Continuous vacua in bilinear soliton equations

We discuss the freedom in the background field (vacuum) on top of which the solitons are built. If the Hirota bilinear form of a soliton equation is given by A(D_{\vec x})\bd GF=0,\, B(D_{\vec x})(\bd FF - \bd GG)=0 where both $A$ and $B$ are even polynomials in their variables, then there can be a continuum of vacua, parametrized by a vacuum angle $\phi$. The ramifications of this freedom on the construction of one- and two-soliton solutions are discussed. We find, e.g., that once the angle $\phi$ is fixed and we choose $u=\arctan G/F$ as the physical quantity, then there are four different solitons (or kinks) connecting the vacuum angles $\pm\phi$, $\pm\phi\pm\Pi2$ (defined modulo $\pi$). The most interesting result is the existence of a ``ghost'' soliton; it goes over to the vacuum in isolation, but interacts with ``normal'' solitons by giving them a finite phase shift.Comment: 9 pages in Latex + 3 figures (not included

Is my ODE a Painleve equation in disguise?

Painleve equations belong to the class y'' + a_1 {y'}^3 + 3 a_2 {y'}^2 + 3 a_3 y' + a_4 = 0, where a_i=a_i(x,y). This class of equations is invariant under the general point transformation x=Phi(X,Y), y=Psi(X,Y) and it is therefore very difficult to find out whether two equations in this class are related. We describe R. Liouville's theory of invariants that can be used to construct invariant characteristic expressions (syzygies), and in particular present such a characterization for Painleve equations I-IV.Comment: 8 pages. Based on talks presented at NEEDS 2000, Gokova, Turkey, 29 June - 7 July, 2000, and at the AMS-HKMS joint meeting 13-16 December, 2000. Submitted to J. Nonlin. Math. Phy

Third-order integrable difference equations generated by a pair of second-order equations

We show that the third-order difference equations proposed by Hirota, Kimura and Yahagi are generated by a pair of second-order difference equations. In some cases, the pair of the second-order equations are equivalent to the Quispel-Robert-Thomson(QRT) system, but in the other cases, they are irrelevant to the QRT system. We also discuss an ultradiscretization of the equations.Comment: 15 pages, 3 figures; Accepted for Publication in J. Phys.

Gene Expression in Experimental Aortic Coarctation and Repair: Candidate Genes for Therapeutic Intervention?

Coarctation of the aorta (CoA) is a constriction of the proximal descending thoracic aorta and is one of the most common congenital cardiovascular defects. Treatments for CoA improve life expectancy, but morbidity persists, particularly due to the development of chronic hypertension (HTN). Identifying the mechanisms of morbidity is difficult in humans due to confounding variables such as age at repair, follow-up duration, coarctation severity and concurrent anomalies. We previously developed an experimental model that replicates aortic pathology in humans with CoA without these confounding variables, and mimics correction at various times using dissolvable suture. Here we present the most comprehensive description of differentially expressed genes (DEGs) to date from the pathology of CoA, which were obtained using this model. Aortic samples (n=4/group) from the ascending aorta that experiences elevated blood pressure (BP) from induction of CoA, and restoration of normal BP after its correction, were analyzed by gene expression microarray, and enriched genes were converted to human orthologues. 51 DEGs with \u3e6 fold-change (FC) were used to determine enriched Gene Ontology terms, altered pathways, and association with National Library of Medicine Medical Subject Headers (MeSH) IDs for HTN, cardiovascular disease (CVD) and CoA. The results generated 18 pathways, 4 of which (cell cycle, immune system, hemostasis and metabolism) were shared with MeSH ID’s for HTN and CVD, and individual genes were associated with the CoA MeSH ID. A thorough literature search further uncovered association with contractile, cytoskeletal and regulatory proteins related to excitation-contraction coupling and metabolism that may explain the structural and functional changes observed in our experimental model, and ultimately help to unravel the mechanisms responsible for persistent morbidity after treatment for CoA

Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions

Splicing factor 3B subunit 1 interacts with HIV Tat and plays a role in viral transcription and reactivation from latency

ABSTRACT The main obstacle to an HIV cure is the transcriptionally inert proviruses that persist in resting CD4 T cells and other reservoirs. None of the current approaches has significantly reduced the size of the viral reservoir. Hence, alternative approaches, such as permanent blocking of viral transcription, to achieve a sustained remission, need urgent attention. To identify cellular factors that may be important for this approach, we sought for host targets that when altered could block HIV transcription and reactivation. Here, we identified splicing factor 3B subunit 1 (SF3B1) as a critical HIV dependency factor required for viral replication. SF3B1 is a splicing factor involved in directing chromatin and nascent gene transcripts to appropriate splice sites. Inhibitors of SF3B1 are currently in development for cancer and have been found to be nontoxic to normal cells compared to malignant cells. Knockdown of SF3B1 abrogated HIV replication in all cell types tested. SF3B1 interacted with viral protein Tat in vitro and in vivo. Genetic or pharmacologic inhibition of SF3B1 prevented Tat-mediated HIV transcription and RNA polymerase II association with the HIV promoter. In addition, an inhibitor of SF3B1 prevented HIV reactivation from latency irrespective of the latency-reversing agent used. The data show that SF3B1 is involved in viral transcription and reactivation from latency and may serve as a therapeutic target in the HIV cure efforts. IMPORTANCE The reason why HIV cannot be cured by current therapy is because of viral persistence in resting T cells. One approach to permanent HIV remission that has received less attention is the so-called “block and lock” approach. The idea behind this approach is that the virus could be permanently disabled in patients if viral genome or surrounding chromatin could be altered to silence the virus, thus enabling patients to stop therapy. In this work, we have identified splicing factor 3B subunit 1 (SF3B1) as a potential target for this approach. SF3B1 interacts with the viral protein Tat, which is critical for viral transcription. Inhibition of SF3B1 prevents HIV transcription and reactivation from latency. Since there are preclinical inhibitors for this protein, our findings could pave the way to silence HIV transcription, potentially leading to prolonged or permanent remission

