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Development of RNA-Based Genetic Control Elements for Predictable Tuning of Protein Expression in Yeast
Get PDFThe proper functioning of many biological processes and synthetic genetic networks depends on the precise tuning of expression levels of key protein components. With growing interests in eukaryotic hosts and the increasing complexity of networks in synthetic biology, there is a need for the expansion of the genetic toolbox, particularly for the bioprocessing and biosynthesis applications in the yeast Saccharomyces cerevisiae. The available control elements in yeast generally focus on the regulation of transcription through alternative promoter systems. Synthetic RNA-based control elements placed in the untranslated regions (UTRs) of transcripts have the ability to regulate the posttranscriptional mechanisms of translation initiation and transcript stability. Such posttranscriptional elements have the added advantage of being coupled to any promoter for enhanced control strategies.
Two types of posttranscriptional elements were examined in this thesis. The first type is a class of RNA hairpins baring AGNN tetraloops that are cleaved by the S. cerevisiae RNase III enzyme Rnt1p. By locating these hairpins in the 3’ UTR of a transcript, the endonucleolytic cleavage due to Rnt1p activity resulted in the rapid degradation of the transcript. We developed two libraries of RNA hairpins based on the randomization of critical regions in Rnt1p substrates that affect the enzyme’s ability to associate and/or cleave the hairpin. The modulation of the strength of binding and cleavage by Rnt1p resulted in changes in the steady-state transcript levels and thus protein levels. Through integration of an aptamer into the stem of an Rnt1p hairpin, we were able to develop a riboswitch based upon the direction inhibition of Rnt1p cleavage through association of the ligand in the sites of cleavage. The second type of posttranscriptional elements examined is the placement of internal ribosome entry sites (IRESes) in the 5’ UTR that initiate translation independent of the 5’ cap through direct interaction with the ribosomal machinery. We propose that the activity of small sequential IRESes can be tuned through varying the complementarity with the 18S ribosomal RNA (rRNA) to advance the creation of yeast multicistronic vectors. The application of Rnt1p hairpins and IRESes provide a key tool in synthetic biology for the construction of complex genetic networks in yeast where the predictable tuning of gene expression is necessitated.</p
Discrete Mechanics and Optimal Control for Space Trajectory Design
Get PDFSpace trajectory design is often achieved through a combination of dynamical systems theory and optimal control. The union of trajectory design techniques utilizing invariant manifolds of the planar circular restricted three-body problem and the optimal control scheme Discrete Mechanics and Optimal Control (DMOC) facilitates the design of low-energy trajectories in the N-body problem. In particular, DMOC is used to optimize a trajectory from the Earth to the Moon in the 4-body problem, removing the mid-course change in velocity usually necessary for such a trajectory while still exploiting the structure from the invariant manifolds.
This thesis also focuses on how to adapt DMOC, a method devised with a constant step size, for the highly nonlinear dynamics involved in trajectory design. Mesh refinement techniques that aim to reduce discretization errors in the solution and energy evolution and their effect on DMOC optimization are explored and compared with trajectories created using time adaptive variational integrators.
Furthermore, a time adaptive form of DMOC is developed that allows for a variable step size that is updated throughout the optimization process. Time adapted DMOC is based on a discretization of Hamilton's principle applied to the time adapted Lagrangian of the optimal control problem. Variations of the discrete action of the optimal control Lagrangian lead to discrete Euler-Lagrange equations that can be enforced as constraints for a boundary value problem. This new form of DMOC leads to the accurate and efficient solution of optimal control problems with highly nonlinear dynamics. Time adapted DMOC is tested on several space trajectory problems including the elliptical orbit transfer in the 2-body problem and the reconfiguration of a cubesat.</p
Random Matrix Recursions in Estimation, Control, and Adaptive Filtering
Get PDFThis dissertation is devoted to the study of estimation and control over systems that can be described by linear time-varying state-space models. Examples of such systems are encountered frequently in systems theory, e.g., wireless sensor networks, adaptive filtering, distributed control, etc. Recent developments in distributed catastrophe surveillance, smart transportation, and power grid control systems further motivate such a study.
While linear time-invariant systems are well-understood, there is no general theory that captures various aspects of time-varying counterparts. With little exception, tackling these problems normally boils down to studying time-varying linear or non-linear recursive matrix equations, known as Lyapunov and Riccati recursions that are notoriously hard to analyze. We employ the theory of random matrices to elucidate different facets of these recursions and answer several important questions about the performance, stability, and convergence of estimation and control over such systems.
