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.

Unilateral contact dermatitis of the chest

Unusual distributions of contact dermatitis often lead to identification of the offending agent. We present a case of unilateral dermatitis of the chest developing in a patient with a history of allergy to metal. A name tag attached magnetically to his work uniform was identified as the cause of the eruption. Unilateral eruption of the chest can be a manifestation of allergic contact dermatitis to metal objects in breast pockets or attached to clothing

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

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

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

The spectrum of large powers of the Laplacian in bounded domains

We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non integer N and for 3D Laplacian problems.Comment: 13 pages, 2 figure

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