Mechanical properties of DNA
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The mechanical properties of DNA, which are directly related to its structure, are a significant problem for cells. Every process which binds or reads DNA is able to use or modify the mechanical properties of DNA for purposes of recognition, packaging and modification. The extreme length, relative rigidity and helical structure of DNA has lead to the evolution of histones and of enzymes such as topoisomerases and helicases to manage a cell's DNA. The properties of DNA are closely related to its molecular structure and sequence, particularly the weakness of the hydrogen bonds and electronic interactions that hold strands of DNA together compared to the strength of the bonds within each strand.
Experimental techniques which can directly measure the mechanical properties of DNA are relatively new, the narrow breadth of the double helix makes it impossible to detect by conventional electron microscopy, except by heavy staining. As such, understanding of the implications of DNA's mechanical properties on cellular processes is still limited.
It is important to note the DNA found in many cells can be macroscopic in length - approximately 5 (<23) centimetres long for each human chromosome. Consequently, cells must compact or "package" DNA to carry it within them. In eukaryotes this is carried by spool-like proteins known as histones, around which DNA winds. It is the further compaction of this DNA-protein complex which produces the well known mitotic eukaryotic chromosomes.
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[edit] Base pair geometry
The geometry of a base pair can be entirely characterised by 6 coordinates: rise, twist, slide, shift, tilt, and roll. These values precisely define the location and orientation in space of each base pair in a DNA molecule relative to its predecessor along the axis of the helix. Together, they characterise the helical structure of the molecule. In regions of a DNA molecule where the normal structure is disrupted these values are used to describe the disruption.
For each base pair, considered relative to its predecessor:
- Rise is displacement along the helix axis.
- Twist is rotation around the helix axis.
- Slide is displacement along an axis in the plane of the base pair directed from one strand to the other.
- Roll is rotation around this axis.
- Shift is displacement along an axis in the base-pair plane perpendicular to the first, directed from the minor to the major groove.
- Tilt is rotation around this axis.
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. A diagram of these coordinates can be found in 3DNA website.
Note that "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".
[edit] DNA helix geometries
Three DNA conformations are believed to be found in nature, A-DNA, B-DNA, and Z-DNA. The "B" form described by James D. Watson and Francis Crick is believed to predominate in cells, although this is not certain[citation needed]. 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 (known as the helical pitch) depends largely on stacking forces that each base exerts on its neighbours in the chain.
Other possible conformations are possible; A-DNA, B-DNA, C-DNA, D-DNA, E-DNA[1], P-DNA, and Z-DNA have been identified. As mentioned above C-DNA, D-DNA, E-DNA, and P-DNA are not thought to be found in nature.
[edit] A- and Z-DNA
A-DNA and Z-DNA differ significantly in their geometry and dimensions to B-DNA, although still form helical structures. The A form appears likely to occur only in dehydrated samples of DNA, such as those used in crystallographic experiments, and possibly in hybrid pairings of DNA and RNA strands. 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.
| 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 | 33.6° | 35.9° | 60°/2bp |
| Mean bp/turn | 10.7 | 10.0 | 12 |
| Inclination of bp to axis | +19° | -1.2° | -9° |
| Rise/bp along axis | 23 Å | 33.2 Å | 38 Å |
| Pitch/turn of helix | 24.6 Å | 33.2 Å | 45.6 Å |
| 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 | 25.5 Å | 23.7 Å | 18.4 Å |
[edit] Supercoiled DNA
- See also: DNA supercoil and Mechanical properties of DNA#DNA topology
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.
[edit] Non-helical forms
Other non-double helical forms of DNA have been described, for example side-by-side (SBS) and triple helical configurations. [[[ssDNA]]|Single stranded DNA] may exist 'in statu nascendi' or as thermaly induced despiralized DNA.
[edit] DNA 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 particular limitations 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.
[edit] Persistence length/Axial stiffness
| 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. Hence, the bending stiffness of DNA is measured by the persistence length, defined as:
- "The length at which the time-averaged angle made between the two ends of a DNA molecule is equal to one radian."
This value may be directly measured using an atomic force microscope to directly image DNA molecules of various lengths. In aqueous solution the average persistence length is 46-50nm or 140-150 base pairs (the diameter of DNA is 2nm), although can vary significantly. This makes DNA a moderately stiff molecule.
The persistence length of a section of DNA is 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.
[edit] Models for DNA bending
DNA may be analysed by standard polymer physics models such as the Kratky-Porod worm-like chain model, however the applicability of these models is limited. At larger scales (i.e. for longer lengths or smaller forces) DNA obeys hookes law, elastic restoring force is proportional to degree of bending and fits the worm-like chain. However at small scales, for example at less than the persistence length, the elastic force is approximately constant and behaviour no longer fits the model.
