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Nucleic acid double helix

From Wikipedia, the free encyclopedia

"Double helix" redirects here. For other uses, see Double helix (disambiguation).
Two complementary regions of nucleic acid molecules will bind and form a double helical structure held together by base pairs.

In molecular biology, the term double helix[1] refers to the structure formed by double-stranded molecules of nucleic acids such as DNA. The double helical structure of a nucleic acid complex arises as a consequence of its secondary structure, and is a fundamental component in determining its tertiary structure. The structure was discovered by Rosalind Franklin and her student Raymond Gosling,[2] but the term "double helix" entered popular culture with the publication in 1968 of The Double Helix: A Personal Account of the Discovery of the Structure of DNA by James Watson.

The DNA double helix biopolymer of nucleic acid is held together by nucleotides which base pair together.[3] In B-DNA, the most common double helical structure found in nature, the double helix is right-handed with about 10–10.5 base pairs per turn.[4] The double helix structure of DNA contains a major groove and minor groove. In B-DNA the major groove is wider than the minor groove.[3] Given the difference in widths of the major groove and minor groove, many proteins which bind to B-DNA do so through the wider major groove.[5]

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  • DNA Structure and Replication: Crash Course Biology #10
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Transcription

It's just beautiful, isn't it? It's just mesmerizing. It's double hel-exciting! You really can tell, just by looking at it, how important and amazing it is. It's pretty much the most complicated molecule that exists, and potentially the most important one. It's so complex that we didn't even know for sure what it looked like until about 60 years ago. So multifariously awesome that if you took all of it from just one of our cells and untangled it, it would be taller than me. Now consider that there are probably 50 trillion cells in my body right now. Laid end to end, the DNA in those cells would stretch to the sun. Not once... but 600 times! Mind blown yet? Hey, you wanna make one? Of course you know I'm talking about deoxyribonucleic acid, known to its friends as DNA. DNA is what stores our genetic instructions -- the information that programs all of our cell's activities. It's a 6-billion letter code that provides the assembly instructions for everything that you are. And it does the same thing for pretty much every other living thing. I'm going to go out on a limb and assume you're human. In which case every body cell, or somatic cell, in you right now, has 46 chromosomes each containing one big DNA molecule. These chromosomes are packed together tightly with proteins in the nucleus of the cell. DNA is a nucleic acid. And so is its cousin, which we'll also be talking about, ribonucleic acid, or RNA. Now if you can make your mind do this, remember all the way back to episode 3, where we talked about all the important biological molecules: carbohydrates, lipids and proteins. That ring a bell? Well nucleic acids are the fourth major group of biological molecules, and for my money they have the most complicated job of all. Structurally they're polymers, which means that each one is made up of many small, repeating molecular units. In DNA, these small units are called nucleotides. Link them together and you have yourself a polynucleotide. Now before we actually put these tiny parts together to build a DNA molecule like some microscopic piece of Ikea furniture, let's first take a look at what makes up each nucleotide. We're gonna need three things: 1. A five-carbon sugar molecule 2. A phosphate group 3. One of four nitrogen bases DNA gets the first part its name from our first ingredient, the sugar molecule, which is called deoxyribose. But all the really significant stuff, the genetic coding that makes you YOU, is found among the four nitrogenous bases: adenine (A), thymine (T), cytosine (C) and guanine (G). It's important to note that in living organisms, DNA doesn't exist as a single polynucleotide molecule, but rather a pair of molecules that are held tightly together. They're like an intertwined, microscopic, double spiral staircase. Basically, just a ladder, but twisted. The famous Double Helix. And like any good structure, we have to have a main support. In DNA, the sugars and phosphates bond together to form twin backbones. These sugar-phosphate bonds run down each side of the helix but, chemically, in opposite directions. In other words, if you look at each of the sugar-phosphate backbones, you'll see that one appears upside-down in relation to the other. One strand begins at the top with the first phosphate connected to the sugar molecule's 5th carbon and then ending where the next phosphate would go, with a free end at the sugar's 3rd carbon. This creates a pattern called 5' (5 prime) and 3' (3 prime). I've always thought of the deoxyribose with an arrow, with the oxygen as the point. It always 