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In this paper, nonlinear parabolic partial differential equations are considered to approximate by multiscale mortar mixed method. The key idea of the multiscale mortar mixed approach is to decompose the domain into the smaller subregions separated by the interfaces with the Dirichlet pressure boundary condition. Each subdomain is partitioned independently on the fine scale and the standard mixed methods are used to solve each local problem. Each interface is partitioned on coarse scale and a finite element space is defined to enforce the weak continuity of flux across the mortar interface. We consider both the continuous time and discrete time settings, and derive optimal error estimates for both scalar and flux unknowns. An error estimate for the mortar pressure is also presented. Several numerical results are presented to justify the theoretical convergence estimates.

In this work, we develop novel adaptive hybrid discontinuous Galerkin algorithms for second-order elliptic problems. For this, two types of reliable and efficient, modulo a data-oscillation term, and fully computable a posteriori error estimators are developed: the first one is a simple residual type error estimator, and the second is a flux reconstruction based error estimator of a guaranteed type for polynomial approximations of any degree by using a simple postprocessing. These estimators can achieve high-order accuracy for both smooth and nonsmooth problems even with high-order approximations. In order to enhance the performance of adaptive algorithms, we introduce 𝐾-means clustering based marking strategy. The choice of marking parameter is crucial in the performance of the existing strategy such as maximum and bulk criteria; however, the optimal choice is not known. The new strategy has no unknown parameter. Several numerical examples are given to illustrate the performance of the new marking strategy along with our estimators.

Two series of novel 4-oxoquinazoline-based N-hydroxypropenamides (9a-m and 10a-m) were designed, synthesized, and evaluated for their inhibitory and cytotoxicity activities against histone deacetylase (HDAC). The compounds showed good to potent HDAC inhibitory activity and cytotoxicity against three human cancer cell lines (SW620, colon; PC-3, prostate; NCI-H23, lung cancer). In this series, compounds with the N-hydroxypropenamide functionality impeded at position 7 on the 4-oxoquinazoline skeleton (10a-m) were generally more potent than compounds with the N-hydroxypropenamide moiety at position 6 (9a-m). Also, the N 3-benzyl-substituted derivatives (9h-m, 10h-m) exhibited stronger bioactivity than the N 3-alkyl-substituted ones (9a-e, 10a-e). Two compounds 10l and 10m were the most potent ones. Their HDAC inhibitory activity (IC50 values, 0.041-0.044 μM) and cytotoxicity (IC50 values, 0.671-1.211 μM) were approximately 2- to 3-fold more potent than suberoylanilide hydroxamic acid (SAHA). Some compounds showed up to 10-fold more potent HDAC6 inhibition compared to their inhibitory activity in total HDAC extract assay. Analysis of selected compounds 10l and 10m revealed that these compounds strongly induced both early and late apoptosis and arrested SW620 cells at the G2/M phase. Docking studies were carried out on the HDAC6 isoform for series 10a-m and revealed some important features contributing to the inhibitory activity of synthesized compounds.

In this paper we investigate staggered discontinuous Galerkin method for the Helmholtz equation with large wave number on general polygonal meshes. The method is highly flexible by allowing rough grids such as the trapezoidal grids and highly distorted grids, and at the same time, is numerical flux free. Furthermore, it allows hanging nodes, which can be simply treated as additional vertices. By exploiting a modified duality argument, the stability and convergence can be proved under the condition that κ h ≤ C 0 ( 1 κ ) 1 m + 1 , where m is the polynomial order, κ is the wave number, h is the mesh size and C 0 is a positive constant independent of κ , h . Error estimates for both the scalar and vector variables in L 2 norm are established. Several numerical experiments are tested to verify our theoretical results and to present the capability of our method for capturing singular solutions.

The root-knot nematode (Meloidogyne incognita) is an important pathogen in crop cultivation, however, few methods are available to control this parasitic roundworm. In this study, the nematicidal effects of approximately 30 Streptomyces strains isolated from soil samples of Mt. Naejang (Korea) were tested against Meloidogyne incognita, and the culture broth of the strains KRA-24 and KRA-28 exhibited approximately 75% and 85% insecticidal activity, respectively, in in vitro assays. In in vivo pot experiments, these strains reduced the number of nematodes in the soil and the number of egg masses in the roots of red peppers. The two strains also survived in the presence of insecticidal agents (0.1 to 3.0%) such as fosthiazate, ethoprophos and terbufos when they were used in parallel. The mixture of KRA-24 or KRA-28 culture broth and fosthiazate exhibited nematicidal effects that were similar to those observed when KRA-24 or KRA-28 were used alone. Our results clearly suggest that the Streptomyces strains KRA-24 and KRA-28 should be promoted as a biocontrol agent against Meloidogyne incognita.

