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{{Babel|en-5|fr-4|it-4|la-3|ro}} 

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[[/Sandbox2]]
== Headline text ==
'''A Main Page for Bci2 Editing'''

===The List of Articles Initiated/Generated on Wikipedia by user Bci2===
* [[Molecular models of DNA]]


[[/Sandbox]]
===Major Projects===
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==References and notes==
{{Reflist}}
.<ref>{{cite web
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The easy link with no numbers, but bullets: 
[http://www.example.org link title]

--Nu 08:13, 2 October 2008 (UTC)signature squiggle  
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#REDIRECT [[Insert Text]]  ?? what does this mean? <s><br />Strike-through text</s>

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{{Babel-9|en|en-5|ro|fr-4|it-4|la-4|ru-2|editor English wiki|10000}}




Wikipedia guidelines for

== "'''inline citations"''' ==
OR Footnotes that are key to "[[Image:Verifiability"]] on wiki as quoted below from this source:

"Footnotes serve two purposes. First, they are used to add material that explains a point in greater detail, particularly if the explanation would be distracting if written out in the main article. Second, they are used to cite the reliable sources that support an assertion in the main article. This is known as an "inline citation". Two different types of footnotes may be used for these two different purposes, as described below.

The prevailing system for adding footnotes to an article involves the <ref> tag. This system has several advantages, including automatic sequential numbering of the footnotes and provisions for multiple references to the same footnote. To add such a footnote to an article, the editor includes the text of the footnote between two HTML-style tags, e.g. <ref>Text of footnote goes here.</ref>. Different classes of footnotes can be defined within an article using the "group" parameter inside the "ref" tag, as described below.

Editors may also use the older system of template-based footnotes, such as {{tl|Ref label}} and {{tl|note label}}. These have the disadvantage that they are not numbered automatically; the editor has to choose a specific label. It is generally expected that footnotes will be labeled in the order in which they occur in the text. Therefore, if an editor adds such a template-based footnote in the middle of an article, the editor should also renumber/increment all the subsequent footnotes of the same type, by hand.

Footnotes are not the only way to cite sources. Alternative methods are embedded links and Harvard referencing (also known as author-date or parenthetical referencing). For more information, see Wikipedia:Citing sources, the main style guide on citations.

 A key content policy, Wikipedia:Verifiability, says that any material that is challenged or likely to be challenged, including any contentious material about living people, and all quotations, must have a source. Unsourced or poorly sourced material may be removed from any article, and if it is, the burden of proof is on the editor who wishes to restore it."

==Further reading==
* "[[Jimmy Wales]]. [http://lists.wikimedia.org/pipermail/wikien-l/2006-July/050773.html "WikiEN-l insist on sources"], WikiEN-l mailing list, July 19, 2006." --A quote from Wikipedia guidelines on references, and see also:
Image:QChip.jpg|The first reported quantum semiconductor chip (QSC) with trapped ions by Michigan University in 2005<ref> http://www.umich.edu/news/index.html?Releases/2005/Dec05/r121205b</ref>
[http://www.umich.edu/news/Releases/2005/Dec05/img/chipCarrier_sm.jpg University of Michigan News Release]

{{User WikiProject Physics}}
{{User WP Math}}
{{User WPBiography}}


==Discussions==
==DNA Structure==
Hello, Tim. I 'm also afraid that the current DNA article version has a '''basic flaw''' in the over-simplified presentation of A-DNA structure and B-DNA configurations in regards to the interpretation of the corresponding X-ray patterns.  This could have been corrected by adding relevant references of published papers that however is being prevented by the over-protection of this entry through locking up the editing. At the very least a new section could be added up that allows the correction of this basic flaw which places in doubt the scientific value of ``comparisons" between A-DNA and what is commonly still called the `B-DNA' configuration set. Furthermore, there are several factual errors also about the conditions under which A-DNA X-ray diffraction patterns have been generated, not to mention the lack of adequate credit to the experimenters involved. For an improved entry such comments with the introduction of the appropriate literature references should help. [[User:Bci2|Bci2]] ([[User talk:Bci2|talk]]) 10:27, 4 May 2009 (UTC).

:Would it be possible for you to also look over [[Mechanical properties of DNA]], which tried to deal with DNA structure in a much more rigorous way than the parent article. However, this isn't one I've spent any time editing, so I can't vouch for the contents. [[User:TimVickers|Tim Vickers]] ([[User talk:TimVickers|talk]]) 22:44, 4 May 2009 (UTC)

I've renamed this article [[DNA structure]] and used your additions to the DNA article to start a section on the determination of DNA structures. Would it be possible for you to expand this? We don't have such a space limitation here as in the general DNA article, and you can write at a bit of a higher level. [[User:TimVickers|Tim Vickers]] ([[User talk:TimVickers|talk]]) 15:39, 5 May 2009 (UTC)

:Hi, Tim: Sounds like a great idea-- why didn't I think of it (rhetorical quaestion!). Will add the required explanation as my time permits, as it involves a lot more referencing and explanation, but it is obviously of the essence. You are correct--the interests of science are best served by cooperation, as everyone stands to benefit from it. I'm glad that you see the point of the X-ray patterns comparison that I was initially trying to introduce in the DNA entry. Until we have the more complete story I am however suggesting that we should keep the minimal explanation in place so that new readers are not being misled by the 50 year old literature.[[User:Bci2|Bci2]] ([[User talk:Bci2|talk]]) 12:27, 5 May 2009 (UTC).

::The section in the DNA article is still a lot too technical for our audience, if I'm struggling to understand what it means, and I studied DNA structure and topology as part of my first degree, then I don't think a high-school student will be able to get anything from the text. For example, some of the text says that the patterns analyzed come from "hydrated, bacterial oriented DNA fibers and trout sperm heads" - but I have no idea what this is referring to. [[User:TimVickers|Tim Vickers]] ([[User talk:TimVickers|talk]]) 17:47, 5 May 2009 (UTC)

==Sign==
Nu 16:52, 12 March 2009 (UTC)Bci2
Nu 17:57, 2 March 2009 (UTC)Bci2Nu 17:57, 2 March 2009 [UTC];[[WP:PHYS]] ; [[WP:WPM]]

{{nutshell|Please: Do not be hostile toward newcomers.  Remember to [[WP:AGF|assume good faith]] first and [[Wikipedia:Welcoming committee|welcome]] them in a [[WP:CRYPTIC|clear]], polite manner. Also, '''please do respect all Wikipedia's members privacy'''}}

==Category theory==
http://en.wikipedia.org/wiki/Category_Theory


== Ronald Brown (mathematician) ==
Completed and styled

http://en.wikipedia.org/wiki/Ronald_Brown_(mathematician)

== [[Quark]] ==
http://en.wikipedia.org/wiki/Quark

== [[Wikipedia:WikiProject_Math]] ==
== [[Nuclear magnetic resonance]] ==

[[http://en.wikipedia.org/wiki/NMR NMR]]

==[[2D-FT NMRI and Spectroscopy]]==
http://en.wikipedia.org/wiki/2D-FT_NMRI_and_Spectroscopy

[[2D-FT NMRI and Spectroscopy]]
'''2D-FT Nuclear Magnetic resonance imaging''' ('''2D-FT NMRI'''), or '''Two-dimensional Fourier transform''' [[magnetic resonance imaging]] ('''NMRI'''), is primarily a non--invasive imaging technique most commonly used in biomedical research and medical [[radiology]]/nuclear medicine/[[MRI]] to visualize structures and functions of the living systems and single cells. For example it can provides fairly detailed images of a human body in any selected cross-sectional plane,
such as longitudinal, transversal, sagital, etc. NMRI provides much greater [[contrast (vision)|contrast]] especially for the different soft tissues of the body than [[computed tomography]] (CT) as its most sensitive option observes the nuclear spin  distribution and dynamics of highly mobile molecules that contain the naturally abundant, stable hydrogen isotope <sup>1</sup>H as in plasma water molecules, blood, disolved metabolites and fats. This approach makes it most useful in  [[cardiovascular magnetic resonance|cardiovascular]],  [[oncology|oncological]] (cancer), [[neurology|neurological]] (brain), [[human musculoskeletal system|musculoskeletal]], and [[cartilage]] imaging. Unlike CT, it uses no [[ionizing radiation]], and also unlike nuclear imaging it does not employ any radioactive isotopes. Some of the first MRI images reported were published in 1973<ref name=lauterbur>{{ cite journal |author=Lauterbur, P.C., Nobel Laureate in 2003 | title=Image Formation by Induced Local Interactions: Examples of Employing Nuclear Magnetic Resonance |journal=Nature |year=1973 |volume=242 |pages=190–1 |doi=10.1038/242190a0 }}</ref> and the first study performed on a human took place on July 3, 1977.<ref>[http://www.howstuffworks.com/mri.htm/printable Howstuffworks "How MRI Works"</ref> Earlier papers were also
published by Peter Mansfield<ref>Peter Mansfield. 2003.[http://www.parteqinnovations.com/pdf-doc/fandr-Gaz1006.pdf Nobel Laureate in Physiology and Medicine for (2D and 3D) MRI]</ref> in UK (Nobel Laureate in 2003), and R. Damadian in the USA, (together with an approved patent for magnetic imaging). Unpublished `high-resolution' (50 micron resolution) images of other living systems, such as hydrated wheat grains, were obtained and communicated in UK in 1977-1979, and were subsequently confirmed by articles published in ''Nature''. 
[[Image:Modern 3T MRI.JPG|thumb|350px|right|Advanced 4.7 [[Tesla (unit)|T]] clinical diagnostics and biomedical research NMR Imaging instrument.]]

== NMRI Principle==
Certain nuclei such as <sup>1</sup>H nuclei, or `fermions' have spin-1/2, because there are two spin states, referred to as "up" and "down" states. The [[nuclear magnetic resonance]] absorption phenomenon occurs when samples containing such nuclear spins are placed in a static magnetic field and a very short radiofrequency pulse is applied with a center, or carrier, frequency matching that of the transition between the up and down states of the spin-1/2 <sup>1</sup>H nuclei that were polarized by the static magnetic field. <ref>Antoine Abragam. 1968. ''Principles of Nuclear Magnetic Resonance.'', 895 pp., Cambridge University Press: Cambridge, UK.</ref>
Very low field schemes have also been recently reported.<ref name= Raftery>{{cite journal
|author=Raftery D |title=MRI without the magnet |journal=Proc Natl Acad Sci USA. |volume=103 |issue=34 |pages=12657–8 |year=2006 |month=August |pmid=16912110 |pmc=1568902 |doi=10.1073/pnas.0605625103
}}</ref>

==Chemical Shifts==
NMR is a very useful family of techniques for chemical and biochemical research because of the [[chemical shift]]; this effect consists in a frequency shift of the nuclear magnetic resonance for specific chemical groups or atoms as a result of the partial [[shielding]] of the corresponding nuclei from the applied, static external magnetic field by the [[electron orbital]]s (or [[molecular orbital]]s) surrounding such nuclei present in the chemical groups. Thus, the higher the [[electron density]] surounding a specific nucleus the larger the chemical shift will be. The resulting magnetic field at the nucleus is thus lower than the applied external magnetic field and the resonance frequencies observed as a result of such shielding are lower than the value that would be observed in the absence of any [[electronic orbital shielding]]. Furthermore, in order to obtain a chemical shift value independent of the strength of the applied magnetic field and allow for the direct comparison of spectra obtained at different magnetic field values, the chemical shift is defined by the ratio of the strength of the [[local magnetic field]] value at the observed (electron orbital-shielded) nucleus by the external magnetic field strength, H<sub>loc</sub>/ H<sub>0</sub>.
The first NMR observations of the chemical shift, with the correct physical chemistry interpretation, were reported for <sup>19</sup>F containing compounds in the early 1950's by [[Herbert S. Gutowsky]] and [[Charles P. Slichter]] from the [[University of Illinois at Urbana]] (USA).

==NMR Imaging Principles==
A number of methods have been devised for combining magnetic field gradients and radiofrequency pulsed excitation to obtain an image. Two major maethods involve either 2D -FT or 3D-FT<ref name=Wu1999>{{cite journal
|author=Wu Y, Chesler DA, Glimcher MJ, ''et al'' |title=Multinuclear solid-state three-dimensional MRI of bone and synthetic calcium phosphates |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=96 |issue=4 |pages=1574–8 |year=1999 |month=February |pmid=9990066 |pmc=15521 |doi=10.1073/pnas.96.4.1574 |url=http://www.pnas.org/cgi/pmidlookup?view=long&pmid=9990066
}}</ref> reconstruction from projections, somewhat similar to [[Computed tomography|Computed Tomography]], with the exception of the image interpretation that in the former case must include dynamic and relaxation/contrast enhancement information as well. Other schemes involve building the NMR image either point-by-point or line-by-line. Some schemes use instead gradients in the rf field rather than in the static magnetic field. The majority of NMR images routinely obtained are either by the [http://www.math.cuhk.edu.hk/course/mat2071a/lec1_08.ppt Two-Dimensional Fourier Transform (2D-FT) technique] (with slice selection), or by the Three-Dimensional Fourier Transform (3D--FT) techniques that are however much more time consuming at present. 2D-FT NMRI is sometime called in common parlance a "spin-warp".  An NMR image corresponds to a spectrum consisting of a number of `spatial frequencies' at different locations in the sample investigated, or in a patient.<ref>*{{cite book |author=Haacke, E Mark; Brown, Robert F; Thompson, Michael; Venkatesan, Ramesh |title=Magnetic resonance imaging: physical principles and sequence design |publisher=J. Wiley & Sons |location=New York |year=1999 |isbn=0-471-35128-8 }}
</ref> 
A two–dimensional [[Fourier transform]]ation of such a "real" image may be considered as a representation of such "real waves" by a matrix of [[spatial frequency|spatial frequencies]] known as the [[k-space (MRI)|k–space]]. 
We shall see next in some mathematical detail how the 2D-FT 
computation works to obtain 2D-FT NMR images.

== Two-dimensional Fourier transform imaging and spectroscopy==

A two-dimensional Fourier transform (2D-FT) is computed numerically or carried out in two stages, both involving `standard', one-dimensional Fourier transforms. However, the second stage Fourier transform is not the inverse Fourier transform (which would result in the original function that was transformed at the first stage), but a Fourier transform in a second variable-- which is `shifted' in value-- relative to that involved in the result of the first Fourier transform. Such 2D-FT analysis is a very powerful method for both NMRI and two-dimensional [[nuclear magnetic resonance]] spectroscopy (2D-FT NMRS)<ref>Richard R. Ernst. 1992. Nuclear Magnetic Resonance Fourier Transform (2D-FT) Spectroscopy.[http://nobelprize.org/nobel_prizes/chemistry/laureates/1991/ernst-lecture.pdf  Nobel Lecture], on December 9, 1992.</ref> that allows the three-dimensional reconstruction of polymer and biopolymer structures at atomic resolution]].<ref>
http://en.wikipedia.org/wiki/Nuclear_magnetic_resonance#Nuclear_spin_and_magnets  Kurt Wutrich in 1982-1986 : 2D-FT NMR of solutions</ref> for molecular weights (Mw) of dissolved biopolymers in aqueous solutions (for example) up to about 50,000 Mw. For larger biopolymers or polymers, more complex methods have been developed to obtain limited structural resolution needed for partial 3D-reconstructions of higher molecular structures, e.g. for up 900,000 Mw or even oriented microcrystals in aqueous suspensions or single crystals; such methods have also been reported for ''in vivo'' 2D-FT NMR spectroscopic studies of algae, bacteria, yeast and certain mammalian cells, including human ones. The 2D-FT method is also widely utilized in optical spectroscopy, such as ''2D-FT NIR hyperspectral imaging'' ([[2D-FT NIR-HS]]), or in MRI imaging for research and clinical, diagnostic applications in Medicine. In the latter case, 2D-FT [[Near infrared spectroscopy|NIR]]-HS has recently allowed the identification of single, malignant cancer cells surrounded by healthy human breast tissue at about 1 micron resolution, well-beyond the resolution obtainable 2D-FT NMRI for such systems in the limited time available for such diagnostic investigations (and also in magnetic fields up to the FDA approved magnetic field strength '''H'''<sub>0</sub> of 4.7 T, as shown in the top image of the state-of-the-art NMRI instrument). A more precise mathematical definition of the `double' (2D) Fourier transform involved in both 2D NMRI and 2D-FT NMRS is specified next, and a precise example follows this generally accepted definition.
=== 2D-FT Definition===
A ''2D-FT, or two-dimensional Fourier transform'', is a standard Fourier transformation of a function of two variables, <math>f(x_1, x_2)</math>, carried first in the first variable <math>x_1</math>, followed by the Fourier transform in the second variable <math>x_2</math> of the resulting function <math>F(s_1, x_2)</math>.                                     Note that in the case of both 2D-FT NMRI and 2D-FT NMRS the two independent variables in this definition are in the time domain, whereas the results of the two successive Fourier transforms have, of course, frequencies as the independent variable in the NMRS, and ultimately spatial coordinates for 
both 2D NMRI and 2D-FT NMRS following computer structural recontructions based on special algorithms that are different from FT or 2D-FT. Moreover, such structural algorithms are different for 2D NMRI and 2D-FT NMRS: in the former case they
involve macroscopic, or anatomical structure detrmination,
whereas in the latter case of 2D-FT NMRS the atomic structure reconstruction algorithms are based on the quantum theory of a microphysical (quantum) process such as nuclear Overhauser enhancement [[NOE]], or specific magnetic dipole-dipole interactions<ref>Charles P. Slichter.1996. ''Principles of Magnetic Resonance.'' Springer: Berlin and New York, Third Edition., 651pp. {{ISBN|0-387-50157-6}}.
</ref> between neighbor nuclei.

=== Example 1===
A 2D Fourier transformation and phase correction is applied to a set of 2D NMR (FID) signals :<math>s(t_1, t_2)</math>  yielding a real 2D-FT NMR `spectrum' (collection of 1D FT-NMR spectra) represented by a matrix '''S''' whose elements are
:<math>S(\nu_1,\nu_2) = \textbf{Re} \int \int cos(\nu_1 t_1)exp^{(-i\nu_2 t_2)} s(t_1, t_2)dt_1 dt_2</math>
where :<math>\nu_1</math> and :<math>\nu_2</math> denote the discrete indirect double-quantum and single-quantum(detection) axes, respectively,
in the 2D NMR experiments. Next, the \emph{covariance matrix} is calculated in the frequency domain according
to the following equation
:<math> C(\nu_2', \nu_2) = S^T S = \sum_{\nu^1}[S(\nu_1,\nu_2')S(\nu_1,\nu_2)],</math> with :<math>\nu_2, \nu_2'</math> taking all possible single-quantum frequency values and with the summation carried out over all discrete, double quantum frequencies :<math>\nu_1</math>.
=== Example 2 ===
[http://www.physorg.com/news129395045.html Atomic Structure from 2D-FT STEM Images] of electron distributions in a high-temperature cuprate superconductor `paracrystal'  reveal both the domains (or `location') and the local symmetry of the 'pseudo-gap' in the electron-pair correlation band responsible for the high--temperature superconductivity effect (obtained at Cornell University). So far there have been three Nobel prizes awarded for 2D-FT NMR/MRI during 1992-2003, and an additional, earlier Nobel prize for 2D-FT of X-ray data (`CAT scans'); recently the advanced possibilities of 2D-FT techniques in  [http://nobelprize.org/nobel_prizes/chemistry/laureates/1991/ernst-lecture.pdf Chemistry, Physiology and Medicine] received very significant recognition.<ref>[http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=2266107&query_hl=33&itool=pubmed_docsum Protein structure determination in solution by NMR spectroscopy] Wuthrich K. J Biol Chem. 1990 [[December 25]];265(36):22059-62.</ref>

==Brief explanation of NMRI diagnostic uses in Pathology ==
As an example, a diseased tissue such as a malign tumor, can be detected by 2D-FT NMRI because the hydrogen nuclei of molecules in different tissues return to their equilibrium spin state at different relaxation rates, and also because of the manner in which a malign tumor spreads and grows rapidly along the blood vessels adjacent to the tumor, also inducing further vascularization to occur. By changing the pulse delays in the [[RF]] pulse sequence employed, and/or the RF pulse sequence itself, one may obtain a `relaxation--based contrast', or contrast enhancement between different types of body tissue, such as normal vs. diseased tissue cells for example. Excluded from such diagnostic observations by NMRI are all patients with ferromagnetic metal implants, (e.g., [[cochlear implant]]s), and all cardiac pacemaker patients who cannot undergo any NMRI scan because of the very intense magnetic and RF fields employed in NMRI which would strongly interfere with the correct functioning of such pacemakers. It is, however, conceivable that future developments may also include along with the NMRI diagnostic treatments with special techniques involving applied magnetic fields and very high frequency RF. Already, surgery with special tools is being experimented on in the presence of NMR imaging of subjects.Thus, NMRI is used to image almost every part of the body, and is especially useful for diagnosis in neurological conditions, disorders of the muscles and joints, for evaluating tumors, such as in lung or skin cancers, abnormalities in the heart (especially in children with hereditary disorders), blood vessels, CAD, atherosclerosis
and [http://www.mr-tip.com/serv1.php?type=img&img=Cardiac%20Infarct%20Short%20Axis%20Cine%204 cardiac infarcts] (courtesy of Dr. Robert R. Edelman)

==See also==

{{Col-begin}}
{{Col-1-of-3}}
*[[Nuclear magnetic resonance]] (NMR)
*[[Medical imaging]]
*[[Protein nuclear magnetic resonance spectroscopy]]
*[[Kurt Wüthrich]]
*[[Chemical shift]]
*[[Computed tomography]] (CT)
*[[Fourier transform spectroscopy]](FTS)
*[[Richard R. Ernst]]
{{Col-2-of-3}}
*[[Magnetic resonance microscopy]]
*[[Solid-state NMR]]
*[[Herbert S. Gutowsky]]
*[[John S. Waugh]]
*[[Charles P. Slichter]]
*[[Near infrared spectroscopy|FT-NIRS]] (NIR)
*[[Magnetic resonance elastography]]
{{Col-3-of-3}}
*[[Relaxation]]
*[[Earth's field NMR]] (EFNMR)
*[[Robinson oscillator]]
{{Commons}}
{{Col-end}}

==Footnotes==
{{Reflist|2}}

==References==
*Antoine Abragam. 1968. ''Principles of Nuclear Magnetic Resonance.'', 895 pp., Cambridge University Press: Cambridge, UK.
*Charles P. Slichter.1996. ''Principles of Magnetic Resonance.'' Springer: Berlin and New York, Third Edition., 651pp. {{ISBN|0-387-50157-6}}.
*Kurt Wüthrich. 1986, ''NMR of Proteins and Nucleic Acids''., J. Wiley and Sons: New York, Chichester, Brisbane, Toronto, Singapore. ([http://nobelprize.org/nobel_prizes/chemistry/laureates/2002/wutrich-lecture.pdf Nobel Laureate in 2002 for 2D-FT NMR Studies of Structure and Function of Biological Macromolecules]
*[http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=2266107&query_hl=33&itool=pubmed_docsum Protein structure determination in solution by NMR spectroscopy] Wuthrich K. J Biol Chem. 1990 [[December 25]];265(36):22059-62

*2D-FT NMRI Instrument image: [http://upload.wikimedia.org/wikipedia/en/b/bf/HWB-NMRv900.jpg  A JPG color image of a 2D-FT NMRI `monster' Instrument]. 

*Richard R. Ernst. 1992. Nuclear Magnetic Resonance Fourier Transform (2D-FT) Spectroscopy. [http://nobelprize.org/nobel_prizes/chemistry/laureates/1991/ernst-lecture.pdf  Nobel Lecture], on December 9, 1992.

*Peter Mansfield. 2003.[http://www.parteqinnovations.com/pdf-doc/fandr-Gaz1006.pdf Nobel Laureate in Physiology and Medicine for (2D and 3D) MRI]

*D. Benett. 2007. PhD Thesis. Worcester Polytechnic Institute. [http://www.wpi.edu/Pubs/ETD/Available/etd-081707-080430/unrestricted/dbennett.pdf PDF of 2D-FT Imaging Applications to NMRI in Medical Research.] Worcester Polytechnic Institute. (Includes many 2D-FT NMR images of human brains.)

*Paul Lauterbur. 2003.[http://nobelprize.org/nobel_prizes/medicine/laureates/2003/    Nobel Laureate in Physiology and Medicine for (2D and 3D) MRI.]

*''Jean Jeener. 1971. Two-dimensional Fourier Transform NMR, presented at an Ampere International Summer School, Basko Polje, unpublished. A verbatim quote follows from Richard R. Ernst's Nobel Laureate Lecture delivered on December 2, 1992, "A new approach to measure two-dimensional (2D) spectra." has been proposed by Jean Jeener at an Ampere Summer School in Basko Polje, Yugoslavia, 1971 (Jean Jeneer,1971}). He suggested a 2D Fourier transform experiment consisting of two $\pi/2$ pulses with a variable time $t_1$ between the pulses and the time variable $t_2$ measuring the time elapsed after the second pulse as shown in Fig. 6 that expands the principles of Fig. 1. Measuring the response $s(t_1,t_2)$ of the two-pulse sequence and Fourier-transformation with respect to both time variables produces a two-dimensional spectrum $S(O_1,O_2)$ of the desired form. This two-pulse experiment by Jean Jeener is the forefather of a whole class of $2D$ experiments that can also easily be expanded to multidimensional spectroscopy.''

*{{cite journal
|author=Dudley, Robert, L |title=High-Field NMR Instrumentation|journal= Ch. 10 in Physical Chemistry of Food Processes |volume=2 |pages=421-30|year=1993 ||publisher= Van Nostrand-Reinhold |location=New York |isbn=0-442-00582-2}}

*{{cite journal
|author=Baianu, I.C.; Kumosinski, Thomas |title=NMR Principles and Applications to Structure and Hydration,|journal= Ch.9 in Physical Chemistry of Food Processes |volume=2 |publisher= Van Nostrand-Reinhold |location=New York ||pages=338-420| year=1993 |month=August|isbn=0-442-00582-2}}
 
*{{cite book |author=Haacke, E Mark; Brown, Robert F; Thompson, Michael; Venkatesan, Ramesh |title=Magnetic resonance imaging: physical principles and sequence design |publisher=J. Wiley & Sons |location=New York |year=1999 |isbn=0-471-35128-8 }}

*{{cite journal
|author=Raftery D |title=MRI without the magnet |journal=Proc Natl Acad Sci USA. |volume=103 |issue=34 |pages=12657–8 |year=2006 |month=August |pmid=16912110 |pmc=1568902 |doi=10.1073/pnas.0605625103}}

*{{cite journal
|author=Wu Y, Chesler DA, Glimcher MJ, ''et al'' |title=Multinuclear solid-state three-dimensional MRI of bone and synthetic calcium phosphates |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=96 |issue=4 |pages=1574–8 |year=1999 |month=February |pmid=9990066 |pmc=15521 |doi=10.1073/pnas.96.4.1574 |url=http://www.pnas.org/cgi/pmidlookup?view=long&pmid=9990066
}}

==External links==
*[http://www.mr-tip.com/exam_gifs/cardiac_infarct_short_axis_cine_6.gif Cardiac Infarct or "heart attack" Imaged in Real Time by 2D-FT NMRI]
*[http://www.patiencys.com/MRI/ 3D Animation Movie about MRI Exam]
*[http://www.e-mri.org Interactive Flash Animation on MRI] - ''Online Magnetic Resonance Imaging physics and technique course''
*[http://www.ismrm.org International Society for Magnetic Resonance in Medicine]
*[http://www.simplyphysics.com/flying_objects.html Danger of objects flying into the scanner]

== Related Wikipedia websites ==
*[[Medical imaging]]
*[[Computed tomography]]
*[[Magnetic resonance microscopy]]
*[[Fourier transform spectroscopy]]
*[[Near infrared spectroscopy|FT-NIRS]]
*[[Magnetic resonance elastography]]
{{Commons}}
*[[Nuclear magnetic resonance]] (NMR)
*[[Chemical shift]]
*[[Relaxation]]
*[[Robinson oscillator]]
*[[Earth's field NMR]] (EFNMR)
*[[Rabi cycle]]

''This article incorporates material by the original author  from [http://planetphysics.org/encyclopedia/2DFTImaging.html 2D-FT MR- Imaging and related Nobel awards] on [http://planetphysics.org/ PlanetPhysics], which is licensed under the [[Wikipedia:Text of the GNU Free Documentation License|GFDL]].''
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== NMRI Principle==
Certain nuclei such as <sup>1</sup>H nuclei, or `fermions' have spin-1/2, because there are two spin states, referred to as "up" and "down" states. The [[nuclear magnetic resonance]] absorption phenomenon occurs when samples containing such nuclear spins are placed in a static magnetic field and a very short radiofrequency pulse is applied with a center, or carrier, frequency matching that of the transition between the up and down states of the spin-1/2 <sup>1</sup>H nuclei that were polarized by the static magnetic field. <ref>Antoine Abragam. 1968. ''Principles of Nuclear Magnetic Resonance.'', 895 pp., Cambridge University Press: Cambridge, UK.</ref>
Very low field schemes have also been recently reported.<ref name= Raftery>{{cite journal
|author=Raftery D |title=MRI without the magnet |journal=Proc Natl Acad Sci USA. |volume=103 |issue=34 |pages=12657–8 |year=2006 |month=August |pmid=16912110 |pmc=1568902 |doi=10.1073/pnas.0605625103
}}</ref>

A number of methods have been devised for combining magnetic field gradients and radiofrequency pulsed excitation to obtain an image. Two major maethods involve either 2D -FT or 3D-FT<ref name=Wu1999>{{cite journal
|author=Wu Y, Chesler DA, Glimcher MJ, ''et al'' |title=Multinuclear solid-state three-dimensional MRI of bone and synthetic calcium phosphates |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=96 |issue=4 |pages=1574–8 |year=1999 |month=February |pmid=9990066 |pmc=15521 |doi=10.1073/pnas.96.4.1574 |url=http://www.pnas.org/cgi/pmidlookup?view=long&pmid=9990066
}}</ref> reconstruction from projections, somewhat similar to [[Computed tomography|Computed Tomography]], with the exception of the image interpretation that in the former case must include dynamic and relaxation/contrast enhancement information as well. Other schemes involve building the NMR image either point-by-point or line-by-line. Some schemes use instead gradients in the rf field rather than in the static magnetic field. The majority of NMR images routinely obtained are either by the [http://www.math.cuhk.edu.hk/course/mat2071a/lec1_08.ppt Two-Dimensional Fourier Transform (2D-FT) technique] (with slice selection), or by the Three-Dimensional Fourier Transform (3D--FT) techniques that are however much more time consuming at present. 2D-FT NMRI is sometime called in common parlance a "spin-warp".  An NMR image corresponds to a spectrum consisting of a number of `spatial frequencies' at different locations in the sample investigated, or in a patient.<ref>*{{cite book |author=Haacke, E Mark; Brown, Robert F; Thompson, Michael; Venkatesan, Ramesh |title=Magnetic resonance imaging: physical principles and sequence design |publisher=J. Wiley & Sons |location=New York |year=1999 |isbn=0-471-35128-8 }}
</ref> 
A two–dimensional [[Fourier transform]]ation of such a "real" image may be considered as a representation of such "real waves" by a matrix of [[spatial frequency|spatial frequencies]] known as the [[k-space (MRI)|k–space]]. 
We shall see next in some mathematical detail how the 2D-FT 
computation works to obtain 2D-FT NMR images.

