Knots in DNA

And how about experiments on polymer knots The most important and, luckily, also the easiest subject of such experiments is double helical DNA. One nice experiment can de done using DNA with sticky ends - a long double helix with each chain extending at one end by 15 or so unpaired nucleotides beyond the counterpart chain. If the sequences of these extending pieces are complementary to each other, they will stick upon first collision due to the random fluctuations of the double helical coil. Can we then determine the topology of the product  

One can also extract the ring DNA plasmid from bacteria and ask what are their topological states. Again, the question is how to determine the topology. As in the theoretical studies, this is the most difficult part. 

Another method is based on the fact that DNA is negatively charged and, therefore, moves when the electric field is applied (see below Section 12.10). It is easy to believe that DNA with a more complex knot is, on average, more compact and, therefore, moves faster through the gel. It is this electrophoresis method that is behind most of the experimental discoveries in the field. In particular, all knots with up to six crossings have been positively identified both in native plasmid and in experiments on DNA with sticky ends. 

Furthermore, the probabilities of knots computed in simulations for chains of various thicknesses and measured in experiments for DNA under different salt conditions agree quantitatively almost perfectly well. (Salt ions screen the Coulomb repulsion between DNA segments and thus control the effective diameter of DNA.) 

We want to note in passing that this creates a situation somewhat unprecedented in the whole of history of science researchers claim a rather complete understanding of DNA knotting, based on the agreement between simulations and experiments, but we have no theory. Will it stay that way, or somebody will eventually be able to crack a theory — remains to be seen. 

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A molecular biology analog of Scheme 4 is the ability of topoisomerases to interchange different knots in DNA [19]. 

Is there anything similar in the physics of biopolymers, any general laws that are not affected by the random choices There certainly are They control the formation of knots in DNA (see Section 2.6), the hydrophobic-hydrophilic separation of a globular protein (Section 5.7), and many other properties most of these laws may still be unknown. 

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