Eigenvalue Problem in Two Dimensions for an Irregular Boundary II: Neumann Condition

We formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions when the normal derivative of {\psi} vanishes on an irregular closed curve. Unique feature of this method, unlike other perturbation schemes, is that it does not require a separate formalism to treat degeneracies. Degenerate states are handled equally elegantly as the non-degenerate ones. A real parameter, extracted from the parameters defining the irregular boundary, serves as a perturbation parameter in this scheme as opposed to earlier schemes where the perturbation parameter is an artificial one. The efficacy of the proposed scheme is gauged by calculating the eigenvalues for elliptical and supercircular boundaries and comparing with the results obtained numerically. We also present a simple and interesting semi-empirical formula, determining the eigenspectrum of the 2D Helmholtz equation with the Dirichlet or the Neumann condition for a supercircular boundary. A comparison of the eigenspectrum for several low-lying modes obtained by employing the formula with the corresponding numerical estimates shows good agreement for a wide range of the supercircular exponent.Comment: 26 pages, 12 figure

Plasminogen Controls Inflammation and Pathogenesis of Influenza Virus Infections via Fibrinolysis

Detrimental inflammation of the lungs is a hallmark of severe influenza virus infections. Endothelial cells are the source of cytokine amplification, although mechanisms underlying this process are unknown. Here, using combined pharmacological and gene-deletion approaches, we show that plasminogen controls lung inflammation and pathogenesis of infections with influenza A/PR/8/34, highly pathogenic H5N1 and 2009 pandemic H1N1 viruses. Reduction of virus replication was not responsible

Interactions between staphylokinase, plasmin(ogen), and fibrin. Staphylokinase discriminates between free plasminogen and plasminogen bound to partially degraded fibrin

Staphylokinase (STA), a protein of bacterial origin, induces highly fibrin-specific thrombolysis both in human plasma in vitro and in pilot clinical trials. Using fluorescence microscopy, we investigated the spatial distribution of fluorescein isothiocyanate (FITC)-labeled STA during lysis of a plasma clot and its binding to purified fibrin clots in the presence or in the absence of plasmin(ogen). STA highly accumulated in a thin superficial layer of the lysing plasma clot following the distribution of plasminogen (Pg) during lysis. Experiments with purified fibrin clots revealed that STA binds to Pg bound to partially degraded fibrin but not to Pg bound to intact fibrin. Binding of FITC-labeled STA to various forms of plasmin(ogen) in a buffer solution was studied by measuring fluorescence anisotropy. The binding constant for Glu-Pg was estimated as 7.4 μM and for Lys-Pg as 0.28 μM; for active-site blocked plasmin the binding constant was less than 0.05 μM. The much lower affinity of STA for Glu-Pg compared with that for active site- blocked plasmin was mainly due to a lower association rate constant, as assessed by real time biospecific interaction analysis. Gel filtration of a mixture of STA with a molar excess of Glu-Pg demonstrated that STA migrated as an unbound 18-kDa protein when activation of Pg into plasmin was precluded by inhibitors of plasmin. When gel-filtered under the same conditions with plasmin, STA migrated in complex with plasmin with an apparent molecular mass of 100 kDa. Confocal fluorescence microscopy finally demonstrated that when FITC-labeled STA was added to plasma before clotting, it did not bind to fibrin fibers during the first minutes (lag phase), although Pg bound to the fibers moderately. Then, both Pg and STA started to accumulate on the fibers progressively, followed by complete lysis of the clot. In conclusion, our results imply that, when STA is added to plasma, only a small percentage associates with Pg. In contrast, STA binds strongly to plasmin and to Pg, which is bound to partially degraded fibrin. These findings add a new mechanism to the known explanations for the inefficient Pg activation by STA in plasma and specify the mechanism for fibrin-dependent activation of Pg. Chemicals/CAS: auR protein, Staphylococcus aureus, EC 3.4.24.29; Fibrin, 9001-31-4; Fibrinolytic Agents; Fluorescein-5-isothiocyanate, 3326-32-7; Metalloendopeptidases, EC 3.4.24.-; Plasmin, EC 3.4.21.7; Plasminogen, 9001-91-6; Recombinant Protein