Posts Tagged ‘Z-DNA’

The thermodynamic energies of left and right handed DNA.

Saturday, March 5th, 2011

In this earlier post, I noted some aspects of the calculated structures of both Z- and B-DNA duplexes. These calculations involved optimising the positions of around 250-254 atoms, for d(CGCG)2 and d(ATAT)2, an undertaking which has taken about two months of computer time! The geometries are finally optimised to the point where 2nd derivatives can be calculated, and which reveal up to 756 all-positive force constants and 6 translations and rotations which are close to zero! This now lets one compute the thermodynamic relative energies using ωB97XD/6-31G(d) (for 2nd derivatives) and 6-31G(d,p) (for dispersion terms). All geometries are optimized using a continuum solvent field (water), and are calculated, without a counterion, as hexa-anions.

Relative thermodynamic energies (kcal mol-1) of DNA duplexes.
system Total energy (duplex) Dispersion term ΔΔH298 Δ(-T.ΔS298) ΔΔG298 duplex ΔG298 single chain ΔΔG298 (Duplex)
Z-CGCG 0.0 0.0 0.0 0.0 0.0 0.0 -60.3
B-CGCG 6.2 -4.2 8.0 3.9 11.9 +3.1 -54.7
Z-ATAT 0.0 0.0 0.0 0. 0.0 0.0 -44.9
B-ATAT -7.6 -12.8 -7.0 2.7 -4.3 -1.8 -45.7

Note how the CGCG duplex is more stable as a Z-helix, whilst the ATAT duplex prefers the B-helix. I will discuss the precise reasons for this elsewhere.

A comparison of left and right handed DNA double-helix models.

Saturday, January 1st, 2011

When Watson and Crick (WC) constructed their famous 3D model for DNA, they had to decide whether to make the double helix left or right handed. They chose a right-handed turn, on the grounds that their attempts at left-handed models all “violated permissible van der Waals contacts“. No details of what these might have been were given in their original full article (or the particular base-pairs which led to the observation). This follow-up to my earlier post explores this aspect, using a computer model.

One half of a (CGCG) DNA strand

The DNA model used here is shown above; in shorthand it is d(CGCG)2. A crystal structure reveals it to form a (non-Watson-Crick) left-handed helix. If you open the 3D model below (based on a ωB97XD/6-31G(d)/SCRF=water optimisation), some of the short van der Waals contacts are measured. Most are around 2.25Å and the shortest is 2.1Å. It is worth noting that WC note in their article that a distance of 2.1Å for the B-form is acceptable (p92, bottom) and not a violation. All twelve hydrogen bond lengths H…O or H…N are normal, with lengths around 1.8Å. Given that a H…H distance is at its most attractive at ~2.4Å, and plenty of H…H distances of ~2.1Å are known from the crystal structures of organic molecules, one might conclude that (for the CG base pair), their hypothesis that the Z-form could be eliminated was wrong.

The DNA duplex d(CGCG) showing a left handed helix with short H...H contacts shown. Click for 3D

But might the original WC-right handed form for this system be at least competitive? There is one H…H of 2.05Å and quite a few at ~2.5Å (3D model below). The “violation” of van der Waals contacts is if anything slightly worse than with the left-handed helix. The total difference in the dispersion energy is a rather astonishing ~12 kcal/mol in favour of the Z-form. I will update this post (as a comment) when the relative free energies of the two forms are available (this calculation takes a while), but there is little doubt that the Z-form is indeed the more stable.

The DNA duplex d(CGCG) showing a right handed helix with short H...H contacts shown. Click for 3D

What can also be said about the Watson-Crick right handed form is that the hydrogen bonding is not so optimal. One of the twelve interactions between a (terminal) CG pair has some signs of being “unzipped“, with an N-H…O=C distance of ~1.9Å (there is no sign of similar unzipping in the Z-form). One must wonder whether this difference in the Z- and B-helices for the CG pair has been exploited in nature.

 

One crucial aspect of DNA is the local conformation about the bond connecting the base and the ribose, N9-C8 in the diagram below(green arrow).

Conformation of the base-ribose unit

An analysis of this bond can be expressed in terms of NBO theory. This clearly shows a strong interaction energy (E2) between the lone pair on N9 and the C8-O4 antibonding orbital of 13.3 kcal/mol, a classical anomeric effectin fact. In this case, it promotes the local conformation of this unit, which has a significant effect on the final model.

What else can analysis of the wavefunction tell us? Well, curiously, the optical rotation of this particular small oligomer has never been reported in the literature, and an intriguing question is whether it might have proved useful to distinguish between B- and Z-forms of the duplex? To do this, one needs a reasonably reliable way of computing [α]D for both isomers. This is because optical rotations are not reliably additive, and it is difficult to estimate them accurately based purely on the fragments present in the molecule. In 2011, is is now perfectly possible to calculate this quantity quantum mechanically, even for 250 atoms, using a reasonable basis set and making allowance for solvation (which is known to affect the calculated rotation). The values (CAM-B3LYP/6-31G(d)/SCRF=water) for the Z-isomer are 66° and 32° for the B-isomer. Of course the model is not complete, lacking a counterion for the phosphate and explicit water molecules, but even so, it might appear that the reason optical rotations are not reported is that they truly are not useful!

