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Études in Homotopical Thinking: F₁-geometry, Concurrent Computing, and Motivic Measures
Get PDFThis thesis weaves together three papers, each of which provides a use of homotopical intuition in a different field of mathematics. The first applies it to the study of various models of F₁-geometry, focusing mainly on the Bost-Connes algebra. The second endeavors to compare two homotopical models for concurrent computing before introducing a new one as well. Finally, the last paper provides a construction for obtaining derived motivic measures from an abstract six functors formalism and, in particular, applies this idea to obtain a lift of the Gillet-Soulé motivic measure
Expanding the Scope of Metalloprotein Families and Substrate Classes in New-to-Nature Reactions
Get PDFHeme proteins, in particular cytochromes P450, have been extensively used in biocatalytic applications due to their high degree of regio-, chemo-, and stereoselectivity in oxene-transfer reactions. In 2013, it was shown for the first time that engineered heme proteins can also catalyze analogous carbene- and nitrene-transfer reactions. Research in this field has since grown dramatically, with emphasis on developing new heme protein variants to increase the scope of biotransformations accessible through these new transfer reactions. This thesis details the expansion of these new-to-nature carbene and nitrene-transfer reactions to include new substrate classes previously unexplored with iron-porphyrin proteins, the use of non-heme metalloproteins for these transformations, and steps toward improving the robustness of the new-to-nature biocatalytic platform. Chapter 1 introduces the steps the field of biocatalysis has taken toward engineering enzymes with new catalytic functions and the process by which these activities are discovered and enhanced. Chapter 2 details the discovery and engineering of heme proteins which catalyze the stereodivergent cyclopropanation of unactivated and electron-deficient alkenes via carbene transfer, expanding the substrate classes beyond styrenyl alkenes. Chapter 3 shows the development of engineered variants of a heme protein (Rhodothermus marinus nitric oxide dioxygenase) for the diastereodivergent synthesis of cyclopropanes functionalized with a pinacolborane moiety, enabling product diversification through standard cross-coupling reactions. In Chapter 4, a collection of non-heme metalloproteins is curated, and a non-heme iron enzyme (Pseudomonas savastanoi ethylene-forming enzyme) is shown to be both amenable to directed evolution and non-native ligand substitution to enhance its nitrene-transfer activity. Chapter 5 describes the expansion of sequence space targeted for screening in the serine-ligated cytochrome P411 from Bacillus megaterium (P411BM3) biocatalytic platform to enhance the mutational robustness of these remarkable enzymes. Overall, this work provides a framework for bringing model new-to-nature reactions to their full potential in synthetic biocatalytic reactions.</p
Mathematical Models of Trading
Get PDFThis thesis presents a mathematical framework to model trading of financial assets on an exchange. The interaction between agents on the exchange is modeled as the Nash equilibrium of a demand schedule auction. The submission of demand schedules in the auction is meant to proxy for the submission of limit and market orders on an exchange. Chapter 1 considers this auction in a one-period setting, highlighting the importance of noisy flow for obtaining a unique Nash equilibrium.
Chapter 2 is the core of the thesis and considers the auction in a continuous time setting. Here the agents trading on the exchange have quadratic-type preferences, and in equilibrium they must clear an exogenously specified stream of market orders. Chapter 3 considers alternative and more realistic dynamics for the exogenous market orders. Chapter 4 endogenizes the market orders by considering an agent executing orders on behalf of noisy clients.. Chapter 5 considers the same model as in Chapter 2, except with a consumption based utility function for each agent.</p
Genetically Encoded 3,4-Ethylenedioxythiophene (EDOT) Functionality for Fabrication of Protein-Based Conductive Polymers
Get PDFGenetic code expansion provides powerful strategies to improve the properties of protein-based materials. One novel application of this technique is to genetically incorporate an electroactive functional group into proteins, which can be subsequently polymerized into conductive polymers, enabling fabrication of various protein–conductive polymer hybrids that are widely applicable in bioelectronics. To this end, we developed a technique to incorporate an amino acid bearing 3,4-ethylenedioxythiophene (EDOT), the monomer precursor of a well-known conductive polymer PEDOT.
In Chapter 1, we review the basics of protein-based materials and genetic code expansion technology. We also highlight some examples where genetic code expansion was used for the development of protein-based materials. Finally, we discuss applications of protein and peptide-based materials in bioelectronics.
