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The chromatic polynomial χG(q)\\chi _G(q) of a graph GG counts the number of proper colorings of GG. We give an affirmative answer to the conjecture of Read and Rota-Heron-Welsh that the absolute values of the coefficients of the chromatic polynomial form a log-concave sequence. The proof is obtained by identifying χG(q)\\chi _G(q) with a sequence of numerical invariants of a projective hypersurface analogous to the Milnor number of a local analytic hypersurface. As a by-product of our approach, we obtain an analogue of Kouchnirenko’s theorem relating the Milnor number with the Newton polytope; we also characterize homology classes of Pn×Pm\\mathbb {P}^n \\times \\mathbb {P}^m corresponding to subvarieties and answer a question posed by Trung-Verma.

We show that the maximum likelihood degree of a smooth very affine variety is equal to the signed topological Euler characteristic. This generalizes Orlik and Terao’s solution to Varchenko’s conjecture on complements of hyperplane arrangements to smooth very affine varieties. For very affine varieties satisfying a genericity condition at infinity, the result is further strengthened to relate the variety of critical points to the Chern–Schwartz–MacPherson class. The strengthened version recovers the geometric deletion–restriction formula of Denham et al. for arrangement complements, and generalizes Kouchnirenko’s theorem on the Newton polytope for nondegenerate hypersurfaces.

We prove the hard Lefschetz theorem and the Hodge-Riemann relations for a commutative ring associated to an arbitrary matroid M. We use the Hodge-Riemann relations to resolve a conjecture of Heron, Rota, and Welsh that postulates the log-concavity of the coefficients of the characteristic polynomial of M. We furthermore conclude that the f-vector of the independence complex of a matroid forms a log-concave sequence, proving a conjecture of Mason and Welsh for general matroids.

Palmitic acid (PA) is the most common fatty acid in humans and mediates palmitoylation through its conversion into palmitoyl coenzyme A. Although palmitoylation affects many proteins, its pathophysiological functions are only partially understood. Here we demonstrate that PA acts as a molecular checkpoint of lipid reprogramming in HepG2 and Hep3B cells. The zinc finger DHHC-type palmitoyltransferase 23 (ZDHHC23) mediates the palmitoylation of plant homeodomain finger protein 2 (PHF2), subsequently enhancing ubiquitin-dependent degradation of PHF2. This study also reveals that PHF2 functions as a tumor suppressor by acting as an E3 ubiquitin ligase of sterol regulatory element-binding protein 1c (SREBP1c), a master transcription factor of lipogenesis. PHF2 directly destabilizes SREBP1c and reduces SREBP1c-dependent lipogenesis. Notably, SREBP1c increases free fatty acids in hepatocellular carcinoma (HCC) cells, and the consequent PA induction triggers the PHF2/SREBP1c axis. Since PA seems central to activating this axis, we suggest that levels of dietary PA should be carefully monitored in patients with HCC. Palmitoylation of proteins can have pathophysiological implications. Here, the authors show that palmitoylation enhances the proteasomal degradation of the histone demethylase PHF2, leading to increased lipogenesis and cell proliferation in an SREBP1c dependent manner and further show that PHF2 acts as an E3 ligase of SREBP1c, suppressing the growth of liver cancer cells.

The photocurrent conversions of transition metal dichalcogenide nanosheets are unprecedentedly impressive, making them great candidates for visible range photodetectors. Here we demonstrate a method for fabricating micron-thick, flexible films consisting of a variety of highly separated transition metal dichalcogenide nanosheets for excellent band-selective photodetection. Our method is based on the non-destructive modification of transition metal dichalcogenide sheets with amine-terminated polymers. The universal interaction between amine and transition metal resulted in scalable, stable and high concentration dispersions of a single to a few layers of numerous transition metal dichalcogenides. Our MoSe 2 and MoS 2 composites are highly photoconductive even at bending radii as low as 200 μm on illumination of near infrared and visible light, respectively. More interestingly, simple solution mixing of MoSe 2 and MoS 2 gives rise to blended composite films in which the photodetection properties were controllable. The MoS 2 /MoSe 2 (5:5) film showed broad range photodetection suitable for both visible and near infrared spectra. Transition metal dichalgogenide sheets prepared by liquid phase exfoliation can be limited in terms of scalability. Here, Velusamy et al . use a scalable liquid phase exfoliation process to fabricate micrometre thick composite nanosheets with amine-terminated polymers, which exhibit photo-detective properties.

