In
chemistry, a molecular knot is a
mechanically interlocked molecular architecture that is analogous to a macroscopic
knot
A knot is an intentional complication in cordage which may be practical or decorative, or both. Practical knots are classified by function, including hitches, bends, loop knots, and splices: a ''hitch'' fastens a rope to another object; a ' ...
.
Naturally-forming molecular knots are found in
organic molecules like
DNA,
RNA, and
protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, res ...
s. It is not certain that naturally occurring knots are evolutionarily advantageous to
nucleic acids or proteins, though knotting is thought to play a role in the structure, stability, and function of knotted biological molecules.
The mechanism by which knots naturally form in molecules, and the mechanism by which a molecule is stabilized or improved by knotting, is ambiguous. The study of molecular knots involves the formation and applications of both naturally occurring and
chemically synthesized molecular knots. Applying
chemical topology and
knot theory to molecular knots allows biologists to better understand the structures and synthesis of knotted organic molecules.
The term ''knotane'' was coined by Vögtle ''et al.'' in 2000 to describe molecular knots by analogy with
rotaxane
In chemistry, a rotaxane () is a mechanically interlocked molecular architecture consisting of a dumbbell-shaped molecule which is threaded through a macrocycle (see graphical representation). The two components of a rotaxane are kinetically t ...
s and
catenane
In macromolecular chemistry, a catenane () is a mechanically interlocked molecular architecture consisting of two or more interlocked macrocycles, i.e. a molecule containing two or more intertwined rings. The interlocked rings cannot be se ...
s, which are other mechanically interlocked molecular architectures.
The term has not been broadly adopted by chemists and has not been adopted by
IUPAC
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
.
Naturally occurring molecular knots
Organic molecules containing knots may fall into the categories of slipknots or pseudo-knots.
They are not considered mathematical knots because they are not a closed curve, but rather a knot that exists within an otherwise linear chain, with termini at each end. Knotted proteins are thought to form molecular knots during their tertiary structure folding process, and knotted nucleic acids generally form molecular knots during genomic replication and transcription, though details of knotting mechanism continue to be disputed and ambiguous. Molecular simulations are fundamental to the research on molecular knotting mechanisms.
Knotted DNA was found first by Liu et al. in 1981, in single-stranded, circular, bacterial DNA, though double-stranded circular DNA has been found to also form knots. Naturally knotted RNA has not yet been reported.
A number of proteins containing naturally occurring molecular knots have been identified. The knot types found to be naturally occurring in proteins are the
and
knots, as identified in the KnotProt database of known knotted proteins.
Chemically synthesized molecular knots
Several synthetic molecular knots have been reported.
Knot types that have been successfully synthesized in molecules are
and 8
19 knots. Though the
and
knots have been found to naturally occur in knotted molecules, they have not been successfully synthesized. Small-molecule composite knots have also not yet been synthesized.
Artificial DNA, RNA, and protein knots have been successfully synthesized. DNA is a particularly useful model of synthetic knot synthesis, as the structure naturally forms interlocked structures and can be easily manipulated into forming knots control precisely the raveling necessary to form knots. Molecular knots are often synthesized with the help of crucial metal ion ligands.
History
The first researcher to suggest the existence of a molecular knot in a protein was Jane Richardson in 1977, who reported that carbonic anhydrase B (CAB) exhibited apparent knotting during her survey of various proteins' topological behavior. However, the researcher generally attributed with the discovery of the first knotted protein is Marc. L. Mansfield in 1994, as he was the first to specifically investigate the occurrence of knots in proteins and confirm the existence of the trefoil knot in CAB. Knotted DNA was found first by Liu et al. in 1981, in single-stranded, circular, bacterial DNA, though double-stranded circular DNA has been found to also form knots.
In 1989, Sauvage and coworkers reported the first synthetic knotted molecule: a trefoil synthesized via a double-helix complex with the aid of Cu+ ions.
Vogtle et al. was the first to describe molecular knots as ''knotanes'' in 2000.
Also in 2000 was William Taylor's creation of an alternative computational method to analyze protein knotting that set the termini at a fixed point far enough away from the knotted component of the molecule that the knot type could be well-defined. In this study, Taylor discovered a deep
knot in a protein. With this study, Taylor confirmed the existence of deeply knotted proteins.
In 2007, Eric Yeates reported the identification of a molecular slipknot, which is when the molecule contains knotted subchains even though their backbone chain as a whole is unknotted and does not contain completely knotted structures that are easily detectable by computational models. Mathematically, slipknots are difficult to analyze because they are not recognized in the examination of the complete structure.
A
pentafoil
In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot. It is listed as the 51 knot in the Alexander-Briggs notation, and ...
knot prepared using dynamic covalent chemistry was synthesized by Ayme et al. in 2012, which at the time was the most complex non-DNA molecular knot prepared to date. Later in 2016, a fully organic pentafoil knot was also reported, including the very first use of a molecular knot to allosterically regulate catalysis. In January 2017, an 8
19 knot was synthesized by
David Leigh's group, making the 8
19 knot the most complex molecular knot synthesized.
An important development in knot theory is allowing for intra-chain contacts within an entangled molecular chain.
Circuit topology
The circuit topology of a folded linear polymer refers to the arrangement of its intra-molecular contacts. Examples of linear polymers with intra-molecular contacts are nucleic acids and proteins. Proteins fold via formation of contacts of variou ...
has recently emerged as a topology framework that formalises the arrangement of contacts as well as chain crossings in a folded linear chain. As a complementary approach, Colin Adams. et al., developed a singular knot theory that is applicable to folded linear chains with intramolecular interactions.
[Colin Adams, Judah Devadoss, Mohamed Elhamdadi and Alireza Mashaghi, Knot theory for proteins: Gauss codes, quandles and bondles. Journal of Mathematical Chemistry volume 58, pages1711–1736(2020)]
Applications
Many synthetic molecular knots have a distinct
globular shape and dimensions that make them potential building blocks in
nanotechnology.
See also
*
Circuit topology
The circuit topology of a folded linear polymer refers to the arrangement of its intra-molecular contacts. Examples of linear polymers with intra-molecular contacts are nucleic acids and proteins. Proteins fold via formation of contacts of variou ...
of folded linear molecules
*
Supramolecular chemistry
Supramolecular chemistry refers to the branch of chemistry concerning chemical systems composed of a discrete number of molecules. The strength of the forces responsible for spatial organization of the system range from weak intermolecular forces ...
*
Knotted protein
Knotted proteins are proteins whose backbones entangle themselves in a knot. One can imagine pulling a protein chain from both termini, as though pulling a string from both ends. When a knotted protein is “pulled” from both termini, it does not ...
*
Knotted polymers Single Chain Cyclized/Knotted Polymers are a new class of polymer architecture with a general structure consisting of multiple intramolecular cyclization units within a single polymer chain. Such a structure was synthesized via the controlled polym ...
*
Topology (chemistry) In chemistry, topology provides a way of describing and predicting the molecular structure within the constraints of three-dimensional (3-D) space. Given the determinants of chemical bonding and the chemical properties of the atoms, topology provi ...
*
Knot theory
References
{{Reflist
Supramolecular chemistry
Macrocycles
Molecular topology