Tendril perversion

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A tendril of Bryonia dioica exhibiting tendril perversion PSM V17 D663 A caught tendril of bryonia dioica.jpg
A tendril of Bryonia dioica exhibiting tendril perversion
Cucurbita pepo exhibiting tendril perversion Cucurbita pepo 02 ies.jpg
Cucurbita pepo exhibiting tendril perversion
A telephone handset cord exhibiting tendril perversion Touch me and I end up singing (6066015622) (2).jpg
A telephone handset cord exhibiting tendril perversion
GIF video showing two different types of tendril perversion Generalized perversions.gif
GIF video showing two different types of tendril perversion

Tendril perversion is a geometric phenomenon sometimes observed in helical structures in which the direction of the helix transitions between left-handed and right-handed. [1] [2] Such a reversal of chirality is commonly seen in helical plant tendrils and telephone handset cords. [3]

Contents

The phenomenon was known to Charles Darwin, [4] who wrote in 1865,

A tendril ... invariably becomes twisted in one part in one direction, and in another part in the opposite direction ... This curious and symmetrical structure has been noticed by several botanists, but has not been sufficiently explained. [5]

The term "tendril perversion" was coined by Alain Goriely and Michael Tabor in 1998 based on the word perversion found in 19th-century science literature. [6] [7] "Perversion" is a transition from one chirality to another and was known to James Clerk Maxwell, who attributed it to topologist J. B. Listing. [4] [8]

Tendril perversion can be viewed as an example of spontaneous symmetry breaking, in which the strained structure of the tendril adopts a configuration of minimum energy while preserving zero overall twist. [2]

Tendril perversion has been studied both experimentally and theoretically. Gerbode et al. have made experimental studies of the coiling of cucumber tendrils. [9] [10] A detailed study of a simple model of the physics of tendril perversion was made by McMillen and Goriely in the early 2000s. [2] Liu et al. showed in 2014 that "the transition from a helical to a hemihelical shape, as well as the number of perversions, depends on the height to width ratio of the strip's cross-section." [3]

Generalized tendril perversions were put forward by Silva et al., to include perversions that can be intrinsically produced in elastic filaments, leading to a multiplicity of geometries and dynamical properties. [11]

See also

Related Research Articles

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An alpha helix is a sequence of amino acids in a protein that are twisted into a coil.

<span class="mw-page-title-main">Beta sheet</span> Protein structural motif

The beta sheet is a common motif of the regular protein secondary structure. Beta sheets consist of beta strands (β-strands) connected laterally by at least two or three backbone hydrogen bonds, forming a generally twisted, pleated sheet. A β-strand is a stretch of polypeptide chain typically 3 to 10 amino acids long with backbone in an extended conformation. The supramolecular association of β-sheets has been implicated in the formation of the fibrils and protein aggregates observed in amyloidosis, Alzheimer's disease and other proteinopathies.

<span class="mw-page-title-main">Vine</span> Plant with a growth habit of trailing or scandent stems or runners

A vine is any plant with a growth habit of trailing or scandent stems, lianas, or runners. The word vine can also refer to such stems or runners themselves, for instance, when used in wicker work.

<span class="mw-page-title-main">Helix</span> Space curve that winds around a line

A helix is a shape like a corkscrew. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices. The word helix comes from the Greek word ἕλιξ, "twisted, curved". A "filled-in" helix – for example, a "spiral" (helical) ramp – is a surface called a helicoid.

<span class="mw-page-title-main">Tendril</span> Specialisation of plant parts used to climb or bind

In botany, a tendril is a specialized stem, leaf or petiole with a threadlike shape used by climbing plants for support and attachment, as well as cellular invasion by parasitic plants such as Cuscuta. There are many plants that have tendrils; including sweet peas, passionflower, grapes and the Chilean glory-flower. Tendrils respond to touch and to chemical factors by curling, twining, or adhering to suitable structures or hosts. Tendrils vary greatly in size from a few centimeters up to 27 inches for Nepenthes harryana The chestnut vine can have tendrils up to 20.5 inches in length. Normally there is only one simple or branched tendril at each node, but the aardvark cucumber can have as many as eight.

