Upper semi-continuity of the Royden-Kobayashi pseudo-norm, a counterexample for H\"olderian almost complex structures

If $X$ is an almost complex manifold, with an almost complex structure $J$ of class \CC^\alpha, for some $\alpha >0$, for every point $p\in X$ and every tangent vector $V$ at $p$, there exists a germ of $J$-holomorphic disc through $p$ with this prescribed tangent vector. This existence result goes back to Nijenhuis-Woolf. All the $J$ holomorphic curves are of class \CC^{1,\alpha} in this case. Then, exactly as for complex manifolds one can define the Royden-Kobayashi pseudo-norm of tangent vectors. The question arises whether this pseudo-norm is an upper semi-continuous function on the tangent bundle. For complex manifolds it is the crucial point in Royden's proof of the equivalence of the two standard definitions of the Kobayashi pseudo-metric. The upper semi-continuity of the Royden-Kobayashi pseudo-norm has been established by Kruglikov for structures that are smooth enough. In [I-R], it is shown that \CC^{1,\alpha} regularity of $J$ is enough. Here we show the following: Theorem. There exists an almost complex structure $J$ of class \CC^{1\over 2} on the unit bidisc \D^2\subset \C^2, such that the Royden-Kobayashi seudo-norm is not an upper semi-continuous function on the tangent bundle.Comment: 5 page

Repulsive Forces Between Looping Chromosomes Induce Entropy-Driven Segregation

One striking feature of chromatin organization is that chromosomes are compartmentalized into distinct territories during interphase, the degree of intermingling being much smaller than expected for linear chains. A growing body of evidence indicates that the formation of loops plays a dominant role in transcriptional regulation as well as the entropic organization of interphase chromosomes. Using a recently proposed model, we quantitatively determine the entropic forces between chromosomes. This Dynamic Loop Model assumes that loops form solely on the basis of diffusional motion without invoking other long-range interactions. We find that introducing loops into the structure of chromatin results in a multi-fold higher repulsion between chromosomes compared to linear chains. Strong effects are observed for the tendency of a non-random alignment; the overlap volume between chromosomes decays fast with increasing loop number. Our results suggest that the formation of chromatin loops imposes both compartmentalization as well as order on the system without requiring additional energy-consuming processes

Diffusion-Driven Looping Provides a Consistent Framework for Chromatin Organization

Chromatin folding inside the interphase nucleus of eukaryotic cells is done on multiple scales of length and time. Despite recent progress in understanding the folding motifs of chromatin, the higher-order structure still remains elusive. Various experimental studies reveal a tight connection between genome folding and function. Chromosomes fold into a confined subspace of the nucleus and form distinct territories. Chromatin looping seems to play a dominant role both in transcriptional regulation as well as in chromatin organization and has been assumed to be mediated by long-range interactions in many polymer models. However, it remains a crucial question which mechanisms are necessary to make two chromatin regions become co-located, i.e. have them in spatial proximity. We demonstrate that the formation of loops can be accomplished solely on the basis of diffusional motion. The probabilistic nature of temporary contacts mimics the effects of proteins, e.g. transcription factors, in the solvent. We establish testable quantitative predictions by deriving scale-independent measures for comparison to experimental data. In this Dynamic Loop (DL) model, the co-localization probability of distant elements is strongly increased compared to linear non-looping chains. The model correctly describes folding into a confined space as well as the experimentally observed cell-to-cell variation. Most importantly, at biological densities, model chromosomes occupy distinct territories showing less inter-chromosomal contacts than linear chains. Thus, dynamic diffusion-based looping, i.e. gene co-localization, provides a consistent framework for chromatin organization in eukaryotic interphase nuclei

Hi-C-constrained physical models of human chromosomes recover functionally-related properties of genome organization

Combining genome-wide structural models with phenomenological data is at the forefront of efforts to understand the organizational principles regulating the human genome. Here, we use chromosome-chromosome contact data as knowledge-based constraints for large-scale three-dimensional models of the human diploid genome. The resulting models remain minimally entangled and acquire several functional features that are observed in vivo and that were never used as input for the model. We find, for instance, that gene-rich, active regions are drawn towards the nuclear center, while gene poor and lamina associated domains are pushed to the periphery. These and other properties persist upon adding local contact constraints, suggesting their compatibility with non-local constraints for the genome organization. The results show that suitable combinations of data analysis and physical modelling can expose the unexpectedly rich functionally-related properties implicit in chromosome-chromosome contact data. Specific directions are suggested for further developments based on combining experimental data analysis and genomic structural modelling

Structure of Metaphase Chromosomes: A Role for Effects of Macromolecular Crowding