== Two-dimensional Fourier transform imaging and spectroscopy==

A two-dimensional Fourier transform (2D-FT) is computed numerically or carried out in two stages, both involving `standard', one-dimensional Fourier transforms. However, the second stage Fourier transform is not the inverse Fourier transform (which would result in the original function that was transformed at the first stage), but a Fourier transform in a second variable-- which is `shifted' in value-- relative to that involved in the result of the first Fourier transform. Such 2D-FT analysis is a very powerful method for both NMRI and two-dimensional [[nuclear magnetic resonance]] spectroscopy (2D-FT NMRS)<ref>Richard R. Ernst. 1992. Nuclear Magnetic Resonance Fourier Transform (2D-FT) Spectroscopy.[http://nobelprize.org/nobel_prizes/chemistry/laureates/1991/ernst-lecture.pdf  Nobel Lecture], on December 9, 1992.</ref> that allows the three-dimensional reconstruction of polymer and biopolymer structures at atomic resolution]].<ref>
http://en.wikipedia.org/wiki/Nuclear_magnetic_resonance#Nuclear_spin_and_magnets  Kurt Wutrich in 1982-1986 : 2D-FT NMR of solutions</ref> for molecular weights (Mw) of dissolved biopolymers in aqueous solutions (for example) up to about 50,000 Mw. For larger biopolymers or polymers, more complex methods have been developed to obtain limited structural resolution needed for partial 3D-reconstructions of higher molecular structures, e.g. for up 900,000 Mw or even oriented microcrystals in aqueous suspensions or single crystals; such methods have also been reported for ''in vivo'' 2D-FT NMR spectroscopic studies of algae, bacteria, yeast and certain mammalian cells, including human ones. The 2D-FT method is also widely utilized in optical spectroscopy, such as ''2D-FT NIR hyperspectral imaging'' ([[2D-FT NIR-HS]]), or in MRI imaging for research and clinical, diagnostic applications in Medicine. In the latter case, 2D-FT [[Near infrared spectroscopy|NIR]]-HS has recently allowed the identification of single, malignant cancer cells surrounded by healthy human breast tissue at about 1 micron resolution, well-beyond the resolution obtainable 2D-FT NMRI for such systems in the limited time available for such diagnostic investigations (and also in magnetic fields up to the FDA approved magnetic field strength '''H'''<sub>0</sub> of 4.7 T, as shown in the top image of the state-of-the-art NMRI instrument). A more precise mathematical definition of the `double' (2D) Fourier transform involved in both 2D NMRI and 2D-FT NMRS is specified next, and a precise example follows this generally accepted definition.
=== 2D-FT Definition===
A ''2D-FT, or two-dimensional Fourier transform'', is a standard Fourier transformation of a function of two variables, <math>f(x_1, x_2)</math>, carried first in the first variable <math>x_1</math>, followed by the Fourier transform in the second variable <math>x_2</math> of the resulting function <math>F(s_1, x_2)</math>.                                     Note that in the case of both 2D-FT NMRI and 2D-FT NMRS the two independent variables in this definition are in the time domain, whereas the results of the two successive Fourier transforms have, of course, frequencies as the independent variable in the NMRS, and ultimately spatial coordinates for 
both 2D NMRI and 2D-FT NMRS following computer structural recontructions based on special algorithms that are different from FT or 2D-FT. Moreover, such structural algorithms are different for 2D NMRI and 2D-FT NMRS: in the former case they
involve macroscopic, or anatomical structure detrmination,
whereas in the latter case of 2D-FT NMRS the atomic structure reconstruction algorithms are based on the quantum theory of a microphysical (quantum) process such as nuclear Overhauser enhancement [[NOE]], or specific magnetic dipole-dipole interactions<ref>Charles P. Slichter.1996. ''Principles of Magnetic Resonance.'' Springer: Berlin and New York, Third Edition., 651pp. {{ISBN|0-387-50157-6}}.
</ref> between neighbor nuclei.

=== Example 1===
A 2D Fourier transformation and phase correction is applied to a set of 2D NMR (FID) signals :<math>s(t_1, t_2)</math>  yielding a real 2D-FT NMR `spectrum' (collection of 1D FT-NMR spectra) represented by a matrix '''S''' whose elements are
:<math>S(\nu_1,\nu_2) = \textbf{Re} \int \int cos(\nu_1 t_1)exp^{(-i\nu_2 t_2)} s(t_1, t_2)dt_1 dt_2</math>
where :<math>\nu_1</math> and :<math>\nu_2</math> denote the discrete indirect double-quantum and single-quantum(detection) axes, respectively,
in the 2D NMR experiments. Next, the \emph{covariance matrix} is calculated in the frequency domain according
to the following equation
:<math> C(\nu_2', \nu_2) = S^T S = \sum_{\nu^1}[S(\nu_1,\nu_2')S(\nu_1,\nu_2)],</math> with :<math>\nu_2, \nu_2'</math> taking all possible single-quantum frequency values and with the summation carried out over all discrete, double quantum frequencies :<math>\nu_1</math>.
=== Example 2 ===
[http://www.physorg.com/news129395045.html Atomic Structure from 2D-FT STEM Images] of electron distributions in a high-temperature cuprate superconductor `paracrystal'  reveal both the domains (or `location') and the local symmetry of the 'pseudo-gap' in the electron-pair correlation band responsible for the high--temperature superconductivity effect (obtained at Cornell University). So far there have been three Nobel prizes awarded for 2D-FT NMR/MRI during 1992-2003, and an additional, earlier Nobel prize for 2D-FT of X-ray data (`CAT scans'); recently the advanced possibilities of 2D-FT techniques in  [http://nobelprize.org/nobel_prizes/chemistry/laureates/1991/ernst-lecture.pdf Chemistry, Physiology and Medicine] received very significant recognition.<ref>[http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=2266107&query_hl=33&itool=pubmed_docsum Protein structure determination in solution by NMR spectroscopy] Wuthrich K. J Biol Chem. 1990 [[December 25]];265(36):22059-62.</ref>

==Brief explanation of NMRI diagnostic uses in Pathology ==
As an example, a diseased tissue such as a malign tumor, can be detected by 2D-FT NMRI because the hydrogen nuclei of molecules in different tissues return to their equilibrium spin state at different relaxation rates, and also because of the manner in which a malign tumor spreads and grows rapidly along the blood vessels adjacent to the tumor, also inducing further vascularization to occur. By changing the pulse delays in the [[RF]] pulse sequence employed, and/or the RF pulse sequence itself, one may obtain a `relaxation--based contrast', or contrast enhancement between different types of body tissue, such as normal vs. diseased tissue cells for example. Excluded from such diagnostic observations by NMRI are all patients with ferromagnetic metal implants, (e.g., [[cochlear implant]]s), and all cardiac pacemaker patients who cannot undergo any NMRI scan because of the very intense magnetic and RF fields employed in NMRI which would strongly interfere with the correct functioning of such pacemakers. It is, however, conceivable that future developments may also include along with the NMRI diagnostic treatments with special techniques involving applied magnetic fields and very high frequency RF. Already, surgery with special tools is being experimented on in the presence of NMR imaging of subjects.Thus, NMRI is used to image almost every part of the body, and is especially useful for diagnosis in neurological conditions, disorders of the muscles and joints, for evaluating tumors, such as in lung or skin cancers, abnormalities in the heart (especially in children with hereditary disorders), blood vessels, CAD, atherosclerosis
and [http://www.mr-tip.com/serv1.php?type=img&img=Cardiac%20Infarct%20Short%20Axis%20Cine%204 cardiac infarcts] (courtesy of Dr. Robert R. Edelman)

==See also==

{{Col-begin}}
{{Col-1-of-3}}
*[[Nuclear magnetic resonance]] (NMR)
*[[Medical imaging]]
*[[Protein nuclear magnetic resonance spectroscopy]]
*[[Computed tomography]] (CT)
*[[Fourier transform spectroscopy]]
{{Col-2-of-3}}
*[[Magnetic resonance microscopy]]
*[[Near infrared spectroscopy|FT-NIRS]] (NIR)
*[[Magnetic resonance elastography]]
{{Col-3-of-3}}
*[[Relaxation]]
*[[Earth's field NMR]] (EFNMR)
*[[Robinson oscillator]]
{{Commons}}
{{Col-end}}

==Footnotes==
{{Reflist|2}}

==References==
*Antoine Abragam. 1968. ''Principles of Nuclear Magnetic Resonance.'', 895 pp., Cambridge University Press: Cambridge, UK.
*Charles P. Slichter.1996. ''Principles of Magnetic Resonance.'' Springer: Berlin and New York, Third Edition., 651pp. {{ISBN|0-387-50157-6}}.
*Kurt W\"{u}trich. 1986, ''NMR of Proteins and Nucleic Acids''., J. Wiley and Sons: New York, Chichester, Brisbane, Toronto, Singapore. ([http://nobelprize.org/nobel_prizes/chemistry/laureates/2002/wutrich-lecture.pdf Nobel Laureate in 2002 for 2D-FT NMR Studies of Structure and Function of Biological Macromolecules]
*[http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=2266107&query_hl=33&itool=pubmed_docsum Protein structure determination in solution by NMR spectroscopy] Wuthrich K. J Biol Chem. 1990 [[December 25]];265(36):22059-62

*2D-FT NMRI Instrument image: [http://upload.wikimedia.org/wikipedia/en/b/bf/HWB-NMRv900.jpg  A JPG color image of a 2D-FT NMRI `monster' Instrument]. 

*Richard R. Ernst. 1992. Nuclear Magnetic Resonance Fourier Transform (2D-FT) Spectroscopy. [http://nobelprize.org/nobel_prizes/chemistry/laureates/1991/ernst-lecture.pdf  Nobel Lecture], on December 9, 1992.

*Peter Mansfield. 2003.[http://www.parteqinnovations.com/pdf-doc/fandr-Gaz1006.pdf Nobel Laureate in Physiology and Medicine for (2D and 3D) MRI]

*D. Benett. 2007. PhD Thesis. Worcester Polytechnic Institute. [http://www.wpi.edu/Pubs/ETD/Available/etd-081707-080430/unrestricted/dbennett.pdf PDF of 2D-FT Imaging Applications to NMRI in Medical Research.] Worcester Polytechnic Institute. (Includes many 2D-FT NMR images of human brains.)

*Paul Lauterbur. 2003.[http://nobelprize.org/nobel_prizes/medicine/laureates/2003/    Nobel Laureate in Physiology and Medicine for (2D and 3D) MRI.]

*''Jean Jeener. 1971. Two-dimensional Fourier Transform NMR, presented at an Ampere International Summer School, Basko Polje, unpublished. A verbatim quote follows from Richard R. Ernst's Nobel Laureate Lecture delivered on December 2, 1992, "A new approach to measure two-dimensional (2D) spectra." has been proposed by Jean Jeener at an Ampere Summer School in Basko Polje, Yugoslavia, 1971 (Jean Jeneer,1971}). He suggested a 2D Fourier transform experiment consisting of two $\pi/2$ pulses with a variable time $t_1$ between the pulses and the time variable $t_2$ measuring the time elapsed after the second pulse as shown in Fig. 6 that expands the principles of Fig. 1. Measuring the response $s(t_1,t_2)$ of the two-pulse sequence and Fourier-transformation with respect to both time variables produces a two-dimensional spectrum $S(O_1,O_2)$ of the desired form. This two-pulse experiment by Jean Jeener is the forefather of a whole class of $2D$ experiments that can also easily be expanded to multidimensional spectroscopy.''

*{{cite journal
|author=Dudley, Robert, L |title=High-Field NMR Instrumentation|journal= Ch. 10 in Physical Chemistry of Food Processes |volume=2 |pages=421-30|year=1993 ||publisher= Van Nostrand-Reinhold |location=New York |isbn=0-442-00582-2}}

*{{cite journal
|author=Baianu, I.C.; Kumosinski, Thomas |title=NMR Principles and Applications to Structure and Hydration,|journal= Ch.9 in Physical Chemistry of Food Processes |volume=2 |publisher= Van Nostrand-Reinhold |location=New York ||pages=338-420| year=1993 |month=August|isbn=0-442-00582-2}}
 
*{{cite book |author=Haacke, E Mark; Brown, Robert F; Thompson, Michael; Venkatesan, Ramesh |title=Magnetic resonance imaging: physical principles and sequence design |publisher=J. Wiley & Sons |location=New York |year=1999 |isbn=0-471-35128-8 }}

*{{cite journal
|author=Raftery D |title=MRI without the magnet |journal=Proc Natl Acad Sci USA. |volume=103 |issue=34 |pages=12657–8 |year=2006 |month=August |pmid=16912110 |pmc=1568902 |doi=10.1073/pnas.0605625103}}

*{{cite journal
|author=Wu Y, Chesler DA, Glimcher MJ, ''et al'' |title=Multinuclear solid-state three-dimensional MRI of bone and synthetic calcium phosphates |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=96 |issue=4 |pages=1574–8 |year=1999 |month=February |pmid=9990066 |pmc=15521 |doi=10.1073/pnas.96.4.1574 |url=http://www.pnas.org/cgi/pmidlookup?view=long&pmid=9990066
}}

==External links==
*[http://www.mr-tip.com/exam_gifs/cardiac_infarct_short_axis_cine_6.gif Cardiac Infarct or "heart attack" Imaged in Real Time by 2D-FT NMRI]
*[http://www.patiencys.com/MRI/ 3D Animation Movie about MRI Exam]
*[http://www.e-mri.org Interactive Flash Animation on MRI] - ''Online Magnetic Resonance Imaging physics and technique course''
*[http://www.ismrm.org International Society for Magnetic Resonance in Medicine]
*[http://www.simplyphysics.com/flying_objects.html Danger of objects flying into the scanner]

== Related Wikipedia websites ==
*[[Medical imaging]]
*[[Computed tomography]]
*[[Magnetic resonance microscopy]]
*[[Fourier transform spectroscopy]]
*[[Near infrared spectroscopy|FT-NIRS]]
*[[Magnetic resonance elastography]]
{{Commons}}
*[[Nuclear magnetic resonance]] (NMR)
*[[Relaxation]]
*[[Robinson oscillator]]
*[[Earth's field NMR]] (EFNMR)
*[[Rabi cycle]]

''This article incorporates material by the original author  from [http://planetphysics.org/encyclopedia/2DFTImaging.html 2D-FT MR- Imaging and related Nobel awards] on [http://planetphysics.org/ PlanetPhysics], which is licensed under the [[Wikipedia:Text of the GNU Free Documentation License|GFDL]].''

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===Nuclear Overhauser effect===
http://en.wikipedia.org/wiki/Nuclear_Overhauser_effect

== [[Magic angle spinning]] ==

== [[Electron paramagnetic resonance]] ==

==Ferromagnetic Spin Wave Resonance (FSWR)==

== [[Resonance]] ==


== Quantum automata==

http://planetphysics.org/encyclopedia/QuantumComputers.html

==Quantum cellular automata==

==Quantum computer==
http://en.wikipedia.org/wiki/Quantum_computer

== [[Quark]] is under peer review ==

I've nominated the [[Quark]] article for peer review. Since I see you have made many edits to that article, you might be interested in watching [[Wikipedia:Peer review/Quark/archive3|the review]]. Thank you. --<span style="font-family: monospace; font-weight: 600; color: #00F; background-color: #FFF"> [[User:Army1987|Army]][[1987]][[User talk:Army1987|&nbsp;(t&nbsp;]][[Special:Contributions/Army1987|—&nbsp;c)]]</span> 09:28, 22 October 2008 (UTC)



== [[Carol I of Romania]] ==

==[[:Esquisse d' un Programme]]==
Updated and improved

'''"Esquisse d'un Programme"''' is a famous proposal for long-term mathematical research made by the German-born, French mathematician [[Alexander Grothendieck]]
<ref>Scharlau, Winifred (September 2008), written at Oberwolfach, Germany, "Who is Alexander Grothendieck", ''Notices of the American Mathematical Society'' (Providence, RI: American Mathematical Society) 55(8): 930–941, ISSN 1088-9477, OCLC 34550461, http://www.ams.org/notices/200808/tx080800930p.pdf</ref>. He pursued the sequence of logically linked ideas in his important project proposal from 1984 until 1988, but his proposed research continues to date to be of major interest in several branches of advanced mathematics. Grothendieck's vision provides inspiration today for several developments in mathematics such as the extension and generalization of Galois theory, which is currently being extended based on his original proposal.  

==Outline of paper's content==
Submitted in 1984, the ''Esquisse d'un Programme''<ref>Alexander Grothendieck, 1984. "Esquisse d'un Programme", (1984 manuscript), finally published in Schneps and Lochak (1997, I), pp.5-48; English transl., ibid., pp. 243-283. MR 99c:14034 </ref> was a successful proposal submitted by Alexander Grothendieck for a position at the [[French National Centre for Scientific Research|Centre National de la Recherche Scientifique]], which Grothendieck held from 1984 till 1988.<ref>Rehmeyer, Julie (May 9, 2008), "Sensitivity to the Harmony of Things", ''Science News''</ref> This proposal was however not formally published until 1997, because the author "could not be found, much less his permission requested".<ref>Schneps and Lochak (1997, I) p.1</ref> The [[dessin d'enfant|dessins d'enfants]], or "children's  drawings" and "anabelian algebraic geometry" — [[non-Abelian algebraic topology]] and [[noncommutative geometry]] — that are contained in this long-term program, continue even today to inspire extensive mathematical studies. 

===Abstract of the paper===
("''Sommaire''") 

*1. The Proposal and enterpise ("Envoi"). 
*2. "Teichmüller's Lego-game and the [[Galois group]] of Q over Q"  ("Un jeu de “Lego-Teichmüller” et le groupe de [[Galois]] de Q sur Q").
*3. [[Number fields]] associated with "dessin d'enfants". ("Corps de nombres associés à un dessin d’enfant").
*4. [[Regular polyhedron|Regular polyhedra]] over [[finite field]]s ("Polyèdres réguliers sur les corps finis").
*5. [[General topology]] or a '[[Moderated Topology]]' ("Haro sur la topologie dite 'générale', et réflexions heuristiques vers une topologie dite 'modérée").
*6. [[Differentiable theories]] and [[moderated theories]] ("Théories différentiables" (à la Nash) et “théories modérées").
*7. Pursuing Stacks ("À la Poursuite des Champs"}<ref>http://www.bangor.ac.uk/r.brown/pstacks.htm</ref>.
*8. [[Two-dimensional geometry]] ("Digressions de géométrie bidimensionnelle"<ref>Cartier, Pierre (2001), "A mad day's work: from Grothendieck to Connes and Kontsevich The evolution of concepts of space and symmetry", ''Bull. Amer. Math. Soc.'' '''38'''(4): 389–408, <http://www.ams.org/bull/2001-38-04/S0273-0979-01-00913-2/S0273-0979-01-00913-2.pdf>. An English translation of Cartier (1998)</ref>.
*9. Summary of proposed studies ("Bilan d’une activité enseignante").
*10. Epilogue.
*Notes

Suggested further reading for the interested mathematical reader is provided
in the ''References'' section.

==Extensions of Galois's theory for groups: Galois groupoids, categories and functors==
[[Galois]] has developed a powerful, fundamental [[algebraic theory]] in mathematics that provides very efficient computations for certain algebraic problems by utilizing the algebraic concept of [[groups]], which is now known as the [[theory of Galois groups]]; such computations were not possible before, and also in many cases are much more effective than the 'direct' calculations without using groups<ref>Cartier, Pierre (1998), "La Folle Journée, de Grothendieck à Connes et Kontsevich — Évolution des Notions d'Espace et de Symétrie", ''Les Relations entre les Mathématiques et la Physique Théorique — Festschrift for the 40th anniversary of the ''IHÉS'', Institut des Hautes Études Scientifiques'', pp. 11–19</ref>. To begin with, Alexander Grothendieck stated in his proposal:'' "Thus, the group of Galois is realized as the [[automorphism group]] of a concrete, [[pro-finite group]] which respects certain structures that are essential to this group."'' This fundamental, Galois group theory in mathematics has been considerably expanded, at first to [[groupoids]]- as proposed in Alexander Grothendieck's ''Esquisse d' un Programme'' (''EdP'')- and now already partially carried out for groupoids; the latter are now further developed beyond groupoids to categories by several groups of mathematicians. Here, we shall focus only on the well-established and fully validated extensions of Galois' theory. Thus, EdP also proposed and anticipated, along previous Alexander Grothendieck's ''IHÉS'' seminars ([[SGA1]] to [[SGA4]]) held in the 1960s, the development of even more powerful extensions of the original Galois's theory for groups by utilizing categories, [[functors]] and [[natural transformations]], as well as further expansion of the manifold of ideas presented in Alexander Grothendieck's ''[[Descent Theory]]''. The notion of [[Motive (algebraic geometry)|motive]] has also been pursued actively <ref>http://en.wikipedia.org/wiki/Motive_(algebraic_geometry) </ref>. This was developed into the motivic [[Galois group]], [[Grothendieck topology]] and Grothendieck category
<ref>http://planetmath.org/encyclopedia/GrothendieckCategory.html</ref>. Such developments were recently extended in [[algebraic topology]] ''via'' [[representable functors]] and the [[fundamental groupoid functor]].

==The Long March acroos the Theory of Gallois==

“This manuscript, consisting of some nearly 800 hand-written double pages, dating from 1981, was left behind with Grothendieck's other unpublished manuscripts when he disappeared in 1991. Typed in Tex, it comes out to about 400 pages. It goes together with a further 1,000 pages or so of additional notes and sections which have not yet been read or typed. Many of the major themes were summarised in the 1983 manuscript Esquisse d'un Programme.”

The Table of Contents for this important work by Alexander Grothendieck was originally compiled in French by the author and is reproduced here after the English Translation of the major parts of the Long March.


Table of Contents for the Long March across Galois Theory
Multi-Galois Toposes (topoi) 
Applications to topos coverings 
Pro-multi-Galois variants 
Complements 
Introducing the arithmetic context; an `anabelian' (non-Abelian) fundamental conjecture 
Local analysis of  for  
Reformulation of the conjecture (the necessary `purgatorium'...) 
A taxonomic reflexion 
Tangential structure at  (sections of second type extensions) 
Adjusting the hypotheses 
Conditions on the Groupoid systems originating from geometric considerations (in the nonabelian case, the groupoid system can be expressed in terms of outer groups) 
Returning to the arithmetic case: the Galois-type formulation, p. 53 
A cohomological digression, p.58 
Returning to the topological case: critical orbits 
Returning to the concept of cyclic group 
Application to the finite subgroups of  (the discrete case, para.18) 
Tour of Teichmüller (spaces) 
Digression: the description of 2-isotopic categories of algebraic curves p.116 
21. Teichmüller spaces p.126 
23. Returning to the surfaces of (finite) groups of operators (`formulating the equations' of the problem) 
“Special” Teichmüller Groups 
The case of “two groups of operators” 
26. Profinite Teichmüller Groups, connection with the modular Teichmüller topos, conjecture 
29. Critique of the previous approach 
31. Digression: a finite group  over a profinite cyclic group  
32 Returning to the arithmetic aspects: a remarkable reconstruction of all of the étale topos of a complete algebraic curve starting from an open nonabelian space... 
37.

== Notes==
<references/>

==References==
===Related works by Alexander Grothendieck=== 
*[[Alexander Grothendieck]]. 1971, [[Revêtements Étales]] et [[Groupe Fondamental]] ([[SGA1]]), chapter VI: ''[[Catégories fibrées et descente]]'', Lecture Notes in Math. 224, Springer-Verlag: Berlin. 
 
*Alexander Grothendieck. 1957, ''Sur quelque point d-algébre homologique''. , ''Tohoku Math. J.,'' '''9''': 119-121. 
 
*Alexander Grothendieck and [[Jean Dieudonné]].: 1960,'' [[Éléments de géométrie algébrique]]''., Publ. ''[[Inst. des Hautes Etudes de Science]],'' ''([[IHÉS]])'', '''4'''. 
 
*Alexander Grothendieck et al.,1971. [[Grothendieck's Séminaire de géométrie algébrique|Séminaire de Géométrie Algébrique du Bois-Marie]], Vol. 1-7, Berlin: Springer-Verlag. 

*Alexander Grothendieck. 1962. ''Séminaires en Géométrie Algébrique du Bois-Marie'', Vol. '''2''' - [[Cohomologie Locale des Faisceaux Cohèrents]] et [[Théorèmes de Lefschetz Locaux et Globaux]]. , pp.287. (''with an additional contributed exposé by Mme. Michele Raynaud''). (Typewritten manuscript available in French; see also a brief summary in English References Cited: 
**[[Jean-Pierre Serre]]. 1964. [[Cohomologie Galoisienne]], Springer-Verlag: Berlin. 
**[[J. L. Verdier]]. 1965. [[Algèbre homologiques et Catégories derivées]]. [[North Holland Publ. Cie]]). 

*Alexander Grothendieck. 1957, Sur Quelques Points d'algèbre homologique, [[Tohoku Mathematics Journal]], 9, 119-221. 

*Alexander Grothendieck et al. Séminaires en Géometrie Algèbrique- 4, Tome 1, Exposé 1 (or the Appendix to Exposée 1, by `[[N. Bourbaki]]' for more detail and a large number of results. [[AG4]] is freely available in French; also available is an extensive Abstract in English. 

*Alexander Grothendieck, 1984. [http://people.math.jussieu.fr/~leila/grothendieckcircle/EsquisseFr.pdf  "Esquisse d'un Programme"], (1984 manuscript), finally published in [["Geometric Galois Actions"]], L. Schneps, P. Lochak, eds., [[London Math. Soc.]] Lecture Notes 242,[[Cambridge University Press]], 1997, pp.5-48; English transl., ibid., pp. 243-283. MR 99c:14034 . 

*Alexander Grothendieck, [["La longue marche in à travers la théorie de Galois."]] = "The Long March Towards/Across the [[Theory of Galois]]", 1981 manuscript, [[University of Montpellier]] preprint series 1996, edited by J. Malgoire.

===Relating to the ''Esquisse''===
*Leila Schneps. 1994. The [[Grothendieck Theory of Dessins d'Enfants]]. (London Mathematical Society Lecture Note Series), [[Cambridge University Press]], 376 pp. 

*{{Citation | editor1-last=Schneps | editor1-first=Leila | editor2-last=Lochak | editor2-first=Pierre | title=Geometric Galois Actions I: Around Grothendieck's Esquisse D'un Programme  | publisher=Cambridge University Press | series=London Mathematical Society Lecture Note Series | volume=242 | isbn=978-0-521-59642-8 | year=1997}}

*{{Citation | editor1-last=Schneps | editor1-first=Leila | editor2-last=Lochak | editor2-first=Pierre | title=Geometric Galois Actions II: The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups | publisher=Cambridge University Press | series=London Mathematical Society Lecture Note Series | volume=243 | isbn=978-0521596411 | year=1997}}

*David Harbater and Leila Schneps. 2000. [[Fundamental groups]] of [[moduli]] and the [[Grothendieck-Teichmüller group]], Trans. Amer. Math. Soc. 352 (2000), 3117-3148. MSC: Primary 11R32, 14E20, 14H10; Secondary 20F29, 20F34, 32G15.


