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.

Multiplexed DNA-mediated electrochemistry

The aromatic core of double helical DNA possesses the unique and remarkable ability to form a conduit for electrons to travel over exceptionally long molecular distances. This core of π-stacked nucleobases creates an efficient pathway for charge transfer to proceed that is exquisitely sensitive to even subtle perturbations. Ground state electrochemistry of DNA-modified electrodes has been one of the major techniques used both to investigate and to harness the property of DNA-mediated charge transfer. DNA-modified electrodes have been an essential tool for both gaining insights into the fundamental properties of DNA and, due to the exquisite specificity of DNA-mediated charge transfer for the integrity of the π-stack, for use in next generation diagnostic sensing. Here, multiplexed DNA-modified electrodes are used to (i) gain new insights on the electrochemical coupling of metalloproteins to the DNA π-stack with relevance to the fundaments of in vivo DNA-mediated charge transfer and (ii) enhance the overall sensitivity of DNA-mediated reduction for use in the detection of low abundance diagnostic targets.

First, Methylene Blue (MB′) was covalently attached to DNA through a flexible C12 alkyl linker to yield a new redox reporter for DNA electrochemistry measurements with enhanced sensitivity. Tethered, intercalated MB′ was reduced through DNA-mediated charge transport. The redox signal intensity for MB′-dT-C12-DNA was found to be at least 3 fold larger than that of previously used Nile Blue (NB)-dT-DNA, which is coupled to the base stack via direct conjugation. The signal attenuation, due to an intervening mismatch, and therefore the degree of DNA-mediated reduction, does, however, depend on the DNA film morphology and the backfilling agent used to passivate the surface. These results highlight two possible mechanisms for the reduction of MB′ on the DNA-modified electrode that are distinguishable by their kinetics: reduction mediated by the DNA base pair stack and direct surface reduction of MB′ at the electrode. The extent of direct reduction at the surface can be minimized by overall DNA assembly conditions.

Next, a series of intercalation-based DNA-mediated electrochemical reporters were developed, using a flexible alkane linkage to validate and explore their DNA-mediated reduction. The general mechanism for the reduction of distally bound redox active species, covalently tethered to DNA through flexible alkyl linkages, was established to be an intraduplex DNA-mediated pathway. MB, NB, and anthraquinone were covalently tethered to DNA with three different covalent linkages. The extent of electronic coupling of the reporter was shown to correlate with the DNA binding affinity of the redox active species, supporting an intercalative mechanism. These electrochemical signals were shown to be exceptionally sensitive to a single intervening π-stack perturbation, an AC mismatch, in a densely packed DNA monolayer, which further supports that the reduction is DNA-mediated. Finally, this DNA-mediated reduction of MB occurs primarily via intra- rather than inter duplex intercalation, as probed through varying the proximity and integrity of the neighboring duplex DNA. Further gains to electrochemical sensitivity of our DNA-modified devices were then achieved through the application of electrocatalytic signal amplification using these solvent accessible intercalative reporters, MB-dT-C8, and hemoglobin as a novel electron sink. Electrocatalysis offers an excellent means of electrochemical signal amplification, yet in DNA based sensors, its application has been limited due to strict assembly conditions. We describe the use of hemoglobin as a robust and effective electron sink for electrocatalysis in DNA sensing on low density DNA films. Protein shielding of the heme redox center minimizes direct reduction at the electrode surface and permits assays on low density DNA films. Electrocatalysis of MB that is covalently tethered to the DNA by a flexible alkyl linkage allows for efficient interactions with both the base stack and hemoglobin. Consistent suppression of the redox signal upon incorporation of single CA mismatch in the DNA oligomer demonstrates that both the unamplified and the electrocatalytically amplified redox signals are generated through DNA-mediated charge transport. Electrocatalysis with hemoglobin is robust: it is stable to pH and temperature variations. The utility and applicability of electrocatalysis with hemoglobin is demonstrated through restriction enzyme detection, and an enhancement in sensitivity permits femtomole DNA sampling.

Finally, we expanded the application of our multiplexed DNA-modified electrodes to the electrochemical characterization of DNA-bound proteins containing [4Fe-4S] clusters. DNA-modified electrodes have become an essential tool for the characterization of the redox chemistry of DNA repair proteins that contain redox cofactors. Multiplexed analysis of EndonucleaseIII (EndoIII), a DNA repair protein containing a [4Fe-4S] cluster known to be accessible via DNA-mediated charge transport, elucidated subtle differences in the electrochemical behavior as a function of DNA morphology. DNA-bound EndoIII is seen to have two different electron transfer pathways for reduction, either through the DNA base stack or through direct surface reduction. Closely packed DNA films, where the protein has limited surface accessibility, produce electrochemical signals reflecting electron transfer that is DNA-mediated. The electrochemical comparison of EndoIII mutants, including a new family of mutations altering the electrostatics surrounding the [4Fe-4S] cluster, was able to be quantitatively performed. While little change in the midpoint potential was found for this family of mutants, significant variations in the efficiency of DNA-mediated electron transfer were apparent. Based on the stability of these proteins, examined by circular dichroism, we propose that the electron transfer pathway can be perturbed not only by the removal of aromatic residues, but also through changes in solvation near the cluster.

