In both bacteria and eukaryotes, maintaining DNA compaction is a sine qua non of chromatin function. At the same time accessibility to transcribing, replicating and recombining enzymes must be maintained. I will argue that these twin requirements can be viewed in the context of the overall topology of, for bacteria, the DNA itself, and of, for eukaryotes, the 30 nm chromatin fibre. In particular, the plectonemic form of supercoiled ropes, either DNA or 30 nm fibres, must, in principle, contain distinguishable structures (interwindings, apical loops, branch points, hammerheads) in contrast to a more monotonous toroid. In exponentially growing Escherichia coli the 2-start helical interwindings of the plectonemic form of plasmid DNA are stabilised by different nucleoid-associated proteins (NAPs). Nucleation of binding of the NAP H-NS at high affinity sites results in gene silencing and plectoneme stabilisation. Plectonemes are also recognised by RNA polymerase and certain recombinases. The binding of RNA polymerase to loop structures formed at some promoters facilitates binding and for the tyrT promoter potentially locates the thermally unstable -10 hexamer adjacent to the interwindings of a negatively supercoiled plectoneme. In eukaryotes the requirement for DNA compaction is greater than in bacteria. Whereas a simple DNA plectoneme compacts DNA by ~~2.5 fold, compaction factors of up to 10000 are required in the eukaryotic nucleus. The initial mechanism for compacting DNA is the tight wrapping of ~146 bp in a nucleosome core particle, resulting in a compaction of ~9-10-fold. In vivo these particles can be accurately positioned such that the midpoint of the bound DNA is approximately defined. We have derived from accurately mapped in vivo positions in yeast a translational positioning signal that identifies the midpoint of histone octamer-bound DNA. The minimal signature is 75% of reported and also our newly determined mapped positions in yeast. This putative positioning signal occurs on average once every ~60 bp in yeast genomic DNA sequences. From this apparent redundancy we infer that the preferred positioning of nucleosomes in an array requires an 'organiser' to select a nucleosome for nucleating an array. This organiser could be a strong intrinsic DNA positioning signal or a transcription factor. We present evidence that the DNA sequences specifying 5' proximal (-1 position) nucleosomes of several genes can, under more physiological conditions, outcompete in vitro the strong 601 positioning sequence originally selected by salt gradient dialysis in vitro. The next stage in the compaction of eukaryotic chromatin is the folding of a nucleosome array into a '30 nm' fibre. We have calculated the dependence of the diameter and packing density of chromatin fibres on linker length and conclude that all current measurements are consistent with a model in which at short linker lengths (corresponding to a nucleosome repeat length of ~ 177 bp) the linker histone can supercoil a 2-start crossed-linker fibre into a helical-ribbon form by changing the exit and entry trajectories of DNA. As the linker length increases in increments of 10 bp (< the 10.5 bp helical repeat of DNA) at a certain point the fibre relaxes into a crossed-linker form with a higher packing density. On this model the 30 nm fibre has a variable topology but maintains a constant packing of nucleosomes. References: Maurer, S., Fritz., J., Muskhelishvili, G. and Travers, A. RNA polymerase and an activator form discrete subcomplexes in a transcription initiation complex. EMBO J. 25, 3784-3790 (2006). Travers, A. and Muskhelishvili, G. A common topology for bacterial and eukaryotic transcription initiation? EMBO Rep. 8, 147-151 (2007). Bouffartigues, E., Buckle, M., Baudaut, C., Travers, A. and Rimsky, S. High affinity sites direct the cooperative binding of H-NS to a regulatory element required for transcriptional silencing. Nat. Struct. Mol. Biol. 14, 441-448 (2007). Lang, B. et al. High affinity DNA binding sites for H-NS provide a molecular basis for selective silencing within proteobacterial genomes. Submitted for publication (2007). Wu, C., Bassett, A. and Travers, A. A variable topology for the '30 nm' chromatin fibre. Submitted for publication (2007). Collaborators: MRC-LMB, Cambridge: M. Madan Babu, Mark Churcher, Edwige Hiriart, Benjamin Lang, Chenyi Wu DAMTP, University of Cambridge: Graeme Mitchison ENS, Cachan: Cyril Baudaut, Emeline Bouffartigues, Malcolm Buckle, Sylvie Rimsky Università di Roma "La Sapienza": Eleonora Agricola, Micaela Caserta, Ernesto Di Mauro, Leonora Verdone Università di Camerino: Claudio Gualerzi, Cynthia Pon, Stefano Stella Jacobs University, Bremen: Claudia Burau, Nicolas Blot, Jurgen Fritz, Marcel Geertz, Sebastian Maurer, Ramesh Mavathur, Georgi Muskhelishvili