== [[Higher dimensional algebra]] ==



== [[Nicolae Popescu]] ==

== [[George Emil Palade]] ==



== [[Mathematical biology]] ==


== [[Mathematical biophysics]] ==

==Florentina Ioana Mosora==

{{Infobox scientist
| name            = Florentina Ioana Mosora 
| image           = F. Mosora.jpg
| image_size      = 300
| birth_date      = 7 January 1940 
| birth_place     = [[Cluj]]  
| death_date      = 1994
| death_place     = Liège, Belgium
| residence       = [[Belgium]]  
| societies       = [[Belgian Academy]] [http://www.kvab.be/  Flemish Academy]
| religion        = Orthodox
| nationality     = [[Romania]]n
| citizenship     = [[Belgium|Belgian]]
| fields          = [[Biophysics]],[[Oceanography]]
| alma_mater      = [[University of Bucharest]]<ref>http://fpce4.fizica.unibuc.ro/scripts/PhysDB/PhysDBQuery.asp</ref>  
| doctoral_students = v. <ref>http://fpce4.fizica.unibuc.ro/scripts/PhysDB/PhysDBQuery.asp</ref>.}}

'''Florentina Ioana Mosora''' (b. 7 January [[1940]] in [[Cluj]], [[Romania]]; d. [[1994]] in  [[Liège]], [[Belgium]]) was a Romanian biohysicist<ref>http://fpce4.fizica.unibuc.ro/scripts/PhysDB/DBDetails.asp?fname=Florentina&sname=Ioana&lname=Mosora&birthyear=1940&birthmonth=01&birthday=07</ref> who graduated from the University of Bucharest in the School of Physics (Facultatea de Fizica)<ref>http://fpce4.fizica.unibuc.ro/scripts/PhysDB/PhysDBQuery.asp</ref>. In her earlier years (before 1964) she was a well-known Romanian actress<ref>http://www.upm.ro/cercetare/studia_historia/docs/studia8.pdf</ref> that played the main feminine character
in at least four movies that were widely distributed in Romania<ref>http://www.videofil.ro/news/stiri/filme-romanesti-la-cinemateca-romana-in-luna-februarie.html</ref>,<ref>http://www.imdb.com/name/nm0608875/</ref>.

== Film career ==

During the 1960s she was a well-known actress<ref>http://www.citwf.com/person309481.htm</ref>,<ref>http://www.upm.ro/cercetare/studia_historia/docs/studia8.pdf</ref> and played romantic roles in four Romanian movies:<ref>http://www.cinemarx.ro/persoane/Florentina-Mosora-123062.html</ref> ''Dragoste la zero grade'' ("''Love at zero degrees''," 1964),<ref>http://cinema.ilsole24ore.com/film/caldi-amori-a-zero-gradi/</ref> ''Sub cupola albastra'' ("''Under the blue arch''," 1962), ''Post-restant'' ("''PO Box''," 1961), and ''Baietii nostri'' ("''Our boys''," 1959).<ref name="Videofil.ro">{{cite web |url=http://www.videofil.ro/actori.php?id=29218 |title=Florentina Mosora, Videofil.ro |format= |work= |accessdate=2009-03-18}}</ref>

== Academic career ==

From 1965 to 1970 Florentina Ioana Mosora worked as a neurobiophysics assistant in Vasile Vasilescu's Laboratory of Medical Biophysics at the School of Medicine and Pharmacy in Bucharest (IMFB)<ref>http://fpce4.fizica.unibuc.ro/scripts/PhysDB/DBDetails.asp?fname=Florentina&sname=Ioana&lname=Mosora&birthyear=1940&birthmonth=01&birthday=07</ref>. In 1972, she became a lecturer at the School of Biology. Later in Belgium, she "pioneered the use of stable isotopes in medicine".<ref>http://jap.physiology.org/cgi/reprint/81/3/1096.pdf</ref>,<ref>http://www.sciencemag.org/cgi/content/abstract/181/4098/445?ck=nck  Marcel Lacroix (1), Florentina Mosora (1), Micheline Pontus 1, Pierre Lefebvre 2, Alfred Luyckx 2, and Gabriel Lopez-Habib (2). Glucose Naturally Labeled with Carbon-13: Use for Metabolic Studies in Man.Science 3 August 1973: Vol. 181. no. 4098, pp. 445--446. DOI:10.1126/science.181.4098.445.</ref> In 1989 she was one of three scientists co-organizing a NATO workshop on "Biomechanical Transport Processes".<ref name="Springer">{{cite article |url=http://www.springerlink.com/content/t6763007pj525504/ |title=Announcements |journal=Archive of Applied Mechanics |volume=58 |year=1988 |page=474 |format= |work= |accessdate=2009-03-19}}</ref>, and subsequently was elected to the [[The Royal Academies for Science and the Arts of Belgium]] [http://www.kvab.be/  (Flemish Academy).]<ref>http://www.kvab.be/</ref>

== Selected works ==

*{{cite journal
  | last = Jandrain BJ, Pallikaris N, Normand S, Pirnay F, Lacroix M, Mosora F, Pachiaudi C, Gautier JF, Scheen AJ, Riou JP, and Lefebvre PJ
  | first = 
  | authorlink = 
  | coauthors = 
  | title = Fructose utilization during exercise in men: rapid conversion of ingested fructose to circulating glucose
  | journal = [[Journal of Applied Physiology]]
  | volume = 74
  | issue = 
  | pages = 2146-54
  | publisher = 
  | location = 
  | date = 1993
  | url = 
  | issn = 
  | doi = 
  | id = 
  | accessdate = 2009-03-18}}
*[http://www.sciencemag.org/cgi/content/abstract/181/4098/445?ck=nck  Marcel Lacroix 1, Florentina Mosora 1, Micheline Pontus 1, Pierre Lefebvre 2, Alfred Luyckx 2, and Gabriel Lopez-Habib 2. Glucose Naturally Labeled with Carbon-13: Use for Metabolic Studies in Man.Science 3 August 1973: Vol. 181. no. 4098, pp. 445--446. DOI:10.1126/science.181.4098.445.]
*{{cite book
  | editors = Baque, C.; Mosora, F.; Caro, C.G.; Krause, E. (et al.) 
  | authorlink = 
  | coauthors = 
  | title = Biomechanical Transport Processes: Proceedings of a NATO Advanced Research Workshop on Biomechanical Transport Processes, held October 9-13, 1989, in Cargèse, France
  | publisher = Plenum Press
  | date = 1990
  | location = New York
  | pages = 426
  | url = http://www.springer.com/new+&+forthcoming+titles+(default)?SGWID=4-40356-580-173623990-DISPLAY_TYPE=DISPLAY_TYPE_TITLES&resultStart=100
  | doi = 
  | id = 
  | isbn = 9780306436765}}
 
*Florentina Mosora, "Experimental Studies of Variations of the State," in {{cite book
  | last = Pullman
  | first = Bernard
  | authorlink = 
  | coauthors = 
  | title = Intermolecular forces: proceedings of the Fourteenth Jerusalem Symposium on Quantum Chemistry and Biochemistry held in Jerusalem, Israel, April 13-16, 1981
  | publisher = D. Reidel
  | date = 1981
  | location = 
  | pages = 489-98
  | url = 
  | doi = 
  | id = 
  | isbn = 9789027713261}}
*{{cite journal
  | last = Mosora F., Lacroix M, Luyckx A
  | first = 
  | authorlink = 
  | coauthors = 
  | title = Glucose oxidation in relation to the size of the oral glucose loading dose
  | journal = [[Metabolism]]
  | volume = 30
  | issue = 1
  | pages = 143-49
  | publisher = 
  | location = 
  | date = 1981
  | url = 
  | issn = 
  | doi = 
  | id = 
  | accessdate = 2009-03-18}}
*{{cite journal
  | last = I. Ebiner JR, Acheson KJ, Doerner A, F. Mosora
  | first = 
  | authorlink = 
  | coauthors = 
  | title = Comparison of carbohydrate utilization in man using indirect calorimetry and mass spectrometry after an oral load of 100 g naturally labelled 13-C glucose
  | journal = [[British Journal of Nutrition]]
  | volume = 41
  | issue = 
  | pages = 419-29
  | publisher = 
  | location = 
  | date = 1979
  | url = 
  | issn = 
  | doi = 
  | id = 
  | accessdate = 2009-03-18}}
*{{cite journal
  | last = Mosora F., Lefebvre P, Pirnay F, Lacroix M, Luyckx A, Duchesne, J.
  | first = 
  | authorlink = 
  | coauthors = 
  | title = Quantitative evaluation of the oxidation of an exogenous glucose load using naturally labelled 13C-glucose
  | journal = Metabolism
  | volume = 25
  | issue = 
  | pages = 1575-82
  | publisher = 
  | location = 
  | date = 1976
  | url = 
  | issn = 
  | doi = 
  | id = 
  | accessdate = 2009-03-18}}
*{{cite journal
  | last = Lefebvre P., Mosora F., Lacroix M, Luyckx A, Lopez-Habib 0, Duchesne, J.
  | first = 
  | authorlink = 
  | coauthors = 
  | title = Naturally labeled 13-C glucose: metabolic studies in human diabetes and obesity
  | journal = Diabetes
  | volume = 24
  | issue = 
  | pages = 185-89
  | publisher = 
  | location = 
  | date = 1975
  | url = 
  | issn = 
  | doi = 
  | id = 
  | accessdate = 2009-03-18}}
*{{cite journal |author=Lacroix M, Mosora F, Pontus M, Lefebvre P, Luyckz A, Lopez-Habib G |title=Glucose naturally labeled with carbon-13: use for metabolic studies in man |journal=[[Science (journal)]] |volume=181 |issue=98 |pages=445–6 |year=1973 |month=August |pmid=4718109 |doi= |url=http://www.sciencemag.org/cgi/pmidlookup?view=long&pmid=4718109 |accessdate=2009-03-18}}
*{{cite journal
  | last = Lacroix M, Mosora F, Pontus P, Lefebvre P. Luyckx A, Lopez-Habib G.
  | first = 
  | authorlink = 
  | coauthors = 
  | title = Glucose naturally labeled with 13-C: use for metabolic studies in man
  | journal = [[Science]]
  | volume = 181
  | issue = 
  | pages = 445-46
  | publisher = 
  | location = 
  | date = 1973
  | url = 
  | issn = 
  | doi = 
  | id = 
  | accessdate = 2009-03-18}}

==External links==
*[http://www.cleopatra-lorintiu.com/fr/documentaires/index.html Documentarii pe internet scrise de D-na Cléopatra-Lorintiu: Les braises de la mémoire==Documentaire sur la vie de Florentina Mosora]
* [http://www.videofil.ro/film.php?id=2337 "Love at zero (C) degrees"]
* [http://www.cleopatra-lorintiu.com/ Interview ]
* [http://www.kvab.be/ Flemish Academy of Belgium]
*[http://www-groups.dcs.st-and.ac.uk/~history/Societies/Belgium_Academy.html The Royal Flemish Academy of Belgium for Arts and Sciences (Koninklijke Academie voor Wetenschappen)]

==Footnotes==
Documentary about Florentina Mosora written in French by Ms. Cléopatra Lorintiu, poet, journalist and freelance Romanian writer, entitled ''Les braises de la mémoire''. The following is a precise English translation of the original article in French- "Documentary on the life of Florentina Mosora:

Paradoxically, with university degrees in both physics (...actually MS in biophysics) and biology, Florentina Mosora was during the years '60 a hope of the cinema in Romania! Some traditional films prove it….("Love at zero degrees C" in 1965 or "Post-restant" (PO Box) in 1961). But by leaving Romania, she became in Belgium an academician, even senior faculty of the Department of Oceanography at the University of Liège. Author of the book "Biomechanical Processes Transport" published in 1991, Florentina Mosora has set a course for very high standards. Having disappeared when she turned fifty-four, her life is evoked in a recent film by her husband Dr. Stefan Stan and also by Professor Jean Nihouil of the University of Liège."<ref>http://www.cleopatra-lorintiu.com/fr/documentaires/index.html</ref>

The original in French follows:
" ''Documentaire sur la vie de Florentina Mosora: Paradoxalement, avec une licence en physique et une autre en biologie , Florentina Mosora était pendant les années ’60 un espoir du cinéma en Roumanie ! Quelques films classiques le prouvent .…( Amour à zéro degrés en 1965 ou Post restant en 1961). Mais en quittant la Roumanie, elle est devenue en Belgique une scientifique, académicienne, même doyen de la chair d’océanographie à l’Université de Liège. Auteur du livre« Biomechanical Transport Processes» publié en 1991, Florentina Mosora a eu un parcours hors norme. Disparue à la cinquantaine, elle est évoquée dans notre film par son époux le docteur Stefan Stan ainsi que par le professeur Jean Nihouil de l’Université de Liége''."<ref>http://www.cleopatra-lorintiu.com/fr/documentaires/index.html</ref>

==Notes==
{{Reflist}}




==Metamathematics==

http://en.wikipedia.org/wiki/Metamathematics


'''Metamathematics''' is `[[mathematics]] used to study mathematics', or it involves the application of a [[philosophy of mathematics]]. The first part of this general description appears [[tautological]], or is perhaps open to Bertrand Russell's and Alfred Whitehead's types of antimonies (e.g., "''the [[set of all sets|<set> of all sets]] is not a set''"), as described in their famous "[[Principia Mathematica]]".
                                                     
An alternative, ''non-circular'' definition is as follows: 


'''Metamathematics''' is the study of [[metatheory|metatheories]] of standard theories in [[mathematics]], or <theories> about ''mathematical''--not `purely logical'-- theories. Thus, in [[Encyclopædia Britannica]], '''[[metatheory]]''' is defined as a "<theory> ,'''M<sub>T</sub>''', the subject matter of which is another theory, '''T''' . A finding proved in the former ('''M<sub>T</sub>''') that deals with the latter ('''T''') is known as a '''[[metatheorem]]''' " [http://www.britannica.com/eb/article-9052301 (cited from Metatheory-Encyclopædia Britannica Online).] Thus, a major part of metamathematics deals with: '''metatheorems''', that is "<theorems> about theorems", meta-propositions about propositions, metatheories about mathematical proofs (that of course utilize logic, but also are based upon fundamental mathematics concepts), and so on.

Meta-mathematical [[metatheorem]]s about mathematics itself were originally differentiated from ordinary [[mathematical theorem]]s in the 19th century, to focus on what was then called the [[foundational crisis of mathematics]]. [[Richard's paradox]] concerning certain 'definitions' of real numbers in the English language is an example of the sort of contradictions which can easily occur if one fails to distinguish between mathematics and metamathematics. Bertrand Russell's and Alfred Whitehead's type of paradoxes is yet another important example of possible contradictions due to such failures in the 'old' set theory.

For example, one of the themes of metamathematics is the analysis of (and hence also discussions about) mathematical elements which are (necessarily) true (or false) in ''any'' mathematical system.

Many issues regarding the [[foundations of mathematics]] and the [[philosophy of mathematics]] touch on or use ideas from metamathematics. The working assumption of metamathematics is that mathematical content can be captured in a [[formal system]], usually a [[list of first order theories|first order theory]] or [[axiomatic set theory]]. 

Metamathematics was intimately connected to [[mathematical logic]], so that the histories of the two fields largely overlap. 

(tag removed) merge from|metalogic|date=May 2010}}

Consider also that many sources define '''Metamathematics''' as the branch of [[mathematics]] (not logic!) that deals with "the logic and consistency of mathematical proofs, formulas, and equations". Thus, a major part of metamathemtics deals with metatheorems, that is "theorems about theorems", and meta-propositions about propositions, and so on.  On the other hand, [[metalogic]] is defined in Wikipedia as: "the study of the metatheory of '''logic.'''" (i.e., not mathematics). To sum up, whereas metamathematics is the study of metatheories in [[mathematics]], '''Metalogic'''  is the study of the metatheories of [[logic]]. Therefore, logically, unless one is willing to say that [[mathematics]] and [[logic]] are identical or even equivalent--which they are not-- [[metamathematics]] and [[metalogic]] are not identical, but substantially different. Moreover, as there is also [[mathematical logic]], one has to conceed there is partial overlap between the two fields of mathematics and logic, but such an overlap is not up to either logical [[identity]] or mathematical [[equivalence]]. Many mathematical logicians would like to think, or define, mathematical logic as comprising the entire field of metamathematics, which it currently does not, but it may have been the case 50 years or a century ago. 

Serious metamathematical reflection began with the work of [[Gottlob Frege]], especially his ''[[Begriffsschrift]]''. [[David Hilbert]] was the first to invoke the term "metamathematics" with regularity (see [[Hilbert's program]]). In his hands, it meant something akin to contemporary [[proof theory]]. Another important contemporary branch is [[model theory]]. Other leading figures in the field include [[Bertrand Russell]], [[Thoralf Skolem]], [[Emil Post]], [[Alonzo Church]], [[Stephen Kleene]], [[Willard Quine]], [[Paul Benacerraf]], [[Hilary Putnam]], [[Gregory Chaitin]], and most important, [[Alfred Tarski]] and [[Kurt Gödel]]. In particular, Gödel's proof that, given any finite number of axioms for [[Peano arithmetic]], there will be true statements about that arithmetic that  cannot be proved from those axioms, a result known as the [[Godel's incompleteness theorems|incompleteness theorem]], is arguably the greatest achievement of metamathematics and the philosophy of mathematics to date.

==The List of articles initiated and created by Bci2 on Wikipedia==

* [[American-Romanian Academy of Arts and Sciences]] 
* [[European CNRS Franco-Romanian Associated Laboratories]]
* [[Higher dimensional algebra]] 
* [[Theodor V. Ionescu]] 
* [[R-algebroid]] 
* [[Double groupoid]]
* [[Society for Mathematical Biology]] 
* [[Complex system biology]]
* [[George Karreman]] 
* [[Nicolas Rashevsky]]
* [[Molecular models of DNA]] 
* [[Florentina Mosora]] 
* [[Esquisse d'un Programme]]
* [[VCD]]
* [[Fraţii Buzeşti High School]]
* [http://en.wikipedia.org/wiki/User:Bci2/2D-FT_NMRI_and_Spectroscopy 2D-FT NMRI and Spectroscopy]

===Other Major contributions to Wikipedia articles===
* [[George Emil Palade]]
* [[Robert Rosen]]
* [[Nicolae Popescu]]
* [[List of important publications in biology]]
* [[Systems biology]]
* [[Mathematical and theoretical biology]]
* [[Quark]]
* [[Tannaka–Krein duality]]
* [[Nuclear magnetic resonance]]
* [[Category theory]]
* [[Category theory]]
* [[Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid]]
* *[[Near infrared spectroscopy|FT-NIRS]] (FT-NIR) Spectroscopy

==See also==
*[[meta-]]
*[[consistency]]
*[[completeness]]
*[[decidable]]
*[[Logic]]
*[[mathematical logic]]
*[[model theory]]
*[[proof theory]]

==References==
==References==
*[[Alfred Whitehead]], and [[Bertrand Russell]].  ''[[Principia Mathematica]]'', 3 vols, Cambridge University Press, 1910, 1912, and 1913. Second edition, 1925 (Vol. 1), 1927 (Vols 2, 3). Abridged as ''Principia Mathematica to *56'', Cambridge University Press, 1962.
* I. J. Good. "A Note on Richard's Paradox". ''Mind'', New Series, Vol. 75, No. 299 (Jul., 1966), p. 431. [http://www.jstor.org/stable/2251836 JStor]]
* Jules Richard, ''Les Principes des Mathématiques et le Problème des Ensembles'', ''Revue Générale des Sciences Pures et Appliquées'' (1905); translated in Heijenoort J. van (ed.), ''Source Book in Mathematical Logic 1879-1931'' (Cambridge, Mass., 1964).
*[[Douglas Hofstadter]], 1980. ''[[Gödel, Escher, Bach]]''. Vintage Books. Aimed at laypeople.
*[[Stephen Cole Kleene]], 1952. ''Introduction to Metamathematics''. North Holland. Aimed at mathematicians.

==Categories==


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==See also==
*[[meta-]]
*[[consistency]]
*[[completeness]]
*[[decidable]]
*[[Logic]]
*[[mathematical logic]]
*[[model theory]]
*[[proof theory]]

==References==
*[[Douglas Hofstadter]], 1980. ''[[Gödel, Escher, Bach]]''. Vintage Books. Aimed at laypeople.
*[[Stephen Cole Kleene]], 1952. ''Introduction to Metamathematics''. North Holland. Aimed at mathematicians.

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==Metalogic==

http://en.wikipedia.org/wiki/Metalogic 

'''Metalogic''' is the study of the [[metatheory]] of [[logic]]. While ''logic'' is the study of the manner in which logical systems can be used to decide the correctness of arguments, metalogic studies the properties of the logical systems themselves.<ref> Harry J. Gensler, Introduction to Logic, Routledge, 2001, p. 253.</ref> According to Geoffrey Hunter, while logic concerns itself with the "truths of logic," metalogic concerns itself with the theory of "sentences used to express truths of logic."<ref name="metalogic">Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Pres, 1971</ref>

The basic objects of study in metalogic are [[formal language]]s, [[formal system]]s, and their [[formal interpretation|interpretations]]. The study of interpretation of formal systems is the branch of [[mathematical logic]] known as [[model theory]], while the study of [[deductive apparatus]] is the branch known as [[proof theory]].

== History ==

Metalogical questions have been asked since the time of [[Aristotle]]. However, it was only with the rise of formal languages in the late 19th and early 20th century that investigations into the foundations of logic began to flourish. In 1904, [[David Hilbert]] observed that in investigating the [[foundations of mathematics]] that logical notions are presupposed, and therefore a simultaneous account of metalogical and [[metamathematics|metamathematical]] principles was required. Today, metalogic and metamathematics are largely synonymous with each other, and both have been substantially subsumed by [[mathematical logic]] in academia.

== Important distinctions in metalogic ==
=== Metalanguage-Object language ===

{{Main|Metalanguage|Object language}}

In metalogic, formal languages are sometimes called ''object languages''. The language used to make statements about an object language is called a ''metalanguage''. This distinction is a key difference between logic and metalogic. While logic deals with ''proofs in a formal system'', expressed in some formal language, metalogic deals with ''proofs about a formal system'' which are expressed in a metalanguage about some object language.

=== Syntax-semantics ===
{{Main|Syntax (logic)|Formal semantics}}

In metalogic, 'syntax' has to do with formal languages or formal systems without regard to any interpretation of them, whereas, 'semantics' has to do with interpretations of formal languages. The term 'syntactic' has a slightly wider scope than 'proof-theoretic', since it may be applied to properties of formal languages without any deductive systems, as well as to formal systems. 'Semantic' is synonymous with 'model-theoretic'.

=== Use-mention===
{{Main|Use-mention distinction}}

In metalogic, the words 'use' and 'mention', in both their noun and verb forms, take on a technical sense in order to identify an important distinction.<ref name="metalogic"/> The ''use–mention distinction'' (sometimes referred to as the ''words-as-words distinction'') is the distinction between ''using'' a word (or phrase) and ''mentioning'' it. Usually it is indicated that an expression is being mentioned rather than used by enclosing it in quotation marks, printing it in italics, or setting the expression by itself on a line. The enclosing in quotes of an expression gives us the [[name]] of an expression, for example:

:'Metalogic' is the name of this article.
:This article is about metalogic.

=== Type-token ===
{{Main|Type-token distinction}}

The ''type-token distinction'' is a distinction in metalogic, that separates an abstract concept from the objects which are particular instances of the concept. For example, the particular bicycle in your garage is a [[token]] of the [[type (metaphysics)|type]] of thing known as "The bicycle." Whereas, the bicycle in your garage is in a particular place at a particular time, that is not true of "the bicycle" as used in the sentence: "''The bicycle'' has become more popular recently." This distinction is used to clarify the meaning of [[symbol]]s of [[formal language]]s.

== Overview ==
=== Formal language ===

{{Main|Formal language}} 

A ''formal language'' is an organized [[set]] of [[symbol]]s the essential feature of which is that it can 
be precisely defined in terms of just the shapes and locations of those symbols. Such a language can be defined, then, without any [[reference]] to any [[meaning (linguistics)|meaning]]s of any of its expressions; it can exist before any [[formal interpretation]] is assigned to it -- that is, before it has any meaning. First order logic is expressed in some formal language. A formal grammar determines which symbols and sets of symbols are [[Formula (mathematical logic)|formula]]s in a formal language.

A formal language can be defined formally as a set ''A'' of strings (finite sequences) on a fixed alphabet α. Some authors, including Carnap, define the language as the ordered pair <α, ''A''>.<ref name="itslaia">[[Rudolf Carnap]] (1958) ''Introduction to Symbolic Logic and its Applications'', p.&nbsp;102.</ref> Carnap also requires that each element of α must occur in at least one string in ''A''.

=== Formal grammar ===

{{Main|Formal grammar}}

A ''formal grammar'' (also called ''formation rules'') is a precise description of a the [[well-formed formula]]s of a formal language. It is synonymous with the [[set]] of [[String (computer science)|strings]] over the [[alphabet]] of the formal language which constitute well formed formulas. However, it does not describe their [[semantics]] (i.e. what they mean).

=== Formal systems ===
{{Main|Formal system}}

A ''formal system'' (also called a ''logical calculus'', or a ''logical system'') consists of a formal language together with a [[deductive apparatus]] (also called a ''deductive system''). The deductive apparatus may consist of a set of [[transformation rule]]s (also called ''inference rules'') or a set of [[axiom]]s, or have both. A formal system is used to [[Proof theory|derive]] one expression from one or more other expressions.

A ''formal system'' can be formally defined as an ordered triple <α,<math>\mathcal{I}</math>,<math>\mathcal{D}</math>d>, where <math>\mathcal{D}</math>d is the relation of direct derivability. This relation is understood in a comprehensive [[Sense and reference|sense]] such that the primitive sentences of the formal system are taken as directly [[formal proof|derivable]] from the [[empty set]] of sentences. Direct derivability is a relation between a sentence and a finite, possibly empty set of sentences. Axioms are laid down in such a way that every first place member of <math>\mathcal{D}</math>d is a member of <math>\mathcal{I}</math> and every second place member is a finite subset of <math>\mathcal{I}</math>.

It is also possible to define a ''formal system'' using only the relation <math>\mathcal{D}</math>d. In this way we can omit <math>\mathcal{I}</math>, and α in the definitions of ''interpreted formal language'', and ''interpreted formal system''. However, this method can be more difficult to understand and work with.<ref name = "itslaia"/>

=== Formal proofs ===

{{Main|Formal proof}}

A ''formal proof'' is a sequences of well-formed formulas of a formal language, the last one of which is a [[theorem]] of a formal system. The theorem is a [[syntactic consequence]] of all the well formed formulae preceding it in the proof. For a well formed formula to qualify as part of a proof, it must be the result of applying a rule of the deductive apparatus of some formal system to the previous well formed formulae in the proof sequence.

=== Formal interpretations ===

{{Main|Formal semantics|Formal interpretation|Interpretation (logic)}}

A ''formal interpretation'' of a formal system is the assignment of meanings, to the symbols, and truth-values to the sentences of the formal system. The study of formal interpretations is called [[Formal semantics]]. ''Giving an interpretation'' is synonymous with ''constructing a [[Structure (mathematical logic)|model]].''


== Results in metalogic ==

Results in metalogic consist of such things as [[formal proof]]s demonstrating the [[consistency]], [[completeness]], and [[decidability]] of particular [[formal system]]s.

Major results in metalogic include:

*Proof of the uncountability of the set of all subsets of the set of natural numbers ([[Cantor's theorem]] 1891)
*[[Löwenheim-Skolem theorem]] ([[Leopold Löwenheim]] 1915 and [[Thoralf Skolem]] 1919)
*Proof of the consistency of truth-functional [[Propositional calculus|propositional logic]] ([[Emil Post]] 1920)
*Proof of the semantic completeness of truth-functional propositional logic ([[Paul Bernays]] 1918)<ref name="reflections">Hao Wang, Reflections on Kurt Gödel</ref>,([[Emil Post]] 1920)<ref name="metalogic"/>
*Proof of the syntactic completeness of truth-functional propositional logic ([[Emil Post]] 1920)<ref name="metalogic"/>
*Proof of the decidability of truth-functional propositional logic ([[Emil Post]] 1920)<ref name="metalogic"/>
*Proof of the consistency of first order [[monadic predicate logic]] ([[Leopold Löwenheim]] 1915)
*Proof of the semantic completeness of first order monadic predicate logic ([[Leopold Löwenheim]] 1915)
*Proof of the decidability of first order monadic predicate logic ([[Leopold Löwenheim]] 1915)
*Proof of the semantic completeness of first order [[predicate logic]] ([[Gödel's completeness theorem]] 1930)
*Proof of the consistency of first order predicate logic ([[David Hilbert]] and [[Wilhelm Ackermann]] 1928)
*Proof of the semantic completeness of first order predicate logic ([[Kurt Gödel]] 1930)
*[[Church's theorem|Proof of the undecidability of first order predicate logic]] ([[Alonzo Church]] 1936)
*[[Gödel's first incompleteness theorem]] 1931
*[[Gödel's second incompleteness theorem]] 1931

== See also ==
*[[Metamathematics]]
*[[Formal semantics]]

==References==
<references/>


{{Portal|Logic}}
{{Logic}}
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[[Image:DNA Overview.png|thumb|220px|The structure of part of a DNA [[double helix]]]]
'''Deoxyribonucleic acid''' ('''DNA''') is a [[nucleic acid]] that contains the [[genetics|genetic]] instructions used in the development and functioning of all known living [[organism]]s and some [[virus]]es. The main role of DNA [[molecule]]s is the long-term storage of [[information]]. DNA is often compared to a set of [[blueprint]]s or a recipe, or a [[code]], since it contains the instructions needed to construct other components of [[cell (biology)|cells]], such as [[protein]]s and [[RNA]] molecules. The DNA segments that carry this genetic information are called [[gene]]s, but other DNA sequences have structural purposes, or are involved in regulating the use of this genetic information.

