Dynamic Interactions in Synthetic Receptors: A Guest Exchange Saturation Transfer Study

The accumulated knowledge regarding molecular architectures is based on established, reliable, and accessible analytical tools that provide robust structural and functional information on assemblies. However, both the dynamicity and low population of noncovalently interacting moieties within studied molecular systems limit the efficiency and accuracy of traditional methods. Herein, the use of a saturation transfer-based NMR approach to study the dynamic binding characteristics of an anion to a series of synthetic receptors derived from bambusuril macrocycles is demonstrated. The exchange rates of BF₄⁻ are mediated by the side chains on the receptor (100 s⁻¹<k_ex<5000 s⁻¹), which play a critical role in receptor-anion binding dynamics. The signal amplification obtained with this approach allows for the identification of different types of intermolecular interactions between the receptor and the anion, something that could not have been detected by techniques hitherto used to study molecular assemblies. These findings, which are supported by a computational molecular dynamic study, demonstrate the uniqueness and added value of this NMR method.     

Analysis of spin states, spin barriers, and trans-effects involved in the coordination and stabilization of dinitrogen by biomimetic iron complexes

Coordination of dinitrogen to Sellmann-type iron (II) complexes in a sulfur-dominated coordination sphere, which emulates the environment of iron centers in the FeMo-cofactor of nitrogenase, is analyzed with respect to spin states, spin barriers, and the effect of trans-ligands. Such detailed investigations became only recently feasible when the reliability of density functional methods, which are the only quantum chemical methods capable of describing large transition metal complexes, could significantly be improved for the calculation of energies for states of different spin. It is found that the actual binding energy of dinitrogen is of sufficient magnitude for a reasonably strong fixation of N₂ by Sellmann-type coordination compounds. However, potential fixation is determined by additional factors which reduce the binding energy. One factor is the change in spin state of the N₂-free metal fragment, which lowers the total energy and quenches the thermodynamic stabilization effect of the binding energy. In addition, the metal fragment rearranges and gains even more stabilization energy for the un-coordinated state. Apart from these thermodynamical effects, the existence of spin barriers, which must be overcome upon binding of dinitrogen, leads to kinetical effects, which cannot be neglected.     

Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings

The density-matrix renormalization group algorithm has emerged as a promising new method in ab initio quantum chemistry. However, many problems still need to be solved before this method can be applied routinely. At the start of such a calculation, the orbitals originating from a preceding quantum chemical calculation must be placed in a specific order on a one-dimensional lattice. This ordering affects the convergence of the density-matrix renormalization group iterations significantly. In this paper, we present two approaches to obtain optimized orderings of the orbitals. First, we use a genetic algorithm to optimize the ordering with respect to a low total electronic energy obtained at a predefined stage of the density-matrix renormalization group algorithm with a given number of total states kept. In addition to that, we derive orderings from the one- and two-electron integrals of our test system. This test molecule is the chromium dimer, which is known to possess a complicated electronic structure. For this molecule, we have carried out calculations for the various orbital orderings obtained. The convergence behavior of the density-matrix renormalization group iterations is discussed in detail.     

Average peptide score: a useful parameter for identification of proteins derived from database searches of liquid chromatography/tandem mass spectrometry data

The quantity and variable quality of data that can be generated from liquid chromatography (LC)/mass spectrometry (MS)-based proteomics analyses creates many challenges in interpreting the spectra in terms of the actual proteins in a complex sample. In spite of improvements in algorithms that match putative peptide sequences to MS/MS spectra, the assembly of these lists of possible or probable peptides into a 'correct' set of proteins is still problematic. We have observed a trend in a simple relationship, derived from standard database search outputs, which can be useful in assessing the quality of a MS/MS-based protein identification. Specifically, the ratio of the protein score and number of non-redundant peptides, or average peptide score (APS), can facilitate initial filtering of database search results in addition to providing a useful measure of confidence for the proteins identified. This parameter has been applied to results from the analysis of multi-protein complexes derived from pull-down experiments analyzed using a two-dimensional LC/MS/MS workflow. In particular, the complex list of protein identifications derived from a drug affinity pull-down with immobilized ampicillin and an E. coli lysate was greatly simplified by applying the APS as a filter, allowing for facile identification of the penicillin-binding proteins known to interact with ampicillin. Furthermore, an APS threshold can be used for any data sets derived from electrospray ionization (ESI)- or matrix-assisted laser desorption/ionization (MALDI)-MS/MS experiments and is also not specific to any database search program.     

