Seleno-Nucleobases and Their Water-Soluble Ruthenium-Arene Half-Sandwich Complexes: Chemistry and Biological Activity

Half-sandwich organometallic ruthenium complexes of seleno-nucleobases, 3 and 4, were synthesized and characterized. The structures of both complexes were determined by X-ray crystallography and are the first crystal structures of ruthenium complexes with seleno-nucleobases. Interestingly, 3 self-assembles aided by adventitious water in DMF to give a tetranuclear square 3a center dot 6H(2)O. Complex 4 is active against Jurkat and Molt-4 cell lines but inactive against the K562 cell line, whereas 3 is completely inactive against all three cell lines. The free ligand 6-selenopurine (1) and 6-selenoguanine (2) are highly active against these cell lines. Compound 2, like its thio analogue, is unstable under UVA light, whereas 4 is stable under similar conditions, which suggests that the ruthenium complex could reduce problems associated with the instability of the free ligand, 2, under irradiation.

Effect of metal oxidation state on FRET: a Cu(I) silent but selectively Cu(II) responsive fluorescent reporter and its bioimaging applications

Copper(II) and copper(I) complexes of a newly designed and crystallographically characterized Schiff base (HL) derived from rhodamine hydrazide and cinnamaldehyde were isolated in pure form formulated as Cu(L)(NO3)] (L-Cu) (1) and Cu(HL)(CH3CN)(H2O)]ClO4 (HL-Cu) (2), and characterized by physicochemical and spectroscopic tools. Interestingly, complex 1 but not 2 offers red fluorescence in solution state, and eventually HL behaves as a Cu(II) ions selective FRET based fluorosensor in HEPES buffer (1 mM, acetonitrile-water: 1/5, v/v) at 25 degrees C at biological pH with almost no interference of other competitive ions. The dependency of the FRET process on the +2 oxidation state of copper has been nicely supported by exhaustive experimental studies comprising electronic, fluorimetric, NMR titration, and theoretical calculations. The sensing ability of HL has been evaluated by the LOD value towards Cu(II) ions (83.7 nM) and short responsive time (5-10 s). Even the discrimination of copper(I) and copper(II) has also been done using only UV-Vis spectroscopic study. The efficacy of this bio-friendly probe has been determined by employing HL to detect the intercellular distribution of Cu(II) ions in HeLa cells by developing image under fluorescence microscope.

2-(Phenylazo)pyridineplatinum(II) Catecholates Showing Photocytotoxicity, Nuclear Uptake, and Glutathione-Triggered Ligand Release

Platinum(II) complexes Pt(pap)(an-cat)] (1) and Pt(pap)(py-cat)] (2) with 2-(phenylazo)pyridine (pap), 4-2-(anthracen-9-ylmethylene)amino]ethyl]benzene-1,2-diol (H(2)an-cat), and 4-2-(pyren-1-ylmethylene)amino]ethyl]benzene-1,2-diol (H2py-cat) were prepared, and their photoinduced cytotoxicity was studied. The complexes were found to release catecholate ligand in the presence of excess glutathione (GSH), resulting in cellular toxicity in the cancer cells. The catecholate complex Pt(pap)(cat)] (3) was prepared and used as a control. Complex 3, which is structurally characterized by X-ray crystallography, has platinum(II) in a distorted square-planar geometry. The complexes are redox-active, showing responses near 0.6 and 1.0 V versus SCE in N,N-dimethylformamide/0.1 M tetrabutylammonium perchlorate corresponding to a two-step catechol oxidation process and at -0.3 and -1.3 V for reduction of the pap ligand. Complex 1 showed remarkable light-induced cytotoxicity in HaCaT (human skin keratinocytes) and MCF-7 (human breast cancer) cells, giving IC50 value of similar to 5 mu M in visible light of 400-700 nm and >40 mu M in the dark. The 2',7'-dichlorofluorescein diacetate (DCFDA) assay showed the generation of reactive oxygen species (ROS), which seems to trigger apoptosis, as is evident from the annexin V-fluorescein isothiocyanate (FITC)/propidium iodide (PI) assay. The fluorescence microscopic images showed significant nuclear localization of the complexes and free ligands. A mechanistic study revealed possible reduction of the coordinated azo bond of pap by cellular GSH, releasing the catecholate ligand and resulting in remarkable photochemotherapeutic action of the complexes.