Chemically, DNA consists of two long [[polymers]] of simple units called [[nucleotide]]s, with backbones made of [[sugar]]s and [[phosphate]] groups joined by [[ester]] bonds. These two strands run in opposite directions to each other and are therefore [[antiparallel (biochemistry)|anti-parallel]]. Attached to each sugar is one of four types of molecules called [[nucleobase|bases]]. It is the sequence of these four bases along the backbone that encodes information. This information is read using the [[genetic code]], which specifies the sequence of the [[amino acid]]s within proteins. The code is read by copying stretches of DNA into the related nucleic acid RNA, in a process called [[transcription (genetics)|transcription]].

Within cells, DNA is organized into structures called [[chromosome]]s. These chromosomes are duplicated before cells [[cell division|divide]], in a process called [[DNA replication]]. [[Eukaryote|Eukaryotic organisms]] ([[animal]]s, [[plant]]s, [[Fungus|fungi]], and [[protist]]s) store their DNA inside the [[cell nucleus]], while in [[prokaryote]]s ([[bacteria]] and [[archaea]]) it is found in the cell's [[cytoplasm]]. Within the chromosomes, [[chromatin]] proteins such as [[histone]]s compact and organize DNA. These compact structures guide the interactions between DNA and other proteins, helping control which parts of the DNA are transcribed.

==Properties==
[[Image:DNA chemical structure.svg|right|thumb|350px|The chemical structure of DNA. [[Hydrogen bond]]s are shown as dotted lines.]]

DNA is a long [[polymer]] made from repeating units called [[nucleotide]]s.<ref>{{cite book | last = Saenger | first = Wolfram | title = Principles of Nucleic Acid Structure | publisher = Springer-Verlag | location = New York | date = 1984 | isbn = 0387907629 }}</ref><ref name=Alberts>{{cite book |last=Alberts |first=Bruce | coauthors=Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts, and Peter Walters |title=Molecular Biology of the Cell; Fourth Edition |publisher=Garland Science|year=2002 |location=New York and London |url=http://www.ncbi.nlm.nih.gov/books/bv.fcgi?call=bv.View..ShowTOC&rid=mboc4.TOC&depth=2 |isbn=0-8153-3218-1 |oclc=145080076 48122761 57023651 69932405}}</ref><ref name=Butler>{{cite book | author=Butler, John M. | year=2001 | title=Forensic DNA Typing | publisher= Elsevier | isbn=978-0-12-147951-0 | oclc=223032110 45406517}}pp. 14&ndash;15.</ref> The DNA chain is 22 to 26&nbsp;[[Ångström]]s wide (2.2 to 2.6&nbsp;[[nanometre]]s), and one nucleotide unit is 3.3&nbsp;Å (0.33&nbsp;nm) long.<ref>{{cite journal |author=Mandelkern M, Elias J, Eden D, Crothers D |title=The dimensions of DNA in solution |journal=J Mol Biol |volume=152 |issue=1 |pages=153–61 |year=1981 |pmid=7338906 |doi=10.1016/0022-2836(81)90099-1}}</ref> Although each individual repeating unit is very small, DNA polymers can be very large molecules containing millions of nucleotides. For instance, the largest [[human chromosome]], chromosome number 1, is approximately 220 million [[base pair]]s long.<ref>{{cite journal |author=Gregory S, ''et al.'' |title=The DNA sequence and biological annotation of human chromosome 1 |journal=Nature |volume=441 |issue=7091 |pages=315–21 |year=2006 |pmid=16710414 | doi = 10.1038/nature04727}}</ref>

In living organisms, DNA does not usually exist as a single molecule, but instead as a tightly associated pair of molecules.<ref name=FWPUB>{{cite journal| author = Watson J.D. and Crick F.H.C. | pmid=13054692 | doi = 10.1038/171737a0 | url= http://www.nature.com/nature/dna50/watsoncrick.pdf | title=A Structure for Deoxyribose Nucleic Acid | journal=Nature | volume=171 | pages=737&ndash;738 | year=1953 | accessdate=4 May 2009|format=PDF}}</ref><ref name=berg>Berg J., Tymoczko J. and Stryer L. (2002) ''Biochemistry.'' W. H. Freeman and Company {{ISBN|0-7167-4955-6}}</ref> These two long strands entwine like vines, in the shape of a [[double helix]]. The nucleotide repeats contain both the segment of the backbone of the molecule, which holds the chain together, and a base, which interacts with the other DNA strand in the helix. In general, a base linked to a sugar is called a [[nucleoside]] and a base linked to a sugar and one or more phosphate groups is called a [[nucleotide]]. If multiple nucleotides are linked together, as in DNA, this polymer is called a [[polynucleotide]].<ref name=IUPAC>[http://www.chem.qmul.ac.uk/iupac/misc/naabb.html Abbreviations and Symbols for Nucleic Acids, Polynucleotides and their Constituents] IUPAC-IUB Commission on Biochemical Nomenclature (CBN), Accessed 03 Jan 2006</ref>

The backbone of the DNA strand is made from alternating [[phosphate]] and [[carbohydrate|sugar]] residues.<ref name=Ghosh>{{cite journal |author=Ghosh A, Bansal M |title=A glossary of DNA structures from A to Z |journal=Acta Crystallogr D Biol Crystallogr |volume=59 |issue=Pt 4 |pages=620–6 |year=2003 |pmid=12657780 |doi=10.1107/S0907444903003251}}</ref> The sugar in DNA is [[deoxyribose|2-deoxyribose]], which is a [[pentose]] (five-[[carbon]]) sugar. The sugars are joined together by phosphate groups that form [[phosphodiester bond]]s between the third and fifth carbon [[atom]]s of adjacent sugar rings. These asymmetric [[covalent bond|bonds]] mean a strand of DNA has a direction. In a double helix the direction of the nucleotides in one strand is opposite to their direction in the other strand. This arrangement of DNA strands is called antiparallel. The asymmetric ends of DNA strands are referred to as the [[directionality (molecular biology)|5′]] (''five prime'') and [[directionality (molecular biology)|3′]] (''three prime'') ends, with the 5' end being that with a terminal phosphate group and the 3' end that with a terminal hydroxyl group. One of the major differences between DNA and RNA is the sugar, with 2-deoxyribose being replaced by the alternative pentose sugar [[ribose]] in RNA.<ref name=berg/>

The DNA double helix is stabilized by [[hydrogen bond]]s between the bases attached to the two strands. The four bases found in DNA are [[adenine]] (abbreviated A), [[cytosine]] (C), [[guanine]] (G) and [[thymine]] (T). These four bases are attached to the sugar/phosphate to form the complete nucleotide, as shown for [[adenosine monophosphate]].

These bases are classified into two types; adenine and guanine are fused five- and six-membered [[heterocyclic compound]]s called [[purine]]s, while cytosine and thymine are six-membered rings called [[pyrimidine]]s.<ref name=berg/> A fifth pyrimidine base, called [[uracil]] (U), usually takes the place of thymine in RNA and differs from thymine by lacking a [[methyl group]] on its ring. Uracil is not usually found in DNA, occurring only as a breakdown product of cytosine.

===Grooves===
[[File:DNA orbit animated static thumb.png|frame|right|Structure of a section of DNA. The bases lie horizontally between the two spiraling strands.<ref>Created from [http://www.rcsb.org/pdb/cgi/explore.cgi?pdbId=1D65 PDB 1D65]</ref> Animated version at [[:File:DNA orbit animated.gif]] - over 3 megabytes.]]

Normally, the double helix is a [[right-handed]] spiral. As the DNA strands wind around each other, they leave gaps between each set of phosphate backbones, revealing the sides of the bases inside (see animation). There are two of these grooves twisting around the surface of the double helix: one groove, the major groove, is 22&nbsp;Å wide and the other, the minor groove, is 12&nbsp;Å wide.<ref>{{cite journal |author=Wing R, Drew H, Takano T, Broka C, Tanaka S, Itakura K, Dickerson R |title=Crystal structure analysis of a complete turn of B-DNA |journal=Nature |volume=287 |issue=5784 |pages=755–8 |year=1980 |pmid=7432492 |doi=10.1038/287755a0}}</ref> The narrowness of the minor groove means that the edges of the bases are more accessible in the major groove. As a result, proteins like [[transcription factor]]s that can bind to specific sequences in double-stranded DNA usually make contacts to the sides of the bases exposed in the major groove.<ref>{{cite journal |author=Pabo C, Sauer R |title=Protein-DNA recognition |journal=Annu Rev Biochem |volume=53 |pages=293–321 |year=1984 |pmid=6236744 | doi = 10.1146/annurev.bi.53.070184.001453}}</ref>  This situation varies in unusual conformations of DNA within the cell ''(see below)'', but the major and minor grooves are always named to reflect the differences in size that would be seen if the DNA is twisted back into the ordinary B form.

===Base pairing===
{{Further2|[[Base pair]]}}

Each type of base on one strand forms a bond with just one type of base on the other strand. This is called complementary [[base pair]]ing. Here, purines form [[hydrogen bond]]s to pyrimidines, with A bonding only to T, and C bonding only to G. This arrangement of two nucleotides binding together across the double helix is called a base pair. As hydrogen bonds are not [[covalent bond|covalent]], they can be broken and rejoined relatively easily. The two strands of DNA in a double helix can therefore be pulled apart like a zipper, either by a mechanical force or high [[temperature]].<ref>{{cite journal |author=Clausen-Schaumann H, Rief M, Tolksdorf C, Gaub H |title=Mechanical stability of single DNA molecules |url=http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1300792&blobtype=pdf |journal=Biophys J |volume=78 |issue=4 |pages=1997–2007 |year=2000 |pmid=10733978 |doi=10.1016/S0006-3495(00)76747-6}}</ref> As a result of this complementarity, all the information in the double-stranded sequence of a DNA helix is duplicated on each strand, which is vital in DNA replication. Indeed, this reversible and specific interaction between complementary base pairs is critical for all the functions of DNA in living organisms.<ref name=Alberts/>
<div class="thumb tleft" style="background-color: #f9f9f9; border: 1px solid #CCCCCC; margin:0.5em;">
{|border="0" width=230 border="0" cellpadding="2" cellspacing="0" style="font-size: 85%; border: 1px solid #CCCCCC; margin: 0.3em;"
|[[Image:GC DNA base pair.svg|281px]]
|}
{|border="0" width=230 border="0" cellpadding="2" cellspacing="0" style="font-size: 85%; border: 1px solid #CCCCCC; margin: 0.3em;"
|[[Image:AT DNA base pair.svg|281px]]
|}
<div style="border: none; width:281px;"><div class="thumbcaption">Top, a '''GC''' base pair with three [[hydrogen bond]]s. Bottom, an '''AT''' base pair with two hydrogen bonds. Non-covalent hydrogen bonds between the pairs are shown as dashed lines.</div></div></div>
The two types of base pairs form different numbers of hydrogen bonds, AT forming two hydrogen bonds, and GC forming three hydrogen bonds (see figures, left). 
DNA with high [[GC-content]] is more stable than DNA with low GC-content, but contrary to popular belief, this is not due to the extra hydrogen bond of a GC basepair but rather the contribution of stacking interactions (hydrogen bonding merely provides specificity of the pairing, not stability).<ref name ="Yakovchuk2006">Peter Yakovchuk, Ekaterina Protozanova and Maxim D. Frank-Kamenetskii. ''Base-stacking and base-pairing contributions into thermal stability of the DNA double helix''. Nucleic Acids Research 2006 34(2):564-574; doi:10.1093/nar/gkj454 {{PMID|16449200}}</ref>
As a result, it is both the percentage of GC base pairs and the overall length of a DNA double helix that determine the strength of the association between the two strands of DNA. Long DNA helices with a high GC content have stronger-interacting strands, while short helices with high AT content have weaker-interacting strands.<ref>{{cite journal |author=Chalikian T, Völker J, Plum G, Breslauer K |title=A more unified picture for the thermodynamics of nucleic acid duplex melting: a characterization by calorimetric and volumetric techniques |url=http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=22151&blobtype=pdf |journal=Proc Natl Acad Sci USA |volume=96 |issue=14 |pages=7853–8 |year=1999 |pmid=10393911 |doi=10.1073/pnas.96.14.7853}}</ref> In biology, parts of the DNA double helix that need to separate easily, such as the TATAAT [[Pribnow box]] in some [[promoter]]s, tend to have a high AT content, making the strands easier to pull apart.<ref>{{cite journal |author=deHaseth P, Helmann J |title=Open complex formation by Escherichia coli RNA polymerase: the mechanism of polymerase-induced strand separation of double helical DNA |journal=Mol Microbiol |volume=16 |issue=5 |pages=817–24 |year=1995 |pmid=7476180 |doi=10.1111/j.1365-2958.1995.tb02309.x}}</ref> In the laboratory, the strength of this interaction can be measured by finding the temperature required to break the hydrogen bonds, their [[DNA melting|melting temperature]] (also called ''T<sub>m</sub>'' value). When all the base pairs in a DNA double helix melt, the strands separate and exist in solution as two entirely independent molecules. These single-stranded DNA molecules have no single common shape, but some conformations are more stable than others.<ref>{{cite journal |author=Isaksson J, Acharya S, Barman J, Cheruku P, Chattopadhyaya J |title=Single-stranded adenine-rich DNA and RNA retain structural characteristics of their respective double-stranded conformations and show directional differences in stacking pattern |journal=Biochemistry |volume=43 |issue=51 |pages=15996–6010 |year=2004 |pmid=15609994 | doi = 10.1021/bi048221v}}</ref>

===Sense and antisense===
{{Further2|[[Sense (molecular biology)]]}}

A DNA sequence is called "sense" if its sequence is the same as that of a [[messenger RNA]] copy that is translated into protein.<ref>[http://www.chem.qmul.ac.uk/iubmb/newsletter/misc/DNA.html Designation of the two strands of DNA] JCBN/NC-IUB Newsletter 1989, Accessed 07 May 2008</ref> The sequence on the opposite strand is called the "antisense" sequence. Both sense and antisense sequences can exist on different parts of the same strand of DNA (i.e. both strands contain both sense and antisense sequences). In both prokaryotes and eukaryotes, antisense RNA sequences are produced, but the functions of these RNAs are not entirely clear.<ref>{{cite journal |author=Hüttenhofer A, Schattner P, Polacek N |title=Non-coding RNAs: hope or hype? |journal=Trends Genet |volume=21 |issue=5 |pages=289–97 |year=2005 |pmid=15851066 |doi=10.1016/j.tig.2005.03.007}}</ref> One proposal is that antisense RNAs are involved in regulating [[gene expression]] through RNA-RNA base pairing.<ref>{{cite journal |author=Munroe S |title=Diversity of antisense regulation in eukaryotes: multiple mechanisms, emerging patterns |journal=J Cell Biochem |volume=93 |issue=4 |pages=664–71 |year=2004 |pmid=15389973 | doi = 10.1002/jcb.20252}}</ref>

A few DNA sequences in prokaryotes and eukaryotes, and more in [[plasmid]]s and [[virus]]es, blur the distinction between sense and antisense strands by having overlapping genes.<ref>{{cite journal |author=Makalowska I, Lin C, Makalowski W |title=Overlapping genes in vertebrate genomes |journal=Comput Biol Chem |volume=29 |issue=1 |pages=1&ndash;12 |year=2005 |pmid=15680581 |doi=10.1016/j.compbiolchem.2004.12.006}}</ref> In these cases, some DNA sequences do double duty, encoding one protein when read along one strand, and a second protein when read in the opposite direction along the other strand. In [[bacteria]], this overlap may be involved in the regulation of gene transcription,<ref>{{cite journal |author=Johnson Z, Chisholm S |title=Properties of overlapping genes are conserved across microbial genomes |journal=Genome Res |volume=14 |issue=11 |pages=2268–72 |year=2004 |pmid=15520290 | doi = 10.1101/gr.2433104}}</ref> while in viruses, overlapping genes increase the amount of information that can be encoded within the small viral genome.<ref>{{cite journal |author=Lamb R, Horvath C |title=Diversity of coding strategies in influenza viruses |journal=Trends Genet |volume=7 |issue=8 |pages=261–6 |year=1991 |pmid=1771674}}</ref>

===Supercoiling===
{{Further2|[[DNA supercoil]]}}
DNA can be twisted like a rope in a process called [[DNA supercoil]]ing. With DNA in its "relaxed" state, a strand usually circles the axis of the double helix once every 10.4 base pairs, but if the DNA is twisted the strands become more tightly or more loosely wound.<ref>{{cite journal |author=Benham C, Mielke S |title=DNA mechanics |journal= Annu Rev Biomed Eng |volume=7 |pages=21–53 |year=2005 |pmid=16004565 | doi = 10.1146/annurev.bioeng.6.062403.132016}}</ref> If the DNA is twisted in the direction of the helix, this is positive supercoiling, and the bases are held more tightly together. If they are twisted in the opposite direction, this is negative supercoiling, and the bases come apart more easily. In nature, most DNA has slight negative supercoiling that is introduced by [[enzyme]]s called [[topoisomerase]]s.<ref name=Champoux>{{cite journal |author=Champoux J |title=DNA topoisomerases: structure, function, and mechanism |journal=Annu Rev Biochem |volume=70 |pages=369–413 |year=2001 |pmid=11395412 | doi = 10.1146/annurev.biochem.70.1.369}}</ref> These enzymes are also needed to relieve the twisting stresses introduced into DNA strands during processes such as [[transcription (genetics)|transcription]] and [[DNA replication]].<ref name=Wang>{{cite journal |author=Wang J |title=Cellular roles of DNA topoisomerases: a molecular perspective |journal=Nat Rev Mol Cell Biol |volume=3 |issue=6 |pages=430–40 |year=2002 |pmid=12042765 | doi = 10.1038/nrm831}}</ref>
[[Image:A-DNA, B-DNA and Z-DNA.png|thumb|right|290px|From left to right, the structures of A, B and Z DNA]]

===Alternate DNA structures===
{{Further2|[[Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid|A Structure for DNA]]}}
{{Further2|[[DNA structure]]}}
[[Image:ABDNAxrgpj.jpg‎|thumb| Comparison of the X-ray diffraction patterns of A- and B- DNA; the marked differences in the quality of the X-ray patterns indicates why only the B-form analysis requires the [[paracrystalline|paracrystal model]] approach: X-ray images are courtesy of Dr. H. R. Wilson, F.R.S.<ref>[http://spdbv.vital-it.ch/TheMolecularLevel/BiochemViews/Nucleotides/Images/CMCC0904.jpg Downloadable X-ray patterns of A-DNA and B-DNA] published by H. R. Wilson in 1958</ref>]]
DNA exists in many possible [[Conformational isomerism|conformations]] that include [[A-DNA]], B-DNA, and [[Z-DNA]] forms, although, only B-DNA and Z-DNA have been directly observed in organisms.<ref name=Ghosh/> The conformation that DNA adopts depends on the hydration level,  DNA sequence, the amount and direction of supercoiling, chemical modifications of the bases, the type and concentration of metal [[ion]]s, as well as the presence of [[polyamine]]s in solution<ref>{{cite journal |author=Basu H, Feuerstein B, Zarling D, Shafer R, Marton L |title=Recognition of Z-RNA and Z-DNA determinants by polyamines in solution: experimental and theoretical studies | journal=J Biomol Struct Dyn |volume=6 |issue=2 | pages=299&ndash;309 |year=1988 |pmid=2482766}}</ref>. 

The first published reports of A-DNA [[X-ray scattering techniques|X-ray diffraction patterns]]-- and also B-DNA-- employed analyses based on [[Patterson function|Patterson transforms]] that provided only a limited amount of structural information for oriented fibers of DNA isolated from calf thymus.<ref>Franklin, R.E. and Gosling, R.G. received 6 March 1953. ''Acta Cryst''. (1953). '''6''', 673: The Structure of Sodium Thymonucleate Fibres I. The Influence of Water Content.; also ''Acta Cryst''. '''6''', 678: The Structure of Sodium Thymonucleate Fibres II. The Cylindrically Symmetrical Patterson Function.</ref><ref name=NatFranGos>{{cite journal| title=Molecular Configuration in Sodium Thymonucleate. Franklin R. and Gosling R.G| journal=Nature | volume= 171 | pages= 740&ndash;741 | year=1953 | url=http://www.nature.com/nature/dna50/franklingosling.pdf | pmid=13054694 | doi= 10.1038/171740a0| author=Franklin, Rosalind |format=PDF}}</ref> An alternate analysis was then proposed by Wilkins et al. in 1953 for B-DNA X-ray diffraction/scattering patterns of hydrated, bacterial oriented DNA fibers and trout sperm heads in terms of squares of [[Bessel function]]s.<ref name=NatWilk>{{cite journal| title=Molecular Structure of Deoxypentose Nucleic Acids | author= Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. | journal=Nature | volume= 171 | pages= 738&ndash;740 | year=1953 | url=http://www.nature.com/nature/dna50/wilkins.pdf| pmid=13054693 | doi=10.1038/171738a0| format=PDF}}</ref> Although the `B-DNA form' is most common under the conditions found in cells,<ref>{{cite journal |author=Leslie AG, Arnott S, Chandrasekaran R, Ratliff RL |title=Polymorphism of DNA double helices |journal=J. Mol. Biol. |volume=143 |issue=1 |pages=49–72 |year=1980 |pmid=7441761 |doi=10.1016/0022-2836(80)90124-2}}</ref> it is not a well-defined conformation but a family or fuzzy set of DNA-conformations that occur at the high hydration levels present in a wide variety of living cells.<ref>{{cite journal |author=Baianu, I.C. |title=Structural Order and Partial Disorder in Biological systems|journal= Bull. Math. Biol. |volume= 42 |issue=4 |pages=464–468|year=1980|doi=10.1016/0022-2836(80)90124-2}}</ref> Their corresponding X-ray diffraction & scattering patterns are characteristic of molecular [[Paracrystalline|paracrystals]] with a significant degree of disorder (>20%)<ref>Hosemann R., Bagchi R.N., ''Direct analysis of diffraction by matter'', North-Holland Publs., Amsterdam – New York, 1962</ref><ref>Baianu I.C., X-ray scattering by partially disordered membrane systems, ''Acta Cryst. A'', '''34''' (1978), 751–753.</ref>, and concomitantly the structure is not tractable using only the standard analysis. 

On the other hand, the standard analysis, involving only [[Fourier transform]]s of Bessel functions<ref>[http://planetphysics.org/encyclopedia/BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures.html Bessel functions and diffraction by helical structures] </ref> and DNA [[molecular model]]s, is still routinely employed for the analysis of A-DNA and Z-DNA X-ray diffraction patterns.<ref>[http://planetphysics.org/encyclopedia/BesselFunctionsApplicationsToDiffractionByHelicalStructures.html X-Ray Diffraction Patterns of Double-Helical Deoxyribonucleic Acid (DNA) Crystals]</ref>

Compared to B-DNA, the A-DNA form is a wider right-handed spiral, with a shallow, wide minor groove and a narrower, deeper major groove. The A form occurs under non-physiological conditions in partially dehydrated samples of DNA, while in the cell it may be produced in hybrid pairings of DNA and RNA strands, as well as in enzyme-DNA complexes.<ref>{{cite journal |author=Wahl M, Sundaralingam M |title=Crystal structures of A-DNA duplexes | journal=Biopolymers |volume=44 |issue=1 | pages=45&ndash;63 |year=1997 |pmid=9097733 | doi = 10.1002/(SICI)1097-0282(1997)44:1 |doi_brokendate=2009-03-14}}</ref><ref>{{cite journal |author=Lu XJ, Shakked Z, Olson WK |title=A-form conformational motifs in ligand-bound DNA structures |journal=J. Mol. Biol. |volume=300 |issue=4 |pages=819–40 |year=2000 |pmid=10891271 |doi=10.1006/jmbi.2000.3690}}</ref> Segments of DNA where the bases have been chemically modified by [[methylation]] may undergo a larger change in conformation and adopt the [[Z-DNA|Z form]]. Here, the strands turn about the helical axis in a [[left-handed]] spiral, the opposite of the more common B form.<ref>{{cite journal |author=Rothenburg S, Koch-Nolte F, Haag F |title=DNA methylation and Z-DNA formation as mediators of quantitative differences in the expression of alleles | journal=Immunol Rev |volume=184 | pages=286&ndash;98 |year=2001|pmid=12086319 |doi=10.1034/j.1600-065x.2001.1840125.x}}</ref> These unusual structures can be recognized by specific Z-DNA binding proteins and may be involved in the regulation of transcription.<ref>{{cite journal |author=Oh D, Kim Y, Rich A |title=Z-DNA-binding proteins can act as potent effectors of gene expression in vivo |url=http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=12486233 |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=99 |issue=26 |pages=16666–71 |year=2002 |pmid=12486233 | doi = 10.1073/pnas.262672699}}</ref>

[[Image:Parallel telomere quadruple.png|thumb|left|300px|Structure of a DNA quadruplex formed by [[telomere]] repeats. The conformation of the DNA backbone diverges significantly from the typical helical structure.<ref>Created from [http://ndbserver.rutgers.edu/atlas/xray/structures/U/ud0017/ud0017.html NDB UD0017]</ref>]]

===Quadruplex structures===
{{Further2|[[G-quadruplex]]}}

At the ends of the linear chromosomes are specialized regions of DNA called [[telomere]]s. The main function of these regions is to allow the cell to replicate chromosome ends using the enzyme [[telomerase]], as the enzymes that normally replicate DNA cannot copy the extreme 3′ ends of chromosomes.<ref name=Greider>{{cite journal |author=Greider C, Blackburn E |title=Identification of a specific telomere terminal transferase activity in Tetrahymena extracts | journal=Cell |volume=43 |issue=2 Pt 1 | pages=405&ndash;13 |year=1985 |pmid=3907856 |doi=10.1016/0092-8674(85)90170-9}}</ref> These specialized chromosome caps also help protect the DNA ends, and stop the [[DNA repair]] systems in the cell from treating them as damage to be corrected.<ref name=Nugent>{{cite journal |author=Nugent C, Lundblad V |title=The telomerase reverse transcriptase: components and regulation | url=http://www.genesdev.org/cgi/content/full/12/8/1073 | journal=Genes Dev |volume=12 |issue=8 | pages=1073&ndash;85 |year=1998 |pmid=9553037 |doi=10.1101/gad.12.8.1073}}</ref> In [[List of distinct cell types in the adult human body|human cells]], telomeres are usually lengths of single-stranded DNA containing several thousand repeats of a simple TTAGGG sequence.<ref>{{cite journal |author=Wright W, Tesmer V, Huffman K, Levene S, Shay J |title=Normal human chromosomes have long G-rich telomeric overhangs at one end | url=http://www.genesdev.org/cgi/content/full/11/21/2801 | journal=Genes Dev |volume=11 |issue=21 | pages=2801&ndash;9 |year=1997 |pmid=9353250 |doi=10.1101/gad.11.21.2801}}</ref>

These guanine-rich sequences may stabilize chromosome ends by forming structures of stacked sets of four-base units, rather than the usual base pairs found in other DNA molecules. Here, four guanine bases form a flat plate and these flat four-base units then stack on top of each other, to form a stable ''[[G-quadruplex]]'' structure.<ref name=Burge>{{cite journal |author=Burge S, Parkinson G, Hazel P, Todd A, Neidle S |title=Quadruplex DNA: sequence, topology and structure | url=http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=17012276 | journal=Nucleic Acids Res |volume=34 |issue=19 | pages=5402&ndash;15 |year=2006 |pmid=17012276 | doi = 10.1093/nar/gkl655}}</ref> These structures are stabilized by hydrogen bonding between the edges of the bases and [[chelation]] of a metal ion in the centre of each four-base unit.<ref>{{cite journal |author=Parkinson G, Lee M, Neidle S |title=Crystal structure of parallel quadruplexes from human telomeric DNA | journal=Nature |volume=417 |issue=6891 | pages=876&ndash;80 |year=2002 |pmid=12050675 | doi = 10.1038/nature755}}</ref> Other structures can also be formed, with the central set of four bases coming from either a single strand folded around the bases, or several different parallel strands, each contributing one base to the central structure.

