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Abstract Integrable systems constitute an essential part of modern physics. Traditionally, to approve a model is integrable one has to find its infinitely many symmetries or conserved quantities. In this letter, taking the well known Korteweg-de Vries and Boussinesq equations as examples, we show that it is enough to find only one nonlocal key-symmetry to guarantee the integrability. Starting from the nonlocal key-symmetry, recursion operator(s) and then infinitely many symmetries and Lax pairs can be successfully found.

Background: Bortezomib (BTZ) is a powerful proteasome inhibitor that has been approved for the treatment of haematologic malignancies. Its effectiveness has been assessed against different types of solid tumours. BTZ is ineffective in most solid tumours because of drug resistance, including cholangiocarcinoma, which is associated with a proteasome bounce-back effect. However, the mechanism through which proteasome inhibitors induce the proteasome bounce-back effect remains largely unknown. Methods: Cholangiocarcinoma cells were treated with BTZ, cisplatin, or a combination of both. The mRNA levels of Nfe2l1 and proteasome subunit genes (PSMA1, PSMB7, PSMD1, PSMD11, PSMD14, and PSME4) were determined using quantitative real time polymerase chain reaction (qPCR). The protein levels of nuclear factor-erythroid 2-related factor 1 (Nfe2l1) and proteasome enzyme activity were evaluated using western blotting and proteasome activity assays, respectively. Transcriptome sequencing was performed to screen for potential transcription factors that regulate Nfe2l1 expression. The effect of zinc finger E-box-binding homeobox 1 (ZEB1) on the expression of Nfe2l1 and proteasome subunit genes, as well as proteasome enzyme activity, was evaluated after the knockdown of ZEB1 expression with siRNA before treatment with BTZ. The transcriptional activity of ZEB1 on the Nfe2l1 promoter was detected using dual-luciferase reporter gene and chromatin immunoprecipitation assays. Cell viability was measured using the cell counting kit-8 (CCK-8) assay and cell apoptosis was assessed using western blotting and flow cytometry. Results: Cisplatin treatment of BTZ-treated human cholangiocarcinoma cell line (RBE) suppressed proteasome subunit gene expression (proteasome bounce-back) and proteasomal enzyme activity. This effect was achieved by reducing the levels of Nfe2l1 mRNA and protein. Our study utilised transcriptome sequencing to identify ZEB1 as an upstream transcription factor of Nfe2l1, which was confirmed using dual-luciferase reporter gene and chromatin immunoprecipitation assays. Notably, ZEB1 knockdown using siRNA (si-ZEB1) hindered the expression of proteasome subunit genes under both basal and BTZ-induced conditions, leading to the inhibition of proteasomal enzyme activity. Furthermore, the combination treatment with BTZ, cisplatin, and si-ZEB1 significantly reduced the viability of RBE cells. Conclusions: Our study uncovered a novel mechanism through which cisplatin disrupts the BTZ-induced proteasome bounce-back effect by suppressing the ZEB1/Nfe2l1 axis in cholangiocarcinoma. This finding provides a theoretical basis for developing proteasome inhibitor-based strategies for the clinical treatment of cholangiocarcinoma and other tumours.

Abstract Metastatic clear cell renal cell carcinoma (ccRCC) is a lethal sub-type of kidney cancer. Vascular mimicry (VM) has been postulated as an alternative route to supply tumors with nutrients, playing key role in tumor development. Whether VM development is linked to pazopanib efficacy, however, remains unclear. Here, our in vitro and in vivo models identified that VM development was profoundly increased in pazopanib resistant ccRCC as compared to the sensitive controls, which was due to the activation of IGFL2-AS1/AR/TWIST1 signaling. IGFL2-AS1, a m6A modified long coding RNA, was demethylated by METTL3/METTL14 complex and stabilized owing to its failing recognition by YTHDF2 upon chronic pazopanib treatment. Further mechanistic dissection illustrated that IGFL2-AS1 physically interacted with the 5’-UTR AR mRNA and neutralized the negative regulation of 5’-uORF (upstream open reading frame) on AR translation. Indeed, IGFL2-AS1 short of AR binding region failed to promote AR expression, VM formation and pazopanib resistance. In vivo xenografted mouse model also elucidated that inhibition of AR activity with enzalutamide or silence of IGFL2-AS1 with siRNAs all led to retarded growth of pazopanib resistant ccRCC tumors. Together, these results suggest that IGFL2-AS1 may represent a key player to mediate pazopanib-induced VM formation of ccRCC cells via regulating AR expression and targeting this newly identified IGFL2-AS1/AR signaling may help us to better suppress ccRCC VM formation and to increase the therapeutic efficacy of pazopanib.

