The protein assembles itself into Sierpiński triangles

An illustration of bacterial molecules forming a triangular fractal.

Researchers have found a bacterial protein that links up to form a type of fractal called a Sierpiński triangle (illustrated). It’s the first known case of a naturally occurring regular fractal on the molecular level.

Franziska Sendker

Fractals are everywhere in nature, from river deltas to tree branches. These structures look similar from afar as when you zoom in close. Certain fractals, called regular fractals, are identical on different scales and include whirls of Romanesco cauliflower (SN: 7/8/21). But regular fractals hadn’t been spotted in nature on the molecular level — until now.

A protein found in the bacterium Synechococcus elongatus assembles itself into a fractal called a Sierpiński triangle, evolutionary biochemist Georg Hochberg and colleagues report April 10 in Nature. When placed in water, the proteins linked up into triangles made up of smaller triangles, consisting of as many as 54 individual proteins, and potentially even more.

Researchers have previously designed synthetic molecules that can form regular fractals. But the bacterial protein, called citrate synthase, is the first with such fractal flair to be discovered in nature.

A grayscale microscope image showing a bacterial molecule forming triangles
These electron microscope images show the bacterial protein citrate synthase assembling into a triangle made up of smaller triangles.F.L. Sendker et al/Nature 2024These electron microscope images show the bacterial protein citrate synthase assembling into a triangle made up of smaller triangles.F.L. Sendker et al/Nature 2024

The scientists couldn’t identify any practical purpose for the pattern and concluded that it’s an evolutionary accident. Accidents occur in other assemblies of proteins, too. “Different kinds of complex-looking structures come and go on evolutionary timescales, sometimes with a use, sometimes without one,” says Hochberg, of the Max Planck Institute for Terrestrial Microbiology in Marburg, Germany. “Their symmetry can be beguiling to us, and that’s why we think they have meaning.”

Physics writer Emily Conover has a Ph.D. in physics from the University of Chicago. She is a two-time winner of the D.C. Science Writers’ Association Newsbrief award.