Systemic lupus erythematosus (SLE) is an autoimmune disease, which is characterized by hyperactivation of T and B cells. Human mesenchymal stem cells (hMSCs) ameliorate the progression of SLE in preclinical studies using lupus-prone MRL.Faslpr mice. However, whether hMSCs inhibit the functions of xenogeneic mouse T and B cells is not clear. To address this issue, we examined the in vitro effects of hMSCs on T and B cells isolated from MRL.Faslpr mice. Naïve hMSCs inhibited the functions of T cells but not B cells. hMSCs preconditioned with IFN-γ (i) inhibited the proliferation of and IgM production by B cells, (ii) attracted B cells for cell–cell interactions in a CXCL10-dependent manner, and (iii) inhibited B cells by producing indoleamine 2,3-dioxygenase. In summary, our data demonstrate that hMSCs exert therapeutic activity in mice in three steps: first, naïve hMSCs inhibit the functions of T cells, hMSCs are then activated by IFN-γ, and finally, they inhibit B cells.

High mobility thin film transistors (TFTs) based on zinc oxynitride (ZnON) semiconductor were fabricated onto polyethylene-2.6-naphthalate (PEN) substrates. The application of a dual gate structure enhanced the field-effect mobility from 65.8 to 147 cm2/ $\text{V}\cdot \text{s}$ , which is generally attributed to the bulk accumulation effect. Dual gate driving also results in improved device stability with respect to bias and illumination stress. This is most likely due to the fact that the bulk channel confines the charge carriers away from the semiconductor-dielectric interfaces, where charge trapping is anticipated. The electrical performance of dual gate devices did not change significantly after 5,000 bending cycles, while the single gate transistors exhibited clear degradation.

Osteoporosis is characterized by the deterioration of bone structures and decreased bone mass, leading to an increased risk of fracture. Estrogen deficiency in postmenopausal women and aging are major factors of osteoporosis and are some of the reasons for reduced quality of life. In this study, we investigated the effects of n-trans-hibiscusamide (NHA) and its derivative 4-O-(E)-feruloyl-N-(E)-hibiscusamide (HAD) on receptor activator of nuclear factor kappa-Β (NF-κB) ligand (RANKL)-induced osteoclast differentiation and an ovariectomized osteoporosis mouse model. NHA and HAD significantly inhibited the differentiation of osteoclasts from bone marrow-derived macrophages (BMMs) and the expression of osteoclast differentiation-related genes. At the molecular level, NHA and HAD significantly downregulated the phosphorylation of mitogen-activated protein kinase (MAPK) signaling molecules. However, Akt and NF-κB phosphorylation was inhibited only after NHA or HAD treatment. In the ovariectomy (OVX)-induced osteoporosis model, both NHA and HAD effectively improved trabecular bone structure. C-terminal telopeptide (CTX), a bone resorption marker, and RANKL, an osteoclast stimulation factor, were significantly reduced by NHA and HAD. The tartrate-resistant acid phosphatase (TRAP)-stained area, which indicates the osteoclast area, was also decreased by these compounds. These results show the potential of NHA and HAD as therapeutic agents for osteoporosis.

The susceptibility of cancer cells to natural killer (NK) cell-mediated cytotoxicity depends on the balance of activating and inhibitory ligands expressed on their surface. Although many types of cancer cells are killed by NK cells, non-small-cell lung cancer (NSCLC) cells are relatively resistant to NK cell-mediated cytotoxicity. In this study, we showed that several NSCLC cell lines have differential sensitivity to NK cell-mediated cytotoxicity: NCI-H522 cells were highly sensitive, but A549, NCI-H23, NCI-H1915, and NCI-H1299 were resistant. Among activating ligands such as CD48, HLA-A/B/G, ICAM-1, MICA/B, and ULBPs, only CD48 rendered NCI-H522 cells susceptible to NK cell-mediated cytotoxicity, which was proved by using CD48 siRNA and neutralizing antibody. CD48-positive NCI-H522 cells established a more stable contact with NK cells than did CD48-negative A549 and CD48 siRNA cell-transfected NCI-H522 cells. Taken together, these data demonstrate that CD48-positive NSCLC cells might be susceptible to NK cell-mediated cytotoxicity, which provide information on how to stratify NSCLC patients potentially responsive to NK-cell therapy.

