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, responding to stimuli, providing structure to cells and organisms, and transporting molecules from one location to another. Proteins differ from one another primarily in their sequence of amino acids, which is dictated by the nucleotide sequence of their genes, and which usually results in protein folding into a specific 3D structure that determines its activity.
Topology is the part of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
Protein folding is the physical process by which a protein, after synthesis by a ribosome as a linear chain of amino acids, changes from an unstable random coil into a more ordered three-dimensional structure. This structure permits the protein to become biologically functional.
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring. In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, . Two mathematical knots are equivalent if one can be transformed into the other via a deformation of upon itself ; these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself.
Soft matter or soft condensed matter is a subfield of condensed matter comprising a variety of physical systems that are deformed or structurally altered by thermal or mechanical stress of the magnitude of thermal fluctuations. These materials share an important common feature in that predominant physical behaviors occur at an energy scale comparable with room temperature thermal energy, and that entropy is considered the dominant factor. At these temperatures, quantum aspects are generally unimportant. Soft materials include liquids, colloids, polymers, foams, gels, granular materials, liquid crystals, flesh, and a number of biomaterials. When soft materials interact favorably with surfaces, they become squashed without an external compressive force. Pierre-Gilles de Gennes, who has been called the "founding father of soft matter," received the Nobel Prize in Physics in 1991 for discovering that methods developed for studying order phenomena in simple systems can be generalized to the more complex cases found in soft matter, in particular, to the behaviors of liquid crystals and polymers.
Protein structure is the three-dimensional arrangement of atoms in an amino acid-chain molecule. Proteins are polymers – specifically polypeptides – formed from sequences of amino acids, which are the monomers of the polymer. A single amino acid monomer may also be called a residue, which indicates a repeating unit of a polymer. Proteins form by amino acids undergoing condensation reactions, in which the amino acids lose one water molecule per reaction in order to attach to one another with a peptide bond. By convention, a chain under 30 amino acids is often identified as a peptide, rather than a protein. To be able to perform their biological function, proteins fold into one or more specific spatial conformations driven by a number of non-covalent interactions, such as hydrogen bonding, ionic interactions, Van der Waals forces, and hydrophobic packing. To understand the functions of proteins at a molecular level, it is often necessary to determine their three-dimensional structure. This is the topic of the scientific field of structural biology, which employs techniques such as X-ray crystallography, NMR spectroscopy, cryo-electron microscopy (cryo-EM) and dual polarisation interferometry, to determine the structure of proteins.
In chemistry, a molecular knot is a mechanically interlocked molecular architecture that is analogous to a macroscopic knot. Naturally-forming molecular knots are found in organic molecules like DNA, RNA, and proteins. 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.
In molecular biology, the term double helix refers to the structure formed by double-stranded molecules of nucleic acids such as DNA. The double helical structure of a nucleic acid complex arises as a consequence of its secondary structure, and is a fundamental component in determining its tertiary structure. The structure was discovered by Rosalind Franklin, her student Raymond Gosling, James Watson, and Francis Crick, while the term "double helix" entered popular culture with the 1968 publication of Watson's The Double Helix: A Personal Account of the Discovery of the Structure of DNA.
In molecular biology, an intrinsically disordered protein (IDP) is a protein that lacks a fixed or ordered three-dimensional structure, typically in the absence of its macromolecular interaction partners, such as other proteins or RNA. IDPs range from fully unstructured to partially structured and include random coil, molten globule-like aggregates, or flexible linkers in large multi-domain proteins. They are sometimes considered as a separate class of proteins along with globular, fibrous and membrane proteins.
The contact order of a protein is a measure of the locality of the inter-amino acid contacts in the protein's native state tertiary structure. It is calculated as the average sequence distance between residues that form native contacts in the folded protein divided by the total length of the protein. Higher contact orders indicate longer folding times, and low contact order has been suggested as a predictor of potential downhill folding, or protein folding that occurs without a free energy barrier. This effect is thought to be due to the lower loss of conformational entropy associated with the formation of local as opposed to nonlocal contacts.
A peculiarity of thermal motion of very long linear macromolecules in entangled polymer melts or concentrated polymer solutions is reptation. Derived from the word reptile, reptation suggests the movement of entangled polymer chains as being analogous to snakes slithering through one another. Pierre-Gilles de Gennes introduced the concept of reptation into polymer physics in 1971 to explain the dependence of the mobility of a macromolecule on its length. Reptation is used as a mechanism to explain viscous flow in an amorphous polymer. Sir Sam Edwards and Masao Doi later refined reptation theory. Similar phenomena also occur in proteins.
Knots have been used for basic purposes such as recording information, fastening and tying objects together, for thousands of years. The early significant stimulus in knot theory would arrive later with Sir William Thomson and his vortex theory of the atom.
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 provides a model for explaining how the atoms ethereal wave functions must fit together. Molecular topology is a part of mathematical chemistry dealing with the algebraic description of chemical compounds so allowing a unique and easy characterization of them.
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 get disentangled. Knotted proteins are very rare, making up only about one percent of the proteins in the Protein Data Bank, and their folding mechanisms and function are not well understood. Although there are experimental and theoretical studies that hint to some answers, systematic answers to these questions have not yet been found.
Polymer architecture in polymer science relates to the way branching leads to a deviation from a strictly linear polymer chain. Branching may occur randomly or reactions may be designed so that specific architectures are targeted. It is an important microstructural feature. A polymer's architecture affects many of its physical properties including solution viscosity, melt viscosity, solubility in various solvents, glass transition temperature and the size of individual polymer coils in solution.
Protein topology is a property of protein molecule that does not change under deformation.
An arc diagram is a style of graph drawing, in which the vertices of a graph are placed along a line in the Euclidean plane, with edges being drawn as semicircles in one or both of the two halfplanes bounded by the line, or as smooth curves formed by sequences of semicircles. In some cases, line segments of the line itself are also allowed as edges, as long as they connect only vertices that are consecutive along the line. Variations of this drawing style in which the semicircles are replaced by convex curves of some other type are also commonly called arc diagrams.
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 polymerization of multivinyl monomers, which was first reported in Dr. Wenxin Wang's research lab. These multiple intramolecular cyclized/knotted units mimic the characteristics of complex knots found in proteins and DNA which provide some elasticity to these structures. Of note, 85% of elasticity in natural rubber is due to knot-like structures within its molecular chain.
An intramolecular cyclization reaction is where the growing polymer chain reacts with a vinyl functional group on its own chain, rather than with another growing chain in the reaction system. In this way the growing polymer chain covalently links to itself in a fashion similar to that of a knot in a piece of string. As such, single chain cyclized/knotted polymers consist of many of these links, as opposed to other polymer architectures including branched and crosslinked polymers that are formed by two or more polymer chains in combination.
Alireza Mashaghi is a physician-scientist and biophysicist at Leiden University. He is known for his contributions to single-molecule analysis of chaperone assisted protein folding, molecular topology and medical systems biophysics and bioengineering. He is a leading advocate for interdisciplinary research and education in medicine and pharmaceutical sciences.
Topological polymers may refer to a polymeric molecule that possesses unique spatial features, such as linear, branched, or cyclic architectures. It could also refer to polymer networks that exhibit distinct topologies owing to special crosslinkers. When self-assembling or crosslinking in a certain way, polymeric species with simple topological identity could also demonstrate complicated topological structures in a larger spatial scale. Topological structures, along with the chemical composition, determine the macroscopic physical properties of polymeric materials.