Experiments with a laser interferometric gravitational wave antenna

Sources and effects of astrophysical gravitational radiation are explained briefly to motivate discussion of the Caltech 40 meter antenna, which employs laser interferometry to monitor proper distances between inertial test masses. Practical considerations in construction of the apparatus are described. Redesign of test mass systems has resulted in a reduction of noise from internal mass vibrations by up to two orders of magnitude at some frequencies. A laser frequency stabilization system was developed which corrects the frequency of an argon ion laser to a residual fluctuation level bounded by the spectral density √s_v(f) ≤ 60µHz/√Hz, at fluctuation frequencies near 1.2 kHz. These and other improvements have contributed to reducing the spectral density of equivalent gravitational wave strain noise to √s_h(f)≈10^(-19)/√ Hz at these frequencies.

Finally, observations made with the antenna in February and March of 1987 are described. Kilohertz-band gravitational waves produced by the remnant of the recent supernova are shown to be theoretically unlikely at the strength required for confident detection in this antenna (then operating at poorer sensitivity than that quoted above). A search for periodic waves in the recorded data, comprising Fourier analysis of four 105-second samples of the antenna strain signal, was used to place new upper limits on periodic gravitational radiation at frequencies between 305 Hz and 5 kHz. In particular, continuous waves of any polarization are ruled out above strain amplitudes of 1.2 x 10^(-18) R.M.S. for waves emanating from the direction of the supernova, and 6.2 x 10^(-19) R.M.S. for waves emanating from the galactic center, between 1.5 and 4 kilohertz. Between 305 Hz and 5kHz no strains greater than 1.2 x 10^(-17) R.M.S. were detected from either direction. Limitations of the analysis and potential improvements are discussed, as are prospects for future searches.

Zirconocenes as models for homogeneous Ziegler-Natta olefin polymerization catalysts

Using density functional theory, we studied the fundamental steps of olefin polymerization for zwitterionic and cationic Group IV ansa-zirconocenes and a neutral ansa- yttrocene. Complexes [H₂E(C₅H₄)₂ZrMe]ⁿ (n = 0: E = BH₂ (1), BF₂ (2), AlH₂(3); n = +: E = CH₂(4), SiH₂(5)) and H₂Si(C₅H₄)₂YMe were used as computational models. The largest differences among these three classes of compounds were the strength of olefin binding and the stability of the β-agostic alkyl intermediate towards β-hydrogen elimination. We investigated the effect of solvent on the reaction energetics for land 5. We found that in benzene the energetics became very similar except that a higher olefin insertion barrier was calculated for 1. The calculated anion affinity of [CH₃BF₃]^- was weaker towards 1 than 5. The calculated olefin binding depended primarily on the charge of the ansa linker, and the olefin insertion barrier was found to decrease steadily in the following order: [H₂C(C₅H₄)₂ZrMe]⁺ > [F₂B(C₅H₄)₂ZrMe] ≈ [H₂B(C₅H₄)₂ZrMe] > [H₂Si(C₅H₄)₂ZrMe]⁺ > [H₂Al(C₅H₄)₂ZrMe].

We prepared ansa-zirconocene dicarbonyl complexes Me₂ECp₂Zr(CO)₂ (E = Si, C), and t-butyl substituted complexes (t-BuCp)₂Zr(CO)₂, Me₂E(t-BuCp)₂Zr(CO)₂ (E = Si, C), (Me₂Si)₂(t-BuCp)₂Zr(CO)₂ as well as analogous zirconocene complexes. Both the reduction potentials and carbonyl stretching frequencies follow the same order: Me₂SiCp₂ZrCl₂> Me₂CCp₂ZrCl₂> Cp₂ZrCl₂> (Me₂Si)₂Cp₂ZrCl₂. This ordering is a result of both the donating abilities of the cyclopentadienyl substituents and the orientation of the cyclopentadiene rings. Additionally, we prepared a series of analogous cationic zirconocene complexes [LZrOCMe₃][MeB(C₆F₅)₃] (L = CP₂, Me₂SiCp₂, Me₂CCP₂, (Me₂Si)₂Cp₂) and studied the kinetics of anion dissociation. We found that the enthalpy of anion dissociation increased from 10.3 kcal•mol^-1 to 17.6 kcal•mol^-1 as exposure of the zirconium center increased.

