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PURPOSE: This study aimed to develop a tumor radiomics quality and quantity model (RQQM) based on preoperative enhanced CT to predict early recurrence after radical surgery for colorectal liver metastases (CRLM). METHODS: A retrospective analysis was conducted on 282 cases from 3 centers. Clinical risk factors were examined using univariate and multivariate logistic regression (LR) to construct the clinical model. Radiomics features were extracted using the least absolute shrinkage and selection operator (LASSO) for dimensionality reduction. The LR learning algorithm was employed to construct the radiomics model, RQQM (radiomics-TBS), combined model (radiomics-clinical), clinical risk score (CRS) model and tumor burden score (TBS) model. Inter-model comparisons were made using area under the curve (AUC), decision curve analysis (DCA) and calibration curve. Log-rank tests assessed differences in disease-free survival (DFS) and overall survival (OS). RESULTS: Clinical features screening identified CRS, KRAS/NRAS/BRAF and liver lobe distribution as risk factors. Radiomics model, RQQM, combined model demonstrated higher AUC values compared to CRS and TBS model in training, internal and external validation cohorts (Delong-test P < 0.05). RQQM outperformed the radiomics model, but was slightly inferior to the combined model. Survival curves revealed statistically significant differences in 1-year DFS and 3-year OS for the RQQM (P < 0.001). CONCLUSIONS: RQQM integrates both "quality" (radiomics) and "quantity" (TBS). The radiomics model is superior to the TBS model and has a greater impact on patient prognosis. In the absence of clinical data, RQQM, relying solely on imaging data, shows an advantage in predicting early recurrence after radical surgery for CRLM.

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In this study, we investigate the COVID-19 epidemics in Brazilian cities, using early-time approximations of the SIR model in networks and combining the VAR (vector autoregressive) model with machine learning techniques. Different from other works, the underlying network was constructed by inputting real-world data on local COVID-19 cases reported by Brazilian cities into a regularized VAR model. This model estimates directional COVID-19 transmission channels (connections or links between nodes) of each pair of cities (vertices or nodes) using spectral network analysis. Despite the simple epidemiological model, our predictions align well with the real COVID-19 dynamics across Brazilian municipalities, using data only up until May 2020. Given the rising number of infectious people in Brazil-a possible indicator of a second wave-these early-time approximations could be valuable in gauging the magnitude of the next contagion peak. We further examine the effect of public health policies, including social isolation and mask usage, by creating counterfactual scenarios to quantify the human impact of these public health measures in reducing peak COVID-19 cases. We discover that the effectiveness of social isolation and mask usage varies significantly across cities. We hope our study will support the development of future public health measures.

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Human periodontal ligament stem cells (hPDLSCs) are promising cells for dental and periodontal regeneration. This study aimed to develop novel alginate-fibrin fibers that encapsulates hPDLSCs and metformin, to investigate the effect of metformin on the osteogenic differentiation of hPDLSCs, and to determine the regulatory role of the Shh/Gli1 signaling pathway in the metformin-induced osteogenic differentiation of hPDLSCs for the first time. CCK8 assay was used to evaluate hPDLSCs. Alkaline phosphatase (ALP) staining, alizarin red S staining, and the expression of osteogenic genes were evaluated. Metformin and hPDLSCs were encapsulated in alginate-fibrinogen solutions, which were injected to form alginate-fibrin fibers. The activation of Shh/Gli1 signaling pathway was examined using qRT-PCR and western blot. A mechanistic study was conducted by inhibiting the Shh/Gli1 pathway using GANT61. The administration of 50 µM metformin resulted in a significant upregulation of osteogenic gene expression in hPDLSCs by 1.4-fold compared to the osteogenic induction group (P < 0.01), including ALP and runt-related transcription factor-2 (RUNX2). Furthermore, metformin increased ALP activity by 1.7-fold and bone mineral nodule formation by 2.6-fold (P<0.001). We observed that hPDLSCs proliferated with the degradation of alginate-fibrin fibers, and metformin induced their differentiation into the osteogenic lineage. Metformin also promoted the osteogenic differentiation of hPDLSCs by upregulating the Shh/Gli1 signaling pathway by 3- to 6- fold compared to the osteogenic induction group (P<0.001). The osteogenic differentiation ability of hPDLSCs were decreased 1.3- to 1.6-fold when the Shh/Gli1 pathway was inhibited, according to ALP staining and alizarin red S staining (P<0.01). Metformin enhanced the osteogenic differentiation of hPDLSCs via the Shh/Gli1 signaling pathway. Degradable alginate-fibrin hydrogel fibers encapsulating hPDLSCs and metformin have significant potential for use in dental and periodontal tissue engineering applications. Alginate-fibrin fibers encapsulating hPDLSCs and metformin have a great potential for use in the treatment of maxillofacial bone defects caused by trauma, tumors, and tooth extraction. Additionally, they may facilitate the regeneration of periodontal tissue in patients with periodontitis.