Ternäre Halogenide der Seltenen Erden vom Typ A2MX5 (A = K,In, NH4, Rb,Cs; X = Cl,Br, I)

Ternary Rare-Earth Halides of the A₂MX₅ Type (A = K, In, NH₄, Rb, Cs; X = Cl, Br, I) Ternary rare-earth (=M) chlorides, bromides, and iodides In₂MCl₅, (NH₄)₂MCl₅, Rb₂MCl₅, Cs₂MCl₅, CsRbMCl₅, K₂MBr₅, Rb₂MBr₅, K₂MI₅, and Rb₂MI₅ have been synthesized. Single crystals of In₂PrCl₅, Rb₂PrCl₅, K₂PrBr₅, and K₂PrI₅ were grown and the structures refined. The other halides were characterized by x-ray powder patterns. They are isotypic either with K₂PrCl₅(orthorhombic, Pnma, Z = 4, hexagonal arrangement of chains of edge-connected polyhedra [PrX₇]) or with Cs₂DyCl₅ (orthorhombic, Pbnm, Z = 4, hexagonal arrangement of cis-corner-connected octahedra [DyCl₆]) which may be discriminated in structure field diagrams. The thermal expansion was investigated für Cs₂LuCl₅ and Rb₂PrX₅ (X = Cl, Br, I).     

Temperature and pH Dependency of Copolymerization Parameters of Acrylic Acid and 2-Hydroxypropyl Acrylate

Summary: Since copolymerization parameters of acrylic acid (AA) and 2-hydroxypropyl acrylate (HPA) in aqueous solutions are scarcely investigated a new method and different experimental setups were developed to run copolymerization experiments at different temperatures and pH values. The experiments were done with UV- or azo- initiation and analyzed by residual monomer analytics with HPLC and GPC methods. Based on the data obtained the conversion and copolymerization parameters were calculated with different mathematical models.     

Nonlinear robust optimization via sequential convex bilevel programming

In this paper, we present a novel sequential convex bilevel programming algorithm for the numerical solution of structured nonlinear min–max problems which arise in the context of semi-infinite programming. Here, our main motivation are nonlinear inequality constrained robust optimization problems. In the first part of the paper, we propose a conservative approximation strategy for such nonlinear and non-convex robust optimization problems: under the assumption that an upper bound for the curvature of the inequality constraints with respect to the uncertainty is given, we show how to formulate a lower-level concave min–max problem which approximates the robust counterpart in a conservative way. This approximation turns out to be exact in some relevant special cases and can be proven to be less conservative than existing approximation techniques that are based on linearization with respect to the uncertainties. In the second part of the paper, we review existing theory on optimality conditions for nonlinear lower-level concave min–max problems which arise in the context of semi-infinite programming. Regarding the optimality conditions for the concave lower level maximization problems as a constraint of the upper level minimization problem, we end up with a structured mathematical program with complementarity constraints (MPCC). The special hierarchical structure of this MPCC can be exploited in a novel sequential convex bilevel programming algorithm. We discuss the surprisingly strong global and locally quadratic convergence properties of this method, which can in this form neither be obtained with existing SQP methods nor with interior point relaxation techniques for general MPCCs. Finally, we discuss the application fields and implementation details of the new method and demonstrate the performance with a numerical example.     

Hedging with temporary price impact

We consider the problem of hedging a European contingent claim in a Bachelier model with temporary price impact as proposed by Almgren and Chriss (J Risk 3:5–39, 2001). Following the approach of Rogers and Singh (Math Financ 20:597–615, 2010) and Naujokat and Westray (Math Financ Econ 4(4):299–335, 2011), the hedging problem can be regarded as a cost optimal tracking problem of the frictionless hedging strategy. We solve this problem explicitly for general predictable target hedging strategies. It turns out that, rather than towards the current target position, the optimal policy trades towards a weighted average of expected future target positions. This generalizes an observation of Gârleanu and Pedersen (Dynamic portfolio choice with frictions. Preprint, 2013b) from their homogenous Markovian optimal investment problem to a general hedging problem. Our findings complement a number of previous studies in the literature on optimal strategies in illiquid markets as, e.g., Gârleanu and Pedersen (Dynamic portfolio choice with frictions. Preprint, 2013b), Naujokat and Westray (Math Financ Econ 4(4):299–335, 2011), Rogers and Singh (Math Financ 20:597–615, 2010), Almgren and Li (Option hedging with smooth market impact. Preprint, 2015), Moreau et al. (Math Financ. doi: 10.1111/mafi.12098, 2015), Kallsen and Muhle-Karbe (High-resilience limits of block-shaped order books. Preprint, 2014), Guasoni and Weber (Mathematical Financ. doi: 10.1111/mafi.12099, 2015a; Nonlinear price impact and portfolio choice. Preprint, 2015b), where the frictionless hedging strategy is confined to diffusions. The consideration of general predictable reference strategies is made possible by the use of a convex analysis approach instead of the more common dynamic programming methods.