Structures of oxaliplatin‐oligonucleotide adducts from DNA

Oxaliplatin, [(1R,2R)‐cyclohexane‐1,2‐diamine](ethanedioato‐O,O')platinum(II) shows a great efficiency against colorectal cancer. Although the mode of action of oxaliplatin is not yet understood, it is commonly accepted that binding of oxaliplatin to DNA prevents DNA synthesis and alters protein to DNA binding. In order to elucidate the modified DNA–protein interaction and thus to understand the mechanisms leading to cellular misinterpretation of DNA information and apoptosis, we have identified the preferential binding sites and the dynamics of the oxaliplatin‐DNA intrastrand and interstrand adducts at the oligomer level using high‐performance liquid chromatography/electrospray ionization‐tandem mass spectrometry (HPLC/ESI‐MS/MS) and HPLC/inductively coupled plasma‐MS for quantitative studies. We used a combination of benzonase, alkaline phosphatase and Nuclease S1 for digestion. This digestion procedure allows the study of platinated oligomeric nucleotides and more complex interstrand adducts. The digestion products were mostly chromatographically separated and characterized using HPLC/ESI‐ion trap MS/MS experiments. We could show that the adducts to guanine and adenine are quite dynamic; that is, the ratios are changing for several days. In addition, the resulting adducts provide evidence for the action of the digesting enzymes and indicate that the adduct spectrum at the oligomeric level is different to that at the commonly studies dinucleotide level. Copyright © 2012 John Wiley & Sons, Ltd.     

Fractal wavelet dimensions and localization

In this paper we want to give a new definition of fractal dimensions as small scale behavior of theq-energy of wavelet transforms. This is a generalization of previous multi-fractal approaches. With this particular definition we will show that the 2-dimension (=correlation dimension) of the spectral measure determines the long time behavior of the time evolution generated by a bounded self-adjoint operator acting in some Hilbert space ?. It will be proved that for φ, ψ∈? we have $$\mathop {\lim \inf }\limits_{T \to \infty } \frac{{\log \int_0^T {d\omega \left| {\left\langle {\psi \left| {e^{ - iA\omega } } \right.\phi } \right\rangle } \right|^2 } }}{{\log T}} = - \kappa ^ + (2)$$ and that $$\mathop {\lim \sup }\limits_{T \to \infty } \frac{{\log \int_0^T {d\omega \left| {\left\langle {\psi \left| {e^{ - iA\omega } } \right.\phi } \right\rangle } \right|^2 } }}{{\log T}} = - \kappa ^ - (2),$$ wherek ^±(2) are the upper and lower correlation dimensions of the spectral measure associated with ψ and ?. A quantitative version of the RAGE theorem shall also be given.     

On a Formula for the L2 Wasserstein Metric between Measures on Euclidean and Hilbert Spaces

For a separable metric space (X, d) L^p Wasserstein metrics between probability measures μ and v on X are defined by where the infimum is taken over all probability measures η on X × X with marginal distributions μ and v, respectively. After mentioning some basic properties of these metrics as well as explicit formulae for X = R a formula for the L² Wasserstein metric with X = Rⁿ will be cited from [5], [9], and [21] and proved for any two probability measures of a family of elliptically contoured distributions. Finally this result will be generalized for Gaussian measures to the case of a separable Hilbert space.     

An adaptive Lagrange‐Galerkin method for the shallow‐water equations on the sphere

The shallow‐water equations on the sphere are compressible Navier‐Stokes equations that describe hydrostatic atmospheric dynamics. An adaptive Lagrange‐Galerkin method is applied on the spherical domain to develop a simplified global atmospheric model. Computational results show the experimental convergence of this numerical method.