In addition to these stacked structures, telomeres also form large loop structures called telomere loops, or T-loops. Here, the single-stranded DNA curls around in a long circle stabilized by telomere-binding proteins.<ref>{{cite journal |author=Griffith J, Comeau L, Rosenfield S, Stansel R, Bianchi A, Moss H, de Lange T |title=Mammalian telomeres end in a large duplex loop | journal=Cell |volume=97 |issue=4 | pages=503&ndash;14 |year=1999 |pmid=10338214 |doi=10.1016/S0092-8674(00)80760-6}}</ref> At the very end of the T-loop, the single-stranded telomere DNA is held onto a region of double-stranded DNA by the telomere strand disrupting the double-helical DNA and base pairing to one of the two strands. This [[Triple-stranded DNA|triple-stranded]] structure is called a displacement loop or [[D-loop]].<ref name=Burge/>

===Branched DNA===
{{Further2|[[Branched DNA]] and [[DNA nanotechnology]]}}
In DNA [[DNA_end#Frayed_ends|fraying]] occurs when non-complementary regions exist at the end of an otherwise complementary double-strand of DNA.  However, branched DNA can occur if a third strand of DNA is introduced and contains adjoining regions able to hybridize with the frayed regions of the pre-existing double-strand. Although the simplest example of branched DNA involves only three strands of DNA, complexes involving additional strands and multiple branches are also possible.<ref>{{cite journal |author=Seeman NC |title=DNA enables nanoscale control of the structure of matter |journal=Q. Rev. Biophys. |volume=38 |issue=4 |pages=363–71 |year=2005 |month=November |pmid=16515737 |doi=10.1017/S0033583505004087}}</ref>

<gallery>
Image:Branch-dna.png|A DNA structure with a single branching point.
Image:Multi-branch-dna.png|A DNA structure with multiple branches.
</gallery>

==Chemical modifications==
<div class="thumb tright" style="background-color: #f9f9f9; border: 1px solid #CCCCCC; margin:0.5em;">
{|border="0" width=300 border="0" cellpadding="2" cellspacing="0" style="font-size: 85%; border: 1px solid #CCCCCC; margin: 0.3em;"
|[[Image:Cytosine chemical structure.png|75px]]
|[[Image:5-methylcytosine.png|95px]]
|[[Image:Thymine chemical structure.png|97px]]
|-
|align=center|[[cytosine]]
|align=center|[[5-Methylcytosine|5-methylcytosine]]
|align=center|[[thymine]]
|}
<div style="border: none; width:300px;font-size: 90%;"><div class="thumbcaption">Structure of cytosine with and without the 5-methyl group. After deamination the 5-methylcytosine has the same structure as thymine</div></div></div>

===Base modifications===
{{Further2|[[DNA methylation]]}}
The expression of genes is influenced by how the DNA is packaged in chromosomes, in a structure called [[chromatin]]. Base modifications can be involved in packaging, with regions that have low or no gene expression usually containing high levels of [[methylation]] of [[cytosine]] bases. For example, cytosine methylation, produces [[5-Methylcytosine|5-methylcytosine]], which is important for [[X-inactivation|X-chromosome inactivation]].<ref>{{cite journal |author=Klose R, Bird A |title=Genomic DNA methylation: the mark and its mediators | journal=Trends Biochem Sci |volume=31 |issue=2 | pages=89&ndash;97 |year=2006 |pmid=16403636 |doi=10.1016/j.tibs.2005.12.008}}</ref> The average level of methylation varies between organisms - the worm ''[[Caenorhabditis elegans]]'' lacks cytosine methylation, while [[vertebrate]]s have higher levels, with up to 1% of their DNA containing 5-methylcytosine.<ref>{{cite journal |author=Bird A |title=DNA methylation patterns and epigenetic memory | journal=Genes Dev |volume=16 |issue=1 | pages=6&ndash;21 |year=2002 |pmid=11782440 |doi=10.1101/gad.947102}}</ref> Despite the importance of 5-methylcytosine, it can [[deamination|deaminate]] to leave a thymine base, methylated cytosines are therefore particularly prone to [[mutation]]s.<ref>{{cite journal |author=Walsh C, Xu G |title=Cytosine methylation and DNA repair | journal=Curr Top Microbiol Immunol |volume=301 | pages=283&ndash;315 |year=2006|pmid=16570853 |doi=10.1007/3-540-31390-7_11}}</ref> Other base modifications include adenine methylation in bacteria and the [[glycosylation]] of uracil to produce the "J-base" in [[kinetoplastid]]s.<ref>{{cite journal |author=Ratel D, Ravanat J, Berger F, Wion D |title=N6-methyladenine: the other methylated base of DNA | journal=Bioessays |volume=28 |issue=3 | pages=309&ndash;15 |year=2006 |pmid=16479578 | doi = 10.1002/bies.20342}}</ref><ref>{{cite journal |author=Gommers-Ampt J, Van Leeuwen F, de Beer A, Vliegenthart J, Dizdaroglu M, Kowalak J, Crain P, Borst P |title=beta-D-glucosyl-hydroxymethyluracil: a novel modified base present in the DNA of the parasitic protozoan T. brucei | journal=Cell |volume=75 |issue=6 | pages=1129&ndash;36 |year=1993 |pmid=8261512 |doi=10.1016/0092-8674(93)90322-H}}</ref>

===Damage===
{{Further2|[[Mutation]]}}
[[Image:Benzopyrene DNA adduct 1JDG.png|thumb|right|250px|A [[covalent]] [[adduct]] between [[Benzo(a)pyrene|benzo[''a'']pyrene]], the major [[mutagen]] in [[tobacco smoking|tobacco smoke]], and DNA<ref>Created from [http://www.rcsb.org/pdb/cgi/explore.cgi?pdbId=1JDG PDB 1JDG]</ref>]]

DNA can be damaged by many different sorts of [[mutagen]]s, which change the DNA sequence. Mutagens include [[oxidizing agent]]s, [[Alkylation|alkylating agents]] and also high-energy [[electromagnetic radiation]] such as [[ultraviolet]] light and [[X-ray]]s. The type of DNA damage produced depends on the type of mutagen. For example, UV light can damage DNA by producing [[thymine dimer]]s, which are cross-links between pyrimidine bases.<ref>{{cite journal |author=Douki T, Reynaud-Angelin A, Cadet J, Sage E |title=Bipyrimidine photoproducts rather than oxidative lesions are the main type of DNA damage involved in the genotoxic effect of solar UVA radiation | journal=Biochemistry |volume=42 |issue=30 | pages=9221&ndash;6 |year=2003 |pmid=12885257 | doi = 10.1021/bi034593c}},</ref> On the other hand, oxidants such as [[Radical (chemistry)|free radicals]] or [[hydrogen peroxide]] produce multiple forms of damage, including base modifications, particularly of guanosine, and double-strand breaks.<ref>{{cite journal |author=Cadet J, Delatour T, Douki T, Gasparutto D, Pouget J, Ravanat J, Sauvaigo S |title=Hydroxyl radicals and DNA base damage | journal=Mutat Res |volume=424 |issue=1&ndash;2 | pages=9&ndash;21 |year=1999 |pmid=10064846}}</ref> A typical human cell contains about 150,000 bases that have suffered oxidative damage.<ref>{{cite journal |author=Beckman KB, Ames BN |title=Oxidative decay of DNA |journal=J. Biol. Chem. |volume=272 |issue=32 |pages=19633–6 |year=1997 |month=August |pmid=9289489 |url=http://www.jbc.org/cgi/pmidlookup?view=long&pmid=9289489}}</ref> Of these oxidative lesions, the most dangerous are double-strand breaks, as these are difficult to repair and can produce [[point mutation]]s, [[Genetic insertion|insertions]] and [[Deletion (genetics)|deletions]] from the DNA sequence, as well as [[chromosomal translocation]]s.<ref>{{cite journal |author=Valerie K, Povirk L |title=Regulation and mechanisms of mammalian double-strand break repair | journal=Oncogene |volume=22 |issue=37 | pages=5792&ndash;812 |year=2003 |pmid=12947387 | doi = 10.1038/sj.onc.1206679}}</ref>

Many mutagens fit into the space between two adjacent base pairs, this is called [[intercalation (chemistry)|''intercalating'']]. Most intercalators are [[aromaticity|aromatic]] and planar molecules, and include [[Ethidium bromide]], [[Daunorubicin|daunomycin]], and [[doxorubicin]]. In order for an intercalator to fit between base pairs, the bases must separate, distorting the DNA strands by unwinding of the double helix. This inhibits both transcription and DNA replication, causing toxicity and mutations. As a result, DNA intercalators are often [[carcinogen]]s, and [[benzo(a)pyrene|Benzo[''a'']pyrene diol epoxide]], [[acridine]]s, [[aflatoxin]] and [[ethidium bromide]] are well-known examples.<ref>{{cite journal |author=Ferguson L, Denny W |title=The genetic toxicology of acridines | journal=Mutat Res |volume=258 |issue=2 | pages=123&ndash;60 |year=1991 |pmid=1881402}}</ref><ref>{{cite journal |author=Jeffrey A |title=DNA modification by chemical carcinogens | journal=Pharmacol Ther |volume=28 |issue=2 | pages=237&ndash;72 |year=1985 |pmid=3936066 |doi=10.1016/0163-7258(85)90013-0}}</ref><ref>{{cite journal |author=Stephens T, Bunde C, Fillmore B |title=Mechanism of action in thalidomide teratogenesis |journal=Biochem Pharmacol |volume=59 |issue=12 |pages=1489&ndash;99 |year=2000 |pmid=10799645 |doi=10.1016/S0006-2952(99)00388-3}}</ref> Nevertheless, due to their ability to inhibit DNA transcription and replication, other similar toxins are also used in [[chemotherapy]] to inhibit rapidly growing [[cancer]] cells.<ref>{{cite journal |author=Braña M, Cacho M, Gradillas A, de Pascual-Teresa B, Ramos A |title=Intercalators as anticancer drugs | journal=Curr Pharm Des |volume=7 |issue=17 | pages=1745&ndash;80 |year=2001 |pmid=11562309 |doi=10.2174/1381612013397113}}</ref>

==Biological functions==
DNA usually occurs as linear [[chromosome]]s in eukaryotes, and circular chromosomes in prokaryotes. The set of chromosomes in a cell makes up its [[genome]]; the [[human genome]] has approximately 3 billion base pairs of DNA arranged into 46 chromosomes.<ref>{{cite journal |author=Venter J, ''et al.'' |title=The sequence of the human genome | journal=Science |volume=291 |issue=5507 | pages=1304&ndash;51 |year=2001 |pmid=11181995 |doi=10.1126/science.1058040}}</ref> The information carried by DNA is held in the [[DNA sequence|sequence]] of pieces of DNA called [[gene]]s. [[Transmission (genetics)|Transmission]] of genetic information in genes is achieved via complementary base pairing. For example, in transcription, when a cell uses the information in a gene, the DNA sequence is copied into a complementary RNA sequence through the attraction between the DNA and the correct RNA nucleotides. Usually, this RNA copy is then used to make a matching [[Peptide sequence|protein sequence]] in a process called [[Translation (biology)|translation]] which depends on the same interaction between RNA nucleotides. Alternatively, a cell may simply copy its genetic information in a process called DNA replication. The details of these functions are covered in other articles; here we focus on the interactions between DNA and other molecules that mediate the function of the genome.

===Genes and genomes===
{{Further2|[[Cell nucleus]], [[Chromatin]], [[Chromosome]], [[Gene]], [[Noncoding DNA]]}}
Genomic DNA is located in the [[cell nucleus]] of eukaryotes, as well as small amounts in [[mitochondrion|mitochondria]] and [[chloroplast]]s. In prokaryotes, the DNA is held within an irregularly shaped body in the cytoplasm called the [[nucleoid]].<ref>{{cite journal |author=Thanbichler M, Wang S, Shapiro L |title=The bacterial nucleoid: a highly organized and dynamic structure | journal=J Cell Biochem |volume=96 |issue=3 | pages=506&ndash;21 |year=2005 |pmid=15988757 | doi = 10.1002/jcb.20519}}</ref> The genetic information in a genome is held within genes, and the complete set of this information in an organism is called its [[genotype]]. A gene is a unit of [[heredity]] and is a region of DNA that influences a particular characteristic in an organism. Genes contain an [[open reading frame]] that can be transcribed, as well as [[regulatory sequence]]s such as [[promoter]]s and [[enhancer (genetics)|enhancers]], which control the transcription of the open reading frame.

In many [[species]], only a small fraction of the total sequence of the [[genome]] encodes protein. For example, only about 1.5% of the human genome consists of protein-coding [[exon]]s, with over 50% of human DNA consisting of non-coding [[repeated sequence (DNA)|repetitive sequences]].<ref>{{cite journal |author=Wolfsberg T, McEntyre J, Schuler G |title=Guide to the draft human genome | journal=Nature |volume=409 |issue=6822 | pages=824&ndash;6 |year=2001 |pmid=11236998 | doi = 10.1038/35057000}}</ref> The reasons for the presence of so much [[noncoding DNA|non-coding DNA]] in eukaryotic genomes and the extraordinary differences in [[genome size]], or ''[[C-value]]'', among species represent a long-standing puzzle known as the "[[C-value enigma]]."<ref>{{cite journal |author=Gregory T |title=The C-value enigma in plants and animals: a review of parallels and an appeal for partnership | url=http://aob.oxfordjournals.org/cgi/content/full/95/1/133 | journal=Ann Bot (Lond) |volume=95 |issue=1 | pages=133&ndash;46 |year=2005 |pmid=15596463 |doi=10.1093/aob/mci009}}</ref> However, DNA sequences that do not code protein may still encode functional [[non-coding RNA]] molecules, which are involved in the [[regulation of gene expression]].<ref>{{cite journal |author=The ENCODE Project Consortium |title=Identification and analysis of functional elements in 1% of the human genome by the ENCODE pilot project |journal=Nature |volume=447 |issue=7146 | pages =799–816 |year=2007 |doi=10.1038/nature05874}}</ref>
[[Image:T7 RNA polymerase at work.png|thumb|left|300px|[[T7 RNA polymerase]] (blue) producing a mRNA (green) from a DNA template (orange).<ref>Created from [http://www.rcsb.org/pdb/explore/explore.do?structureId=1MSW PDB 1MSW]</ref>]]
Some non-coding DNA sequences play structural roles in chromosomes. [[Telomere]]s and [[centromere]]s typically contain few genes, but are important for the function and stability of chromosomes.<ref name=Nugent/><ref>{{cite journal |author=Pidoux A, Allshire R |title=The role of heterochromatin in centromere function | url=http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1569473 | journal=Philos Trans R Soc Lond B Biol Sci |volume=360 |issue=1455 | pages=569&ndash;79 |year=2005 |pmid=15905142 | doi = 10.1098/rstb.2004.1611}}</ref> An abundant form of non-coding DNA in humans are [[pseudogene]]s, which are copies of genes that have been disabled by mutation.<ref>{{cite journal |author=Harrison P, Hegyi H, Balasubramanian S, Luscombe N, Bertone P, Echols N, Johnson T, Gerstein M |title=Molecular fossils in the human genome: identification and analysis of the pseudogenes in chromosomes 21 and 22 | url=http://www.genome.org/cgi/content/full/12/2/272 | journal=Genome Res |volume=12 |issue=2 | pages=272&ndash;80 |year=2002 |pmid=11827946 |doi=10.1101/gr.207102}}</ref> These sequences are usually just molecular [[fossil]]s, although they can occasionally serve as raw genetic material for the creation of new genes through the process of [[gene duplication]] and [[divergent evolution|divergence]].<ref>{{cite journal |author=Harrison P, Gerstein M |title=Studying genomes through the aeons: protein families, pseudogenes and proteome evolution | journal=J Mol Biol |volume=318 |issue=5 | pages=1155&ndash;74 |year=2002 |pmid=12083509 |doi=10.1016/S0022-2836(02)00109-2}}</ref>

===Transcription and translation===
{{Further2|[[Genetic code]], [[Transcription (genetics)]], [[Protein biosynthesis]]}}
A gene is a sequence of DNA that contains genetic information and can influence the [[phenotype]] of an organism. Within a gene, the sequence of bases along a DNA strand defines a [[messenger RNA]] sequence, which then defines one or more protein sequences. The relationship between the nucleotide sequences of genes and the [[amino acid|amino-acid]] sequences of proteins is determined by the rules of [[Translation (biology)|translation]], known collectively as the [[genetic code]]. The genetic code consists of three-letter 'words' called ''codons'' formed from a sequence of three nucleotides (e.g. ACT, CAG, TTT).

In transcription, the codons of a gene are copied into messenger RNA by [[RNA polymerase]]. This RNA copy is then decoded by a [[ribosome]] that reads the RNA sequence by base-pairing the messenger RNA to [[transfer RNA]], which carries amino acids. Since there are 4 bases in 3-letter combinations, there are 64 possible codons (<math>4^3</math> combinations). These encode the twenty [[list of standard amino acids|standard amino acids]], giving most amino acids more than one possible codon. There are also three 'stop' or 'nonsense' codons signifying the end of the coding region; these are the TAA, TGA and TAG codons.

[[Image:DNA_replication.svg|thumb|450px|right|DNA replication. The double helix is unwound by a [[helicase]] and [[topoisomerase]]. Next, one [[DNA polymerase]] produces the [[Replication fork|leading strand]] copy. Another DNA polymerase binds to the [[Replication fork|lagging strand]]. This enzyme makes discontinuous segments (called [[Okazaki fragment]]s) before [[DNA ligase]] joins them together.]]

===Replication===
{{Further2|[[DNA replication]]}}

[[Cell division]] is essential for an organism to grow, but when a cell divides it must replicate the DNA in its genome so that the two daughter cells have the same genetic information as their parent. The double-stranded structure of DNA provides a simple mechanism for [[DNA replication]]. Here, the two strands are separated and then each strand's [[complementary DNA]] sequence is recreated by an [[enzyme]] called [[DNA polymerase]]. This enzyme makes the complementary strand by finding the correct base through complementary base pairing, and bonding it onto the original strand. As DNA polymerases can only extend a DNA strand in a 5′ to 3′ direction, different mechanisms are used to copy the antiparallel strands of the double helix.<ref>{{cite journal |author=Albà M |title=Replicative DNA polymerases | url=http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=11178285 | journal=Genome Biol |volume=2 |issue=1 | pages=REVIEWS3002 |year=2001 |pmid=11178285 |doi=10.1186/gb-2001-2-1-reviews3002 |nopp=true}}</ref> In this way, the base on the old strand dictates which base appears on the new strand, and the cell ends up with a perfect copy of its DNA.

==Interactions with proteins==
All the functions of DNA depend on interactions with proteins. These [[protein interactions]] can be non-specific, or the protein can bind specifically to a single DNA sequence. Enzymes can also bind to DNA and of these, the polymerases that copy the DNA base sequence in transcription and DNA replication are particularly important.

===[[DNA-binding protein]]s===
<div class="thumb tleft" style="background-color: #f9f9f9; border: 1px solid #CCCCCC; margin:0.5em;">
{|border="0" width=260 border="0" cellpadding="0" cellspacing="0" style="font-size: 85%; border: 1px solid #CCCCCC; margin: 0.3em;"
|[[Image:Nucleosome 2.jpg|260px]]
|-
|
|}
<div style="border: none; width:260px;"><div class="thumbcaption">Interaction of DNA with [[histone]]s (shown in white, top). These proteins' basic amino acids (below left, blue) bind to the acidic phosphate groups on DNA (below right, red).</div></div></div>

Structural proteins that bind DNA are well-understood examples of non-specific DNA-protein interactions. Within chromosomes, DNA is held in complexes with structural proteins. These proteins organize the DNA into a compact structure called [[chromatin]]. In eukaryotes this structure involves DNA binding to a complex of small basic proteins called [[histone]]s, while in prokaryotes multiple types of proteins are involved.<ref>{{cite journal |author=Sandman K, Pereira S, Reeve J |title=Diversity of prokaryotic chromosomal proteins and the origin of the nucleosome | journal=Cell Mol Life Sci |volume=54 |issue=12 | pages=1350&ndash;64 |year=1998 |pmid=9893710 |doi=10.1007/s000180050259}}</ref><ref>{{cite journal |author=Dame RT |title=The role of nucleoid-associated proteins in the organization and compaction of bacterial chromatin |journal=Mol. Microbiol. |volume=56 |issue=4 |pages=858–70 |year=2005 |pmid=15853876 |doi=10.1111/j.1365-2958.2005.04598.x}}</ref> The histones form a disk-shaped complex called a [[nucleosome]], which contains two complete turns of double-stranded DNA wrapped around its surface. These non-specific interactions are formed through basic residues in the histones making [[ionic bond]]s to the acidic sugar-phosphate backbone of the DNA, and are therefore largely independent of the base sequence.<ref>{{cite journal |author=Luger K, Mäder A, Richmond R, Sargent D, Richmond T |title=Crystal structure of the nucleosome core particle at 2.8 A resolution | journal=Nature |volume=389 |issue=6648 | pages=251&ndash;60 |year=1997 |pmid=9305837 | doi = 10.1038/38444}}</ref> Chemical modifications of these basic amino acid residues include [[methylation]], [[phosphorylation]] and [[acetylation]].<ref>{{cite journal |author=Jenuwein T, Allis C |title=Translating the histone code | journal=Science |volume=293 |issue=5532 | pages=1074&ndash;80 |year=2001 |pmid=11498575 |doi=10.1126/science.1063127}}</ref> These chemical changes alter the strength of the interaction between the DNA and the histones, making the DNA more or less accessible to [[transcription factor]]s and changing the rate of transcription.<ref>{{cite journal |author=Ito T |title=Nucleosome assembly and remodelling | journal=Curr Top Microbiol Immunol |volume=274 | pages=1&ndash;22 |pmid=12596902}}</ref> Other non-specific DNA-binding proteins in chromatin include the high-mobility group proteins, which bind to bent or distorted DNA.<ref>{{cite journal |author=Thomas J |title=HMG1 and 2: architectural DNA-binding proteins | journal=Biochem Soc Trans |volume=29 |issue=Pt 4 | pages=395&ndash;401 |year=2001 |pmid=11497996 |doi=10.1042/BST0290395}}</ref> These proteins are important in bending arrays of nucleosomes and arranging them into the larger structures that make up chromosomes.<ref>{{cite journal |author=Grosschedl R, Giese K, Pagel J |title=HMG domain proteins: architectural elements in the assembly of nucleoprotein structures | journal=Trends Genet |volume=10 |issue=3 | pages=94–100 |year=1994 |pmid=8178371 |doi=10.1016/0168-9525(94)90232-1}}</ref>

A distinct group of DNA-binding proteins are the DNA-binding proteins that specifically bind single-stranded DNA. In humans, replication [[protein A]] is the best-understood member of this family and is used in processes where the double helix is separated, including DNA replication, recombination and DNA repair.<ref>{{cite journal |author=Iftode C, Daniely Y, Borowiec J |title=Replication protein A (RPA): the eukaryotic SSB | journal=Crit Rev Biochem Mol Biol |volume=34 |issue=3 | pages=141&ndash;80 |year=1999 |pmid=10473346 |doi=10.1080/10409239991209255}}</ref> These binding proteins seem to stabilize single-stranded DNA and protect it from forming [[stem-loop]]s or being degraded by [[nuclease]]s.

[[Image:Lambda repressor 1LMB.png|thumb|right|185px|The lambda repressor [[helix-turn-helix]] transcription factor bound to its DNA target<ref>Created from [http://www.rcsb.org/pdb/explore/explore.do?structureId=1LMB PDB 1LMB]</ref>]]
In contrast, other proteins have evolved to bind to particular DNA sequences. The most intensively studied of these are the various [[transcription factor]]s, which are proteins that regulate transcription. Each transcription factor binds to one particular set of DNA sequences and activates or inhibits the transcription of genes that have these sequences close to their promoters. The transcription factors do this in two ways. Firstly, they can bind the RNA polymerase responsible for transcription, either directly or through other mediator proteins; this locates the polymerase at the promoter and allows it to begin transcription.<ref>{{cite journal |author=Myers L, Kornberg R |title=Mediator of transcriptional regulation | journal=Annu Rev Biochem |volume=69 | pages=729&ndash;49 |year=2000 |pmid=10966474 | doi = 10.1146/annurev.biochem.69.1.729}}</ref> Alternatively, transcription factors can bind [[enzyme]]s that modify the histones at the promoter; this will change the accessibility of the DNA template to the polymerase.<ref>{{cite journal |author=Spiegelman B, Heinrich R |title=Biological control through regulated transcriptional coactivators | journal=Cell |volume=119 |issue=2 | pages=157–67 |year=2004 |pmid=15479634 |doi=10.1016/j.cell.2004.09.037}}</ref>

As these DNA targets can occur throughout an organism's genome, changes in the activity of one type of transcription factor can affect thousands of genes.<ref>{{cite journal |author=Li Z, Van Calcar S, Qu C, Cavenee W, Zhang M, Ren B |title=A global transcriptional regulatory role for c-Myc in Burkitt's lymphoma cells | url=http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=12808131 | journal=Proc Natl Acad Sci USA |volume=100 |issue=14 | pages=8164&ndash;9 |year=2003 |pmid=12808131 | doi = 10.1073/pnas.1332764100}}</ref> Consequently, these proteins are often the targets of the [[signal transduction]] processes that control responses to environmental changes or [[cellular differentiation]] and development. The specificity of these transcription factors' interactions with DNA come from the proteins making multiple contacts to the edges of the DNA bases, allowing them to "read" the DNA sequence. Most of these base-interactions are made in the major groove, where the bases are most accessible.<ref>{{cite journal |author=Pabo C, Sauer R |title=Protein-DNA recognition | journal=Annu Rev Biochem |volume=53 | pages=293&ndash;321 |year=1984 |pmid=6236744 | doi = 10.1146/annurev.bi.53.070184.001453}}</ref>

[[Image:EcoRV 1RVA.png|thumb|left|255px|The [[restriction enzyme]] [[EcoRV]] (green) in a complex with its substrate DNA<ref>Created from [http://www.rcsb.org/pdb/explore/explore.do?structureId=1RVA PDB 1RVA]</ref>]]

===DNA-modifying enzymes===
====Nucleases and ligases====
[[Nuclease]]s are [[enzyme]]s that cut DNA strands by catalyzing the [[hydrolysis]] of the [[phosphodiester bond]]s. Nucleases that hydrolyse nucleotides from the ends of DNA strands are called [[exonuclease]]s, while [[endonuclease]]s cut within strands. The most frequently used nucleases in [[molecular biology]] are the [[restriction enzyme|restriction endonucleases]], which cut DNA at specific sequences. For instance, the EcoRV enzyme shown to the left recognizes the 6-base sequence 5′-GAT|ATC-3′ and makes a cut at the vertical line. In nature, these enzymes protect [[bacteria]] against [[Bacteriophage|phage]] infection by digesting the phage DNA when it enters the bacterial cell, acting as part of the [[restriction modification system]].<ref>{{cite journal |author=Bickle T, Krüger D |title=Biology of DNA restriction | url=http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=372918&blobtype=pdf | journal=Microbiol Rev |volume=57 |issue=2 | pages=434&ndash;50 |year=1993 |pmid=8336674}}</ref> In technology, these sequence-specific nucleases are used in [[molecular cloning]] and [[Genetic fingerprinting|DNA fingerprinting]].

Enzymes called [[DNA ligase]]s can rejoin cut or broken DNA strands.<ref name=Doherty>{{cite journal |author=Doherty A, Suh S |title=Structural and mechanistic conservation in DNA ligases | url=http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=11058099 | journal=Nucleic Acids Res |volume=28 |issue=21 | pages=4051&ndash;8 |year=2000 |pmid=11058099 |doi=10.1093/nar/28.21.4051}}</ref> Ligases are particularly important in [[Replication fork|lagging strand]] DNA replication, as they join together the short segments of DNA produced at the [[replication fork]] into a complete copy of the DNA template. They are also used in [[DNA repair]] and [[genetic recombination]].<ref name=Doherty/>

====Topoisomerases and helicases====
[[Topoisomerase]]s are enzymes with both nuclease and ligase activity. These proteins change the amount of [[DNA supercoil|supercoiling]] in DNA. Some of these enzyme work by cutting the DNA helix and allowing one section to rotate, thereby reducing its level of supercoiling; the enzyme then seals the DNA break.<ref name=Champoux/> Other types of these enzymes are capable of cutting one DNA helix and then passing a second strand of DNA through this break, before rejoining the helix.<ref>{{cite journal |author=Schoeffler A, Berger J |title=Recent advances in understanding structure-function relationships in the type II topoisomerase mechanism | journal=Biochem Soc Trans |volume=33 |issue=Pt 6 | pages=1465&ndash;70 |year=2005 |pmid=16246147 |doi=10.1042/BST20051465}}</ref> Topoisomerases are required for many processes involving DNA, such as DNA replication and transcription.<ref name=Wang/>

[[Helicase]]s are proteins that are a type of [[molecular motor]]. They use the chemical energy in [[nucleoside triphosphate]]s, predominantly [[Adenosine triphosphate|ATP]], to break hydrogen bonds between bases and unwind the DNA double helix into single strands.<ref>{{cite journal |author=Tuteja N, Tuteja R |title=Unraveling DNA helicases. Motif, structure, mechanism and function | doi= 10.1111/j.1432-1033.2004.04094.x | journal=Eur J Biochem |volume=271 |issue=10 | pages=1849–63 |year=2004 |pmid=15128295}}</ref> These enzymes are essential for most processes where enzymes need to access the DNA bases.

====Polymerases====
[[Polymerase]]s are [[enzyme]]s that synthesize polynucleotide chains from [[nucleoside triphosphate]]s. The sequence of their products are copies of existing polynucleotide chains - which are called ''templates''. These enzymes function by adding nucleotides onto the 3′ [[hydroxyl|hydroxyl group]] of the previous nucleotide in a DNA strand. Consequently, all polymerases work in a 5′ to 3′ direction.<ref name=Joyce>{{cite journal |author=Joyce C, Steitz T |title=Polymerase structures and function: variations on a theme? | url=http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=177480&blobtype=pdf | journal=J Bacteriol |volume=177 |issue=22 | pages=6321&ndash;9 |year=1995 |pmid=7592405}}</ref> In the [[active site]] of these enzymes, the incoming nucleoside triphosphate base-pairs to the template: this allows polymerases to accurately synthesize the complementary strand of their template. Polymerases are classified according to the type of template that they use.

