Long time behaviour of diffusing particles in constrained geometries; application to chromatin motion

Inspired by experiments that use single-particle tracking to measure the regions of confinement of selected chromosomal regions within cell nuclei, we have developed an analytical approach that takes into account various possible positions and shapes of the confinement regions. We show, in particular, that confinement of a particle into a subregion that is entirely enclosed within a spherical volume can lead to a higher limit of the mean radial square displacement value than the one associated with a particle that can explore the entire spherical volume. Finally, we apply the theory to analyse the motion of extrachromosomal chromatin rings within nuclei of living yeast.

Simulations of electrophoretic collisions of DNA knots with gel obstacles

Gel electrophoresis can be used to separate nicked circular DNA molecules of equal length but forming different knot types. At low electric fields, complex knots drift faster than simpler knots. However, at high electric field the opposite is the case and simpler knots migrate faster than more complex knots. Using Monte Carlo simulations we investigate the reasons of this reversal of relative order of electrophoretic mobility of DNA molecules forming different knot types. We observe that at high electric fields the simulated knotted molecules tend to hang over the gel fibres and require passing over a substantial energy barrier to slip over the impeding gel fibre. At low electric field the interactions of drifting molecules with the gel fibres are weak and there are no significant energy barriers that oppose the detachment of knotted molecules from transverse gel fibres.