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Encyclopedia > Random coil
Illustration of a 3-dimensional polypeptide
Illustration of a 3-dimensional polypeptide

A random coil is a polymer conformation where the monomer subunits are oriented randomly while still being bonded to adjacent units. It is not one specific shape, but a statistical distribution of shapes for all the chains in a population of macromolecules. The conformation's name is derived from the idea that, in the absence of specific, stabilizing interactions, a polymer backbone will "sample" all possible conformations randomly. Many linear, unbranched homopolymers — in solution, or above their melting temperatures — assume (approximate) random coils. Even copolymers with monomers of unequal length will distribute in random coils if the subunits lack any specific interactions. The parts of branched polymers may also assume random coils. Image File history File links Download high resolution version (984x629, 220 KB) Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Download high resolution version (984x629, 220 KB) Licensing File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Peptides are the family of molecules formed from the linking, in a defined order, of various amino acids. ... Polymer is a term used to describe a very long molecule consisting of structural units and repeating units connected by covalent chemical bonds. ... Conformation generally means structural arrangement. ... In chemistry, a monomer (from Greek mono one and meros part) is a small molecule that may become chemically bonded to other monomers to form a polymer. ... The word random is used to express apparent lack of purpose, cause, or order. ... A chemical bond is the physical phenomenon of chemical substances being held together by attraction of atoms to each other through sharing, as well as exchanging, of electrons or electrostatic forces. ... A labeled graph with 6 vertices (nodes) and 7 edges. ... In geometry, two sets have the same shape if one can be transformed to another by a combination of translations, rotations and uniform scalings. ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... A macromolecule is a molecule with a large molecular mass, but generally the use of the term is restricted to polymers and molecules which structurally include polymers. ... In chemistry, a chemical conformation is the spatial arrangement of atoms in a molecule. ... Branching, in organic chemistry, is when a hydrogen on a polymer is replaced by another chain of that polymer, that is, a polymer that at some point looks like: / - - - - - - - < - - - In linguistics, branching refers to the way in which a language constructs phrases with a head (or nucleus) and modifiers (or... A homopolymer is a polymer which is formed from only one type of monomer. ... A material’s glass transition temperature, Tg, is the temperature below which molecules have little relative mobility. ... An approximation is an inexact representation of something that is still close enough to be useful. ... A heteropolymer, also called a copolymer, is a polymer formed when two different types of monomer are linked in the same polymer chain. ... Length is the long dimension of any object. ...


Below their melting temperatures, most thermoplastic polymers (polyethylene, nylon, etc.) have amorphous regions in which the chains approximate random coils, alternating with regions which are crystalline. The amorphous regions contribute elasticity and the crystalline regions contribute strength and rigidity. A thermoplastic is a material that is plastic or deformable, melts to a liquid when heated and freezes to a brittle, glassy state when cooled sufficiently. ... Polyethylene or polyethene is a thermoplastic commodity heavily used in consumer products (over 60M tons are produced worldwide every year). ... Nylon represents a family of synthetic polymers, a thermoplastic material, invented in 1935 by Wallace Carothers at DuPont. ... An amorphous solid is a solid in which there is no long-range order of the positions of the atoms. ... Quartz crystal A crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions. ...


More complex polymers such as proteins, with various interacting chemical groups attached to their backbones, self-assemble into well-defined structures. But segments of proteins, and polypeptides that lack secondary structure, are often assumed to exhibit a random coil conformation in which the only fixed relationship is the joining of adjacent amino acid residues by a peptide bond. This is not actually the case, since the ensemble will be energy weighted due to interactions between amino acid side chains, with lower-energy conformations being present more frequently. In addition, even arbitrary sequences of amino acids tend to exhibit some hydrogen bonding and secondary structure. For this reason, the term "statistical coil" is occasionally preferred. A representation of the 3D structure of myoglobin, showing coloured alpha helices. ... Self-assembly is the fundamental principle which generates structural organization on all scales from molecules to galaxies. ... Peptides (from the Greek πεπτος, digestible), are the family of short molecules formed from the linking, in a defined order, of various α-amino acids. ... A representation of the 3D structure of the Myoglobin protein. ... An amino acid residue is what is left of an amino acid once a molecule of water has been lost (an H+ from the nitrogenous side and an OH- from the carboxylic side) in the formation of a peptide bond. ... A residue, broadly, is anything left behind by a reaction or event. ... A peptide bond is a chemical bond formed between two molecules when the carboxyl group of one molecule reacts with the amino group of the other molecule, releasing a molecule of water (H2O). ... In mathematical physics, especially as introduced into statistical mechanics and thermodynamics by J. Willard Gibbs in 1878, an ensemble (also statistical ensemble or thermodynamic ensemble) is an idealization consisting of a large number of mental copies (possibly infinitely many) of a system, considered all at once, each of which represents... The term Side chain can have different meanings depending on the context: In chemistry and biochemistry a side chain is a part of a molecule attached to a core structure. ... Snapshot from a simulation of liquid water. ...