We also prepared series of zirconocene complexes bearing 2,2-dimethyl-2-sila-4-pentenyl substituents (and methyl-substituted olefin variants). Methide abstraction with B(C₆F₅) results in reversible coordination of the tethered olefin to the cationic zirconium center. The kinetics of olefin dissociation have been examined using NMR methods, and the effects of ligand variation for unlinked, singly [SiMe₂]-linked and doubly [SiMe₂]-linked bis(cyclopentadienyl) arrangements has been compared (ΔG‡ for olefin dissociation varies from 12.8 to 15.6 kcal•mol^-1). Methide abstraction from 1,2-(SiMe₂)₂(η⁵-C₅H₃)₂Zr(CH₃)-(CH₂CMe₂CH₂CH = CH₂) results in rapid β-allyl elimination with loss of isobutene yielding the allyl cation [{1,2-(SiMe₂)₂(η⁵-C₅H₃)₂Zr(η³-CH₂CH=CH₂)]⁺.

Succinate:ubiquinone oxidoreductase from Paracoccus denitrificans and particulate methane monooxygenase from Methylococcus capsulatus (Bath): experimental and theoretical EPR studies of the metal cofactors

This thesis summarizes the application of conventional and modern electron paramagnetic resonance (EPR) techniques to establish proximity relationships between paramagnetic metal centers in metalloproteins and between metal centers and magnetic ligand nuclei in two important and timely membrane proteins: succinate:ubiquinone oxidoreductase (SQR) from Paracoccus denitrificans and particulate methane monooxygenase (pMMO) from Methylococcus capsulatus. Such proximity relationships are thought to be critical to the biological function and the associated biochemistry mediated by the metal centers in these proteins. A mechanistic understanding of biological function relies heavily on structure-function relationships and the knowledge of how molecular structure and electronic properties of the metal centers influence the reactivity in metalloenzymes. EPR spectroscopy has proven to be one of the most powerful techniques towards obtaining information about interactions between metal centers as well as defining ligand structures. SQR is an electron transport enzyme wherein the substrates, organic and metallic cofactors are held relatively far apart. Here, the proximity relationships of the metallic cofactors were studied through their weak spin-spin interactions by means of EPR power saturation and electron spin-lattice (T_1) measurements, when the enzyme was poised at designated reduction levels. Analysis of the electron T_1 measurements for the S-3 center when the b-heme is paramagnetic led to a detailed analysis of the dipolar interactions and distance determination between two interacting metal centers. Studies of ligand environment of the metal centers by electron spin echo envelope modulation (ESEEM) spectroscopy resulted in the identication of peptide nitrogens as coupled nuclei in the environment of the S-1 and S-3 centers.

Finally, an EPR model was developed to describe the ferromagnetically coupled trinuclear copper clusters in pMMO when the enzyme is oxidized. The Cu(II) ions in these clusters appear to be strongly exchange coupled, and the EPR is consistent with equilateral triangular arrangements of type 2 copper ions. These results offer the first glimpse of the magneto-structural correlations for a trinuclear copper cluster of this type, which, until the work on pMMO, has had no precedent in the metalloprotein literature. Such trinuclear copper clusters are even rare in synthetic models.

The application of trimethylsilyl diazomethane to the synthesis of optically active pyrazolines and related studies

The 1,3-dipolar cycloadditions of trimethylsilyl diazomethane with camphorsultam-derived acrylates are reported as a means for the efficient synthesis of optically active pyrazolines. Trimethylsilyl diazomethane is a safe, commercially available diazoalkane which provides Δ¹-pyrazolines 1n good yield and diastereoselectivity when camphorsultam-derived acrylates are used as the reaction dipolarophiles . These initial cycloadducts are subsequently converted to stable, characterizable Δ²-pyrazolines upon desilylation.

A manifold of reactions that can be applied to these Δ²-pyrazolines has been developed which includes pyrazoline reduction, N-N bond reduction, addition to the pyrazoline C=N by mild carbon nucleophiles, and both solvolytic and reductive chiral auxiliary removal. Additionally, it has been demonstrated that the pyrazoline reduction products can take part in peptide coupling reactions that allow for the pyrazolidines to serve as proline-like molecules. The development of this methodology is a general solution to the problem of highly substituted, functionalized pyrazoline synthesis. Importantly, the pyrazolines thus provided have been demonstrated to be amenable to reactions that add to their value as synthetic intermediates.

