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Exploiting the Reactivity of Arynes in the Total Synthesis of Natural Products
Get PDFWithin 14 years of the seminal experiments of J. D. Roberts leading to the first proposal of the structure of benzyne, synthetic organic chemists recognized the potential to exploit this highly reactive intermediate (and its substituted variants) in the synthesis of natural products. More specifically, it was recognized that arynes offered the strategic advantage of rapidly functionalizing an aromatic ring by forming multiple carbon–carbon or carbon–heteroatom bonds in a single operation, often in a regioselective manner. Herein are reported three separate efforts aimed at constructing natural products by aryne-based methodologies. In each of the studies described in the following chapters, the implementation of new aryne technologies developed in our group to natural product synthesis has resulted in concise, convergent, and general strategies to our targets.
The first project discussed in this work is the enantioselective total synthesis of (–)-curvularin by an acyl-alkylation reaction of a protected resorcinylic silyl aryl triflate aryne precursor with a β-ketolactone. Application of this strategic disconnection resulted in a six-step convergent synthesis of the polyketide natural product, the shortest to date. These efforts also resulted in the syntheses of curvulin and diplodialide C.
In our efforts toward the total synthesis of two naturally occurring HIV integrase inhibitors, integrastatins A and B, we attempted to utilize a sequence involving an acyl-alkylation followed by an ortho-Fries-type rearrangement to access the tetracyclic core of the natural products. However, this proved to be a significant challenge and led to the development of an alternative route to the tetracyclic integrastatin core by a Wacker cyclization of a diol onto a pendant olefin.
Finally, ongoing progress toward the synthesis of the bis-tetrahydroisoquinoline natural product jorumycin is detailed. In a departure from the efforts toward curvularin and the integrastatins, jorumycin has been targeted through the application of a combination of aryne annulation and acyl-alkylation/condensation methodologies aimed at the synthesis of a functionalized bis-isoquinoline intermediate. Reduction of this key bis-isoquinoline to a bis-tetrahydroisoquinoline and subsequent lactamization provided the pentacyclic core of jorumycin and related natural products in only two steps from simple isoquinoline building blocks.</p
A Study of the Thermodynamics and Kinetics of LiₓFePO₄ as a Cathode Material for Li Batteries
Get PDFOlivine-type LiFePO4 has been recognized as one of the most promising cathode materials for rechargeable Li batteries. Its advantages include high capacity, high stability, nontoxicity, and low cost. Our methods for synthesizing nanocrystalline LixFePO4 with the olivine structure are described. Solid-state reactions and precipitation reactions were both successful, and ball milling was especially effective at reducing crystallite sizes. Diffractometry and microscopy were used to characterize these materials, and results of impurity phases, excess Fe3+, and internal stresses are reported for the different types of synthesis.
Applications of lithium-ion batteries, including automotive applications, require fast kinetics and high conductivity of ions and electrons. Unfortunately, LixFePO4 has the electronic structure of an insulator, an entirely unsatisfactory situation if it is to be used as a battery electrode. Electrical conductivity in LixFePO4 occurs by the motion of small polarons, which are valence electrons at Fe atoms plus their distorted local environments. Electrical conductivity of LixFePO4 is interpreted in terms of small polaron hopping. There are other factors of importance in these measurements, such as impurities or defects that block the one-dimensional conduction channels of the olivine structure of LixFePO4.
We studied the polaron hopping directly, which allows us to understand the intrinsic electrical conductivity, and how it depends on microstructure and composition of LixFePO4. The experimental technique was Mossbauer spectrometry, which has been used for many years as a means for determining the fractions of Fe2+ and Fe3+ in a material. Usually the spectral signatures of Fe2+ and Fe3+ are distinct. When valence electrons hop between Fe2+ and Fe3+ at a frequency of 108 Hz or higher, however, the valence changes during the timescale of the Mossbauer measurement and the spectrum is blurred. By measuring Mossbauer spectra at elevated temperatures, we can determine the fractions of Fe atoms participating in polaron hopping, and determine the activation energy of the process. From this we estimate intrinsic electrical conductivities of 10-7S/cm at room temperature for nanocrystalline Li0.5FePO4, for example. We find a comparable conductivity for LixFePO4 prepared as a solid solution, but the conductivity of conventional LixFePO4 is much lower.