A random coil conformation can be detected using spectroscopic techniques. The arrangement of the planar amide bonds results in a distinctive signal in circular dichroism. The chemical shift of amino acids in a random coil conformation is well known in nuclear magnetic resonance (NMR). Deviations from these signatures often indicates the presence of some secondary structure, rather than complete random coil. Furthermore, there are signals in multidimensional NMR experiments which indicate that stable, non-local amino acid interactions are absent for polypeptides in a random coil conformation. Likewise, in the images produced by crystallography experiments, segments of random coil simply result in a reduction in "electron density" or contrast. A randomly coiled state for any polypeptide chain can be attained by denaturing the system. However, there is evidence that proteins are perhaps never truly random coils, even when denatured (Shortle & Ackerman). Circular dichroism (CD), is the differential absorption of left and right hand circularly polarized light. ... In nuclear magnetic resonance (NMR), the chemical shift describes the dependence of nuclear magnetic energy levels on the electronic environment in a molecule. ... Pacific Northwest National Laboratorys high magnetic field (800 MHz) NMR spectrometer being loaded with a sample. ... X-ray crystallography is a technique in crystallography in which the pattern produced by the diffraction of X-rays through the closely spaced lattice of atoms in a crystal is recorded and then analyzed to reveal the nature of that lattice. ... Irreversible egg protein denaturation and loss of solubility, caused by the high temperature (while cooking it) In biochemistry, denaturation is a structural change in biomolecules such as nucleic acids and proteins, such that they are no longer in their native state, and their shape which allows for optimal activity. ...

Contents


Random walk model

There are an enormous number of different ways in which a chain can be curled around in a relatively compact shape, like an unraveling ball of twine with lots of open space, and comparatively few ways it can be more or less stretched out. So if each conformation has an equal probability or statistical weight, chains are much more likely to be ball-like than they are to be extended — a purely entropic effect. In an ensemble of chains, most of them will therefore be loosely balled up. Or, equivalently, this is the kind of shape any one of them will have most of the time. Image File history File linksMetadata Ideal_chain_random_walk. ... Image File history File linksMetadata Ideal_chain_random_walk. ... An ideal chain (or freely-jointed chain) is the simplest model to describe a polymer. ... Ludwig Boltzmann Ludwig Eduard Boltzmann (Vienna, Austria-Hungary, February 20, 1844 – Duino near Trieste, September 5, 1906) is an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. ... Space has been an interest for philosophers and scientists for much of human history, and hence it is difficult to provide an uncontroversial and clear definition outside of specific defined contexts. ... The word probability derives from the Latin probare (to prove, or to test). ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... Ice melting - a classic example of entropy increasing Entropy is a concept in thermodynamics, statistical mechanics and information theory. ... In mathematical physics, especially as introduced into statistical mechanics and thermodynamics by J. Willard Gibbs in 1878, an ensemble (also statistical ensemble or thermodynamic ensemble) is an idealization consisting of a large number of mental copies (possibly infinitely many) of a system, considered all at once, each of which represents... A sphere (< Greek σφαίρα) is a perfectly symmetrical geometrical object. ...


Consider a linear polymer to be a freely-jointed chain with N subunits, each of length l, that occupy zero volume, so that no part of the chain excludes another from any location. One can regard the segments of each such chain in an ensemble as performing a random walk (or "random flight") in three dimensions, limited only by the constraint that each segment must be joined to its neighbors. This is the ideal chain mathematical model. The maximum, fully-extended length L of the chain is clearly N x l. If we assume that each possible chain conformation has an equal statistical weight, it can be shown that number of polymer chains in the population with any given distance between the ends will obey a normal (Gaussian) distribution. The average (root mean square) end-to-end distance for the chain turns out to be l times the square root of N. 0 (zero) is both a number and a numeral. ... GEE GUY dimensions is called content. ... In mathematics and physics, a random walk, sometimes called a drunkards walk, is a formalisation of the intuitive idea of taking successive steps, each in a random direction. ... 2-dimensional renderings (ie. ... An ideal chain (or freely-jointed chain) is the simplest model to describe a polymer. ... A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. ... An ideal chain (or freely-jointed chain) is the simplest model to describe a polymer. ... The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields. ... In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ...