Multiscale model reduction methods for deterministic and stochastic partial differential equations

Partial differential equations (PDEs) with multiscale coefficients are very difficult to solve due to the wide range of scales in the solutions. In the thesis, we propose some efficient numerical methods for both deterministic and stochastic PDEs based on the model reduction technique.

For the deterministic PDEs, the main purpose of our method is to derive an effective equation for the multiscale problem. An essential ingredient is to decompose the harmonic coordinate into a smooth part and a highly oscillatory part of which the magnitude is small. Such a decomposition plays a key role in our construction of the effective equation. We show that the solution to the effective equation is smooth, and could be resolved on a regular coarse mesh grid. Furthermore, we provide error analysis and show that the solution to the effective equation plus a correction term is close to the original multiscale solution.

For the stochastic PDEs, we propose the model reduction based data-driven stochastic method and multilevel Monte Carlo method. In the multiquery, setting and on the assumption that the ratio of the smallest scale and largest scale is not too small, we propose the multiscale data-driven stochastic method. We construct a data-driven stochastic basis and solve the coupled deterministic PDEs to obtain the solutions. For the tougher problems, we propose the multiscale multilevel Monte Carlo method. We apply the multilevel scheme to the effective equations and assemble the stiffness matrices efficiently on each coarse mesh grid. In both methods, the $\KL$ expansion plays an important role in extracting the main parts of some stochastic quantities.

For both the deterministic and stochastic PDEs, numerical results are presented to demonstrate the accuracy and robustness of the methods. We also show the computational time cost reduction in the numerical examples.

Biological electron transfer in copper proteins

Nature has used a variety of protein systems to mediate electron transfer. In this thesis I examine aspects of the control of biological electron transfer by two copper proteins that act as natural electron carriers.

In the first study, I have made a mutation to one of the ligand residues in the azurin blue copper center, methionine 121 changed to a glutamic acid. Studies of intramolecular electron transfer rates from that mutated center to covalently attached ruthenium complexes indicate that the weak axial methionine ligand is important not only for tuning the reduction potential of the blue copper site but also for maintaining the low reorganization energy that is important for fast electron transfer at long distances.

In the second study, I begin to examine the reorganization energy of the purple copper center in the CuA domain of subunit II of cytochrome c oxidase. In this copper center, the unpaired electron is delocalized over the entire binuclear site. Because long-range electron transfer into and out of this center occurs over long distances with very small driving forces, the reorganization energy of the CuA center has been predicted to be extremely low. I describe a strategy for measuring this reorganization energy starting with the construction of a series of mutations introducing surface histidines. These histidines can then be labeled with a series of ruthenium compounds that differ primarily in their reduction potentials. The electron transfer rates to these ruthenium compounds can then be used to determine the reorganization energy of the CuA site.

A fundamental approach to phase noise reduction in hybrid Si/III-V lasers

Spontaneous emission into the lasing mode fundamentally limits laser linewidths. Reducing cavity losses provides two benefits to linewidth: (1) fewer excited carriers are needed to reach threshold, resulting in less phase-corrupting spontaneous emission into the laser mode, and (2) more photons are stored in the laser cavity, such that each individual spontaneous emission event disturbs the phase of the field less. Strong optical absorption in III-V materials causes high losses, preventing currently-available semiconductor lasers from achieving ultra-narrow linewidths. This absorption is a natural consequence of the compromise between efficient electrical and efficient optical performance in a semiconductor laser. Some of the III-V layers must be heavily doped in order to funnel excited carriers into the active region, which has the side effect of making the material strongly absorbing.

This thesis presents a new technique, called modal engineering, to remove modal energy from the lossy region and store it in an adjacent low-loss material, thereby reducing overall optical absorption. A quantum mechanical analysis of modal engineering shows that modal gain and spontaneous emission rate into the laser mode are both proportional to the normalized intensity of that mode at the active region. If optical absorption near the active region dominates the total losses of the laser cavity, shifting modal energy from the lossy region to the low-loss region will reduce modal gain, total loss, and the spontaneous emission rate into the mode by the same factor, so that linewidth decreases while the threshold inversion remains constant. The total spontaneous emission rate into all other modes is unchanged.

Modal engineering is demonstrated using the Si/III-V platform, in which light is generated in the III-V material and stored in the low-loss silicon material. The silicon is patterned as a high-Q resonator to minimize all sources of loss. Fabricated lasers employing modal engineering to concentrate light in silicon demonstrate linewidths at least 5 times smaller than lasers without modal engineering at the same pump level above threshold, while maintaining the same thresholds.