The handedness of DNA: an unheralded connection.

Wednesday, December 29th, 2010

Science is about making connections. Plenty are on show in Watson and Crick’s famous 1953 article on the structure of DNA (DOI: 10.1038/171737a0), but often with the tersest of explanations. Take for example their statement “Both chains follow right-handed helices“. Where did that come from? This post will explore the subtle implications of that remark (and how in one aspect they did not quite get it right!).

The right handed helix is illustrated in the article cited above as perhaps the most famous scientific diagram of the 20th century (as recounted in the TV program by Marcus du Sautoy). It was drawn by Odile Crick, a professional artist, and it is easily her best known work (the original, sadly, appears lost). Many say it has never been bettered; I do not reproduce it here for fear of copyright infringement, but you can see Odile (who died only recently) and her diagram here. One however has to go to the Watson-Crick (WC) full paper (DOI: 10.1098/rspa.1954.0101) for an explanation of why they decided the helix was right-handed, or (P)- in CIP terminology. In my opinion (as a chemist), this is a far better read than the short and more famous note in Nature. There (on page 87) one finds the immortal statement “we find by trial and error that the model can only be built in a right-handed sense”. They follow that remark with another which I will quote later in this post. But the preceding observation is footnoted, and that footnote must rank as one of the most unheralded in science (unlike e.g. Fermat’s). For this footnote notes another article, published just two years earlier (DOI: 10.1038/168271a0) in which the absolute handedness of a small molecule was finally confirmed after ~50 years. The molecule is shown below, and again in modern CIP terminology, the two chiral carbon atoms both have (R) configurations rather than (S). Until this point, the (R) configuration had merely been a guess with an evens chance of it being right (and had it been wrong, imagine how many textbook diagrams would have needed changing!).

The absolute configuration of natural tartaric acid.

Chemists had, in the preceding 50 years, by synthesis and transformation, connected the configuration of tartrate to the ribose sugars that form the linker in DNA, and so Watson and Crick built their famous model of DNA assured in the knowledge that the absolute configuration of their ribose sugar was correct. But that assurance, it is important to remember, had only come two years earlier! The (correct) structure of DNA was very much a discovery of its time, and this connection between tartrate and DNA I think deserves the accolade of great connections in science (I write this in the Semantic Web sense).

On to another statement to be found in the full WC article: “Left handed helices can only be constructed by violating the permissible van der Waals contacts” Given the nature of the molecular model building tools that WC had at their disposal,* I suspect we must forgive them this assertion. But of course, building models using the van der Waals constraints (amongst others of course) is what modern computers are really very good at. So what might a modern visitation of this very issue yield? Shown below is a small DNA duplex, named d(CGCG)2 (DOI: 10.2210/pdb1zna/pdb) This uses only the CG base-pairing motif (the other of course is AT). Well, it turns out that DNA constructed from CG-rich duplexes does NOT necessarily adopt a right handed helix after all! WC (for this particular condition) were in fact wrong, and clearly the van der Waals contacts are not after all objectionable. Left-handed helices (as a left hander myself, I am naturally drawn to them) are also known as Z-DNA (the right handed form is called B-DNA), although many left-handed representations have in fact been drawn in error.

The DNA duplex d(CGCG) showing a left handed helix. The ribose is in the 2E conformation. Click for 3D and see if you can find any objectionable van der Waals contacts!

The model when stripped of its water molecules, is then of a size (250 atoms) which is easily amenable to a modern quantum-mechanical DFT calculation. Importantly, this has to include dispersion corrections (the van der Waals contacts referred to above) to get the correct geometry, and one can use e.g. ωB97XD/6-31G(d) + continuum water solvation correction to compensate for the missing waters (see DOI: 10.1039/C0CC04023A for an example of its use for a large molecule, or indeed this post). In truth, this combination of characteristics in a model has only recently become possible for a molecule of such size.

 

Well, now that a good accuracy wavefunction for e.g. d(CGCG) is possible, what might one do with it? Well, the chiro-optical properties might be calculated (see DOI: 10.1002/chir.20804), including the optical rotation at a specified frequency, or e.g. the electronic circular dichroism spectrum. Such properties are normally computed only for much smaller molecules. Watch this space (or the journals).


* Note added in proof (as the saying goes): This article by Derek Barton published in 1947, some six years before WC claimed “violation of  the permissible van der Waals contacts“, established clearly the principles behind the model building by WC and in many ways could be described as the start of quantitative molecular model building. The very same equation used by Barton to model dispersion attractions is still used in e.g. the ωB97XD DFT method noted above.