Browsing by Subject "Dynamics"

Just as heat, light and electricity do, mechanical forces can also stimulate reactions. Conventionally, these processes - known as mechanochemistry - were viewed as comprising only destructive events, such as bond scission and material failure. Recently, Moore and coworkers demonstrated that the incorporation of mechanophores, i.e., mechanochemically active moieties, can bring new types of chemistry. This demonstration has inspired a series of fruitful works, at both the molecular and material levels, in both theoretical and experimental aspects, for both fundamental research and applications. This dissertation evaluates mechanochemical behavior in all of these contexts.

At the level of fundamental reactivity, forbidden reactions, such as those that violate orbital symmetry effects as captured in the Woodward-Hoffman rules, remain an ongoing challenge for experimental characterization, because when the competing allowed pathway is available, the reactions are intrinsically difficult to trigger. Recent developments in covalent mechanochemistry have opened the door to activating otherwise inaccessible reactions. This dissertation describes the first real-time observation and quantified measurement of four mechanically activated forbidden reactions. The results provide the experimental benchmarks for mechanically induced forbidden reactions, including those that violate the Woodward-Hoffmann and Woodward-Hoffmann-DePuy rules, and in some cases suggest revisions to prior computational predictions. The single-molecule measurement also captured competing reactions between isomerization and bimolecular reaction, which to the best of our knowledge, is the first time that competing reactions are probed by force spectroscopy.

Most characterization for mechanochemistry has been focused on the reactivity of mechanophores, and investigations of the force coupling efficiency are much less reported. We discovered that the stereochemistry of a non-reactive alkene pendant to a reacting mechanophore has a dramatic effect on the magnitude of the force required to trigger reactivity on a given timescale (here, a 400 pN difference for reactivity on the timescale of 100 ms). The stereochemical perturbation has essentially no measurable effect on the force-free reactivity, providing an almost perfectly orthogonal handle for tuning mechanochemical reactivity independently of intrinsic reactivity.

Mechanochemical coupling is also applied here to the study of reaction dynamics. The dynamics of reactions at or in the immediate vicinity of transition states are critical to reaction rates and product distributions, but direct experimental probes of those dynamics are rare. The s-trans, s-trans 1,3-diradicaloid transition states are trapped by tension along the backbone of purely cis-substituted gem-difluorocyclopropanated polybutadiene using the extensional forces generated by pulsed sonication of dilute polymer solutions. Once released, the branching ratio between symmetry-allowed disrotatory ring closing (of which the trapped diradicaloid structure is the transition state) and symmetry-forbidden conrotatory ring closing (whose transition state is nearby) can be inferred. Net conrotatory ring closing occurred in 5.0 ± 0.5% of the released transition states, as compared to 19 out of 400 such events in molecular dynamics simulations.

On the materials level, the inevitable stress in materials during usage causes bond breakage, materials aging and failure. A strategy for solving this problem is to learn from biological materials, which are capable to remodel and become stronger in response to the otherwise destructive forces. Benzocyclobutene has been demonstrated to mechanically active to ortho-quinodimethide, an intermediate capable for [4+4] dimerization and [4+2] cycloaddition. These features make it an excellent candidate for and synthesis of mechanochemical remodeling. A polymer containing hundreds of benzocyclobutene on the backbone was synthesized. When the polymer was exposed to otherwise destructive shear forces generated by pulsed ultrasound, its molecular weight increased as oppose to other mechanophore-containing polymers. When a solution of the polymer with bismaleimide was subjected to pulsed ultrasonication, crosslink occurred and the modulus increased by two orders of magnitude.

RNA recognition frequently results in conformational changes that optimize

intermolecular binding. As a consequence, the overall binding affinity of RNA

to its binding partners depends not only on the intermolecular interactions

formed in the bound state, but also on the energy cost associated with changing

the RNA conformational distribution. Measuring these conformational penalties

is however challenging because bound RNA conformations tend to have equilibrium

populations in the absence of the binding partner that fall outside detection by

conventional biophysical methods.

In this work we employ as a model system HIV-1 TAR RNA and its interaction with

the ligand argininamide (ARG), a mimic of TAR’s cognate protein binding partner,

the transactivator Tat. We use NMR chemical shift perturbations (CSP) and NMR

relaxation dispersion (RD) in combination with Bayesian inference to develop a

detailed thermodynamic model of coupled conformational change and ligand

binding. Starting from a comprehensive 12-state model of the equilibrium, we

estimate the energies of six distinct detectable thermodynamic states that are

not accessible by currently available methods.