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Platelets use signal transduction pathways facilitated by class I phosphatidylinositol transfer proteins (PITPs). The 2 mammalian class I PITPs, PITPα and PITPß, are single PITP domain soluble proteins that are encoded by different genes and share 77% sequence identity, although their individual roles in mammalian biology remain uncharacterized. These proteins are believed to shuttle phosphatidylinositol and phosphatidylcholine between separate intracellular membrane compartments, thereby regulating phosphoinositide synthesis and second messenger formation. Previously, we observed that platelet-specific deletion of PITPα, the predominantly expressed murine PITP isoform, had no effect on hemostasis but impaired tumor metastasis formation and disrupted phosphoinositide signaling. Here, we found that mice lacking the less expressed PITPß in their platelets exhibited a similar phenotype. However, in contrast to PITPα-null platelet lysates, which have impaired lipid transfer activity, PITPß-null platelet lysates have essentially normal lipid transfer activity, although both isoforms contribute to phosphoinositide synthesis in vitro. Moreover, we found that platelet-specific deletion of both PITPs led to ex vivo platelet aggregation/secretion and spreading defects, impaired tail bleeding, and profound tumor dissemination. Our study also demonstrated that PITP isoforms are required to maintain endogenous phosphoinositide PtdInsP2 levels and agonist-stimulated second messenger formation. The data shown here demonstrate that the 2 isoforms are functionally overlapping and that a single isoform is able to maintain the homeostasis of platelets. However, both class I PITP isoforms contribute to phosphoinositide signaling in platelets through distinct biochemical mechanisms or different subcellular domains.

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Abstract Human periodontal ligament stem cells (hPDLSCs) are promising cells for dental and periodontal regeneration. Objective This study aimed to develop novel alginate-fibrin fibers that encapsulates hPDLSCs and metformin, to investigate the effect of metformin on the osteogenic differentiation of hPDLSCs, and to determine the regulatory role of the Shh/Gli1 signaling pathway in the metformin-induced osteogenic differentiation of hPDLSCs for the first time. Methodology CCK8 assay was used to evaluate hPDLSCs. Alkaline phosphatase (ALP) staining, alizarin red S staining, and the expression of osteogenic genes were evaluated. Metformin and hPDLSCs were encapsulated in alginate-fibrinogen solutions, which were injected to form alginate-fibrin fibers. The activation of Shh/Gli1 signaling pathway was examined using qRT-PCR and western blot. A mechanistic study was conducted by inhibiting the Shh/Gli1 pathway using GANT61. Results The administration of 50 μM metformin resulted in a significant upregulation of osteogenic gene expression in hPDLSCs by 1.4-fold compared to the osteogenic induction group (P < 0.01), including ALP and runt-related transcription factor-2 (RUNX2). Furthermore, metformin increased ALP activity by 1.7-fold and bone mineral nodule formation by 2.6-fold (P<0.001). We observed that hPDLSCs proliferated with the degradation of alginate-fibrin fibers, and metformin induced their differentiation into the osteogenic lineage. Metformin also promoted the osteogenic differentiation of hPDLSCs by upregulating the Shh/Gli1 signaling pathway by 3- to 6- fold compared to the osteogenic induction group (P<0.001). The osteogenic differentiation ability of hPDLSCs were decreased 1.3- to 1.6-fold when the Shh/Gli1 pathway was inhibited, according to ALP staining and alizarin red S staining (P<0.01). Conclusions Metformin enhanced the osteogenic differentiation of hPDLSCs via the Shh/Gli1 signaling pathway. Degradable alginate-fibrin hydrogel fibers encapsulating hPDLSCs and metformin have significant potential for use in dental and periodontal tissue engineering applications. Clinical Significance Alginate-fibrin fibers encapsulating hPDLSCs and metformin have a great potential for use in the treatment of maxillofacial bone defects caused by trauma, tumors, and tooth extraction. Additionally, they may facilitate the regeneration of periodontal tissue in patients with periodontitis.

