Naimark's dilation theorem: Difference between revisions

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Some preliminary notions: Fix the proof of the Self adjointness of E
 
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[[Image:1m8n_Choristoneura_fumiferana.png|thumb|right|200px|Monomeric, left-handed β-helix antifreeze protein from the spruce budworm ''[[Choristoneura fumiferana]]'' (PDB accession code 1M8N).]]
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[[Image:1ezg_Tenebrio_molitor.png|thumb|350px|Dimeric, right-handed β-helix antifreeze protein from the beetle ''[[Tenebrio molitor]]'' (PDB accession code 1EZG). Face-to-face association of β-helices.]]
A '''beta helix''' is a [[protein]] structure formed by the association of parallel [[beta sheet|beta strands]] in a helical pattern with either two or three faces. The beta helix is a type of [[solenoid protein domain]]. The structure is stabilized by inter-strand [[hydrogen bond]]s, [[protein-protein interaction]]s, and sometimes bound metal [[ion]]s. Both left- and right-handed beta helices have been identified.
 
==Two-stranded helices==
The simplest beta helix contains two "layers" of beta sheets connected by [[glycine]]-rich six-residue loops that invariably contain an [[aspartate]] to bind one [[calcium]] ion per loop. Each layer consists of a nearly-planar series of parallel hydrogen-bonded beta strands and the two layers together enclose a [[hydrophobic]] core.
 
==Three-stranded helices==
Three-stranded beta helices form a distorted triangular prism shape in which each face exhibits parallel inter-strand hydrogen bonding. One of the three sheets that form the repeating [[structural motif]] can appear "bent" relative to the other two, which face each other as in the two-stranded helix. Two of the three linking loops between the sheets can be of arbitrary length and can even contain other [[structural domain]]s; the third is restricted to two residues. A characteristic common hexapeptide repeat found in both left- and right-handed helices is the sequence <math>\mathrm{[LIV]-[GAED]-X_{2}-[STAV]-X}</math>. Known three-stranded helices are appreciably longer than their two-stranded counterparts.
 
The first beta-helix was observed in the enzyme [[pectate lyase]], which contains a seven-turn helix that reaches 34 Å (3.4 [[nanometer|nm]]) long. The [[P22 phage]] tailspike protein, a component of the P22 [[bacteriophage]], has 13 turns and in its assembled homo[[protein trimer|trimer]] is 200 Å (20 nm) in length. Its interior is close-packed with no central pore and contains both hydrophobic residues and charged residues neutralized by [[salt bridge]]s.
 
Both pectate lyase and P22 tailspike protein contain right-handed helices; left-handed versions have been observed in [[enzyme]]s such as [[UDP-N-acetylglucosamine acyltransferase]] and archaeal [[carbonic anhydrase]].<ref name="pmid8665839">{{cite journal |author=Kisker C, Schindelin H, Alber BE, Ferry JG, Rees DC |title=A left-hand beta-helix revealed by the crystal structure of a carbonic anhydrase from the archaeon Methanosarcina thermophila |journal=EMBO J. |volume=15 |issue=10 |pages=2323–30 |date=May 1996 |pmid=8665839 |pmc=450161 |doi= |url=}}</ref> Other proteins that contain beta helices include the [[antifreeze]] proteins from the beetle ''[[Tenebrio molitor]]'' (right-handed)<ref name="pmid10917536">{{cite journal |author=Liou YC, Tocilj A, Davies PL, Jia Z |title=Mimicry of ice structure by surface hydroxyls and water of a beta-helix antifreeze protein |journal=Nature |volume=406 |issue=6793 |pages=322–4 |date=July 2000 |pmid=10917536 |doi=10.1038/35018604 |url=}}</ref> and from the spruce budworm, ''[[Choristoneura fumiferana]]'' (left-handed),<ref name="pmid12015145">{{cite journal |author=Leinala EK, Davies PL, Jia Z |title=Crystal structure of beta-helical antifreeze protein points to a general ice binding model |journal=Structure |volume=10 |issue=5 |pages=619–27 |date=May 2002 |pmid=12015145 |doi= |url=}}</ref> where regularly spaced [[threonine]]s on the β-helices bind to the surface of [[ice]] crystals and inhibit their growth.
 
Beta helices can associate with each other effectively, either face-to-face (mating the faces of their triangular prisms) or end-to-end (forming hydrogen bonds).  Hence, β-helices can be used as "tags" to induce other proteins to associate, similar to [[coiled coil]] segments.
 
==Four-stranded helices==
Members of the [[Pentapeptide repeat]] family have been shown to possess a quadrilateral beta-helix structure.<ref name="pmid16388575">{{cite journal |author=Vetting MW, Hegde SS, Fajardo JE, ''et al.'' |title=Pentapeptide repeat proteins |journal=Biochemistry |volume=45 |issue=1 |pages=1–10 |date=January 2006 |pmid=16388575 |pmc=2566302 |doi=10.1021/bi052130w |url=}}</ref>
 
==References==
{{Reflist}}
*Branden C, Tooze J. (1999). ''Introduction to Protein Structure'' 2nd ed. Garland Publishing: New York, NY. pp 84-6.
*Dicker IB and Seetharam S. (1992) "What is known about the structure and function of the ''Escherichia coli'' protein FirA?" ''Mol. Microbiol.'', '''6''', 817-823.
*Raetz CRH and Roderick SL. (1995) "A Left-Handed Parallel β Helix in the Structure of UDP-''N''-Acetylglucosamine Acyltransferase", ''Science'', '''270''', 997-1000. (Left-handed)
*Steinbacher S, Seckler R, Miller S, Steipe B, Huber R and Reinemer P. (1994) "Crystal structure of P22 tailspike protein: interdigitated subunits in a thermostable trimer", ''Science'', '''265''', 383-386. (Right-handed)
*Vaara M. (1992) "Eight bacterial proteins, including UDP-N-acetylglucosamine acyltransferase (LpxA) and three other transferases of Escherichia coli, consist of a six-residue periodicity theme", ''FEMS Microbiol. Lett'', '''97''', 249-254.
*Yoder MD, Keen NT and Jurnak F. (1993) "New domain motif:the structure of pectate lyase C, a secreted plant virulence factor", ''Science'', '''260''', 1503-1507. (Right-handed)
 
==External links==
 
* [http://scop.mrc-lmb.cam.ac.uk/scop/data/scop.b.c.bbf.html SCOP family of right-handed β-helices]
* [http://scop.mrc-lmb.cam.ac.uk/scop/data/scop.b.c.bbg.html SCOP family of left-handed β-helices]
* [http://www.cathdb.info/cathnode/2.160 CATH β-helix protein family]
 
{{Protein secondary structure}}
 
[[Category:Protein folds]]
[[Category:Protein structural motifs]]
[[Category:Helices]]

Latest revision as of 17:25, 12 December 2014

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