Electronic and spectroscopic studies of the non-heme reduced binuclear iron sites of two ribonucleotide reductase variants: comparison to reduced methane monooxygenase and contributions to O2 reactivity

Circular dichroism (CD), magnetic circular dichroism (MCD), and variable-temperature variable-field (VTVH) MCD have been used to probe the biferrous active site of two variants of ribonucleotide reductase. The aspartate to glutamate substitution (R2-D84E) at the binuclear iron site modifies the endogenous ligand set of ribonucleotide reductase to match that of the binuclear center in the hydroxylase component of methane monooxygenase (MMOH). The crystal structure of chemically reduced R2-D84E suggests that the active-site structure parallels that of MMOH. However, CD, MCD, and VTVH MCD data combined with spin-Hamiltonian analysis of reduced R2-D84E indicate a different coordination environment relative to reduced MMOH, with no mu-(1,1)(eta(1),eta(2)) carboxylate bridge. To further understand the variations in geometry of the active site, which lead to differences in reactivity, density functional theory (DFT) calculations have been carried out to identify active-site structures for R2-wt and R2-D84E consistent with these spectroscopic data. The effects of varying the ligand set, positions of bound and free waters, and additional protein constraints on the geometry and energy of the binuclear site of both R2-wt and variant R2s are also explored to identify the contributions to their structural differences and their relation to reduced MMOH.     

Monolayer Filaments versus Multilayer Stacking of Bent‐Core Molecules

Bent‐core materials exhibiting lamellar crystals (B4 phase), when dissolved in organic solvents, formed gels with helical ribbons made of molecular monolayers and bilayers, whereas strongly deformed stacks of 5–6 layers were found in the bulk samples. The width and pitch of the helical filaments were governed by molecular length; they both increased with terminal‐chain elongation. It was also found that bulk samples were optically active, in contrast to the corresponding gels, which lacked optical activity. The optical activity of samples originated from the internal structure of the crystal layers rather than from the helicity of the filaments. A theoretical model predicts a strong increase in optical activity as the number of layers in the stack increases and its saturation for few layers, thus explaining the smaller optical activity for gels than for bulk samples. A strong increase and redshift in fluorescence was detected in gels as compared to the sol state.     

Chemical composition, antioxidant and antibacterial properties of Achillea collina Becker ex Heimerl s.l. and A. pannonica Scheele essential oils

The in vitro antioxidant and antimicrobial activities of two Achillea millefolium (Adanson) Koch s.l species essential oils (A. collina Becker ex Heimerl s.l. and A. pannonica Scheele, Asteraceae) originating from the Golija and Radan mountains (Serbia) were investigated. The chemical profiles of the essential oils were evaluated by GC-MS. Antioxidant activity was assessed as free radical scavenging capacity (RSC) towards 2,2-diphenyl-1-picrylhydrazil (DPPH) radicals, together with effects on lipid peroxidation (LP). Antibacterial activity was examined on 21 bacterial strains. Based on the chemical composition of the essential oil, A. collina s.l. from Mount Golija was classified as a chamazulene chemotype (tetraploid). The high percentage of oxygenated monoterpenes and absence of azulene in the essential oil obtained from A. pannonica from Radan pointing that this population is octaploid. Essential oil of A. pannonica expressed stronger antimicrobial activity on almost all tested bacteria. Furthermore, this essential oil expressed higher scavenging effects on DPPH radical (IC(50) = 0.52 comparing to 0.62 mug/mL). Only in the LP evaluation, essential oil of A. collina s.l. from Golija exhibited stronger antioxidant activity (IC(50) = 0.75 comparing to 2.12 mug/mL).     

Rate of convergence of the mean curvature flow

We study the flow M_t of a smooth, strictly convex hypersurface by its mean curvature in ?^{n + 1}. The surface remains smooth and convex, shrinking monotonically until it disappears at a critical time T and point x^* (which is due to Huisken). This is equivalent to saying that the corresponding rescaled mean curvature flow converges to a sphere Sⁿ of radius √n. In this paper we will study the rate of exponential convergence of a rescaled flow. We will present here a method that tells us that the rate of the exponential decay is at least 2/n. We can define the “arrival time” u of a smooth, strictly convex, n‐dimensional hypersurface as it moves with normal velocity equal to its mean curvature via u(x) = t if x ∈ M_t for x ∈ Int(M₀). Huisken proved that, for n ≥ 2, u(x) is C² near x^*. The case n = 1 has been treated by Kohn and Serfaty [11]; they proved C³‐regularity of u. As a consequence of the obtained rate of convergence of the mean curvature flow, we prove that u is not necessarily C³ near x^* for n ≥ 2. We also show that the obtained rate of convergence 2/n, which arises from linearizing a mean curvature flow, is the optimal one, at least for n ≥ 2. © 2007 Wiley Periodicals, Inc.     

Finite time blow-up for a dyadic model of the Euler equations

We introduce a dyadic model for the Euler equations and the Navier-Stokes equations with hyper-dissipation in three dimensions. For the dyadic Euler equations we prove finite time blow-up. In the context of the dyadic Navier-Stokes equations with hyper-dissipation we prove finite time blow-up in the case when the dissipation degree is sufficiently small.

     

Convergence of Kähler-Einstein orbifolds

We proved the convergence of a sequence of two-dimensional compact Kähler-Einstein orbifolds with rational quotient singularities and with some uniform bounds on the volumes and on the Euler characteristics of our orbifolds, to a Kähler-Einstein two-dimensional orbifold. Our limit orbifold can have worse singularities than the orbifolds in our sequence. We will also derive some estimates on the norms of the sections of plurianticanonical bundles of our orbifolds in the sequence that we are considering and our limit orbifold.     

The stationary solution of a random dynamical model

This paper studies the stationary probability density function (PDF) solution of a nonlinear business cycle model subjected to random shocks of Gaussian white-noise type. The PDF solution is controlled by a Fokker–Planck–Kolmogorov (FPK) equation, and we use exponential polynomial closure (EPC) method to derive an approximate solution for the FPK equation. Numerical results obtained from EPC method, better than those from Gaussian closure method, show good agreement with the probability distribution obtained with Monte Carlo simulation including the tail regions.