'points' from from 3' to 5'. Now on the other strand, it's exactly the opposite. It begins up top with a free end at the sugar's 3rd carbon and the phosphates connect to the sugars' fifth carbons all the way down. And it ends at the bottom with a phosphate. And you've probably figured this out already, but this is called the 3' to 5' direction. Now it is time to make ourselves one of these famous double helices. These two long chains are linked by the nitrogenous bases via relatively weak hydrogen bonds. But they can't be just any pair of nitrogenous bases. Thankfully, when it comes to figuring out what part goes where, all you have to do is remember is that if one nucleotide has an adenine base (A), only thymine (T) can be its counterpart (A-T). Likewise, guanine (G) can only bond with cytosine [C] (G-C). These bonded nitrogenous bases are called base pairs. The G-C pairing has three hydrogen bonds, making it slightly stronger than the A-T base-pair, which only has two bonds. It's the order of these four nucleobases or the Base Sequence that allows your DNA to create you. So, AGGTCCATG means something completely different as a base sequence than, say, TTCAGTCG. Human chromosome 1, the largest of all our chromosomes, contains a single molecule of DNA with 247 million base pairs. If you printed all of the letters of chromosome 1 into a book, it would be about 200,000 pages long. And each of your somatic cells has 46 DNA molecules tightly packed into its nucleus -- that's one for each of your chromosomes. Put all 46 molecules together and we're talking about roughly 6 billion base pairs .... In every cell! This is the longest book I've ever read. It's about 1,000 pages long. If we were to fill it with our DNA sequence, we'd need about 10,000 of them to fit our entire genome. POP QUIZ!!! Let's test your skills using a very short strand of DNA. I'll give you one base sequence -- you give me the base sequence that appears on the other strand. Okay, here goes: 5' -- AGGTCCG -- 3' And... time's up. The answer is: 3' -- TCCAGGC -- 5' See how that works? It's not super complicated. Since each nitrogenous base only has one counterpart, you can use one base sequence to predict what its matching sequence is going to look like. So could I make the same base sequence with a strand of that "other" nucleic acid, RNA? No, you could not. RNA is certainly similar to its cousin DNA -- it has a sugar-phosphate backbone with nucleotide bases attached to it. But there are THREE major differences: 1. RNA is a single-stranded molecule -- no double helix here. 2. The sugar in RNA is ribose, which has one more oxygen atom than deoxyribose, hence the whole starting with an R instead of a D thing. 3. Also, RNA does not contain thymine. Its fourth nucleotide is the base uracil, so it bonds with adenine instead. RNA is super important in the production of our proteins, and you'll see later that it has a crucial role in the replication of DNA. But first... Biolo-graphies! Yes, plural this week! Because when you start talking about something as multitudinously awesome and elegant as DNA, you have to wonder: WHO figured all of this out? And how big was their brain? Well unsurprisingly, it actually took a lot of different brains, in a lot of different countries and nearly a hundred years of thinking to do it. The names you usually hear when someone asks who discovered DNA are James Watson and Francis Crick. But that's BUNK. They did not discover DNA. Nor did they discover that DNA contained genetic information. DNA itself was discovered in 1869 by a Swiss biologist named Friedrich Miescher. His deal was studying white blood cells. And he got those white blood cells in the most horrible way you could possibly imagine, from collecting used bandages from a nearby hospital. It's for science he did it! He bathed the cells in warm alcohol to remove the lipids, then he set enzymes loose on them to digest the proteins. What was left, after all that, was snotty gray stuff that he knew must be some new kind of biological substance. He called it nuclein, but was later to become known as nucleic acid. But Miescher didn't know what its role was or what it looked like. One of those scientists who helped figure that out was Rosalind Franklin, a young biophysicist in London nearly a hundred years later. Using a technique called x-ray diffraction, Franklin may have been the first to confirm the helical structure of DNA. She also figured out that the sugar-phosphate backbone existed on the outside of its structure. So why is Rosalind Franklin not exactly a household name? Two reasons: 1. Unlike Watson & Crick, Franklin was happy to share data with her rivals. It was Franklin who informed Watson & Crick that an earlier theory of a triple-helix structure was not possible, and in doing so she indicated that DNA may indeed be a double helix. Later, her images confirming the helical structure of DNA were shown to Watson without her knowledge. Her work was eventually published in Nature, but not until after two papers by Watson and Crick had already appeared in which the duo only hinted at her contribution. 