Identifying and interpreting stratification in sedimentary rocks on Mars : insight from Rover and orbital observations and terrestrial field analogs

Sedimentary rocks on Mars provide insight into past aqueous and atmospheric processes, climate regimes, and potential habitability. The stratigraphic architecture of sedimentary rocks on Mars is similar to that of Earth, indicating that the processes that govern deposition and erosion on Mars can be reasonably inferred through reference to analogous terrestrial systems. This dissertation aims to understand Martian surface processes through the use of (1) ground-based observations from the Mars Exploration Rovers, (2) orbital data from the High Resolution Imaging Science Experiment onboard the Mars Reconnaissance Orbiter, and (3) the use of terrestrial field analogs to understand bedforms and sediment transport on Mars. Chapters 1 and 2 trace the history of aqueous activity at Meridiani Planum, through the reconstruction of eolian bedforms at Victoria crater, and the identification of a potential mudstone facies at Santa Maria crater. Chapter 3 uses Terrestrial Laser Scanning to study cross-bedding in pyroclastic surge deposits on Earth in order to understand sediment transport in these events and to establish criteria for their identification on Mars. The final chapter analyzes stratal geometries in the Martian North Polar Layered Deposits using tools for sequence stratigraphic analysis, to better constrain past surface processes and past climate conditions on Mars.

Constraints on the carbon cycle and climate during the early evolution of animals

One of the greatest challenges in science lies in disentangling causality in complex, coupled systems. This is illustrated no better than in the dynamic interplay between the Earth and life. The early evolution and diversification of animals occurred within a backdrop of global change, yet reconstructing the potential role of the environment in this evolutionary transition is challenging. In the 200 million years from the end-Cryogenian to the Ordovician, enigmatic Ediacaran fauna explored body plans, animals diversified and began to biomineralize, forever changing the ocean's chemical cycles, and the biological community in shallow marine ecosystems transitioned from a microbial one to an animal one.

In the following dissertation, a multi-faceted approach combining macro- and micro-scale analyses is presented that draws on the sedimentology, geochemistry and paleontology of the rocks that span this transition to better constrain the potential environmental changes during this interval.

In Chapter 1, the potential of clumped isotope thermometry in deep time is explored by assessing the importance of burial and diagenesis on the thermometer. Eocene- to Precambrian-aged carbonates from the Sultanate of Oman were analyzed from current burial depths of 350-5850 meters. Two end-member styles of diagenesis independent of burial depth were observed.

Chapters 2, 3 and 4 explore the fallibility of the Ediacaran carbon isotope record and aspects of the sedimentology and geochemistry of the rocks preserving the largest negative carbon isotope excursion on record---the Shuram Excursion. Chapter 2 documents the importance of temperature, fluid composition and mineralogy on the delta 18-O min record and interrogates the bulk trace metal signal. Chapter 3 explores the spatial variability in delta 13-C recorded in the transgressive Johnnie Oolite and finds a north-to-south trend recording the onset of the excursion. Chapter 4 investigates the nature of seafloor precipitation during this excursion and more broadly. We document the potential importance of microbial respiratory reactions on the carbonate chemistry of the sediment-water interface through time.

Chapter 5 investigates the latest Precambrian sedimentary record in carbonates from the Sultanate of Oman, including how delta 13-C and delta 34-S CAS vary across depositional and depth gradients. A new model for the correlation of the Buah and Ara formations across Oman is presented. Isotopic results indicate delta 13-C varies with relative eustatic change and delta 34-S CAS may vary in absolute magnitude across Oman.

Chapter 6 investigates the secular rise in delta 18-Omin in the early Paleozoic by using clumped isotope geochemistry on calcitic and phosphatic fossils from the Cambrian and Ordovician. Results do not indicate extreme delta 18-O seawater depletion and instead suggest warmer equatorial temperatures across the early Paleozoic.

Tools for the study of dynamical spacetimes

This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program.

We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi_4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction.

Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6.

For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various properties of these modes to wave packets traveling on unstable photon orbits around the black hole. In Chapter 8, we study a bifurcation in the QNM spectrum as the spin of the black hole a approaches extremality.

