Phase Locked Loop and Modulo Games, The Dogma Loops; and “Finding Ibrida”

This dissertation consists of two independent musical compositions and an article detailing the process of the design and assembly of an electric guitar with particular emphasis on the carefully curated suite of embedded effects.

The first piece, 'Phase Locked Loop and Modulo Games' is scored for electric guitar and a single echo of equal volume less than a beat away. One could think of the piece as a 15 minute canon at the unison at the dotted eighth note (or at times the quarter or triplet-quarter), however the compositional motivation is more about weaving a composite texture between the guitar and its echo that is, while in theory extremely contrapuntal, in actuality is simply a single [superhuman] melodic line.

The second piece, 'The Dogma Loops' picks up a few compositional threads left by ‘Phase Locked Loop’ and weaves them into an entirely new tapestry. 'Phase Locked Loop' is motivated by the creation of a complex musical composite that is for the most part electronically transparent. 'The Dogma Loops' questions that same notion of composite electronic complexity by essentially asking a question: "what are the inputs to an interactive electronic system that create the most complex outputs via the simplest musical means possible?"

'The Dogma Loops' is scored for Electric Guitar (doubling on Ukulele), Violin and Violoncello. All of the principal instruments require an electronic pickup (except the Uke). The work is in three sections played attacca; [Automation Games], [Point of Origin] and [Cloning Vectors].

The third and final component of the document is the article 'Finding Ibrida.' This article details the process of the design and assembly of an electric guitar with integrated effects, while also providing the deeper context (conceptual and technical) which motivated the efforts and informed the challenges to hybridize the various technologies (tubes, transistors, digital effects and a microcontroller subsystem). The project was motivated by a desire for rigorous technical and hands-on engagement with analog signal processing as applied to the electric guitar. ‘Finding Ibrida’ explores sound, some myths and lore of guitar tech and the history of electric guitar distortion and its culture of sonic exploration.

Structural Basis of RNA Recognition by Mycobacterium tuberculosis MazF Homologues

The MazEF toxin-antitoxin (TA) system consists of the antitoxin MazE and the toxin MazF. MazF is a sequence-specific endoribonuclease that upon activation causes cellular growth arrest and increass the level of persisters. Moreover, MazF-induced cells are in a quasi-dormant state that cells remain metabolically active while stop dividing. The quasi-dormancy is similar to the nonreplicating state of M. tuberculosis during latent tuberculosis, thus suggesting the role of mazEF in M. tuberculosis dormancy and persistence. M. tuberculosis has nine mazEF TA modules, each with different RNA cleavage specificities and implicated in selective gene expression during stress conditions. To date only the Bacillus subtilis MazF-RNA complex structure has been determined. As M. tuberculosis MazF homologues recognize distinct RNA sequences, their molecular mechanisms of substrate specificity remain unclear. By taking advantage of X-ray crystallography, we have determined structures of two M. tuberculosis MazF-RNA complexes, MazF-mt1 (Rv2801c) and MazF-mt3 (Rv1991c) in complex with an uncleavable RNA substrate. These structures have provided the molecular basis of sequence-specific RNA recognition and cleavage by MazF toxins.

Both MazF-mt1-RNA and MazF-mt3-RNA complexes showed similar structural organization with one molecule of RNA bound to a MazF-mt1 or MazF-mt3 dimer and occupying the same pocket within the MazF dimer interface. Similar to B. subtilis MazF-RNA complex, MazF-mt1 and MazF-mt3 displayed a conserved active site architecture, where two highly conserved residues, Arg and Thr, form hydrogen bonds with the scissile phosphate group in the cleavage site of the bound RNA. The MazF-mt1-RNA complex also showed specific interactions with its three-base RNA recognition element. Compared with the B. subtilis MazF-RNA complex, our structures showed that residues involved in sequence-specific recognition of target RNA vary between the MazF homologues, therefore explaining the molecular basis for their different RNA recognition sequences. In addition, local conformational changes of the loops in the RNA binding site of MazF-mt1 appear to play a role in MazF targeting different RNA lengths and sequences. In contrast, the MazF-mt3-RNA complex is in a non-optimal RNA binding state with a symmetry-related MazF-mt3 molecule found to make interactions with the bound RNA in the crystal. The crystal-packing interactions were further examined by isothermal titration calorimetry (ITC) studies on selected MazF-mt3 mutants. Our attempts to utilize a MazF-mt3 mutant bearing mutations involved in crystal contacts all crystallized with few nucleotides, which are still found to interact with a symmetry mate. However, these different crystal forms revealed the conformational flexibility of loops in the RNA binding interface of MazF-mt3, suggesting their role in RNA binding and recognition, which will require further studies on additional MazF-mt3-RNA complex interactions.

