Topology matters: Some aspects of DNA physics
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Topology matters: Some aspects of DNA physics Ralf Metzler NORDITA, Blegdamsvej 17, 2100 København Ø, Denmark ABSTRACT Biological cells, in some sense, are all about topology: Biomembranes separating different volumes from one another, ions or even macromolecules having to cross these membranes in controlled fashion through membrane pores; or certain proteins moving along the DNA to find their target sequence instead of searching for this site in the full 3-dimensional cell volume. Even on the single biopolymer level, topology is an essential ingredient: Intriguingly, in bacteria DNA occurs knotted, i.e., in a state topologically different from a simply connected ring. It is a key question to understand the statistical behaviour of such knotted DNA to understand a number of physiological processes having to overcome this knottedness, or to quantify results from DNA separation techniques such as electrophoresis, in which the knottedness influences the mobility. At the same time, double-stranded DNA continuously opens up floppy single-stranded bubbles, which fluctuate in size, exposing the single Watson-Crick bases to binding proteins. Again, statistical mechanical tools can be employed to examine the bubble dynamics. Here, we introduce some recent results on DNA knots and bubble fluctuations. INTRODUCTION Biological macromolecules split up into fairly unspecific molecules such as polysaccharides (cellulose, chitin, starch, etc.), actin filaments, or microtubules; and the highly specific biopolymers with their unique sequence of building blocks, namely nucleic acids (DNA and RNA) and polypeptides (proteins). These latter are characterised by their specific biological function, which is due to some uncommon hierarchical structure, being fully determined by the primary structure, i.e., the sequence of nucleotides or peptides formed during synthesis. This primary structure uniquely defines the local interactions within the biopolymer (α-helices and β-sheets in proteins, or stacking interactions, local twist and curvatures in nucleic acids), the secondary structure. Finally, volume interactions (tertiary structure) of chemically remote monomers or segments of the biopolymer such as pseudoknots in RNA or looping in DNA, ensure its 3-dimensional shape, making the biopolymer ready to function.
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The relation between DNA, RNA, and proteins is governed by the central dogma of molecular biology: Starting from its complementary double-strand formed by Watson-Crick bonds and stacking of the base pairs G-C and A-T, DNA is replicated (copied) through helicase and DNA polymerase by continuous separation into the two single strands, each of which acts as a template for two new double strands, which are completed by adding new nucleotides. Similarly, from DNA by transcription through RNA polymerase, messenger RNA is created, a single strand consisting of the nucleotides G, C, A, and U; and finally, via translation by ribosomes (and others) the polypeptidic proteins with their 22 different amino acids are synthesised. This opens up t
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