Financial equilibrium, voting procedures, and coalition structures in allocational mechanisms

This thesis is comprised of three chapters, each of which is concerned with properties of allocational mechanisms which include voting procedures as part of their operation. The theme of interaction between economic and political forces recurs in the three chapters, as described below.

Chapter One demonstrates existence of a non-controlling interest shareholders' equilibrium for a stylized one-period stock market economy with fewer securities than states of the world. The economy has two decision mechanisms: Owners vote to change firms' production plans across states, fixing shareholdings; and individuals trade shares and the current production / consumption good, fixing production plans. A shareholders' equilibrium is a production plan profile, and a shares / current good allocation stable for both mechanisms. In equilibrium, no (Kramer direction-restricted) plan revision is supported by a share-weighted majority, and there exists no Pareto superior reallocation.

Chapter Two addresses efficient management of stationary-site, fixed-budget, partisan voter registration drives. Sufficient conditions obtain for unique optimal registrar deployment within contested districts. Each census tract is assigned an expected net plurality return to registration investment index, computed from estimates of registration, partisanship, and turnout. Optimum registration intensity is a logarithmic transformation of a tract's index. These conditions are tested using a merged data set including both census variables and Los Angeles County Registrar data from several 1984 Assembly registration drives. Marginal registration spending benefits, registrar compensation, and the general campaign problem are also discussed.

The last chapter considers social decision procedures at a higher level of abstraction. Chapter Three analyzes the structure of decisive coalition families, given a quasitransitive-valued social decision procedure satisfying the universal domain and ITA axioms. By identifying those alternatives X* ⊆ X on which the Pareto principle fails, imposition in the social ranking is characterized. Every coaliton is weakly decisive for X* over X~X*, and weakly antidecisive for X~X* over X*; therefore, alternatives in X~X* are never socially ranked above X*. Repeated filtering of alternatives causing Pareto failure shows states in X^n*~X^((n+1))* are never socially ranked above X^((n+1))*. Limiting results of iterated application of the *-operator are also discussed.

Where Tori fear to tread : hypermassive neutron star remnants and absolute event horizons Or topics in computational general relativity

Computational general relativity is a field of study which has reached maturity only within the last decade. This thesis details several studies that elucidate phenomena related to the coalescence of compact object binaries. Chapters 2 and 3 recounts work towards developing new analytical tools for visualizing and reasoning about dynamics in strongly curved spacetimes. In both studies, the results employ analogies with the classical theory of electricity and magnitism, first (Ch. 2) in the post-Newtonian approximation to general relativity and then (Ch. 3) in full general relativity though in the absence of matter sources. In Chapter 4, we examine the topological structure of absolute event horizons during binary black hole merger simulations conducted with the SpEC code. Chapter 6 reports on the progress of the SpEC code in simulating the coalescence of neutron star-neutron star binaries, while Chapter 7 tests the effects of various numerical gauge conditions on the robustness of black hole formation from stellar collapse in SpEC. In Chapter 5, we examine the nature of pseudospectral expansions of non-smooth functions motivated by the need to simulate the stellar surface in Chapters 6 and 7. In Chapter 8, we study how thermal effects in the nuclear equation of state effect the equilibria and stability of hypermassive neutron stars. Chapter 9 presents supplements to the work in Chapter 8, including an examination of the stability question raised in Chapter 8 in greater mathematical detail.

Bis(thiophenolate)pyridine pincer ligands and trivalent zirconocene complexes relevant to early transition metal polymerization catalysts

Two major topics are covered: the first chapter is focused on the development of post-metallocene complexes for propylene polymerization. The second and third chapters investigate the consequences of diisobutylaluminum hydride (HAlⁱBu₂) additives in zirconocene based polymerization systems.

