Molecular and Spectroscopic Characterization of Green and Red Cyanine Fluorophores from the Alexa Fluor and AF Series**

The use of fluorescence techniques has an enormous impact on various research fields including imaging, biochemical assays, DNA-sequencing and medical technologies. This has been facilitated by the development of numerous commercial dyes with optimized photophysical and chemical properties. Often, however, information about the chemical structures of dyes and the attached linkers used for bioconjugation remain a well-kept secret. This can lead to problems for research applications where knowledge of the dye structure is necessary to predict or understand (unwanted) dye-target interactions, or to establish structural models of the dye-target complex. Using a combination of optical spectroscopy, mass spectrometry, NMR spectroscopy and molecular dynamics simulations, we here investigate the molecular structures and spectroscopic properties of dyes from the Alexa Fluor (Alexa Fluor 555 and 647) and AF series (AF555, AF647, AFD647). Based on available data and published structures of the AF and Cy dyes, we propose a structure for Alexa Fluor 555 and refine that of AF555. We also resolve conflicting reports on the linker composition of Alexa Fluor 647 maleimide. We also conducted a comprehensive comparison between Alexa Fluor and AF dyes by continuous-wave absorption and emission spectroscopy, quantum yield determination, fluorescence lifetime and anisotropy spectroscopy of free and protein-attached dyes. All these data support the idea that Alexa Fluor and AF dyes have a cyanine core and are a derivative of Cy3 and Cy5. In addition, we compared Alexa Fluor 555 and Alexa Fluor 647 to their structural homologs AF555 and AF(D)647 in single-molecule FRET applications. Both pairs showed excellent performance in solution-based smFRET experiments using alternating laser excitation. Minor differences in apparent dye-protein interactions were investigated by molecular dynamics simulations. Our findings clearly demonstrate that the AF-fluorophores are an attractive alternative to Alexa- and Cy-dyes in smFRET studies or other fluorescence applications.     

Tight bounds on indefinite separable singly-constrained quadratic programs in linear-time

This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first-stage approximation is solved by a branch-and-bound algorithm with its nodes inheriting Benders’ cuts that are valid for their ancestor nodes. In addition, we develop two closely related convexification schemes which use multi-term disjunctive cuts to obtain approximations of the second-stage mixed-integer programs. We prove that the proposed methods are finitely convergent. One of the main advantages of our decomposition scheme is that we use a Benders-based branch-and-cut approach in which linear programming approximations are strengthened sequentially. Moreover as in many decomposition schemes, these subproblems can be solved in parallel. We also illustrate these algorithms using several variants of an SMIP example from the literature, as well as a new set of test problems, which we refer to as Stochastic Server Location and Sizing. Finally, we present our computational experience with previously known examples as well as the new collection of SMIP instances. Our experiments reveal that our algorithm is able to produce provably optimal solutions (within an hour of CPU time) even in instances for which a highly reliable commercial MIP solver is unable to provide an optimal solution within an hour of CPU time.     

Implementing bounds-based approximations in convex-concave two-stage stochastic programming

This paper is concerned with implementational issues and computational testing of bounds-based approximations for solving two-stage stochastic programs with fixed recourse. The implemented bounds are those derived by the authors previously, using first and cross moment information of the random parameters and a convex-concave saddle property of the recourse function. The paper first examines these bounds with regard to their tightness, monotonic behavior, convergence properties, and computationally exploitable decomposition structures. Subsequently, the bounds are implemented under various partitioning/refining strategies for the successive approximation. The detailed numerical experiments demonstrate the effectiveness in solving large scenario-based two-stage stochastic optimization problems throughsuccessive scenario clusters induced by refining the approximations.     

Thermal,Magnetic, Electronic,and Superconducting Properties of Rare‐Earth Metal Pentagermanides REGe5 (RE = La,Nd, Sm,Gd) and Synthesis of TbGe5

A series of isotypic rare‐earth metal pentagermanides including the new compound TbGe₅ were prepared by high‐pressure synthesis. They crystallize in the orthorhombic space group Immm [No. 71; a = 395.70(9) pm; b = 611.1(2) pm, and c = 983.6(3) pm for TbGe₅]. The crystal structure is isotypic to LaGe₅ and consists of puckered germanium slabs, which sandwich a second germanium species and the rare‐earth metal atoms. At ambient pressure, the thermal decomposition of the phases REGe₅ (RE = La, Nd, Sm, Gd, and Tb) proceeds via discrete intermediate steps into Ge(cF8) and thermodynamically stable germanium‐poorer phases. The investigated compounds REGe₅ are paramagnetic metallic conductors, which order antiferromagnetically at low temperatures. Specific heat measurements reveal that the superconducting state of LaGe₅ below T_c = 7.1(1) K is characterized by a critical field of μ₀H_c2 = 0.2 T and weak electron‐phonon coupling. Density‐functional based band‐structure calculations yield a very similar electronic structure for all the isotypic REGe₅ compounds. Besides a slight increase in the width of the valence band for smaller RE atoms, only minor differences are found for the two different germanium environments.     