2. Even worse than that, the Nobel Prize Committee couldn't even consider her for the prize that they awarded in 1962 because of how dead she was. The really tragic thing is that it's totally possible that her scientific work may have led to her early death of ovarian cancer at the age of 37. At the time, the X-Ray diffraction technology that she was using to photograph DNA required dangerous amounts of radiation exposure, and Franklin rarely took precautions to protect herself. Nobel Prizes cannot be awarded posthumously. Many believe she would have shared Watson and Crick's medal if she had been alive to receive it. Now that we know the basics of DNA's structure, we need to understand how it copies itself, because cells are constantly dividing, and that requires a complete copy of all of that DNA information. It turns out that our cells are extremely good at this -- our cells can create the equivalent 10,000 copies of this book in just a few hours. That, my friends, is called replication. Every cell in your body has a copy of the same DNA. It started from an original copy and it will copy itself trillions of times over the course of a lifetime, each time using half of the original DNA strand as a template to build a new molecule. So, how is a teenage boy like the enzyme Helicase? They both want to unzip your genes. Helicase is marvelous, unwinding the double helix at breakneck speeds, slicing open those loose hydrogen bonds between the base pairs. The point where the splitting starts is known as the replication fork, has a top strand, called the leading strand, or the good guy strand as I call it and another bottom strand called the lagging strand, which I like to call the scumbag strand, because it is a pain in the butt to deal with. These unwound sections can now be used as templates to create two complementary DNA strands. But remember the two strands go in opposite directions, in terms of their chemical structure, which means making a new DNA strand for the leading strand is going to be much easier for the lagging strand. For the leading, good guy, strand an enzyme called DNA polymerase just adds matching nucleotides onto the main stem all the way down the molecule. But before it can do that it needs a section of nucleotides that fill in the section that's just been unzipped. Starting at the very beginning of the DNA molecule, DNA polymerase needs a bit of a primer, just a little thing for it to hook on to so that it can start building the new DNA chain. And for that little primer, we can thank the enzyme RNA primase. The leading strand only needs this RNA primer once at the very beginning. Then DNA polymerase is all, "I got this" and just follows the unzipping, adding new nucleotides to the new chain continuously, all the way down the molecule. Copying the lagging, or scumbag strand, is, well, he's a freaking scumbag. This is because DNA polymerase can only copy strands in the 5' -- 3' direction, and the lagging strand is 3' -- 5', so DNA polymerase can only add new nucleotides to the free, 3' end of a primer. So maybe the real scumbag here is the DNA polymerase. Since the lagging strand runs in the opposite direction, it has to be copied as a series of segments. Here that awesome little enzyme RNA Primase does its thing again, laying down an occasional short little RNA primer that gives the DNA Polymerase a starting point to then work backwards along the strand. This is done in a ton of individual segments, each 1,000 to 2,000 base pairs long and each starting with an RNA primer, called Okazaki fragments after the couple of married scientists who discovered this step of the process in the 1960s. And thank goodness they were married so we can just call them Okazaki fragments instead of Okazaki-someone's-someone fragments. These allow the strands to be synthesized in short bursts. Then another kind of DNA Polymerase has to go back over and replace all those RNA Primers and THEN all of the little fragments get joined up by a final enzyme called DNA Ligase. And that is why I say the lagging strand is such a scumbag! DNA replication gets it wrong about one in every 10 billion nucleotides. But don't think your body doesn't have an app for that! It turns out DNA polymerases can also proofread, in a sense, removing nucleotides from the end of a strand when they discover a mismatched base. Because the last thing we want is an A when it would have been a G! Considering how tightly packed DNA is into each one of our cells, it's honestly amazing that more mistakes don't happen. Remember, we're talking about millions of miles worth of this stuff inside us. And this, my friends, is why scientists are not exaggerating when they call DNA the most celebrated molecule of all time. So, you might as well look this episode over a couple of times and appreciate it for yourself. And in the mean time, gear up for next week, when we're going to talk about how those six feet of kick-ass actually makes you, you. Thank you to all the people here at Crash Course who helped make this episode awesome. You can click on any of these things to go back to that section of the video. If you have any questions, please, of course, ask them in the comments or on Facebook or Twitter.

