An international group of researchers has recently discovered the first naturally occurring regular molecular fractal.
Fractals, structures where every sub-part replicates the overall shape, are found in nature, such as in snowflakes or fern leaves. However, regular molecular fractals, where this self-similarity is maintained at all scales, had never been observed until now.
Credit: MPI f. Terrestrial Microbiology/ Hochberg
Researchers from the Max Planck Institutes and the University of Philipps in Marburg discovered a microbial enzyme, the citrate synthase from a cyanobacterium, that spontaneously assembles into a regular fractal known as the Sierpiński triangle. This pattern is a series of triangles that repeat infinitely, with progressively smaller triangles.
The enzyme forms unique geometric triangles during its assembly, a phenomenon observed by chance through electron microscopy. This discovery has surprised researchers with its rarity and unexpected complexity.
To understand how this extraordinary structure formed, the team collaborated with a biologist from the University of Marburg to determine the molecular structure of the assembly. Their study revealed that this fractal formation results from a violation of the usual symmetry in protein assemblies. Typically, interactions among proteins are symmetrical, leading to structures that become uniform at a large scale.
a - Schematic representation of the conditions necessary to produce a Sierpiński fractal from hexamer blocks and symmetry-based constraints on oligomeric assembly. The green and blue dots represent the active or open interfaces, respectively.
b - Cryo-EM density maps of Sierpiński triangles from levels zero, one, and two. The role of this fractal structure remains uncertain. When the team genetically modified the bacterium to prevent the fractal assembly of citrate synthase, the cells continued to grow normally. This suggests that the existence of this structure could be an evolutionary accident with no significant consequence for the bacterium.
To explore this hypothesis, researchers recreated in the laboratory the evolutionary development of this protein structure. They used statistical methods to trace the protein sequence of the enzyme as it was millions of years ago. The results show that this fractal arrangement appeared suddenly following a small number of mutations and disappeared quickly in several cyanobacteria lineages, persisting only in this specific species.
This discovery highlights that complex biological structures, seemingly without function, can emerge and persist in nature.