In DNA replication, a DNA-dependent [[DNA polymerase]] makes a copy of a DNA sequence. Accuracy is vital in this process, so many of these polymerases have a [[Proofreading (Biology)|proofreading]] activity. Here, the polymerase recognizes the occasional mistakes in the synthesis reaction by the lack of base pairing between the mismatched nucleotides. If a mismatch is detected, a 3′ to 5′ [[exonuclease]] activity is activated and the incorrect base removed.<ref>{{cite journal |author=Hubscher U, Maga G, Spadari S |title=Eukaryotic DNA polymerases | journal=Annu Rev Biochem |volume=71 | pages=133&ndash;63 |year=2002 |pmid=12045093 | doi = 10.1146/annurev.biochem.71.090501.150041}}</ref> In most organisms DNA polymerases function in a large complex called the [[replisome]] that contains multiple accessory subunits, such as the [[DNA clamp]] or [[helicase]]s.<ref>{{cite journal |author=Johnson A, O'Donnell M |title=Cellular DNA replicases: components and dynamics at the replication fork | journal=Annu Rev Biochem |volume=74 | pages=283&ndash;315 |year=2005 |pmid=15952889 | doi = 10.1146/annurev.biochem.73.011303.073859}}</ref>

RNA-dependent DNA polymerases are a specialized class of polymerases that copy the sequence of an RNA strand into DNA. They include [[reverse transcriptase]], which is a [[virus|viral]] enzyme involved in the infection of cells by [[retrovirus]]es, and [[telomerase]], which is required for the replication of telomeres.<ref name=Greider/><ref>{{cite journal |author=Tarrago-Litvak L, Andréola M, Nevinsky G, Sarih-Cottin L, Litvak S |title=The reverse transcriptase of HIV-1: from enzymology to therapeutic intervention | url=http://www.fasebj.org/cgi/reprint/8/8/497 | journal=Faseb J |volume=8 |issue=8 | pages=497–503 |date=1 May 1994|pmid=7514143 }}</ref> Telomerase is an unusual polymerase because it contains its own RNA template as part of its structure.<ref name=Nugent/>

Transcription is carried out by a DNA-dependent [[RNA polymerase]] that copies the sequence of a DNA strand into RNA. To begin transcribing a gene, the RNA polymerase binds to a sequence of DNA called a promoter and separates the DNA strands. It then copies the gene sequence into a [[messenger RNA]] transcript until it reaches a region of DNA called the [[terminator (genetics)|terminator]], where it halts and detaches from the DNA. As with human DNA-dependent DNA polymerases, [[RNA polymerase II]], the enzyme that transcribes most of the genes in the human genome, operates as part of a large [[protein complex]] with multiple regulatory and accessory subunits.<ref>{{cite journal |author=Martinez E |title=Multi-protein complexes in eukaryotic gene transcription | journal=Plant Mol Biol |volume=50 |issue=6 | pages=925&ndash;47 |year=2002 |pmid=12516863 |doi=10.1023/A:1021258713850}}</ref>

==Genetic recombination==
<div class="thumb tright" style="background-color: #f9f9f9; border: 1px solid #CCCCCC; margin:0.5em;">
{|border="0" width=250 border="0" cellpadding="0" cellspacing="0" style="font-size: 85%; border: 1px solid #CCCCCC; margin: 0.3em;"
|[[Image:Holliday Junction cropped.png|250px]]
|-
|[[Image:Holliday junction coloured.png|250px]]
|}
<div style="border: none; width:250px;"><div class="thumbcaption">Structure of the [[Holliday junction]] intermediate in [[genetic recombination]]. The four separate DNA strands are coloured red, blue, green and yellow.<ref>Created from [http://www.rcsb.org/pdb/explore/explore.do?structureId=1M6G PDB 1M6G]</ref></div></div></div>
{{Further2|[[Genetic recombination]]}}
[[Image:Chromosomal Recombination.svg|thumb|250px|left|Recombination involves the breakage and rejoining of two chromosomes (M and F) to produce two re-arranged chromosomes (C1 and C2).]]

A DNA helix usually does not interact with other segments of DNA, and in human cells the different chromosomes even occupy separate areas in the nucleus called "chromosome territories".<ref>{{cite journal |author=Cremer T, Cremer C |title=Chromosome territories, nuclear architecture and gene regulation in mammalian cells | journal=Nat Rev Genet |volume=2 |issue=4 | pages=292–301 |year=2001 |pmid=11283701 | doi = 10.1038/35066075}}</ref> This physical separation of different chromosomes is important for the ability of DNA to function as a stable repository for information, as one of the few times chromosomes interact is during [[chromosomal crossover]] when they [[genetic recombination|recombine]]. Chromosomal crossover is when two DNA helices break, swap a section and then rejoin.

Recombination allows chromosomes to exchange genetic information and produces new combinations of genes, which increases the efficiency of [[natural selection]] and can be important in the rapid evolution of new proteins.<ref>{{cite journal |author=Pál C, Papp B, Lercher M |title=An integrated view of protein evolution | journal=Nat Rev Genet |volume=7 |issue=5 | pages=337&ndash;48 |year=2006 |pmid=16619049 | doi = 10.1038/nrg1838}}</ref> Genetic recombination can also be involved in DNA repair, particularly in the cell's response to double-strand breaks.<ref>{{cite journal |author=O'Driscoll M, Jeggo P |title=The role of double-strand break repair - insights from human genetics | journal=Nat Rev Genet |volume=7 |issue=1 | pages=45&ndash;54 |year=2006 |pmid=16369571 | doi = 10.1038/nrg1746}}</ref>

The most common form of chromosomal crossover is [[homologous recombination]], where the two chromosomes involved share very similar sequences. Non-homologous recombination can be damaging to cells, as it can produce [[chromosomal translocation]]s and genetic abnormalities. The recombination reaction is catalyzed by enzymes known as ''recombinases'', such as [[RAD51]].<ref>{{cite journal |author=Vispé S, Defais M |title=Mammalian Rad51 protein: a RecA homologue with pleiotropic functions |journal=Biochimie |volume=79 |issue=9-10 |pages=587–92 |year=1997 |pmid=9466696 |doi=10.1016/S0300-9084(97)82007-X}}</ref> The first step in recombination is a double-stranded break either caused by an [[endonuclease]] or damage to the DNA.<ref>{{cite journal |author=Neale MJ, Keeney S |title=Clarifying the mechanics of DNA strand exchange in meiotic recombination |journal=Nature |volume=442 |issue=7099 |pages=153–8 |year=2006 |pmid=16838012 | doi = 10.1038/nature04885}}</ref> A series of steps catalyzed in part by the recombinase then leads to joining of the two helices by at least one [[Holliday junction]], in which a segment of a single strand in each helix is annealed to the complementary strand in the other helix. The Holliday junction is a tetrahedral junction structure that can be moved along the pair of chromosomes, swapping one strand for another. The recombination reaction is then halted by cleavage of the junction and re-ligation of the released DNA.<ref>{{cite journal |author=Dickman M, Ingleston S, Sedelnikova S, Rafferty J, Lloyd R, Grasby J, Hornby D |title=The RuvABC resolvasome | journal=Eur J Biochem |volume=269 |issue=22 | pages=5492&ndash;501 |year=2002 |pmid=12423347 |doi=10.1046/j.1432-1033.2002.03250.x}}</ref>

==Evolution==
{{Further2|[[RNA world hypothesis]]}}
DNA contains the genetic information that allows all modern living things to function, grow and reproduce. However, it is unclear how long in the 4-billion-year [[Timeline of evolution|history of life]] DNA has performed this function, as it has been proposed that the earliest forms of life may have used RNA as their genetic material.<ref name=Joyce>{{cite journal |author=Joyce G |title=The antiquity of RNA-based evolution |journal=Nature |volume=418 |issue=6894 |pages=214&ndash;21 |year=2002 |pmid=12110897 | doi = 10.1038/418214a}}</ref><ref>{{cite journal |author=Orgel L |title=Prebiotic chemistry and the origin of the RNA world | url=http://www.crbmb.com/cgi/reprint/39/2/99.pdf |journal=Crit Rev Biochem Mol Biol |volume=39 |issue=2 |pages=99&ndash;123 |pmid=15217990 | doi = 10.1080/10409230490460765|format=PDF |year=2004}}</ref> RNA may have acted as the central part of early [[cell metabolism]] as it can both transmit genetic information and carry out [[catalysis]] as part of [[ribozyme]]s.<ref>{{cite journal |author=Davenport R |title=Ribozymes. Making copies in the RNA world |journal=Science |volume=292 |issue=5520 |pages=1278 |year=2001 |pmid=11360970 | doi = 10.1126/science.292.5520.1278a}}</ref> This ancient [[RNA world hypothesis|RNA world]] where nucleic acid would have been used for both catalysis and genetics may have influenced the [[evolution]] of the current genetic code based on four nucleotide bases. This would occur since the number of unique bases in such an organism is a trade-off between a small number of bases increasing replication accuracy and a large number of bases increasing the catalytic efficiency of ribozymes.<ref>{{cite journal |author=Szathmáry E |title=What is the optimum size for the genetic alphabet? |url=http://www.pnas.org/cgi/reprint/89/7/2614.pdf |journal=Proc Natl Acad Sci USA |volume=89 |issue=7 |pages=2614&ndash;8 |year=1992 |pmid=1372984 |doi=10.1073/pnas.89.7.2614|format=PDF}}</ref>

Unfortunately, there is no direct evidence of ancient genetic systems, as recovery of DNA from most fossils is impossible. This is because DNA will survive in the environment for less than one million years and slowly degrades into short fragments in solution.<ref>{{cite journal |author=Lindahl T |title=Instability and decay of the primary structure of DNA |journal=Nature |volume=362 |issue=6422 |pages=709&ndash;15 |year=1993 |pmid=8469282 | doi = 10.1038/362709a0}}</ref> Claims for older DNA have been made, most notably a report of the isolation of a viable bacterium from a salt crystal 250-million years old,<ref>{{cite journal |author=Vreeland R, Rosenzweig W, Powers D |title=Isolation of a 250 million-year-old halotolerant bacterium from a primary salt crystal |journal=Nature |volume=407 |issue=6806 |pages=897&ndash;900 |year=2000 |pmid=11057666 | doi = 10.1038/35038060}}</ref> but these claims are controversial.<ref>{{cite journal |author=Hebsgaard M, Phillips M, Willerslev E |title=Geologically ancient DNA: fact or artefact? |journal=Trends Microbiol |volume=13 |issue=5 |pages=212&ndash;20 |year=2005 |pmid=15866038 |doi=10.1016/j.tim.2005.03.010}}</ref><ref>{{cite journal |author=Nickle D, Learn G, Rain M, Mullins J, Mittler J |title=Curiously modern DNA for a "250 million-year-old" bacterium |journal=J Mol Evol |volume=54 |issue=1 |pages=134&ndash;7 |year=2002 |pmid=11734907 | doi = 10.1007/s00239-001-0025-x}}</ref>

==Uses in technology==
===Genetic engineering===
{{Further2|[[Molecular biology]], [[nucleic acid methods]] and [[genetic engineering]]}}

Methods have been developed to purify DNA from organisms, such as [[phenol-chloroform extraction]] and manipulate it in the laboratory, such as [[restriction digest]]s and the [[polymerase chain reaction]]. Modern [[biology]] and [[biochemistry]] make intensive use of these techniques in recombinant DNA technology. [[Recombinant DNA]] is a man-made DNA sequence that has been assembled from other DNA sequences. They can be [[transformation (genetics)|transformed]] into organisms in the form of [[plasmid]]s or in the appropriate format, by using a [[viral vector]].<ref>{{cite journal |author=Goff SP, Berg P |title=Construction of hybrid viruses containing SV40 and lambda phage DNA segments and their propagation in cultured monkey cells |journal=Cell |volume=9 |issue=4 PT 2 |pages=695–705 |year=1976 |pmid=189942 |doi=10.1016/0092-8674(76)90133-1}}</ref> The [[genetic engineering|genetically modified]] organisms produced can be used to produce products such as recombinant [[protein]]s, used in [[medical research]],<ref>{{cite journal |author=Houdebine L |title=Transgenic animal models in biomedical research |journal=Methods Mol Biol |volume=360 |pages=163&ndash;202 |pmid=17172731}}</ref> or be grown in [[agriculture]].<ref>{{cite journal |author=Daniell H, Dhingra A |title=Multigene engineering: dawn of an exciting new era in biotechnology |journal=Curr Opin Biotechnol |volume=13 |issue=2 |pages=136&ndash;41 |year=2002 |pmid=11950565 |doi=10.1016/S0958-1669(02)00297-5}}</ref><ref>{{cite journal |author=Job D |title=Plant biotechnology in agriculture |journal=Biochimie |volume=84 |issue=11 |pages=1105&ndash;10 |year=2002 |pmid=12595138 |doi=10.1016/S0300-9084(02)00013-5}}</ref>

===Forensics===
{{Further2|[[Genetic fingerprinting]]}}

[[Forensic science|Forensic scientists]] can use DNA in [[blood]], [[semen]], [[skin]], [[saliva]] or [[hair]] found at a [[crime scene]] to identify a matching DNA of an individual, such as a perpetrator. This process is called [[genetic fingerprinting]], or more accurately, DNA profiling. In DNA profiling, the lengths of variable sections of repetitive DNA, such as [[short tandem repeat]]s and [[minisatellite]]s, are compared between people. This method is usually an extremely reliable technique for identifying a matching DNA.<ref>{{cite journal |author=Collins A, Morton N |title=Likelihood ratios for DNA identification | url=http://www.pnas.org/cgi/reprint/91/13/6007.pdf | journal=Proc Natl Acad Sci USA |volume=91 |issue=13 | pages=6007&ndash;11 |year=1994 |pmid=8016106 |doi=10.1073/pnas.91.13.6007|format=PDF}}</ref> However, identification can be complicated if the scene is contaminated with DNA from several people.<ref>{{cite journal |author=Weir B, Triggs C, Starling L, Stowell L, Walsh K, Buckleton J |title=Interpreting DNA mixtures | journal=J Forensic Sci |volume=42 |issue=2 | pages=213&ndash;22 |year=1997 |pmid=9068179}}</ref> DNA profiling was developed in 1984 by British geneticist Sir [[Alec Jeffreys]],<ref>{{cite journal |author=Jeffreys A, Wilson V, Thein S |title=Individual-specific 'fingerprints' of human DNA | journal=Nature |volume=316 |issue=6023 | pages=76&ndash;9 |year=1985|pmid=2989708 |doi=10.1038/316076a0}}</ref> and first used in forensic science to convict Colin Pitchfork in the 1988 [[Colin Pitchfork|Enderby murders]] case.<ref>[http://www.forensic.gov.uk/forensic_t/inside/news/list_casefiles.php?case=1 Colin Pitchfork — first murder conviction on DNA evidence also clears the prime suspect] Forensic Science Service Accessed 23 Dec 2006</ref>

People convicted of certain types of crimes may be required to provide a sample of DNA for a database. This has helped investigators solve old cases where only a DNA sample was obtained from the scene. DNA profiling can also be used to identify victims of mass casualty incidents.<ref>{{cite web |url=http://massfatality.dna.gov/Introduction/ |title=DNA Identification in Mass Fatality Incidents |month=September | year=2006 |publisher=National Institute of Justice}}</ref> On the other hand, many convicted people have been released from prison on the basis of DNA techniques, which were not available when a crime had originally been committed.

===Bioinformatics===
{{Further2|[[Bioinformatics]]}}
[[Bioinformatics]] involves the manipulation, searching, and [[data mining]] of DNA sequence data. The development of techniques to store and search DNA sequences have led to widely applied advances in [[computer science]], especially [[string searching algorithm]]s, [[machine learning]] and [[database theory]].<ref>{{Citation | last1=Baldi|first1= Pierre|author1-link=Pierre Baldi|last2= Brunak|first2= Soren | title=Bioinformatics: The Machine Learning Approach | publisher= MIT Press | year=2001| isbn=978-0-262-02506-5 | oclc=45951728 57562233}}.</ref> String searching or matching algorithms, which find an occurrence of a sequence of letters inside a larger sequence of letters, were developed to search for specific sequences of nucleotides.<ref>Gusfield, Dan. ''Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology''. [[Cambridge University Press]], 15 January 1997. {{ISBN|978-0-521-58519-4}}.</ref> In other applications such as [[text editor]]s, even simple algorithms for this problem usually suffice, but DNA sequences cause these algorithms to exhibit near-worst-case behaviour due to their small number of distinct characters. The related problem of [[sequence alignment]] aims to identify [[homology (biology)|homologous]] sequences and locate the specific [[mutation]]s that make them distinct. These techniques, especially [[multiple sequence alignment]], are used in studying [[phylogenetics|phylogenetic]] relationships and protein function.<ref>{{cite journal |author=Sjölander K |title=Phylogenomic inference of protein molecular function: advances and challenges | url=http://bioinformatics.oxfordjournals.org/cgi/reprint/20/2/170 | journal=Bioinformatics |volume=20 |issue=2 | pages=170–9 |year=2004 |pmid=14734307 | doi = 10.1093/bioinformatics/bth021}}</ref> Data sets representing entire genomes' worth of DNA sequences, such as those produced by the [[Human Genome Project]], are difficult to use without annotations, which label the locations of genes and regulatory elements on each chromosome. Regions of DNA sequence that have the characteristic patterns associated with protein- or RNA-coding genes can be identified by [[Gene prediction|gene finding]] algorithms, which allow researchers to predict the presence of particular [[gene product]]s in an organism even before they have been isolated experimentally.<ref name="Mount">{{cite book|author = Mount DM |title=Bioinformatics: Sequence and Genome Analysis | edition = 2 | publisher = Cold Spring Harbor Laboratory Press | year = 2004 | isbn = 0879697121|oclc = 55106399|location=Cold Spring Harbor, NY}}</ref>

===DNA nanotechnology===
[[Image:DNA nanostructures.png|thumb|400px|The DNA structure at left (schematic shown) will self-assemble into the structure visualized by [[Atomic force microscope|atomic force microscopy]] at right. [[DNA nanotechnology]] is the field which seeks to design nanoscale structures using the [[molecular recognition]] properties of DNA molecules. Image from Strong, 2004. {{doi-inline|10.1371/journal.pbio.0020073}}]]

{{Further2|[[DNA nanotechnology]]}}
DNA nanotechnology uses the unique [[molecular recognition]] properties of DNA and other nucleic acids to create self-assembling branched DNA complexes with useful properties. DNA is thus used as a structural material rather than as a carrier of biological information. This has led to the creation of two-dimensional periodic lattices (both tile-based as well as using the "[[DNA origami]]" method) as well as three-dimensional structures in the shapes of [[Polyhedron|polyhedra]]. [[DNA machine|Nanomechanical devices]] and [[DNA computing|algorithmic self-assembly]] have also been demonstrated, and these DNA structures have been used to template the arrangement of other molecules such as [[Colloidal gold|gold nanoparticles]] and [[streptavidin]] proteins.

===History and anthropology===
{{Further2|[[Phylogenetics]] and [[Genetic genealogy]]}}
Because DNA collects mutations over time, which are then inherited, it contains historical information and by comparing DNA sequences, geneticists can infer the evolutionary history of organisms, their [[Phylogenetics|phylogeny]].<ref>{{cite journal |author=Wray G |title=Dating branches on the tree of life using DNA | url=http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=11806830 | journal=Genome Biol |volume=3 |issue=1 | pages=REVIEWS0001 |year=2002 |pmid=11806830 | doi = 10.1046/j.1525-142X.1999.99010.x |nopp=true}}</ref> This field of phylogenetics is a powerful tool in [[evolutionary biology]]. If DNA sequences within a species are compared, [[population genetics|population geneticists]] can learn the history of particular populations. This can be used in studies ranging from [[ecological genetics]] to [[anthropology]]; for example, DNA evidence is being used to try to identify the [[Ten Lost Tribes|Ten Lost Tribes of Israel]].<ref>''Lost Tribes of Israel'', [[Nova (TV series)|NOVA]], PBS airdate: 22 February 2000. Transcript available from [http://www.pbs.org/wgbh/nova/transcripts/2706israel.html PBS.org,] (last accessed on 4 March 2006)</ref><ref>Kleiman, Yaakov. [http://www.aish.com/societywork/sciencenature/the_cohanim_-_dna_connection.asp "The Cohanim/DNA Connection: The fascinating story of how DNA studies confirm an ancient biblical tradition".] ''aish.com'' (January 13, 2000). Accessed 4 March 2006.</ref>

DNA has also been used to look at modern family relationships, such as establishing family relationships between the descendants of [[Sally Hemings]] and [[Thomas Jefferson]]. This usage is closely related to the use of DNA in criminal investigations detailed above. Indeed, some criminal investigations have been solved when DNA from crime scenes has matched relatives of the guilty individual.<ref>Bhattacharya, Shaoni. [http://www.newscientist.com/article.ns?id=dn4908 "Killer convicted thanks to relative's DNA".] ''newscientist.com'' (20 April 2004). Accessed 22 Dec 06</ref>

==History of DNA research==
{{Further2|[[History of molecular biology]]}}

[[Image:Francis Crick.png|thumb|125px|right|[[Francis Crick]]]]
[[File:NonFreeImageRemoved.svg|thumb|125px|right|[[Rosalind Franklin]]]]

DNA was first isolated by the [[Switzerland|Swiss]] physician [[Friedrich Miescher]] who, in 1869, discovered a microscopic substance in the [[pus]] of discarded surgical bandages. As it resided in the nuclei of cells, he called it "nuclein".<ref>{{cite journal |author=Dahm R |title=Discovering DNA: Friedrich Miescher and the early years of nucleic acid research |journal=Hum. Genet. |volume=122 |issue=6 |pages=565–81 |year=2008 |month=January |pmid=17901982 |doi=10.1007/s00439-007-0433-0}}</ref> In 1919, [[Phoebus Levene]] identified the base, sugar and phosphate nucleotide unit.<ref>{{cite journal |author=Levene P, |title=The structure of yeast nucleic acid | url=http://www.jbc.org/cgi/reprint/40/2/415 | journal=J Biol Chem |volume=40 |issue=2 | pages=415&ndash;24 |date=1 December 1919}}</ref> Levene suggested that DNA consisted of a string of nucleotide units linked together through the phosphate groups. However, Levene thought the chain was short and the bases repeated in a fixed order. In 1937 [[William Astbury]] produced the first [[X-ray scattering techniques|X-ray diffraction]] patterns that showed that DNA had a regular structure.<ref>{{cite journal | author =Astbury W, |title=Nucleic acid | journal=Symp. SOC. Exp. Bbl |volume=1 |issue=66 |year=1947}}</ref>

In 1928, [[Frederick Griffith]] discovered that [[trait (biology)|traits]] of the "smooth" form of the ''Pneumococcus'' could be transferred to the "rough" form of the same bacteria by mixing killed "smooth" bacteria with the live "rough" form.<ref>{{cite journal |author=Lorenz MG, Wackernagel W |title=Bacterial gene transfer by natural genetic transformation in the environment |journal=Microbiol. Rev. |volume=58 |issue=3 |pages=563–602 |date=1 September 1994|pmid=7968924 |url=http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=7968924 }}</ref> This system provided the first clear suggestion that DNA carried genetic information&mdash;the [[Avery-MacLeod-McCarty experiment]]&mdash;when [[Oswald Avery]], along with coworkers [[Colin Munro MacLeod|Colin MacLeod]] and [[Maclyn McCarty]], identified DNA as the [[Griffith's experiment|transforming principle]] in 1943.<ref>{{cite journal |author=Avery O, MacLeod C, McCarty M |title=Studies on the chemical nature of the substance inducing transformation of pneumococcal types. Inductions of transformation by a desoxyribonucleic acid fraction isolated from pneumococcus type III | url=http://www.jem.org/cgi/reprint/149/2/297 | journal=J Exp Med |volume=79 |issue=2 | pages=137&ndash;158 |year=1944 |doi=10.1084/jem.79.2.137}}</ref> DNA's role in [[heredity]] was confirmed in 1952, when [[Alfred Hershey]] and [[Martha Chase]] in the [[Hershey-Chase experiment]] showed that DNA is the [[genetic material]] of the [[Enterobacteria phage T2|T2 phage]].<ref>{{cite journal |author=Hershey A, Chase M |title=Independent functions of viral protein and nucleic acid in growth of bacteriophage | url=http://www.jgp.org/cgi/reprint/36/1/39.pdf | journal=J Gen Physiol |volume=36 |issue=1 | pages=39&ndash;56 |year=1952 |pmid=12981234 |doi=10.1085/jgp.36.1.39|format=PDF}}</ref>

In 1953, based on [[Photo 51|X-ray diffraction images]] taken by [[Rosalind Franklin]] and the information that the bases were paired, [[James D. Watson]] and [[Francis Crick]] suggested what is now accepted as the first accurate model of [[Molecular structure of Nucleic Acids|DNA structure]] in the journal [[Nature (journal)|''Nature'']].<ref name=FWPUB/> Experimental evidence for Watson and Crick's model were published in a series of five articles in the same issue of ''Nature''.<ref name=NatureDNA50>Nature Archives [http://www.nature.com/nature/dna50/archive.html Double Helix of DNA: 50 Years]</ref> Of these, [[Rosalind Franklin|Franklin]] and [[Raymond Gosling]]'s paper was the first publication of X-ray diffraction data that supported the [[Watson and Crick]] model;<ref name=NatFranGos>{{cite journal| title=Molecular Configuration in Sodium Thymonucleate. Franklin R. and Gosling R.G| journal=Nature | volume= 171 | pages= 740&ndash;741 | year=1953 | url=http://www.nature.com/nature/dna50/franklingosling.pdf | pmid=13054694 | doi= 10.1038/171740a0| author=Franklin, Rosalind |format=PDF}}</ref><ref>[http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/dna/pictures/franklin-typeBphoto.html Original X-ray diffraction image]</ref> this issue also contained an article on DNA structure by [[Maurice Wilkins]] and two of his colleagues.<ref name=NatWilk>{{cite journal| title=Molecular Structure of Deoxypentose Nucleic Acids | author= Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. | journal=Nature | volume= 171 | pages= 738&ndash;740 | year=1953 | url=http://www.nature.com/nature/dna50/wilkins.pdf| pmid=13054693 | doi=10.1038/171738a0|format=PDF}}</ref> In 1962, after Franklin's death, Watson, Crick, and Wilkins jointly received the [[Nobel Prize]] in [[Nobel Prize in Physiology or Medicine|Physiology or Medicine]]<ref>[http://nobelprize.org/nobel_prizes/medicine/laureates/1962/ The Nobel Prize in Physiology or Medicine 1962] Nobelprize .org Accessed 22 Dec 06</ref> Unfortunately, Nobel rules of the time allowed only living recipients, but a vigorous debate continues on who should receive credit for the discovery.<ref>{{cite journal | title=The double helix and the 'wronged heroine' | author= Brenda Maddox| journal= Nature | volume= 421 | pages= 407–408 | date=23 January 2003 | url=http://www.biomath.nyu.edu/index/course/hw_articles/nature4.pdf | pmid=12540909 | doi = 10.1038/nature01399 |format=PDF}}</ref>

In an influential presentation in 1957, Crick laid out the [[central dogma of molecular biology|"Central Dogma" of molecular biology]], which foretold the relationship between DNA, RNA, and proteins, and articulated the "adaptor hypothesis".<ref>Crick, F.H.C. [http://genome.wellcome.ac.uk/assets/wtx030893.pdf On degenerate templates and the adaptor hypothesis (PDF).] genome.wellcome.ac.uk (Lecture, 1955). Accessed 22 Dec 2006</ref> Final confirmation of the replication mechanism that was implied by the double-helical structure followed in 1958 through the [[Meselson-Stahl experiment]].<ref>{{cite journal |author=Meselson M, Stahl F |title=The replication of DNA in ''Escherichia coli'' | journal=Proc Natl Acad Sci USA |volume=44 |issue=7 | pages=671&ndash;82 |year=1958 |pmid=16590258 |doi=10.1073/pnas.44.7.671}}</ref> Further work by Crick and coworkers showed that the genetic code was based on non-overlapping triplets of bases, called codons, allowing [[Har Gobind Khorana]], [[Robert W. Holley]] and [[Marshall Warren Nirenberg]] to decipher the genetic code.<ref>[http://nobelprize.org/nobel_prizes/medicine/laureates/1968/ The Nobel Prize in Physiology or Medicine 1968] Nobelprize.org Accessed 22 Dec 06</ref> These findings represent the birth of [[molecular biology]].

