Darboux Transformations of Bispectral Quantum Integrable Systems

We present an approach to higher-dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators. Specifically, working with the algebro-geometric definition of quantum integrability, we utilize the bispectral duality of quantum Hamiltonian systems to construct nontrivial Darboux transformations between completely integrable quantum systems. As an application, we are able to construct new quantum integrable systems as the Darboux transforms of trivial examples (such as symmetric products of one dimensional systems) or by Darboux transformation of well-known bispectral systems such as quantum Calogero–Moser.     

Natural-like Chalcones with Antitumor Activity on Human MG63 Osteosarcoma Cells

Osteosarcoma (OS) is a malignant disease characterized by poor prognosis due to a high incidence of metastasis and chemoresistance. Recently, Licochalcone A (Lic-A) has been reported as a promising agent against OS. Starting from chalcones selected from a wide in-house library, a new series was designed and synthetized. The antitumor activity of the compounds was tested on the MG63 OS cell line through the innovative Quantitative Phase Imaging technique and MTT assay. To further investigate the biological profile of active derivatives, cell cycle progression and apoptosis induction were evaluated. An earlier and more consistent arrest in the G2-M phase with respect to Lic-A was observed. Moreover, apoptosis was assessed by Annexin V staining as well as by the detection of typical morphological features of apoptotic cells. Among the selected compounds, 1e, 1q, and 1r proved to be the most promising antitumor molecules. This study pointed out that an integrated methodological approach may constitute a valuable platform for the rapid screening of large series of compounds.     

DNA Damage Clustering after Ionizing Radiation and Consequences in the Processing of Chromatin Breaks

Charged-particle radiotherapy (CPRT) utilizing low and high linear energy transfer (low-/high-LET) ionizing radiation (IR) is a promising cancer treatment modality having unique physical energy deposition properties. CPRT enables focused delivery of a desired dose to the tumor, thus achieving a better tumor control and reduced normal tissue toxicity. It increases the overall radiation tolerance and the chances of survival for the patient. Further improvements in CPRT are expected from a better understanding of the mechanisms governing the biological effects of IR and their dependence on LET. There is increasing evidence that high-LET IR induces more complex and even clustered DNA double-strand breaks (DSBs) that are extremely consequential to cellular homeostasis, and which represent a considerable threat to genomic integrity. However, from the perspective of cancer management, the same DSB characteristics underpin the expected therapeutic benefit and are central to the rationale guiding current efforts for increased implementation of heavy ions (HI) in radiotherapy. Here, we review the specific cellular DNA damage responses (DDR) elicited by high-LET IR and compare them to those of low-LET IR. We emphasize differences in the forms of DSBs induced and their impact on DDR. Moreover, we analyze how the distinct initial forms of DSBs modulate the interplay between DSB repair pathways through the activation of DNA end resection. We postulate that at complex DSBs and DSB clusters, increased DNA end resection orchestrates an increased engagement of resection-dependent repair pathways. Furthermore, we summarize evidence that after exposure to high-LET IR, error-prone processes outcompete high fidelity homologous recombination (HR) through mechanisms that remain to be elucidated. Finally, we review the high-LET dependence of specific DDR-related post-translational modifications and the induction of apoptosis in cancer cells. We believe that in-depth characterization of the biological effects that are specific to high-LET IR will help to establish predictive and prognostic signatures for use in future individualized therapeutic strategies, and will enhance the prospects for the development of effective countermeasures for improved radiation protection during space travel.     

Coupling of Gaussian Beam and Finite Difference Solvers for Semiclassical Schrödinger Equations

In the semiclassical regime, solutions to the time-dependent Schrödinger equation for molecular dynamics are highly oscillatory. The number of grid points required for resolving the oscillations may become very large even for simple model problems, making solution on a grid intractable. Asymptotic methods like Gaussian beams can resolve the oscillations with little effort and yield good approximations when the atomic nuclei are heavy and the potential is smooth. However, when the potential has variations on a small length-scale, quantum phenomena become important. Then asymptotic methods are less accurate. The two classes of methods perform well in different parameter regimes. This opens for hybrid methods, using Gaussian beams where we can and finite differences where we have to. We propose a new method for treating the coupling between the finite difference method and Gaussian beams. The new method reduces the needed amount of overlap regions considerably compared to previous methods, which improves the efficiency.     