Synthesis, crystal structure and spectroscopic and electrochemical properties of bridged trisbenzoato copper-zinc heterobinuclear complex of 2,2 `-bipyridine

The synthesis of the heterobinuclear copper-zinc complex CuZn(bz)(3)(bpy)(2)]ClO4 (bz = benzoate) from benzoic acid and bipyridine is described. Single crystal X-ray diffraction studies of the heterobinuclear complex reveals the geometry of the benzoato bridged Cu(II)-Zn(II) centre. The copper or zinc atom is pentacoordinate, with two oxygen atoms from bridging benzoato groups and two nitrogen atoms from one bipyridine forming an approximate plane and a bridging oxygen atom from a monodentate benzoate group. The Cu-Zn distance is 3.345 angstrom. The complex is normal paramagnetic having mu(eff) value equal to 1.75 BM, ruling out the possibility of Cu-Cu interaction in the structural unit. The ESR spectrum of the complex in CH3CN at RT exhibit an isotropic four line spectrum centred at g = 2.142 and hyperfine coupling constants A(av) = 63 x 10(-4) cm(-1), characteristic of a mononuclear square-pyramidal copper(II) complexes. At LNT, the complex shows an isotropic spectrum with g(parallel to) = 2.254 and g(perpendicular to) =2.071 and A(parallel to) = 160 x 10(-4) cm(-1). The Hamiltonian parameters are characteristic of distorted square pyramidal geometry. Cyclic voltammetric studies of the complex have indicated quasi-reversible behaviour in acetonitrile solution. (C) 2014 Elsevier B.V. All rights reserved.

The beta hairpin structure within ribosomal protein S5 mediates interplay between domains II and IV and regulates HCV IRES function

Translation initiation in Hepatitis C Virus (HCV) is mediated by Internal Ribosome Entry Site (IRES), which is independent of cap-structure and uses a limited number of canonical initiation factors. During translation initiation IRES-40S complex formation depends on high affinity interaction of IRES with ribosomal proteins. Earlier, it has been shown that ribosomal protein S5 (RPS5) interacts with HCV IRES. Here, we have extensively characterized the HCV IRES-RPS5 interaction and demonstrated its role in IRES function. Computational modelling and RNA-protein interaction studies demonstrated that the beta hairpin structure within RPS5 is critically required for the binding with domains II and IV. Mutations disrupting IRES-RPS5 interaction drastically reduced the 80S complex formation and the corresponding IRES activity. Computational analysis and UV cross-linking experiments using various IRES-mutants revealed interplay between domains II and IV mediated by RPS5. In addition, present study demonstrated that RPS5 interaction is unique to HCV IRES and is not involved in 40S-3 ` UTR interaction. Further, partial silencing of RPS5 resulted in preferential inhibition of HCV RNA translation. However, global translation was marginally affected by partial silencing of RPS5. Taken together, results provide novel molecular insights into IRES-RPS5 interaction and unravel its functional significance in mediating internal initiation of translation.