Our approach identifies a minimum of four RNA intermediates that differ in terms

of the TAR conformation and ARG-occupancy. The dominant bound TAR conformation

features two bound ARG ligands and has an equilibrium population in the absence

of ARG that is below detection limit. Consequently, even though ARG binds to TAR

with an apparent overall weak affinity ($\Kdapp \approx \SI{0.2}{\milli

\Molar}$), it binds the prefolded conformation with a $K_{\ch{d}}$ in the nM

range. Our results show that conformational penalties can be major determinants

of RNA-ligand binding affinity as well as a source of binding cooperativity,

with important implications for a predictive understanding of how RNA is

recognized and for RNA-targeted drug discovery.

Additionally, we describe in detail the development of our approach for fitting

complex ligand binding data to mathematical models using Bayesian

inference. We provide crucial benchmarks and demonstrate the

robustness of our fitting approach with the goal of application

to other systems. This thesis aims to provide new insight into

the dynamics of RNA-ligand recognition as well as provide new

methods that can be applied to achieve this goal.

Swarm robotics and distributed control offer the promise of enhanced performance and robustness relative to that of individual and centrally-controlled robots, with decreased cost or time-to-completion for certain tasks. Having many degrees of freedom, swarm-related control and estimation problems are challenging specifically when the solutions depend on a great amount of communication among the robots. Swarm controllers minimizing communication requirements are quite desirable.

Swarms are inherently more robust to uncertainties and failures, including complete loss of individual agents, due to the averaging inherent in convergence and agreement problems. Exploitation of this robustness to minimize processing and communication complexity is desirable.

This research focuses on simple but robust controllers for swarming problems, maximizing the likelihood of objective success while minimizing controller complexity and specialized communication or sensing requirements.

In addition, it develops distributed solutions for swarm control by examining and exploiting graph theoretic constructs. Details of specific implementations, such as nonholonomic motion and and numerosity constraints, were explored with some unexpectedly positive results.

In summary, this research focused on the development of control strategies for the distributed control of a swarm of robots, and graph-theoretic analysis of these controllers. These control strategies specifically consider probabilistic connectivity functions, based on requirements for sensing or communication. The developed control strategies are validated in both simulation and experiment.

Switching networks are a common model for biological systems, especially

for genetic transcription networks. Stuart Kaufman originally proposed

the usefulness of the Boolean framework, but much of the dynamical

features there are not realizable in a continuous analogue. We introduce the notion

of braid-like dynamics as a bridge between Boolean and continuous dynamics and

study its importance in the local dynamics of ring and ring-like networks. We discuss

a near-theorem on the global dynamics of general feedback networks, and in the final

chapter study the main ideas of this thesis in models of a yeast cell transcription network.

The focus of this dissertation is on the dynamics of electromagnetic systems for energy harvesting and filtering applications. The inclusion of magnets into systems generates nonlinearity due to the nature of electromagnetic interactions. In this work, magnetic nonlinearity manifests in tip interactions for cantilever beams, coupling effects for electromagnetic transduction, and bistable potential wells for a two beam system. These electromagnetic interactions are used to add non-contact coupling effects for the creation of bistable oscillators or arrays of coupled beams for energy filtering.

Nonlinearity at the tip of cantilever beams acts to change the dynamic and static behavior of the system. In this dissertation, these interactions are analyzed both with and without the nonlinear tip interactions. A linear analysis of the system without the tip interaction first provides insight into the shifting frequencies of the first four natural oscillation modes when considering a rigid body tip mass with rotational inertia and a center of mass that is offset from the tip of the beam. Then, the characterization of the nonlinearities in the beam stiffness and magnetic interaction provide insight into the static and dynamic behavior of the beam. The analytical and numerical investigations, using Rayleigh-Ritz methods and an assumed static deflection, are shown to be consistent with experimental tests. These methods provide a framework for theoretically establishing nonlinear static modes and small-amplitude linear modes that are consistent with physical behavior.

In electromagnetic coupling, the role of nonlinearity can have a detrimental or beneficial effect on energy harvesting. This work includes an investigation of the response of an energy harvester that uses electromagnetic induction to convert ambient vibration into electrical energy. The system's response behavior with linear coupling or a physically motivated form of nonlinear coupling is compared with single and multi-frequency base excitation. This analysis is performed with combined theoretical and numerical studies.