This effect results in unusual ease in circularising small DNA molecules and a higher probability of finding highly bent sections of DNA.
[edit] Bending preference
| 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 |
DNA molecules often have a preferred direction to bend, ie. 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, 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.
[edit] DNA circularisation
DNA circularisation depends on both the axial (bending) stiffness and torsional (rotational) stiffness of the molecule. For a DNA molecule to successfully circularise 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 circularisation of DNA is around 400 base pairs (1360nm), 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 circularisation, for example a 10.4 x 30 = 312 base pair molecule will circularise hundreds of times faster than 10.4 x 30.5 ≈ 317 base pair molecule.
[edit] DNA stretching
A straight section of DNA is resistant to both extension and compression, however under sufficient tension (65 pN) DNA undergoes 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 honour of Linus Pauling who originally presented it as a possible structure of DNA.
The properties of compressed DNA are not characterised due to experimental difficulties in stopping the DNA bending under the force.
Longer stretches of DNA are elastic under tension. When DNA is in solution, it undergoes continuous structural variations due to the energy available in the solvent. This is (in short) 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, a single molecule of DNA will stretch under a force, straightening it out. Using optical tweezers, the entropic stretching behaviour of DNA has been studied and analysed from a polymer physics perspective, and it has been found that DNA behaves largely like the Kratky-Porod worm-like chain model.
[edit] DNA melting
| Step | Melting ΔG /Kcal mol-1 |
|---|---|
| T A | -0.12 |
| T G or C A | -0.78 |
| C G | -1.44 |
| A G or C T | -1.29 |
| A A or T T | -1.04 |
| A T | -1.27 |
| G A or T C | -1.66 |
| C C or G G | -1.97 |
| A C or G T | -2.04 |
| G C | -2.70 |
DNA melting is the process by which the hydrogen bonds between the strands of the double helix are broken, separating the two strands of DNA. These bonds are weak, easily separated by gentle heating, enzymes or physical force. DNA melting preferentially occurs at certain points in the DNA. T and A rich sequences are more easily melted because T and A are only held together by two hydrogen bonds per base pair, unlike C and G which are held together by three. Particular base steps are also susceptible to DNA melting, particularly T A and T G base steps. 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 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. DNA melting enzymes (helicases) avoid this tangling of strands by melting the DNA and chemically cleaving the phosphate backbone of one of the strands so that it can swivel around the other. Helicases unwind the strands to facilitate the advance of sequence-reading enzymes such as DNA polymerase.
[edit] DNA topology
Within the cell most DNA is topologically restricted. DNA is typically found in closed loops (such as plasmids) which are topologically closed, or as very long molecules whose inertia produces 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.[2]
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 try to be equal to the number turns a DNA molecule will make while free in solution, ie. number of bases/10.4.
- 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 known as 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.
[edit] The linking number paradox
The "linking number paradox" has puzzled scientists for many years. Prunell described the paradox in a 1998 paper as follows:
The linking number paradox of DNA in chromatin (two negative crossings around the octamer, associated with a unit linking number reduction), which is 21 years old this year, has come of age. After stirring much debate in the past, the initially hypothetical explanation of the paradox by DNA overtwisting on the nucleosome surface is now presented as a hard fact in recent textbooks. The first part of this article presents a historical perspective of the problem and details the numerous attempts to measure DNA local periodicity, which in one remarkable example sowed the seeds for the discovery of DNA bending. The second part is devoted to the DNA minicircle system, which has been developed in the author's laboratory as an alternative to the local-periodicity-measurement approach. It offers a simple proposal: a unit linking number reduction associated with a single crossing. This conclusion is contrasted with the latest high-resolution crystallographic data of the nucleosome in the third part of the article, and the fourth part examines the available evidence supporting an extension of these results to nucleosomes in chromatin. The last part addresses another basic question pertaining to nucleosome dynamics, the conformational flexibility of the histone tetramer.[3]
[edit] References
- ^ Vargason JM, Eichman BF, Ho PS (2000). "The extended and eccentric E-DNA structure induced by cytosine methylation or bromination". Nature Structural Biology 7: 758-761.
- ^ Crick FH (1976). "Linking numbers and nucleosomes". Proc Natl Acad Sci USA 73 (8): 2639-43. PMID 1066673.
- ^ Prunell A (1998). "A topological approach to nucleosome structure and dynamics: the linking number paradox and other issues". Biophys J 74 (5): 2531-2544. PMID 9591679.
