Insights from the x-ray crystal structure of coral 8R-lipoxygenase: Calcium activation via a C2-like domain and a structural basis of product chirality

Lipoxygenases (LOXs) catalyze the regio- and stereospecific dioxygenation of polyunsaturated membrane-embedded fatty acids. We report here the 3.2 Å resolution structure of 8R-LOX from the Caribbean sea whip coral Plexaura homomalla, a LOX isozyme with calcium dependence and the uncommon R chiral stereospecificity. Structural and spectroscopic analyses demonstrated calcium binding in a C2-like membrane-binding domain, illuminating the function of similar amino acids in calcium-activated mammalian 5-LOX, the key enzyme in the pathway to the pro-inflammatory leukotrienes. Mutation of Ca2+- ligating amino acids in 8R-LOX resulted not only in a diminished capacity to bind membranes, as monitored by fluorescence resonance energy transfer, but also in an associated loss of Ca2+-regulated enzyme activity. Moreover, a structural basis for R chiral specificity is also revealed; creation of a small oxygen pocket next to Gly428 (Ala in all S-LOX isozymes) promoted C-8 oxygenation with R chirality on the activated fatty acid substrate. © 2005 by The American Society for Biochemistry and Molecular Biology, Inc

Dynamics of Fractal Solids

We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some generalized equations which are derived by using integrals of fractional order. The order of fractional integral can be equal to the fractal mass dimension of the solid. Fractional integrals are considered as an approximation of integrals on fractals. We suggest the approach to compute the moments of inertia for fractal solids. The dynamics of fractal solids are described by the usual Euler's equations. The possible experimental test of the continuous medium model for fractal solids is considered.Comment: 12 pages, LaTe

Fractional derivatives of random walks: Time series with long-time memory

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-known fractionally integrated autoregressive (FIGARCH) models, commonly used in econometric studies, is discussed. The application of correlated random walks to simulate empirical financial times series is considered and compared with the predictions from FIGARCH and the simpler FIARCH processes. A comparison with empirical data is performed.Comment: 10 pages, 14 figure

State transition of a non-Ohmic damping system in a corrugated plane

Anomalous transport of a particle subjected to non-Ohmic damping of the power $\delta$ in a tilted periodic potential is investigated via Monte Carlo simulation of generalized Langevin equation. It is found that the system exhibits two relative motion modes: the locking state and the running state. Under the surrounding of sub-Ohmic damping ($0<\delta<1$), the particle should transfer into a running state from a locking state only when local minima of the potential vanish; hence the particle occurs a synchronization oscillation in its mean displacement and mean square displacement (MSD). In particular, the two motion modes are allowed to coexist in the case of super-Ohmic damping ($1<\delta<2$) for moderate driving forces, namely, where exists double centers in the velocity distribution. This induces the particle having faster diffusion, i.e., its MSD reads $= 2D^{(\delta)}_{eff} t^{\delta_{eff}}$. Our result shows that the effective power index $\delta_{\textmd{eff}}$ can be enhanced and is a nonmonotonic function of the temperature and the driving force. The mixture effect of the two motion modes also leads to a breakdown of hysteresis loop of the mobility.Comment: 7 pages,7 figure

Levi-Civita cylinders with fractional angular deficit

The angular deficit factor in the Levi-Civita vacuum metric has been parametrized using a Riemann-Liouville fractional integral. This introduces a new parameter into the general relativistic cylinder description, the fractional index {\alpha}. When the fractional index is continued into the negative {\alpha} region, new behavior is found in the Gott-Hiscock cylinder and in an Israel shell.Comment: 5 figure

Anomalous Rotational Relaxation: A Fractional Fokker-Planck Equation Approach

In this study we obtained analytically relaxation function in terms of rotational correlation functions based on Brownian motion for complex disordered systems in a stochastic framework. We found out that rotational relaxation function has a fractional form for complex disordered systems, which indicates relaxation has non-exponential character obeys to Kohlrausch-William-Watts law, following the Mittag-Leffler decay.Comment: Revtex4, 9 pages. Paper was revised. References adde

Transport Equations from Liouville Equations for Fractional Systems

We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are defined. Hydrodynamic equations for fractional systems are derived from the generalized transport equation.Comment: 11 pages, LaTe

Fractional Generalization of Gradient Systems

We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these systems.Comment: 11 pages, LaTe

Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe

Psi-Series Solution of Fractional Ginzburg-Landau Equation

One-dimensional Ginzburg-Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order $alpha$ with polynomial nonlinearity of order $s$ have the noninteger power-like behavior of order $\alpha/(1-s)$ near the singularity.Comment: LaTeX, 19 pages, 2 figure