In our continuing search for novel small-molecule anticancer agents, we designed and synthesized a series of novel (E)-N'-(3-allyl-2-hydroxy)benzylidene-2-(4-oxoquinazolin-3(4H)-yl)acetohydrazides (5), focusing on the modification of substitution in the quinazolin-4(3H)-one moiety. The biological evaluation showed that all 13 designed and synthesized compounds displayed significant cytotoxicity against three human cancer cell lines (SW620, colon cancer; PC-3, prostate cancer; NCI-H23, lung cancer). The most potent compound 5l displayed cytotoxicity up to 213-fold more potent than 5-fluorouracil and 87-fold more potent than PAC-1, the first procaspase-activating compound. Structure-activity relationship analysis revealed that substitution of either electron-withdrawing or electron-releasing groups at positions 6 or 7 on the quinazolin-4(3H)-4-one moiety increased the cytotoxicity of the compounds, but substitution at position 6 seemed to be more favorable. In the caspase activation assay, compound 5l was found to activate the caspase activity by 291% in comparison to PAC-1, which was used as a control. Further docking simulation also revealed that this compound may be a potent allosteric inhibitor of procaspase-3 through chelation of the inhibitory zinc ion. Physicochemical and ADMET calculations for 5l provided useful information of its suitable absorption profile and some toxicological effects that need further optimization to be developed as a promising anticancer agent.

In this paper we propose a locally conservative, lowest-order staggered discontinuous Galerkin method for the coupled Stokes–Darcy problem on general quadrilateral and polygonal meshes. This model is composed of Stokes flow in the fluid region and Darcy flow in the porous media region, coupling together through mass conservation, balance of normal forces and the Beavers–Joseph–Saffman condition. Stability of the proposed method is proved. A new regularization operator is constructed to show the discrete trace inequality. Optimal convergence estimates for all the approximations covering low regularity are achieved. Numerical experiments are given to illustrate the performances of the proposed method. The numerical results indicate that the proposed method can be flexibly applied to rough grids such as the trapezoidal grid and $h$-perturbation grid.

Rationale: Systemic lupus erythematosus (SLE) is a multi-organ autoimmune disease characterized by autoantibody production by hyper-activated B cells. Although mesenchymal stem cells (MSCs) ameliorate lupus symptoms by inhibiting T cells, whether they inhibit B cells has been controversial. Here we address this issue and reveal how to prime MSCs to inhibit B cells and improve the efficacy of MSCs in SLE. Methods: We examined the effect of MSCs on purified B cells in vitro and the therapeutic efficacy of MSCs in lupus-prone MRL.Faslpr mice. We screened chemicals for their ability to activate MSCs to inhibit B cells. Results: Mouse bone marrow-derived MSCs inhibited mouse B cells in a CXCL12-dependent manner, whereas human bone marrow-derived MSCs (hMSCs) did not inhibit human B (hB) cells. We used a chemical approach to overcome this hurdle and found that phorbol myristate acetate (PMA), phorbol 12,13-dibutyrate, and ingenol-3-angelate rendered hMSCs capable of inhibiting IgM production by hB cells. As to the mechanism, PMA-primed hMSCs attracted hB cells in a CXCL10-dependent manner and induced hB cell apoptosis in a PD-L1-dependent manner. Finally, we showed that PMA-primed hMSCs were better than naive hMSCs at ameliorating SLE progression in MRL.Faslpr mice. Conclusion: Taken together, our data demonstrate that phorbol esters might be good tool compounds to activate MSCs to inhibit B cells and suggest that our chemical approach might allow for improvements in the therapeutic efficacy of hMSCs in SLE.

In this paper, we introduce staggered discontinuous Galerkin methods for the stationary Stokes flow on polygonal meshes. The proposed method is based on the pseudostress-velocity formulation. A Lag...

In our search for novel bioactive molecules, three series of indolin-2-one derivatives incorporating 1-benzyl-1H-1,2,3-triazole moiety were synthesized. The compounds were initially designed as acetylcholine esterase (AChE) inhibitors based on the structural feature of donepezil, a known AChE inhibitor which is currently used clinically to treat Alzheimer’s disease (AD). Two compounds 4g and 3a were found to be the most potent in inhibition of AChE with inhibition percentages of 51 and 50% when tested at the concentration of 100 μM. Docking assays were carried out in order to explain the structure–activity relationships of these compounds compared with Donepezil against AChE enzyme. In DPPH free radical-scavenging assay, most compounds showed only weak scavenging activity. Noteworthy, additional cytotoxic evaluation of the compounds against three human cancer cell lines (SW620, human colon cancer; PC3, prostate cancer; NCI-H23, lung cancer) revealed that five compounds, including 3c, 3e, 5c, 5e, and 5g, exhibited strong cytotoxicity (IC50 values in the range of 0.65–7.17 µM). Compound 5g was the most potent one with IC50 values as low as 0.65 μM, even more potent than adriamycin, a positive control. Thus, compound 5g would be promising for further development as an anticancer agent.