Abstract Utilizing some conservation laws of (1+1)-dimensional integrable local evolution systems, it is conjectured that higher dimensional integrable equations may be regularly constructed by a deformation algorithm. The algorithm can be applied to Lax pairs and higher order flows. In other words, if the original lower dimensional model is Lax integrable (possesses Lax pairs) and symmetry integrable (possesses infinitely many higher order symmetries and/or infinitely many conservation laws), then the deformed higher order systems are also Lax integrable and symmetry integrable. For concreteness, the deformation algorithm is applied to the usual (1 + 1)-dimensional Korteweg-de Vries (KdV) equation and the (1 + 1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) system (including nonlinear Schrödinger (NLS) equation as a special example). It is interesting that the deformed (3+1)-dimensional KdV equation is also an extension of the (1 + 1)-dimensional Harry-Dym (HD) type equations which are reciprocal links of the (1+1)-dimensional KdV equation. The Lax pairs of the (3 + 1)-dimensional KdV-HD system and the (2 + 1)-dimensional AKNS system are explicitly given. The higher order symmetries, i.e., the whole (3 + 1)-dimensional KdV-HD hierarchy, are also explicitly obtained via the deformation algorithm. The single soliton solution of the (3 + 1)-dimensional KdV-HD equation is implicitly given. Because of the effects of the deformation, the symmetric soliton shape of the usual KdV equation is no longer conserved and deformed to be asymmetric and/or multi-valued. The deformation conjecture holds for all the known (1 +1)-dimensional integrable local evolution systems that have been checked, and we have not yet found any counter-example so far. The introduction of a large number of (D + 1)-dimensional integrable systems of this paper explores a serious challenge to all mathematicians and theoretical physicists because the traditional methods are no longer directly valid to solve these integrable equations.

Fluorescence images enhancement is important as it can provide more information for medical diagnosis. In this work, we design three simple yet useful filters based on the combinations of mathematical functions, which are proved to be effective in strengthening the images acquired from the fluorescence microscope. Using these filters, detailed objects can be found in the dark sections of the fluorescence images. In addition, these filters can be used to enhance the low-light image, which provide satisfactory visual information and marginal profile for the blurred objects in the image. Moreover, these filters have been used to enhance the image with high degradation by the Gaussian noise, where clear edge profile can be extracted. Finally, we have shown that these filters can be utilized for the image compression. Compression ratio can be obtained to be 0.9688. This study shows the making of the filters with dual functions for the image enhancement and the image compression. Our designed filters are showing the potentials in the field of biomedical imaging and pattern identification.

Prostate cancer (PCa) continues to rank as the second leading cause of cancer-related mortality in western countries, despite the golden treatment using androgen deprivation therapy (ADT) or anti-androgen therapy. With decades of research, scientists have gradually realized that the existence of prostate cancer stem cells (PCSCs) successfully explains tumor recurrence, metastasis and therapeutic failure of PCa. Theoretically, eradication of this small population may improve the efficacy of current therapeutic approaches and prolong PCa survival. However, several characteristics of PCSCs make their diminishment extremely challenging: inherent resistance to anti-androgen and chemotherapy treatment, over-activation of the survival pathway, adaptation to tumor micro-environments, escape from immune attack and being easier to metastasize. For this end, a better understanding of PCSC biology at the molecular level will definitely inspire us to develop PCSC targeted approaches. In this review, we comprehensively summarize signaling pathways responsible for homeostatic regulation of PCSCs and discuss how to eliminate these fractional cells in clinical practice. Overall, this study deeply pinpoints PCSC biology at the molecular level and provides us some research perspectives.

Post-stroke anxiety severely affects recovery in patients with intracerebral hemorrhage (ICH). Dexmedetomidine (Dex), a highly selective alpha 2 adrenal receptor (α2-AR) agonist, was recently found to exert an excellent protective effect against mental disorders including anxiety. The transient receptor potential vanilloid 4 (TRPV4) channel is involved in a series of diseases such as asthma, cancer, anxiety, and cardiac hypertrophy. This study examines whether Dex improved ICH-induced anxiety via the inhibition of TRPV4 channel opening. A rodent model of moderate ICH in the basal ganglia was established using autologous blood injection (20 μl). Mice were treated with Dex (25 μg/kg, intraperitoneal injection) every day for 3 days post-ICH. GSK1016790A (1 μmol/2 μl), an agonist of TRPV4, was administered via the left lateral ventricle. Thirty days post-ICH, post-stroke anxiety was evaluated by elevated plus-maze and open-field tests. Following behavioral tests, superoxide dismutase (SOD), malondialdehyde (MDA), astrocytic activation, and A1-and A2-type astrocytes were determined. Primary astrocytes were exposed to hemin to simulate ICH in vitro. Compared with sham-treated mice, Dex administration ameliorates ICH-induced decreases of distance and time in the open-arm, reduces distance and time in the central zone, increases astrocytic activation and A1-type astrocytes, elevates MDA content, downregulates total SOD contents, and decreases A2-type astrocytes. However, GSK1016790A partially reversed the neuroprotective effects of Dex. In addition, Dex significantly inhibited hemin-induced astrocytic activation in vitro. Dex improves ICH-induced anxiety-like behaviors in mice, and the mechanism might be associated with the inhibition of TRPV4-channel opening.