Strong-coupling perturbation theory for the two-dimensional Bose-Hubbard model in a magnetic field

The Bose-Hubbard model in an external magnetic field is investigated with strong-coupling perturbation theory. The lowest-order secular equation leads to the problem of a charged particle moving on a lattice in the presence of a magnetic field, which was first treated by Hofstadter. We present phase diagrams for the two-dimensional square and triangular lattices, showing a change in shape of the phase lobes away from the well-known power-law behavior in zero magnetic field. Some qualitative agreement with experimental work on Josephson-junction arrays is found for the insulating phase behavior at small fields.Comment: 7 pages, 5 figures include

Patched receptors sense, interpret and establish an epidermal Hedgehog signalling gradient

By employing the sensitivity of single molecule fluorescent in situ hybridisation (smFISH) we have precisely quantified the levels and defined the temporal and spatial distribution of Hedgehog signalling activity during embryonic skin development, and uncovered that there is a Hedgehog signalling gradient along the proximal-distal axis of developing hair follicles. In order to explore the contribution of Hedgehog receptors Ptch1 and Ptch2 in establishing the epidermal signalling gradient, we quantitated the level of pathway activity generated in Ptch1 and Ptch1;Ptch2-deficient skin and defined the contribution of each receptor to regulation of the levels of Hedgehog signalling identified in wild-type skin. Moreover, we show that both the cellular phenotype and level of pathway activity featured in Ptch1;Ptch2-deficient cells faithfully recapitulates the Peak level of endogenous Hedgehog signalling detected at the base of developing follicles, where the concentration of endogenous Shh is predicted to be highest. Taken together, these data demonstrate that both Ptch1 and Ptch2 play a crucial role in sensing the concentration of Hedgehog ligand and regulating the appropriate dose-dependent response

Стратегії проповідницького дискурсу І. Галятовського: антропологічний аспект

How cells in developing organisms interpret the quantitative information contained in morphogen gradients is an open question. Here we address this question using a novel integrative approach that combines quantitative measurements of morphogen-induced gene expression at single-mRNA resolution with mathematical modelling of the induction process. We focus on the induction of Notch ligands by the LIN-3/EGF morphogen gradient during vulva induction in Caenorhabditis elegans. We show that LIN-3/EGF-induced Notch ligand expression is highly dynamic, exhibiting an abrupt transition from low to high expression. Similar transitions in Notch ligand expression are observed in two highly divergent wild C. elegans isolates. Mathematical modelling and experiments show that this transition is driven by a dynamic increase in the sensitivity of the induced cells to external LIN-3/EGF. Furthermore, this increase in sensitivity is independent of the presence of LIN-3/EGF. Our integrative approach might be useful to study induction by morphogen gradients in other systems

A systems-level analysis of perfect adaptation in yeast osmoregulation

available in PMC 2011 June 7.Negative feedback can serve many different cellular functions, including noise reduction in transcriptional networks and the creation of circadian oscillations. However, only one special type of negative feedback (“integral feedback”) ensures perfect adaptation, where steady-state output is independent of steady-state input. Here we quantitatively measure single-cell dynamics in the Saccharomyces cerevisiae hyperosmotic shock network, which regulates membrane turgor pressure. Importantly, we find that the nuclear enrichment of the MAP kinase Hog1 perfectly adapts to changes in external osmolarity, a feature robust to signaling fidelity and operating with very low noise. By monitoring multiple system quantities (e.g., cell volume, Hog1, glycerol) and using varied input waveforms (e.g., steps and ramps), we assess in a minimally invasive manner the network location of the mechanism responsible for perfect adaptation. We conclude that the system contains only one effective integrating mechanism, which requires Hog1 kinase activity and regulates glycerol synthesis but not leakage.National Science Foundation (U.S.) (Graduate Research Fellowship)Massachusetts Institute of Technology (MIT-Merck Graduate Fellowship)National Institutes of Health (U.S.) (NIH grant R01-GM068957)National Institutes of Health (U.S.) (NIH grant 5 R90 DK071511-01