In this paper, a locally conservative, lowest order staggered discontinuous Galerkin method is developed for the Stokes equations. The proposed method allows rough grids and is based on the partition of the domain into arbitrary shapes of quadrilaterals or polygons, which makes the method highly desirable for practical applications. A priori error analysis covering low regularity is demonstrated. A new postprocessing scheme for the velocity earning faster convergence is constructed. Next, adaptive mesh refinement is highly appreciated on quadrilateral and polygonal meshes since hanging nodes are allowed. Therefore, we propose two guaranteed-type error estimators in L 2 error of stress and energy error of the postprocessed velocity, respectively. Numerical experiments confirm our theoretical findings and illustrate the flexibility of the proposed method and accuracy of the guaranteed upper bounds.

Natural killer (NK) cell killing of melanoma cells involves perforin-mediated delivery of granzymes from NK cells to cancer cells; however, how melanoma cells die remains poorly characterized. Here, we examined the dying process of melanoma cells by using time-lapse imaging. Upon contact with NK cells, B16-F10 cells rounded and most of them showed membrane rupture (98 min); however, B16 parent cells showed writhing and delayed membrane rupture (235 min). This morphological difference depended on the expression levels of myosin regulatory light chain 9 (MYL9) but not activating ligands (CD112, CD155, Rae-1, and MULT-1), SPI, FasL, or PD-L1. Taken together, our data show that melanoma cells show two distinct types of morphological changes upon contact with NK cells and suggest that a strategy to decrease MYL9 expression by melanoma cells may improve the efficacy of NK cell–based immunotherapy.

Many studies have reported the biological activities of retrofractamide C (RAC). However, few studies have investigated the anti-inflammatory effect of RAC. In the present study, we investigated the anti-inflammatory effect of RAC using lipopolysaccharide (LPS)-induced J774A.1 cells and a xylene-induced mouse ear edema model. Treatment with RAC decreased LPS-induced nitric oxide (NO) and prostaglandin E2 (PGE2) secretion and inducible NO synthase (iNOS) and cyclooxygenase 2 (COX2) protein expression. It also downregulated the LPS-induced production of interleukin-1&beta, (IL-1&beta, ) and interleukin-6 (IL-6) but not tumor necrosis factor &alpha, (TNF-&alpha, ). In the LPS-induced signaling pathway, RAC inhibited the phosphorylation of extracellular signal-regulated kinase (ERK) and nuclear factor kappa light chain enhancer of activated B cells (NF-&kappa, B) but not c-Jun N-terminal kinase (JNK) or p38. In a xylene-induced mouse ear edema model, RAC treatment alleviated edema formation and inflammatory cell infiltration. In conclusion, the present study indicates that RAC has the potential to have anti-inflammatory effects and could be a prospective functional food.

In this article, we develop and analyze two-grid/multi-level algorithms via mesh refinement in the abstract framework of Brezzi, Rappaz, and Raviart for approximation of branches of nonsingular solutions. Optimal fine grid accuracy of two-grid/multi-level algorithms can be achieved via the proper scaling of relevant meshes. An important aspect of the proposed algorithms is the use of mesh refinement in conjunction with Newton-type methods for system solution in contrast to the usual Newton’s method on a fixed mesh. The pseudostress-velocity formulation of the stationary, incompressible Navier–Stokes equations is considered as an application and the Raviart–Thomas mixed finite element spaces are used for the approximation. Finally, several numerical examples are presented to test the performance of the algorithm and validity of the theory developed.

