Variational multiscale methods, and their precursors, stabilized methods, have been very popular in flow computations in the past several decades. Stabilization parameters embedded in most of these methods play a significant role. The parameters almost always involve element length scales, most of the time in specific directions, such as the direction of the flow or solution gradient. We require the length scales, including the directional length scales, to have node-numbering invariance for all element types, including simplex elements. We propose a length scale expression meeting that requirement. We analytically evaluate the expression in the context of simplex elements and compared to one of the most widely used length scale expressions and show the levels of noninvariance avoided.

In the horseshoe crab, the recognition of β-1,3-d-glucans by factor G triggers hemolymph coagulation. Factor G contains a domain of two tandem xylanase Z-like modules (Z1-Z2), each of which recognizes β-1,3-d-glucans. To gain an insight into the recognition of β-1,3-d-glucans from a structural view point, recombinants of Z1-Z2, the C-terminal module Z2, Z2 with a Cys to Ala substitution (Z2A), and its tandem repeat Z2A-Z2A were characterized. Z2 and Z1-Z2, but not Z2A and Z2A-Z2A, formed insoluble aggregates at higher concentrations more than ∼30 and 3 μM, respectively. Z1-Z2 and Z2A-Z2A bound more strongly to an insoluble β-1,3-d-glucan (curdlan) than Z2A. The affinity of Z2A for a soluble β-1,3-d-glucan (laminarin) was equivalent to those of Z1-Z2, Z2A-Z2A, and native factor G, suggesting that the binding of a single xylanase Z-like module prevents the subsequent binding of another module to laminarin. Interestingly, Z2A as well as intact factor G exhibited fungal agglutinating activity, and fungi were specifically detected with fluorescently tagged Z2A by microscopy. The chemical shift perturbation of Z2A induced by the interaction with laminaripentaose was analyzed by nuclear magnetic resonance spectroscopy. The ligand-binding site of Z2A was located in a cleft on a β-sheet in a predicted β-sandwich structure, which was superimposed onto cleft B in a cellulose-binding module of endoglucanase 5A from the soil bacterium Cellvibrio mixtus. We conclude that the pattern recognition for β-1,3-d-glucans by factor G is accomplished via a carbohydrate-binding cleft that is evolutionally conserved between horseshoe crab and bacteria.

Variational multiscale methods and their precursors, stabilized methods, which are sometimes supplemented with discontinuity-capturing (DC) methods, have been playing their core-method role in flow computations increasingly with isogeometric discretization. The stabilization and DC parameters embedded in most of these methods play a significant role. The parameters almost always involve some local-length-scale expressions, most of the time in specific directions, such as the direction of the flow or solution gradient. Until recently, local-length-scale expressions originally intended for finite element discretization were being used also for isogeometric discretization. The direction-dependent expressions introduced in [Y. Otoguro, K. Takizawa and T. E. Tezduyar, Element length calculation in B-spline meshes for complex geometries, Comput. Mech. 65 (2020) 1085–1103, https://doi.org/10.1007/s00466-019-01809-w ] target B-spline meshes for complex geometries. The key stages of deriving these expressions are mapping the direction vector from the physical element to the parent element in the parametric space, accounting for the discretization spacing along each of the parametric coordinates, and mapping what has been obtained back to the physical element. The expressions are based on a preferred parametric space and a transformation tensor that represents the relationship between the integration and preferred parametric spaces. Element splitting may be a part of the computational method in a variety of cases, including computations with T-spline discretization and immersed boundary and extended finite element methods and their isogeometric versions. We do not want the element splitting to influence the actual discretization, which is represented by the control or nodal points. Therefore, the local length scale should be invariant with respect to element splitting. In element definition, invariance of the local length scale is a crucial requirement, because, unlike the element definition choices based on implementation convenience or computational efficiency, it influences the solution. We provide a proof, in the context of B-spline meshes, for the element-splitting invariance of the local-length-scale expressions introduced in the above reference.

The split Bregman framework for Osher-Solé-Vese (OSV) model and fourth order total variation flow are studied. We discretize the problem by piecewise constant function and compute ∇(−∆ av ) −1 approximately and exactly. Furthermore, we provide a new shrinkage operator for Spohn's fourth order model. Numerical experiments are demonstrated for fourth order problems under periodic boundary condition.

Nagilactone E, an antifungal agent derived from the root bark of Podocarpus nagi, inhibits 1,3-β glucan synthesis; however, its inhibitory activity is weak. Anethole, the principal component of anise oil, enhances the antifungal activity of nagilactone E. We aimed to determine the combinatorial effect and underlying mechanisms of action of nagilactone E and anethole against the budding yeast Saccharomyces cerevisiae. Analyses using gene-deficient strains showed that the multidrug efflux pump PDR5 is associated with nagilactone E resistance; its transcription was gradually restricted in cells treated with the drug combination for a prolonged duration but not in nagilactone-E-treated cells. Green-fluorescent-protein-tagged Pdr5p was intensively expressed and localized on the plasma membrane of nagilactone-E-treated cells but not in drug-combination-treated cells. Quick-freeze deep-etch electron microscopy revealed the smoothening of intertwined fiber structures on the cell surface of drug-combination-treated cells and spheroplasts, indicating a decline in cell wall components and loss of cell wall strength. Anethole enhanced the antifungal activity of nagilactone E by enabling its retention within cells, thereby accelerating cell wall damage. The combination of nagilactone E and anethole can be employed in clinical settings as an antifungal, as well as a food preservative to restrict food spoilage.