History

Further information: History of molecular biology

The double-helix model of DNA structure was first published in the journal Nature by James Watson and Francis Crick in 1953,[6] (X,Y,Z coordinates in 1954[7]) based on the work of Rosalind Franklin and her student Raymond Gosling, who took the crucial X-ray diffraction image of DNA labeled as "Photo 51",[8][9] and Maurice Wilkins, Alexander Stokes, and Herbert Wilson,[10] and base-pairing chemical and biochemical information by Erwin Chargaff.[11][12][13][14][15][16] Before this, Linus Pauling—who had already accurately characterised the conformation of protein secondary structure motifs—and his collaborator Robert Corey had posited, erroneously, that DNA would adopt a triple-stranded conformation.[17]

The realization that the structure of DNA is that of a double-helix elucidated the mechanism of base pairing by which genetic information is stored and copied in living organisms and is widely considered one of the most important scientific discoveries of the 20th century. Crick, Wilkins, and Watson each received one-third of the 1962 Nobel Prize in Physiology or Medicine for their contributions to the discovery.[18]

Nucleic acid hybridization

Main article: Nucleic acid thermodynamics

Hybridization is the process of complementary base pairs binding to form a double helix. Melting is the process by which the interactions between the strands of the double helix are broken, separating the two nucleic acid strands. These bonds are weak, easily separated by gentle heating, enzymes, or mechanical force. Melting occurs preferentially at certain points in the nucleic acid.[19] T and A rich regions are more easily melted than C and G rich regions. Some base steps (pairs) are also susceptible to DNA melting, such as T A and T G.[20] These mechanical features are reflected by the use of sequences such as TATA at the start of many genes to assist RNA polymerase in melting the DNA for transcription.

Strand separation by gentle heating, as used in polymerase chain reaction (PCR), is simple, providing the molecules have fewer than about 10,000 base pairs (10 kilobase pairs, or 10 kbp). The intertwining of the DNA strands makes long segments difficult to separate.[21] The cell avoids this problem by allowing its DNA-melting enzymes (helicases) to work concurrently with topoisomerases, which can chemically cleave the phosphate backbone of one of the strands so that it can swivel around the other.[22] Helicases unwind the strands to facilitate the advance of sequence-reading enzymes such as DNA polymerase.[23]

Base pair geometry

Base pair geometries

The geometry of a base, or base pair step can be characterized by 6 coordinates: shift, slide, rise, tilt, roll, and twist. These values precisely define the location and orientation in space of every base or base pair in a nucleic acid molecule relative to its predecessor along the axis of the helix. Together, they characterize the helical structure of the molecule. In regions of DNA or RNA where the normal structure is disrupted, the change in these values can be used to describe such disruption.

For each base pair, considered relative to its predecessor, there are the following base pair geometries to consider:[24][25][26]

  • Shear
  • Stretch
  • Stagger
  • Buckle
  • Propeller: rotation of one base with respect to the other in the same base pair.
  • Opening
  • Shift: displacement along an axis in the base-pair plane perpendicular to the first, directed from the minor to the major groove.
  • Slide: displacement along an axis in the plane of the base pair directed from one strand to the other.
  • Rise: displacement along the helix axis.
  • Tilt: rotation around the shift axis.
  • Roll: rotation around the slide axis.
  • Twist: rotation around the rise axis.
  • x-displacement
  • y-displacement
  • inclination
  • tip
  • pitch: the height per complete turn of the helix.

Rise and twist determine the handedness and pitch of the helix. The other coordinates, by contrast, can be zero. Slide and shift are typically small in B-DNA, but are substantial in A- and Z-DNA. Roll and tilt make successive base pairs less parallel, and are typically small.

"Tilt" has often been used differently in the scientific literature, referring to the deviation of the first, inter-strand base-pair axis from perpendicularity to the helix axis. This corresponds to slide between a succession of base pairs, and in helix-based coordinates is properly termed "inclination".

Helix geometries

At least three DNA conformations are believed to be found in nature, A-DNA, B-DNA, and Z-DNA. The B form described by James Watson and Francis Crick is believed to predominate in cells.[27] It is 23.7 Å wide and extends 34 Å per 10 bp of sequence. The double helix makes one complete turn about its axis every 10.4–10.5 base pairs in solution. This frequency of twist (termed the helical pitch) depends largely on stacking forces that each base exerts on its neighbours in the chain. The absolute configuration of the bases determines the direction of the helical curve for a given conformation.