There has been much discussion about how surface area might thermodynamically stabilize the solid solution phase of nanocrystalline LixFePO4. In a series of X-ray diffraction measurements, some at elevated temperatures, we found the solid solution phase of LixFePO4 to be especially robust at room temperature when the material was prepared in nanocrystalline form. Moreover, the consistent phase transition temperature around 200°C was observed, as evidence for the unchanged equilibrium phase diagram by crystallite size. This is consistent with our evaluation on the boundaries of the two-phase mixture of triphylite and heterosite during Li insertion and extraction. Profiles of entropy and enthalpy changes were evaluated by open-circuit voltage measurements. The boundaries were found at x=0.05 and 0.95 in the LixFePO4 with crystal size of 70 nm, similar to the reported values on bulk-LixFePO4. These are important in practice, because electrochemical lithiation and delithiation at room temperature should remain as a two-phase transformation, even if a solid solution of lithium is present in the initial electrode material.</p
Mass Spectrometric Analysis of Organic Aerosol Composition: Laboratory and Ambient
Get PDFOrganic compounds contribute a significant mass fraction of ambient aerosol and play a role in determining the physiochemical properties of ambient aerosol. A significant fraction of organic aerosol is secondary organic aerosol (SOA), which is produced when the volatile organic compounds (VOCs) originated from various anthropogenic and biogenic sources react with atmospheric oxidants such as ozone, hydroxyl radicals, and nitrate radicals to form lower volatility organic compounds, which subsequently partition into the particle phase. Understanding the composition of ambient aerosol is crucial for identifying their sources and formation mechanisms and predicting their properties and effects on various ambient processes. This thesis focuses on investigating the composition of laboratory–generated SOA formed from the oxidation of biogenic VOCs of atmospheric importance (isoprene and β–caryophyllene) and ambient aerosol collected in the field campaigns using advanced mass spectrometric techniques. By comparing the mass spectrometric data collected for the both laboratory–generated SOA and ambient aerosol, we propose reaction pathways and new chemical tracers for these biogenic VOCs, which enhance our knowledge of the composition, sources, and formation pathways of SOA in the atmosphere. With a better knowledge of the SOA composition, a product–specific model is proposed to predict the composition and aerosol mass yields (mass of SOA formed per mass of hydrocarbon reacted) of laboratory–generated α–pinene SOA
Recombinatorial and Predictive Methods to Increase Cellulase Thermostability and Structural Analysis of a Thermostable P450
Get PDFTo address the world’s need for improved biomass breakdown for the production of renewable fuel, we sought to improve cellulase thermostability and thereby enzyme lifetime, operating temperature, and specific activity. We created an eight block SCHEMA recombination library based on five fungal cellobiohydrolase class I (CBHI) enzymes. By characterizing this library, we identified several stabilizing sequence blocks and combined these to produce a set of well-expressed, thermostable CBHI chimeras. To further increase the stability of these chimeras, we used a combination of the chimera thermostability screening data, a consensus analysis of 40 naturally occurring CBHI sequences, and FoldX ΔΔG predictions to identify individual mutations for testing. Our final enzyme has a T50 9.3 °C greater than that of the most stable parental CBHI, resulting in a 10 °C increase in optimal temperature and a 50% increase in total sugar production at the optimal temperature.
To produce an ideal parent for directed evolution for improved activity on varied compounds, we increased the thermostability of a P450BM3 enzyme with broad substrate specificity to produce enzyme 9-10ATS. Directed evolution libraries based on 9-10ATS produced variants with improved activity on a number of structurally diverse compounds. We determined the structure of 9-10ATS using x-ray crystallography and compared it to other P450BM3 structures. Examination of the stucture shows clear structural basis for the thermostabilizing mutations and broad substrate specificity.</p
Geometric Descriptions of Couplings in Fluids and Circuits
Get PDFGeometric mechanics is often commended for its breadth (e.g., fluids, circuits, controls) and depth (e.g., identification of stability criteria, controllability criteria, conservation laws). However, on the interface between disciplines it is commonplace for the analysis previously done on each discipline in isolation to break down. For example, when a solid is immersed in a fluid, the particle relabeling symmetry is broken because particles in the fluid behave differently from particles in the solid. This breaks conservation laws, and even changes the configuration manifolds. A second example is that of the interconnection of circuits. It has been verified that LC-circuits satisfy a variational principle. However, when two circuits are soldered together this variational principle must transform to accommodate the interconnection.