BODIPY appended copper(II) complexes of curcumin showing mitochondria targeted remarkable photocytotoxicity in visible light

Copper(II) complexes of BODIPY (borondipyrromethene) derivatives (L-1, L-2) and curcumin (Hcur), viz. Cu(L-1)(cur)]Cl (1) and Cu(L-2)(cur)]Cl (2), where L-1 and L-2 are the non-iodinated and diiodinated BODIPY appended dipicolylamine ligands, are prepared and characterized and their photocytotoxic activity in visible light studied. Binding to copper(II) has rendered stability to curcumin from its hydrolytic degradation in buffer medium. The complexes show mitochondrial localization in HeLa cells emphasizing the findings that both 1 and 2 are mitochondria-targeting complexes and induce cancer cell death. Complex 1 with a fluorophoric BODIPY moiety in L-1 gave IC50 values of 7.9(+/- 0.3) mu M in visible light (400-700 nm) and 29.1(+/- 0.5) mu M in the dark. Complex 2 having a diiodo BODIPY moiety in L-2 as a photosensitizer gave IC50 values of 3.8(+/- 0.2) mu M in visible light and 32.1(+/- 0.4) mu M in the dark. The PDT effect of 2 is comparable to that of Photofrin (R), an FDA approved PDT drug. Cell death follows an apoptotic pathway with the formation of reactive oxygen species (ROS).

Polypyridyl iron(II) complexes showing remarkable photocytotoxicity in visible light

Iron(II) complexes of polypyridyl ligands (B), viz. Fe(B)(2)]Cl-2 (1 and 2) of N, N, N-donor 2-(2-pyridyl)-1,10-phenanthroline (pyphen in 1) and 3-(pyridin-2-yl)dipyrido3,2-a:2',3'-c]phenazine (pydppz in 2), are prepared and characterized. They are 1:2 electrolytes in aqueous DMF. The diamagnetic complexes exhibit metal to ligand charge transfer band near 570 nm in DMF. The complexes are avid binders to calf thymus DNA giving binding constant (K (b)) values of similar to 10(6) M-1 suggesting significant intercalative DNA binding of the complexes due to presence of planar phenanthroline bases. Complex 2 exhibits significant photocytotoxicity in immortalized human keratinocyte cells HaCaT and breast cancer cell line MCF-7 giving IC50 values of 0.08 and 13 mu M in visible light (400-700 nm). Complex 2 shows only minor dark toxicity in HaCaT cells but is non-toxic in dark in MCF-7 cancer cells. The light-induced cellular damage follows apoptotic pathway on generation of reactive oxygen species as evidenced from the dichlorofluorescein diacetate (DCFDA) assay.

Photocytotoxic ternary copper(II) complexes of histamine Schiff base and pyridyl ligands

Ternary copper(Il) complexes of salicylaldehyde-histamine Schiff base (HL) and pyridyl ligands, viz. Cu(bpy)(L)](ClO4) (1) and Cu(dppz)(L)](C104) (2), where bpy is 2,2'-bipyridine (in 1) and dppz is dipyrido3,2-a:2',3'-c]phenazine (in 2), were synthesized, characterized and their DNA binding, photo-activated DNA cleavage activity and photocytotoxicity studied. The 1:1 electrolytic one-electron paramagnetic complexes showed a d-d band near 670 nm in aqueous DMF (1:1 v/v). The crystal structure of complex 1 showed the metal in CuN4O distorted square-pyramidal geometry. Complex 2 intercalatively binds to calf-thymus (ct) DNA with a binding constant (K-b) of similar to 10(5) M-1. It exhibited moderate chemical nuclease activity but excellent DNA photocleavage activity in red light of 647 nm forming (OH)-O-center dot radicals. It showed remarkable photocytotoxicity in human cervical cancer cells (HeLa) giving IC50 of 1.6 mu M in visible light (400-700 nm) with low dark toxicity. The photo-induced cell death is via generation of oxidative stress by reactive oxygen species.