==See also==
<div style="-moz-column-count:2; column-count:2;">
* [[Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid]]
* [[DNA microarray]]
* [[DNA sequencing]]
* [[Paracrystalline|Paracrystal model and theory]]
* [[X-ray scattering]]
* [[Crystallography]]
* [[Genetic disorder]]
* [[Junk DNA]]
* [[Nucleic acid analogue]]s
* [[Nucleic acid methods]]
* [[Comparison of nucleic acid simulation software|Nucleic acid modeling]]
* [[Nucleic acid notation]]s
* [[Phosphoramidite]]
* [[Plasmid]]
* [[Polymerase chain reaction]]
* {{Proteopedia|DNA}}
* [[Southern blot]]
* [[Triple-stranded DNA]]
</div>

==Notes==
{{Reflist|2}}

==Further reading==
* Calladine, Chris R.; Drew, Horace R.; Luisi, Ben F. and Travers, Andrew A. ''Understanding DNA'', Elsevier Academic Press, 2003. {{ISBN|978-0-12155089-9}}
* Clayton, Julie. (Ed.). ''50 Years of DNA'', Palgrave MacMillan Press, 2003. {{ISBN|978-1-40-391479-8}}
* Judson, Horace Freeland. ''The Eighth Day of Creation: Makers of the Revolution in Biology'', Cold Spring Harbor Laboratory Press, 1996. {{ISBN|978-0-87-969478-4}}
* [[Robert Olby|Olby, Robert]]. ''The Path to The Double Helix: Discovery of DNA'', first published in October 1974 by MacMillan, with foreword by Francis Crick; {{ISBN|978-0-48-668117-7}}; the definitive DNA textbook, revised in 1994, with a 9 page postscript.
* [[Matt Ridley|Ridley, Matt]]. ''Francis Crick: Discoverer of the Genetic Code (Eminent Lives)'' HarperCollins Publishers; 192 pp, {{ISBN|978-0-06-082333-7}} 2006
* Rose, Steven. ''The Chemistry of Life'', Penguin, {{ISBN|978-0-14-027273-4}}.
* Watson, James D. and Francis H.C. Crick. [http://www.nature.com/nature/dna50/watsoncrick.pdf A structure for Deoxyribose Nucleic Acid] (PDF). ''[[Nature (journal)|Nature]]'' 171, 737&ndash;738, 25 April 1953.
* Watson, James D. ''DNA: The Secret of Life'' {{ISBN|978-0-375-41546-3}}.
* Watson, James D. ''[[The Double Helix|The Double Helix: A Personal Account of the Discovery of the Structure of DNA (Norton Critical Editions)]]''. {{ISBN|978-0-393-95075-5}}
* Watson, James D. "Avoid boring people and other lessons from a life in science" (2007) New York: Random House. {{ISBN|978-0-375-41284-4}}

==External links==
{{Portal|Molecular and Cellular Biology}}
{{Spoken Wikipedia|dna.ogg|date=2007-02-12}}
{{Commons category|DNA}}
* [http://pipe.scs.fsu.edu/displar.html DNA binding site prediction on protein]
* [http://biostudio.com/c_%20education%20mac.htm DNA coiling to form chromosomes]
* [http://www.dnaftb.org/dnaftb/ DNA from the Beginning] Another DNA Learning Center site on DNA, genes, and heredity from Mendel to the human genome project.
* [http://ca.youtube.com/watch?v=iyb7fwduuGM DNA Lab, demonstrates how to extract DNA from wheat using readily available equipment and supplies.]
* [http://nobelprize.org/educational_games/medicine/dna_double_helix/ DNA the Double Helix Game] From the official Nobel Prize web site
* [http://www.fidelitysystems.com/Unlinked_DNA.html DNA under electron microscope]
* [http://www.dnalc.org/ Dolan DNA Learning Center]
* [http://www.nature.com/nature/dna50/archive.html Double Jelix: 50 years of DNA], ''[[Nature (journal)|Nature]]''
* [http://www.ncbe.reading.ac.uk/DNA50/ Double Helix 1953&ndash;2003] National Centre for Biotechnology Education
* [http://www.bbc.co.uk/bbcfour/audiointerviews/profilepages/crickwatson1.shtml Francis Crick and James Watson talking on the BBC in 1962, 1972, and 1974]
* [http://www.genome.gov/10506718 Genetic Education Modules for Teachers] — ''DNA from the Beginning'' Study Guide
* [http://www.blackwellpublishing.com/trun/artwork/Animations/cloningexp/cloningexp.html Guide to DNA cloning]
* [[Robert Olby|Olby, R.]] (2003) [http://chem-faculty.ucsd.edu/joseph/CHEM13/DNA1.pdf "Quiet debut for the double helix"] ''Nature'' '''421''' (January 23): 402&ndash;405.
* {{PDB Molecule of the Month|pdb23_1}}
* [http://mason.gmu.edu/~emoody/rfranklin.html Rosalind Franklin's contributions to the study of DNA]
* [http://orpheus.ucsd.edu/speccoll/testing/html/mss0660a.html#abstract The Register of Francis Crick Personal Papers 1938 - 2007] at Mandeville Special Collections Library, Geisel Library, [[University of California, San Diego]]
* [http://www.tjmitchell.com/stuart/dna.html The Secret Life of DNA - DNA Music compositions]
* [http://www.genome.gov/10506367 U.S. National DNA Day] — watch videos and participate in real-time chat with top scientists

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=PM Entry on WikiP=
{{Infobox website
| name = PlanetMath
| logo = [[Image:pmlogo.png|182px]]
| screenshot = 
| caption = 
| url = http://planetmath.org/
| commercial = No
| type = [[Internet encyclopedia project]]
| language = [[English language|English]]
| registration = Available
| owner = [[Virginia Tech]]
| author = Nathan Egge, Aaron Krowne
| launch_date =
| current_status = active
| revenue = 
}}

'''PlanetMath''' is a [[free content|free]], collaborative, online [[mathematics]] [[encyclopedia]]. The emphasis is on [[peer review]], rigour, openness, [[pedagogy]], real-time content, interlinked content, and [[community]].<ref name="autogenerated1">[http://planetmath.org/?op=about PlanetMath:<!-- Bot generated title -->]</ref> Intended to be comprehensive, the project is located at the Digital Library Research Lab at [[Virginia Tech]].<ref>[http://planetmath.org/?op=getobj&from=collab&id=36#mathworld PlanetMath: New User Guide<!-- Bot generated title -->]</ref>

PlanetMath was started when the popular free online mathematics encyclopedia [[MathWorld]] was taken offline for 12 months by a court injunction as a result of the [[CRC Press]] lawsuit against the [[Wolfram Research]] company and its employee (and MathWorld's author) [[Eric Weisstein]].<ref name="autogenerated1" />

==PlanetMath.org website contents==
PlanetMath content is licensed under the ‘[[copyleft]]’ [[GNU Free Documentation License]].<ref>[http://planetmath.org/?op=license PlanetMath:<!-- Bot generated title -->]</ref> An author who starts a new article becomes the ''owner'' of that article; he or she may then choose to grant editing rights to other individuals or groups. All content is written in [[LaTeX]], a typesetting system popular among [[mathematician]]s because of its support of the technical needs of mathematical typesetting and its high-quality output. The user can explicitly create links to other articles, and the system also automatically turns certain words into  links to the defining articles. The topic area of every article is classified by the [[Mathematics Subject Classification]] (MSC) of the [[American Mathematical Society]] (AMS). 

Users may attach [[addenda]], [[errata]] and discussions to articles. A system for private messaging among users is also in place.

As of April 2009, the encyclopedia hosted about 8470 entries and over 14000 ''concepts'' (a concept may be e.g. a specific notion defined within a more general entry). About 600 Wikipedia pages incorporate text from PlanetMath and/or [http://planetphysics.org/ PlanetPhysics.org] articles [http://en.wikipedia.org/wiki/Category:Wikipedia_articles_incorporating_text_from_PlanetMath]

The software running PlanetMath is written in [[Perl]] and runs on [[Linux]] and the web server [[apache server|Apache]]. It is known as Noösphere and has been released under the free [[BSD License]].<ref name="autogenerated1" />

A PM book of 2,300 pages in PDF format is now available for the PM Free Encyclopedia contents up to 2006 as [http://aux.planetphysics.org/files/books/207/APMvol1.pdf a free download PDF file] of 18Mb <ref>http://planetphysics.org/?op=getobj&from=books&id=207 Joseph Cornelli and A. Krowne, Editors,  with the following list of contributing PM members as co-authors: Aatu, ack, akrowne, alek thiery, alinabi, almann, alozano, antizeus, antonio, aparna, ariels, armbrusterb, AxelBoldt, basseykay, bbukh, benjaminfjones, bhaire, brianbirgen, bs, bshanks, bwebste, cryo, danielm, Daume, debosberg, deiudi, digitalis, djao, Dr Absentius, draisma, drini, drummond, dublisk, Evandar, fibonaci, flynnheiss, gabor sz, GaloisRadical, gantsich, gaurminirick, gholmes74, giri, greg, grouprly, gumau, Gunnar, Henry, iddo, igor, imran, jamika chris, jarino, jay, jgade, jihemme, Johan, karteef, karthik, kemyers3, Kevin OBryant, kidburla2003, KimJ, Koro, lha, lieven, livetoad, liyang, Logan, Luci, m759, mathcam, mathwizard, matte, mclase, mhale, mike, mikestaflogan, mps, msihl, muqabala, n3o, nerdy2, nobody, npolys, Oblomov, ottocolori, paolini, patrickwonders, pbruin, petervr, PhysBrain, quadrate, quincynoodles, rspuzio, RevBobo, Riemann, rmilson, ratboy, ruiyang, Sabean, saforres, saki, say 10, scanez, scineram, seonyoung, slash, sleske, slider142, sprocketboy, sucrose, superhiggs, tensorking, thedagit, Thomas Heye, thouis, Timmy, tobix, tromp, tz26, unlord, uriw, urz, vampyr, vernondalhart, vitriol, vladm, volator, vypertd, wberry, Wkbj79, wombat, x bas, xiaoyanggu, XJamRastafire, xriso, yark et al.</ref>. Additional, applied mathematics content<ref>http://planetphysics.org/encyclopedia/OverviewOfTheContentOfPlanetPhysics.html Overview of the Contents of PlanetPhysics</ref> and
over 2 Gb of bibliographic materials, as well as Encyclopedia entries (currently at >40Mb) related to mathematics applications and Theoretical Physics can be also freely downloaded from the related, but independent, Noosphere-based 
[http://planetphysics.org/ PlanetPhysics. org] website<ref>http://planetphysics.org/ PlanetPhysics. org</ref><ref>http://planetphysics.org/?op=listobj&from=books Free Book downloads in PDF format, Original Papers (~10 pages) and Expositions (>30 pages)</ref>.

==See also==
*[[List of online encyclopedias]]
* [http://planetphysics.org/?op=getobj&from=books&id=207 ''PM Free Encyclopedia v.1.0'' Book '''volumes 1 and 2'''. 2005., 2305 pages, J. Cornelli and A. Krowne, Eds., GNU License].  <ref>http://aux.planetphysics.org/files/books/207/APMvol1.pdf</ref>
* [http://planetmath.org/encyclopedia/OverviewOfTheContentOfPlanetMath.html Overview of the current contents of PlanetMath]
* [[Wikipedia:WikiProject Mathematics]]
* [[Wikipedia:WikiProject Mathematics/PlanetMath Exchange]]
* [http://planetphysics.org/ PlanetPhysics.org]
* [[Wikipedia:WikiProject Physics]]

* [http://planetphysics.org/encyclopedia/OverviewOfTheContentOfPlanetPhysics.html Overview of the Contents of PlanetPhysics]
* [http://planetphysics.org/encyclopedia/IHES.html IHES: The fusion of theoretical physics with mathematics at IHES org]
* [http://en.wikipedia.org/w/index.php?title=Wikipedia:WikiProject_Mathematics/PlanetMath_Exchange/Table_of_topics Table of fields of mathematics covered by the PlanetMath.org exchange with Wikipedia]
* [[Higher-dimensional algebra]]
* [[Category theory]]
* [http://categorieslogicphysics.wikidot.com/ Categories, Logic and Foundations of Physics]
* [http://cdsweb.cern.ch/record/1173951?ln=en Algebraic Topology Foundations of Quantum Field Theory]
* [http://planetmath.org/?op=search&term=topic+entry+on+mathematical+physics+and+physical+mathematics Applied mathematics: mathematical physics and physical mathematics]
* [[Stanford Encyclopedia of Philosophy]]: "[http://plato.stanford.edu/entries/category-theory/ Category Theory]". 

* [[List of category theory topics]]
*[[List of publications in mathematics#Category theory| Important publications in category theory]]
* [[Glossary of category theory]]
* [[Domain theory]]
* [[Enriched category|Enriched category theory]]
* [[Higher category theory]]
* [[Higher dimensional algebra|Higher Dimensional Algebra]]
* [[Timeline of category theory and related mathematics]]
* [[Mathematical biology]] and [http://planetphysics.org/encyclopedia/MRSystem.html Category theory in Biology]
*  [http://en.wikipedia.org/wiki/Wikipedia:WikiProject_Mathematics/PlanetMath_Exchange#Converting_text_from_PlanetMath_to_Wikipedia_formats Converting between PlanetMath & PlanetPhysics TeX and Wikipedia mathematical formats.]
* [http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Computer_graphics Computer graphics in mathematics and physics]
* [http://commons.wikimedia.org/wiki/Category:Pictures_and_images Wikimedia Commons:Pictures and images]
* [http://commons.wikimedia.org/wiki/Category:Science Wikimedia Commons]
* [[MathWorld]]

==References==
{{Reflist}}

==External links==
* [http://planetmath.org PlanetMath]
* [http://planetphysics.org/ PlanetPhysics.org]
* [http://categorieslogicphysics.wikidot.com/ Categories, Logic and Foundations of Physics] 
* [[arXiv]]
* [http://front.math.ucdavis.edu/ Archives for Mathematics: arXiv]
* [http://www.sciencemag.org/cgi/reprint/308/5729/1721c.pdf Article on PlanetMath in the science magazine] of the [[American Association for the Advancement of Science|AAAS]]
* [http://eprintweb.org/S/ eprintweb archive]
* [[CogPrints]]
* [http://cdsweb.cern.ch/collection/Preprints?ln=en Preprint archives at CERN, the EU High Energy Physics International Faciltiy server]
* Christoph Lange, [http://kwarc.info/projects/swim/pubs/eswc07-web20-swim.pdf "Towards Scientific Collaboration in a Semantic Wiki"]
* Aaron E. Klemm, [http://www.freesoftwaremagazine.com/files/www.freesoftwaremagazine.com/nodes/1107/1107.pdf "Motivation and value of free resources: Wikipedia and Planetmath show the way"]
* Robert Milson, Aaron Krowne, [http://arxiv.org/pdf/cs/0507028 Adapting CBPP platforms for instructional use]
* [http://en.wikipedia.org/wiki/Category:Mathematics_websites Mathematics Websites listed on Wikipedia]
* Alex M. Andrew, [http://www.emeraldinsight.com/10.1108/03684920810907805 "Archives, mathematics encyclopaedia, dancing robots, ASC"], Kybernetes 2008 v. 37: 9/10 pp. 1466 - 1468.
* [http://mathworld.wolfram.com/ MathWorld]


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==DNA Molecular Models==
'''Molecular models of DNA structures''' are representations of the [[molecular geometry]] and [[DNA topology|topology]] of Deoxyribonucleic acid ([[DNA]]) molecules using one of several means, such as: closely packed spheres ([[CPK]] models) made of plastic, metal wires for 'skeletal models', graphic computations and animations by computers, artistic rendering, and so on, with the aim of simplifying and presenting the essential, physical and chemical, properties of DNA molecular structures either ''in vivo'' or ''in vitro''. Computer molecular models also allow animations and molecular dynamics
simulations that are very important for understanding how DNA functions ''in vivo''. Thus, an old standing dynamic problem is how DNA "self-replication" takes place in living cells that should involve transient uncoiling of supercoiled DNA fibers. Altough DNA consists of relatively rigid, very large elongated biopolymer molecules called "fibers" or chains (that are made of repeating [[nucleotide]] units of four basic types, attached to deoxyribose and phospate groups), its molecular stucture ''in vivo'' undergoes dynamic configuration changes that involve dynamically attached water molecules and ions. Supercoiling, packing with histones in chromosome structures, and other such supramolecular aspects also involve  ''in vivo'' [[DNA topology]] which is even more complex than DNA molecular geometry, thus turning molecular modeling of DNA into an especially challenging problem for both molecular biologists and biotechnologists. Like other large molecules and biopolymers, DNA often exists in multiple stable geometries (that is, it exhibits [[conformational isomerism]]) and configurational, quantum states which are close to each other in energy on the potential energy surface of the DNA molecule. Such geometries can also be computed, at least in principle, by employing ''ab initio'' [[quantum chemistry]] methods that have high accuracy for small molecules. Such quantum geometries define an important class of ''ab initio'' molecular models of DNA whose exploration has barely started. 

[[Image:Sarfus.DNABiochip.jpg|thumb|80px|right|DNA computing biochip:3D]]
In an interesting twist of roles, the DNA molecule itself was proposed to be utilized for [[DNA computing|quantum computing]]. Both DNA nanostructures as well as DNA 'computing' biochips have been built (see biochip image at right). 

The more advanced, computer-based [[molecular model]]s of DNA involve [[molecular dynamics]] simulations as well as [[quantum mechanics|quantum mechanical]] computations of vibro-rotations, delocalized [[molecular orbital]]s (MOs), [[electric dipole moment]]s, [[hydrogen-bonding]], and so on.
[[Image:Spinning DNA.gif|thumb|100px|left|Spinning DNA generic model.]]
==Importance==  
From the very early stages of structural studies of DNA by [[X-ray diffraction]] and biochemical means, molecular models such as the [[Double helix|Watson-Crick double-helix model]] were succesfully employed to solve the 'puzzle' of DNA structure, and also find how the latter relates to its key functions in living cells. The first high quality X-ray diffraction patterns
of A-DNA were reported by [[Rosalind Franklin]] and [[Raymond Gosling]] in 1953<ref>Franklin, R.E. and Gosling, R.G. recd.6 March 1953. Acta Cryst. (1953). 6, 673 The Structure of Sodium Thymonucleate Fibres I. The Influence of Water Content Acta Cryst. (1953). and 6, 678 The Structure of Sodium Thymonucleate Fibres II. The Cylindrically Symmetrical Patterson Function. </ref>. The first calculations of the Fourier transform of an atomic helix were reported one year earlier by Cochran, Crick and Vand <ref>Cochran, W., Crick, F.H.C. and Vand V. 1952. The Structure of Synthetic Polypeptides. 1. The Transform of Atoms on a Helix. Acta Cryst. 5(5):581-586.</ref>, and were followed in 1953 by the computation of the Fourier transform of a coiled-coil by Crick<ref>Crick, F.H.C. 1953a. The Fourier Transform of a Coiled-Coil., Acta Crystallographica 6(8-9):685-689.</ref>.
The first reports of a double-helix molecular model of B-DNA structure were made by Watson and Crick in 1953<ref>Watson, J.D; Crick F.H.C. 1953a. Molecular Structure of Nucleic Acids- A Structure for Deoxyribose Nucleic Acid., Nature 171(4356):737-738. </ref><ref>Watson, J.D; Crick F.H.C. 1953b. The Structure of DNA., Cold Spring Harbor Symposia on Qunatitative Biology 18:123-131.</ref>. Last-but-not-least, Maurice F. Wilkins,
A. Stokes and H.R. Wilson, reported the first X-ray patterns
of ''in vivo'' B-DNA in partially oriented salmon sperm heads <ref name=NatWilk>{{cite journal| title=Molecular Structure of Deoxypentose Nucleic Acids | author= Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. | journal=Nature | volume= 171 | pages= 738&ndash;740 | year=1953 | url=http://www.nature.com/nature/dna50/wilkins.pdf| pmid=13054693 | doi=10.1038/171738a0| format=PDF}}</ref>.
The development of the first correct double-helix molecular model of DNA by Crick and Watson may not have been possible without the biochemical evidence for the nucleotide base-pairing ([A---T]; [C---G]), or [[Chargaff's rules]]<ref name="Elson1952">{{cite journal |author=Elson D, Chargaff E |year=1952 |title=On the deoxyribonucleic acid content of sea urchin gametes |journal=Experientia |volume=8 |issue=4 |page=143-145}}</ref><ref name="Chargaff1952">{{cite journal |author=Chargaff E, Lipshitz R, Green C |year=1952 |title=Composition of the deoxypentose nucleic acids of four genera of sea-urchin |journal=J Biol Chem |volume=195 |issue=1 |page=155-160 |pmid=14938364}}</ref><ref name="Chargaff1951a">{{cite journal |author=Chargaff E, Lipshitz R, Green C, Hodes ME |year=1951 |title=The composition of the deoxyribonucleic acid of salmon sperm |journal=J Biol Chem |volume=192 |issue=1 |page=223-230 |pmid=14917668}}</ref><ref name="Chargaff1951b">{{cite journal |author=Chargaff E |year=1951 |title=Some recent studies on the composition and structure of nucleic acids |journal=J Cell Physiol Suppl |volume=38 |issue=Suppl}}</ref><ref name="Magasanik1950">{{cite journal |author=Magasanik B, Vischer E, Doniger R, Elson D, Chargaff E |year=1950 |title=The separation and estimation of ribonucleotides in minute quantities |journal=J Biol Chem |volume=186 |issue=1 |page=37-50 |pmid=14778802}}</ref><ref name="Chargaff1950">{{cite journal |author=Chargaff E |year=1950 |title=Chemical specificity of nucleic acids and mechanism of their enzymatic degradation |journal=Experientia |volume=6 |issue=6 |page=201-209}}</ref>.

==Examples of DNA molecular models==
Animated molecular models allow one to visually explore the three-dimensional (3D) structure of DNA. The first DNA model is a space-filling, or [[CPK]], model of the DNA double-helix  whereas the third is an animated wire, or skeletal type, molecular model of DNA. The last two DNA molecular models in this series depict [http://ndbserver.rutgers.edu/atlas/xray/structures/U/ud0017/ud0017.html quadruplex DNA] that may be involved in certain cancers<ref>http://www.phy.cam.ac.uk/research/bss/molbiophysics.php</ref><ref>http://planetphysics.org/encyclopedia/TheoreticalBiophysics.html</ref>. The last figure on this panel is a molecular model of hydrogen bonds between water molecules in ice that are similar to those found in DNA.
<gallery>
File:Methanol.pdb.png 
File:DNA-fragment-3D-vdW.png
File:Bdna.gif
File:Simple harmonic oscillator.gif
File:DNA chemical structure.svg
File:DNA animation.gif
File:ABDNAxrgpj.jpg<ref>http://commons.wikimedia.org/wiki/File:ABDNAxrgpj.jpg</ref>
File:Parallel telomere quadruple.png
File:Four-way DNA junction.gif
File:DNA_replication.svg
File:ABDNAxrgpj.jpg

File:3D model hydrogen bonds in water.svg
[A- and B-DNA X-ray Patterns  http://commons.wikimedia.org/wiki/Category:DNA]
</gallery>
*[[Spacefilling model|Spacefilling models]] or [[CPK model|CPK models]] - a molecule is represented by overlapping spheres representing the atoms:

 :{| class=wikitable
 |-
 |<!--col1-->[[Image:Methanol.pdb.png|center|110px|]]
 |}

==Images for DNA Structure Determination from X-Ray Patterns==
The following images illustrate both the principles and the main steps involved in generating structural information from X-ray diffraction studies of oriented DNA fibers with the help of molecular models of DNA that are combined with crystallographic and mathematical analysis of the X-ray patterns.  From left to right the gallery of images shows:
**''First row'':
*1. Constructive X-ray interference, or diffraction, following Bragg's Law of X-ray "''reflection by the crystal planes''";
*2. A comparison of A-DNA (crystalline) and highly hydrated B-DNA (paracrystalline) X-ray diffraction, and respectively, X-ray scattering patterns (courtesy of Dr. Herbert R. Wilson, FRS- see refs. list);
*3. Purified DNA precipitated in a water jug;
*4. The major steps involved in DNA structure determination by X-ray crystallography showing the important role played by molecular models of DNA structure in this iterative, structure--determination process;
**''Second row'':
*5. Photo of a modern X-ray diffractometer employed for recording X-ray patterns of DNA with major components: X-ray source, goniometer, sample holder, X-ray detector and/or plate holder;
*6. Illustrated animation of an X-ray goniometer;
*7. X-ray detector at the SLAC synchrotron facility;
*8. Neutron scattering facility at ISIS in UK;
** ''Third and fourth rows'': ''Molecular models of DNA structure at various scales''; figure #11 is an actual electron micrograph of a DNA fiber bundle, presumably of a single bacterial chromosome loop. 
<gallery>
File:Bragg diffraction.png
File:ABDNAxrgpj.jpg
File:DNA in water.jpg
File:X ray diffraction.png
File:X Ray Diffractometer.JPG
File:Kappa goniometer animation.ogg
File:SLAC detector edit1.jpg
File:ISIS exptal hall.jpg
File:Dna-SNP.svg
File:DNA_replication.svg
File:DNA Under electron microscope Image 3576B-PH.jpg
File:DNA Model Crick-Watson.jpg
File:DNA labels.jpg
File:AT DNA base pair pt.svg
File:A-B-Z-DNA Side View.png
File:Museo Príncipe Felipe. ADN.jpg
File:AGCT DNA mini.png
File:BU Bio5.jpg
File:Circular DNA Supercoiling.png
File:NonFreeImageRemoved.svg
</gallery>

==Paracrystalline lattice models of B-DNA structures==

A [[paracrystalline|paracrystalline lattice]], or paracrystal,
is a molecular or atomic lattice with significant amounts (e.g., larger than a few percent) of partial disordering of molecular arranegements. Limiting cases of the paracrystal model are [[nanostructure]]s, such as [[glass]]es, [[liquid]]s, etc., that may possess only local ordering and no global order.
[[Liquid crystal]]s also have paracrystalline rather than [[crystal]]line structures.

[[:Image:Rosalindfranklinsjokecard.jpg|thumb|500px|center|DNA Helix controversy in 1952]]

Highly hydrated B-DNA occurs naturally in living cells in such a paracrystalline state, which is a dynamic one in spite of the relatively rigid DNA double-helix stabilized by parallel hydrogen bonds between the nucleotide base-pairs in the two complementary, helical DNA chains (see figures). For simplicity most DNA molecular models ommit both water and ions dynamically bound to B-DNA, and are thus less useful for understanding the dynamic behaviors of B-DNA ''in vivo''. The physical and mathematical analysis of X-ray<ref>Hosemann R., Bagchi R.N., ''Direct analysis of diffraction by matter'', North-Holland Publs., Amsterdam – New York, 1962.</ref><ref>{{cite journal|author=Baianu, I.C. |title=X-ray scattering by partially disordered membrane systems.|journal=Acta Cryst., |volume=A34 |issue=5 |pages=751–753|year=1978|doi=10.1107/S0567739478001540}}</ref> and spectroscopic data for paracrystalline B-DNA is therefore much more complicated than that of crystalline, A-DNA X-ray diffraction patterns. The paracrystal model is also important for DNA technological applications such as [[DNA nanotechnology]]. Novel techniques that combine X-ray diffraction of DNA with X-ray microscopy in hydrated living cells are now also being developed (see, for example, [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=12379938  "Application of X-ray microscopy in the analysis of living hydrated cells"]).

==Genomic and Biotechnology Applications of DNA molecular modeling==
The following gallery of images illustrates various uses of DNA molecular modeling in Genomics and Biotechnology research applications from DNA repair to PCR and DNA nanostructures; each slide contains its own explanation and/or details. The first slide presents an overview of DNA applications, including DNA molecular models, with emphasis on Genomics and Biotechnology.

===Gallery: DNA Molecular modeling applications===
<gallery>
File:Genomics GTL Pictorial Program.jpg
File:RNA pol.jpg
File:Primase 3B39.png
File:Museo Príncipe Felipe. ADN.jpg
File:DNA Repair.jpg
File:MGMT+DNA 1T38.png
File:DNA_damaged_by_carcinogenic_2-aminofluorene_AF.jpg
File:A-DNA orbit animated small.gif
File:DNA labels.jpg
File:AT DNA base pair pt.svg
File:AGCT DNA mini.png
File:A-B-Z-DNA Side View.png
File:BU Bio5.jpg
File:Plasmid emNL.jpg
File:Circular DNA Supercoiling.png
File:Chromatin chromosom.png
File:Chromosome.svg
File:Chr2 orang human.jpg
File:3D-SIM-3 Prophase 3 color.jpg
File:Chromosome2 merge.png
File:Transkription Translation 01.jpg
File:RibosomaleTranskriptionsEinheit.jpg
File:Chromosome Conformation Capture Technology.jpg
File:Mitochondrial DNA and diseases.png
File:PCR.svg
File:Pcr gel.png
File:DNA nanostructures.png
File:SFP discovery principle.jpg
File:Cdnaarray.jpg
File:Expression of Human Wild-Type and P239S Mutant Palladin.png
File:Random genetic drift chart.png
File:Co-dominance Rhododendron.jpg
</gallery>

==[[Database]]s for DNA molecular models and sequences==

===X-ray diffraction===
* [http://ndbserver.rutgers.edu/atlas/xray/structures/U/ud0017/ud0017.html NDB ID: UD0017 Database]
*[http://ndbserver.rutgers.edu/atlas/xray/index.html X-ray Atlas -database]
* [http://ndbserver.rutgers.edu/ftp/NDB/coordinates/na-biol/ PDB files of coordinates for nucleic acid structures from X-ray diffraction by NA (incl. DNA) crystals]
* [http://ndbserver.rutgers.edu/ftp/NDB/structure-factors/ Structure factors dowloadable files in CIF format]

===Neutron scattering===
* [[ISIS neutron source]]
* [http://www.isis.rl.ac.uk/ ISIS pulsed neutron source:A world centre for science with neutrons & muons at Harwell, near Oxford, UK.]