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Bipartite networks are pervasive in modeling real-world phenomena and play a fundamental role in graph theory. Interactive exploratory visualization of such networks is an important problem, and particularly challenging when handling large networks. In this paper we present results from an investigation on using a general multilevel method for this purpose. Multilevel methods on networks have been introduced as a general approach to increase scalability of community detection and other complex optimization algorithms. They employ graph coarsening algorithms to create a hierarchy of increasingly coarser (reduced) approximations of an original network. Multilevel coarsening has been applied, e.g., to the problem of drawing simple ("unipartite") networks. We build on previous work that extended multilevel coarsening to bipartite graphs to propose a visualization interface that uses multilevel coarsening to compute a multi-resolution hierarchical representation of an input bipartite network. From this hierarchy, interactive node-link drawings are displayed following a genuine route of the "overview first, zoom and filter, details on demand" visual information seeking mantra. Analysts may depart from the coarsest representation and select nodes or sub-graphs to be expanded and shown at greater detail. Besides intuitive navigation of large-scale networks, this solution affords great flexibility, as users are free to select different coarsening strategies in different scenarios. We illustrate its potential with case studies involving real networks on distinct domains. The experimental analysis shows our strategy is effective to reveal topological structures, such as communities and holes, that may remain hidden in a conventional node-link layout. It is also useful to highlight connectivity patterns across the bipartite layers, as illustrated in an example that emphasizes the correlation between diseases and genes in genetic disorders, and in a study of a scientific collaboration network of authors and papers.

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The number of spatiotemporal data sets has increased rapidly in the last years, which demands robust and fast methods to extract information from this kind of data. Here, we propose a network-based model, called Chronnet, for spatiotemporal data analysis. The network construction process consists of dividing a geometric space into grid cells represented by nodes connected chronologically. Strong links in the network represent consecutive recurrent events between cells. The chronnet construction process is fast, making the model suitable to process large data sets. Using artificial and real data sets, we show how chronnets can capture data properties beyond simple statistics, like frequent patterns, spatial changes, outliers, and spatiotemporal clusters. Therefore, we conclude that chronnets represent a robust tool for the analysis of spatiotemporal data sets.

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Edematous severe acute childhood malnutrition (edematous SAM or ESAM), which includes kwashiorkor, presents with more overt multi-organ dysfunction than non-edematous SAM (NESAM). Reduced concentrations and methyl-flux of methionine in 1-carbon metabolism have been reported in acute, but not recovered, ESAM, suggesting downstream DNA methylation changes could be relevant to differences in SAM pathogenesis. Here, we assess genome-wide DNA methylation in buccal cells of 309 SAM children using the 450 K microarray. Relative to NESAM, ESAM is characterized by multiple significantly hypomethylated loci, which is not observed among SAM-recovered adults. Gene expression and methylation show both positive and negative correlation, suggesting a complex transcriptional response to SAM. Hypomethylated loci link to disorders of nutrition and metabolism, including fatty liver and diabetes, and appear to be influenced by genetic variation. Our epigenetic findings provide a potential molecular link to reported aberrant 1-carbon metabolism in ESAM and support consideration of methyl-group supplementation in ESAM.

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In this paper, we propose a network-based technique to analyze bills-voting data comprising the votes of Brazilian congressmen for a period of 28 years. The voting sessions are initially mapped into static networks, where each node represents a congressman and each edge stands for the similarity of votes between a pair of congressmen. Afterwards, the constructed static networks are converted to temporal networks. Our analyses on the temporal networks capture some of the main political changes happened in Brazil during the period of time under consideration. Moreover, we find out that the bills-voting networks can be used to identify convicted politicians, who commit corruption or other financial crimes. Therefore, we propose two conviction prediction methods, one is based on the highest weighted convicted neighbor and the other is based on link prediction techniques. It is a surprise to us that the high accuracy (up to 90% by the link prediction method) on predicting convictions is achieved only through bills-voting data, without taking into account any financial information beforehand. Such a feature makes possible to monitor congressmen just by considering their legal public activities. In this way, our work contributes to the large scale public data study using complex networks.