Phase transition in a chain of quantum vortices

We consider interacting vortices in a quasi-one-dimensional array of Josephson junctions with small capacitance. If the charging energy of a junction is of the order of the Josephson energy, the fluctuations of the superconducting order parameter in the system are considerable, and the vortices behave as quantum particles. Their density may be tuned by an external magnetic field, and therefore one can control the commensurability of the one-dimensional vortex lattice with the lattice of Josephson junctions. We show that the interplay between the quantum nature of a vortex, and the long-range interaction between the vortices leads to the existence of a specific commensurate-incommensurate transition in a one-dimensional vortex lattice. In the commensurate phase an elementary excitation is a soliton, with energy separated from the ground state by a finite gap. This gap vanishes in the incommensurate phase. Each soliton carries a fraction of a flux quantum; the propagation of solitons leads to a finite resistance of the array. We find the dependence of the resistance activation energy on the magnetic field and parameters of the Josephson array. This energy consists of the above-mentioned gap, and also of a boundary pinning term, which is different in the commensurate and incommensurate phases. The developed theory allows us to explain quantitatively the available experimental data.Comment: 14 pages, 7 eps figure

Single-Cell Expression Analyses during Cellular Reprogramming Reveal an Early Stochastic and a Late Hierarchic Phase

SummaryDuring cellular reprogramming, only a small fraction of cells become induced pluripotent stem cells (iPSCs). Previous analyses of gene expression during reprogramming were based on populations of cells, impeding single-cell level identification of reprogramming events. We utilized two gene expression technologies to profile 48 genes in single cells at various stages during the reprogramming process. Analysis of early stages revealed considerable variation in gene expression between cells in contrast to late stages. Expression of Esrrb, Utf1, Lin28, and Dppa2 is a better predictor for cells to progress into iPSCs than expression of the previously suggested reprogramming markers Fbxo15, Fgf4, and Oct4. Stochastic gene expression early in reprogramming is followed by a late hierarchical phase with Sox2 being the upstream factor in a gene expression hierarchy. Finally, downstream factors derived from the late phase, which do not include Oct4, Sox2, Klf4, c-Myc, and Nanog, can activate the pluripotency circuitry

The low-energy theory for the Bose-Hubbard model and the normal ground state of bosons

A bosonic realization of the SU(2) Lie algebra and of its vector representation is constructed, and an effective low-energy description of the Bose-Hubbard model in the form of anisotropic theory of quantum rotors is proposed and discussed. A possibility of a normal zero-temperature bosonic phase with neither crystalline nor superfluid order around the tip of the checkerboard-solid lobe at half-integer fillings is examined.Comment: 8 pages, LaTex, one postscript figur

Meissner effect in a bosonic ladder

We investigate the effect of a magnetic field on a bosonic ladder. We show that such a system leads to the one dimensional equivalent of a vortex lattice in a superconductor. We investigate the physical properties of the vortex phase, such as vortex density and vortex correlation functions and show that magnetization has plateaus for some commensurate values of the mag netic field. The lowest plateau corresponds to a true Meissner to vortex transition at a critical field $H_{c1}$ that exists although the system has no long range superconducting order. Implications for experimental realizations such as Josephson junction arrays are discussed.Comment: 4 pages, 2 Encapsulated Postscript figures, RevTe

Massively parallel clonal analysis using CRISPR/Cas9 induced genetic scars

A key goal of developmental biology is to understand how a single cell transforms into a full-grown organism consisting of many cells. Although impressive progress has been made in lineage tracing using imaging approaches, analysis of vertebrate lineage trees has mostly been limited to relatively small subsets of cells. Here we present scartrace, a strategy for massively parallel clonal analysis based on Cas9 induced genetic scars in the zebrafish

Phases of the one-dimensional Bose-Hubbard model

The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearest-neighbor interaction is investigated using the Density-Matrix Renormalization Group. Recently normal phases without long-range order have been conjectured between the charge density wave phase and the superfluid phase in one-dimensional bosonic systems without disorder. Our calculations demonstrate that there is no intermediate phase in the one-dimensional Bose-Hubbard model but a simultaneous vanishing of crystalline order and appearance of superfluid order. The complete phase diagrams with and without nearest-neighbor interaction are obtained. Both phase diagrams show reentrance from the superfluid phase to the insulator phase.Comment: Revised version, 4 pages, 5 figure