Harmful effects of high fructose intake on health have been widely reported. Although fructose is known to promote cancer, little is known about the underlying mechanisms. Here, we found that fructose triggers breast cancer metastasis through the ketohexokinase-A signaling pathway. Molecular experiments showed that ketohexokinase-A, rather than ketohexokinase-C, is necessary and sufficient for fructose-induced cell invasion. Ketohexokinase-A-overexpressing breast cancer was found to be highly metastatic in fructose-fed mice. Mechanistically, cytoplasmic ketohexokinase-A enters into the nucleus during fructose stimulation, which is mediated by LRRC59 and KPNB1. In the nucleus, ketohexokinase-A phosphorylates YWHAH at Ser25 and the YWHAH recruits SLUG to the CDH1 promoter, which triggers cell migration. This study provides the effect of nutrition on breast cancer metastasis. High intake of fructose should be restricted in cancer patients to reduce the risk of metastasis. From a therapeutic perspective, the ketohexokinase-A signaling pathway could be a potential target to prevent cancer metastasis. Apart from the enzymatic role of ketohexokinase isoform A (KHK-A) in fructose metabolism the alternative physiological functions of the enzyme are unclear. Here, the authors show that KHK-A mediates fructose-induced metastasis in breast cancer through a nuclear role in repressing the transcriptional activity of the cell-adhesion molecule CDH1.

Diabetes might be associated with increased cancer risk, with several studies reporting hyperglycemia as a primary oncogenic stimulant. Since glucose metabolism is linked to numerous metabolic pathways, it is difficult to specify the mechanisms underlying hyperglycemia-induced cancer progression. Here, we focused on the polyol pathway, which is dramatically activated under hyperglycemia and causes diabetic complications. We investigated whether polyol pathway-derived fructose facilitates hyperglycemia-induced gastric cancer metastasis. We performed bioinformatics analysis of gastric cancer datasets and immunohistochemical analyses of gastric cancer specimens, followed by transcriptomic and proteomic analyses to evaluate phenotypic changes in gastric cancer cells. Consequently, we found a clinical association between the polyol pathway and gastric cancer progression. In gastric cancer cell lines, hyperglycemia enhanced cell migration and invasion, cytoskeletal rearrangement, and epithelial-mesenchymal transition (EMT). The hyperglycemia-induced acquisition of metastatic potential was mediated by increased fructose derived from the polyol pathway, which stimulated the nuclear ketohexokinase-A (KHK-A) signaling pathway, thereby inducing EMT by repressing the CDH1 gene. In two different xenograft models of cancer metastasis, gastric cancers overexpressing AKR1B1 were found to be highly metastatic in diabetic mice, but these effects of AKR1B1 were attenuated by KHK-A knockdown. In conclusion, hyperglycemia induces fructose formation through the polyol pathway, which in turn stimulates the KHK-A signaling pathway, driving gastric cancer metastasis by inducing EMT. Thus, the polyol and KHK-A signaling pathways could be potential therapeutic targets to decrease the metastatic risk in gastric cancer patients with diabetes. Gastric cancer’s deadly dance with diabetes: the role of fructose in metastasis Diabetes and cancer, two major worldwide health concerns, often coexist in patients. Recent research suggests diabetes can heighten the risk of various cancers. However, the precise reasons behind this link remain unknown. In this study, researchers discovered that high glucose levels (sugar in the blood), a diabetes hallmark, can enhance cancer cell aggression. This occurs via the polyol pathway (a process where glucose transforms into a substance named fructose). The fructose then triggers a specific signaling pathway (a series of chemical reactions) in the cancer cells, leading to their increased movement and invasion, signs of more aggressive cancers. This study offers a potential reason for the diabetes-cancer connection and implies that managing blood sugar levels in cancer patients with diabetes could be vital in preventing cancer progression. This summary was initially drafted using artificial intelligence, then revised and fact-checked by the author.

