From chromosome crumpling to the interacting randomly branched polymers

The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for non-concatenated unknotted rings, which are known to crumple and segregate and which have been implicated as models for the generic behavior of interphase chromosomes. In [1] we have used a computationally efficient multi-scale approach to identify the subtle physics underlying their behavior, where we combine massive Molecular Dynamics simulations on the fiber level with Monte Carlo simulations of a wide range of lattice models for the large scale structure. This allowed us to show that ring melts can be \textit{quantitatively} mapped to coarse-grained melts of \textit{interacting} randomly branched primitive paths. To elucidate the behavior of interacting branched polymers, we use a combination of scaling arguments and computer simulations[2]. The simulations are carried out for different statistical ensembles: ideal randomly branching polymers, melts of interacting randomly branching polymers, and self-avoiding trees with annealed and quenched connectivities. In all cases, we perform a detailed analysis of the tree connectivities and conformations. We find that the scaling behaviour of average properties is very well described by the Flory theory of Gutin et al. [Macromolecules 26, 1293 (1993)]. A detailed study of the corresponding distribution functions allows us to propose a coherent framework of the behavior of interacting trees, including generalised Fisher-Pincus relationships and the detailed analysis of contacts statistics. [1] Ring Polymers in the Melt State: The Physics of Crumpling, Angelo Rosa and Ralf Everaers, Phys. Rev. Lett. 112, 118302 (2014) \newline [2] Conformations of randomly branching polymers with volume interactions, Angelo Rosa, A.Y. Grosberg, M. Rubinstein and Ralf Everaers, in preparation.