We make two general assumptions. First, we assume that the coefficient matrices are drawn from jointly stationary matrix-valued random processes. The stationarity assumption hardly restricts the analysis since almost all cases of practical interest fall into this category. We further assume that the state vector size, n, is relatively large. The law of large numbers however guarantees fast convergence to the asymptotic results for n being as small as 10. Under these assumptions, we develop a framework capable of characterizing steady-state and transient behavior of adaptive filters and control and estimation over communication networks. This framework proves promising by successfully tackling several problems for the first time in the literature.
We first study random Lyapunov recursions and characterize their transient and steady-state behavior. Lyapunov recursions appear in several classes of adaptive filters and also as lower bounds of random Riccati recursions in distributed Kalman filtering. We then look at random Riccati recursions whose nonlinearity makes them much more complicated to study. We investigate standard recursive-least-squares (RLS) filtering and extend our analysis beyond the standard case to filtering with multiple measurements, as well as the case of intermittent measurements. Finally, we study Kalman filtering with intermittent observations, which is frequently used to model wireless sensor networks. In all of these cases we obtain interesting universal laws that depend on the structure of the problem, rather than specific model parameters. We verify the accuracy of our results through various simulations for systems with as few as 10 states.</p
The Roles of Majorization and Generalized Triangular Decomposition in Communication and Signal Processing
Get PDFSignal processing is an art that deals with the representation, transformation, and manipulation of the signals and the information they contain based on their specific features. The field of signal processing has always benefited from the interaction between theory, applications, and technologies for implementing the systems. The development of signal processing theory, in particular, relies heavily on mathematical tools including analysis, probability theory, matrix theory, and many others.
Recently, the theory of majorization, which is an extremely useful tool for deriving inequalities, was introduced to the signal processing society in the context of MIMO communication system design. This also led many researchers to develop a fundamental matrix decomposition called generalized triangular decomposition (GTD), which was general enough to include many existing matrix orthogonal decompositions as special cases.
The main contribution of this thesis is toward the use of majorization and GTD to the theory and many applications of signal processing. In particular, the focus is on developing new signal processing methods based on these mathematical tools for digital communication, data compression, and filter bank design. We revisit some classical problems and show that the theories of majorization and GTD provide a general framework for solving these problems. For many important new problems not solved earlier, they also provide elegant solutions.
The first part of the thesis focuses on transceiver design for multiple-input multiple-output (MIMO) communications. The first problem considered is the joint optimization of transceivers with linear precoders, decision feedback equalizers (DFEs), and bit allocation schemes for frequency flat MIMO channels. We show that the generalized triangular decomposition offers an optimal family of solutions to this problem. This general framework incorporates many existing designs, such as the optimal linear transceiver, the ZF-VBLAST system, and the geometric mean decomposition (GMD) transceiver, as special cases. It also predicts many novel optimal solutions that have not been observed before. We also discuss the use of each of these theoretical solutions under practical considerations. In addition to total power constraints, we also consider the transceiver optimization under individual power constraints and other linear constraints on the transmitting covariance matrix, which includes a more realistic individual power constraint on each antenna. We show the use of semi-definite programming (SDP), and the theory of majorization again provides a general framework for optimizing the linear transceivers as well as the DFE transceivers. The transceiver design for frequency selective MIMO channels is then considered. Block diagonal GMD (BD-GMD), which is a special instance of GTD with block diagonal structure in one of the semi-unitary matrices, is used to design transceivers that have many desirable properties in both performance and computation.
The second part of the thesis focuses on signal processing algorithms for data compressions and filter bank designs. We revisit the classical transform coding problem (for optimizing the theoretical coding gain in the high bit rate regime) from the view point of GTD and majorization theory. A general family of optimal transform coders is introduced based on GTD. This family includes the Karhunen-Lo\'{e}ve transform (KLT), and the prediction-based lower triangular transform (PLT) as special cases. The coding gain of the entire family, with optimal bit allocation, is maximized and equal to those of the KLT and the PLT. Other special cases of the GTD-TC are the GMD (geometric mean decomposition) and the BID (bidiagonal transform). The GMD in particular has the property that the optimum bit allocation is a uniform allocation. We also propose using dither quantization in the GMD transform coder. Under the uniform bit loading scheme, it is shown that the proposed dithered GMD transform coders perform significantly better than the original GMD coder in the low rate regime.
