The role of transcription factories-mediated interchromosomal contacts in the organization of nuclear architecture

Using numerical simulations, we investigate the underlying physical effects responsible for the overall organization of chromosomal territories in interphase nuclei. In particular, we address the following three questions: (i) why are chromosomal territories with relatively high transcriptional activity on average, closer to the centre of cell's nucleus than those with the lower activity? (ii) Why are actively transcribed genes usually located at the periphery of their chromosomal territories? (iii) Why are pair-wise contacts between active and inactive genes less frequent than those involving only active or only inactive genes? We show that transcription factories-mediated contacts between active genes belonging to different chromosomal territories are instrumental for all these features of nuclear organization to emerge spontaneously due to entropic effects arising when chromatin fibres are highly crowde

Modelling of crowded polymers elucidate effects of double-strand breaks in topological domains of bacterial chromosomes

Using numerical simulations of pairs of long polymeric chains confined in microscopic cylinders, we investigate consequences of double-strand DNA breaks occurring in independent topological domains, such as these constituting bacterial chromosomes. Our simulations show a transition between segregated and mixed state upon linearization of one of the modelled topological domains. Our results explain how chromosomal organization into topological domains can fulfil two opposite conditions: (i) effectively repulse various loops from each other thus promoting chromosome separation and (ii) permit local DNA intermingling when one or more loops are broken and need to be repaired in a process that requires homology search between broken ends and their homologous sequences in closely positioned sister chromati

Topological origins of chromosomal territories

Using freely jointed polymer model we compare equilibrium properties of crowded polymer chains whose segments are either permeable or not permeable for other segments to pass through. In particular, we addressed the question whether non-permeability of long chain molecules, in the absence of excluded volume effect, is sufficient to compartmentalize highly crowded polymer chains, similarly to what happens during formation of chromosomal territories in interphase nuclei. Our results indicate that even polymers without excluded volume compartmentalize and show strongly reduced intermingling when they are mutually non-permeable. Judging from the known fact that chromatin fibres originating from different chromosomes show very limited intermingling in interphase nuclei, we propose that regular chromatin fibres during chromosome decondensation can hardly serve as a substrate of cellular type II DNA topoisomerase

The Quantum Compass Model on the Square Lattice

Using exact diagonalizations, Green's function Monte Carlo simulations and high-order perturbation theory, we study the low-energy properties of the two-dimensional spin-1/2 compass model on the square lattice defined by the Hamiltonian $H = - \sum_{\bm{r}} (J_x \sigma_{\bm{r}}^x \sigma_{\bm{r} + \bm{e}_x}^x + J_z \sigma_{\bm{r}}^z \sigma_{\bm{r} + \bm{e}_z}^z)$. When $J_x\ne J_z$, we show that, on clusters of dimension $L\times L$, the low-energy spectrum consists of $2^L$ states which collapse onto each other exponentially fast with $L$, a conclusion that remains true arbitrarily close to $J_x=J_z$. At that point, we show that an even larger number of states collapse exponentially fast with $L$ onto the ground state, and we present numerical evidence that this number is precisely $2\times 2^L$. We also extend the symmetry analysis of the model to arbitrary spins and show that the two-fold degeneracy of all eigenstates remains true for arbitrary half-integer spins but does not apply to integer spins, in which cases eigenstates are generically non degenerate, a result confirmed by exact diagonalizations in the spin-1 case. Implications for Mott insulators and Josephson junction arrays are briefly discussed.Comment: 8 pages, 8 figure

Solids and supersolids of three-body interacting polar molecules in an optical lattice

We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by B\"uchler [Nature Phys. 3, 726 (2007)]. To this end quantum Monte Carlo simulations, exact diagonalization and a semiclassical approach are used to explore hardcore bosons on the two-dimensional square lattice which interact solely by long ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.Comment: 4+ pages, 4 figures, published versio

Models that include supercoiling of topological domains reproduce several known features of interphase chromosomes

Understanding the structure of interphase chromosomes is essential to elucidate regulatory mechanisms of gene expression. During recent years, high-throughput DNA sequencing expanded the power of chromosome conformation capture (3C) methods that provide information about reciprocal spatial proximity of chromosomal loci. Since 2012, it is known that entire chromatin in interphase chromosomes is organized into regions with strongly increased frequency of internal contacts. These regions, with the average size of ∼1 Mb, were named topological domains. More recent studies demonstrated presence of unconstrained supercoiling in interphase chromosomes. Using Brownian dynamics simulations, we show here that by including supercoiling into models of topological domains one can reproduce and thus provide possible explanations of several experimentally observed characteristics of interphase chromosomes, such as their complex contact map

Magnetization plateaux in an extended Shastry-Sutherland model

We study an extended two-dimensional Shastry-Sutherland model in a magnetic field where besides the usual Heisenberg exchanges of the Shastry-Sutherland model two additional SU(2) invariant couplings are included. Perturbative continous unitary transformations are used to determine the leading order effects of the additional couplings on the pure hopping and on the long-range interactions between the triplons which are the most relevant terms for small magnetization. We then compare the energy of various magnetization plateaux in the classical limit and we discuss the implications for the two-dimensional quantum magnet SrCu$_2$(BO$_3$)$_2$.Comment: 8 pages, Proceedings of the HFM2008 Conferenc

Generation of supercoils in nicked and gapped DNA drives DNA unknotting and postreplicative decatenation

Due to the helical structure of DNA the process of DNA replication is topologically complex. Freshly replicated DNA molecules are catenated with each other and are frequently knotted. For proper functioning of DNA it is necessary to remove all of these entanglements. This is done by DNA topoisomerases that pass DNA segments through each other. However, it has been a riddle how DNA topoisomerases select the sites of their action. In highly crowded DNA in living cells random passages between contacting segments would only increase the extent of entanglement. Using molecular dynamics simulations we observed that in actively supercoiled DNA molecules the entanglements resulting from DNA knotting or catenation spontaneously approach sites of nicks and gaps in the DNA. Type I topoisomerases, that preferentially act at sites of nick and gaps, are thus naturally provided with DNA-DNA juxtapositions where a passage results in an error-free DNA unknotting or DNA decatenatio