Remarkable photo-induced anticancer activity of vitamin-S6 Schiff base copper(II) complexes of pyridyl bases

Vitamin-B6 (VB6) Schiff base (H2L) copper(II) complexes of pyridyl bases, viz. Cu(bpy)(L)] (1), Cu(phen)(L)] (2) and Cu(dppz)(L)] (3), where bpy is 2,2'-bipyridine, phen is 1,10-phenanthroline and dppz is dipyrido3,2-a:2',3'c]phenazine are synthesized, characterized and their phto-induced anticancer activity studied. The non-electrolytic one electron paramagnetic complexes exhibit a d-d band near 700 nm in DMF. The dppz complex intercalatively binds to calf-thymus DNA with binding constant (K-b) values of similar to 10(6) M-1. This complex exhibits low chemical nuclease activity but excellent DNA photocleavage activity when irradiated with red light of 705 nm forming (OH)-O-center dot radical. It displays remarkable photocytotoxicity in human cervical cancer cells (HeLa) giving IC50 value of 0.9 mu M in visible light (400-700 nm) while being less toxic in darkness (IC50 : 23 mu M). The cellular uptake of the complexes seems to be via VB6 transporting membrane carrier mediated diffusion pathway. Photo-induced cell death follows apoptotic pathway involving photo-generated intracellular reactive oxygen species.

Inlet stability and case histories, Part II

Inlets which require frequent channel dredging due to gradual shoaling, exhibit migration, or shoal up during storms, are in general unstable and pose a problem to the engineer. This problem of inlet stability is a complex one, because of the rather large number of variables that go into defining stability. The reference here is to inlets on sandy coasts only, because the absence of sand or similar sedimentary material the problem does not arise. Shell is also found in varying proportions with sand. Some of this is. new, whereas in some areas it is ancient reworked material whose size distribution is close to that of the sand with which it is associated. (PDF has 24 pages.)

Observations of deep coral and sponge assemblages in Olympic Coast National Marine Sanctuary, Washington. Cruise Report: NOAA Ship McArthur II Cruise AR06-07/07

From May 22 to June 4, 2006, NOAA scientists led a research cruise using the ROPOS Remotely Operated Vehicle (ROV) to conduct a series of dives at targeted sites in the Olympic Coast National Marine Sanctuary (OCNMS) with the goal of documenting deep coral and sponge communities. Dive sites were selected from areas for which OCNMS had side scan sonar data indicating the presence of hard or complex substrate. The team completed 11 dives in sanctuary waters ranging from six to 52 hours in length, at depths ranging from 100 to 650 meters. Transect surveys were completed at 15 pre-selected sites, with additional observations made at five other sites. The survey locations included sites both inside and outside the Essential Fish Habitat (EFH) Conservation Area, known as Olympic 2, established by the Pacific Fishery Management Council, enacted on June 12, 2006. Bottom trawling is prohibited in the Olympic 2 Conservation Area for nontribal fishermen. The Conservation Area covers 159.4 square nautical miles or about 15 percent of the sanctuary. Several species of corals and sponges were documented at 14 of the 15 sites surveyed, at sites both inside and outside the Conservation Area, including numerous gorgonians and the stony corals Lophelia pertusa and Desmophyllum dianthus, as well as small patches of the reef building sponge Farrea occa. The team also documented Lophelia sp. and Desmophyllum sp. coral rubble, dead gorgonians, lost fishing gear, and other anthropogenic debris, supporting concerns over potential risks of environmental disturbances to coral health. (PDF contains 60 pages.)

Brain type II calcium and calmodulin-dependent protein kinase: characterization of a brain-region specific isozyme and regulation by autophosphorylation

A variety of molecular approaches have been used to investigate the structural and enzymatic properties of rat brain type ll Ca^(2+) and calmodulin-dependent protein kinase (type ll CaM kinase). This thesis describes the isolation and biochemical characterization of a brain-region specific isozyme of the kinase and also the regulation the kinase activity by autophosphorylation.

