Functional genomic studies of the structure and regulation of eukaryotic transcriptomes

The main focus of this thesis is the use of high-throughput sequencing technologies in functional genomics (in particular in the form of ChIP-seq, chromatin immunoprecipitation coupled with sequencing, and RNA-seq) and the study of the structure and regulation of transcriptomes. Some parts of it are of a more methodological nature while others describe the application of these functional genomic tools to address various biological problems. A significant part of the research presented here was conducted as part of the ENCODE (ENCyclopedia Of DNA Elements) Project.

The first part of the thesis focuses on the structure and diversity of the human transcriptome. Chapter 1 contains an analysis of the diversity of the human polyadenylated transcriptome based on RNA-seq data generated for the ENCODE Project. Chapter 2 presents a simulation-based examination of the performance of some of the most popular computational tools used to assemble and quantify transcriptomes. Chapter 3 includes a study of variation in gene expression, alternative splicing and allelic expression bias on the single-cell level and on a genome-wide scale in human lymphoblastoid cells; it also brings forward a number of critical to the practice of single-cell RNA-seq measurements methodological considerations.

The second part presents several studies applying functional genomic tools to the study of the regulatory biology of organellar genomes, primarily in mammals but also in plants. Chapter 5 contains an analysis of the occupancy of the human mitochondrial genome by TFAM, an important structural and regulatory protein in mitochondria, using ChIP-seq. In Chapter 6, the mitochondrial DNA occupancy of the TFB2M transcriptional regulator, the MTERF termination factor, and the mitochondrial RNA and DNA polymerases is characterized. Chapter 7 consists of an investigation into the curious phenomenon of the physical association of nuclear transcription factors with mitochondrial DNA, based on the diverse collections of transcription factor ChIP-seq datasets generated by the ENCODE, mouseENCODE and modENCODE consortia. In Chapter 8 this line of research is further extended to existing publicly available ChIP-seq datasets in plants and their mitochondrial and plastid genomes.

The third part is dedicated to the analytical and experimental practice of ChIP-seq. As part of the ENCODE Project, a set of metrics for assessing the quality of ChIP-seq experiments was developed, and the results of this activity are presented in Chapter 9. These metrics were later used to carry out a global analysis of ChIP-seq quality in the published literature (Chapter 10). In Chapter 11, the development and initial application of an automated robotic ChIP-seq (in which these metrics also played a major role) is presented.

The fourth part presents the results of some additional projects the author has been involved in, including the study of the role of the Piwi protein in the transcriptional regulation of transposon expression in Drosophila (Chapter 12), and the use of single-cell RNA-seq to characterize the heterogeneity of gene expression during cellular reprogramming (Chapter 13).

The last part of the thesis provides a review of the results of the ENCODE Project and the interpretation of the complexity of the biochemical activity exhibited by mammalian genomes that they have revealed (Chapters 15 and 16), an overview of the expected in the near future technical developments and their impact on the field of functional genomics (Chapter 14), and a discussion of some so far insufficiently explored research areas, the future study of which will, in the opinion of the author, provide deep insights into many fundamental but not yet completely answered questions about the transcriptional biology of eukaryotes and its regulation.

Density functional theory embedding for correlated wavefunctions

Methods that exploit the intrinsic locality of molecular interactions show significant promise in making tractable the electronic structure calculation of large-scale systems. In particular, embedded density functional theory (e-DFT) offers a formally exact approach to electronic structure calculations in which the interactions between subsystems are evaluated in terms of their electronic density. In the following dissertation, methodological advances of embedded density functional theory are described, numerically tested, and applied to real chemical systems.

First, we describe an e-DFT protocol in which the non-additive kinetic energy component of the embedding potential is treated exactly. Then, we present a general implementation of the exact calculation of the non-additive kinetic potential (NAKP) and apply it to molecular systems. We demonstrate that the implementation using the exact NAKP is in excellent agreement with reference Kohn-Sham calculations, whereas the approximate functionals lead to qualitative failures in the calculated energies and equilibrium structures.

Next, we introduce density-embedding techniques to enable the accurate and stable calculation of correlated wavefunction (CW) in complex environments. Embedding potentials calculated using e-DFT introduce the effect of the environment on a subsystem for CW calculations (WFT-in-DFT). We demonstrate that WFT-in-DFT calculations are in good agreement with CW calculations performed on the full complex.