The ability of magnets to add nonlinearity to a system allows for the expansion of the phenomenological behavior of said system and potential advantages and disadvantages for energy harvesting. This work studies a two beam system made up of carbon fiber cantilever beams and attached magnetic tip masses with a focus on energy harvesting potential. Numerical and experimental investigations reveal an array of phenomena from static bifurcations, chaotic oscillations, and sub-harmonic orbits. These features are used to highlight the harvesting prospects for a similarly coupled system.

Beyond nonlinearity, the non-contacting coupling effects of magnets allow for the hypothetical creation of energy filtering systems. In this work, the band structure of a two dimensional lattice of oscillating beams with magnetic tip masses is explored. The focus of the wave propagation analysis is primarily on regions in the band structure where propagation does not occur for the infinite construction of the system. These band gaps are created in this system of 2 x 2 repeating unit cells by periodically varying the mass properties and, for certain configurations, the frequency band gaps manifest in different size and band location. Uncertainty in these regions is analyzed using potential variations associated with specific physical parameters in order to elucidate their influence on the band gap regions. Boundary effects and damping are also investigated for a finite-dimensional array, revealing an erosion of band gaps that could limit the expected functionality.

The work presented here describes the electrostatic force, it’s nature, and it’s use in electromechanical systems. Energy transfer from both electrical-to-mechanical and mechanical-to-electrical are described. The electrostatic force is investigated in detail.Patterning of electrostatic rotary capacitive plates provides a novel strategy for up-converting low frequency mechanical excitation sources. The rotating plates allow for output waveform signal conditioning in both control of frequency and waveform shaping. An experimental set-up consisting of a 5.08 cm (2”) diameter rotary electrostatic capacitor harvester was designed and tested at mechanical rotation frequencies ranging from 1–35 Hz. Quarter plates were used to double the rate of change in area. Plates were spaced 3 mm apart with an applied voltage of 6.55 kV maintained by a 8.3 nF capacitor bank. Resistive loads between 10kΩ−10M Ω were used to verify current flow from the rotary capacitor. Simulation was carried out using a current source GTABLE model in PSPICE. Electrostatic theory demonstrates similar current magnitudes and the same upward trend with frequency. Further experimental analysis of a translating spring-mass system with a constant electrostatic force in the presence of viscous damping is presented and compared with simulation. A model for the linear translating electrostatic system not under the influence of viscous damping is first considered. An analytical equation is derived which provides a theoretical model for the behavior of the system and simulation in carried out and compared with the solution and theoretical model. Next, an approximate analytical solution to the electrostatic oscillator system in the presence of viscous damping is completed and a recursive relationship for the piecewise solution is presented. Conclusions and future work suggest several avenues for further investigation where the electrostatic force in electromechanical systems could be advanced including application areas.

The aeroelastic stability of beams and plates in three-dimensional flows is explored as the elastic and aerodynamic parameters are varied. First principal energy methods are used to derive the structural equations of motion. The structural models are coupled with a three-dimensional linear vortex lattice model of the aerodynamics. An aeroelastic model with the beam structural model is used to explore the transition between different fixed boundary conditions and the effect of varying two non-dimensional parameters, the mass ratio $\mu$ and aspect ratio $H^*$, for a beam with a fixed edge normal to the flow. The trends matched previously published theoretical and experimental data, validating the current aeroelastic model. The transition in flutter velocity between the clamped free and pinned free configuration is a non-monotomic transition, with the lowest flutter velocity coming with a finite size spring stiffness. Next a plate-membrane model is used to explore the instability dynamics for different combinations of boundary conditions. For the specific configuration of the trailing edge free and all other edges clamped, the sensitivity to the physical parameters shows that decreasing the streamwise length and increasing the tension in the direction normal to the flow can increase the onset instability velocity. Finally the transition in aeroelastic instabilities for non-axially aligned flows is explored for the cantilevered beam and three sides clamped plate. The cantilevered beam configuration transitions from an entirely bending motion when the clamped edge is normal to the flow to a typical bending/torsional wing flutter when the clamped edge is aligned with the flow. As the flow is rotated the transition to the wing flutter occurs when the flow angle is only 10 deg from the perfectly normal configuration. With three edges clamped, the motion goes from a divergence instability when the free edge is aligned with the flow to a flutter instability when the free edge is normal to the flow. The transition occurs at an intermediate angle. Experiments are carried out to validate the beam and plate elastic models. The beam aeroelastic results are also confirmed experimentally. Experimental values consistently match well with the theoretical predictions for both the aeroelastic and structural models.

