np.

らせん体、らせん

関: helical、helix、spiral

WordNet

form a spiral; "The path spirals up the mountain"
a continuously accelerating change in the economy
a plane curve traced by a point circling about the center but at increasing distances from the center
ornament consisting of a curve on a plane that winds around a center with an increasing distance from the center (同)volute
flying downward in a helical path with a large radius
a curve that lies on the surface of a cylinder or cone and cuts the element at a constant angle (同)spiral

PrepTutorEJDIC

らせん(helix) / らせん状のもの;らせんばね;巻き貝 / (物価・賃金などの)らせん状上昇(下降) / らせん状の /… ‘を'らせん形にする / らせん形になる;らせん状に動く
らせん / らせん形のもの
らせん形の

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2019/08/17 16:30:57」(JST)

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The right-handed helix (cos t, sin t, t) from t = 0 to 4π with arrowheads showing direction of increasing t

A helix (/ˈhiːlɪks/), plural helixes or helices (/ˈhɛlɪsiːz/), is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helices are coil springs and the handrails of spiral staircases. A "filled-in" helix – for example, a "spiral" (helical) ramp – is called a helicoid.^[1] 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".^[2]

Types

Helices can be either right-handed or left-handed. With the line of sight along the helix's axis, if a clockwise screwing motion moves the helix away from the observer, then it is called a right-handed helix; if towards the observer, then it is a left-handed helix. Handedness (or chirality) is a property of the helix, not of the perspective: a right-handed helix cannot be turned to look like a left-handed one unless it is viewed in a mirror, and vice versa.

Two types of helix shown in comparison. This shows the two chiralities of helices. One is left-handed and the other is right-handed. Each row compares the two helices from a different perspective. The chirality is a property of the object, not of the perspective (view-angle)

Most hardware screw threads are right-handed helices. The alpha helix in biology as well as the A and B forms of DNA are also right-handed helices. The Z form of DNA is left-handed.

The pitch of a helix is the height of one complete helix turn, measured parallel to the axis of the helix.

A double helix consists of two (typically congruent) helices with the same axis, differing by a translation along the axis.^[3]

A conic helix may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of the angle indicating direction from the axis. An example is the Corkscrew roller coaster at Cedar Point amusement park.

A circular helix, (i.e. one with constant radius) has constant band curvature and constant torsion.

A curve is called a general helix or cylindrical helix^[4] if its tangent makes a constant angle with a fixed line in space. A curve is a general helix if and only if the ratio of curvature to torsion is constant.^[5]

Geometric pitch is the distance an element of an airplane propeller would advance in one revolution if it were moving along a helix having an angle equal to that between the chord of the element and a plane perpendicular to the propeller axis.

A curve is called a slant helix if its principal normal makes a constant angle with a fixed line in space.^[6] It can be constructed by applying a transformation to the moving frame of a general helix.^[7]

Some curves found in nature consist of multiple helices of different handedness joined together by transitions known as tendril perversions.

Mathematical description

A helix composed of sinusoidal x and y components

In mathematics, a helix is a curve in 3-dimensional space. The following parametrisation in Cartesian coordinates defines a particular helix,^[8] Perhaps the simplest equations for one is

x(t)=\cos(t),\,

y(t)=\sin(t),\,

z(t)=t.\,

As the parameter t increases, the point (x(t),y(t),z(t)) traces a right-handed helix of pitch 2π (or slope 1) and radius 1 about the z-axis, in a right-handed coordinate system.

In cylindrical coordinates (r, θ, h), the same helix is parametrised by:

r(t)=1,\,

\theta (t)=t,\,

h(t)=t.\,

A circular helix of radius a and slope b/a (or pitch 2πb) is described by the following parametrisation:

x(t)=a\cos(t),\,

y(t)=a\sin(t),\,

z(t)=bt.\,

Another way of mathematically constructing a helix is to plot the complex-valued function e^xi as a function of the real number x (see Euler's formula). The value of x and the real and imaginary parts of the function value give this plot three real dimensions.

Except for rotations, translations, and changes of scale, all right-handed helices are equivalent to the helix defined above. The equivalent left-handed helix can be constructed in a number of ways, the simplest being to negate any one of the x, y or z components.

Arc length, curvature and torsion

The length of a circular helix of radius a and slope b/a (or pitch 2πb) expressed in rectangular coordinates as

t\mapsto (a\cos t,a\sin t,bt),t\in [0,T]

equals $T\cdot {\sqrt {a^{2}+b^{2}}}$ , its curvature is ${\frac {|a|}{a^{2}+b^{2}}}$ and its torsion is ${\frac {b}{a^{2}+b^{2}}}.$ A helix has constant non-zero curvature and torsion.

Examples

In music, pitch space is often modeled with helices or double helices, most often extending out of a circle such as the circle of fifths, so as to represent octave equivalency.

Crystal structure of a folded molecular helix reported by Lehn et al. in Helv. Chim. Acta., 2003, 86, 1598–1624.
A natural left-handed helix, made by a climber plant
A charged particle in a uniform magnetic field following a helical path
A helical coil spring

References

^ Weisstein, Eric W. "Helicoid". MathWorld.
^ ἕλιξ Archived 2012-10-16 at the Wayback Machine, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
^ "Double Helix Archived 2008-04-30 at the Wayback Machine" by Sándor Kabai, Wolfram Demonstrations Project.
^ O'Neill, B. Elementary Differential Geometry, 1961 pg 72
^ O'Neill, B. Elementary Differential Geometry, 1961 pg 74
^ Izumiya, S. and Takeuchi, N. (2004) New special curves and developable surfaces. Turk J Math Archived 2016-03-04 at the Wayback Machine, 28:153–163.
^ Menninger, T. (2013), An Explicit Parametrization of the Frenet Apparatus of the Slant Helix. arXiv:1302.3175 Archived 2018-02-05 at the Wayback Machine.
^ Weisstein, Eric W. "Helix". MathWorld.