In Chapter 2, we describe our effort to incorporate an amino acid bearing EDOT group (EDOT-Ala) designed as an analogue of aromatic canonical amino acids. We synthesized EDOT-Ala in three steps of organic reaction, and evaluated the activity of known aminoacyl-tRNA synthetase (aaRS) variants for EDOT-Ala. In addition, we performed evolution of aaRS for EDOT-Ala using two different evolution techniques: cell viability- based approach and phage-assisted approach. Although the evolution experiment did not yield an aaRS variant that can incorporate EDOT-Ala, the results presented in this chapter provide valuable information for engineering of aaRS and incorporation of non-canonical amino acids (ncAA) with bulky functional groups.
In Chapter 3, we describe the incorporation of another EDOT-functionalized amino acid (EDOT-Lys) designed as an analogue of a canonical amino acid pyrrolysine (Pyl). When we co-expressed a GFP reporter and a mutant pyrrolysyl-tRNA synthetase (PylRS) in E. coli in the presence of EDOT-Lys, the cells exhibited strong fluorescence as an indication of successful incorporation of EDOT-Lys into GFP. We further confirmed the incorporation using MALDI-TOF mass spectrometry.
In Chapter 4, we describe the electropolymerization of a model protein XTEN that carries genetically incorporated EDOT-Lys (XTEN-E49am). We performed electropolymerization of XTEN-E49am in the presence of a self-doping EDOT monomer (EDOT-S) by cyclic voltammetry. The solution formed dark blue solids immediately after the potential cycles. The composition of the product was determined by FT-IR spectroscopy, suggesting that one protein is found per 12.5 monomer units of PEDOT. In addition, we investigated the effect of amino acids located adjacent to EDOT-Lys. Although the presence of cysteine (Cys), lysine (Lys), methionine (Met), arginine (Arg), and tryptophan (Trp) located adjacent to EDOT-Lys had an impact on the electropolymerization of model peptides, XTEN proteins carrying these adjacent residues (XTEN-E49am-G50Z; Z = Cys, Lys, Met, Arg, Trp) were electropolymerized with EDOT-S without noticeable effect from these adjacent residues, indicating that the EDOT-Lys residues in proteins undergo electropolymerization with EDOT-S in different chemical environments.
In Chapter 5, we describe the oxidative chemical polymerization of XTEN proteins and model peptides. When XTEN-E49am was polymerized with EDOT-S by addition of ammonium persulfate (APS) and iron(III) chloride (FeCl3), the solution yielded dark blue solids. To evaluate the reactivity of the EDOT-Lys residue in the protein, we reacted the protein with an end-capped EDOT derivative (EDOT-cap). MALDI-TOF mass spectrometry revealed the appearance of new peaks corresponding to the addition of one or two EDOT-caps to the protein, suggesting that EDOT-Lys residue in the protein can react with EDOT derivatives. We also investigated the effect of adjacent amino acids using a series of model peptides. In polymerization using APS without FeCl3 catalyst, peptides carrying basic amino acids (His, Lys, Arg) adjacent to EDOT-Lys showed enhanced polymerization compared to the ones carrying neutral and acidic adjacent residues. All the tested peptides polymerized well when FeCl3 was added as a catalyst. The results presented in this chapter provide valuable insights into synthesis of protein–PEDOT conjugates via oxidative chemical polymerization.</p
Attention, Strategy, and the Human Mind
Get PDFThe current dissertation chapters try to discover the role of visual attention in decision making from three different perspectives: 1) how attention bias affects strategic decision makings, 2) how to model eye movement data to better understand strategic decisions, 3) how to manipulate simple choices through visual saliency.
The second chapter introduces a series of novel image games, where players need to match, hide, or seek against other players. We apply a pure computational way: the state-of-art visual saliency algorithm, Saliency Attentive Map (SAM) to measure visual saliency. We find that visual saliency can predict strategic behaviors well. The concentration of salience is correlated with the rate of matching when players are both trying to match location choices (r=.64). In hider-seeker games, all players choose salient locations more often than predicted in equilibrium, creating a ``seeker’s advantage'' (seekers win 9\% of games rather than the 7\% predicted in equilibrium). The 9\% win rate is robust for paying higher stakes and using a between-subjects design. Salience-choice relations are consistent with cognitive hierarchy and level-k models in which strategically naive level 0's are biased toward salience, and higher-level types are not directly biased toward salience, but choose salient locations because they believe lower-level types do. Other links between salience as understood in psychology and hypothesized in economics are suggested.