Motivated by these difficulties, this thesis analyzes the following couplings: fluid-particle, fluid-structure, and circuit-circuit. For the case of fluid-particle interactions we understand the system as a Lagrangian system evolving on a Lagrange-Poincare bundle. We leverage this interpretation to propose a class of particle methods by "ignoring" the vertical Lagrange-Poincare equation. In a similar vein, we can analyze fluids interacting with a rigid body. We then generalize this analysis to view fluid-structure problems as Lagrangian systems on a Lie algebroid. The simplicity of the reduction process for Lie algebroids allows us to propose a mechanism in which swimming corresponds to a limit-cycle in a reduced Lie algebroid. In the final section we change gears and understand non-energetic interconnection as Dirac structures. In particular we find that any (linear) non-energetic interconnection is equivalent to some Dirac structure. We then explore what this insight has to say about variational principles, using interconnection of LC-circuits as a guiding example.</p
Visualizing, Approximating, and Understanding Black-Hole Binaries
Get PDFNumerical-relativity simulations of black-hole binaries and advancements in gravitational-wave detectors now make it possible to learn more about the collisions of compact astrophysical bodies. To be able to infer more about the dynamical behavior of these objects requires a fuller analysis of the connection between the dynamics of pairs of black holes and their emitted gravitational waves. The chapters of this thesis describe three approaches to learn more about the relationship between the dynamics of black-hole binaries and their gravitational waves: modeling momentum flow in binaries with the Landau-Lifshitz formalism, approximating binary dynamics near the time of merger with post-Newtonian and black-hole-perturbation theories, and visualizing spacetime curvature with tidal tendexes and frame-drag vortexes.
In Chapters 2--4, my collaborators and I present a method to quantify the flow of momentum in black-hole binaries using the Landau-Lifshitz formalism. Chapter 2 reviews an intuitive version of the formalism in the first-post-Newtonian approximation that bears a strong resemblance to Maxwell’s theory of electromagnetism. Chapter 3 applies this approximation to relate the simultaneous bobbing motion of rotating black holes in the superkick configuration---equal-mass black holes with their spins anti-aligned and in the orbital plane---to the flow of momentum in the spacetime, prior to the black holes’
merger. Chapter 4 then uses the Landau-Lifshitz formalism to explain the dynamics of a head-on merger of spinning black holes, whose spins are anti-aligned and transverse to the infalling motion. Before they merge, the black holes move with a large, transverse, velocity, which we can explain using the post-Newtonian approximation; as the holes merge and form a single black hole, we can use the Landau-Lifshitz formalism without any approximations to connect the slowing of the final black hole to its absorbing momentum density during the merger.
In Chapters 5--7, we discuss using analytical approximations, such as post-Newtonian and black-hole-perturbation theories, to gain further understanding into how gravitational waves are generated by black-hole binaries. Chapter 5 presents a way of combining post-Newtonian and black-hole-perturbation theories---which we call the hybrid method---for head-on mergers of black holes. It was able to produce gravitational waveforms and gravitational recoils that agreed well with comparable results from numerical-relativity simulations. Chapter 6 discusses a development of the hybrid model to include a radiation-reaction force, which is better suited for studying inspiralling black-hole binaries. The gravitational waveform from the hybrid method for inspiralling mergers agreed qualitatively with that from numerical-relativity simulations; when applied to the superkick configuration, it gave a simplified picture of the formation of the large black-hole kick. Chapter 7 describes an approximate method of calculating the frequencies of the ringdown gravitational waveforms of rotating black holes (quasinormal modes). The method generalizes a geometric interpretation of black-hole quasinormal modes and explains a degeneracy in the spectrum of these modes.
