DNA composed of four bases (or nucleotides) A, T, C, and G which pair according to the pairing rules :    A-T and C-G

DNA is composed of two complementary strands (or sequences) e.g.

Sequence on first strand arbitrary, and then sequence on the other strand forced by pairing rules.

Along each strand the bases are connected through a covalently bonded (i.e. very strong) sugar-phosphate backbone. Moreover the sugar-phosphate backbones have a direction (determined by the detailed shape of the sugars). In most configurations of DNA including the standard one, called B-DNA, the two backbones run anti-parallel. However parallel stranded DNA can occur.
 

The two backbones are linked through (relatively weak) hydrogen bonds between the base pairs, in general 2 for A-T and 3 for G-C basepairs respectively.
 

Again in standard B-DNA, the three-dimensional conformation (minimum energy shape) has the paired bases in the interior of a right-handed `helix? formed by the two backbones.

The three-dimensional shape is determined by the interplay between relatively weak rotational degrees of freedom in the otherwise strong backbone bonds, and the relatively weak hydrogen bonding between base pairs.
 

The geometry of the base pairing and the helical backbones lead to what are called the major and minor grooves of B-DNA. Essentially the backbones forming the helix are not at the two ends of a diameter across the helix, but are offset. This leads to very important biochemical phenomena--for example there are major groove and minor groove binding proteins.

The parameters of B-form DNA are shown in the cartoon.
 

All of these numbers must be taken with a grain of salt: in fact salt concentration can substantially alter them :-).

Even without changing solution conditions, these numbers must be interpreted as some form of average.

DNA in solution is fluctuating at all times, so some form of time average is involved.

The details of the shape of the helix are also believed to depend on the base pair sequence--see detailed discussion later---so a space or sequence average is also involved.
 

The relation between the sugar-phosphate backbone and each of the 4 bases is nearly identical so that the B-form of DNA can occur for just about any sequence of bases on either strand.

However B'-DNA occurs when one strand has several A residues in close proximity (and the complementary strand therefore has several T residues). In B'-DNA the two paired bases are no longer close to co-planar, but instead have an angle between their planes of about 20 degrees (This is sometimes called propeller twist.)
 
B'-DNA is still a right-handed helix, but the presence of the so-called A-tracts is known to cause the centerline of the double helix to bend. There is still controversy as to whether the bend arises at localized kinks at the points where the B-form helix switches to the B'-form (the junction model), or whether the whole axis of the B'-form helical segment is curved (the wedge angle model).

In any case A-tracts are known to cause some sort of curvature, they are known to occur in natural DNA, and they seem to be play a very important biological role.

Short DNA molecules containing a number of phased A-tracts that provide an overall bend of 110 degrees or so in the helix axis play a crucial role in the continuum mechanics models of mini-circles that will be described later.

More esoteric forms of DNA

A-DNA also is right-handed, but sugars are in a different conformation than for the B-DNA, and the two grooves are less deep.

Z-DNA has anti-parallel strands as in the B and B' forms, but in the Z-form a left handed helix is formed (as well as there being many other differences).

Z-form is difficult to achieve under physiological conditions. Sequences in which purines (A or G) alternate with pyrimidines (T or C) along one strand seem to enhance the formation of the Z-form, as does a loading yielding a twist stress favoring left handed twist over right handed (see discussion of mini-circles and plasmids below). 

Parallel stranded or ps-DNA can be formed, particularly if both strands comprise only A or T base pairs. The helix is right handed, but the hydrogen bonds that join the base pairs are not the standard ones and the base pair geometry differs from the usual one.

In some circumstances (e.g. very special base pair sequences) it is also possible to form triplex helices containing three backbones (of course two of the backbones must be parallel!)

Quadruplex structures are also possible!

(back to the standard B-form double helix)

Each base pair is about 20x10^-10 meters wide (which is the geometrical diameter of the helix)

Each base pair is about 3.4x10^-10 meters high (which is the contribution of each base pair to the length of the double helix)

But there are approximately 10¹⁰ base pairs or 3.4 meters of DNA
in each of the cells in your body!
 
Actually the total length of DNA in each cell is between 1 and 2 meters, all of which is not in one piece. Human DNA comes in 22 homologous pairs + X and Y chromosomes. Longest single piece of DNA is about 10 centimeters.

Understanding which bits of the 10¹⁰ base pairs are responsible for what genes, is the topic of the human genome project

10 cm or 10^-1 m of DNA of width
20x10^-10 m is still very long and skinny.

Multiply by 10⁶ then:
Diameter 2x10^-3 or 2mm
Length 10⁵ m or 100km

A thin chalk line to Geneva and back

 
The total volume of the DNA double helix is still rather small so it can be packed in individual cells with plenty of space left over. But it must be very organized so that it can do its job and, for example, be exactly duplicated when the cell divides.

Much known and conjectured about the structure of this organization. In humans the DNA is wrapped on nucleosomes (groups of small globular proteins). Then the composite fiber so formed is wrapped and coiled into another fiber, and so on, with the final arrangement or this hierarchy of fiber is known as the chromosome.
 
Perhaps the most basic function of DNA is to code the proteins that make the cells work. There is a mapping from triplets (or a codon) of base pairs to the amino acids that make up proteins. This is the genetic code. Usually one gene encodes one entire protein, and a typical length of a gene is 500 to 600 base pairs (although there is certainly much variation in this length).

The length of scale of 500 bp or so is an important one for the mechanical properties of DNA. The length will re-appear later.

Given that the total number of base pairs in the human genome is 10¹⁰ it seems that to model say a few hundred bp sequence would be a rather modest goal. However a few hundred bp is still essentially beyond the scope of practical MD simulations. Each base pair has around 60 atoms so a 200 bp sequence involves around 12000 atoms in the DNA itself.

However an explicit treatment of solvent makes the number of molecules explode, and a practical current day simulation is limited to a few nano-seconds for a 20 or 30 base pair sequence. Thus the need for better multi-scale models is apparent.

There are a number of different hierarchies of models available above the atomic one.

Bases or base pairs can be modelled as rigid bodies with potentials between the sub-units defined by summing atomistic potentials over the constituent bodies.

Models can also be based on larger units than individual base pairs, e.g. Monte Carlo simulations.

The DNA can be smoothed or averaged to yield a model as an elastic line (a system with an infinite number of degrees of freedom) and then re-discretized for simulations with the discretization chosen according to purely numerical analysis criteria.
 
Experimental data allow the following conclusions to be drawn:

• DNA is big enough to be seen with various microscopy techniques. In particular cryo-EM allows 3D shapes to be measured, which are hopefully close to the shape in solution
• DNA quite often occurs (or can be made into) closed loops, varying from 150 bp (or less) mini-circles, to naturally occurring plasmids of a thousand base pairs
• DNA is rather stiff. For lengths of a few hundred base pair (compare typical length of a gene fragment) DNA apparently has a well-defined shape, in which the centerline of the double helix may be far from straight (cf. Tortillon cryo-pictures)