How Is Methane Formed and Oxidized Reversibly When Catalyzed by Ni‐Containing Methyl‐Coenzyme M Reductase?

Ni‐containing methyl‐coenzyme M reductase (MCR) is capable of catalyzing methane formation and has recently been observed to also be able to catalyze the reverse reaction, the anaerobic oxidation of methane. The forward reaction has been extensively studied theoretically before and was found to consist of two steps. The first step is rate‐limiting and the second step was therefore treated at a lower level. For an accurate treatment of the reverse reaction, both steps have to be studied at the same level. In the present paper, the mechanisms for the reversible formation and oxidation of methane catalyzed by MCR have been investigated using hybrid density functional theory with recent developments, in particular including dispersion effects. An active‐site model was constructed based on the X‐ray crystal structure. The calculations indicate that the MCR reaction is indeed reversible and proceeds via a methyl radical and a Ni‐S(CoM) intermediate with reasonable reaction barriers in both directions. In a competing mechanism, the formation of the crucial Ni‐methyl intermediate, was found to be strongly endergonic by over 20 kcal mol^?1 (including a barrier) with dispersion and entropy effects considered, and thus would not be reachable in a reasonable time under natural conditions.     

The Genuine Bernstein–Durrmeyer Operators and Quasi-Interpolants

In this paper we consider the so-called genuine Bernstein–Durrmeyer operators and define corresponding quasi-interpolants of order ${r \in \mathbb{N}_0}$ in terms of certain differential operators. These quasi-interpolants preserve all polynomials of degree at most r?+?1. We analyse the eigenstructure of the differential operators and the quasi-interpolants and prove as main results an error estimate of Jackson–Favard type for sufficiently smooth functions and an upper bound for the error of approximation in the sup-norm in terms of an appropriate K-functional.     

Frequency locking in a forced Mathieu–van der Pol–Duffing system

Optically actuated radio frequency microelectromechanical system (MEMS) devices are seen to self-oscillate or vibrate under illumination of sufficient strength (Aubin, Pandey, Zehnder, Rand, Craighead, Zalalutdinov, Parpia (Appl. Phys. Lett. 83, 3281–3283, 2003)). These oscillations can be frequency locked to a periodic forcing, applied through an inertial drive at the forcing frequency, or subharmonically via a parametric drive, hence providing tunability. In a previous work~(Aubin, Zalalutdinov, Alan, Reichenbach, Rand, Zehnder, Parpia, Craighead (IEEE/ASME J. Micromech. Syst. 13, 1018–1026, 2004)), this MEMS device was modeled by a three-dimensional system of coupled thermo-mechanical equations requiring experimental observations and careful finite element simulations to obtain the model parameters. The resulting system of equations is relatively computationally expensive to solve, which could impede its usage in a complex network of such resonators. In this paper, we present a simpler model that shows similar behavior to the MEMS device. We investigate the dynamics of a Mathieu–van der Pol–Duffing equation, which is forced both parametrically and nonparametrically. It is shown that the steady-state response can consist of either 1:1 frequency locking, or 2:1 subharmonic locking, or quasiperiodic motion. The system displays hysteresis when the forcing frequency is slowly varied. We use perturbations to obtain a slow flow, which is then studied using the bifurcation software package AUTO.     

Sambucinic Acid,a New Metabolite of Fusarium sambacinum. 45th communication on verrucarins and roridins

Sambucinic acid (5), a C₁₅-trichothecene with a modified strure, has been isolated from cultures of Fusarium sambucinum. The structure is established by spectroscopic data and X-ray diffraction analysis. A hypothetical biogenetic pathway is proposed.     

Rodriguez-type Representation for the Eigenfunctions of Durrmeyer-type Operators

In this paper we consider a generalization of different variants of Durrmeyer- type modifications of Baskakov and Meyer- König and Zeller operators. We prove a general result concerning the commutativity of these operators with certain differential operators. Prom this result a Rodriguez- type formula for the eigenfunctions follows as a corollary.     

Enantioselective Allylic Substitution Catalyzed by Chiral [Bis(dihydrooxazole)]palladium Complexes: Catalyst structure and possible mechanism of enantioselection

Allylpalladium complexes with chiral bis(dihydrooxazole) ligands were studied as catalysts for the enantioselective allylic substitution reaction of rac-1,3-diphenylprop-2-enyl acetate (rac- 5 ) with the anion of dimethyl malonate (Scheme 1). Using enantiomerically pure (S,E)-1-(4-tolyl)-3-phenylprop-2-enyl acatete ((S)- 25 ) as substrate, the reaction was shown to proceed by a clean ‘syn’ displacement of acetate by dimethyl malonate (Scheme 6). The [Pd¹¹(η³-allyl)] complex 18 and the analogous [Pd(η³-1,3-diphenylallyl)] complex 20 , both containing the same bis(dihydrooxazole) ligand, were characterized by X-ray structure analysis and by NMR spectroscopy in solution. The structural data reveal that steric interactions of the allyl system with the chiral ligand result in selective electronic activation of one of the allylic termini. The higher reactivity of one allylic terminus toward nucleophilic attack is reflected in a significantly longer Pd? C bond and a shift of the corresponding ¹³C-NMR resonance to higher frequency.     

A comparative study of high-spin manganese and iron complexes

Different metal complexes of the general form M(OH) _n (H₂O)_{6– n} have been studied for manganese and iron. Oxidation states considered for manganese are Mn(III), Mn(IV) and Mn(V) and for iron Fe(II), Fe(III) and Fe(IV). Oxygen containing ligands are used throughout with varying numbers of hydroxyl and water ligands. Some metal-oxo and some charged complexes were also studied. Large Jahn-Teller distortions were found for the Mn(III) and Fe(IV) complexes. Consequences of these distortions are that water ligands have to be placed along the weak JT-axis and that five-coordination by a loss of one of these water ligands is quite competitive with six-coordination in particular for manganese. For Fe(II) and Fe(III) lower coordinations than six are preferred due to the presence of two repulsive e _g electrons. For the metal-oxo complexes five-coordination is also preferred due to the strong trans effect from the oxo ligand. All complexes studied have high-spin ground states. An interesting effect is that the spin is much more delocalized on the ligands for the iron complexes than for the manganese complexes. This effect, which is chemically important for certain iron enzymes, is rationalized by the large number of 3d electrons on iron. For manganese with only five 3d electrons no spin delocalization is needed to obtain the proper high-spin states. Received: 4 February 1997 / Accepted: 24 February 1997