The synthesis, structure, and solution behavior of early metal complexes with a new tridentate LX₂ type ligand, bis(thiophenolate)pyridine ((SNS) = (2-C₆H₄S)₂-2,6-C₅H₃N) are investigated. SNS complexes of Ti, Zr, and Ta having dialkylamido coligands were synthesized and structurally characterized. The zirconium complex, (SNS)Zr(NMe₂)₂, displays C₂ symmetry in the solid state. Solid-state structures of tantalum complexes (SNS)Ta(NMe₂)₃ and (SNS)TaCl(NEt₂)₂ also display pronounced C₂ twisting of the SNS ligand. 1D and 2D NMR experiments show that (SNS)Ta(NMe₂)₃ is fluxional with rotation about the Ta N(amide) bonds occurring on the NMR timescale. The fluxional behavior of (SNS)TaCl(NEt₂)₂ in solution was also studied by variable temperature ¹H NMR. Observation of separate signals for the diastereotopic protons of the methylene unit of the diethylamide indicates that the complex remains locked on the NMR timescale in one diastereomeric conformation at temperatures below -50 °C.

Reduction of Zr(IV) metallocenium cations with sodium amalgam (NaHg) produces EPR signals assignable to Zr(III) metallocene complexes. Thus, chloro-bridged heterobinuclear ansa-zirconocenium cation [((SBI))Zr(μ-Cl)₂AlMe₂]⁺B(C₆F₅)_4¯ (SBI = rac-dimethylsilylbis(1-indenyl)), gives rise to an EPR signal assignable to the complex (SBI)Zr^III(μ-Cl)₂AlMe₂, while (SBI)Zr^III-Me and (SBI)Zr^III(-H)2AlⁱBu₂ are formed by reduction of [(SBI)Zr(μ-Me)₂AlMe₂]⁺B(C₆F₅)_4¯ and [(SBI)Zr(μ-H)₃(AlⁱBu₂)₂]⁺B(C₆F₅)4¯, respectively. These products are also formed, along with (SBI)Zr^III-ⁱBu and [(SBI)Zr^III]⁺ AlR4¯ when (SBI)ZrMe₂ reacts with HAlⁱBu₂, eliminating isobutane en route to the Zr(III) complex. Studies concerning the interconversion reactions between these and other (SBI)Zr(III) complexes and reaction mechanisms involved in their formation are also reported.

The addition of HAlⁱBu₂ to precatalyst [(SBI)Zr(µ-H)₃(AlⁱBu₂)₂]⁺ significantly slows the polymerization of propylene and changes the kinetics of polymerization from 1st to 2nd order with respect to propylene. This is likely due to competitive inhibition by HAlⁱBu₂. When the same reaction is investigated using [(ⁿBuCp)₂Zr(μ-H)₃(AlⁱBu₂)₂]⁺, hydroalumination between propylene and HAlⁱBu₂ is observed instead of propylene polymerization.

Crustal structure in Southern California from array data

Crustal structure in Southern California is investigated using travel times from over 200 stations and thousands of local earthquakes. The data are divided into two sets of first arrivals representing a two-layer crust. The Pg arrivals have paths that refract at depths near 10 km and the Pn arrivals refract along the Moho discontinuity. These data are used to find lateral and azimuthal refractor velocity variations and to determine refractor topography.

In Chapter 2 the Pn raypaths are modeled using linear inverse theory. This enables statistical verification that static delays, lateral slowness variations and anisotropy are all significant parameters. However, because of the inherent size limitations of inverse theory, the full array data set could not be processed and the possible resolution was limited. The tomographic backprojection algorithm developed for Chapters 3 and 4 avoids these size problems. This algorithm allows us to process the data sequentially and to iteratively refine the solution. The variance and resolution for tomography are determined empirically using synthetic structures.

The Pg results spectacularly image the San Andreas Fault, the Garlock Fault and the San Jacinto Fault. The Mojave has slower velocities near 6.0 km/s while the Peninsular Ranges have higher velocities of over 6.5 km/s. The San Jacinto block has velocities only slightly above the Mojave velocities. It may have overthrust Mojave rocks. Surprisingly, the Transverse Ranges are not apparent at Pg depths. The batholiths in these mountains are possibly only surficial.

