Physics of (or inspired by) the folding of chromosomes

Eukaryotic genomes are organized in sets of chromosomes. Each chromosome consists of a single continuous DNA double-helix and associated proteins that organize locally in the form of a chromatin fiber. During cell division (mitosis) chromosomes adopt a compact form that is suitable for transport. During periods of normal cell activity (interphase), chromosomes decondense inside the cell nucleus. Being long chain molecules (in the case of human chromosomes the contour length of the chromatin fiber is on the order of 1 mm), the random thermal motion of interphase chromatin fibers is hindered by topological constraints, similar to those restricting the manipulation of a knotted ball of wool.

In the first part of the talk, I will recall some results from a simulation study of de-condensing model chromosomes, where we have explored the consequences of this effect.  Not only did the model reproduce the sequence-averaged experimental behavior, but it also suggested a quantitative equilibrium model for the territory formation and the crumpled chain statistics: dense solutions of non-concatenated ring polymers. In the second part, I will illustrate how to extend our approach to modeling specific biological systems, notably the large scale chromosome folding in Drosophila nuclei during the course of development. The third part will hoepfully provide a deeper understanding of the nature of the crumpled state, where chains occupy distinct territories and where the relation between the spatial and genomic or contour distance is of the form R^2(L) ~ L^{2 \nu} with \nu=1/3,  which is markedly different from the strong mutual interpenetration of Gaussian chains with \nu=1/2 characterizing equilibrated linear polymer melts or solutions. I will discuss the relation to the statistics of lattice animals or trees, the understanding of the average tree behavior with the help of Flory arguments as well as scaling arguments allowing to rationalize the distribution functions of the corresponding observables with the help of a small number of additional exponents.