In metaphase chromosomes, chromatin is compacted to a concentration of several hundred mg/ml by mechanisms which remain elusive. Effects mediated by the ionic environment are considered most frequently because mono- and di-valent cations cause polynucleosome chains to form compact ∼30-nm diameter fibres in vitro, but this conformation is not detected in chromosomes in situ. A further unconsidered factor is predicted to influence the compaction of chromosomes, namely the forces which arise from crowding by macromolecules in the surrounding cytoplasm whose measured concentration is 100–200 mg/ml. To mimic these conditions, chromosomes were released from mitotic CHO cells in solutions containing an inert volume-occupying macromolecule (8 kDa polyethylene glycol, 10.5 kDa dextran, or 70 kDa Ficoll) in 100 µM K-Hepes buffer, with contaminating cations at only low micromolar concentrations. Optical and electron microscopy showed that these chromosomes conserved their characteristic structure and compaction, and their volume varied inversely with the concentration of a crowding macromolecule. They showed a canonical nucleosomal structure and contained the characteristic proteins topoisomerase IIα and the condensin subunit SMC2. These observations, together with evidence that the cytoplasm is crowded in vivo, suggest that macromolecular crowding effects should be considered a significant and perhaps major factor in compacting chromosomes. This model may explain why ∼30-nm fibres characteristic of cation-mediated compaction are not seen in chromosomes in situ. Considering that crowding by cytoplasmic macromolecules maintains the compaction of bacterial chromosomes and has been proposed to form the liquid crystalline chromosomes of dinoflagellates, a crowded environment may be an essential characteristic of all genomes

Matériaux pour l'enregistrement magnétique haute densité

Les prochaines générations de media mettront en jeu des densités d'information beaucoup plus importantes que celles actuellement utilisées : accroissement des densités linéaires d'un facteur 3 à 5, des densités radiales d'un facteur 2 à 3. Diverses technologies (enregistrement magnétique sur couche particulaire ou sur film mince, enregistrement magnétooptique ou optique réversible) sont potentiellement capables de satisfaire ces exigences, mais c'est l'enregistrement magnétique sur couche particulaire qui paraît le candidat le mieux placé du point de vue pratique, en raison d'une part de l'acquis (moyens de production éprouvés, performances et flexibilité d'emploi des produits) et d'autre part de ses capacités non encore exploitées (passage du mode d'enregistrement longitudinal aux modes vertical et isotrope, évolution des particules, amélioration des procédés de dispersion, enduction et finition). L'objet de cette présentation est de montrer comment les problèmes liés à l'enregistrement haute densité (résolution, rapport signal/bruit ...) gouvernent l'évolution en matière de particules : hausse de la coercivité et de l'aimantation spécifique par unité de volume, tendance à des particules de plus en plus fines (tendance limitée par le phénomène de superparamagnétisme) contrôle de la taille, de la morphologie, de l'homodispersité et de l'état de surface, particules se prêtant particulièrement bien à l'enregistrement isotrope ou vertical (particules isotropes et/ou à anisotropie multiaxiale, plaquettes d'hexaferrite de baryum). L'accent est mis sur la nécessité de prendre en compte les problèmes de stabilité chimique et de sensibilité vis-à-vis des contraintes thermiques et mécaniques, problèmes non encore résolus sur les deux types de particules largement utilisées que sont le fer métal et les oxydes dopés cobalt

Matériaux pour l'enregistrement magnétique haute densité

The next generations of media will use recording densities much greater than those in use today : linear densities will be multiplied by a factor of 3 to 5 and radial densities by a factor of 2 to 3. Different technologies (particulate or thin film recording, optics or magnetooptics), are theoretically capable of meeting these requirements, but among them it is the particulate magnetic recording which is the most suitable : first because of its present qualities (tested production methods, performance and flexibility of use), and second, because of its as yet unexplored capabilities (transition from the longitudinal mode to the vertical or isotropic one, evolution of particles, improvement of dispersion, enduction and finishing processes). The purpose of this review is to show how the constraints of high density recording (resolution, signal to noise ratio...) will condition the evolution of particles : higher coercivity and magnetization by volume unit, trend towards smaller particles (limited by the phenomenon of superparamagnetism), better control of the size, morphology, homodispersity and surface aspect, isotropic particles with multiaxial anisotropy, baryum hexaferrites. A special emphasis is laid on the need to take account of the problems of temperature and stress dependence of the cobalt doped iron oxides and of chemical stability of iron particles.Les prochaines générations de media mettront en jeu des densités d'information beaucoup plus importantes que celles actuellement utilisées : accroissement des densités linéaires d'un facteur 3 à 5, des densités radiales d'un facteur 2 à 3. Diverses technologies (enregistrement magnétique sur couche particulaire ou sur film mince, enregistrement magnétooptique ou optique réversible) sont potentiellement capables de satisfaire ces exigences, mais c'est l'enregistrement magnétique sur couche particulaire qui paraît le candidat le mieux placé du point de vue pratique, en raison d'une part de l'acquis (moyens de production éprouvés, performances et flexibilité d'emploi des produits) et d'autre part de ses capacités non encore exploitées (passage du mode d'enregistrement longitudinal aux modes vertical et isotrope, évolution des particules, amélioration des procédés de dispersion, enduction et finition). L'objet de cette présentation est de montrer comment les problèmes liés à l'enregistrement haute densité (résolution, rapport signal/bruit ...) gouvernent l'évolution en matière de particules : hausse de la coercivité et de l'aimantation spécifique par unité de volume, tendance à des particules de plus en plus fines (tendance limitée par le phénomène de superparamagnétisme) contrôle de la taille, de la morphologie, de l'homodispersité et de l'état de surface, particules se prêtant particulièrement bien à l'enregistrement isotrope ou vertical (particules isotropes et/ou à anisotropie multiaxiale, plaquettes d'hexaferrite de baryum). L'accent est mis sur la nécessité de prendre en compte les problèmes de stabilité chimique et de sensibilité vis-à-vis des contraintes thermiques et mécaniques, problèmes non encore résolus sur les deux types de particules largement utilisées que sont le fer métal et les oxydes dopés cobalt