In conclusion, the structures of the MazF-mt1-RNA and MazF-mt3-RNA complexes provide the first structural information on any M. tuberculosis MazF homologues. Supplemented with structure-guided mutational studies on MazF toxicity in vivo, this study has addressed the structural basis of different RNA cleavage specificities among MazF homologues. Our work will guide future studies on the function of other M. tuberculosis MazF and MazE-MazF homologues, and will help delineate their physiological roles in M. tuberculosis stress responses and pathogenesis.

Mathematical Modeling of Perifusion Cell Culture Experiments

In perifusion cell cultures, the culture medium flows continuously through a chamber containing immobilized cells and the effluent is collected at the end. In our main applications, gonadotropin releasing hormone (GnRH) or oxytocin is introduced into the chamber as the input. They stimulate the cells to secrete luteinizing hormone (LH), which is collected in the effluent. To relate the effluent LH concentration to the cellular processes producing it, we develop and analyze a mathematical model consisting of coupled partial differential equations describing the intracellular signaling and the movement of substances in the cell chamber. We analyze three different data sets and give cellular mechanisms that explain the data. Our model indicates that two negative feedback loops, one fast and one slow, are needed to explain the data and we give their biological bases. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics. We analyze the model to understand the influence of parameters, like the rate of the medium flow or the fraction collection time, on the experimental outcomes. We investigate how the rate of binding and dissociation of the input hormone to and from its receptor influence its movement down the chamber. Finally, we formulate and analyze simpler models that allow us to predict the distortion of a square pulse due to hormone-receptor interactions and to estimate parameters using perifusion data. We show that in the limit of high binding and dissociation the square pulse moves as a diffusing Gaussian and in this limit the biological parameters can be estimated.

Numerical Simulations for the Design of Novel Integrated Parallel Reception, Excitation, and Shimming (iPRES) Coil Arrays

Magnetic field inhomogeneity results in image artifacts including signal loss, image blurring and distortions, leading to decreased diagnostic accuracy. Conventional multi-coil (MC) shimming method employs both RF coils and shimming coils, whose mutual interference induces a tradeoff between RF signal-to-noise (SNR) ratio and shimming performance. To address this issue, RF coils were integrated with direct-current (DC) shim coils to shim field inhomogeneity while concurrently emitting and receiving RF signal without being blocked by the shim coils. The currents applied to the new coils, termed iPRES (integrated parallel reception, excitation and shimming), were optimized in the numerical simulation to improve the shimming performance. The objectives of this work is to offer a guideline for designing the optimal iPRES coil arrays to shim the abdomen.

In this thesis work, the main field () inhomogeneity was evaluated by root mean square error (RMSE). To investigate the shimming abilities of iPRES coil arrays, a set of the human abdomen MRI data was collected for the numerical simulations. Thereafter, different simplified iPRES(N) coil arrays were numerically modeled, including a 1-channel iPRES coil and 8-channel iPRES coil arrays. For 8-channel iPRES coil arrays, each RF coil was split into smaller DC loops in the x, y and z direction to provide extra shimming freedom. Additionally, the number of DC loops in a RF coil was increased from 1 to 5 to find the optimal divisions in z direction. Furthermore, switches were numerically implemented into iPRES coils to reduce the number of power supplies while still providing similar shimming performance with equivalent iPRES coil arrays.

The optimizations demonstrate that the shimming ability of an iPRES coil array increases with number of DC loops per RF coil. Furthermore, the z direction divisions tend to be more effective in reducing field inhomogeneity than the x and y divisions. Moreover, the shimming performance of an iPRES coil array gradually reach to a saturation level when the number of DC loops per RF coil is large enough. Finally, when switches were numerically implemented in the iPRES(4) coil array, the number of power supplies can be reduced from 32 to 8 while keeping the shimming performance similar to iPRES(3) and better than iPRES(1). This thesis work offers a guidance for the designs of iPRES coil arrays.

