New insights into the formation and modification of carbonate-bearing minerals and methane gas in geological systems using multiply substituted isotopologues

This thesis describes the use of multiply-substituted stable isotopologues of carbonate minerals and methane gas to better understand how these environmentally significant minerals and gases form and are modified throughout their geological histories. Stable isotopes have a long tradition in earth science as a tool for providing quantitative constraints on how molecules, in or on the earth, formed in both the present and past. Nearly all studies, until recently, have only measured the bulk concentrations of stable isotopes in a phase or species. However, the abundance of various isotopologues within a phase, for example the concentration of isotopologues with multiple rare isotopes (multiply substituted or 'clumped' isotopologues) also carries potentially useful information. Specifically, the abundances of clumped isotopologues in an equilibrated system are a function of temperature and thus knowledge of their abundances can be used to calculate a sample’s formation temperature. In this thesis, measurements of clumped isotopologues are made on both carbonate-bearing minerals and methane gas in order to better constrain the environmental and geological histories of various samples.

Clumped-isotope-based measurements of ancient carbonate-bearing minerals, including apatites, have opened up paleotemperature reconstructions to a variety of systems and time periods. However, a critical issue when using clumped-isotope based measurements to reconstruct ancient mineral formation temperatures is whether the samples being measured have faithfully recorded their original internal isotopic distributions. These original distributions can be altered, for example, by diffusion of atoms in the mineral lattice or through diagenetic reactions. Understanding these processes quantitatively is critical for the use of clumped isotopes to reconstruct past temperatures, quantify diagenesis, and calculate time-temperature burial histories of carbonate minerals. In order to help orient this part of the thesis, Chapter 2 provides a broad overview and history of clumped-isotope based measurements in carbonate minerals.

In Chapter 3, the effects of elevated temperatures on a sample’s clumped-isotope composition are probed in both natural and experimental apatites (which contain structural carbonate groups) and calcites. A quantitative model is created that is calibrated by the experiments and consistent with the natural samples. The model allows for calculations of the change in a sample’s clumped isotope abundances as a function of any time-temperature history.

In Chapter 4, the effects of diagenesis on the stable isotopic compositions of apatites are explored on samples from a variety of sedimentary phosphorite deposits. Clumped isotope temperatures and bulk isotopic measurements from carbonate and phosphate groups are compared for all samples. These results demonstrate that samples have experienced isotopic exchange of oxygen atoms in both the carbonate and phosphate groups. A kinetic model is developed that allows for the calculation of the amount of diagenesis each sample has experienced and yields insight into the physical and chemical processes of diagenesis.

The thesis then switches gear and turns its attention to clumped isotope measurements of methane. Methane is critical greenhouse gas, energy resource, and microbial metabolic product and substrate. Despite its importance both environmentally and economically, much about methane’s formational mechanisms and the relative sources of methane to various environments remains poorly constrained. In order to add new constraints to our understanding of the formation of methane in nature, I describe the development and application of methane clumped isotope measurements to environmental deposits of methane. To help orient the reader, a brief overview of the formation of methane in both high and low temperature settings is given in Chapter 5.

In Chapter 6, a method for the measurement of methane clumped isotopologues via mass spectrometry is described. This chapter demonstrates that the measurement is precise and accurate. Additionally, the measurement is calibrated experimentally such that measurements of methane clumped isotope abundances can be converted into equivalent formational temperatures. This study represents the first time that methane clumped isotope abundances have been measured at useful precisions.

In Chapter 7, the methane clumped isotope method is applied to natural samples from a variety of settings. These settings include thermogenic gases formed and reservoired in shales, migrated thermogenic gases, biogenic gases, mixed biogenic and thermogenic gas deposits, and experimentally generated gases. In all cases, calculated clumped isotope temperatures make geological sense as formation temperatures or mixtures of high and low temperature gases. Based on these observations, we propose that the clumped isotope temperature of an unmixed gas represents its formation temperature — this was neither an obvious nor expected result and has important implications for how methane forms in nature. Additionally, these results demonstrate that methane-clumped isotope compositions provided valuable additional constraints to studying natural methane deposits.

Some constructions, related to noncommutative tori; Fredholm modules and the Beilinson-Bloch regulator

A noncommutative 2-torus is one of the main toy models of noncommutative geometry, and a noncommutative n-torus is a straightforward generalization of it. In 1980, Pimsner and Voiculescu in [17] described a 6-term exact sequence, which allows for the computation of the K-theory of noncommutative tori. It follows that both even and odd K-groups of n-dimensional noncommutative tori are free abelian groups on 2^n-1 generators. In 1981, the Powers-Rieffel projector was described [19], which, together with the class of identity, generates the even K-theory of noncommutative 2-tori. In 1984, Elliott [10] computed trace and Chern character on these K-groups. According to Rieffel [20], the odd K-theory of a noncommutative n-torus coincides with the group of connected components of the elements of the algebra. In particular, generators of K-theory can be chosen to be invertible elements of the algebra. In Chapter 1, we derive an explicit formula for the First nontrivial generator of the odd K-theory of noncommutative tori. This gives the full set of generators for the odd K-theory of noncommutative 3-tori and 4-tori.