In plasma physics, magnetic helicity is a measure of the linkage, twist, and writhe of a magnetic field. In ideal magnetohydrodynamics, magnetic helicity is conserved. When a magnetic field contains magnetic helicity, it tends to form large-scale structures from small-scale ones. This process can be referred to as an inverse transfer in Fourier space.

<span class="mw-page-title-main">Nucleic acid double helix</span> Structure formed by double-stranded 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 and her student Raymond Gosling, but the term "double helix" entered popular culture with the publication in 1968 of The Double Helix: A Personal Account of the Discovery of the Structure of DNA by James Watson.

<span class="mw-page-title-main">Helicene</span> Class of chemical compounds

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3<sub>10</sub> helix Type of secondary structure

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A helix bundle is a small protein fold composed of several alpha helices that are usually nearly parallel or antiparallel to each other.

<span class="mw-page-title-main">Helical growth</span>

Helical growth is when cells or organs expand, resulting in helical shaped cells or organs and typically including the breakage of symmetry. This is seen in fungi, algae, and other higher plant cells or organs. Helical growth can occur naturally, such as in tendrils or in twining plants. Asymmetry can be caused by changes in pectin or through mutation and result in left- or right-handed helices. Tendril perversion, during which a tendril curves in opposite directions at each end, is seen in many cases. The helical growth of twining plants is based on the circumnutational movement, or circular growth, of stems. Most twining plans have right-handed helices regardless of the plant's growth hemisphere.

<span class="mw-page-title-main">Boerdijk–Coxeter helix</span> Linear stacking of regular tetrahedra that form helices

The Boerdijk–Coxeter helix, named after H. S. M. Coxeter and A. H. Boerdijk, is a linear stacking of regular tetrahedra, arranged so that the edges of the complex that belong to only one tetrahedron form three intertwined helices. There are two chiral forms, with either clockwise or counterclockwise windings. Unlike any other stacking of Platonic solids, the Boerdijk–Coxeter helix is not rotationally repetitive in 3-dimensional space. Even in an infinite string of stacked tetrahedra, no two tetrahedra will have the same orientation, because the helical pitch per cell is not a rational fraction of the circle. However, modified forms of this helix have been found which are rotationally repetitive, and in 4-dimensional space this helix repeats in rings of exactly 30 tetrahedral cells that tessellate the 3-sphere surface of the 600-cell, one of the six regular convex polychora.

<span class="mw-page-title-main">Chiral media</span> Applied to electromagnetism

The term chiral describes an object, especially a molecule, which has or produces a non-superposable mirror image of itself. In chemistry, such a molecule is called an enantiomer or is said to exhibit chirality or enantiomerism. The term "chiral" comes from the Greek word for the human hand, which itself exhibits such non-superimposeability of the left hand precisely over the right. Due to the opposition of the fingers and thumbs, no matter how the two hands are oriented, it is impossible for both hands to exactly coincide. Helices, chiral characteristics (properties), chiral media, order, and symmetry all relate to the concept of left- and right-handedness.

A liquid-crystal laser is a laser that uses a liquid crystal as the resonator cavity, allowing selection of emission wavelength and polarization from the active laser medium. The lasing medium is usually a dye doped into the liquid crystal. Liquid-crystal lasers are comparable in size to diode lasers, but provide the continuous wide spectrum tunability of dye lasers while maintaining a large coherence area. The tuning range is typically several tens of nanometers. Self-organization at micrometer scales reduces manufacturing complexity compared to using layered photonic metamaterials. Operation may be either in continuous wave mode or in pulsed mode.

<span class="mw-page-title-main">Chirality</span> Difference in shape from a mirror image

Chirality is a property of asymmetry important in several branches of science. The word chirality is derived from the Greek χειρ (kheir), "hand", a familiar chiral object.

<span class="mw-page-title-main">Obsolete models of DNA structure</span>

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<span class="mw-page-title-main">Subi Jacob George</span> Indian organic chemist

Subi Jacob George is an Indian organic chemist, known for his work in the fields of supramolecular chemistry, materials chemistry, and polymer chemistry. His research interests includes organic and supramolecular synthesis, functional organic materials, supramolecular polymers, chiral amplification, hybrid materials, and optoelectronic materials.