A-DNA and Z-DNA differ significantly in their geometry and dimensions to B-DNA, although still form helical structures. It was long thought that the A form only occurs in dehydrated samples of DNA in the laboratory, such as those used in crystallographic experiments, and in hybrid pairings of DNA and RNA strands, but DNA dehydration does occur in vivo, and A-DNA is now known to have biological functions. Segments of DNA that cells have methylated for regulatory purposes may adopt the Z geometry, in which the strands turn about the helical axis the opposite way to A-DNA and B-DNA. There is also evidence of protein-DNA complexes forming Z-DNA structures.

See also: Nucleic acid tertiary structure

Other conformations are possible; A-DNA, B-DNA, C-DNA, E-DNA,[28] L-DNA (the enantiomeric form of D-DNA),[29] P-DNA,[30] S-DNA, Z-DNA, etc. have been described so far.[31] In fact, only the letters F, Q, U, V, and Y are now available to describe any new DNA structure that may appear in the future.[32][33] However, most of these forms have been created synthetically and have not been observed in naturally occurring biological systems.[citation needed] There are also triple-stranded DNA forms and quadruplex forms such as the G-quadruplex and the i-motif.

The structures of A-, B-, and Z-DNA.
The helix axis of A-, B-, and Z-DNA.
Structural features of the three major forms of DNA[34][35][36]
Geometry attribute A-DNA B-DNA Z-DNA
Helix sense right-handed right-handed left-handed
Repeating unit 1 bp 1 bp 2 bp
Rotation/bp 32.7° 34.3° 60°/2
bp/turn 11 10.5 12
Inclination of bp to axis +19° −1.2° −9°
Rise/bp along axis 2.3 Å (0.23 nm) 3.32 Å (0.332 nm) 3.8 Å (0.38 nm)
Pitch/turn of helix 28.2 Å (2.82 nm) 33.2 Å (3.32 nm) 45.6 Å (4.56 nm)
Mean propeller twist +18° +16° 0°
Glycosyl angle anti anti C: anti,
G: syn
Sugar pucker C3'-endo C2'-endo C: C2'-endo,
G: C2'-exo
Diameter 23 Å (2.3 nm) 20 Å (2.0 nm) 18 Å (1.8 nm)

Grooves

Major and minor grooves of DNA. Minor groove is a binding site for the dye Hoechst 33258.

Twin helical strands form the DNA backbone. Another double helix may be found by tracing the spaces, or grooves, between the strands. These voids are adjacent to the base pairs and may provide a binding site.[37] As the strands are not directly opposite each other, the grooves are unequally sized. One groove, the major groove, is 22 Å wide and the other, the minor groove, is 12 Å wide.[38] 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 factors that can bind to specific sequences in double-stranded DNA usually make contacts to the sides of the bases exposed in the major groove.[5] 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.[39]

Non-double helical forms

Alternative non-helical models were briefly considered in the late 1970s as a potential solution to problems in DNA replication in plasmids and chromatin. However, the models were set aside in favor of the double-helical model due to subsequent experimental advances such as X-ray crystallography of DNA duplexes and later the nucleosome core particle, and the discovery of topoisomerases. Also, the non-double-helical models are not currently accepted by the mainstream scientific community.[40][41]

Bending

DNA is a relatively rigid polymer, typically modelled as a worm-like chain. It has three significant degrees of freedom; bending, twisting, and compression, each of which cause certain limits on what is possible with DNA within a cell. Twisting-torsional stiffness is important for the circularisation of DNA and the orientation of DNA bound proteins relative to each other and bending-axial stiffness is important for DNA wrapping and circularisation and protein interactions. Compression-extension is relatively unimportant in the absence of high tension.

Persistence length, axial stiffness

Main article: Persistence length
Example sequences and their persistence lengths (B DNA)[citation needed]
Sequence Persistence length
/ base pairs
Random 154±10
(CA)repeat 133±10
(CAG)repeat 124±10
(TATA)repeat 137±10

DNA in solution does not take a rigid structure but is continually changing conformation due to thermal vibration and collisions with water molecules, which makes classical measures of rigidity impossible to apply. Hence, the bending stiffness of DNA is measured by the persistence length, defined as:

Bending flexibility of a polymer is conventionally quantified in terms of its persistence length, Lp, a length scale below which the polymer behaves more or less like a rigid rod. Specifically, Lp is defined as length of the polymer segment over which the time-averaged orientation of the polymer becomes uncorrelated...[42]

This value may be directly measured using an atomic force microscope to directly image DNA molecules of various lengths. In an aqueous solution, the average persistence length is 46–50 nm or 140–150 base pairs (the diameter of DNA is 2 nm), although can vary significantly. This makes DNA a moderately stiff molecule.