Non-local Dirichlet forms generated by pseudodifferential operators on compact abelian groups

Let G_i, 1 ≤ i ≤ n, be compact abelian groups and let Γ_i , 1 ≤ i ≤ n, be countable dual groups. We consider G = G₁ ⊕ G₂ ⊕ … ⊕ G_n and Γ = Γ₁ ⊕ Γ₂ ⊕ … ⊕ Γ_n . For 1 ≤ j ≤ n, let a_j be a negative definite function on Γ_j and a (γ) = . For φ ∈ S (G), the set of all generalized trigonometrical polynomials on G, we define , where (γ) = a_j (γ_j) (γ), 1 ≤ j ≤ n. Then is a Dirichlet form with the domain on L² (G). (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Tool in Metabolism Research—Combination of OPLC On-Line Radioactivity Detection with HPLC—RD Technique

JPC – Journal of Planar Chromatography – Modern TLC - This paper reports a recently developed technique, coupling of optimum-performance laminar chromatography (OPLC) with online...     

The structure of human dermatan sulfate epimerase 1 emphasizes the importance of C5-epimerization of glucuronic acid in higher organisms

Dermatan sulfate epimerase 1 (DS-epi1, EC 5.1.3.19) catalyzes the conversion of d-glucuronic acid to l-iduronic acid on the polymer level, a key step in the biosynthesis of the glycosaminoglycan dermatan sulfate. Here, we present the first crystal structure of the catalytic domains of DS-epi1, solved at 2.4 Å resolution, as well as a model of the full-length luminal protein obtained by a combination of macromolecular crystallography and targeted cross-linking mass spectrometry. Based on docking studies and molecular dynamics simulations of the protein structure and a chondroitin substrate, we suggest a novel mechanism of DS-epi1, involving a His/double-Tyr motif. Our work uncovers detailed information about the domain architecture, active site, metal-coordinating center and pattern of N-glycosylation of the protein. Additionally, the structure of DS-epi1 reveals a high structural similarity to proteins from several families of bacterial polysaccharide lyases. DS-epi1 is of great importance in a range of diseases, and the structure provides a necessary starting point for design of active site inhibitors.     

Size Effects of the Anions in the Ionothermal Synthesis of Carbon Nitride Materials

Semiconducting carbon nitride polymers are used in metal-free photocatalysts and in opto-electronic devices. Conventionally, they are obtained using thermal and ionothermal syntheses in inscrutable, closed systems and therefore, their condensation behavior is poorly understood. Here, the synthetic protocols and properties are compared for two types of carbon nitride materials – 2D layered poly(triazine imide) (PTI) and hydrogen-bonded melem hydrate – obtained from three low-melting salt eutectics taken from the systematic series of the alkali metal halides: LiCl/KCl, LiBr/KBr, and LiI/KI. The size of the anion plays a significant role in the formation process of the condensed carbon nitride polymers, and it suggests a strong templating effect. The smaller anions (chloride and bromide) become incorporated into triazine (C₃N₃)-based PTI frameworks. The larger iodide does not stabilize the formation of a triazine-based polymer, but instead it leads to the formation of the heptazine (C₆N₇)-based hydrogen-bonded melem hydrate as the main crystalline phase. Melem hydrate, obtained as single-crystalline powders, was compared with PTI in photocatalytic hydrogen evolution from water and in an OLED device. Further, the emergence of each carbon nitride species from its corresponding salt eutectic was rationalized via density functional theory calculations. This study highlights the possibilities to further tailor the properties of eutectic salt melts for ionothermal synthesis of organic functional materials.