In Chapters 8--11, we describe a new way of visualizing spacetime curvature using tools called tidal tendexes and frame-drag vortexes. This relies upon a time-space split of spacetime, which allows one to break the vacuum Riemann curvature tensor into electric and magnetic parts (symmetric, trace-free tensors that have simple physical interpretations). The regions where the eigenvalues of these tensors are large form the tendexes and vortexes of a spacetime, and the integral curves of their eigenvectors are its tendex and vortex lines, for the electric and magnetic parts, respectively. Chapter 8 provides an overview of these visualization tools and presents initial results from numerical-relativity simulations. Chapter 9 uses topological properties of vortex and tendex lines to classify properties of gravitational waves far from a source. Chapter 10 describes the formalism in more detail, and discusses the vortexes and tendexes of multipolar spacetimes in linearized gravity about flat space. The chapter helps to explain how near-zone vortexes and tendexes become gravitational waves far from a weakly gravitating, time-varying source. Chapter 11 is a detailed investigation of the vortexes and tendexes of stationary and perturbed black holes. It develops insight into how perturbations of (strongly gravitating) black holes extend from near the horizon to become gravitational waves.</p
Three Essays on Microeconomic Theory
Get PDFThis thesis considers three issues in microeconomic theory - two-sided matching, strategic voting, and revealed preferences.
In the first chapter I discuss the strategic manipulation of stable matching mechanisms commonly used in two-sided matching markets. Stable matching mechanisms are very successful in practice, despite theoretical concerns that they are manipulable by participants. The key finding is that most agents in large markets are close to being indifferent among partners in all stable matchings. It is known that the utility gain by manipulating a stable matching mechanism is bounded by the difference between utilities from the best and the worst stable matching partners. Thus, the main finding implies that the proportion of agents who may obtain a significant utility gain from manipulation vanishes in large markets. This result reconciles the success of stable mechanisms in practice with the theoretical concerns about strategic manipulation. Methodologically, I introduce techniques from the theory of random bipartite graphs for the analysis of large matching markets.
In the second chapter I study the criminal court process, focusing on plea bargaining. Plea bargains screen the types of defendants, guilty or innocent, who go to jury trial, which affects the jurors' voting decision and, in turn, the performance of the entire criminal court. The equilibrium jurors' voting behavior in the case of plea bargaining resembles the equilibrium behavior in the classical jury model in the absence of plea bargaining. By optimizing a plea bargain offer, a prosecutor, however, may induce jurors to act as if they echo the prosecutor's preferences against convicting innocent defendants and acquitting guilty defendants. With reference to Feddersen and Pesendorfer (1998), I study different voting rules in the trial stage and their consequences in the entire court process. Compared to general super-majority rules, we find that a court using the unanimity rule delivers more expected punishment to innocent defendants and less punishment to guilty defendants.
In the third chapter I study collective choices from the revealed preference theory viewpoint. For every product set of individual actions, joint choices are called Nash-rationalizable if there exists a preference relation for each player such that the selected joint actions are Nash equilibria of the corresponding game. I characterize Nash-rationalizable joint choice behavior by zero-sum games, or games of conflicting interests. If the joint choice behavior forms a product subset, the behavior is called interchangeable. I prove that interchangeability is the only additional empirical condition which distinguishes zero-sum games from general noncooperative games.</p
Effects of Ca-Doping on the Vortex Properties and Pairing Symmetry of (Y1-xCax)Ba2Cu3O7-δ
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Noncanonical Amino Acids in the Interrogation of Cellular Protein Synthesis
Get PDFProteins in living cells can be made receptive to bioorthogonal chemistries through metabolic labeling with appropriately designed noncanonical amino acids (ncAAs). In the simplest approach to metabolic labeling, an amino acid analog replaces one of the natural amino acids specified by the protein’s gene (or genes) of interest. This approach, often termed “residue-specific incorporation,” allows the ncAA to be incorporated in controlled proportions into positions normally occupied by the natural amino acid residue. Chapter I of this thesis describes how this strategy has been used to track cellular protein synthesis with reactive ncAAs. In procedures similar to isotopic labeling, translationally active ncAAs are incorporated into proteins during a "pulse" in which newly synthesized proteins are tagged. The set of tagged proteins can be distinguished from those made before the pulse by bioorthogonally ligating the ncAA side chain to probes that permit detection, isolation, and visualization of the labeled proteins.
Chapter II of this thesis describes how the selectivity of the method can be enhanced through the use of mutant aminoacyl tRNA synthetases (aaRSs) that permit incorporation of ncAAs not used by the endogenous biomachinery. Expression of a mutant synthetase in a portion of cells within a complex cellular mixture restricts labeling to that subset of cells. In multicellular environments, this approach permits the identification of the cellular origins of labeled proteins. The work in Chapter III illustrates how the extent of temporal and spatial resolution of protein labeling can be enhanced through controlled expression of mutant synthetases. Use of characterized promoters to direct transcription of mutant synthetase genes can limit labeling to relevant cells and physiological states in settings of increased complexity. Chapter IV presents a novel strategy with which ncAAs can be uniquely incorporated at the N-terminal positions of nascent proteins while excluded from insertion at internal positions. This approach permits "site-selective" tagging of cellular proteins, and its use in tagging and visualization of cell-cycle dependent protein synthesis is described.