Two series of 3-[(1-benzyl-1H-1,2,3-triazol-4-yl)methyl]quinazolin-4(3H)-ones and N-(1-benzylpiperidin-4-yl)quinazolin-4-amines were designed initially as potential acetylcholine esterase inhibitors. Biological evaluation demonstrated that N-(1-benzylpiperidin-4-yl)quinazolin-4-amines significantly inhibited AChE activity. Especially, two compounds of them were found to be the most potent with relative AChE inhibition percentages of 87 % in comparison to donepezil. The docking studies with AChE showed similar interactions between donepezil and four derivatives. N-(1-Benzylpiperidin-4-yl)quinazolin-4-amines also exhibited significant DPPH scavenging effects. The two series of compound also exerted moderate to good cytotoxicity against three human cancer cell lines, including SW620 (human colon cancer), PC-3 (prostate cancer), and NCI-H23 (lung cancer), with 3-[(1-benzyl-1H-1,2,3-triazol-4-yl)methyl]quinazolin-4(3H)-one being the most cytotoxic agent. 3-[(1-Benzyl-1H-1,2,3-triazol-4-yl)methyl]quinazolin-4(3H)-one significantly induced early apoptosis and arrested the SW620 cells at G2/M phase. From this study, two compounds of N-(1-benzylpiperidin-4-yl)quinazolin-4-amines could serve as new leads for further design and AChE inhibitors, while 3-[(1-benzyl-1H-1,2,3-triazol-4-yl)methyl]quinazolin-4(3H)-one could serve as a new lead for the design and development of more potent anticancer agents.

In this study, we investigated the effects of intense pulsed light (IPL) on the electrical performance properties of zinc oxynitride (ZnON) thin films and thin-film transistors (TFTs) with different irradiation energies. Using the IPL process on the oxide/oxynitride semiconductors has various advantages, such as an ultrashort process time (∼100 ms) and high electrical performance without any additional thermal processes. As the irradiation energy of IPL increased from 30 to 50 J/cm

In our search for novel small molecules activating procaspase-3, we have designed and synthesised a series of novel acetohydrazides incorporating quinazolin-4(3H)-ones (5, 6, 7). Biological evaluation revealed eight compounds with significant cytotoxicity against three human cancer cell lines (SW620, colon cancer; PC-3, prostate cancer; NCI-H23, lung cancer). The most potent compound 5t displayed cytotoxicity up to 5-fold more potent than 5-FU. Analysis of structure-activity relationships showed that the introduction of different substituents at C-6 position on the quinazolin-4(3H)-4-one moiety, such as 6-chloro or 6-methoxy potentially increased the cytotoxicity of the compounds. In term of caspase activation activity, several compounds were found to exhibit potent effects, (e.g. compounds 7 b, 5n, and 5l). Especially, compound 7 b activated caspases activity by almost 200% in comparison to that of PAC-1. Further docking simulation also revealed that this compound potentially is a potent allosteric inhibitor of procaspase-3., Graphical Abstract

Two series of 3-[(1-benzyl-1H-1,2,3-triazol-4-yl)methyl]quinazolin-4(3H)-ones and N-(1-benzylpiperidin-4-yl)quinazolin-4-amines were designed initially as potential acetylcholine esterase inhibitors. Biological evaluation demonstrated that N-(1-benzylpiperidin-4-yl)quinazolin-4-amines significantly inhibited AChE activity. Especially, two compounds of them were found to be the most potent with relative AChE inhibition percentages of 87 % in comparison to donepezil. The docking studies with AChE showed similar interactions between donepezil and four derivatives. N-(1-Benzylpiperidin-4-yl)quinazolin-4-amines also exhibited significant DPPH scavenging effects. The two series of compound also exerted moderate to good cytotoxicity against three human cancer cell lines, including SW620 (human colon cancer), PC-3 (prostate cancer), and NCI-H23 (lung cancer), with 3-[(1-benzyl-1H-1,2,3-triazol-4-yl)methyl]quinazolin-4(3H)-one being the most cytotoxic agent. 3-[(1-Benzyl-1H-1,2,3-triazol-4-yl)methyl]quinazolin-4(3H)-one significantly induced early apoptosis and arrested the SW620 cells at G2/M phase. From this study, two compounds of N-(1-benzylpiperidin-4-yl)quinazolin-4-amines could serve as new leads for further design and AChE inhibitors, while 3-[(1-benzyl-1H-1,2,3-triazol-4-yl)methyl]quinazolin-4(3H)-one could serve as a new lead for the design and development of more potent anticancer agents.

