A Domain Decomposition Method for the Steady-State Navier-Stokes-Darcy Model with Beavers-Joseph Interface Condition

This paper proposes and analyzes a Robin-type multiphysics domain decomposition method (DDM) for the steady-state Navier-Stokes-Darcy model with three interface conditions. In addition to the two regular interface conditions for the mass conservation and the force balance, the Beavers-Joseph condition is used as the interface condition in the tangential direction. The major mathematical difficulty in adopting the Beavers-Joseph condition is that it creates an indefinite leading order contribution to the total energy budget of the system [Y. Cao et al., Comm. Math. Sci., 8 (2010), pp. 1-25; Y. Cao et al., SIAM J. Numer. Anal., 47 (2010), pp. 4239-4256]. In this paper, the well-posedness of the Navier-Stokes-Darcy model with Beavers-Joseph condition is analyzed by using a branch of nonsingular solutions. By following the idea in [Y. Cao et al., Numer. Math., 117 (2011), pp. 601-629], the three physical interface conditions are utilized together to construct the Robin-type boundary conditions on the interface and decouple the two physics which are described by Navier-Stokes and Darcy equations, respectively. Then the corresponding multiphysics DDM is proposed and analyzed. Three numerical experiments using finite elements are presented to illustrate the features of the proposed method and verify the results of the theoretical analysis

A Multigrid Multilevel Monte Carlo Method for Stokes–Darcy Model with Random Hydraulic Conductivity and Beavers–Joseph Condition

A multigrid multilevel Monte Carlo (MGMLMC) method is developed for the stochastic Stokes–Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Three interface conditions with randomness are considered on the interface between Stokes and Darcy equations, especially the Beavers–Joesph interface condition with random hydraulic conductivity. Because the randomness through the interface affects the flow in the Stokes domain, we investigate the coupled stochastic Stokes–Darcy model to improve the fidelity. Under suitable assumptions on the random coefficient, we prove the existence and uniqueness of the weak solution of the variational form. To construct the numerical method, we first adopt the Monte Carlo (MC) method and finite element method, for the discretization in the probability space and physical space, respectively. In order to improve the efficiency of the classical single-level Monte Carlo (SLMC) method, we adopt the multilevel Monte Carlo (MLMC) method to dramatically reduce the computational cost in the probability space. A strategy is developed to calculate the number of samples needed in MLMC method for the stochastic Stokes–Darcy model. In order to accomplish the strategy for MLMC method, we also present a practical method to determine the variance convergence rate for the stochastic Stokes–Darcy model with Beavers–Joseph interface condition. Furthermore, MLMC method naturally provides the hierarchical grids and sufficient information on these grids for multigrid (MG) method, which can in turn improve the efficiency of MLMC method. In order to fully make use of the dynamical interaction between these two methods, we propose a multigrid multilevel Monte Carlo (MGMLMC) method with finite element discretization for more efficiently solving the stochastic model, while additional attention is paid to the interface and the random Beavers–Joesph interface condition. The computational cost of the proposed MGMLMC method is rigorously analyzed and compared with the SLMC method. Numerical examples are provided to verify and illustrate the proposed method and the theoretical conclusions

Dual fluorescent molecular substrates selectively report the activation, sustainability and reversibility of cellular PKB/Akt activity

Using a newly developed near-infrared (NIR) dye that fluoresces at two different wavelengths (dichromic fluorescence, DCF), we discovered a new fluorescent substrate for Akt, also known as protein kinase B, and a method to quantitatively report this enzyme\u27s activity in real time. Upon insulin activation of cellular Akt, the enzyme multi-phosphorylated a single serine residue of a diserine DCF substrate in a time-dependent manner, culminating in monophospho- to triphospho-serine products. The NIR DCF probe was highly selective for the Akt1 isoform, which was demonstrated using Akt1 knockout cells derived from MMTV-ErbB2 transgenic mice. The DCF mechanism provides unparalleled potential to assess the stimulation, sustainability, and reversibility of Akt activation longitudinally. Importantly, NIR fluorescence provides a pathway to translate findings from cells to living organisms, a condition that could eventually facilitate the use of these probes in humans

Tbx20 Is Required in Mid-Gestation Cardiomyocytes and Plays a Central Role in Atrial Development.