The third chapter is a continuation of the second chapter, but with a different emphasis. The third chapter proposes a way to dynamically model gaze transitional data in games utilizing a class of machine learning model: hidden markov models(HMM). The HMM model reveals how the attentional bias affects strategies on different time point. Besides, this model well connects to the k level behavioral method and can make novel predictions on strategic levels. With further containing the fixation duration data, we developed a continuous-time hidden Markov model (cgtHMM), which can be used to predict how exactly time pressure changes choices and the seeker’s advantage.
Distinct from the other two, chapter four aims at manipulating binary choice outcomes through the change of visual saliency distribution under SAM. We design a value-based choice paradigm where both the reward property and the attention property are well separated and controlled. The experimental results indicate that visual saliency can enhance the choice correction rates when the more rewarding outcome is also labeled salient. It can also shorten the decision time needed. Such a result can be explained by a saliency-enhanced rational inattention model by incorporating attention factors in the traditional RI model.</p
Finite Temperature Simulations of Strongly Correlated Systems
Get PDFThis thesis describes several topics related to finite temperature studies of strongly correlated systems: finite temperature density matrix embedding theory (FT-DMET), finite temperature metal-insulator transition, and quantum algorithms including quantum imaginary time evolution (QITE), quantum Lanczos (QLanczos), and quantum minimally entangled typical thermal states (QMETTS) algorithms.
While the absolute zero temperature is not reachable, studies of physical and chemical problems at finite temperatures, especially at low temperature, is essential for understanding the quantum behaviors of materials in realistic conditions. Here we define low temperature as the temperature regime where the quantum effect is not largely dissipated due to thermal fluctuation. Treatment of systems at low temperature is specially difficult compared to both high temperature - where classical approximation can be applied - and zero temperature where only the ground state is required to describe the system of interest. FT-DMET is a wavefunction-based embedding scheme which can handle finite temperature simulations of a variety of strongly correlated problems. The "high-level in low-level" framework enables FT-DMET to tackle large bulk sizes and capture the majority of the entanglement at the same time. FT-DMET formulations and implementation details for both model systems and ab initio problems are provided in Chapter 2 and Chapter 3.
Metal-insulator transition is a common but important phase transition in many strongly correlated materials. The widely accepted scheme to distinguish an insulator from a metal is band structure theory based on a single-particle picture. However, insulating phases caused by disorder or strong correlation cannot be explained merely with the band structure. In Chapter 4, we demonstrate that electron locality/mobility is a more general criteria to detect metal-insulator transition. We further introduce complex polarization as the order parameter to reflect the electron locality/mobility and provide a formalism based on thermofield theory to evaluate the complex polarization at finite temperature.
Quantum algorithms are designed to perform simulations on a quantum device. The infrastructure of a quantum processing unit (QPU) utilizes the superposition property of quantum bits (qubits), and thus can potentially outplay the classical simulations in computational scaling for certain problems. In Chapter 5, we introduce the QITE algorithm, which can be applied to quantum simulations of both ground state and finite temperature problems. We further introduce a subspace method, QLanczos algorithm, and a a finite temperature quantum algorithm, QMETTS, where QITE is used as a building block for the two algorithms. We demonstrate above quantum algorithms with simulations on both classical computers and quantum computers.</p
Mechanism and Scaling of Eukaryotic Transcription Activation
Get PDFTranscription activation is a universal process by which living cells adapt. Decades of work in this field have produced an intelligible paradigm of transcription activation that provides fundamental insights into its underlying molecular mechanisms. This thesis attempts to extend such paradigm to explain how transcription activation can be implemented across the diversity of molecular environments found in eukaryotic nuclei. Specifically, this diversity calls for an explanation of how this process scales throughout a range of genome sizes that spans five orders of magnitude, and of how to think about this subject in the increasingly relevant context of liquid-liquid phase-separation. We leverage data from RNA-seq, smFISH, growth-rate, fluorescence microscopy, computer simulations and literature to identify an appropriate and useful level of abstraction in which to grow our current paradigm. We propose scaling and phase-separation, two seemingly disparate aspects of transcription, are explained and intrinsically linked by a novel molecular state in which multiple RNA polymerases can bind the transcription complex. We provide support and rationale for this addition to the transcription model, and generate testable hypotheses that may further clarify the mechanism and evolution of eukaryotic transcription activation.</p