Pn velocities are fast in the Mojave, slow in Southern California Peninsular Ranges and slow north of the Garlock Fault. Pn anisotropy of 2% with a NWW fast direction exists in Southern California. A region of thin crust (22 km) centers around the Colorado River where the crust bas undergone basin and range type extension. Station delays see the Ventura and Los Angeles Basins but not the Salton Trough, where high velocity rocks underlie the sediments. The Transverse Ranges have a root in their eastern half but not in their western half. The Southern Coast Ranges also have a thickened crust but the Peninsular Ranges have no major root.

Quantifying synergistic information

Within the microcosm of information theory, I explore what it means for a system to be functionally irreducible. This is operationalized as quantifying the extent to which cooperative or “synergistic” effects enable random variables X₁, ... , X_n to predict (have mutual information about) a single target random variable Y . In Chapter 1, we introduce the problem with some emblematic examples. In Chapter 2, we show how six different measures from the existing literature fail to quantify this notion of synergistic mutual information. In Chapter 3 we take a step towards a measure of synergy which yields the first nontrivial lowerbound on synergistic mutual information. In Chapter 4, we find that synergy is but the weakest notion of a broader concept of irreducibility. In Chapter 5, we apply our results from Chapters 3 and 4 towards grounding Giulio Tononi’s ambitious φ measure which attempts to quantify the magnitude of consciousness experience.

Chemical-scale studies of G protein-coupled receptors and ligand-gated ion channels

This dissertation describes studies of G protein-coupled receptors (GPCRs) and ligand-gated ion channels (LGICs) using unnatural amino acid mutagenesis to gain high precision insights into the function of these important membrane proteins.

Chapter 2 considers the functional role of highly conserved proline residues within the transmembrane helices of the D2 dopamine GPCR. Through mutagenesis employing unnatural α-hydroxy acids, proline analogs, and N-methyl amino acids, we find that lack of backbone hydrogen bond donor ability is important to proline function. At one proline site we additionally find that a substituent on the proline backbone N is important to receptor function.

In Chapter 3, side chain conformation is probed by mutagenesis of GPCRs and the muscle-type nAChR. Specific side chain rearrangements of highly conserved residues have been proposed to accompany activation of these receptors. These rearrangements were probed using conformationally-biased β-substituted analogs of Trp and Phe and unnatural stereoisomers of Thr and Ile. We also modeled the conformational bias of the unnatural Trp and Phe analogs employed.

Chapters 4 and 5 examine details of ligand binding to nAChRs. Chapter 4 describes a study investigating the importance of hydrogen bonds between ligands and the complementary face of muscle-type and α4β4 nAChRs. A hydrogen bond involving the agonist appears to be important for ligand binding in the muscle-type receptor but not the α4β4 receptor.

Chapter 5 describes a study characterizing the binding of varenicline, an actively prescribed smoking cessation therapeutic, to the α7 nAChR. Additionally, binding interactions to the complementary face of the α7 binding site were examined for a small panel of agonists. We identified side chains important for binding large agonists such as varenicline, but dispensable for binding the small agonist ACh.

Chapter 6 describes efforts to image nAChRs site-specifically modified with a fluorophore by unnatural amino acid mutagenesis. While progress was hampered by high levels of fluorescent background, improvements to sample preparation and alternative strategies for fluorophore incorporation are described.

Chapter 7 describes efforts toward a fluorescence assay for G protein association with a GPCR, with the ultimate goal of probing key protein-protein interactions along the G protein/receptor interface. A wide range of fluorescent protein fusions were generated, expressed in Xenopus oocytes, and evaluated for their ability to associate with each other.

Bimetallic olefin polymerization catalysis : mechanisms and applications of proximal effects

This dissertation covers progress with bimetallic polymerization catalysts. The complexes we have designed were aimed at expanding the capabilities of homogeneous polymerization catalysts by taking advantage of multimetallic effects. Such effects were examined in group 4 and group 10 bimetallic complexes; proximity and steric repulsion were determined to be major factors in the effects observed.