The persistence length of a section of DNA is somewhat dependent on its sequence, and this can cause significant variation. The variation is largely due to base stacking energies and the residues which extend into the minor and major grooves.

Models for DNA bending

Stacking stability of base steps (B DNA)[43]
Step Stacking ΔG
/kcal mol−1
T A -0.19
T G or C A -0.55
C G -0.91
A G or C T -1.06
A A or T T -1.11
A T -1.34
G A or T C -1.43
C C or G G -1.44
A C or G T -1.81
G C -2.17

At length-scales larger than the persistence length, the entropic flexibility of DNA is remarkably consistent with standard polymer physics models, such as the Kratky-Porod worm-like chain model.[44] Consistent with the worm-like chain model is the observation that bending DNA is also described by Hooke's law at very small (sub-piconewton) forces. For DNA segments less than the persistence length, the bending force is approximately constant and behaviour deviates from the worm-like chain predictions.

This effect results in unusual ease in circularising small DNA molecules and a higher probability of finding highly bent sections of DNA.[45]

Bending preference

DNA molecules often have a preferred direction to bend, i.e., anisotropic bending. This is, again, due to the properties of the bases which make up the DNA sequence - a random sequence will have no preferred bend direction, i.e., isotropic bending.

Preferred DNA bend direction is determined by the stability of stacking each base on top of the next. If unstable base stacking steps are always found on one side of the DNA helix then the DNA will preferentially bend away from that direction. As bend angle increases then steric hindrances and ability to roll the residues relative to each other also play a role, especially in the minor groove. A and T residues will be preferentially be found in the minor grooves on the inside of bends. This effect is particularly seen in DNA-protein binding where tight DNA bending is induced, such as in nucleosome particles. See base step distortions above.

DNA molecules with exceptional bending preference can become intrinsically bent. This was first observed in trypanosomatid kinetoplast DNA. Typical sequences which cause this contain stretches of 4-6 T and A residues separated by G and C rich sections which keep the A and T residues in phase with the minor groove on one side of the molecule. For example:

¦ ¦ ¦ ¦ ¦ ¦
G A T T C C C A A A A A T G T C A A A A A A T A G G C A A A A A A T G C C A A A A A A T C C C A A A C

The intrinsically bent structure is induced by the 'propeller twist' of base pairs relative to each other allowing unusual bifurcated Hydrogen-bonds between base steps. At higher temperatures this structure is denatured, and so the intrinsic bend is lost.

All DNA which bends anisotropically has, on average, a longer persistence length and greater axial stiffness. This increased rigidity is required to prevent random bending which would make the molecule act isotropically.

Circularization

DNA circularization depends on both the axial (bending) stiffness and torsional (rotational) stiffness of the molecule. For a DNA molecule to successfully circularize it must be long enough to easily bend into the full circle and must have the correct number of bases so the ends are in the correct rotation to allow bonding to occur. The optimum length for circularization of DNA is around 400 base pairs (136 nm)[citation needed], with an integral number of turns of the DNA helix, i.e., multiples of 10.4 base pairs. Having a non integral number of turns presents a significant energy barrier for circularization, for example a 10.4 x 30 = 312 base pair molecule will circularize hundreds of times faster than 10.4 x 30.5 ≈ 317 base pair molecule.[46]

The bending of short circularized DNA segments is non-uniform. Rather, for circularized DNA segments less than the persistence length, DNA bending is localised to 1-2 kinks that form preferentially in AT-rich segments. If a nick is present, bending will be localised to the nick site.[45]

Stretching

Elastic stretching regime

Longer stretches of DNA are entropically elastic under tension. When DNA is in solution, it undergoes continuous structural variations due to the energy available in the thermal bath of the solvent. This is due to the thermal vibration of the molecule combined with continual collisions with water molecules. For entropic reasons, more compact relaxed states are thermally accessible than stretched out states, and so DNA molecules are almost universally found in a tangled relaxed layouts. For this reason, one molecule of DNA will stretch under a force, straightening it out. Using optical tweezers, the entropic stretching behavior of DNA has been studied and analyzed from a polymer physics perspective, and it has been found that DNA behaves largely like the Kratky-Porod worm-like chain model under physiologically accessible energy scales.