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Purpose: The research is intended for clarification of the efficacy as well as the underlying mechanism of GSK-3β inhibitors on the advancement of acute lung injuries in acute necrotizing pancreatitis (ANP) in rats. Methods: Seventy-two rats were randomly divided into 6 groups: (1)ANP-vehicle; (2)ANP-TDZD-8;(3)ANP-SB216763;(4)Sham-vehicle;(5)Sham-TDZD-8;(6)Sham-SB216763; Blood biochemical test, histopathological examination and immunohistochemical analysis of rats pancreas and lung tissues were performed. The protein expression of GSK-3β, phospho-GSK-3β (Ser9), iNOS, ICAM-1, TNF-α, and IL-10 were detected in lung tissues by Western-blot. Results: The outcomes revealed that the intervention of GSK-3β inhibitors alleviated the pathological damage of pancreas and lung (P<0.01), reduced serum amylase, lipase, hydrothorax and lung Wet-to-Dry Ratio, attenuated serum concentrations of IL-1β and IL-6 (P<0.01), inhibited the activation of NF-κB, and abated expression of iNOS, ICAM-1 and TNF-α protein, but up-regulated IL-10 expression in lung of ANP rats (P<0.01). The inflammatory response and various indicators in ANP-TDZD-8 groups were lower than those in ANP-SB216763 groups. Conclusions: Inhibition of GSK-3β weakens acute lung injury related to ANP via the inhibitory function of NF-κB signaling pathway. Different kinds of GSK-3β inhibitors have different effects to ANP acute lung injury.(AU)

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PURPOSE: The research is intended for clarification of the efficacy as well as the underlying mechanism of GSK-3ß inhibitors on the advancement of acute lung injuries in acute necrotizing pancreatitis (ANP) in rats. METHODS: Seventy-two rats were randomly divided into 6 groups: (1)ANP-vehicle; (2)ANP-TDZD-8;(3)ANP-SB216763;(4)Sham-vehicle;(5)Sham-TDZD-8;(6)Sham-SB216763; Blood biochemical test, histopathological examination and immunohistochemical analysis of rats pancreas and lung tissues were performed. The protein expression of GSK-3ß, phospho-GSK-3ß (Ser9), iNOS, ICAM-1, TNF-α, and IL-10 were detected in lung tissues by Western-blot. RESULTS: The outcomes revealed that the intervention of GSK-3ß inhibitors alleviated the pathological damage of pancreas and lung (P<0.01), reduced serum amylase, lipase, hydrothorax and lung Wet-to-Dry Ratio, attenuated serum concentrations of IL-1ß and IL-6 (P<0.01), inhibited the activation of NF-κB, and abated expression of iNOS, ICAM-1 and TNF-α protein, but up-regulated IL-10 expression in lung of ANP rats (P<0.01). The inflammatory response and various indicators in ANP-TDZD-8 groups were lower than those in ANP-SB216763 groups. CONCLUSIONS: Inhibition of GSK-3ß weakens acute lung injury related to ANP via the inhibitory function of NF-κB signaling pathway. Different kinds of GSK-3ß inhibitors have different effects to ANP acute lung injury.

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Abstract Purpose The research is intended for clarification of the efficacy as well as the underlying mechanism of GSK-3β inhibitors on the advancement of acute lung injuries in acute necrotizing pancreatitis (ANP) in rats. Methods Seventy-two rats were randomly divided into 6 groups: (1)ANP-vehicle; (2)ANP-TDZD-8;(3)ANP-SB216763;(4)Sham-vehicle;(5)Sham-TDZD-8;(6)Sham-SB216763; Blood biochemical test, histopathological examination and immunohistochemical analysis of rats pancreas and lung tissues were performed. The protein expression of GSK-3β, phospho-GSK-3β (Ser9), iNOS, ICAM-1, TNF-α, and IL-10 were detected in lung tissues by Western-blot. Results The outcomes revealed that the intervention of GSK-3β inhibitors alleviated the pathological damage of pancreas and lung (P<0.01), reduced serum amylase, lipase, hydrothorax and lung Wet-to-Dry Ratio, attenuated serum concentrations of IL-1β and IL-6 (P<0.01), inhibited the activation of NF-κB, and abated expression of iNOS, ICAM-1 and TNF-α protein, but up-regulated IL-10 expression in lung of ANP rats (P<0.01). The inflammatory response and various indicators in ANP-TDZD-8 groups were lower than those in ANP-SB216763 groups. Conclusions Inhibition of GSK-3β weakens acute lung injury related to ANP via the inhibitory function of NF-κB signaling pathway. Different kinds of GSK-3β inhibitors have different effects to ANP acute lung injury.