We significantly improve the numerics of the algorithm by enforcing orthogonality between subsystems by introduction of a projection operator. Utilizing the projection-based embedding scheme, we rigorously analyze the sources of error in quantum embedding calculations in which an active subsystem is treated using CWs, and the remainder using density functional theory. We show that the embedding potential felt by the electrons in the active subsystem makes only a small contribution to the error of the method, whereas the error in the nonadditive exchange-correlation energy dominates. We develop an algorithm which corrects this term and demonstrate the accuracy of this corrected embedding scheme.

Advanced density functional theory methods for materials science

In this work we chiefly deal with two broad classes of problems in computational materials science, determining the doping mechanism in a semiconductor and developing an extreme condition equation of state. While solving certain aspects of these questions is well-trodden ground, both require extending the reach of existing methods to fully answer them. Here we choose to build upon the framework of density functional theory (DFT) which provides an efficient means to investigate a system from a quantum mechanics description.

Zinc Phosphide (Zn₃P₂) could be the basis for cheap and highly efficient solar cells. Its use in this regard is limited by the difficulty in n-type doping the material. In an effort to understand the mechanism behind this, the energetics and electronic structure of intrinsic point defects in zinc phosphide are studied using generalized Kohn-Sham theory and utilizing the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. Novel 'perturbation extrapolation' is utilized to extend the use of the computationally expensive HSE functional to this large-scale defect system. According to calculations, the formation energy of charged phosphorus interstitial defects are very low in n-type Zn₃P₂ and act as 'electron sinks', nullifying the desired doping and lowering the fermi-level back towards the p-type regime. Going forward, this insight provides clues to fabricating useful zinc phosphide based devices. In addition, the methodology developed for this work can be applied to further doping studies in other systems.

Accurate determination of high pressure and temperature equations of state is fundamental in a variety of fields. However, it is often very difficult to cover a wide range of temperatures and pressures in an laboratory setting. Here we develop methods to determine a multi-phase equation of state for Ta through computation. The typical means of investigating thermodynamic properties is via ’classical’ molecular dynamics where the atomic motion is calculated from Newtonian mechanics with the electronic effects abstracted away into an interatomic potential function. For our purposes, a ’first principles’ approach such as DFT is useful as a classical potential is typically valid for only a portion of the phase diagram (i.e. whatever part it has been fit to). Furthermore, for extremes of temperature and pressure quantum effects become critical to accurately capture an equation of state and are very hard to capture in even complex model potentials. This requires extending the inherently zero temperature DFT to predict the finite temperature response of the system. Statistical modelling and thermodynamic integration is used to extend our results over all phases, as well as phase-coexistence regions which are at the limits of typical DFT validity. We deliver the most comprehensive and accurate equation of state that has been done for Ta. This work also lends insights that can be applied to further equation of state work in many other materials.

A variational framework for spectral discretization of the density matrix in Kohn Sham density functional theory

Kohn-Sham density functional theory (KSDFT) is currently the main work-horse of quantum mechanical calculations in physics, chemistry, and materials science. From a mechanical engineering perspective, we are interested in studying the role of defects in the mechanical properties in materials. In real materials, defects are typically found at very small concentrations e.g., vacancies occur at parts per million, dislocation density in metals ranges from $10^{10} m^{-2}$ to $10^{15} m^{-2}$, and grain sizes vary from nanometers to micrometers in polycrystalline materials, etc. In order to model materials at realistic defect concentrations using DFT, we would need to work with system sizes beyond millions of atoms. Due to the cubic-scaling computational cost with respect to the number of atoms in conventional DFT implementations, such system sizes are unreachable. Since the early 1990s, there has been a huge interest in developing DFT implementations that have linear-scaling computational cost. A promising approach to achieving linear-scaling cost is to approximate the density matrix in KSDFT. The focus of this thesis is to provide a firm mathematical framework to study the convergence of these approximations. We reformulate the Kohn-Sham density functional theory as a nested variational problem in the density matrix, the electrostatic potential, and a field dual to the electron density. The corresponding functional is linear in the density matrix and thus amenable to spectral representation. Based on this reformulation, we introduce a new approximation scheme, called spectral binning, which does not require smoothing of the occupancy function and thus applies at arbitrarily low temperatures. We proof convergence of the approximate solutions with respect to spectral binning and with respect to an additional spatial discretization of the domain. For a standard one-dimensional benchmark problem, we present numerical experiments for which spectral binning exhibits excellent convergence characteristics and outperforms other linear-scaling methods.

