The ability of cells to pack, use and duplicate DNA remains one of the most fascinating questions in biology. To understand DNA organization and dynamics, it is important to consider the physical and topological constraints acting on it. In the eukaryotic cell nucleus, DNA is organized by proteins acting as spools on which DNA can be wrapped. These proteins can subsequently interact and form a structure called the chromatin fibre. Using a simple geometric model, we propose a general method for computing topological properties (twist, writhe and linking number) of the DNA embedded in those fibres. The relevance of the method is reviewed through the analysis of magnetic tweezers single molecule experiments that revealed unexpected properties of the chromatin fibre. Possible biological implications of these results are discussed.Keywords: chromatin; topology; DNA
DNA SUPERCOILING AND TRANSCRIPTIONAccording to the 'central dogma' of molecular biology, the DNA double helix codes for the sequence of all proteins in the cell. However, in eukaryotic cells, the coding sequences can vary from 90 per cent (in yeast) to less than 1.5 per cent of the DNA sequence (in higher eukaryotes, such as humans). A role of non-coding DNA in the assembling of the hierarchical architecture of the genome has been, therefore, proposed. This architecture must, at a time, compact DNA in the nucleus and let it be accessible when requested by the cell functioning. Besides the geometrical puzzling that these questions imply, the architecture of DNA and its dynamical modifications have to deal with the mechanical response of DNA that behaves as a rather rigid screw. In particular, gene transcription imposes strong mechanical constraints. The crucial step of protein synthesis, the transcription elongation, is performed by a dedicated enzyme, the RNA-polymerase (RNAP). RNAP opens locally the double helix, reads it and makes a copy of the coding DNA template onto a RNA stretch. The transcription activation requires the formation of a large protein complex, consisting of up to 60 different proteins. Owing to the large dimension of the transcription complex, it is very unlikely that the RNAP rotates around DNA during the elongation process [1]: the DNA has, therefore, to rotate inside the RNAP. This process leads to topological and mechanical constraints upstream and downstream of the transcription site. Indeed, as the elongation complex progresses along the genomic sequence, the DNA double helix in front of it becomes overwound ( positively supercoiled), whereas the DNA behind it becomes underwound (negatively supercoiled). This is the so-called twin-supercoiled-domain (TSD) model, first introduced by Liu & Wang [2] and extensively acknowledged since (for a review, see Lavelle [3]). In this paper, we will deal with the problem of building the appropriate theoretical frame where mechanical and topological constraints acting on DNA can be accounted for, in the perspective of studying the implications of these constraints for different biological proce...