RationaleMutations in the transcription factor TBX20 (T-box 20) are associated with congenital heart disease. Germline ablation of Tbx20 results in abnormal heart development and embryonic lethality by embryonic day 9.5. Because Tbx20 is expressed in multiple cell lineages required for myocardial development, including pharyngeal endoderm, cardiogenic mesoderm, endocardium, and myocardium, the cell type-specific requirement for TBX20 in early myocardial development remains to be explored.ObjectiveHere, we investigated roles of TBX20 in midgestation cardiomyocytes for heart development.Methods and resultsAblation of Tbx20 from developing cardiomyocytes using a doxycycline inducible cTnTCre transgene led to embryonic lethality. The circumference of developing ventricular and atrial chambers, and in particular that of prospective left atrium, was significantly reduced in Tbx20 conditional knockout mutants. Cell cycle analysis demonstrated reduced proliferation of Tbx20 mutant cardiomyocytes and their arrest at the G1-S phase transition. Genome-wide transcriptome analysis of mutant cardiomyocytes revealed differential expression of multiple genes critical for cell cycle regulation. Moreover, atrial and ventricular gene programs seemed to be aberrantly regulated. Putative direct TBX20 targets were identified using TBX20 ChIP-Seq (chromatin immunoprecipitation with high throughput sequencing) from embryonic heart and included key cell cycle genes and atrial and ventricular specific genes. Notably, TBX20 bound a conserved enhancer for a gene key to atrial development and identity, COUP-TFII/Nr2f2 (chicken ovalbumin upstream promoter transcription factor 2/nuclear receptor subfamily 2, group F, member 2). This enhancer interacted with the NR2F2 promoter in human cardiomyocytes and conferred atrial specific gene expression in a transgenic mouse in a TBX20-dependent manner.ConclusionsMyocardial TBX20 directly regulates a subset of genes required for fetal cardiomyocyte proliferation, including those required for the G1-S transition. TBX20 also directly downregulates progenitor-specific genes and, in addition to regulating genes that specify chamber versus nonchamber myocardium, directly activates genes required for establishment or maintenance of atrial and ventricular identity. TBX20 plays a previously unappreciated key role in atrial development through direct regulation of an evolutionarily conserved COUPT-FII enhancer

Cyclin D1 integrates G9a-mediated histone methylation.

Lysine methylation of histones and non-histone substrates by the SET domain containing protein lysine methyltransferase (KMT) G9a/EHMT2 governs transcription contributing to apoptosis, aberrant cell growth, and pluripotency. The positioning of chromosomes within the nuclear three-dimensional space involves interactions between nuclear lamina (NL) and the lamina-associated domains (LAD). Contact of individual LADs with the NL are dependent upon H3K9me2 introduced by G9a. The mechanisms governing the recruitment of G9a to distinct subcellular sites, into chromatin or to LAD, is not known. The cyclin D1 gene product encodes the regulatory subunit of the holoenzyme that phosphorylates pRB and NRF1 thereby governing cell-cycle progression and mitochondrial metabolism. Herein, we show that cyclin D1 enhanced H3K9 dimethylation though direct association with G9a. Endogenous cyclin D1 was required for the recruitment of G9a to target genes in chromatin, for G9a-induced H3K9me2 of histones, and for NL-LAD interaction. The finding that cyclin D1 is required for recruitment of G9a to target genes in chromatin and for H3K9 dimethylation, identifies a novel mechanism coordinating protein methylation

Cyclin D1-mediated microRNA expression signature predicts breast cancer outcome

Background: Genetic classification of breast cancer based on the coding mRNA suggests the evolution of distinct subtypes. Whether the non-coding genome is altered concordantly with the coding genome and the mechanism by which the cell cycle directly controls the non-coding genome is poorly understood. Methods: Herein, the miRNA signature maintained by endogenous cyclin D1 in human breast cancer cells was defined. In order to determine the clinical significance of the cyclin D1-mediated miRNA signature, we defined a miRNA expression superset from 459 breast cancer samples. We compared the coding and non-coding genome of breast cancer subtypes. Results: Hierarchical clustering of human breast cancers defined four distinct miRNA clusters (G1-G4) associated with distinguishable relapse-free survival by Kaplan-Meier analysis. The cyclin D1-regulated miRNA signature included several oncomirs, was conserved in multiple breast cancer cell lines, was associated with the G2 tumor miRNA cluster, ERα+ status, better outcome and activation of the Wnt pathway. The coding and non-coding genome were discordant within breast cancer subtypes. Seed elements for cyclin D1-regulated miRNA were identified in 63 genes of the Wnt signaling pathway including DKK. Cyclin D1 restrained DKK1 via the 3\u27UTR. In vivo studies using inducible transgenics confirmed cyclin D1 induces Wnt-dependent gene expression. Conclusion: The non-coding genome defines breast cancer subtypes that are discordant with their coding genome subtype suggesting distinct evolutionary drivers within the tumors. Cyclin D1 orchestrates expression of a miRNA signature that induces Wnt/β-catenin signaling, therefore cyclin D1 serves both upstream and downstream of Wnt/β-catenin signaling

A cyclin D1/microRNA 17/20 regulatory feedback loop in control of breast cancer cell proliferation

Decreased expression of specific microRNAs (miRNAs) occurs in human tumors, which suggests a function for miRNAs in tumor suppression. Herein, levels of the miR-17-5p/miR-20a miRNA cluster were inversely correlated to cyclin D1 abundance in human breast tumors and cell lines. MiR-17/20 suppressed breast cancer cell proliferation and tumor colony formation by negatively regulating cyclin D1 translation via a conserved 3′ untranslated region miRNA-binding site, thereby inhibiting serum-induced S phase entry. The cell cycle effect of miR-17/20 was abrogated by cyclin D1 siRNA and in cyclin D1–deficient breast cancer cells. Mammary epithelial cell–targeted cyclin D1 expression induced miR-17-5p and miR-20a expression in vivo, and cyclin D1 bound the miR-17/20 cluster promoter regulatory region. In summary, these studies identify a novel cyclin D1/miR-17/20 regulatory feedback loop through which cyclin D1 induces miR-17-5p/miR-20a. In turn, miR-17/20 limits the proliferative function of cyclin D1, thus linking expression of a specific miRNA cluster to the regulation of oncogenesis