In Chapter 2, we apply the graded-commutative framework of differential geometry to the polynomial subalgebra of the noncommutative torus algebra. We use the framework of differential geometry described in [27], [14], [25], [26]. In order to apply this framework to noncommutative torus, the notion of the graded-commutative algebra has to be generalized: the "signs" should be allowed to take values in U(1), rather than just {-1,1}. Such generalization is well-known (see, e.g., [8] in the context of linear algebra). We reformulate relevant results of [27], [14], [25], [26] using this extended notion of sign. We show how this framework can be used to construct differential operators, differential forms, and jet spaces on noncommutative tori. Then, we compare the constructed differential forms to the ones, obtained from the spectral triple of the noncommutative torus. Sections 2.1-2.3 recall the basic notions from [27], [14], [25], [26], with the required change of the notion of "sign". In Section 2.4, we apply these notions to the polynomial subalgebra of the noncommutative torus algebra. This polynomial subalgebra is similar to a free graded-commutative algebra. We show that, when restricted to the polynomial subalgebra, Connes construction of differential forms gives the same answer as the one obtained from the graded-commutative differential geometry. One may try to extend these notions to the smooth noncommutative torus algebra, but this was not done in this work.

A reconstruction of the Beilinson-Bloch regulator (for curves) via Fredholm modules was given by Eugene Ha in [12]. However, the proof in [12] contains a critical gap; in Chapter 3, we close this gap. More specifically, we do this by obtaining some technical results, and by proving Property 4 of Section 3.7 (see Theorem 3.9.4), which implies that such reformulation is, indeed, possible. The main motivation for this reformulation is the longer-term goal of finding possible analogs of the second K-group (in the context of algebraic geometry and K-theory of rings) and of the regulators for noncommutative spaces. This work should be seen as a necessary preliminary step for that purpose.

For the convenience of the reader, we also give a short description of the results from [12], as well as some background material on central extensions and Connes-Karoubi character.

Efficiency and inefficiency in the operation of the Bureau of Power and Light of Los Angeles, California

In work of this nature it is advisable to state definitely the problem attempted in order that the reader may have a clear understanding of the object of the work undertaken. The problem involved is to determine the efficiency and inefficiency in the operation of the Bureau of Power and Light of Los Angeles, California, as it exists at the present time. This will be more on the order of a government investigation than a purely engineering thesis. An engineering thesis consists or reports based on experiments and tests, etc., while the present undertaking will consist of investigation of the facts concerning the organization, operation and conduct of the business of the Bureau of Power and Light. The facts presented were obtained from several sources: (1) the writer's knowledge of the business; (2) books written on municipal ownership; (3) reports published by the Bureau, and (4) personal interviews with men connected with the organization. I have endeavored to draw conclusions from the facts thus obtained, as to the present status of the Bureau of Power and Light.

The Molecular Basis of Lysine Acetylation: Addition, Removal, and Recognition

Acetyltransferases and deacetylases catalyze the addition and removal, respectively, of acetyl groups to the epsilon-amino group of protein lysine residues. This modification can affect the function of a protein through several means, including the recruitment of specific binding partners called acetyl-lysine readers. Acetyltransferases, deacetylases, and acetyl-lysine readers have emerged as crucial regulators of biological processes and prominent targets for the treatment of human disease. This work describes a combination of structural, biochemical, biophysical, cell-biological, and organismal studies undertaken on a set of proteins that cumulatively include all steps of the acetylation process: the acetyltransferase MEC-17, the deacetylase SIRT1, and the acetyl-lysine reader DPF2. Tubulin acetylation by MEC-17 is associated with stable, long-lived microtubule structures. We determined the crystal structure of the catalytic domain of human MEC-17 in complex with the cofactor acetyl-CoA. The structure in combination with an extensive enzymatic analysis of MEC-17 mutants identified residues for cofactor and substrate recognition and activity. A large, evolutionarily conserved hydrophobic surface patch distal to the active site was shown to be necessary for catalysis, suggesting that specificity is achieved by interactions with the alpha-tubulin substrate that extend outside of the modified surface loop. Experiments in C. elegans showed that while MEC-17 is required for touch sensitivity, MEC-17 enzymatic activity is dispensible for this behavior. SIRT1 deacetylates a wide range of substrates, including p53, NF-kappaB, FOXO transcription factors, and PGC-1-alpha, with roles in cellular processes ranging from energy metabolism to cell survival. SIRT1 activity is uniquely controlled by a C-terminal regulatory segment (CTR). Here we present crystal structures of the catalytic domain of human SIRT1 in complex with the CTR in an apo form and in complex with a cofactor and a pseudo-substrate peptide. The catalytic domain adopts the canonical sirtuin fold. The CTR forms a beta-hairpin structure that complements the beta-sheet of the NAD^+-binding domain, covering an essentially invariant, hydrophobic surface. A comparison of the apo and cofactor bound structures revealed conformational changes throughout catalysis, including a rotation of a smaller subdomain with respect to the larger NAD^+-binding subdomain. A biochemical analysis identified key residues in the active site, an inhibitory role for the CTR, and distinct structural features of the CTR that mediate binding and inhibition of the SIRT1 catalytic domain. DPF2 represses myeloid differentiation in acute myelogenous leukemia. Finally, we solved the crystal structure of the tandem PHD domain of human DPF2. We showed that DPF2 preferentially binds H3 tail peptides acetylated at Lys14, and binds H4 tail peptides with no preference for acetylation state. Through a structural and mutational analysis we identify the molecular basis of histone recognition. We propose a model for the role of DPF2 in AML and identify the DPF2 tandem PHD finger domain as a promising novel target for anti-leukemia therapeutics.