Guiding Self-Organization in Active Matter with Spatiotemporal Boundary Conditions
Get PDFIn this thesis, I demonstrate that self-organized structures and forces can be guided by modulating the interactions between force-generating molecules in space and time. The physics of self-organizing systems is an open frontier. We do not have a complete set of principles that can describe how a dynamic structure forms based on the non-equilibrium dynamics of its constituent components. Yet, living systems appear to depend on some set of rules of self-organization in order to reliably carry out their mechanical functions. Force-generating, active, molecules in the form of motor proteins and filamentous polymers are responsible for performing fundamental tasks in living matter, such as locomotion and division. While it is known that the regulation of motor-filament interactions is necessary to achieve the dynamic structures that drive movement and propagation, the role of spatial and temporal patterning in self-organizing systems has not been explored. I design a artificial system of purified molecules where the interactions between motors and filaments are toggled with light. By patterning molecular interactions in space and time, I show that it is possible to localize the formation of spherically symmetric asters, which can be moved, merged, and used to generate advective fluid flows. The ability to pattern molecular interactions in space and time offers a new perspective in the search for principles of active self-organization. Spatial and temporal control makes it possible to start distilling how the interactions between active molecules determine the mesoscopic behaviors of self-organized structures. These rules ultimately govern the physics of living matter and may eventually be harnessed to build new materials and cell-like machines.</p
How to Beat Diffusion: Explorations of Energetics and Spatial Relationships in Microbial Ecosystems
Get PDFThis thesis investigates four microbial systems, with a particular focus for how spatial considerations shape the behavior and evolution of microorganisms. After a general introduction in Chapter 1, Chapter 2 presents the results of experiments demonstrating how cellular activity varies through space within an anode-reducing biofilm. Chapter 3 presents a comprehensive comparative genomic analysis of all known marine anaerobic methanotrophic archaea, supporting the notion that these organisms share many energetic similarities with the anode reducing organisms in Chapter 2. These are interpreted as specific adaptations to life in highly structured microbial communities. Chapter 4 describes the enrichment and characterization of a new member of the purple sulfur bacteria, and the adaptations that may improve substrate acquisition beyond the normal limitations of diffusion. Chapter 5 describes the convergent evolution of novel Complex I gene clusters that have incorporated new proton pumping subunits, and the modifications made to the protein structure to facilitate the incorporation of these new subunits into the quaternary structure of the complex.</p
From Metasurfaces to Compact Optical Metasystems
Get PDFOptical metasurfaces are a class of ultra-thin diffractive optical elements, which can control different properties of light such as amplitude, phase, polarization and direction at various wavelengths. The compatibility of optical metasurfaces with standard micro- and nano-fabrication processes makes them highly-suitable for realization of compact and planar form optical devices and systems. In addition, optical metasurfaces have achieved unique and unprecedented functionalities not possible by conventional diffractive or refractive optical elements. In this thesis, after a short review on the history and state of the art optical metasurfaces, I will discuss the systems consisting of optical metasurfaces, called optical meta-systems, which allow for implementations of complicated optical functions, such as wide field of view imaging and projection, tunable cameras, retro-reflection, phase-imaging, multi-color imaging, etc. Thereafter, the concept of folded metasurface optics is introduced and a compact folded metasurface spectrometer is showcased to demonstrate how the folded meta-systems can be designed, fabricated and practically utilized for real-life applications. Furthermore, different approaches for implementation of miniaturized hyperspectral imagers are investigated, among which the folded metasurface optics and a computational scheme using a random metasurface mask will be highlighted. Other potentials of optical metasurfaces achieved by the employment of optimization techniques to improve their multi-functional performances, as well as example applications in realizing optical vortex cornographs are studied. Finally, I will conclude the dissertation with an outlook on further applications of optical metasurfaces, where they can surpass the performance of current optical devices and systems and what limitations are still to be overcome before we can expect their wide-spread applications in our daily life.</p