Critical Role of the Secondary Binding Pocket in Modulating the Enzymatic Activity of DUSP5 toward Phosphorylated ERKs

DUSP5 is an inducible nuclear dual-specificity phosphatase that specifically interacts with and deactivates extracellular signal-regulated kinases ERK1 and ERK2, which are responsible for cell proliferation, differentiation, and survival. The phosphatase domain (PD) of DUSP5 has unique structural features absent from other nuclear DUSPs, such as the presence of a secondary anion-binding site in the proximity of the reaction center and a glutamic acid E264 positioned next to the catalytic cysteine C263, as well as a remote intramolecular disulfide linkage. The overall 400 ns molecular dynamics simulations indicate that the secondary binding site of DUSP5 PD acts as an allosteric regulator of the phosphatase activity of DUSP5. Our studies have identified E264 as a critical constituent of the dual binding pocket, which regulates the catalytic activity of DUSP5 by forming a salt bridge with arginine R269. Molecular dynamics studies showed that initial occupation of the secondary binding pocket leads to the breakage of the salt bridge, which then allows the occupation of the active site. Indeed, biochemical analysis using the pERK assay on mutant E264Q demonstrated that mutation of glutamic acid E264 leads to an increase in the DUSP5 catalytic activity. The role of the secondary binding site in assembling the DUSP5–pERK pre-reactive complex was further demonstrated by molecular dynamics simulations that showed that the remote C197–C219 disulfide linkage controls the structure of the secondary binding pocket based on its redox state (i.e., disulfide/dithiol) and, in turn, the enzymatic activity of DUSP5

Combinations of isoform-targeted histone deacetylase inhibitors and bryostatin analogues display remarkable potency to activate latent HIV without global T-cell activation

AbstractCurrent antiretroviral therapy (ART) for HIV/AIDS slows disease progression by reducing viral loads and increasing CD4 counts. Yet ART is not curative due to the persistence of CD4+ T-cell proviral reservoirs that chronically resupply active virus. Elimination of these reservoirs through the administration of synergistic combinations of latency reversing agents (LRAs), such as histone deacetylase (HDAC) inhibitors and protein kinase C (PKC) modulators, provides a promising strategy to reduce if not eradicate the viral reservoir. Here, we demonstrate that largazole and its analogues are isoform-targeted histone deacetylase inhibitors and potent LRAs. Significantly, these isoform-targeted HDAC inhibitors synergize with PKC modulators, namely bryostatin-1 analogues (bryologs). Implementation of this unprecedented LRA combination induces HIV-1 reactivation to unparalleled levels and avoids global T-cell activation within resting CD4+ T-cells.</jats:p

Protein Expression, Characterization and Activity Comparisons of Wild Type and Mutant DUSP5 Proteins

Background The mitogen-activated protein kinases (MAPKs) pathway is critical for cellular signaling, and proteins such as phosphatases that regulate this pathway are important for normal tissue development. Based on our previous work on dual specificity phosphatase-5 (DUSP5), and its role in embryonic vascular development and disease, we hypothesized that mutations in DUSP5 will affect its function. Results In this study, we tested this hypothesis by generating full-length glutathione-S-transferase-tagged DUSP5 and serine 147 proline mutant (S147P) proteins from bacteria. Light scattering analysis, circular dichroism, enzymatic assays and molecular modeling approaches have been performed to extensively characterize the protein form and function. We demonstrate that both proteins are active and, interestingly, the S147P protein is hypoactive as compared to the DUSP5 WT protein in two distinct biochemical substrate assays. Furthermore, due to the novel positioning of the S147P mutation, we utilize computational modeling to reconstruct full-length DUSP5 and S147P to predict a possible mechanism for the reduced activity of S147P. Conclusion Taken together, this is the first evidence of the generation and characterization of an active, full-length, mutant DUSP5 protein which will facilitate future structure-function and drug development-based studies

On a q-difference Painlev\'e III equation: I. Derivation, symmetry and Riccati type solutions

A q-difference analogue of the Painlev\'e III equation is considered. Its derivations, affine Weyl group symmetry, and two kinds of special function type solutions are discussed.Comment: arxiv version is already officia