Nathalie Helene Katsonis is a Professor of Active Molecular Systems at the Stratingh Institute for Chemistry, University of Groningen. In 2016 she was awarded the Royal Netherlands Chemical Society Gold Medal.

Sharon J. Gerbode is a soft matter physicist and the Iris and Howard Critchell Associate Professor of Physics at Harvey Mudd College. She is recognized for her contributions to the fields of soft matter and biomechanics and is a 2016 Cottrell Scholar, a distinction given to top early career academic scientists by the Research Corporation for Science Advancement (RCSA).

<span class="mw-page-title-main">Alain Goriely</span> Belgian mathematician

Alain Goriely is a Belgian mathematician, currently holding the statutory professorship (chair) of mathematical modelling at the University of Oxford, Mathematical Institute. He is director of the Oxford Centre for Industrial Mathematics (OCIAM), of the International Brain and Mechanics Lab (IBMTL) and Professorial Fellow at St Catherine's College, Oxford. At the Mathematical Institute, he was the director of external relations and public engagement, from 2013 until 2022, initiating the Oxford Mathematics series of public lectures. In 2022, he was elected to the Royal Society.

References

  1. Goriely, Alain (2017). The mathematics and mechanics of biological growth. New York: Springer. ISBN   978-0-387-87709-9. OCLC   989037743.
  2. 1 2 3 McMillen; Goriely (2002). "Tendril Perversion in Intrinsically Curved Rods". Journal of Nonlinear Science. 12 (3): 241. Bibcode:2002JNS....12..241M. CiteSeerX   10.1.1.140.352 . doi:10.1007/s00332-002-0493-1. S2CID   18480860.
  3. 1 2 Liu, J.; Huang, J.; Su, T.; Bertoldi, K.; Clarke, D. R. (2014). "Structural Transition from Helices to Hemihelices". PLOS ONE. 9 (4): e93183. Bibcode:2014PLoSO...993183L. doi: 10.1371/journal.pone.0093183 . PMC   3997338 . PMID   24759785.
  4. 1 2 Alain Goriely (2013). "Inversion, Rotation, and Perversion in Mechanical Biology: From Microscopic Anisotropy to Macroscopic Chirality" (PDF). p. 9.
  5. Charles Darwin, "On the movements and habits of climbing plants", Journal of the Linnean Society, 1865.
  6. Goriely, Alain; Tabor, Michael (1998-02-16). "Spontaneous Helix Hand Reversal and Tendril Perversion in Climbing Plants". Physical Review Letters. American Physical Society (APS). 80 (7): 1564–1567. Bibcode:1998PhRvL..80.1564G. doi:10.1103/physrevlett.80.1564. ISSN   0031-9007.
  7. McMillen; Goriely (2002). "Tendril Perversion in Intrinsically Curved Rods". Journal of Nonlinear Science. 12 (3): 241. Bibcode:2002JNS....12..241M. CiteSeerX   10.1.1.140.352 . doi:10.1007/s00332-002-0493-1. S2CID   18480860.
  8. James Clerk Maxwell (1873). A Treatise of Electricity and Magnetism. Oxford: Clarendon Press. The operation of passing from one system to the other is called by Listing, Perversion. The reflection of an object in a mirror image is a perverted image of the object.
  9. Gerbode, S. J.; Puzey, J. R.; McCormick, A. G.; Mahadevan, L. (2012). "How the Cucumber Tendril Coils and Overwinds". Science. 337 (6098): 1087–91. Bibcode:2012Sci...337.1087G. doi:10.1126/science.1223304. PMID   22936777. S2CID   17405225.
  10. Geraint Jones (30 August 2012). "Scientists unwind the secrets of climbing plants' tendrils". The Guardian.
  11. Silva, Pedro E. S.; Trigueiros, Joao L.; Trindade, Ana C.; Simoes, Ricardo; Dias, Ricardo G.; Godinho, Maria Helena; Abreu, Fernao Vistulo de (2016-03-30). "Perversions with a twist". Scientific Reports. 6: 23413. Bibcode:2016NatSR...623413S. doi:10.1038/srep23413. PMC   4812244 . PMID   27025549.