A general approach for prediction of motional EPR spectra from Molecular Dynamics (MD) simulations: application to spin labelled protein

A general approach for the prediction of EPR spectra directly and completely from single dynamical trajectories generated from Molecular Dynamics (MD) simulations is described. The approach is applicable to an arbitrary system of electron and nuclear spins described by a general form of the spin-Hamiltonian for the entire motional range. It is shown that for a reliable simulation of motional EPR spectra only a single truncated dynamical trajectory generated until the point when correlation functions of rotational dynamics are completely relaxed is required. The simulation algorithm is based on a combination of the propagation of the spin density matrix in the Liouville space for this initial time interval and the use of well defined parameters calculated entirely from the dynamical trajectory for prediction of the evolution of the spin density matrix at longer times. A new approach is illustrated with the application to a nitroxide spin label MTSL attached to the protein sperm whale myoglobin. It is shown that simulation of the EPR spectrum, which is in excellent agreement with experiment, can be achieved from a single MD trajectory. Calculations reveal the complex nature of the dynamics of a spin label which is a superposition of the fast librational motions within dihedral states, of slow rotameric dynamics among different conformational states of the nitroxide tether and of the slow rotational diffusion of the protein itself. The significance of the slow rotameric dynamics of the nitroxide tether on the overall shape of the EPR spectrum is analysed and discussed.     

Mechanistic insight into the nitrosylation of the [4Fe-4S] cluster of WhiB-like proteins

The reactivity of protein bound iron-sulfur clusters with nitric oxide (NO) is well documented, but little is known about the actual mechanism of cluster nitrosylation. Here, we report studies of members of the Wbl family of [4Fe-4S] containing proteins, which play key roles in regulating developmental processes in actinomycetes, including Streptomyces and Mycobacteria, and have been shown to be NO responsive. Streptomyces coelicolor WhiD and Mycobacterium tuberculosis WhiB1 react extremely rapidly with NO in a multiphasic reaction involving, remarkably, 8 NO molecules per [4Fe-4S] cluster. The reaction is 10(4)-fold faster than that observed with O(2) and is by far the most rapid iron-sulfur cluster nitrosylation reaction reported to date. An overall stoichiometry of [Fe(4)S(4)(Cys)(4)](2-) + 8NO → 2[Fe(I)(2)(NO)(4)(Cys)(2)](0) + S(2-) + 3S(0) has been established by determination of the sulfur products and their oxidation states. Kinetic analysis leads to a four-step mechanism that accounts for the observed NO dependence. DFT calculations suggest the possibility that the nitrosylation product is a novel cluster [Fe(I)(4)(NO)(8)(Cys)(4)](0) derived by dimerization of a pair of Roussin's red ester (RRE) complexes.     

Formality Theorem for Hochschild Cochains via Transfer

We construct a 2-colored operad Ger _∞ which, on the one hand, extends the operad Ger _∞ governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad governing open-closed homotopy algebras. We show that Tamarkin’s Ger _∞-structure on the Hochschild cochain complex C ^•(A, A) of an A _∞-algebra A extends naturally to a Ger⁺_￥{{\bf Ger}^+_{\infty}}-structure on the pair (C ^•(A, A), A). We show that a formality quasi-isomorphism for the Hochschild cochains of the polynomial algebra can be obtained via transfer of this Ger⁺_￥{{\bf Ger}^+_{\infty}}-structure to the cohomology of the pair (C ^•(A, A), A). We show that Ger⁺_￥{{\bf Ger}^+_{\infty}} is a sub DG operad of the first sheet E ¹(SC) of the homology spectral sequence for the Fulton–MacPherson version SC of Voronov’s Swiss Cheese operad. Finally, we prove that the DG operads Ger⁺_￥{{\bf Ger}^+_{\infty}} and E ¹(SC) are non-formal.     

Trends,directions for further research,and some open problems of fractional calculus

Nonlinear Dynamics - The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present...     

Variational analysis in dynamical problems of linear elasticity

The initial–boundary value problems in the linear theory of elasticity is considered. Based on the method of integrodifferential relations (MIDR) two dynamical variational principles is proposed and discussed. It is shown that the Hamilton principle as well as the corresponding complementary principle stated for dynamic boundary value problems follow out the variational formulations proposed. To minimize the nonnegative functional under algebraic and differential constraints a regular finite element algorithm is worked out. The algorithm allows us to estimate explicitly the local and integral quality of numerical solutions obtained. A 3D problem of lateral motions of a rectilinear elastic prism with a rectangular cross section are considered. The numerical results are presented and discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetics and mechanism for acid‐catalyzed disproportionation of 2,2,6,6‐tetramethylpiperidine‐1‐oxyl

Disproportionation of cyclic nitroxyl radicals (NRs) in acid solutions is of key importance for the chemistry of these compounds. Meanwhile, the data reported on the mechanism of this reaction in dilute acids are inconsistent with those on the stability of NRs in concentrated acids. Here we have examined the kinetics and stoichiometry for the disproportionation of 2,2,6,6‐tetramethylpiperidine‐1‐oxyl ( 1 ) in aqueous H₂SO₄ (1.0–99.3 wt%) and found that (1) the disproportionation of 1 proceeds by the same mechanism over the entire range of acid concentrations, (2) the effective rate constant of the process exhibits a bell‐shaped dependence on the excess acidity function X peaked at X = ?pK _1H+ = 5.8 ± 0.3, (3) a key step of the process involves the oxidation of 1 with its protonated counterpart 1H ⁺ yielding oxopiperidinium cation 2 and hydroxypiperidine 3 at a rate constant of (1.4 ± 0.8) × 10⁵ M^?1 · s^?1, and (4) the reaction is reversible and, upon neutralization of acid, disproportionation products 2 and 3H ⁺ comproportionate to starting 1 . In highly acidic media, the protonated form 1H ⁺ is relatively stable due to a low disproportionation rate. Based on the known and newly obtained values of equilibrium constants, both the standard redox potential for the 1H ⁺ / 3 pair (955 ± 15 mV) and the pH‐dependences have been calculated for the reduction potentials of 1 and 2 to hydroxylamine 3 that is in equilibrium with its protonated 3H ⁺ and deprotonated 3 ^? forms. The data obtained provide a deeper insight into the mechanism of nitroxyl‐involving reactions in chemical and biological systems. Copyright © 2008 John Wiley & Sons, Ltd.     

Theory for the determination of activity coefficients of strong electrolytes with regard to concentration dependence of hydration numbers

A new theory of electrolyte solutions is discussed which, as opposed to the Debye–Huckel method valid for relatively small concentrations only, enables one to describe the thermodynamic properties of electrolyte solutions over a wide range of state parameters. The novelty of the proposed theory is that it takes into account the dependence of hydration numbers upon concentration, the fact that failed to attract much attention before. The applicability of the theory to the calculation of activity coefficients of some electrolytes (LiCl, NaCl, KCl, RbCl, and CsCl) is demonstrated. A method is proposed for the determination of the thermodynamic parameters of solvation of separate ions.     

Unexpected reaction pathway during the palladation of 2,5-diphenylphosphacymantrene

A new reaction of P-alkoxypalladation was found. 2,5-Diphenylphosphacymantrene reacts with Na₂PdCl₄ and NaOAc in MeOH or EtOH to give P-methoxy or P-ethoxy derivatives with Pd₂Cl₂ dimeric core. The products 2 and 3 were characterized by ¹H, ³¹P, ¹³C NMR spectra and X-ray crystal structure data.