Real polymers

A real polymer is not freely-jointed. A -C-C- single bond has a fixed tetrahedral angle of 109.5 degrees. The value of L is well-defined for, say, a fully-extended polyethylene or nylon, but it is less than N x l because of the zig-zag backbone. There is, however, free rotation about many chain bonds. The model above can be enhanced. A longer, "effective" unit length can be defined such that the chain can be regarded as freely-jointed, along with a smaller N, such that the constraint L = N x l is still obeyed. It, too, gives a Gaussian distribution. However, specific cases can also be precisely calculated. The average end-to-end distance for freely-rotating (not freely-jointed) polymethylene (polyethylene with each -C-C- considered as a subunit) is l times the square root of 2N, an increase by a factor of about 1.4. Unlike the zero volume assumed in a random walk calculation, all real polymers' segments occupy space because of the van der Waals radii of their atoms, including bulky substituent groups which interfere with bond rotations. This can also be taken into account in calculations. All such effects increase the mean end-to-end distance. A chemical bond is the physical phenomenon of chemical substances being held together by attraction of atoms to each other through sharing, as well as exchanging, of electrons or electrostatic forces. ... An alkane in organic chemistry is a saturated hydrocarbon without cycles, that is, an acyclic hydrocarbon in which the molecule has the maximum possible number of hydrogen atoms and so has no double bonds. ... Polyethylene or polyethene is a thermoplastic commodity heavily used in consumer products (over 60M tons are produced worldwide every year). ... Nylon represents a family of synthetic polymers, a thermoplastic material, invented in 1935 by Wallace Carothers at DuPont. ... The van der Waals radius of an atom is the radius of an imaginary hard sphere which can be used to model the atom for many purposes. ... Steric effects are the interaction of molecules dictated by their shape and/or spatial relationships. ... Geometry of the water molecule Molecular geometry or molecular structure is the three dimensional arrangement of the atoms that constitute a molecule, inferred from the spectroscopic studies of the compound. ...


Because their polymerization is stochastically driven, chain lengths in any real population of synthetic polymers will obey a statistical distribution. In that case, we should take N to be an average value. Also, many polymers have random branching. Stochastic, from the Greek stochos or goal, means of, relating to, or characterized by conjecture; conjectural; random. ... In chemistry, the phrase chemical synthesis appears to have one of two meanings. ...


Even with corrections for local constraints, the random walk model ignores steric interference between chains, and between distal parts of the same chain. A chain often can’t move from a given conformation to a closely related one by a small displacement because one part of it would have to pass through another part, or through a neighbor. We may still hope that the ideal-chain, random-coil model will be at least a qualitative indication of the shapes and dimensions of real polymers in solution, and in the amorphous state, so long as there are only weak physicochemical interactions between the monomers. This model, and the Flory-Huggins Solution Theory, for which Paul Flory received the Nobel Prize in Chemistry in 1974, ostensibly apply only to ideal, dilute solutions. But there is reason to believe (e.g., neutron diffraction studies) that excluded volume effects may cancel out, so that under certain conditions, chain dimensions in amorphous polymers have approximately the ideal, calculated size.[1] A constraint is a limitation of possibilities. ... 2-dimensional renderings (ie. ... Dissolving table salt in water In chemistry, a solution is a homogeneous mixture composed of one or more substances, known as solutes, dissolved in another substance, known as a solvent. ... Intermolecular forces are electromagnetic forces which act between molecules or between widely separated regions of a macromolecule. ... ... Paul John Flory (June 19, 1910 – September 9, 1985) was an American chemist who was known for his prodigious volume of work in the field of polymers, or macromolecules. ... This is a list of Nobel Prize laureates in Chemistry from 1901 to the present day. ... 1974 (MCMLXXIV) was a common year starting on Tuesday (the link is to a full 1974 calendar). ... In chemistry, an ideal solution is a solution where the enthalpy of solution is zero. ... Neutron diffraction is a crystallography technique that uses neutrons to determine the atomic structure of a material. ... Steric effects are the interaction of molecules dictated by their shape and/or spatial relationships. ...


When separate chains interact cooperatively, notably in forming crystalline regions in solid thermoplastics, a different mathematical approach must be used. In jewelry, a solid gold piece is the alternative to gold-filled or gold-plated jewelry. ...


Stiffer polymers such as helical polypeptides, Kevlar, and double-stranded DNA can be treated by the worm-like chain model. A diagram of the alpha helix structure of amino acids In proteins, the α helix is a major structural motif in secondary structure. ... Kevlar is the DuPont Companys brand name for material made out of synthetic fiber of poly-paraphenylene terephthalamide which is constructed of para-aramid fibers that the company claims is five times stronger than the same weight of steel, while being lightweight, flexible and comfortable. ... The general structure of a section of DNA Deoxyribonucleic acid (DNA) is a nucleic acid —usually in the form of a double helix— that contains the genetic instructions specifying the biological development of all cellular forms of life, and most viruses. ... The worm-like chain (WLC) model in polymer physics is used to describe the behavior of semi-flexible polymers; it is sometimes referred to as the Kratky-Porod worm-like chain model. ...


See also

Protein folding is the process by which a protein structure assumes its functional shape or conformation. ... In biochemistry, the native state of a protein is its operative or functional form. ... A molten globule (MG) is a stable, partially folded protein structure found in mildly denaturing conditions such as low pH (generally pH = 2), mild denaturant, or high temperature. ...

External links and references

  • polymer statistical mechanics
  • A topological problem in polymer physics: configurational and mechanical properties of a random walk enclosing a constant are
  • Flory, P.J. (1953) Principles of Polymer Chemistry, Cornell Univ. Press, ISBN 0801401348
  • Flory, P.J. (1969) Statistical Mechanics of Chain Molecules, Wiley, ISBN 0470264950; reissued 1989, ISBN 1569900191
  • D. Shortle and M. Ackerman, Persistence of native-like topology in a denatured protein in 8 M urea, Science 293 (2001), pp. 487–489
  • 1. "Conformations, Solutions, and Molecular Weight" (book chapter)

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