Synthesis, Oxidation and Photophysics of Perfluoroborated Tetrakis(pyrophosphito)diplatinate (II) and Density Functional Theory (DFT) Study of Electrochemical CO2 Reduction by Mn Catalysts

In the first part of this thesis (Chapters I and II), the synthesis, characterization, reactivity and photophysics of per(difluoroborated) tetrakis(pyrophosphito)diplatinate(II) (Pt(POPBF₂)) are discussed. Pt(POP-BF₂) was obtained by reaction of [Pt₂(POP)₄]^4- with neat boron trifluoride diethyl etherate (BF₃·Et₂O). While Pt(POP-BF₂) and [Pt₂(POP)₄]^4- have similar structures and absorption spectra, they differ in significant ways. Firstly, as discussed in Chapter I, the former is less susceptible to oxidation, as evidenced by the reversibility of its oxidation by I2. Secondly, while the first excited triplet states (T₁) of both Pt(POP-BF₂) and [Pt₂(POP)₄]^4- exhibit long lifetimes (ca. 0.01 ms at room temperature) and substantial zero-field splitting (40 cm^-1), Pt(POP-BF₂) also has a remarkably long-lived (1.6 ns at room temperature) singlet excited state (S₁), indicating slow intersystem crossing (ISC). Fluorescence lifetime and quantum yield (QY) of Pt(POP-BF₂) were measured over a range of temperatures, providing insight into the slow ISC process. The remarkable spectroscopic and photophysical properties of Pt(POP-BF₂), both in solution and as a microcrystalline powder, form the theme of Chapter II.

In the second part of the thesis (Chapters III and IV), the electrochemical reduction of CO₂ to CO by [(L)Mn(CO)₃]^- catalysts is investigated using density functional theory (DFT). As discussed in Chapter III, the turnover frequency (TOF)-limiting step is the dehydroxylation of [(bpy)Mn(CO)₃(CO₂H)]^0/- (bpy = bipyridine) by trifluoroethanol (TFEH) to form [(bpy)Mn(CO)₄]^+/0. Because the dehydroxylation of [(bpy)Mn(CO)₃(CO₂H)]^- is faster, maximum TOF (TOF_max) is achieved at potentials sufficient to completely reduce [(bpy)Mn(CO)₃(CO₂H)]⁰ to [(bpy)Mn(CO)₃(CO₂H)]^-. Substitution of bipyridine with bipyrimidine reduces the overpotential needed, but at the expense of TOF_max. In Chapter IV, the decoration of the bipyrimidine ligand with a pendant alcohol is discussed as a strategy to increase CO₂ reduction activity. Our calculations predict that the pendant alcohol acts in concert with an external TFEH molecule, the latter acidifying the former, resulting in a ~ 80,000-fold improvement in the rate of TOF-limiting dehydroxylation of [(L)Mn(CO)₃(CO₂H)]^-.

An interesting strategy for the co-upgrading of light olefins and alkanes into heavier alkanes is the subject of Appendix B. The proposed scheme involves dimerization of the light olefin, operating in tandem with transfer hydrogenation between the olefin dimer and the light alkane. The work presented therein involved a Ta olefin dimerization catalyst and a silica-supported Ir transfer hydrogenation catalyst. Olefin dimer was formed under reaction conditions; however, this did not undergo transfer hydrogenation with the light alkane. A significant challenge is that the Ta catalyst selectively produces highly branched dimers, which are unable to undergo transfer hydrogenation.

Methods of determining the quality of water using the functional characteristics of algae

In the study of questions relating to the quality of raw water and the biological produc- tivity of water bodies algal indicators have an important place. Despite the importance of these functional indicators in determining the quality of water and the nature of the production processes as a basis for preserving the ecological equilibrium of aquatic ecosystems, their use in the system of hydrobiological methods of monitoring the quality of surface water has not received proper consideration. This paper aims to analyse the matter and the possibl use of functional algal criteria in the system for the biological monitoring of aquatic objects and also to give some results in using these criteria.