Chapters 2 and 3 introduce the rigid p-terphenyl dinucleating framework utilized in most of this thesis. The permethylation of the central arene allows for the separation of syn and anti atropisomers of the terphenyl compounds. Kinetic studies were carried out to examine the isomerization of the dinucleating bis(salicylaldimine) ligand precursors. Metallation of the syn and anti bis(salicylaldimine)s using Ni(Me)2(tmeda) and excess pyridine afforded dinickel bisphenoxyiminato complexes with a methyl and a pyridyl ligand on each nickel. The syn and anti atropisomers of the dinickel complexes were structurally characterized and utilized in ethylene and ethylene/α-olefin polymerizations. Monometallic analogues were also synthesized and tested for polymerization activity. Ethylene polymerizations were performed in the presence of primary, secondary, and tertiary amines – additives that generally deactivate nickel polymerization catalysts. Inhibition of this deactivation was observed with the syn atropisomer of the bimetallic species, but not with the anti or monometallic analogues. A mechanism was proposed wherein steric repulsion of the substituents on proximal nickel centers disfavors simultaneous ligation of base to both of the metal centers. The bimetallic effect has been explored with respect to size and binding ability of the added base.

Chapter 4 presents the optimization of the bisphenoxyimine ligand synthesis and synthesis of syn and anti m-terphenyl analogues. Metallation with NiClMe(PMe₃)₂ yielded phosphine-ligated dinickel complexes, which have been structurally characterized. Ethylene/1-hexene copolymerizations in the presence of amines using Ni(COD)₂ as a phosphine scavenger showed significantly improved activity relative to the pyridine-ligated analogues. Incorporation of amino olefins in copolymerizations with ethylene was accomplished, and a mechanism was proposed based on proximal effects. Copolymerization trials with a variety of amino olefins and ethylene/1-hexene/amino olefin terpolymerizations were completed.

Early transition metal complexes based on the rigid p-terphenyl framework were designed with a variety of donor sets (Chapter 5 and Appendix B). Chapter 5 details the use of syn dizirconium di[amine bis(phenolate)] complexes for isoselective 1-hexene and propylene homopolymerizations. Ligand variation and monometallic complexes were studied to determine the origin of tacticity control. A mechanistic proposal was presented based on the symmetry at zirconium and the steric effects of the proximal metal center. Appendix B covers additional studies of bimetallic early transition metal complexes based on the p-terphenyl. Dititanium, dizirconium, and asymmetric complexes with bisphenoxyiminato ligands and derivatives thereof were targeted. Progress toward the synthesis of these complexes is described along with preliminary polymerization data. 1-hexene/diene copolymerizations and attempted polymerizations in the presence of ethers and esters with the syn dizirconium di[amine bis(phenolate)] complexes demonstrate the potential for further applications of this system in catalysis.

Appendix A includes work toward palladium catalysts for insertion polymerization of polar monomers. These complexes were based on dioxime and diimine frameworks with the intent of binding Lewis acidic metals at the oxime oxygens, at pendant phenolic donors, or at pendant aminediol moieties. The synthesis and structural characterization of a number of palladium and Lewis acid complexes is presented. Due to the instability of the desired species, efforts toward isolation of the desired complexes proved unsuccessful, though preliminary ethylene/methyl acrylate copolymerizations using in situ activation of the palladium species were attempted.

Topics in LIGO-related physics: interferometric speed meters and tidal work

In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors, one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. The most straightforward design for a speed-meter interferometer that accomplishes this is described and analyzed in Chapter 2. This design (due to Braginsky, Gorodetsky, Khalili, and Thorne) is analogous to a microwave-cavity speed meter conceived by Braginsky and Khalili. A mathematical mapping between the microwave speed meter and the optical interferometric speed meter is developed and used to show (in accord with the speed being a quantum nondemolition observable) that in principle the interferometric speed meter can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies . However, in practice, to reach or beat the SQL, this specific speed meter requires exorbitantly high input light power. The physical reason for this is explored, along with other issues such as constraints on performance due to optical dissipation.

