Application of the bifurcation method to the modified Boussinesq equation

In this paper, we investigate the modified Boussinesq equation $$u_{tt}- u_{xx}-\varepsilon u_{xxxx}-3(u^2)_{xx}+3(u^2u_x)_{x}=0.$$ Firstly, we give a property of the solutions of the equation, that is, if $1+u(x, t)$ is a solution, so is $1-u(x, t)$. Secondly, by using the bifurcation method of dynamical systems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended

The Application of Bifurcation Method to Klein-Gordon-Zakharov Equations

Bifurcation method of dynamical systems is employed to study the Klein-Gordon-Zakharov equations. Under some parameter conditions, some explicit expressions of solutions for the equation are obtained. These solutions contain solitary wave solutions, blow-up solutions, periodic solutions, periodic blow-up solutions and kink-shaped solutions. Key Words: Klein-Gordon-Zakharov equations; Exact solutions; Bifurcation metho

The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation

A nonlinear generalization of the Camassa-Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev space HS(R) with s>3/2 is established via a limiting procedure. Provided that the initial value u0 satisfies the sign condition and u0∈Hs(R)  (s>3/2), it is shown that there exists a unique global solution for the equation in space C([0,∞);Hs(R))∩C1([0,∞);Hs−1(R))

Economic Research on Energy Storage Auxiliary Frequency Regulation of Lithium Iron Phosphate Battery for 2 × 600 MW Coal-fired Unit in Guangdong

[Introduction] In view of the economic benefits of AGC frequency regulation project of combined energy storage in Guangdong coal-fired power plant, the method of establishing typical engineering cases is demonstrated. [Method] This article summarized the latest version of frequency regulation auxiliary market revenue settlement rules in the southern region and calculated the frequency regulation performance index of typical 2 × 600 MW coal-fired units using lithium iron phosphate battery energy storage in Guangdong Province, then established a revenue model, estimated or assumed the key parameters such as cost, mileage, clearing price, running time, etc. Finally, under the contract energy management mode, it calculated its economy from the perspective of investors and analyzed the changes of financial index under different total investment, operation year and revenue sharing. [Result] The results show that in the measured case, except for the first sharing scheme, the internal rate of return of capital in other scenarios all exceeds 7%. [Conclusion] The frequency regulation project of lithium iron phosphate battery energy storage in Guangdong has a good return on investment within four years. After that, investors can still be attracted to participate in this project with the decrease of total investment and the increase of share

Resveratrol mediates mitochondrial function through the sirtuin 3 pathway to improve abnormal metabolic remodeling in atrial fibrillation

This study investigated the impact of resveratrol on abnormal metabolic remodeling in atrial fibrillation (AF) and explored potential molecular mechanisms. An AF cell model was established by high-frequency electrical stimulation of HL-1 atrial muscle cells. Resveratrol concentrations were optimized using CCK-8 and flow cytometry. AF-induced increases in ROS and mitochondrial calcium, along with decreased adenosine triphosphate (ATP) and mitochondrial membrane potential, were observed. Resveratrol mitigated these changes and maintained normal mitochondrial morphology. Moreover, resveratrol acted through the SIRT3-dependent pathway, as evidenced by its ability to suppress AF-induced acetylation of key metabolic enzymes. SIRT3 overexpression controls acetylation modifications, suggesting its regulatory role. In conclusion, resveratrol's SIRT3-dependent pathway intervenes in AF-induced mitochondrial dysfunction, presenting a potential therapeutic avenue for AF-related metabolic disorders. This study sheds light on the role of resveratrol in mitigating AF-induced mitochondrial remodeling and highlights its potential as a novel treatment for AF

Adenovirus-Mediated Somatic Genome Editing of Pten by CRISPR/Cas9 in Mouse Liver in Spite of Cas9-Specific Immune Responses

CRISPR/Cas9 derived from the bacterial adaptive immunity pathway is a powerful tool for genome editing, but the safety profiles of in vivo delivered Cas9 (including host immune responses to the bacterial Cas9 protein) have not been comprehensively investigated in model organisms. Nonalcoholic steatohepatitis (NASH) is a prevalent human liver disease characterized by excessive fat accumulation in the liver. In this study, we used adenovirus (Ad) vector to deliver a Streptococcus pyogenes–derived Cas9 system (SpCas9) targeting Pten, a gene involved in NASH and a negative regulator of the PI3K-AKT pathway, in mouse liver. We found that the Ad vector mediated efficient Pten gene editing even in the presence of typical Ad vector-associated immunotoxicity in the liver. Four months after vector infusion, mice receiving the Pten gene-editing Ad vector showed massive hepatomegaly and features of NASH, consistent with the phenotypes following Cre-loxP-induced Pten deficiency in mouse liver. We also detected induction of humoral immunity against SpCas9 and the potential presence of an SpCas9-specific cellular immune response. Our findings provide a strategy to model human liver diseases in mice and highlight the importance considering Cas9-specific immune responses in future translational studies involving in vivo delivery of CRISPR/Cas9

Recombinant adeno-associated virus integration sites in murine liver after ornithine transcarbamylase gene correction

Recombinant adeno-associated viruses (rAAVs) have been tested in humans and other large mammals without adverse events. However, one study of mucopolysaccharidosis VII correction in mice showed repeated integration of rAAV in cells from hepatocellular carcinoma (HCC) in the Dlk1-Dio3 locus, suggesting possible insertional mutagenesis. In contrast, another study found no association of rAAV integration with HCC, raising questions about the generality of associations between liver transformation and integration at Dlk1-Dio3. Here we report that in rAAV-treated ornithine transcarbamylase (Otc)-deficient mice, four examples of integration sites in Dlk1-Dio3 could be detected in specimens from liver nodule/tumors, confirming previous studies of rAAV integration in the Dlk1-Dio3 locus in the setting of another murine model of metabolic disease. In one case, the integrated vector was verified to be present at about one copy per cell, consistent with clonal expansion. Another verified integration site in liver nodule/tumor tissue near the Tax1bp1 gene was also detected at about one copy per cell. The Dlk1-Dio3 region has also been implicated in human HCC and so warrants careful monitoring in ongoing human clinical trials with rAAV vectors

The Mechanism of ATP-Dependent Allosteric Protection of Akt Kinase Phosphorylation

SummaryKinases use ATP to phosphorylate substrates; recent findings underscore the additional regulatory roles of ATP. Here, we propose a mechanism for allosteric regulation of Akt1 kinase phosphorylation by ATP. Our 4.7-μs molecular dynamics simulations of Akt1 and its mutants in the ATP/ADP bound/unbound states revealed that ATP occupancy of the ATP-binding site stabilizes the closed conformation, allosterically protecting pT308 by restraining phosphatase access and key interconnected residues on the ATP→pT308 allosteric pathway. Following ATP→ADP hydrolysis, pT308 is exposed and readily dephosphorylated. Site-directed mutagenesis validated these predictions and indicated that the mutations do not impair PDK1 and PP2A phosphatase recruitment. We further probed the function of residues around pT308 at the atomic level, and predicted and experimentally confirmed that Akt1H194R/R273H double mutant rescues pathology-related Akt1R273H. Analysis of classical Akt homologs suggests that this mechanism can provide a general model of allosteric kinase regulation by ATP; as such, it offers a potential avenue for allosteric drug discovery