DEVELOPMENT AND APPLICATIONS OF TIME-DEPENDENT DENSITY MATRIX FUNCTIONAL THEORY

En esta tesis estudiamos las teorías sobre la Matriz Densidad Reducida (MDR) como un marco prometedor. Nos enfocamos sobre esta teorías desde dos aspectos: Primero, usamos algunos modelos sencillos hechos con dos partículas las cuales estan armónicamente confinadas como una base para ilustrar la utilidad de la matriz densidad. Para tales sistemas, usamos la MDR de un cuerpo para calcular algunas cantidades de interés tales como densidad de momentum. Posteriormente obtenemos los orbitales naturales y su número de ocupación para algunos de los modelos, y en uno de los casos expresamos la MDR de dos cuerpos de manera exacta en términos de la MDR de un cuerpo. También usamos el teorema diferencial del virial para establecer una descripción unificada de la familia entera de estos sistemas modelo en términos de la densidad. En la seguna parte cambiamos a casos fuera del equilibrio y analizamos la así llamada jerarquía BBGKY de ecuaciones para describir la evolución temporal de un sistema de muchos cuerpos en términos de sus MDRs (a todos los órdenes). Proveemos un exhaustivo estudio de los desafíos y problemas abiertos ligados a la truncación de tales jerarquías de ecuaciones para hacerlas aplicables. Restringimos nuestro análisis a la evolución acoplada de la MDR de uno y dos cuerpos, donde los efectos de correlación de alto orden estan embebidos dentro de la aproximación usada para cerrar las ecuaciones. Probamos que dentro de esta aproximación, el número de electrones y la energía total se conservan, sin importar la aproximación usada. Luego, demostramos que aplicando los esquemas de truncación de estado base para llevar los electrones a comportamientos indeseables y no físicos, tales como la violación e incluso la divergencia en la densidad electrónica local, tanto en regímenes correlacionados débiles y fuertes.

Calculations of bond dissociation energies and dipole moments in energetic materials using density-functional methods

We compare the effectiveness of six exchange/correlation functional combinations (Becke/Lee, Yang and Parr; Becke-3/Lee, Yang and Parr; Becke/Perdew-Wang 91; Becke-3/Perdew-Wang 91; Becke/Perdew 86; Becke-3/Perdew 86) for computing C-N, O-O and N-NO2 dissociation energies and dipole moments of five compounds. The studied compounds are hexabydro-1,3,5-trinitro-1,3,5-triazine (RDX), dimethylnitramine, cyanogen, nitromethane and ozone. The Becke-3/Perdew 86 in conjunction with 6-31G

Specific Interaction with Cardiolipin Triggers Functional Activation of Dynamin-Related Protein 1

Dynamin-Related Protein 1 (Drp1), a large GTPase of the dynamin superfamily, is required for mitochondrial fission in healthy and apoptotic cells. Drp1 activation is a complex process that involves translocation from the cytosol to the mitochondrial outer membrane (MOM) and assembly into rings/spirals at the MOM, leading to membrane constriction/division. Similar to dynamins, Drp1 contains GTPase (G), bundle signaling element (BSE) and stalk domains. However, instead of the lipid-interacting Pleckstrin Homology (PH) domain present in the dynamins, Drp1 contains the so-called B insert or variable domain that has been suggested to play an important role in Drp1 regulation. Different proteins have been implicated in Drp1 recruitment to the MOM, although how MOM-localized Drp1 acquires its fully functional status remains poorly understood. We found that Drp1 can interact with pure lipid bilayers enriched in the mitochondrion-specific phospholipid cardiolipin (CL). Building on our previous study, we now explore the specificity and functional consequences of this interaction. We show that a four lysine module located within the B insert of Drp1 interacts preferentially with CL over other anionic lipids. This interaction dramatically enhances Drp1 oligomerization and assembly-stimulated GTP hydrolysis. Our results add significantly to a growing body of evidence indicating that CL is an important regulator of many essential mitochondrial functions.

Density-potential mapping in the standard and quantum electrodynamical time-dependent density functional theory

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