Soluble methane monooxygenase (sMMO) oxidizes a wide range of carbon feedstocks (C1 to C8) directly using intracellular NADH and is a useful means in developing green routes for industrial manufacturing of chemicals. However, the high-throughput biosynthesis of active recombinant sMMO and the ensuing catalytic oxidation have so far been unsuccessful due to the structural and functional complexity of sMMO, comprised of three functionally complementary components, which remains a major challenge for its industrial applications. Here we develop a catalytically active miniature of sMMO (mini-sMMO), with a turnover frequency of 0.32 s −1 , through an optimal reassembly of minimal and modified components of sMMO on catalytically inert and stable apoferritin scaffold. We characterise the molecular characteristics in detail through in silico and experimental analyses and verifications. Notably, in-situ methanol production in a high-cell-density culture of mini-sMMO-expressing recombinant Escherichia coli resulted in higher yield and productivity (~ 3.0 g/L and 0.11 g/L/h, respectively) compared to traditional methanotrophic production. Soluble methane monooxygenase (sMMO) is a potentially value biocatalyst, but production of active recombinant sMMO is very challenging. Here the authors report the rational design and construction of a catalytically active miniature sMMO which enables high-yield production of methanol in E. coli.

Precise control over the structure of metal nanomaterials is important for developing advanced nanobiotechnology. Assembly methods of nanoparticles into structured blocks have been widely demonstrated recently. However, synthesis of nanocrystals with controlled, three-dimensional structures remains challenging. Here we show a directed crystallization of gold by a single DNA molecular regulator in a sequence-independent manner and its applications in three-dimensional topological controls of crystalline nanostructures. We anchor DNA onto gold nanoseed with various alignments to form gold nanocrystals with defined topologies. Some topologies are asymmetric including pushpin-, star- and biconcave disk-like structures, as well as more complex jellyfish- and flower-like structures. The approach of employing DNA enables the solution-based synthesis of nanocrystals with controlled, three-dimensional structures in a desired direction, and expands the current tools available for designing and synthesizing feature-rich nanomaterials for future translational biotechnology. Bottom-up synthesis of colloidal metallic nanomaterials with a designable structure is challenging. Here, the authors report the directed crystallisation of gold by a single DNA molecular regulator, using it to synthesise gold nanocrystals with defined complex morphologies.

Purpose The objective of this study was to demonstrate that the gastric cross-sectional area (CSA) in the right lateral decubitus position (RLDP) during a 2-h fasting period is not larger than that during a conventional 4-h fasting period prior to pediatric echocardiography. Methods 93 patients aged under 3 years scheduled for echocardiography under sedation were enrolled and randomly allocated into two groups; 2-h fasting vs 4-h fasting. For group 4 h ( n  = 46), the patients were asked to be fasted for all types of liquid for more than 4 h, while group 2 h ( n  = 47) were asked to be fasted for all types of liquid for 2 h before echocardiography. Gastric ultrasound was performed before echocardiography, and CSA RLDP was measured. We compared CSA RLDP, incidence of at-risk stomach, fasting duration, and the incidence of major (pulmonary aspiration, aspiration pneumonia) and minor complications (nausea, retching, and vomiting, apnea, and bradycardia) between two groups. Results The mean difference of CSA RLDP (group 2 h–group 4 h) was 0.49 (– 0.18 to 1.17) cm 2 , and it was within the non-inferiority margin ( Δ  = 2.1 cm 2 ). There was no difference in the incidence of at-risk stomach ( P  = 0.514). There was no significant difference in the incidence of major and minor complications between the two groups. Conclusion Two-hour fasting in pediatric patients who need an echocardiography did not increase major and minor complications and CSA significantly.