The cerebellar isozyme of the type ll CaM kinase was purified and its biochemical properties were compared to the forebrain isozyme. The cerebellar isozyme is a large (500-kDa) multimeric enzyme composed of multiple copies of 50-kDa α subunits and 60/58-kDa β/β’ subunits. The holoenzyme contains approximately 2 α subunits and 8 β subunits. This contrasts to the forebrain isozyme, which is also composed of and β/β'subunits, but they are assembled into a holoenzyme of approximately 9 α subunits and 3 β/β ' subunits. The biochemical and enzymatic properties of the two isozymes are similar. The two isozymes differ in their association with subcellular structures. Approximately 85% of the cerebellar isozyme, but only 50% of the forebrain isozyme, remains associated with the particulate fraction after homogenization under standard conditions. Postsynaptic densities purified from forebrain contain the forebrain isozyme, and the kinase subunits make up about 16% of their total protein. Postsynaptic densities purified from cerebellum contain the cerebellar isozyme, but the kinase subunits make up only 1-2% of their total protein.

The enzymatic activity of both isozymes of the type II CaM kinase is regulated by autophosphorylation in a complex manner. The kinase is initially completely dependent on Ca^(2+)/calmodulin for phosphorylation of exogenous substrates as well as for autophosphorylation. Kinase activity becomes partially Ca^(2+) independent after autophosphorylation in the presence of Ca^(2+)/calmodulin. Phosphorylation of only a few subunits in the dodecameric holoenzyme is sufficient to cause this change, suggesting an allosteric interaction between subunits. At the same time, autophosphorylation itself becomes independent of Ca^(2+) These observations suggest that the kinase may be able to exist in at least two stable states, which differ in their requirements for Ca^(2+)/calmodulin.

The autophosphorylation sites that are involved in the regulation of kinase activity have been identified within the primary structure of the α and β subunits. We used the method of reverse phase-HPLC tryptic phosphopeptide mapping to isolate individual phosphorylation sites. The phosphopeptides were then sequenced by gas phase microsequencing. Phosphorylation of a single homologous threonine residue in the α and β subunits is correlated with the production of the Ca^(2+) -independent activity state of the kinase. In addition we have identified several sites that are phosphorylated only during autophosphorylation in the absence of Ca^(2+)/ calmodulin.

The electrocatalytic and stoichiometric oxidation chemistry of binuclear ruthenium complexes incorporating the anionic tripod ligand {(η5-C5H5)Co[P(OCH3)2(=O)]3}-