Another important signal processing problem, namely the filter bank optimization based on the knowledge of input signal statistics, is then considered. GTD and the theory of majorization are again used to give a new look to this classical problem. We propose GTD filter banks as subband coders for optimizing the theoretical coding gain. The orthonormal GTD filter bank and the biorthogonal GTD filter bank are discussed in detail. We show that in both cases there are two fundamental properties in the optimal solutions, namely, {\it total decorrelation} and {\it spectrum equalization}. The optimal solutions can be obtained by performing the frequency dependent GTD on the Cholesky factor of the input power spectrum density matrices. We also show that in both theory and numerical simulations, the optimal GTD subband coders have superior performance than optimal traditional subband coders. In addition, the uniform bit loading scheme can be used in the optimal biorthogonal GTD coders with no loss of optimality. This solves the granularity problem in the conventional optimum bit loading formula. The use of the GTD filter banks in frequency selective MIMO communication systems is also discussed. Finally, the connection between the GTD filter bank and the traditional filter bank is clearly indicated.</p
Emissive Monocopper Amidophosphine Complexes and Lewis Acid-Assisted Reductive Coupling of Carbon Monoxide
Get PDFTwo major themes are presented, in roughly chronological order: the synthesis and characterization of photoluminescent copper complexes are described, followed by studies on the selective conversion of synthesis gas (CO and H2) to oxygenates. With the latter comprising the majority of the work, it is the subject of the introductory Chapter 1. In Chapter 2, the photoluminescent copper chemistry is introduced, and the synthesis and photophysics of monomeric amidophosphine complexes of copper is presented. The copper complexes are exceptional luminophores, with quantum efficiency up to 70% and lifetimes up to 150 μs. In Chapter 3, homogeneous CO hydrogenation is pursued using a strategy reliant on the incorporation of pendent Lewis acidic groups into the secondary coordination sphere of a metal carbonyl complex. This design feature promotes facile C–H and C–C bond formation, with transition metal hydrides as the hydrogen source. A structure-function study investigating the specific role of the Lewis acid determined that thefirst C–H bond formation is not particularly sensitive to the acid, whereas the second C–H bond formation and C–C coupling are both highly sensitive to the length of the tether between the metal and the borane. In Chapter 4, this chemistry is extended to utilize dihydrogen directly as a reductant, in a "frustrated Lewis pair" (FLP) mechanism. A strong phosphazene base is too bulky to interact with the pendent borane, but can heterolytically cleave dihydrogen in concert with the borane to generate a borohydride that transforms the carbonyl ligands into a metal-bound C2 organic fragment. In Chapter 5, Lewis acidic boranes are again employed as promoters of reductive chemistry, this time for CO2 reduction. The same late transition metal hydrides that were employed for CO reduction, such as [HNi(dmpe)2][BF4] (dmpe = 1,2-bis(dimethylphosphino)ethane), are able to reduce CO2 gas when used in concert with the appropriate borane, affording a borane-formate adduct. In Chapter 6, the "frustrated Lewis pair" concept is extended to a different problem: the dehydrogenation of amine-boranes, which are candidates for hydrogen storage applications. Treatment of amine-boranes with the FLP tBu3P/B(C6F5)3 effects rapid and quantitative transfer of H2 from the amine-borane, forming cyclic aminoborane products along with [tBu3PH][HB(C6F5)3]. Appendices are provided, including early work on Brønsted acid-assisted CO reduction, speciation of trialkylborohydrides, tabulating NMR impurities in deuterated solvents of interest to the organometallic chemist, and crystallographic tables
The Simulation of Shock- and Impact-Driven Flows with Mie-Grüneisen Equations of State
Get PDFAn investigation of shock- and impact-driven flows with Mie-Grüneisen equation of state derived from a linear shock-particle speed Hugoniot relationship is presented. Cartesian mesh methods using structured adaptive refinement are applied to simulate several flows of interest in an Eulerian frame of reference. The flows central to the investigation include planar Richtmyer-Meshkov instability, the impact of a sphere with a plate, and an impact-driven Mach stem.
