Statistical-mechanical lattice models for protein-DNA binding in chromatin

Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibriums measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription factors to the DNA sequence. New approaches have to be developed to derive statistical mechanical lattice descriptions of chromatin-associated protein-DNA interactions. Here, we present the theoretical framework for lattice models of histone-DNA interactions in chromatin and investigate the (competitive) DNA binding of other chromosomal proteins and transcription factors. The results have a number of applications for quantitative models for the regulation of gene expression.Comment: 19 pages, 7 figures, accepted author manuscript, to appear in J. Phys.: Cond. Mat

Universal geometrical factor of protein conformations as a consequence of energy minimization

The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein conformation as a consequence of energy minimization in protein folding. Folding simulations of 10 polypeptides with chain length ranging from 183 to 548 residues manifest that the dimensionless ratio (V/(A)) of the van der Waals volume V to the surface area A and average atomic radius of the folded structures, calculated with atomic radii setting used in SMMP [Eisenmenger F., et. al., Comput. Phys. Commun., 138 (2001) 192], approach 0.49 quickly during the course of energy minimization. A large scale analysis of protein structures show that the ratio for real and well-designed proteins is universal and equal to 0.491\pm0.005. The fractional composition of hydrophobic and hydrophilic residues does not affect the ratio substantially. The ratio also holds for intrinsically disordered proteins, while it ceases to be universal for polypeptides with bad folding properties.Comment: 6 pages, 1 table, 4 figure

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets

The merger of vertically offset quasi-geostrophic vortices

We examine the critical merging distance between two equal-volume, equal-potential-vorticity quasi-geostrophic vortices. We focus on how this distance depends on the vertical offset between the two vortices, each having a unit mean height-to-width aspect ratio. The vertical direction is special in the quasi-geostrophic model (used to capture the leading-order dynamical features of stably stratified and rapidly rotating geophysical flows) since vertical advection is absent. Nevertheless vortex merger may still occur by horizontal advection. In this paper, we first investigate the equilibrium states for the two vortices as a function of their vertical and horizontal separation. We examine their basic properties together with their linear stability. These findings are next compared to numerical simulations of the nonlinear evolution of two spheres of potential vorticity. Three different regimes of interaction are identified, depending on the vertical offset. For a small offset, the interaction differs little from the case when the two vortices are horizontally aligned. On the other hand, when the vertical offset is comparable to the mean vortex radius, strong interaction occurs for greater horizontal gaps than in the horizontally aligned case, and therefore at significantly greater full separation distances. This perhaps surprising result is consistent with the linear stability analysis and appears to be a consequence of the anisotropy of the quasi-geostrophic equations. Finally, for large vertical offsets, vortex merger results in the formation of a metastable tilted dumbbell vortex.Publisher PDFPeer reviewe

Genome-Wide Studies of Histone Demethylation Catalysed by the Fission Yeast Homologues of Mammalian LSD1

In order to gain a more global view of the activity of histone demethylases, we report here genome-wide studies of the fission yeast SWIRM and polyamine oxidase (PAO) domain homologues of mammalian LSD1. Consistent with previous work we find that the two S. pombe proteins, which we name Swm1 and Swm2 (after SWIRM1 and SWIRM2), associate together in a complex. However, we find that this complex specifically demethylates lysine 9 in histone H3 (H3K9) and both up- and down-regulates expression of different groups of genes. Using chromatin-immunoprecipitation, to isolate fragments of chromatin containing either H3K4me2 or H3K9me2, and DNA microarray analysis (ChIP-chip), we have studied genome-wide changes in patterns of histone methylation, and their correlation with gene expression, upon deletion of the swm1+ gene. Using hyper-geometric probability comparisons we uncover genetic links between lysine-specific demethylases, the histone deacetylase Clr6, and the chromatin remodeller Hrp1. The data presented here demonstrate that in fission yeast the SWIRM/PAO domain proteins Swm1 and Swm2 are associated in complexes that can remove methyl groups from lysine 9 methylated histone H3. In vitro, we show that bacterially expressed Swm1 also possesses lysine 9 demethylase activity. In vivo, loss of Swm1 increases the global levels of both H3K9me2 and H3K4me2. A significant accumulation of H3K4me2 is observed at genes that are up-regulated in a swm1 deletion strain. In addition, H3K9me2 accumulates at some genes known to be direct Swm1/2 targets that are down-regulated in the swm1¿ strain. The in vivo data indicate that Swm1 acts in concert with the HDAC Clr6 and the chromatin remodeller Hrp1 to repress gene expression. In addition, our in vitro analyses suggest that the H3K9 demethylase activity requires an unidentified post-translational modification to allow it to act. Thus, our results highlight complex interactions between histone demethylase, deacetylase and chromatin remodelling activities in the regulation of gene expression

3D structure of individual mammalian genomes studied by single cell Hi-C

The folding of genomic DNA from the beads-on-a-string like structure of nucleosomes into higher order assemblies is critically linked to nuclear processes. We have calculated the first 3D structures of entire mammalian genomes using data from a new chromosome conformation capture procedure that allows us to first image and then process single cells. This has allowed us to study genome folding down to a scale of <100 kb and to validate the structures. We show that the structures of individual topological-associated domains and loops vary very substantially from cell-to-cell. By contrast, A/B compartments, lamin-associated domains and active enhancers/promoters are organized in a consistent way on a genome-wide basis in every cell, suggesting that they could drive chromosome and genome folding. Through studying pluripotency factor- and NuRD-regulated genes, we illustrate how single cell genome structure determination provides a novel approach for investigating biological processes.We thank the Wellcome Trust (082010/Z/07/Z), the EC FP7 4DCellFate project (277899) and the MRC (MR/M010082/1) for financial support

BGWM as Second Constituent of Complex Matrix Model

Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less topical complex matrix model appeared to be an exception: its decomposition involved not only the Kontsevich tau-function but also another constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition function. The BGW tau-function can be represented either as a generating function of all unitary-matrix integrals or as a Kontsevich-Penner model with potential 1/X (instead of X^3 in the cubic Kontsevich model).Comment: 42 page

Challenges of beta-deformation

A brief review of problems, arising in the study of the beta-deformation, also known as "refinement", which appears as a central difficult element in a number of related modern subjects: beta \neq 1 is responsible for deviation from free fermions in 2d conformal theories, from symmetric omega-backgrounds with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras etc. The main attention is paid to the context of AGT relation and its possible generalizations.Comment: 20 page