Several novel series of hydroxamic acids bearing 2-benzamidooxazole/thiazole (5a-g, 6a-g) or 2-phenylsulfonamidothiazole (8a-c) were designed and synthesized. The compounds were obtained straightforwards via a two step pathway, starting from commercially available ethyl 2-aminooxazole-4-carboxylate or ethyl 2-aminothiazole-4-carboxylate. Biological evaluation showed that these hydroxamic acids generally exhibited good cytotoxicity against three human cancer cell lines (SW620, colon; PC-3, prostate; NCI-H23, lung cancer), with IC50 values in low micromolar range and comparable to that of SAHA. These compounds also comparably inhibited HDACs with IC50 values in sub-micromolar range (0.010–0.131 µM) and some compounds (e.g 5f, IC50, 0.010 µM) were even more potent than SAHA (IC50, 0.025 µM) in HDAC inhibition. Representative compounds 6a and 8a appeared to arrest the SW620 cell cycle at G2 phase and significantly induced both early and late apoptosis of SW620 colon cancer cells. Docking experiments on HDAC2 and HDAC6 isozymes revealed favorable interactions at the tunnel of the HDAC active site which positively contributed to the inhibitory activity of synthesized compound. The binding affinity predicted by docking program showed good correlation with the experimental IC50 values. This study demonstrates that simple 1,3-oxazole- and 1,3-thiazole-based hydroxamic acids are also promising as antitumor agents and HDAC inhibitors and these results should provide valuable information for further design of more potent HDAC inhibitors and antitumor agents.

In our search for new small molecules activating procaspase-3, we have designed and synthesized a series of new acetohydrazides incorporating both 2-oxoindoline and 4-oxoquinazoline scaffolds. Biological evaluation showed that a number of these acetohydrazides were comparably or even more cytotoxic against three human cancer cell lines (SW620, colon cancer; PC-3, prostate cancer; NCI-H23, lung cancer) in comparison to PAC-1, a first procaspase-3 activating compound, which was used as a positive control. One of those new compounds, 2-(6-chloro-4-oxoquinazolin-3(4H)-yl)-N'-[(3Z)-5-methyl-2-oxo-1,2-dihydro-3H-indol-3-ylidene]acetohydrazide activated the caspase-3 activity in U937 human lymphoma cells by 5-fold higher than the untreated control. Three of the new compounds significantly induced necrosis and apoptosis in U937 cells.

Hybrid difference methods are a kind of finite difference methods which is similar to hybrid discontinuous Galerkin methods introduced by Jeon and Park (SIAM J. Numer. Anal., 2010). In the previous hybrid difference method, the approximate solution is only defined on the lines parallel to the coordinate axes, but the approximation is not defined at the corner/edge nodes. Thus, it is hard to calculate the approximation value without loosing accuracy at any point in the domain due to the aforementioned missing information. To overcome this issue, we first propose a novel hybrid difference method by imposing some conditions to determine the missing information. With this, we are able to provide not only continuous approximations in the whole domain, but also the gradient of the numerical solution becomes continuous under certain conditions. Next, we prove that the proposed method is stable and locally conservative. The proposed method can be also viewed as the existing hybrid difference method with a simple postprocessing. The postprocessing not only induces a simple tridiagonal system on each mesh line, but also it can be done efficiently line by line or in parallel. Lastly, a reliable and efficient a posteriori error estimate is established for computational efficiency. Several numerical results are presented to confirm our findings.

In this work, we aim to develop efficient numerical schemes for a nonlinear fourth-order partial differential equation arising from the so-called dynamic Gao beam model. We use C 0 interior penalty finite element methods over the spatial domain to set up the semi-discrete formulations. Convergence results for the semi-discrete case are shown, based on a truncated variational formulation and its equivalent abstract formulations. We combine time discretizations to derive fully discrete numerical formulations. Newton’s method is applied to compute one time step numerical solutions of a nonlinear system. Two numerical examples are provided: one supports our theoretical results and the other presents a buckling state of the Gao beams.

Natural killer (NK) cells eliminate cancer cells in a contact-dependent manner. However, how NK cells find cancer cells remain unclear. Here, using time-lapse imaging, we investigated how individual NK cells migrate toward cancer cells. Although naïve B16F10 cancer cells produce low levels of chemokines, IFN-γ-treated B16F10 cells secreted high levels of CXCL10, low levels of CCL5, but did not secrete CCL2, CCL7, or CXCL12. Wild-type NK cells migrated well toward cancer cells and killed them, whereas NK cells deficient in CXCR3 did not. CXCR3-deficient NK cells also showed slower migration speed than did wild-type NK cells. Taken together, our data show that NK cells find cancer cells, at least in part, by sensing CXCL10 produced by cancer cells and suggest that a strategy to increase CXCL10 secretion by cancer cells may improve the efficacy of NK cell-based immunotherapy.