Trends in Chemistry
OpinionTopology of Folded Molecular Chains: From Single Biomolecules to Engineered Origami
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Topology: A Key Property to Disentangle Folding Complexity
Despite their apparent simplicity, linear heteropolymer chains may fold into distinct topologically diverse structures. In polymer chemistry, the diverse collection of linear polymers is supplemented by branched and cyclical structures, while in biological chemistry linear protein and nucleic acid chains adopt various topologies via chain folding. Folding involves rearrangements of the chain and the formation of contacts. In biology, we encounter a vast multiplicity of folded polymer
Knot Theory and CT: Basic Definitions
Formally, a knot is an embedding of the circle in 3D space. A knot may be equivalent (through stretching and bending operations, without allowing the knot to pass through itself) to the trivial knot, or circle, or to other knots with greater minimal numbers of crossings in their projections onto the plane. In contrast to proteins, RNA, and linear DNA, such knots lack a start and end point. However, linear molecules, on connecting the endpoints across an external arc traversing the 3D surface,
Topological Analysis of Proteins
Proteins, known as the primary machinery of life [14], often need to fold transiently or permanently into one or more specific spatial conformations, mostly driven by noncovalent interactions [15,16]. Among the unlimited possibilities of arrangements, a limited number of motifs and domains is exhibited by nature, evidencing some general rules that govern the complexities of protein structure [17]. Various theoretical methods, including knot theory [18], knotoids [19], and, recently, CT [5],
Topological Analysis of Nucleic Acids
Cellular nucleic acids often fold into globular structures to achieve function. Folding happens at various scales, from small RNA molecules to large eukaryotic genomes. Various topological concepts, including supercoiling, knot theory, and contact arrangement, have been developed to describe folded nucleic acids. In what follows, we summarize these developments and discuss how CT can be used as a universal topology framework.
Topology of Organic and Bioinspired Polymers
Advances in molecular-engineering-enabled synthesis of molecular knots and topological polymers have led the way towards applications in several fields, including chemical biology, medicine, and materials science.
Concluding Remarks and Future Perspectives
Contact-based CT and knot theory form two complementary frameworks for describing, understanding, and engineering linear biopolymers such as proteins and nucleic acids, as summarized in the Outstanding Questions. An important future development will be further integration of these two applied theories and the establishment of how they can be more generally utilized in prediction and design. Towards this goal, it is likely that machine learning and artificial intelligence (AI), including recent
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Cited by (19)
Circuit topology analysis of cellular genome reveals signature motifs, conformational heterogeneity, and scaling
2022, iScienceCitation Excerpt :Both network topology and persistent homology are mostly focused on connectivity, which cannot describe the actual arrangement of the fold and provide a qualitative description of three-dimensional motifs. Our aim is to propose a topological toolbox based on circuit topology (CT) (Golovnev and Mashaghi, 2020; Heidari et al., 2020; Mashaghi et al., 2014; Scalvini et al., 2020; Schullian et al., 2020), capable of detecting not only recurring topological features in genome structure but also of quantifying cell-to-cell variability. CT is the only topology framework for folded linear polymers that categorizes the arrangement of polymer loops or their associated contacts and complements the well-established knot theory (where contacts are typically ignored).
Macromolecular Topology Engineering
2021, Trends in ChemistryCitation Excerpt :In biology, topology is often loosely used to describe spatial relationships. For example, genome topology refers to the spatial genome organization as shaped by the long-range interactions of chromatins in the intact cell nucleus and protein topology refers to the mutual orientations of secondary structural elements of proteins in 3D space [3,4]. In chemistry, since its first introduction by Frisch and Wasserman in 1961 [5], chemical topology has grown into a diverse and popular research field covering rather broad and distinct topics, including the supercoiling of macromolecules, shapes of curves and surfaces, and molecules with nonplanar graphs [6–11].
Generalized Circuit Topology of Folded Linear Chains
2020, iScienceCitation Excerpt :In order to describe the immense structural diversity of proteins, nucleic acids or other linear molecular chains, the concept of circuit topology was recently introduced to formally categorize the arrangement of intrachain contacts (Heidari et al., 2020) (Scalvini et al., 2020) (Mashaghi et al., 2014).
Protein structural features predict responsiveness to pharmacological chaperone treatment for three lysosomal storage disorders
2021, PLoS Computational BiologyCytosolic Interactome Protects Against Protein Unfolding in a Single Molecule Experiment
2023, Advanced BiologyCrystal Structure of de Novo Designed Coiled-Coil Protein Origami Triangle
2023, Journal of the American Chemical Society