The anionic tripod ligand NaLoMe (L_(oMe) - = [(η^5-C_5H_5)Co{P(O)(OCH_3)_2}_3]^-) reacts with RuO_4 in a biphasic reaction mixture of 1% H_2SO_4 and CCI_4 to afford [(L_(oMe) (HO)Ru^(IV) (µ-O)_2Ru ^(IV)(OH)(L_(oMe)] (1), which is treated with aqueous CF_3S0_3H to generate [(L_(oMe)(H_2O)Ru^(IV) (µ-O)_2R^(IV) (OH_2)(L_(oMe)][CF_3SO_3]_2 ([H_21][CF_3SO_3]_2). Addition of iodosobenzene to an acetonitrile solution of this salt yields [(L_(oMe)(O)Ru^v(µ-0)2Ru^v-(O)(_(LoMe)] (2). The dimer 1 can be reduced chemically or electrochemically to the Ru^(III)- Ru^(III) dimers [(L_(oMe)(H_20)Ru^(III) (µ-OH)_2Ru^(III) (OH_2)(L_(oMe)) ]^2+ and [(L_(oMe)) ^(III) (µ-0Hh(µ-0H2)Ru^(III) (L_(oMe)]^2+ which interconvert in aqueous media. Two electron processes dominate both the bulk chemistry and the electrochemistry of 1. Among these processes are the quasi-reversible Ru^(IV) - Ru^(IV)/Ru^(III)- Ru^(III) and Ru^(III)- Ru^(III)/ Ru^(II)- Ru^(II) reductions and a largely irreversible Ru^(V) - Ru^(V)/ Ru^(IV) - Ru^(IV)/oxidation. The dioxo dimer 2 oxidizes alcohols and aldehydes in organic media to afford 1 and the corresponding aldehydes and acids. Analogously, the Ru^(V) - Ru^(V)/ Ru^(IV)- Ru^(IV) redox wave mediates the electrooxidation of alcohols and aldehydes in aqueous buffer. In this system, substrates can be oxidized completely to CO_2. The kinetic behavior of these oxidations was examined by UV-vis and chronoamperometry, respectively, and the chemistry is typical of metal-oxo complexes, indicating that electronic coupling between two metal centers does not dramatically affect the metal-oxo chemistry. Dimer [H_21]^(2+) also reacts with alcohols, aldehydes, and triphenylphosphine in CH_3CN to afford Ru^(III)- Ru^(III) products including [(L_(oMe))CH_3CN) Ru^(III) (µ-OH)_2 Ru^(III) (NCCH_3)( L_(oMe))][CF_3SO_3]2 (characterized by X-ray crystallography) and the corresponding organic products. Reaction of 1 with formaldehyde in aqueous buffer quantitatively affords the triply bridged dimer [(L_(oMe)Ru^(III) (µ-OH)2- (µ-HCOO) Ru^(III) (L_(oMe)][CF_3SO_3] (characterized by X-ray crystallography). This reaction evidently proceeds by two parallel inner-sphere pathways, one of which is autocatalytic. Neither pathway exhibits a primary isotope effect suggesting the rate determining process could be the formation of an intermediate, perhaps a Ru^(IV) - Ru^(IV) formate adduct. The Ru^(III)- Ru^(III)formate adduct is easily oxidized to the Ru^(IV) - Ru^(IV) analog [(L_(oMe)Ru^(IV)(µ-OH)_2-(µ-HCOO) Ru^(IV) (L_(oMe)][CF_3SO_3], which, after isolation, reacts slowly with aqueous formaldehyde to generate free formate and the Ru^(III)- Ru^(III) formate adduct. These dimers function as catalysts for the electrooxidation of formaldehyde at low anodic potentials (+0.0 V versus SCE in aqueous buffer, pH 8.5) and enhance the activity of Nafion treated palladium/carbon heterogeneous fuel cell catalysts.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Catalytic conversion of nitrogen to ammonia by an iron model complex

Threefold symmetric Fe phosphine complexes have been used to model the structural and functional aspects of biological N₂ fixation by nitrogenases. Low-valent bridging Fe-S-Fe complexes in the formal oxidation states Fe(II)Fe(II), Fe(II)/Fe(I), and Fe(I)/Fe(I) have been synthesized which display rich spectroscopic and magnetic behavior. A series of cationic tris-phosphine borane (TPB) ligated Fe complexes have been synthesized and been shown to bind a variety of nitrogenous ligands including N₂H₄, NH₃, and NH₂-. These complexes are all high spin S = 3/2 and display EPR and magnetic characteristics typical of this spin state. Furthermore, a sequential protonation and reduction sequence of a terminal amide results in loss of NH₃ and uptake of N₂. These stoichiometric transformations represent the final steps in potential N₂ fixation schemes.

Treatment of an anionic FeN₂ complex with excess acid also results in the formation of some NH₃, suggesting the possibility of a catalytic cycle for the conversion of N₂ to NH₃ mediated by Fe. Indeed, use of excess acid and reductant results in the formation of seven equivalents of NH₃ per Fe center, demonstrating Fe mediated catalytic N₂ fixation with acids and protons for the first time. Numerous control experiments indicate that this catalysis is likely being mediated by a molecular species.

A number of other phosphine ligated Fe complexes have also been tested for catalysis and suggest that a hemi-labile Fe-B interaction may be critical for catalysis. Additionally, various conditions for the catalysis have been investigated. These studies further support the assignment of a molecular species and delineate some of the conditions required for catalysis.

Finally, combined spectroscopic studies have been performed on a putative intermediate for catalysis. These studies converge on an assignment of this new species as a hydrazido(2-) complex. Such species have been known on group 6 metals for some time, but this represents the first characterization of this ligand on Fe. Further spectroscopic studies suggest that this species is present in catalytic mixtures, which suggests that the first steps of a distal mechanism for N₂ fixation are feasible in this system.