Orthodiagonal anti-involutive Kokotsakis polyhedra

We study the properties of Kokotsakis polyhedra of orthodiagonal anti-involutive type. Stachel conjectured that a certain resultant connected to a polynomial system describing flexion of a Kokotsakis polyhedron must be reducible. Izmestiev \cite{izmestiev2016classification} showed that a polyhedron of the orthodiagonal anti-involutive type is the only possible candidate to disprove Stachel's conjecture. We show that the corresponding resultant is reducible, thereby confirming the conjecture. We do it in two ways: by factorization of the corresponding resultant and providing a simple geometric proof. We describe the space of parameters for which such a polyhedron exists and show that this space is non-empty. We show that a Kokotsakis polyhedron of orthodiagonal anti-involutive type is flexible and give explicit parameterizations in elementary functions and in elliptic functions of its flexion

Influence of sulphide Cu (I) promoting additives concentration on acid and catalytic properties of high-silica zeolites in straight-run gasoline conversion

In present article the influence of Cu[2]S promoting additives concentration on acid and catalytic properties of high silica MFI-type zeolites is investigated in the process of conversion of straight-run gasoline fractions of gas condensate into high octane components of motor fuels. It was shown that zeolite modified with 1% of Cu[2]S nanoscaled powder possesses the highest acid centers concentration and highest catalytic activity

Stochastic contraction of myosin minifilaments drives evolution of microridge protrusion patterns in epithelial cells

Actin-based protrusions vary in morphology, stability, and arrangement on cell surfaces. Microridges are laterally elongated protrusions on mucosal epithelial cells, where they form evenly spaced, mazelike patterns that dynamically remodel by fission and fusion. To characterize how microridges form their highly ordered, subcellular patterns and investigate the mechanisms driving fission and fusion, we imaged microridges in the maturing skin of zebrafish larvae. After their initial development, microridge spacing and alignment became increasingly well ordered. Imaging F-actin and non-muscle myosin II (NMII) revealed that microridge fission and fusion were associated with local NMII activity in the apical cortex. Inhibiting NMII blocked fission and fusion rearrangements, reduced microridge density, and altered microridge spacing. High-resolution imaging allowed us to image individual NMII minifilaments in the apical cortex of cells in live animals, revealing that minifilaments are tethered to protrusions and often connect adjacent microridges. NMII minifilaments connecting the ends of two microridges fused them together, whereas minifilaments oriented perpendicular to microridges severed them or pulled them closer together. These findings demonstrate that as cells mature, cortical NMII activity orchestrates a remodeling process that creates an increasingly orderly microridge arrangement

A multiscale generative model to understand disorder in domain boundaries

A continuing challenge in atomic resolution microscopy is to identify significant structural motifs and their assembly rules in synthesized materials with limited observations. Here we propose and validate a simple and effective hybrid generative model capable of predicting unseen domain boundaries in a potassium sodium niobate thin film from only a small number of observations, without expensive first-principles calculation. Our results demonstrate that complicated domain boundary structures can arise from simple interpretable local rules, played out probabilistically. We also found new significant tileable boundary motifs and evidence that our system creates domain boundaries with the highest entropy. More broadly, our work shows that simple yet interpretable machine learning models can help us describe and understand the nature and origin of disorder in complex materials

Mechanosensitive calcium flashes promote sustained RhoA activation during tight junction remodeling

Epithelial cell–cell junctions remodel in response to mechanical stimuli to maintain barrier function. Previously, we found that local leaks in tight junctions (TJs) are rapidly repaired by local, transient RhoA activation, termed “Rho flares,” but how Rho flares are regulated is unknown. Here, we discovered that intracellular calcium flashes and junction elongation are early events in the Rho flare pathway. Both laser-induced and naturally occurring TJ breaks lead to local calcium flashes at the site of leaks. Additionally, junction elongation induced by optogenetics increases Rho flare frequency, suggesting that Rho flares are mechanically triggered. Depletion of intracellular calcium or inhibition of mechanosensitive calcium channels (MSCs) reduces the amplitude of calcium flashes and diminishes the sustained activation of Rho flares. MSC-dependent calcium influx is necessary to maintain global barrier function by regulating reinforcement of local TJ proteins via junction contraction. In all, we uncovered a novel role for MSC-dependent calcium flashes in TJ remodeling, allowing epithelial cells to repair local leaks induced by mechanical stimuli

Cortical contraction drives the 3D patterning of epithelial cell surfaces

Cellular protrusions create complex cell surface topographies, but biomechanical mechanisms regulating their formation and arrangement are largely unknown. To study how protrusions form, we focused on the morphogenesis of microridges, elongated actin-based structures that are arranged in maze-like patterns on the apical surfaces of zebrafish skin cells. Microridges form by accreting simple finger-like precursors. Live imaging demonstrated that microridge morphogenesis is linked to apical constriction. A nonmuscle myosin II (NMII) reporter revealed pulsatile contractions of the actomyosin cortex, and inhibiting NMII blocked apical constriction and microridge formation. A biomechanical model suggested that contraction reduces surface tension to permit the fusion of precursors into microridges. Indeed, reducing surface tension with hyperosmolar media promoted microridge formation. In anisotropically stretched cells, microridges formed by precursor fusion along the stretch axis, which computational modeling explained as a consequence of stretch-induced cortical flow. Collectively, our results demonstrate how contraction within the 2D plane of the cortex can pattern 3D cell surfaces