First, for multicomponent shock-driven flows, a dimensionally unsplit, spatially high-order, hybrid, center-difference, limiter methodology is developed. Effective switching between center-difference and upwinding schemes is achieved by a set of robust tolerance and Lax-entropy-based criteria [49]. Oscillations that result from such a mixed stencil scheme are minimized by requiring that the upwinding method approaches the center-difference method in smooth regions. To attain this property a blending limiter is introduced based on the norm of the deviation of WENO reconstruction weights from ideal. The scheme is first demonstrated successfully for the linear advection equation in spatially fourth- and sixth-order forms. A spatially fourth-order version of the method that combines a skew-symmetric kinetic-energy preserving center-difference scheme with a Roe-Riemann solver is then developed and implemented in Caltech's Adaptive Mesh Refinement, Object-oriented C++ (AMROC) [16,17] framework for Euler flows.
The solver is then applied to investigate planar Richtmyer-Meshkov instability in the context of an equation of state comparison. Comparisons of simulations with materials modeled by isotropic stress Mie-Grüneisen equations of state derived from a linear shock-particle speed Hugoniot relationship [36,52] to those of perfect gases are made with the intention of exposing the role of the equation of state. First, results for single- and triple-mode planar Richtmyer-Meshkov instability between mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Grüneisen equations of state are presented for the case of a reflected shock. The single-mode case is explored for incident shock Mach numbers of 1.5 and 2.5. For the planar triple-mode case a single incident Mach number of 2.5 is examined with the initial corrugation wave numbers related by k₁=k₂+k₃. A comparison is drawn to Richtmyer-Meshkov instability in fluids with perfect gas equations of state utilizing matching of a nondimensional pressure jump across the incident shock, the post-shock Atwood ratio, post-shock amplitude-to-wavelength ratio, and time nondimensionalized by the Rcithmyer linear-growth rate time constant prediction. Result comparison demonstrates difference in start-up time and growth rate oscillations. Growth rate oscillation frequency is seen to correlate directly to the expected oscillation frequency of the transmitted and reflected shocks. For the single-mode cases, further comparison is given for vorticity distribution and corrugation centerline shortly after shock interaction that demonstrates only minor differences.
Additionally, examined is single-mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. Vorticity distribution and corrugation centerline shortly after shock interaction is also examined. The formation of incipient weak shock waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected.
Next, the ghost fluid method [83] is explored for application to impact-driven flows with Mie-Grüneisen equations of state in a vacuum. Free surfaces are defined utilizing a level-set approach. The level-set is reinitialized to the signed distance function periodically by solution to a Hamilton-Jacobi differential equation in artificial time. Flux reconstruction along each Cartesian direction of the domain is performed by subdividing in a way that allows for robust treatment of grid-scale sized voids. Ghost cells in voided regions near the material-vacuum interface are determined from surface-normal Riemann problem solution. The method is then applied to several impact problems of interest. First, a one-dimensional impact problem is examined in Mie-Grüneisen aluminum with simple point erosion used to model separation by spallation under high tension. A similar three-dimensional axisymmetric simulation of two rods impacting is then performed without a model for spallation. Further results for three-dimensional axisymmetric simulation of a sphere hitting a plate are then presented.
Finally, a brief investigation of the assumptions utilized in modeling solids as isotropic fluids is undertaken. An Eulerian solver approach to handling elastic and elastic-plastic solids is utilized for comparison to the simple fluid model assumption. First, in one dimension an impact problem is examined for elastic, elastic-plastic, and fluid equations of state for aluminum. The results demonstrate that in one dimension the fluid models the plastic shock structure of the flow well. Further investigation is made using a three-dimensional axisymmetric simulation of an impact problem involving a copper cylinder surrounded by aluminum. An aluminum slab impact drives a faster shock in the outer aluminum region yielding a Mach reflection in the copper. The results demonstrate similar plastic shock structures. Several differences are also notable that include a lack of roll-up instability at the material interface and slip-line emanating from the Mach stem's triple point.</p
A Measurement of Jet Shapes in Proton-Proton Collisions at 7.0 TeV Center-of-Mass Energy with the ATLAS Detector at the Large Hadron Collider
Get PDFA study of jet shapes is presented using 300 nb−1 of proton-proton collision data collected at a center of mass energy of 7 TeV using the ATLAS detector at the Large Hadron Collider. The analysis includes jets with rapidity |y| < 2.8 and with calibrated transverse momentum 40 < pT < 600 GeV. Results are compared with several tuned Monte Carlo programs. Jets are found to be wider than predicted, although the evolution of the jet shape with transverse momentum is well described