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Mexicans are a recent admixture of Amerindians, Europeans, and Africans. We performed local ancestry analysis of Mexican samples from two genome-wide association studies obtained from dbGaP, and discovered that at the MHC region Mexicans have excessive African ancestral alleles compared to the rest of the genome, which is the hallmark of recent selection for admixed samples. The estimated selection coefficients are 0.05 and 0.07 for two datasets, which put our finding among the strongest known selections observed in humans, namely, lactase selection in northern Europeans and sickle-cell trait in Africans. Using inaccurate Amerindian training samples was a major concern for the credibility of previously reported selection signals in Latinos. Taking advantage of the flexibility of our statistical model, we devised a model fitting technique that can learn Amerindian ancestral haplotype from the admixed samples, which allows us to infer local ancestries for Mexicans using only European and African training samples. The strong selection signal at the MHC remains without Amerindian training samples. Finally, we note that medical history studies suggest such a strong selection at MHC is plausible in Mexicans.

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Of the 97 currently recognized genera of Celastraceae, 19 are native to Madagascar, including six endemics. In this study we conducted the most thorough phylogenetic analysis of Celastraceae yet completed with respect to both character and taxon sampling, and include representatives of five new endemic genera. Fifty-one new accessions, together with 328 previously used accessions of Celastrales, were sampled for morphological characters, two rDNA gene regions, and two plastid gene regions. The endemic Malagasy genera are resolved in two separate lineages-Xenodrys by itself and all other endemic genera in a clade that also includes four lineages inferred to have dispersed from Madagascar: Brexia madagascariensis (Mascarene Islands, coastal Africa), Elaeodendron (West Indies, Africa to New Caledonia), and Pleurostylia (Africa to New Caledonia). Of the 12 extant Malagasy Celastraceae lineages identified, eight are clearly of African origin. The origins of the remaining four lineages are less clear, but reasonable possibilities include America, Eurasia, Africa, southern India, Malesia, and Australia. Based on 95% credible age intervals from fossil-calibrated molecular dating, all 12 extant Malagasy Celastraceae lineages appear to have arisen following dispersal after the separation of Madagascar from other landmasses within the last 70 million years.

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Interactions among species determine local-scale diversity, but local interactions are thought to have minor effects at larger scales. However, quantitative comparisons of the importance of biotic interactions relative to other drivers are rarely made at larger scales. Using a data set spanning 78 sites and five continents, we assessed the relative importance of biotic interactions and climate in determining plant diversity in alpine ecosystems dominated by nurse-plant cushion species. Climate variables related with water balance showed the highest correlation with richness at the global scale. Strikingly, although the effect of cushion species on diversity was lower than that of climate, its contribution was still substantial. In particular, cushion species enhanced species richness more in systems with inherently impoverished local diversity. Nurse species appear to act as a 'safety net' sustaining diversity under harsh conditions, demonstrating that climate and species interactions should be integrated when predicting future biodiversity effects of climate change.

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Semisupervised learning is a machine learning approach which is able to employ both labeled and unlabeled samples in the training process. It is an important mechanism for autonomous systems due to the ability of exploiting the already acquired information and for exploring the new knowledge in the learning space at the same time. In these cases, the reliability of the labels is a crucial factor, because mislabeled samples may propagate wrong labels to a portion of or even the entire data set. This paper has the objective of addressing the error propagation problem originated by these mislabeled samples by presenting a mechanism embedded in a network-based (graph-based) semisupervised learning method. Such a procedure is based on a combined random-preferential walk of particles in a network constructed from the input data set. The particles of the same class cooperate among them, while the particles of different classes compete with each other to propagate class labels to the whole network. Computer simulations conducted on synthetic and real-world data sets reveal the effectiveness of the model.

