Coarse-Grain Mechanics of DNA: Bases to Chromosomes
- Ralf Everaers (École Normale Supérieure de Lyon, France)
- Helmut Schiessel (Instituut-Lorentz for Theoretical Physics, Leiden, The Netherlands)
- John H. Maddocks (Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland)
Rigid base-pair models:
The elasticity of double-helical DNA on a nm length scale is captured in detail by the rigid base-pair model (rbpm), whose conformation variables are the relative positions and orientations of adjacent base pairs [Coleman03]. Corresponding sequence-dependent elastic potentials have been obtained from (combinations of) all-atom MD simulation and from high-resolution structural data [Olson98,Lankas03,Becker06a]. The description on the nano-scale is the natural complement for experiments such as molecular rulers or footprinting, which do not yield structural information with atomic resolution. They also lend themselves naturally to a standard exercise in mechanical engineering: the inference of external forces and torques on a body from a given static shape and known elastic properties as a means to reveal the complex nano-mechanical patterns of interaction between proteins and DNA [Becker09a].
DNA in the continuum limit:
Beyond the 100nm scale, DNA is successfully described by a wormlike chain model with homogeneous elastic properties [Marko94], which can be determined via a systematic coarse-graining procedure from the rbpm [Becker06b]. On the wormlike chain level a systematic treatment (semiclassical approximation) of the statistical mechanics of chains under tension featuring kinks and loops is now available [Kulic07]. In addition, this method has been applied to Euler buckling [Emanuel07].
A drastic example for strongly deformed DNA is the nucleosome core particle. The structure is know with atomic resolution [Luger97] and a nano-mechanical analyis recovers the 12 known DNA backbone-histone contact sites at points where the DNA minor grove faces the histone complex [Becker09b]. The sequence-dependent affinity of nucleosomes can be estimated using empirical [Segal06] and mechanical models [Morozov09] and explains part of the in vivo nucleosome positions. Nevertheless, the concept of the histone code remains controversial [Zhang06] and important aspects such as the role of electrostatic interactions and histone modifications, or the structure of the so-called „stem“ formed by the linker DNA and histone H1 remain unclear, even though they have a profound impact on the structure of chromatin on larger scales.
The structures beyond the nucleosome are poorly understood. Presumably the next level of folding is that of the 33nm wide chromatin fiber that is at least typically observed in in vitro experiments. However, its structure remains elusive. Several experimental breakthroughs, e.g. the assembly of regularly spaced nucleosome arrays that fold into superdense fibers [Robinson06] might allow now to understand their geometry. For example, only very recently a model has been put forward that can predict the observed diameters, by postulating that the fiber geometry follows from the stacking of the wedge shaped nucleosomes [Depken09].
Chromosome undergo large conformational changes during the cell cycle involving decondensation after cell division, replication, and condensation/segregation before the following division. The mechanism behind the various structural transitions are still unknown. Physical approaches often coarse-grain the chromatin fiber to generic polymer models [Emanuel09] of cross-linked or entangled [Rosa08] solutions or fibers.
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