Low-Degree Hardness of Detection for Correlated Erd\H{o}s-R\'enyi Graphs

Given two Erd\H{o}s-R\'enyi graphs with $n$ vertices whose edges are correlated through a latent vertex correspondence, we study complexity lower bounds for the associated correlation detection problem for the class of low-degree polynomial algorithms. We provide evidence that any degree-$O(\rho^{-1})$ polynomial algorithm fails for detection, where $\rho$ is the edge correlation. Furthermore, in the sparse regime where the edge density $q=n^{-1+o(1)}$, we provide evidence that any degree-$d$ polynomial algorithm fails for detection, as long as $\log d=o\big( \frac{\log n}{\log nq} \wedge \sqrt{\log n} \big)$ and the correlation $\rho<\sqrt{\alpha}$ where $\alpha\approx 0.338$ is the Otter's constant. Our result suggests that several state-of-the-art algorithms on correlation detection and exact matching recovery may be essentially the best possible.Comment: 40 page

Regulation of junction configuration by cell tension

The maintenance of cell-cell contacts is essential for tissue cohesion and a variety of different physiological processes in morphogenesis and homeostasis. Adherens junctions are protein complexes that mediate cell-cell contacts in epithelial cells and E-cadherin receptors are their main component. During junction formation, thin bundles of actin localise towards cell-cell contacts in the characteristic cytoskeletal organization of epithelia. Tension at the underlying cortex and thin bundle compaction help form tight, straight junctions and maintain cadherin receptors in place. However, how these epithelia-specific structures are formed and remodelled lacks in-depth understanding. In this study, I have addressed how contractile forces modulate junction configuration and molecular composition (adhesion receptors and actin cytoskeleton). Micropatterning was used to precisely confine the geometry of cells, control cortical forces and provide a permissive, simplistic way in which cells are allowed to interact. Three different shapes, namely squares, triangles and circles were patterned to study biophysical and junction properties. Although the average cell heights and volumes are similar between different geometries, cortical stiffness (i.e. Young’s modulus) is two-fold higher in cells grown in geometries that impose higher contractility: squares and triangles. Doublets seeded on these shapes also position their nuclei further apart and exhibit preferences in junction orientation. A majority of cells cultured on triangular and square geometries have shorter and straighter junctions with a clear presence of thin bundles parallel to the cell-cell interface. Localisation of phosphorylated myosin light chain to thin bundles reinforce the notion that these are the main contractile pool instead of the junctional actin at contacts. Counter-intuitively, E-cadherin and F-actin density are also reduced with increased contractility and tension. Taken together, higher levels of contractility and cortical tension imposed by the square and triangle geometric shapes, are necessary to properly generate the epithelial cellular architecture, configuration of junctions and their molecular makeup. This suggests that tensional constraints play an important role in regulating the stability of junctions and the organization of underlying actin filaments that support the characteristic epithelial cell shape.Open Acces

Transcriptomic changes triggered by ouabain in rat cerebellum granule cells: Role of α3- and α1-Na+,K+-ATPase-mediated signaling

It was shown previously that inhibition of the ubiquitous α1 isoform of Na+,K+-ATPase by ouabain sharply affects gene expression profile via elevation of intracellular [Na+]i/[K+]i ratio. Unlike other cells, neurons are abundant in the α3 isoform of Na+,K+-ATPase, whose affinity in rodents to ouabain is 104-fold higher compared to the α1 isoform. With these sharp differences in mind, we compared transcriptomic changes in rat cerebellum granule cells triggered by inhibition of α1- and α3-Na+,K+-ATPase isoforms. Inhibition of α1- and α3-Na+,K+-ATPase isoforms by 1 mM ouabain resulted in dissipation of transmembrane Na+ and K+ gradients and differential expression of 994 transcripts, whereas selective inhibition of α3-Na+,K+-ATPase isoform by 100 nM ouabain affected expression of 144 transcripts without any impact on the [Na+]i/[K+]i ratio. The list of genes whose expression was affected by 1 mM ouabain by more than 2-fold was abundant in intermediates of intracellular signaling and transcription regulators, including augmented content of Npas4, Fos, Junb, Atf3, and Klf4 mRNAs, whose upregulated expression was demonstrated in neurons subjected to electrical and glutamatergic stimulation. The role [Na+]i/[K+]i-mediated signaling in transcriptomic changes involved in memory formation and storage should be examined further

Quantum tunneling from a new type of Unified Cantor Potential

We introduce a new type of potential system that combines the families of general Cantor (fractal system) and general Smith-Volterra-Cantor (non-fractal system) potentials. We call this system as Unified Cantor Potential (UCP) system. The UCP system of total span $L$ is characterized by scaling parameter $\rho >1$, stage $G$ and two real numbers $\alpha$ and $\beta$. For $\alpha=1$, $\beta=0$, the UCP system represents general Cantor potential while for $\alpha=0$, $\beta=1$, this system represent general Smith-Volterra-Cantor (SVC) potential. We provide close-form expression of transmission probability from UCP system for arbitrary $\alpha$ and $\beta$ by using $q$-Pochhammer symbol. Several new features of scattering are reported for this system. The transmission probability $T_{G}(k)$ shows a scaling behavior with $k$ which is derived analytically for this potential. The proposed system also opens up the possibility for further generalization of new potential systems that encompass a large class of fractal and non-fractal systems. The analytical formulation of tunneling from this system would help to study the transmission feature at breaking threshold when a system transit from fractal to non-fractal domain.Comment: 23 Pages, 11 captioned fig

SILAC-based proteomic quantification of chemoattractant-induced cytoskeleton dynamics on a second to minute timescale

Cytoskeletal dynamics during cell behaviours ranging from endocytosis and exocytosis to cell division and movement is controlled by a complex network of signalling pathways, the full details of which are as yet unresolved. Here we show that SILAC-based proteomic methods can be used to characterize the rapid chemoattractant-induced dynamic changes in the actin–myosin cytoskeleton and regulatory elements on a proteome-wide scale with a second to minute timescale resolution. This approach provides novel insights in the ensemble kinetics of key cytoskeletal constituents and association of known and novel identified binding proteins. We validate the proteomic data by detailed microscopy-based analysis of in vivo translocation dynamics for key signalling factors. This rapid large-scale proteomic approach may be applied to other situations where highly dynamic changes in complex cellular compartments are expected to play a key role