<https://www.merriam-webster.com/dictionary/geometrical%20pitch

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1. 食物アレルゲンの分子機能molecular features of food allergens [show details]
…close to the C-terminus of Cor a 14 was released, while the core structure of disulfide-bonded alpha-helices remained intact . Pin p 1, the 2S albumin from pine nuts, was heat stable for 120 minutes at 100°C …
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…permit folding of the polypeptide upon itself. Individual residues can be assigned to one of eight helices (A to H) or to adjacent nonhelical stretches. The various globin chains are designated by Greek letters …
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…subjects without clinical reactivity. nsLTPs are remarkably heat-stable, presumably due to four alpha-helices stabilized by four disulfide bonds. nsLTPs retain their allergenicity in processed foods, such as…
4. 脊椎関節炎の病因pathogenesis of spondyloarthritis [show details]
…composed of three domains. The first two domains (alpha-1 and alpha-2) together form two antiparallel helices resting on a platform of an eight-stranded pleated sheet, which itself rests on two barrel-shaped…
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…and the vitreous of the eye . Type IX collagen, a fibril-associated form with interrupted triple helices, has proteoglycan properties. It is a molecular coupler that organizes and anchors type II collagen…

English Journal

Characterizing salt substitution in beef meat processing by vibrational spectroscopy and sensory analysis.

Perisic N, Afseth NK, Ofstad R, Narum B, Kohler A.SourceNofima AS, Osloveien 1, N-1430 Aas, Norway; Institute of Mathematical Sciences and Technology, Norwegian University of Life Sciences, PO Box 5003, 1432 Aas, Norway. Electronic address: nebojsa.perisic@nofima.no.
Meat science.Meat Sci.2013 Nov;95(3):576-85. doi: 10.1016/j.meatsci.2013.05.043. Epub 2013 Jun 5.
In this investigation, the effect of NaCl, KCl and MgSO4 on bovine meat was studied, where the salts were used in standard marinades in 5.5% concentration. The effect of salts on secondary structure of the myofibrillar proteins, protein-water interactions, WHC, and sensory properties of the meat was
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Supersandwich-type electrochemiluminescenct aptasensor based on Ru(phen)3(2+) functionalized hollow gold nanoparticles as signal-amplifying tags.

Gui G, Zhuo Y, Chai YQ, Liao N, Zhao M, Han J, Zhu Q, Yuan R, Xiang Y.SourceKey Laboratory on Luminescence and Real-Time Analysis, Ministry of Education, College of Chemistry and Chemical Engineering, Southwest University, Chongqing 400715, China.
Biosensors & bioelectronics.Biosens Bioelectron.2013 Sep 15;47:524-9. doi: 10.1016/j.bios.2013.03.075. Epub 2013 Apr 6.
An electrochemiluminescent (ECL) aptasensor was fabricated and used for the amplified detection of thrombin (TB) based on DNA supersandwich structure. Herein, hollow gold nanospheres (HGNPs) were firstly employed as effective tag-carriers for the immobilization of detection aptamer (TBA 2) to form t
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Stabilization of α-helices by the self-assembly of macrocyclic peptides on the surface of gold nanoparticles for molecular recognition.

Kim B, Choi SJ, Han SH, Choi KY, Lim YB.SourceTranslational Research Center for Protein Function Control, Yonsei University, Seoul 120-749, Korea. yblim@yonsei.ac.kr.
Chemical communications (Cambridge, England).Chem Commun (Camb).2013 Sep 7;49(69):7617-9. doi: 10.1039/c3cc44644a. Epub 2013 Jul 19.
A novel strategy to stabilize the α-helical secondary structures of peptides upon binding to gold nanoparticles is described. Using a model protein-protein interaction system, we showed that AuNPs decorated with stabilized p53 α-helix peptides can mediate specific molecular recognition with their
PMID 23873019

Japanese Journal

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Imamoto Yasushi,Kojima Keiichi,Oka Toshihiko,Maeda Ryo,Shichida Yoshinori
The Journal of Physical Chemistry B 123(43), 9134-9142, 2019-10-31
… Among the photoproducts of vertebrate rhodopsin, only metarhodopsin II (Meta-II) preferentially adopts the active structure in which transmembrane helices are rearranged. … However, the displaced helices III and V in Meta-II resulting from the disruption of cytoplasmic ionic lock were restored in Opsin*, which is likely to destabilize the G-protein-activating structure of opsin. …
NAID 120006764461

Membrane-deformation ability of ANKHD1 is involved in the early endosome enlargement

Kitamata Manabu,Hanawa-Suetsugu Kyoko,Maruyama Kohei,Suetsugu Shiro
2019-07-26
… BAR domains sometimes have amphipathic helices for membrane tubulation and vesiculation. …
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Insights into the Molecular Mechanisms of Eg5 Inhibition by (+)-Morelloflavone

Ogunwa Tomisin Happy,Laudadio Emiliano,Galeazzi Roberta,Miyanishi Takayuki
Pharmaceuticals 12(2), 58, 2019-04-16
… Altered structural conformations were also visible within various regions of Eg5, including switch I, switch II, α2/α3 helices, and the tubulin-binding region, indicating that MF might induce modifications in the Eg5 structure to compromise its ATP/ADP binding and conversion process as well as its interaction with microtubules. …
NAID 120006712968

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リンク元	「helix」「らせん」「helical」「spiral」「らせん体」
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