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It has been revealed that the network of excitable neurons via attractive coupling can generate spikes under stimuli of subthreshold signals with disordered phases. In this paper, we explore the firing activity induced by phase disorder in excitable neuronal networks consisting of both attractive and repulsive coupling. By increasing the fraction of repulsive coupling, we find that, in the weak coupling strength case, the firing threshold of phase disorder is increased and the system response to subthreshold signals is decreased, indicating that the effect of inducing neuron firing by phase disorder is weakened with repulsive coupling. Interestingly, in the large coupling strength case, we see an opposite situation, where the coupled neurons show a rather large response to the subthreshold signals even with small phase disorder. The latter case implies that the effect of phase disorder is enhanced by repulsive coupling. A system of two-coupled excitable neurons is used to explain the role of repulsive coupling on phase-disorder-induced firing activity.

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Reports remain insufficient on whether and how prostate-specific membrane antigen (PSMA) can influence in vivo osseous metastasis of prostate cancer (PCa). In the present study, the authors induced stable expression of PSMA in mouse PCa cell line RM-1. In vivo osseous metastasis was induced in 37 6-week-old female C57BL/6 mice weighing 22.45 ± 0.456 g. RM-1 cells were actively injected into the femoral bone cavity, leading to bilateral dissymmetry of bone density in the femoral bone. Tumor cells were also detected in bone tissue by pathological examination. The impact on bone density was demonstrated by the significant difference between animals injected with RM-PSMA cells (0.0738 ± 0.0185 g/cm²) and animals injected with RM-empty plasmid cells (0.0895 ± 0.0241 g/cm²). The lytic bone lesion of the RM-PSMA group (68.4%) was higher than that of the control group (27.8%). Immunohistochemistry showed that the expression of both vascular endothelial growth factor (VEGF) and matrix metalloproteinase-9 (MMP-9) was distinctly higher in the RM-PSMA group than in the control group, while ELISA and Western blot assay indicated that VEGF and MMP-9 were higher in the RM-PSMA group compared to the control group (in vitro). Thus, the present study proposed and then confirmed for the first time that PSMA can promote in vivo osseous metastasis of PCa by increasing sclerotic destruction of PCa cells. Further analyses also suggested that PSMA functions positively on the invasive ability of RM-1 by increasing the expression of MMP-9 and VEGF by osseous metastases in vivo.

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Reports remain insufficient on whether and how prostate-specific membrane antigen (PSMA) can influence in vivo osseous metastasis of prostate cancer (PCa). In the present study, the authors induced stable expression of PSMA in mouse PCa cell line RM-1. In vivo osseous metastasis was induced in 37 6-week-old female C57BL/6 mice weighing 22.45 ± 0.456 g. RM-1 cells were actively injected into the femoral bone cavity, leading to bilateral dissymmetry of bone density in the femoral bone. Tumor cells were also detected in bone tissue by pathological examination. The impact on bone density was demonstrated by the significant difference between animals injected with RM-PSMA cells (0.0738 ± 0.0185 g/cm²) and animals injected with RM-empty plasmid cells (0.0895 ± 0.0241 g/cm²). The lytic bone lesion of the RM-PSMA group (68.4%) was higher than that of the control group (27.8%). Immunohistochemistry showed that the expression of both vascular endothelial growth factor (VEGF) and matrix metalloproteinase-9 (MMP-9) was distinctly higher in the RM-PSMA group than in the control group, while ELISA and Western blot assay indicated that VEGF and MMP-9 were higher in the RM-PSMA group compared to the control group (in vitro). Thus, the present study proposed and then confirmed for the first time that PSMA can promote in vivo osseous metastasis of PCa by increasing sclerotic destruction of PCa cells. Further analyses also suggested that PSMA functions positively on the invasive ability of RM-1 by increasing the expression of MMP-9 and VEGF by osseous metastases in vivo.

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Phase-disorder-induced resonance has been recently uncovered in an ensemble of coupled excitable neurons with weak external signal, where each neuron takes a constant initial signal phase [Phys. Rev. E 82, 010902(R) (2010)]. However, it is unclear how the initial phase disorder influences the behavior of a single or isolated neuron, which constitutes the ensemble. In order to answer this question, we here consider the case of a single neuron with phase noise originated from the time-varying initial signal phase, in contrast to the constant initial phase in each neuron studied in the above referenced paper. Interestingly, we find that the phase noise can induce resonance even in the single neuronal system with subthreshold signal. Moreover, we reveal that, with the presence of phase noise, the neuron also shows another resonance behavior by varying the period of the external signal. An analysis is conducted to uncover the mechanisms behind these resonance phenomena.

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