A Study of Information Processing in the Sea Urchin Embryo by Rewiring Mesodermal Gene Regulatory Networks and cis-Regulatory Analysis of Skeletogenic Regulators
Get PDFThis work focuses on the GRNs specifying embryonic skeletogenesis and the pigment cell differentiation in the purple sea urchin, Strongylocentrotus purpuratus. These networks make predictions about the necessity of regulatory gene expression and cis-regulatory wiring for directing development. Here, these predictions are tested in a novel way, by add regulatory linkages to the GRN, and effectively rewiring development at the level of genomic DNA. The rewiring experiment presented here showed a previously unknown repression function for the pigment-cell terminal differentiation regulator, gcm, on an important regulator of skeletogenesis, alx1. This result motivated a complete cis-regulatory analysis of alx1 that identified a potential mechanism for gcm repression. Finally, this work describes a method for measuring GFP reporter activity in live sea-urchin embryos that will permit real-time cis-regulatory analysis
Compressed Sensing, Sparse Approximation, and Low-Rank Matrix Estimation
Get PDFThe importance of sparse signal structures has been recognized in a plethora of applications ranging from medical imaging to group disease testing to radar technology. It has been shown in practice that various signals of interest may be (approximately) sparsely modeled, and that sparse modeling is often beneficial, or even indispensable to signal recovery. Alongside an increase in applications, a rich theory of sparse and compressible signal recovery has recently been developed under the names compressed sensing (CS) and sparse approximation (SA). This revolutionary research has demonstrated that many signals can be recovered from severely undersampled measurements by taking advantage of their inherent low-dimensional structure. More recently, an offshoot of CS and SA has been a focus of research on other low-dimensional signal structures such as matrices of low rank. Low-rank matrix recovery (LRMR) is demonstrating a rapidly growing array of important applications such as quantum state tomography, triangulation from incomplete distance measurements, recommender systems (e.g., the Netflix problem), and system identification and control.
In this dissertation, we examine CS, SA, and LRMR from a theoretical perspective. We consider a variety of different measurement and signal models, both random and deterministic, and mainly ask two questions.
How many measurements are necessary? How large is the recovery error?
We give theoretical lower bounds for both of these questions, including oracle and minimax lower bounds for the error. However, the main emphasis of the thesis is to demonstrate the efficacy of convex optimization---in particular l1 and nuclear-norm minimization based programs---in CS, SA, and LRMR. We derive upper bounds for the number of measurements required and the error derived by convex optimization, which in many cases match the lower bounds up to constant or logarithmic factors. The majority of these results do not require the restricted isometry property (RIP), a ubiquitous condition in the literature.</p
Dynamic Regulation of the Dauer Decision
Get PDFMany animals can choose between different developmental fates to maximize fitness. Despite the complexity of environmental cues and life history, different developmental fates are executed in a robust fashion. The mechanisms that guarantee robust execution of a development choice in such environments remain unknown. The nematode Caenorhabditis elegans serves as a powerful model to examine this phenomenon because it has an advanced toolkit for cellular and genetic manipulations, and can adopt one of two developmental fates depending on environmental conditions. Nematodes grown in favorable conditions (sufficient food, low population density) develop into adults, whereas nematodes grown in unfavorable conditions (insufficient food, high population density) arrest development as a stress-resistant diapause form called dauer.
The steroid hormone dafachronic acid (DA), product of DAF-9/cytochrome P450, directs development to adulthood by regulating the transcriptional activity of the nuclear hormone receptor DAF-12. The known role of DA suggests that it may be the molecular mediator of environmental condition effects on the developmental fate decision, although the mechanism is yet unknown. We hypothesize that information from the environment is integrated and reduced to a single cell nonautonomous environmental integrator, thereby explaining the tight binary nature of the developmental fate decision. We propose a fate coordination mechanism in which production of a small amount of DA is amplified, locking in the adult fate. Using a combination of laser ablations and time lapse image analysis, we demonstrate that upon the decision to become an adult, the XXX neuroendocrine cells act as a source releasing DA. As a result, DAF-12 dependent expression of daf-9 in the epidermis is amplified and propagated from anterior to posterior, dispersing high amounts of DA throughout the body. This dispersion of DA drives adult programs in the gonad, epidermis and vulva. Furthermore, we demonstrate that the XXX cells are not necessary for maintaining the adult fate after the signal amplification has started. This indicates that the epidermal amplification also confers the irreversibility of the decision by uncoupling the execution of the decision from the environmental integrator. We propose that this relay serves as a robust fate-locking mechanism to enforce an organism wide binary decision, despite noisy and complex environmental cues.</p