Halogenomercury Salts of Sterically Crowded Triazenides – Convenient Starting Materials for Redox‐Transmetallation Reactions

Diaryl‐substituted triazenides Ar(Ar′)N₃HgX [Ar/Ar′ = Dmp/Mph, X = Cl ( 2a ), Br ( 3a ), I ( 4a ); Ar/Ar′ = Dmp/Tph, X = Cl ( 2b ), I ( 4b ) with Mph = 2‐MesC₆H₄, Mes = 2,4,6‐Me₃C₆H₂, Tph = 2′,4′,6′‐triisopropylbiphenyl‐2‐yl and Dmp = 2,6‐Mes₂C₆H₃] were synthesized by salt‐metathesis reactions in ethyl ether from the readily available starting materials Ar(Ar′)N₃Li and HgX₂. These compounds may be used for redox‐transmetallation reactions with rare‐earth or alkaline earth metals. Thus, reaction of 4b or 2b with magnesium or ytterbium in tetrahydrofuran afforded the triazenides Dmp(Tph)N₃MX(thf) ( 5b : M = Mg, X = I; 6b : M = Yb, X = Cl) in good yield. All new compounds were characterized by melting point, ¹H and ¹³C NMR spectroscopy and for selected species by IR spectroscopy or mass spectrometry. In addition, the solid‐state structures of triazenides 2a , 2b , 3a , 4b , 5b and 6b were investigated by single‐crystal X‐ray diffraction.     

Reaktionen des metalloiden Clusteranions {Ge9[Si(SiMe3)3]3}– in der Gasphase. Oxidations‐ und Reduktionsschritte geben Einblicke in den Bereich zwischen metalloiden Clustern und Zintl‐Ionen

The cluster anion {Ge₉[Si(SiMe₃)₃]₃}^– ( 1 ) is transferred intact into the gas phase via the electro spray method. Subsequently the fragmentation of 1 after resonant excitation as well as the oxidation reaction with O₂ and Cl₂ are investigated in an FT‐ICR mass spectrometer (Fourier Transform Ion Cyclotron Resonance). Unlike former results with off‐resonant excitation the fragmentation leads mainly to the end‐product Ge₉^–. Moreover, applying an on‐resonant excitation the dissociation experiment can be quantified; 2.0 ± 0.15 eV (193 ± 15kJ · mol^–1) for the elimination of the first two ligands and 2.7 ± 0.15 eV (261 ± 15 kJ · mol^–1) for all ligands, respectively. Particular attention is turned on the first step, where sterically encumbered Si₂(SiMe₃)₆ molecules are formed in a concerted reaction. This result, which is also important for elemental reactions on metal surfaces in catalyses, is based on experimentally determined threshold energies, DFT calculations and calculations on the lifetime of the involved species., In contrast to the high reactivity of crystalline 1 ·Li(THF)₄, gaseous 1 is inert against oxygen. The analogy to recently published spin forbidden reactions of Al₁₃^– with O₂ hints to a general importance of spin conversion during gas phase reactions of larger cluster molecules. The oxidation of 1 with Cl₂ proceeds through different reaction channels. DFT calculations give a first insight on the complex primary oxidation steps. These calculations also reveal that the delocalized bonding situation in the Ge₉ core is distorted upon oxidation. This result together with the dissociation experiments shed more light on differences and similarities between metalloid clusters and Zintl ions.     

Second-order scenario approximation and refinement in optimization under uncertainty

When solving scenario-based stochastic programming problems, it is imperative that the employed solution methodology be based on some form of problem decomposition: mathematical, stochastic, or scenario decomposition. In particular, the scenario decomposition resulting from scenario approximations has perhaps the least tendency to be computationally tedious due to increases in the number of scenarios. Scenario approximations discussed in this paper utilize the second-moment information of the given scenarios to iteratively construct a (relatively) small number of representative scenarios that are used to derive bounding approximations on the stochastic program. While the sizes of these approximations grow only linearly in the number of random parameters, their refinement is performed by exploiting the behavior of the value function in the most effective manner. The implementation SMART discussed here demonstrates the aptness of the scheme for solving two-stage stochastic programs described with a large number of scenarios.This paper was presented at the IFIP Workshop onStochastic Programming: Algorithms and Models, Lillehammer, Norway, January 1994.