Continuation Sheaves in Dynamics: Sheaf Cohomology and Bifurcation

Continuation of algebraic structures in families of dynamical systems is described using category theory, sheaves, and lattice algebras. Well-known concepts in dynamics, such as attractors or invariant sets, are formulated as functors on appropriate categories of dynamical systems mapping to categories of lattices, posets, rings or abelian groups. Sheaves are constructed from such functors, which encode data about the continuation of structure as system parameters vary. Similarly, morphisms for the sheaves in question arise from natural transformations. This framework is applied to a variety of lattice algebras and ring structures associated to dynamical systems, whose algebraic properties carry over to their respective sheaves. Furthermore, the cohomology of these sheaves are algebraic invariants which contain information about bifurcations of the parametrized systems

Suppression of planar cell polarity signaling and migration in glioblastoma by Nrdp1-mediated Dvl polyubiquitination.

The lethality of the aggressive brain tumor glioblastoma multiforme (GBM) results in part from its strong propensity to invade surrounding normal brain tissue. Although oncogenic drivers such as epidermal growth factor receptor activation and Phosphatase and Tensin homolog inactivation are thought to promote the motility and invasiveness of GBM cells via phosphatidylinostitol 3-kinase activation, other unexplored mechanisms may also contribute to malignancy. Here we demonstrate that several components of the planar cell polarity (PCP) arm of non-canonical Wnt signaling including VANGL1, VANGL2 and FZD7 are transcriptionally upregulated in glioma and correlate with poorer patient outcome. Knockdown of the core PCP pathway component VANGL1 suppresses the motility of GBM cell lines, pointing to an important mechanistic role for this pathway in glioblastoma malignancy. We further observe that restoration of Nrdp1, a RING finger type E3 ubiquitin ligase whose suppression in GBM also correlates with poor prognosis, reduces GBM cell migration and invasiveness by suppressing PCP signaling. Our observations indicate that Nrdp1 physically interacts with the Vangl1 and Vangl2 proteins to mediate the K63-linked polyubiquitination of the Dishevelled, Egl-10 and Pleckstrin (DEP) domain of the Wnt pathway protein Dishevelled (Dvl). Ubiquitination hinders Dvl binding to phosphatidic acid, an interaction necessary for efficient Dvl recruitment to the plasma membrane upon Wnt stimulation of Fzd receptor and for the propagation of downstream signals. We conclude that the PCP pathway contributes significantly to the motility and hence the invasiveness of GBM cells, and that Nrdp1 acts as a negative regulator of PCP signaling by inhibiting Dvl through a novel polyubiquitination mechanism. We propose that the upregulation of core PCP components, together with the loss of the key negative regulator Nrdp1, act coordinately to promote GBM invasiveness and malignancy

Understanding the effect of confinement in scanning spreading resistance microscopy measurements

Scanning spreading resistance microscopy (SSRM) is a powerful technique for quantitative two-and three-dimensional carrier profiling of semiconductor devices with sub-nm spatial resolution. However, considering the sub-10 nm dimensions of advanced devices and the introduction of three-dimensional architectures like fin field effect transistor (FinFET) and nanowires, the measured spreading resistance is easily impacted by parasitic series resistances present in the system. The limited amount of material, the presence of multiple interfaces, and confined current paths may increase the total resistance measured by SSRM beyond the expected spreading resistance, which can ultimately lead to an inaccurate carrier quantification. Here, we report a simulation assisted experimental study to identify the different parameters affecting the SSRM measurements in confined volumes. Experimentally, the two-dimensional current confinement is obtained by progressively thinning down uniformly doped blanket silicon on insulator wafers using scalpel SSRM. The concomitant SSRM provides detailed electrical information as a function of depth up to oxide interface. We show that the resistance is most affected by the interface traps in case of a heterogeneous sample, followed by the intrinsic resistance of the current carrying paths. Furthermore, we show that accurate carrier quantification is ensured for typical back contact distances of 1 μm if the region of interest is at least nine times larger than the probe radius. © 2020 Author(s)

Membrane Mucin Muc4 promotes blood cell association with tumor cells and mediates efficient metastasis in a mouse model of breast cancer

Mucin-4 (Muc4) is a large cell surface glycoprotein implicated in the protection and lubrication of epithelial structures. Previous studies suggest that aberrantly expressed Muc4 can influence the adhesiveness, proliferation, viability and invasiveness of cultured tumor cells, as well as the growth rate and metastatic efficiency of xenografted tumors. Although it has been suggested that one of the major mechanisms by which Muc4 potentiates tumor progression is via its engagement of the ErbB2/HER2 receptor tyrosine kinase, other mechanisms exist and remain to be delineated. Moreover, the requirement for endogenous Muc4 for tumor growth progression has not been previously explored in the context of gene ablation. To assess the contribution of endogenous Muc4 to mammary tumor growth properties, we first created a genetically engineered mouse line lacking functional Muc4 (Muc4 ko), and then crossed these animals with the NDL (Neu DeLetion mutant) model of ErbB2-induced mammary tumorigenesis. We observed that Muc4 ko animals are fertile and develop normally, and adult mice exhibit no overt tissue abnormalities. In tumor studies, we observed that although some markers of tumor growth such as vascularity and cyclin D1 expression are suppressed, primary mammary tumors from Muc4 ko /NDL female mice exhibit similar latencies and growth rates as Muc4 wt /NDL animals. However, the presence of lung metastases is markedly suppressed in Muc4 ko /NDL mice. Interestingly, histological analysis of lung lesions from Muc4 ko /NDL mice revealed a reduced association of disseminated cells with platelets and white blood cells. Moreover, isolated cells derived from Muc4 ko /NDL tumors interact with fewer blood cells when injected directly into the vasculature or diluted into blood from wild type mice. We further observed that blood cells more efficiently promote the viability of non-adherent Muc4 wt /NDL cells than Muc4 ko /NDL cells. Together, our observations suggest that Muc4 may facilitate metastasis by promoting the association of circulating tumor cells with blood cells to augment tumor cell survival in circulation