The work described throughout this thesis was designed with the objective of providing powerful and versatile methods for the study of protein synthesis in complex multicellular systems, including live animals. Thus, Chapter V considers how these strategies might be used to dissect protein synthesis in living animals.</p
Identifying the Unique Ground Motion Signatures of Supershear Earthquakes: Theory and Experiments
Get PDFThe near-field ground motion signatures associated with sub-Rayleigh and supershear ruptures are investigated using the laboratory earthquake experiment originally developed by Rosakis and co-workers (Xia et al., 2004, 2005a; Lu et al., 2007; Rosakis et al., 2007). Heterodyne laser interferometers enable continuous, high-bandwidth measurements of fault-normal (FN), fault-parallel (FP), and vertical (V) particle velocity ``ground motion" records at discrete locations on the surface of a Homalite-100 test specimen as a sub-Rayleigh or a supershear rupture sweeps along the frictional fault. Photoelastic interference fringes, acquired using high-speed digital photography, provide a synchronized, spatially resolved, whole field view of the advancing rupture tip and surrounding maximum shear stress field.
The first phase of experimental investigations examine and verify the ground motion signatures of supershear ruptures. Experimental results demonstrate that a shear Mach front produced by a stable supershear rupture is characterized by a dominant FP velocity component. The situation is shown to reverse in the sub-Rayleigh rupture speed regime whereby the FN particle velocity component dominates the ground motion record. Additional distinguishing particle velocity signatures, consistent with theoretical and numerical predictions, and repeatedly observed in experimental records are, (1) a pronounced peak in the FP velocity record induced by the leading dilatational field, which sweeps the measurement station in advance of the shear Mach front, and (2) a pronounced velocity swing in the FN record associated with the arrival of a trailing Rayleigh sub-Rayleigh (secondary) rupture, which follows the arrival of the shear Mach front. Analysis of the particle velocity records also confirms 2D steady-state theoretical predictions pertaining to the separation, attenuation, and radiation partitioning of the shear and dilatational portions of the rupture velocity field components.
The second phase of our experimental investigations re-examine the 2002, Mw7.9, Denali fault earthquake and the remarkable set of near-source ground motion records obtained at (PS10), located approximately 85 km east of the epicenter and just 3 km north of the fault along the Alaska pipeline. Motivated by the analysis and interpretation of these records by (Ellsworth et al., 2004; Dunham and Archuleta, 2004, 2005), we attempt to mimic the Denali strike-slip rupture scenario and replicate the PS10 ground motion signatures using a laboratory earthquake experiment. The experiments feature a left-to-right (west-to-east) propagating right lateral rupture within a Homalite-100 test specimen with particle velocity data collected at a near-field station situated just above (north of) the fault. Both sub-Rayleigh and supershear laboratory earthquake experiments are conducted using the Denali PS10 configuration in order to compare and contrast the resulting particle velocity signatures. Supershear laboratory records capture all of the prominent features displayed within the PS10 ground motion records. Noted velocity signatures are correlated to the location of the rupture fronts and their noted arrival times in the synchronized photoelastic image sequence. Scaling relationships are also presented which transform the laboratory records through six orders of magnitude in time, to match the scale of the PS10 ground motion records. The strong correlation between the scaled experimental records and the actual PS10 ground motion records support the hypothesis that the Denali strike-slip fault exhibited a supershear burst.
Finally, we present a 2D steady state, stress-velocity formulation that relates the FP and FN particle velocity records measured close to the fault, to the evolution of the stress tensor at the same location. A locally steady-state condition is assumed within a restricted time interval in order to invoke these relationships and estimate the dynamic stresses, σxx(t) and τ(t), at the near-fault station. Dynamic stress measurements enable a new class of friction investigations using the laboratory earthquake configuration. Experimental findings are presented, which capture the temporal and spatial distributions of σxx and τ, evolution of the dynamic friction coefficient, and velocity weakening behavior of a supershear slip-pulse.</p