Chapter 3 proposes a more sophisticated version of a speed meter. This new design requires only a modest input power and appears to be a fully practical candidate for third-generation LIGO. It can beat the SQL (the approximate sensitivity of second-generation LIGO interferometers) over a broad range of frequencies (~ 10 to 100 Hz in practice) by a factor h/h_SQL ~ √W^(SQL)_(circ)/W_circ. Here W_circ is the light power circulating in the interferometer arms and W_SQL ≃ 800 kW is the circulating power required to beat the SQL at 100 Hz (the LIGO-II power). If squeezed vacuum (with a power-squeeze factor e^-2R) is injected into the interferometer's output port, the SQL can be beat with a much reduced laser power: h/h_SQL ~ √W^(SQL)_(circ)/W_circe^-2R. For realistic parameters (e^-2R ≃ 10 and W_circ ≃ 800 to 2000 kW), the SQL can be beat by a factor ~ 3 to 4 from 10 to 100 Hz. [However, as the power increases in these expressions, the speed meter becomes more narrow band; additional power and re-optimization of some parameters are required to maintain the wide band.] By performing frequency-dependent homodyne detection on the output (with the aid of two kilometer-scale filter cavities), one can markedly improve the interferometer's sensitivity at frequencies above 100 Hz.

Chapters 2 and 3 are part of an ongoing effort to develop a practical variant of an interferometric speed meter and to combine the speed meter concept with other ideas to yield a promising third- generation interferometric gravitational-wave detector that entails low laser power.

Chapter 4 is a contribution to the foundations for analyzing sources of gravitational waves for LIGO. Specifically, it presents an analysis of the tidal work done on a self-gravitating body (e.g., a neutron star or black hole) in an external tidal field (e.g., that of a binary companion). The change in the mass-energy of the body as a result of the tidal work, or "tidal heating," is analyzed using the Landau-Lifshitz pseudotensor and the local asymptotic rest frame of the body. It is shown that the work done on the body is gauge invariant, while the body-tidal-field interaction energy contained within the body's local asymptotic rest frame is gauge dependent. This is analogous to Newtonian theory, where the interaction energy is shown to depend on how one localizes gravitational energy, but the work done on the body is independent of that localization. These conclusions play a role in analyses, by others, of the dynamics and stability of the inspiraling neutron-star binaries whose gravitational waves are likely to be seen and studied by LIGO.

Dynamical stability of nascent neutron stars

This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the accretion induced collapse of rapidly rotating white dwarfs.

Chapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are constructed by assuming that the neutron stars have the same masses, angular momenta, and specific angular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is rapidly rotating, the collapsed object will contain a high density central core of size about 20 km, surrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis. The ratio of the rotational kinetic energy to gravitational binding energy, β, of these neutron stars is all found to be less than 0.27.

Chapter 3 studies the dynamical stability of these neutron stars by numerically evolving the linearized hydrodynamical equations. A dynamical bar-mode instability is observed when the β of the star is greater than the critical value β_d ≈ 0.25. It is expected that the unstable mode will persist until a substantial amount of angular momentum is carried away by gravitational radiation. The detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect them unless the event rate is greater than 10^-6/year/galaxy.

All the calculations on the structure and stability of the neutron stars in Chapters 2 and 3 are carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic effects on the structure of these neutron stars. New techniques are developed and used to construct neutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models are qualitatively similar to the corresponding Newtonian models, but the values of β are somewhat smaller. The maximum β for these 1PN neutron stars is found to be 0.24, which is 8% smaller than the Newtonian result (0.26). However, relativistic effects will also change the critical value β_d. A detailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects on the dynamical stability of these neutron stars.

New materials for biological applications prepared by olefin metathesis reactions

With the advent of well-defined ruthenium olefin metathesis catalysts that are highly active and stable to a variety of functional groups, the synthesis of complex organic molecules and polymers is now possible; this is reviewed in Chapter 1. The majority of the rest of this thesis describes the application of these catalysts towards the synthesis of novel polymers that may be useful in biological applications and investigations into their efficacy.

