The fractal structures in clouds or river deltas (top) are created by random processes; ferns (bottom left) and Romanesco broccoli (bottom right) exhibit regular fractals. Image source: Max Planck Institute for Terrestrial Microbiology.
Researchers from the Max Planck Institute for Terrestrial Microbiology in Germany and the University of Marburg, leading an international research team, have serendipitously discovered the first regular molecular fractal in nature. They found that citrate lyase from cyanobacteria spontaneously assembles into a Sierpinski triangle pattern. Electron microscopy and evolutionary biochemical studies suggest that this fractal may represent an "evolutionary accident." The findings were published in the latest issue of the journal Nature.
Many structures in nature exhibit a certain level of regularity, with parts resembling the shape of the whole. This repeating shape from large to small is called a fractal. Many fractal structures, such as those found in clouds or river deltas, are created by random processes, where the structure of smaller riverbeds does not perfectly correspond to larger river channels. Ferns and Romanesco broccoli, on the other hand, are examples of regular fractals. However, regular fractals that match almost perfectly in scale are extremely rare in nature.
While molecules can self-assemble into various intricate shapes, they also exhibit a certain level of regularity. Scientists have cataloged a plethora of complex self-assembled molecular structures, none of which have exhibited regular fractals.
In this discovery, the research team found that citrate lyase spontaneously assembles into a regular fractal pattern known as a Sierpinski triangle. This consists of an infinite series of triangles made up of smaller triangles. Proteins form these beautiful patterns, with larger triangular gaps becoming visible as the fractal grows.
The researchers noted that while the pattern is highly symmetrical as proteins self-assemble, the assembly of fractal proteins violates this symmetry rule: different protein chains interact at different positions within the fractal, forming the basis for the formation of the Sierpinski triangle.
Indeed, complex phenomena like molecular fractals, which appear highly intricate, are easily accessible in evolution, indicating that many more surprises and beauties may still be hidden within many yet undiscovered molecular combinations.
