The structures of Micrococcus lysodeikticus catalase, its ferryl intermediate (compound II) and NADPH complex

The crystal structure of the bacterial catalase from Micrococcus lysodeikticus has been refined using the gene-derived sequence both at 0.88 Angstrom resolution using data recorded at 110 K and at 1.5 Angstrom resolution with room-temperature data. The atomic resolution structure has been refined with individual anisotropic atomic thermal parameters. This has revealed the geometry of the haem and surrounding protein, including many of the H atoms, with unprecedented accuracy and has characterized functionally important hydrogen-bond interactions in the active site. The positions of the H atoms are consistent with the enzymatic mechanism previously suggested for beef liver catalase. The structure reveals that a 25 Angstrom long channel leading to the haem is filled by partially occupied water molecules, suggesting an inherent facile access to the active site. In addition, the structures of the ferryl intermediate of the catalase, the so-called compound II, at 1.96 Angstrom resolution and the catalase complex with NADPH at 1.83 Angstrom resolution have been determined. Comparison of compound II and the resting state of the enzyme shows that the binding of the O atom to the iron (bond length 1.87 Angstrom) is associated with increased haem bending and is accompanied by a distal movement of the iron and the side chain of the proximal tyrosine. Finally, the structure of the NADPH complex shows that the cofactor is bound to the molecule in an equivalent position to that found in beef liver catalase, but that only the adenine part of NADPH is visible in the present structure

Dielectric function of a two-component plasma including collisions

A multiple-moment approach to the dielectric function of a dense non-ideal plasma is treated beyond RPA including collisions in Born approximation. The results are compared with the perturbation expansion of the Kubo formula. Sum rules as well as Ward identities are considered. The relations to optical properties as well as to the dc electrical conductivity are pointed out.Comment: latex, 10 pages, 7 figures in ps forma

Weakly coupled states on branching graphs

We consider a Schr\"odinger particle on a graph consisting of $\,N\,$ links joined at a single point. Each link supports a real locally integrable potential $\,V_j\,$; the self--adjointness is ensured by the $\,\delta\,$ type boundary condition at the vertex. If all the links are semiinfinite and ideally coupled, the potential decays as $\,x^{-1-\epsilon}$ along each of them, is non--repulsive in the mean and weak enough, the corresponding Schr\"odinger operator has a single negative eigenvalue; we find its asymptotic behavior. We also derive a bound on the number of bound states and explain how the $\,\delta\,$ coupling constant may be interpreted in terms of a family of squeezed potentials.Comment: LaTeX file, 7 pages, no figure

Scattering theory on graphs (2): the Friedel sum rule

We consider the Friedel sum rule in the context of the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples of graphs where the state counting method given by the Friedel sum rule is not working. The reason for the failure of the Friedel sum rule to count the states is the existence of states localized in the graph and not coupled to the leads, which occurs if the spectrum is degenerate and the number of leads too small.Comment: 20 pages, LaTeX, 6 eps figure

Scattering theory on graphs

We consider the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.Comment: 21 pages, LaTeX, 10 eps figure

Left atrial strain as a predictor of atrial fibrillation in patients with asymptomatic severe aortic stenosis and preserved left ventricular systolic function

Aim. To study the structural and functional left heart parameters in patients with severe aortic stenosis (AS) and preserved ejection fraction (EF) in order to determine the risk of atrial fibrillation (AF).Material and methods. The study included 84 patients (men, 37; mean age, 68±8 years) with severe AS and EF >55%. All patients had sinus rhythm and were asymptomatic. Echocardiography was performed to assess longitudinal strain of the left ventricle (LVLS), right ventricle, left atrium (LALS) and the left atrial stiffness (LAS) using the speckle tracking method. Left ventricular mass index (LVMI) and maximum left atrium volume index (LAVI) were also determined. Patients were followed up for 1 year.Results. AF was reported in 27 (32%) patients, of which 9 (33%) had asymptomatic AF episodes detected by 48-hour electrocardiography. Eighteen (67%) patients with AF felt palpitations. Patients with and without episodes of atrial fibrillation had non-significant differences in LVMI, LAVI, and LVLS. Patients with atrial fibrillation had a lower LALS and a higher LAS compared with patients without atrial fibrillation. Regression analysis revealed that LALS and LAS were independent predictors of AF.Conclusion. AF develops in about one third of asymptomatic patients with severe AS and normal EF. The development of AF predisposes to the onset of AS symptoms in most patients. LALS and LAS were predictors of AF in these patients. Identification of patients at risk of AF will allow for earlier aortic valve replacement

Thermodynamic properties and electrical conductivity of strongly correlated plasma media

We study thermodynamic properties and the electrical conductivity of dense hydrogen and deuterium using three methods: classical reactive Monte Carlo (REMC), direct path integral Monte Carlo (PIMC) and a quantum dynamics method in the Wigner representation of quantum mechanics. We report the calculation of the deuterium compression quasi-isentrope in good agreement with experiments. We also solve the Wigner-Liouville equation of dense degenerate hydrogen calculating the initial equilibrium state by the PIMC method. The obtained particle trajectories determine the momentum-momentum correlation functions and the electrical conductivity and are compared with available theories and simulations

Band spectra of rectangular graph superlattices

We consider rectangular graph superlattices of sides l1, l2 with the wavefunction coupling at the junctions either of the delta type, when they are continuous and the sum of their derivatives is proportional to the common value at the junction with a coupling constant alpha, or the "delta-prime-S" type with the roles of functions and derivatives reversed; the latter corresponds to the situations where the junctions are realized by complicated geometric scatterers. We show that the band spectra have a hidden fractal structure with respect to the ratio theta := l1/l2. If the latter is an irrational badly approximable by rationals, delta lattices have no gaps in the weak-coupling case. We show that there is a quantization for the asymptotic critical values of alpha at which new gap series open, and explain it in terms of number-theoretic properties of theta. We also show how the irregularity is manifested in terms of Fermi-surface dependence on energy, and possible localization properties under influence of an external electric field. KEYWORDS: Schroedinger operators, graphs, band spectra, fractals, quasiperiodic systems, number-theoretic properties, contact interactions, delta coupling, delta-prime coupling.Comment: 16 pages, LaTe

A bootstrap method for sum-of-poles approximations

A bootstrap method is presented for finding efficient sum-of-poles approximations of causal functions. The method is based on a recursive application of the nonlinear least squares optimization scheme developed in (Alpert et al. in SIAM J. Numer. Anal. 37:1138–1164, 2000), followed by the balanced truncation method for model reduction in computational control theory as a final optimization step. The method is expected to be useful for a fairly large class of causal functions encountered in engineering and applied physics. The performance of the method and its application to computational physics are illustrated via several numerical examples

Spectra of self-adjoint extensions and applications to solvable Schroedinger operators

We give a self-contained presentation of the theory of self-adjoint extensions using the technique of boundary triples. A description of the spectra of self-adjoint extensions in terms of the corresponding Krein maps (Weyl functions) is given. Applications include quantum graphs, point interactions, hybrid spaces, singular perturbations.Comment: 81 pages, new references added, subsection 1.3 extended, typos correcte