A method was developed to produce polyethers by metathesis, and this is described in Chapters 2 and 3. An unsaturated 12-crown-4 analog was made by template- directed ring-closing metathesis (RCM) and utilized as a monomer for the synthesis of unsaturated polyethers by ring-opening metathesis polymerization (ROMP). The yields were high and a range of molecular weights was accessible. In a similar manner, substituted polyethers with various backbones were synthesized: polymers with benzo groups along the backbone and various concentrations of amino acids were prepared. The results from in vitro toxicity tests of the unsubstituted polyethers are considered.

The conditions necessary to synthesize polynorbornenes with pendent bioactive peptides were explored as illustrated in Chapter 4. First, the polymerization of various norbornenyl monomers substituted with glycine, alanine or penta(ethylene glycol) is described. Then, the syntheses of polymers substituted with peptides GRGD and SRN, components of a cell binding domain of fibronectin, using newly developed ruthenium initiators are discussed.

In Chapter 5, the syntheses of homopolymers and a copolymer containing GRGDS and PHSRN, the more active forms of the peptides, are described. The ability of the polymers to inhibit human dermal fibroblast cell adhesion to fibronectin was assayed using an in vitro competitive inhibition assay, and the results are discussed. It was discovered that the copoymer substituted with both GRGDS and PHSR peptides was more active than both the GRGDS-containing homopolymer and the GRGDS free peptide.

Historically, one of the drawbacks to using metathesis is the removal of the residual ruthenium at the completion of the reaction. Chapter 6 describes a method where the water soluble tris(hydroxymethyl)phosphine is utilized to facilitate the removal of residual ruthenium from RCM reaction products.

Electron flow through cytochrome P450

The cytochromes P450 (P450s) are a remarkable class of heme enzymes that catalyze the metabolism of xenobiotics and the biosynthesis of signaling molecules. Controlled electron flow into the thiolate-ligated heme active site allows P450s to activate molecular oxygen and hydroxylate aliphatic C–H bonds via the formation of high-valent metal-oxo intermediates (compounds I and II). Due to the reactive nature and short lifetimes of these intermediates, many of the fundamental steps in catalysis have not been observed directly. The Gray group and others have developed photochemical methods, known as “flash-quench,” for triggering electron transfer (ET) and generating redox intermediates in proteins in the absence of native ET partners. Photo-triggering affords a high degree of temporal precision for the gating of an ET event; the initial ET and subsequent reactions can be monitored on the nanosecond-to-second timescale using transient absorption (TA) spectroscopies. Chapter 1 catalogues critical aspects of P450 structure and mechanism, including the native pathway for formation of compound I, and outlines the development of photochemical processes that can be used to artificially trigger ET in proteins. Chapters 2 and 3 describe the development of these photochemical methods to establish electronic communication between a photosensitizer and the buried P450 heme. Chapter 2 describes the design and characterization of a Ru-P450-BM3 conjugate containing a ruthenium photosensitizer covalently tethered to the P450 surface, and nanosecond-to-second kinetics of the photo-triggered ET event are presented. By analyzing data at multiple wavelengths, we have identified the formation of multiple ET intermediates, including the catalytically relevant compound II; this intermediate is generated by oxidation of a bound water molecule in the ferric resting state enzyme. The work in Chapter 3 probes the role of a tryptophan residue situated between the photosensitizer and heme in the aforementioned Ru-P450 BM3 conjugate. Replacement of this tryptophan with histidine does not perturb the P450 structure, yet it completely eliminates the ET reactivity described in Chapter 2. The presence of an analogous tryptophan in Ru-P450 CYP119 conjugates also is necessary for observing oxidative ET, but the yield of heme oxidation is lower. Chapter 4 offers a basic description of the theoretical underpinnings required to analyze ET. Single-step ET theory is first presented, followed by extensions to multistep ET: electron “hopping.” The generation of “hopping maps” and use of a hopping map program to analyze the rate advantage of hopping over single-step ET is described, beginning with an established rhenium-tryptophan-azurin hopping system. This ET analysis is then applied to the Ru-tryptophan-P450 systems described in Chapter 2; this strongly supports the presence of hopping in Ru-P450 conjugates. Chapter 5 explores the implementation of flash-quench and other phototriggered methods to examine the native reductive ET and gas binding events that activate molecular oxygen. In particular, TA kinetics that demonstrate heme reduction on the microsecond timescale for four Ru-P450 conjugates are presented. In addition, we implement laser flash-photolysis of P450 ferrous–CO to study the rates of CO rebinding in the thermophilic P450 CYP119 at variable temperature. Chapter 6 describes the development and implementation of air-sensitive potentiometric redox titrations to determine the solution reduction potentials of a series of P450 BM3 mutants, which were designed for non-native cyclopropanation of styrene in vivo. An important conclusion from this work is that substitution of the axial cysteine for serine shifts the wild type reduction potential positive by 130 mV, facilitating reduction by biological redox cofactors in the presence of poorly-bound substrates. While this mutation abolishes oxygenation activity, these mutants are capable of catalyzing the cyclopropanation of styrene, even within the confines of an E. coli cell. Four appendices are also provided, including photochemical heme oxidation in ruthenium-modified nitric oxide synthase (Appendix A), general protocols (Appendix B), Chapter-specific notes (Appendix C) and Matlab scripts used for data analysis (Appendix D).

