Assembling Shape-Persistent High-Order Sierpiński Triangular Fractals

Emergence of fractal geometries in the evolution of a metabolic enzyme

Fractals are patterns that are self-similar across multiple length-scales1. Macroscopic fractals are common in nature2-4; however, so far, molecular assembly into fractals is restricted to synthetic systems5-12. Here we report the discovery of a natural protein, citrate synthase from the cyanobacterium Synechococcus elongatus, which self-assembles into Sierpiński triangles. Using cryo-electron microscopy, we reveal how the fractal assembles from a hexameric building block. Although different stimuli modulate the formation of fractal complexes and these complexes can regulate the enzymatic activity of citrate synthase in vitro, the fractal may not serve a physiological function in vivo. We use ancestral sequence reconstruction to retrace how the citrate synthase fractal evolved from non-fractal precursors, and the results suggest it may have emerged as a harmless evolutionary accident. Our findings expand the space of possible protein complexes and demonstrate that intricate and regulatable assemblies can evolve in a single substitution.

The Marriage of Sierpiński Triangles and Platonic Polyhedra

Fractal structures with self-similarity are of fundamental importance in the fields of aesthetic, chemistry and mathematics. Here, by taking advantage of constructs the rational geometry-directed precursor design, we report the construction of two fascinating Platonic solids, the Sierpiński tetrahedron ST-T and the Sierpiński octahedron ST-O, in which each possesses a fractal Sierpiński triangle on their independent faces. These two discrete complexes are formed in near-quantitative yield from the multi-component self-assembly of truncated Sierpiński triangular kernel L¹ with tribenzotriquinacene-based hexatopic and anthracene-based tetratopic terpyridine ligands (L³ and L⁴ ) in the presence of metal ions, respectively. The enhanced stabilities of the 3D discrete structures were investigated by gradient tandem mass spectrometry (gMS² ). This work provides new constructs for the imitation of complex virus assemblies and for the molecular encapsulation of giant guest molecules.

Review about the Application of Fractal Theory in the Research of Packaging Materials

The work is intended to summarize the recent progress in the work of fractal theory in packaging material to provide important insights into applied research on fractal in packaging materials. The fractal analysis methods employed for inorganic materials such as metal alloys and ceramics, polymers, and their composites are reviewed from the aspects of fractal feature extraction and fractal dimension calculation methods. Through the fractal dimension of packaging materials and the fractal in their preparation process, the relationship between the fractal characteristic parameters and the properties of packaging materials is discussed. The fractal analysis method can qualitatively and quantitatively characterize the fractal characteristics, microstructure, and properties of a large number of various types of packaging materials. The method of using fractal theory to probe the preparation and properties of packaging materials is universal; the relationship between the properties of packaging materials and fractal dimension will be a critical trend of fractal theory in the research on properties of packaging materials.

Customized self-assembled molecules: rim adjustable coronal polygons with multiple-folds symmetry

Three desired discrete metallomacrocyclic wreaths with four-, five- and six-fold symmetry were successfully realized in a controlled fashion.

Construction of Macromolecular Pinwheels Using Predesigned Metalloligands

Developing a methodology to build target structures is one of the major themes of synthetic chemistry. However, it has proven to be immensely challenging to achieve multilevel elaborate molecular architectures in a predictable way. Herein, we describe the self-assembly of a series of pinwheel-shaped starlike supramolecules through three rationally preorganized metalloligands L1-L3. The key octa-uncomplexed terpyridine (tpy) metalloligand L3, synthesized with an 8-fold Suzuki coupling reaction to metal-containing complexes, has four different types of terpyridines connected with three ⟨tpy-Ru²⁺-tpy⟩ units, making this the most subunits known so far for a preorganized module. Based on the principle of geometric complementation and the high "density of coordination sites", these metalloligands were assembled with Zn²⁺ ions to form a pinwheel-shaped star trigon P1, pentagram P2, and hexagram P3 with precisely controlled shapes in nearly quantitative yields. With molecular weights ranging from 16756 to 56053 Da and diameters of 6.7-13.6 nm, the structural composition, shape, and rigidity of these pinwheel-shaped architectures have been fully characterized by 1D and 2D (NMR), electrospray ionization mass spectrometry, traveling-wave ion mobility mass spectrometry, and transmission electron microscopy.