On the convergence of additive and multiplicative splitting iterations for systems of linear equations

AbstractWe study convergence conditions for the additive and the multiplicative splitting iteration methods, i.e., two generalizations of the additive and the multiplicative Schwarz iterations, for Hermitian and non-Hermitian systems of linear equations, under an algebraic setting. Theoretical analyses show that when the coefficient and the splitting matrices are Hermitian, or non-Hermitian but diagonalizable, satisfying mild conditions, both additive and multiplicative splitting iteration methods are convergent, even if the coefficient matrix is indefinite

On convergence conditions of waveform relaxation methods for linear differential-algebraic equations

AbstractFor linear constant-coefficient differential-algebraic equations, we study the waveform relaxation methods without demanding the boundedness of the solutions based on infinite time interval. In particular, we derive explicit expression and obtain asymptotic convergence rate of this class of iteration schemes under weaker assumptions, which may have wider and more useful application extent. Numerical simulations demonstrate the validity of the theory

Diversity-Oriented Synthesis for Novel, Selective and Drug-like Inhibitors for a Phosphatase from Mycobacterium Tuberculosis

Mycobacterium protein tyrosine phosphatase B (mPTPB) is a potential drug target of Tuberculosis (TB). Small molecule inhibitors of mPTPB could be a treatment to overcome emerging TB drug resistance. Using a Diversity-Oriented Synthesis (DOS) strategy, we successfully developed a salicylic acid based and drug-like mPTPB inhibitor with an IC50 of 2 μM and >20-fold specificity over many human PTPs, making it an excellent lead molecule for anti-TB drug discovery. In addition, DOS generated bicyclic salicylic acids are also promising starting points for acquiring inhibitors targeting other PTPs

SHP2 phosphatase as a novel therapeutic target for melanoma treatment

Melanoma ranks among the most aggressive and deadly human cancers. Although a number of targeted therapies are available, they are effective only in a subset of patients and the emergence of drug resistance often reduces durable responses. Thus there is an urgent need to identify new therapeutic targets and develop more potent pharmacological agents for melanoma treatment. Herein we report that SHP2 levels are frequently elevated in melanoma, and high SHP2 expression is significantly associated with more metastatic phenotype and poorer prognosis. We show that SHP2 promotes melanoma cell viability, motility, and anchorage-independent growth, through activation of both ERK1/2 and AKT signaling pathways. We demonstrate that SHP2 inhibitor 11a-1 effectively blocks SHP2-mediated ERK1/2 and AKT activation and attenuates melanoma cell viability, migration and colony formation. Most importantly, SHP2 inhibitor 11a-1 suppresses xenografted melanoma tumor growth, as a result of reduced tumor cell proliferation and enhanced tumor cell apoptosis. Taken together, our data reveal SHP2 as a novel target for melanoma and suggest SHP2 inhibitors as potential novel therapeutic agents for melanoma treatment

Novel anticancer agents based on targeting the trimer interface of the PRL phosphatase

PRL oncoproteins are phosphatases overexpressed in numerous types of human cancer. Elevated levels of PRL associate with metastasis and poor clinical outcomes. In principle, PRL phosphatases offer appealing therapeutic targets, but they remain underexplored due to the lack of specific chemical probes. In this study, we address this issue by exploiting a unique property of PRL phosphatases, namely, that they may function as homotrimers. Starting from a sequential structure-based virtual screening and medicinal chemistry strategy, we identified Cmpd-43 and several analogs which disrupt PRL1 trimerization. Biochemical and structural analyses demonstrate that Cmpd-43 and its close analogs directly bind the PRL1 trimer interface and obstruct PRL1 trimerization. Cmpd-43 also specifically blocks the PRL1-induced cell proliferation and migration through attenuation of both ERK1/2 and Akt activity. Importantly, Cmpd-43 exerted potent anticancer activity both in vitro and in vivo in a murine xenograft model of melanoma. Our results validate a trimerization-dependent signaling mechanism for PRL and offer proof-of-concept for trimerization inhibitors as candidate therapeutics to treat PRL-driven cancer

Block triangular and skew-Hermitian splitting methods for positive-definite linear systems

By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, we introduce a new splitting, called positive-definite and skew-Hermitian splitting (PSS), and then establish a class of PSS methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS) method for iteratively solving the positive-definite systems of linear equations. Theoretical analysis shows that the PSS method converges unconditionally to the exact solution of the linear system, with the upper bound of its convergence factor dependent only on the spectrum of the positive-definite splitting matrix and independent of the spectrum of the skew-Hermitian splitting matrix as well as the eigenvectors of all matrices involved. When we specialize the PSS to block triangular ( or triangular) and skew-Hermitian splitting (BTSS or TSS), the PSS method naturally leads to a BTSS or TSS iteration method, which may be more practical and efficient than the HSS and NSS iteration methods. Applications of the BTSS method to the linear systems of block two-by-two structures are discussed in detail. Numerical experiments further show the effectiveness of our new methods

Erythromycin Enhances CD4+Foxp3+ Regulatory T-Cell Responses in a Rat Model of Smoke-Induced Lung Inflammation

Heavy smoking can induce airway inflammation and emphysema. Macrolides can modulate inflammation and effector T-cell response in the lungs. However, there is no information on whether erythromycin can modulate regulatory T-cell (Treg) response. This study is aimed at examining the impact of erythromycin on Treg response in the lungs in a rat model of smoking-induced emphysema. Male Wistar rats were exposed to normal air or cigarette smoking daily for 12 weeks and treated by gavage with 100 mg/kg of erythromycin or saline daily beginning at the forth week for nine weeks. The lung inflammation and the numbers of inflammatory infiltrates in bronchoalveolar lavage fluid (BALF) were characterized. The frequency, the number of Tregs, and the levels of Foxp3 expression in the lungs and IL-8, IL-35, and TNF-α in BALF were determined by flow cytometry, RT-PCR and ELISA, respectively. Treatment with erythromycin reduced smoking-induced inflammatory infiltrates, the levels of IL-8 and TNF-α in the BALF and lung damages but increased the numbers of CD4+Foxp3+ Tregs and the levels of Foxp3 transcription in the lungs, accompanied by increased levels of IL-35 in the BALF of rats. Our novel data indicated that erythromycin enhanced Treg responses, associated with the inhibition of smoking-induced inflammation in the lungs of rats