Math 412 - Topology with Applications

Highlights of Data Expedition: • Students explored daily observations of local climate data spanning the past 35 years. • Topological Data Analysis, or TDA for short, provides cutting-edge tools for studying the geometry of data in arbitrarily high dimensions. • Using TDA tools, students discovered intrinsic dynamical features of the data and learned how to quantify periodic phenomenon in a time-series. • Since nature invariably produces noisy data which rarely has exact periodicity, students also considered the theoretical basis of almost-periodicity and even invented and tested new mathematical definitions of almost-periodic functions. Summary The dataset we used for this data expedition comes from the Global Historical Climatology Network. “GHCN (Global Historical Climatology Network)-Daily is an integrated database of daily climate summaries from land surface stations across the globe.” Source: https://www.ncdc.noaa.gov/oa/climate/ghcn-daily/ We focused on the daily maximum and minimum temperatures from January 1, 1980 to April 1, 2015 collected from RDU International Airport. Through a guided series of exercises designed to be performed in Matlab, students explore these time-series, initially by direct visualization and basic statistical techniques. Then students are guided through a special sliding-window construction which transforms a time-series into a high-dimensional geometric curve. These high-dimensional curves can be visualized by projecting down to lower dimensions as in the figure below (Figure 1), however, our focus here was to use persistent homology to directly study the high-dimensional embedding. The shape of these curves has meaningful information but how one describes the “shape” of data depends on which scale the data is being considered. However, choosing the appropriate scale is rarely an obvious choice. Persistent homology overcomes this obstacle by allowing us to quantitatively study geometric features of the data across multiple-scales. Through this data expedition, students are introduced to numerically computing persistent homology using the rips collapse algorithm and interpreting the results. In the specific context of sliding-window constructions, 1-dimensional persistent homology can reveal the nature of periodic structure in the original data. I created a special technique to study how these high-dimensional sliding-window curves form loops in order to quantify the periodicity. Students are guided through this construction and learn how to visualize and interpret this information. Climate data is extremely complex (as anyone who has suffered from a bad weather prediction can attest) and numerous variables play a role in determining our daily weather and temperatures. This complexity coupled with imperfections of measuring devices results in very noisy data. This causes the annual seasonal periodicity to be far from exact. To this end, I have students explore existing theoretical notions of almost-periodicity and test it on the data. They find that some existing definitions are also inadequate in this context. Hence I challenged them to invent new mathematics by proposing and testing their own definition. These students rose to the challenge and suggested a number of creative definitions. While autocorrelation and spectral methods based on Fourier analysis are often used to explore periodicity, the construction here provides an alternative paradigm to quantify periodic structure in almost-periodic signals using tools from topological data analysis.

Genetic Analysis of Mitotic Recombination in Saccharomyces cerevisiae

Mitotic genome instability can occur during the repair of double-strand breaks (DSBs) in DNA, which arise from endogenous and exogenous sources. Studying the mechanisms of DNA repair in the budding yeast, Saccharomyces cerevisiae has shown that Homologous Recombination (HR) is a vital repair mechanism for DSBs. HR can result in a crossover event, in which the broken molecule reciprocally exchanges information with a homologous repair template. The current model of double-strand break repair (DSBR) also allows for a tract of information to non-reciprocally transfer from the template molecule to the broken molecule. These “gene conversion” events can vary in size and can occur in conjunction with a crossover event or in isolation. The frequency and size of gene conversions in isolation and gene conversions associated with crossing over has been a source of debate due to the variation in systems used to detect gene conversions and the context in which the gene conversions are measured.

In Chapter 2, I use an unbiased system that measures the frequency and size of gene conversion events, as well as the association of gene conversion events with crossing over between homologs in diploid yeast. We show mitotic gene conversions occur at a rate of 1.3x10-6 per cell division, are either large (median 54.0kb) or small (median 6.4kb), and are associated with crossing over 43% of the time.

DSBs can arise from endogenous cellular processes such as replication and transcription. Two important RNA/DNA hybrids are involved in replication and transcription: R-loops, which form when an RNA transcript base pairs with the DNA template and displaces the non-template DNA strand, and ribonucleotides embedded into DNA (rNMPs), which arise when replicative polymerase errors insert ribonucleotide instead of deoxyribonucleotide triphosphates. RNaseH1 (encoded by RNH1) and RNaseH2 (whose catalytic subunit is encoded by RNH201) both recognize and degrade the RNA in within R-loops while RNaseH2 alone recognizes, nicks, and initiates removal of rNMPs embedded into DNA. Due to their redundant abilities to act on RNA:DNA hybrids, aberrant removal of rNMPs from DNA has been thought to lead to genome instability in an rnh201Δ background.