Transition metal clusters supported by multinucleating ligand frameworks as models of biological active sites

This dissertation describes efforts to model biological active sites with small molecule clusters. The approach used took advantage of a multinucleating ligand to control the structure and nuclearity of the product complexes, allowing the study of many different homo- and heterometallic clusters. Chapter 2 describes the synthesis of the multinucleating hexapyridyl trialkoxy ligand used throughout this thesis and the synthesis of trinuclear first row transition metal complexes supported by this framework, with an emphasis on tricopper systems as models of biological multicopper oxidases. The magnetic susceptibility of these complexes were studied, and a linear relation was found between the Cu-O(alkoxide)-Cu angles and the antiferromagnetic coupling between copper centers. The triiron(II) and trizinc(II) complexes of the ligand were also isolated and structurally characterized.

Chapter 3 describes the synthesis of a series of heterometallic tetranuclear manganese dioxido complexes with various incorporated apical redox-inactive metal cations (M = Na⁺, Ca²⁺, Sr²⁺, Zn²⁺, Y³⁺). Chapter 4 presents the synthesis of heterometallic trimanganese(IV) tetraoxido complexes structurally related to the CaMn₃ subsite of the oxygen-evolving complex (OEC) of Photosystem II. The reduction potentials of these complexes were studied, and it was found that each isostructural series displays a linear correlation between the reduction potentials and the Lewis acidities of the incorporated redox-inactive metals. The slopes of the plotted lines for both the dioxido and tetraoxido clusters are the same, suggesting a more general relationship between the electrochemical potentials of heterometallic manganese oxido clusters and their “spectator” cations. Additionally, these studies suggest that Ca²⁺ plays a role in modulating the redox potential of the OEC for water oxidation.

Chapter 5 presents studies of the effects of the redox-inactive metals on the reactivities of the heterometallic manganese complexes discussed in Chapters 3 and 4. Oxygen atom transfer from the clusters to phosphines is studied; although the reactivity is kinetically controlled in the tetraoxido clusters, the dioxido clusters with more Lewis acidic metal ions (Y³⁺ vs. Ca²⁺) appear to be more reactive. Investigations of hydrogen atom transfer and electron transfer rates are also discussed.

Appendix A describes the synthesis, and metallation reactions of a new dinucleating bis(N-heterocyclic carbene)ligand framework. Dicopper(I) and dicobalt(II) complexes of this ligand were prepared and structurally characterized. A dinickel(I) dichloride complex was synthesized, reduced, and found to activate carbon dioxide. Appendix B describes preliminary efforts to desymmetrize the manganese oxido clusters via functionalization of the basal multinucleating ligand used in the preceding sections of this dissertation. Finally, Appendix C presents some partially characterized side products and unexpected structures that were isolated throughout the course of these studies.