===X-ray microscopy===
*[http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=12379938  Application of X-ray microscopy in the analysis of living hydrated cells]

===Electron microscopy===
* [http://www.fidelitysystems.com/Unlinked_DNA.html DNA under electron microscope]

===Atomic Force Microscopy (AFM)===
Two-dimensional DNA junction arrays have been visualized by [[Atomic force microscopy|Atomic Force Microscopy (AFM)]]<ref>{{cite journal |last=Mao |first=Chengde |authorlink= |coauthors=Sun, Weiqiong & Seeman, Nadrian C. |year=1999 |month=16 June|title=Designed Two-Dimensional DNA Holliday Junction Arrays Visualized by Atomic Force Microscopy |journal=[[Journal of the American Chemical Society]] |volume=121 |issue=23 |pages=5437–5443 |issn=0002-7863|doi=10.1021/ja9900398}}</ref>. Other imaging resources for AFM/[[Scanning probe microscopy|Scanning probe microscopy(SPM)]] can be freely accessed at:
*[http://www.parkafm.com/New_html/resources/01general.php How SPM Works]
*[http://www.rhk-tech.com/results/showcase.php SPM Image Gallery - AFM STM SEM MFM NSOM and more.]
====Gallery of AFM Images====
<gallery>
File:DNA_nanostructures.png
File:Holliday junction coloured.png
File:Holliday Junction cropped.png
File:Atomic force microscope by Zureks.jpg
File:Atomic force microscope block diagram.png

File:Single-Molecule-Under-Water-AFM-Tapping-Mode.jpg
File:AFMimageRoughGlass20x20.png
</gallery>

===Mass spectrometry--Maldi informatics===
<gallery>
File:Maldi informatics figure 6.JPG
</gallery>

===Spectroscopy===

* [[Vibrational circular dichroism]] (VCD) 
* [[NMR spectroscopy|FT-NMR]]<ref>[http://www.jonathanpmiller.com/Karplus.html http://www.jonathanpmiller.com/Karplus.html]- obtaining dihedral angles from <sup>3</sup>J coupling constants</ref><ref>[http://www.spectroscopynow.com/FCKeditor/UserFiles/File/specNOW/HTML%20files/General_Karplus_Calculator.htm http://www.spectroscopynow.com/FCKeditor/UserFiles/File/specNOW/HTML%20files/General_Karplus_Calculator.htm] Another Javascript-like NMR coupling constant to dihedral</ref>
**[http://ndbserver.rutgers.edu/atlas/nmr/index.html NMR Atlas--database]
** [http://ndbserver.rutgers.edu/ftp/NDB/coordinates/na-nmr-mmcif/ mmcif downloadable coordinate files of nucleic acids in solution from 2D-FT NMR data]
** [http://ndbserver.rutgers.edu/ftp/NDB/nmr-restraints/ NMR constraints files for NAs in PDB format]
* [[NMR imaging|NMR microscopy]]<ref>Lee, S. C. et al., (2001). One Micrometer Resolution NMR Microscopy. ''J. Magn. Res''., '''150''': 207-213.</ref>
* [[Microwave spectroscopy]] 
* FT-[[IR]]
* FT-[[NIR]]<ref>Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High Resolution Nuclear Magnetic Resonance Analysis of Soybean  Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In ''Oil Extraction and Analysis.'', D. Luthria, Editor pp.241-273, AOCS Press., Champaign, IL.</ref><ref>Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban, [http://arxiv.org/abs/q-bio/0407006 q-bio/0407006 (July 2004)]</ref><ref>Raghavachari, R., Editor. 2001.'' Near-Infrared Applications in Biotechnology'', Marcel-Dekker, New York, NY.</ref>
* [[Spectral imaging|Spectral]], [[Hyperspectral imaging|Hyperspectral]],  and [[Chemical imaging]])<ref>http://www.imaging.net/chemical-imaging/  Chemical imaging</ref><ref>http://www.malvern.com/LabEng/products/sdi/bibliography/sdi_bibliography.htm E. N. Lewis, E. Lee and L. H. Kidder, Combining Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical Imaging. Microscopy Today, Volume 12, No. 6, 11/2004.</ref><ref>D.S. Mantus and G. H. Morrison. 1991. Chemical imaging in biology and medicine using ion microscopy., ''Microchimica Acta'', '''104''', (1-6) January 1991, doi: 10.1007/BF01245536</ref><ref>Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High Resolution Nuclear Magnetic Resonance Analysis of Soybean  Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In ''Oil Extraction and Analysis.'', D. Luthria, Editor pp.241-273, AOCS Press., Champaign, IL.</ref><ref>Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban, [http://arxiv.org/abs/q-bio/0407006 q-bio/0407006 (July 2004)]</ref><ref>J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical Industry, G.I.T. Laboratory Journal Europe, No.1-2, 2007.</ref><ref>Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology.(June 2004).,I. C. Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin [http://arxiv.org/abs/q-bio/0406047 q-bio/0406047]</ref>.
* [[Raman]] spectroscopy/microscopy<ref>[http://witec.de/en/download/Raman/ImagingMicroscopy04.pdf  Chemical Imaging Without Dyeing]</ref> and [[CARS]]<ref>C.L. Evans and X.S. Xie.2008. Coherent Anti-Stokes Raman Scattering Microscopy: Chemical Imaging for Biology and Medicine., doi:10.1146/annurev.anchem.1.031207.112754 ''Annual Review of Analytical Chemistry'', '''1''': 883-909.</ref>.
* [[Fluorescence correlation spectroscopy]]<ref>Eigen, M., Rigler, M. Sorting single molecules: application to diagnostics and evolutionary biotechnology,(1994) ''Proc. Natl. Acad. Sci. USA'', 91,5740-5747.</ref><ref>Rigler, M. Fluorescence correlations, single molecule detection and large number screening. Applications in biotechnology,(1995) J. Biotechnol., 41,177-186.</ref><ref>Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation spectroscopy, ''BioScience'' (Ed. Klinge & Owman) p.180.</ref><ref>Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al., [http://arxiv.org/abs/q-bio/0407006 q-bio/0407006 (July 2004)]</ref><ref>Oehlenschläger F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid sequence-based amplification combined with fluorescence correlation spectroscopy, ''Proc. Natl. Acad. Sci. USA'' '''93''':1281.</ref><ref>Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in giant unilamellar vesicles of binary phospholipid mixtures. Biophys J., 78:290-305.</ref><ref>Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by fluorescence correlation spectroscopy with one- and two-photon excitation. Biophysical Journal, 77(10):2251-2265.</ref><ref>Near Infrared Microspectroscopy, Fluorescence Microspectroscopy,Infrared Chemical Imaging and High Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In ''Oil Extraction and Analysis.'', D. Luthria, Editor pp.241-273, AOCS Press., Champaign, IL.</ref>, [[Fluorescence cross-correlation spectroscopy]] and [[FRET]]<ref>[http://dwb.unl.edu/Teacher/NSF/C08/C08Links/pps99.cryst.bbk.ac.uk/projects/gmocz/fret.htm FRET description]</ref><ref>[http://dx.doi.org/10.1016/S0959-440X(00)00190-1 doi:10.1016/S0959-440X(00)00190-1]Recent advances in FRET: distance determination in protein–DNA complexes.  ''Current Opinion in Structural Biology'' '''2001''', ''11(2)'', 201-207 </ref><ref>http://www.fretimaging.org/mcnamaraintro.html FRET imaging introduction</ref>.
*[[Confocal microscopy]]<ref>Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics and evolutionary biotechnology, Proc. Natl. Acad. Sci. USA 91:5740.</ref>

===Gallery: CARS (Raman spectroscopy), Fluorescence confocal microscopy, and Hyperspectral imaging ===
<gallery>
File:Stokes shift.png
File:CARS Scheme.svg
File:HyperspectralCube.jpg
File:MultispectralComparedToHyperspectral.jpg
File:Confocalprinciple in English.svg
File:3D-SIM-1 NPC Confocal vs 3D-SIM detail.jpg
File:Tirfm.svg
File:Inverted microscope.jpg
File:Fluorescence microscop.jpg
File:Microscope And Digital Camera.JPG
File:FluorescenceFilters 2008-09-28.svg
File:FluorescentCells.jpg
File:Yeast membrane proteins.jpg

File:Dividing Cell Fluorescence.jpg
File:HeLa Hoechst 33258.jpg
File:FISH 13 21.jpg

File:Bloodcell sun flares pathology.jpeg
File:Carboxysome 3 images.png
</gallery>

===Genomic and structural databases===
* [http://www.cbs.dtu.dk/services/GenomeAtlas/ CBS Genome Atlas Database] &mdash; contains examples of base skews.<ref name="Hallin2004">{{cite journal |author=Hallin PF, David Ussery D |year=2004 |title=CBS Genome Atlas Database: A dynamic storage for bioinformatic results and DNA sequence data |journal=Bioinformatics |volume=20 |page=3682-3686}}</ref>
* [http://tubic.tju.edu.cn/zcurve/ The Z curve database of genomes &mdash; a 3-dimensional visualization and analysis tool of genomes]<ref>Zhang CT, Zhang R, Ou HY (2003). "The Z curve database: a graphic representation of genome sequences". Bioinformatics 19 (5): 593-599. doi:10.1093/bioinformatics/btg041</ref>.
* [http://ndbserver.rutgers.edu/ftp/NDB/models/ DNA and other nucleic acids' molecular models: Coordinate files of nucleic acids molecular structure models in PDB and CIF formats]

==Notes==
{{Reflist|2}}

==References==
* ''Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology''.(June 2004) I. C. Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin., q-bio/0406047.
* F. Bessel, ''Untersuchung des Theils der planetarischen Störungen'', Berlin Abhandlungen (1824), article 14.
* Sir Lawrence Bragg, FRS. ''The Crystalline State, A General survey.'' London: G. Bells and Sons, Ltd., vols. 1 and 2., 1966., 2024 pages.
* Cantor, C. R.  and Schimmel, P.R. ''Biophysical Chemistry, Parts I and II''., San Franscisco: W.H. Freeman and Co. 1980. 1,800 pages.
*Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics and evolutionary biotechnology, ''Proc. Natl. Acad. Sci. USA'' '''91''':5740.
* Raghavachari, R., Editor. 2001. ''Near-Infrared Applications in Biotechnology'', Marcel-Dekker, New York, NY.
* Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation spectroscopy, ''BioScience'' (Ed. Klinge & Owman) p.180. 
* Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and Fluorescence Microspectroscopy.2004. I. C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al., q-bio/0407006 (July 2004). 
* Voet, D. and J.G. Voet. ''Biochemistry'', 2nd Edn., New York, Toronto, Singapore: John Wiley & Sons, Inc., 1995, ISBN: 0-471-58651-X., 1361 pages.  
* Watson, G. N. ''A Treatise on the Theory of Bessel Functions''., (1995) Cambridge University Press. {{ISBN|0-521-48391-3}}. 
* Watson, James D. and Francis H.C. Crick. [http://www.nature.com/nature/dna50/watsoncrick.pdf A structure for Deoxyribose Nucleic Acid] (PDF). ''[[Nature (journal)|Nature]]'' 171, 737&ndash;738, 25 April 1953.
* Watson, James D. ''Molecular Biology of the Gene.'' New York and Amsterdam: W.A. Benjamin, Inc. 1965., 494 pages.
* Wentworth, W.E. ''Physical Chemistry. A short course.'', Malden (Mass.): Blackwell Science, Inc. 2000.
* Herbert R. Wilson, FRS. ''Diffraction of X-rays by proteins, Nucleic Acids and Viruses''., London: Edward Arnold (Publishers) Ltd. 1966.
* Kurt Wuthrich. ''NMR of Proteins and Nucleic Acids.'', New York, Brisbane,Chicester, Toronto, Singapore: J. Wiley & Sons. 1986., 292 pages.
*{{cite journal |last=Robinson |first=Bruche H. |authorlink= |coauthors=Seeman, Nadrian C. |year=1987 |month=August |title=The Design of a Biochip: A Self-Assembling Molecular-Scale Memory Device |journal=[[Protein Engineering (journal)|Protein Engineering]] |volume=1 |issue=4 |pages=295–300 |issn=0269-2139}} [http://peds.oxfordjournals.org/cgi/content/abstract/1/4/295 Link]
*{{cite journal |last=Rothemund |first=Paul W. K. |authorlink=Paul W. K. Rothemund |coauthors=Ekani-Nkodo, Axel; Papadakis, Nick; Kumar, Ashish; Fygenson, Deborah Kuchnir & Winfree, Erik |year=2004 |month=22 December|title=Design and Characterization of Programmable DNA Nanotubes |journal=[[Journal of the American Chemical Society]] |volume=126 |issue=50 |pages=16344–16352 |issn=0002-7863|doi=10.1021/ja044319l}}
*{{cite journal |coauthors = Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun | year = 2003 | month = November |  title = DNA-Templated Carbon Nanotube Field-Effect Transistor | journal = [[Science (journal)|Science]] |  volume = 302 | issue = 6549 | pages = 1380&ndash;1382 | issn = 1095-9203 |  doi = 10.1126/science.1091022 |  url = http://www.sciencemag.org/cgi/content/abstract/sci;302/5649/1380|author = Keren, K. }}
*{{cite journal |last=Zheng |first=Jiwen |authorlink= |coauthors=Constantinou, Pamela E.; Micheel, Christine; Alivisatos, A. Paul; Kiehl, Richard A. & Seeman Nadrian C. |year=2006 |title=2D Nanoparticle Arrays Show the Organizational Power of Robust DNA Motifs |journal=[[Nano Letters]] |volume=6 |issue= |pages=1502–1504 |issn=1530-6984|doi=10.1021/nl060994c}}
*{{cite journal |last=Cohen |first=Justin D. |authorlink= |coauthors=Sadowski, John P.; Dervan, Peter B. |year=2007 |title=Addressing Single Molecules on DNA Nanostructures |journal=[[Angewandte Chemie]] |volume=46 |issue=42 |pages=7956&ndash;7959 |issn=0570-0833|doi=10.1002/anie.200702767}}
*{{cite journal |last=Mao |first=Chengde |authorlink= |coauthors=Sun, Weiqiong & Seeman, Nadrian C. |year=1999 |month=16 June|title=Designed Two-Dimensional DNA Holliday Junction Arrays Visualized by Atomic Force Microscopy |journal=[[Journal of the American Chemical Society]] |volume=121 |issue=23 |pages=5437–5443 |issn=0002-7863|doi=10.1021/ja9900398}}
*{{cite journal |last=Constantinou |first=Pamela E. |authorlink= |coauthors=Wang, Tong; Kopatsch, Jens; Israel, Lisa B.; Zhang, Xiaoping; Ding, Baoquan; Sherman, William B.; Wang, Xing; Zheng, Jianping; Sha, Ruojie & Seeman, Nadrian C.|year=2006 |title=Double cohesion in structural DNA nanotechnology |journal=[[Organic and Biomolecular Chemistry]] |volume=4 |issue= |pages=3414–3419 |issn=|doi=10.1039/b605212f}}

==See also==
* [[DNA]]
* [[Molecular graphics]]
* [[DNA structure]]
* [[X-ray scattering]]
* [[Neutron scattering]]
* [[Crystallography]]
* [[Crystal lattice]]s
* [[Paracrystalline|Paracrystalline lattices/Paracrystals]]
* [[2D-FT NMRI and Spectroscopy]]
* [[NMR Spectroscopy]]
* [[Microwave spectroscopy]] 
* [[IR spectroscopy|Two-dimensional IR spectroscopy]]
* [[Spectral imaging]]
* [[Hyperspectral imaging]]
* [[Chemical imaging]]
* [[NMR imaging|NMR microscopy]]
* [[Vibrational circular dichroism|VCD or Vibrational circular dichroism]]
* [[Förster resonance energy transfer|FRET and FCS- Fluorescence correlation spectroscopy]]
* [[Fluorescence cross-correlation spectroscopy|Fluorescence cross-correlation spectroscopy (FCCS)]]
* [[Molecular geometry|Molecular structure]]
* [[Molecular geometry]]
* [[Molecular dynamics|Molecular topology]]
* [[DNA topology]]
* [[Nanostructure]]
* [[DNA nanotechnology]]
* [[Imaging]]
* [[Atomic force microscopy]]
* [[X-ray microscopy]]
* [[Liquid crystal]]
* [[Glass]]es
* [[QMC@Home]]
* Sir [[Lawrence Bragg]], FRS
* Sir [[John Randall]]
* [[James Watson]]
* [[Francis Crick]]
* [[Maurice Wilkins]]
* [[Herbert Wilson]], FRS
* [[Alex Stokes]]

==External links==
* [http://nobelprize.org/educational_games/medicine/dna_double_helix/ DNA the Double Helix Game] From the official Nobel Prize web site
*[http://humphry.chem.wesleyan.edu:8080/MDDNA/ MDDNA: Structural Bioinformatics of DNA]
* [http://www.ncbe.reading.ac.uk/DNA50/ Double Helix 1953&ndash;2003] National Centre for Biotechnology Education
* [http://www.fidelitysystems.com/Unlinked_DNA.html DNA under electron microscope]
*[http://www.agilemolecule.com/Ascalaph/Ascalaph_DNA.html Ascalaph DNA] &mdash; Commercial software for DNA modeling
*[http://mmb.pcb.ub.es/DNAlive DNAlive: a web interface to compute DNA physical properties]. Also allows cross-linking of the results with the UCSC [[Genome browser]] and DNA dynamics.
*[http://diprodb.fli-leibniz.de DiProDB: Dinucleotide Property Database]. The database is designed to collect and analyse thermodynamic, structural and other dinucleotide properties.
* [http://planetphysics.org/encyclopedia/BesselFunctionsApplicationsToDiffractionByHelicalStructures.html Further details of mathematical and molecular analysis of DNA structure based on X-ray data]
* [http://planetphysics.org/?op=getobj&from=objects&name=BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures Bessel functions corresponding to Fourier transforms of atomic or molecular helices.]
*[http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=12379938 Application of X-ray microscopy in analysis of living hydrated cells]
*[http://nanocharacterization.sitesled.com/ Characterization in nanotechnology some pdfs]
*[http://www.ntmdt.ru/SPM-Techniques/Principles/ overview of STM/AFM/SNOM principles with educative videos]
*[http://www.rhk-tech.com/results/showcase.php SPM Image Gallery - AFM STM SEM MFM NSOM and More]
*[http://www.parkafm.com/New_html/resources/01general.php How SPM Works]
* [http://www.genome.gov/10506367 U.S. National DNA Day] — watch videos and participate in real-time discusssions with scientists.
* [http://www.tjmitchell.com/stuart/dna.html The Secret Life of DNA - DNA Music compositions]



{{Nucleic acids}}
{{Commons category|Database}}
{{SPM2}}
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[[:Category:Diffraction]]
[[:Category:Molecular dynamics]]
[[:Category:Scattering]]
[[:Category:Quantum chemistry]]
[[:Category:Computational models]]
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[[:Category:Molecular genetics]]
[[:Category:Genomics]]
[[:Category:Genetics]]
[[:Category:Crystallography]] 
[[:Category:Spectroscopy]]
[[:Category:Quantum information science| ]]
[[:Category:Computational complexity theory|*]]
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[[:Category:Biophysicists]]


[[Image:QChipjpeg.jpg|thumb| The first reported quantum semiconductor chip (QSC) with trapped ions]]
==Projects==
* [[WP-Math]]

* [[WP:WikiProject Physics]]

* [[WPBiography]]

==Complex Systems Biology and Complexity Science==
The '''Complexity science field''' is the new science field about complexity, which treats complex systems as a field of [[science]]. This scientific field studies the common properties of [[system]]s that are considered fundamentally [[complexity|complex]]. Such systems may exist in [[nature]], [[society]], [[science]] and other many fields. It is also called ''complex systems theory'', ''complexity science'', ''study of complex systems'', ''sciences of complexity'', ''non-equilibrium physics'', and ''historical physics''.
The key problems of such systems are difficulties with their formal [[modeling]] and [[simulation]]. From such perspective, in different research contexts complex systems are defined on the base of their different attributes.
At present, the consensus related to one universal definition of ''[[complex system]]'' does not exist yet.

== Overview ==
[[Image:Braitenberg vehicle (simulation made with breve).jpg|thumb|right|210px|A Braitenberg simulation, programmed in [[breve (software)|breve]], an [[artificial life]] simulator.]] The study of complex systems is bringing a new approach to the many scientific questions that are a poor fit for the usual mechanistic view of reality present in science <ref>http://www.narberthpa.com/Bale/lsbale_dop/cybernet.htm Bale, L.S. 1995, ''Gregory Bateson, Cybernetics and the Social/Behavioral Sciences''</ref>. ''Complex systems'' is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines including [[anthropology]], [[artificial life]], [[chemistry]], [[computer science]], [[economics]], [[evolutionary computation]], [[earthquake]] prediction, [[meteorology]], [[molecular biology]], [[neuroscience]], [[physics]], [[psychology]] and [[sociology]].

In these endeavors, scientists often seek simple non-linear coupling rules which ''lead to'' complex phenomena (rather than describe - see above), but this need not be the case. Human societies (and probably human [[brains]]) are complex systems in which neither the components nor the couplings are simple. Nevertheless, they exhibit many of the hallmarks of complex systems. 
It is worth remarking that [[nonlinear system|non-linearity]] is not a necessary feature of complex systems modeling: macro-analyses that concern unstable equilibrium and evolution processes of certain biological/social/economic systems can usefully be carried out also by sets of linear equations, which do nevertheless entail reciprocal dependence between variable parameters.

Traditionally, engineering has striven to keep its systems linear, because that makes them simpler to build and to predict. However, many physical systems (for example [[lasers]]) are inherently "complex systems" in terms of the definition above, and engineering practice must now include elements of complex systems research.

[[Information theory]] applies well to the [[complex adaptive systems]], CAS, through the concepts of object oriented design, as well as through formalized concepts of organization and disorder that can be associated with any systems evolution process.

== History == 
Complex Systems is a new approach to science that studies how relationships between parts give rise to the collective behaviors of a [[system]] and how the system interacts and forms relationships with its environment.

The earliest precursor to modern complex systems theory can be found in the classical political economy of the [[Scottish Enlightenment]], later developed by the [[Austrian school of economics]], which says that order in market systems is spontaneous (or emergent) in that it is the result of human action, but not the execution of any human design.<ref>
{{cite book
  | last = [[Adam Ferguson|Ferguson]]
  | first = Adam
  | authorlink = 
  | coauthors = 
  | title = An Essay on the History of Civil Society
  | publisher = T. Cadell
  | date = 1767
  | location = London
  | pages = art Third, Section II, p. 205
  | url = http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=1428&Itemid=28
  | doi = 
  | id = 
  | isbn =
  | nopp = true }}</ref><ref>Friedrich Hayek, ''The Results of Human Action but Not of Human Design'', in ''New Studies in Philosophy, Politics, Economics'', Chicago: University of Chicago Press, (1978), pp. 96-105.</ref>

Upon this the Austrian school developed from the 19th to the early 20th century the [[economic calculation problem]], along with the concept of [[dispersed knowledge]], which were to fuel debates against the then-dominant [[Keynesian economics]]. This debate would notably lead economists, politicians and other parties to explore the question of [[Economic calculation problem#Computational complexity|computational complexity]].

A pioneer in the field, and inspired by [[Karl Popper]]'s and [[Warren Weaver]]'s works, Nobel prize economist and philosopher [[Friedrich Hayek]] dedicated much of his work, from early to the late 20th century, to the study of complex phenomena,<ref>Bruce J. Caldwell, Popper and Hayek: [http://www.unites.uqam.ca/philo/pdf/Caldwell_2003-01.pdf Who influenced whom?], Karl Popper 2002 Centenary Congress, 2002.</ref> not constraining his work to human economies but to other fields such as [[psychology]],<ref>Friedrich von Hayek, ''The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology'', The University of Chicago Press, 1952.</ref> [[biology]] and [[cybernetics]].

Further [[Steven Strogatz]] from ''Sync'' stated that "every decade or so, a grandiose theory comes along, bearing similar aspirations and often brandishing an ominous-sounding C-name. In the 1960s it was [[cybernetics]]. In the '70s it was [[catastrophe theory]]. Then came [[chaos theory]] in the '80s and complexity theory in the '90s."

== Topics in the complex systems study ==
=== Complexity and modeling ===
[[Image:Complex-adaptive-system.jpg|300px|right|thumb|A way of modelling a Complex Adaptive System]] One of Hayek's main contributions to early complexity theory is his distinction between the human capacity to predict the behaviour of simple systems and its capacity to predict the behaviour of complex systems through [[modeling]]. He believed that economics and the sciences of complex phenomena in general, which in his view included biology, psychology, and so on, could not be modeled after the sciences that deal with essentially simple phenomena like physics.<ref>[http://www.reason.com/news/show/33304.html Reason Magazine - The Road from Serfdom<!-- Bot generated title -->]</ref> Hayek would notably explain that complex phenomena, through modeling, can only allow pattern predictions, compared with the precise predictions that can be made out of non-complex phenomena.<ref>[http://nobelprize.org/nobel_prizes/economics/laureates/1974/hayek-lecture.html Friedrich August von Hayek - Prize Lecture<!-- Bot generated title -->]</ref>

=== Complexity and chaos theory ===
Complexity theory is rooted in [[Chaos theory]], which in turn has its origins more than a century ago in the work of the French mathematician [[Henri Poincaré]]. Chaos is sometimes viewed as extremely complicated information, rather than as an absence of order.<ref> Hayles, N. K. (1991). ''Chaos Bound: Orderly Disorder in Contemporary Literature and Science''. Cornell University Press, Ithaca, NY.</ref> The point is that chaos remains deterministic. With perfect knowledge of the initial conditions and of the context of an action, the course of this action can be predicted in chaos theory. As argued by [[Ilya Prigogine]],<ref> Prigogine, I. (1997). ''The End of Certainty'', The Free Press, New York.</ref> Complexity is non-deterministic, and gives no way whatsoever to predict the future. The emergence of complexity theory shows a domain between deterministic order and randomness which is complex.<ref name = "PC98"> Cilliers, P. (1998). ''Complexity and Postmodernism: Understanding Complex Systems'', Routledge, London. </ref> This is referred as the '[[edge of chaos]]'.<ref> [[Per Bak]] (1996). ''How Nature Works: The Science of Self-Organized Criticality'', Copernicus, New York, USA.</ref>

[[Image:Lorenz attractor yb.svg|thumb|left|200px|A plot of the [[Lorenz attractor]]]]
When one analyses complex systems, sensitivity to initial conditions, for example, is not an issue as important as within the chaos theory in which it prevails. As stated by Colander,<ref> Colander, D. (2000). ''The Complexity Vision and the Teaching of Economics'', E. Elgar, Northampton, MA. </ref> the study of complexity is the opposite of the study of chaos. Complexity is about how a huge number of extremely complicated and dynamic set of relationships can generate some simple behavioural patterns, whereas chaotic behaviour, in the sense of deterministic chaos, is the result of a relatively small number of non-linear interactions.<ref name = "PC98"/>

Therefore, the main difference between Chaotic systems and complex systems is their history.<ref> Buchanan, M.(2000). ''Ubiquity : Why catastrophes happen'', three river press, New-York. </ref> Chaotic systems don’t rely on their history as complex ones do. Chaotic behaviour pushes a system in equilibrium into chaotic order, which means, in other words, out of what we traditionally define as 'order'. On the other hand, complex systems evolve far from equilibrium at the edge of chaos. They evolve at a critical state built up by a history of irreversible and unexpected events. In a sense chaotic systems can be regarded as a subset of complex systems distinguished precisely by this absence of historical dependence. Many real complex systems are, in practice and over long but finite time periods, robust. However, they do possess the potential for radical qualitative change of kind whilst retaining systemic integrity. Metamorphosis serves as perhaps more than a metaphor for such transformations.

== Research centers, conferences, and journals ==
'''Institutes and research centers'''

* [[New England Complex Systems Institute]]
* [[Santa Fe Institute]]
* [http://csdc.asu.edu/ Center for Social Dynamics & Complexity (CSDC) at Arizona State University]
* Southampton [http://www.icss.soton.ac.uk Institute for Complex Systems Simulation]
* [http://www.cscs.umich.edu/ Center for the Study of Complex Systems at the University of Michigan]
* [http://www.ccs.fau.edu/ Center for Complex Systems and Brain Sciences at Florida Atlantic University]

'''Journals'''
* [[Complex Systems (journal)|Complex Systems]] journal
* [[Interdisciplinary Description of Complex Systems]] journal

== See also ==
{{Col-begin}}
{{Col-break}}
* [[Cognitive Science]]
* [[Complex adaptive system]]
* [[Complexity]]
* [[Complexity economics]]
* [[Dynamical system]]
* [[Dynamical systems theory]]
* [[Emergence]]
* [[Enterprise systems engineering]]
{{Col-break}}
{{Portal|Systems science}}
* [[Generative sciences]]
* [[Multi-agent system]]
* [[Nonlinearity]]
* [[Pattern oriented modeling]]
* [[Process architecture]]
* [[Systems theory]]
* [[Systems theory in anthropology]]
* [[Self organization]]
* [[Sociology and complexity science]]
{{col-end}}

==References==
{{Reflist}}

== Further reading ==
* L.A.N. Amaral and J.M. Ottino, [http://amaral.northwestern.edu/Publications/Papers/Amaral-2004-Eur.Phys.J.B-38-147.pdf ''Complex networks — augmenting the framework for the study of complex system''], 2004.
* [[Murray Gell-Mann]], [http://www.santafe.edu/~mgm/plectics.html ''Let's Call It Plectics''], 1995/96.
* Nigel Goldenfeld and Leo P. Kadanoff, [http://guava.physics.uiuc.edu/~nigel/articles/complexity.html ''Simple Lessons from Complexity''], 1999
* A. Gogolin, A. Nersesyan and A. Tsvelik, [http://www.cmth.bnl.gov/~tsvelik/theory.html ''Theory of strongly correlated systems ''], Cambridge University Press, 1999. 
* 
* Kelly, K. (1995). [http://www.kk.org/outofcontrol/contents.php ''Out of Control''], Perseus Books Group. 
* Graeme Donald Snooks, "A general theory of complex living systems: Exploring the demand side of dynamics", ''Complexity'', vol. 13, no. 6, July/August 2008.
* Sorin Solomon and Eran Shir, [http://www.europhysicsnews.org/index.php?option=article&access=standard&Itemid=129&url=/articles/epn/abs/2003/02/epn03204/epn03204.html ''Complexity; a science at 30''], 2003.

==External links==
* [http://www.openabm.org The Open Agent-Based Modeling Consortium]
* [http://www.complexity.ecs.soton.ac.uk/ Complexity Science Focus]

{{Wiktionary|complex systems}}

{{Systems}}

==Page categories==
[[:Category:WikiProject Mathematics|*]]
[http://en.wikipedia.org/wiki/User_talk:Bci2 Bci2]

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==Reference list==
{{Reflist}}
 <references/>
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