In Chapter 3, I characterize (1) non-selective genome-wide homologous recombination events and (2) crossing over on chromosome IV in mutants defective in RNaseH1, RNaseH2, or RNaseH1 and RNaseH2. Using a mutant DNA polymerase that incorporates 4-fold fewer rNMPs than wild type, I demonstrate that the primary recombinogenic lesion in the RNaseH2-defective genome is not rNMPs, but rather R-loops. This work suggests different in-vivo roles for RNaseH1 and RNaseH2 in resolving R-loops in yeast and is consistent with R-loops, not rNMPs, being the the likely source of pathology in Aicardi-Goutières Syndrome patients defective in RNaseH2.

Mechanochemistry for Active Materials and Devices

The coupling of mechanical stress fields in polymers to covalent chemistry (polymer mechanochemistry) has provided access to previously unattainable chemical reactions and polymer transformations. In the bulk, mechanochemical activation has been used as the basis for new classes of stress-responsive polymers that demonstrate stress/strain sensing, shear-induced intermolecular reactivity for molecular level remodeling and self-strengthening, and the release of acids and other small molecules that are potentially capable of triggering further chemical response. The potential utility of polymer mechanochemistry in functional materials is limited, however, by the fact that to date, all reported covalent activation in the bulk occurs in concert with plastic yield and deformation, so that the structure of the activated object is vastly different from its nascent form. Mechanochemically activated materials have thus been limited to “single use” demonstrations, rather than as multi-functional materials for structural and/or device applications. Here, we report that filled polydimethylsiloxane (PDMS) elastomers provide a robust elastic substrate into which mechanophores can be embedded and activated under conditions from which the sample regains its original shape and properties. Fabrication is straightforward and easily accessible, providing access for the first time to objects and devices that either release or reversibly activate chemical functionality over hundreds of loading cycles.

While the mechanically accelerated ring-opening reaction of spiropyran to merocyanine and associated color change provides a useful method by which to image the molecular scale stress/strain distribution within a polymer, the magnitude of the forces necessary for activation had yet to be quantified. Here, we report single molecule force spectroscopy studies of two spiropyran isomers. Ring opening on the timescale of tens of milliseconds is found to require forces of ~240 pN, well below that of previously characterized covalent mechanophores. The lower threshold force is a combination of a low force-free activation energy and the fact that the change in rate with force (activation length) of each isomer is greater than that inferred in other systems. Importantly, quantifying the magnitude of forces required to activate individual spiropyran-based force-probes enables the probe behave as a “scout” of molecular forces in materials; the observed behavior of which can be extrapolated to predict the reactivity of potential mechanophores within a given material and deformation.

We subsequently translated the design platform to existing dynamic soft technologies to fabricate the first mechanochemically responsive devices; first, by remotely inducing dielectric patterning of an elastic substrate to produce assorted fluorescent patterns in concert with topological changes; and second, by adopting a soft robotic platform to produce a color change from the strains inherent to pneumatically actuated robotic motion. Shown herein, covalent polymer mechanochemistry provides a viable mechanism to convert the same mechanical potential energy used for actuation into value-added, constructive covalent chemical responses. The color change associated with actuation suggests opportunities for not only new color changing or camouflaging strategies, but also the possibility for simultaneous activation of latent chemistry (e.g., release of small molecules, change in mechanical properties, activation of catalysts, etc.) in soft robots. In addition, mechanochromic stress mapping in a functional actuating device might provide a useful design and optimization tool, revealing spatial and temporal force evolution within the actuator in a way that might also be coupled to feedback loops that allow autonomous, self-regulation of activity.

In the future, both the specific material and the general approach should be useful in enriching the responsive functionality of soft elastomeric materials and devices. We anticipate the development of new mechanophores that, like the materials, are reversibly and repeatedly activated, expanding the capabilities of soft, active devices and further permitting dynamic control over chemical reactivity that is otherwise inaccessible, each in response to a single remote signal.