Phase transitions under stretching

Under sufficient tension and positive torque, DNA is thought to undergo a phase transition with the bases splaying outwards and the phosphates moving to the middle. This proposed structure for overstretched DNA has been called P-form DNA, in honor of Linus Pauling who originally presented it as a possible structure of DNA.[30]

Evidence from mechanical stretching of DNA in the absence of imposed torque points to a transition or transitions leading to further structures which are generally referred to as S-form DNA. These structures have not yet been definitively characterised due to the difficulty of carrying out atomic-resolution imaging in solution while under applied force although many computer simulation studies have been made (for example,[47][48]).

Proposed S-DNA structures include those which preserve base-pair stacking and hydrogen bonding (GC-rich), while releasing extension by tilting, as well as structures in which partial melting of the base-stack takes place, while base-base association is nonetheless overall preserved (AT-rich).

Periodic fracture of the base-pair stack with a break occurring once per three bp (therefore one out of every three bp-bp steps) has been proposed as a regular structure which preserves planarity of the base-stacking and releases the appropriate amount of extension,[49] with the term "Σ-DNA" introduced as a mnemonic, with the three right-facing points of the Sigma character serving as a reminder of the three grouped base pairs. The Σ form has been shown to have a sequence preference for GNC motifs which are believed under the GNC hypothesis to be of evolutionary importance.[50]

Supercoiling and topology

Main article: DNA supercoil
Supercoiled structure of circular DNA molecules with low writhe. The helical aspect of the DNA duplex is omitted for clarity.

The B form of the DNA helix twists 360° per 10.4-10.5 bp in the absence of torsional strain. But many molecular biological processes can induce torsional strain. A DNA segment with excess or insufficient helical twisting is referred to, respectively, as positively or negatively supercoiled. DNA in vivo is typically negatively supercoiled, which facilitates the unwinding (melting) of the double-helix required for RNA transcription.

Within the cell most DNA is topologically restricted. DNA is typically found in closed loops (such as plasmids in prokaryotes) which are topologically closed, or as very long molecules whose diffusion coefficients produce effectively topologically closed domains. Linear sections of DNA are also commonly bound to proteins or physical structures (such as membranes) to form closed topological loops.

Francis Crick was one of the first to propose the importance of linking numbers when considering DNA supercoils. In a paper published in 1976, Crick outlined the problem as follows:

In considering supercoils formed by closed double-stranded molecules of DNA certain mathematical concepts, such as the linking number and the twist, are needed. The meaning of these for a closed ribbon is explained and also that of the writhing number of a closed curve. Some simple examples are given, some of which may be relevant to the structure of chromatin.[51]

Analysis of DNA topology uses three values:

  • L = linking number - the number of times one DNA strand wraps around the other. It is an integer for a closed loop and constant for a closed topological domain.
  • T = twist - total number of turns in the double stranded DNA helix. This will normally tend to approach the number of turns that a topologically open double stranded DNA helix makes free in solution: number of bases/10.5, assuming there are no intercalating agents (e.g., ethidium bromide) or other elements modifying the stiffness of the DNA.
  • W = writhe - number of turns of the double stranded DNA helix around the superhelical axis
  • L = T + W and ΔL = ΔT + ΔW

Any change of T in a closed topological domain must be balanced by a change in W, and vice versa. This results in higher order structure of DNA. A circular DNA molecule with a writhe of 0 will be circular. If the twist of this molecule is subsequently increased or decreased by supercoiling then the writhe will be appropriately altered, making the molecule undergo plectonemic or toroidal superhelical coiling.

When the ends of a piece of double stranded helical DNA are joined so that it forms a circle the strands are topologically knotted. This means the single strands cannot be separated any process that does not involve breaking a strand (such as heating). The task of un-knotting topologically linked strands of DNA falls to enzymes termed topoisomerases. These enzymes are dedicated to un-knotting circular DNA by cleaving one or both strands so that another double or single stranded segment can pass through. This un-knotting is required for the replication of circular DNA and various types of recombination in linear DNA which have similar topological constraints.

The linking number paradox

For many years, the origin of residual supercoiling in eukaryotic genomes remained unclear. This topological puzzle was referred to by some as the "linking number paradox".[52] However, when experimentally determined structures of the nucleosome displayed an over-twisted left-handed wrap of DNA around the histone octamer,[53][54] this paradox was considered to be solved by the scientific community.

See also

Wikimedia Commons has media related to DNA helix-structures.

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