Ribonucleic acid (RNA) is a versatile and dynamic biomolecule that serves as an indispensable component in the central dogma of molecular biology. The realization that RNA plays a wide variety of roles in gene expression and regulation has been accompanied by the discovery that virtually all types of RNA are chemically modified. These modifications have profound effects on RNA metabolism. N6-Methyladenosine (m6A) is an abundant post-transcriptional RNA modification that influences multiple aspects of gene expression. While m6A is thought to mainly function by recruiting reader proteins to specific RNA sites, the modification can also reshape RNA-protein and RNA−RNA interactions by altering RNA structure mainly by destabilizing base pairing. Here we sought to provide a broad and deep description of how m6A reshapes the folding and recognition landscape of RNA, which provides detailed mechanisms via which m6A exerts its biological functions.First, we show that when neighbored by a 5ʹ bulge, m6A stabilizes m6A–U base pairs and global RNA structure by ~1 kcal/mol. The bulge most likely provides the flexibility needed to allow optimal stacking between the methyl group and 3ʹ neighbor through a conformation that is stabilized by Mg2+. A bias toward this motif can help explain the global impact of methylation on RNA structure in transcriptome-wide studies. While m6A embedded in duplex RNA is poorly recognized by the YTH domain reader protein and m6A antibodies, both readily recognize m6A in this newly identified motif. The results uncover potentially abundant and functional m6A motifs that can modulate the epitranscriptomic structure landscape with important implications for the interpretation of transcriptome-wide data. In addition to altering RNA stability, m6A has also been shown to slow the kinetics of biochemical processes involving RNA-RNA interactions. However, little is known about how m6A affects the kinetic rates of RNA folding and conformational transitions that are important for RNA functions. We developed an NMR relaxation dispersion (RD) method to non-invasively and site-specifically measure nucleic acid hybridization kinetics. Using this method, we discovered that m6A selectively slows annealing rate while has minimal impact on melting rate in different sequence contexts and buffer conditions. To understand the mechanism of the m6A-induced slowdown of hybridization, we used NMR RD to dissect the kinetic pathways of duplex hybridization. We show that m6A pairs with uridine with the methylamino group in the anti conformation to form a Watson-Crick base pair that transiently exchanges on the millisecond timescale with a singly hydrogen-bonded low-populated (1%) mismatch-like conformation in which the methylamino group is syn. This ability to rapidly interchange between Watson-Crick or mismatch-like forms, combined with different syn:anti isomer preferences when paired (~1:100) versus unpaired (~10:1), explains how m6A robustly slows duplex annealing without affecting melting via two pathways in which isomerization occurs before or after duplex annealing. Our model quantitatively predicts how m6A reshapes the kinetic landscape of nucleic acid hybridization and conformational transitions and provides an explanation for why the modification robustly slows diverse cellular processes. Taken together, these results uncover the important role of m6A on modulating RNA-RNA and RNA-protein interactions through altering RNA structure and dynamics, highlighting the structural-dynamics-function relationship.

Biomolecules are dynamic entities that adopt a variety of conformations in solution. Conformational changes in biomolecules routinely take place when they take part in biochemical processes such as binding and catalysis. The energetic cost or conformational penalty to adopt an alternative conformation, which typically is paid for by thermal fluctuations or inter-molecular contacts with a partner molecule, can be an important determinant of these efficacy and selectivity of these biochemical processes. These conformational penalties can also be modulated by changes in physiological conditions and chemical modifications, enabling fine control over these biochemical processes, and aberrant changes to these conformational penalties can also be associated with disease. Thus, measurement of conformational penalties in biomolecules and how they can be tuned by external cues are essential to understand the role of conformational dynamics in biology.In this thesis, a combination of experimental and computational techniques such as NMR spectroscopy, UV melting and MD simulations are used to measure conformational penalties in nucleic acids and how they are modulated by post-transcriptional and epigenetic modifications, with particular applications to the formation of Watson-Crick like mismatches in DNA, and Hoogsteen base pairs in RNA and DNA. Improved methods that enable measurements of these conformational penalties with increased throughput and sensitivity, involving the use of NMR spectroscopy and UV melting, are also presented.

During embryogenesis, a single zygote gives rise to a multicellular embryo with distinct spatial territories marked by differential gene expression. How is this patterning process organized? How robust is this function to perturbations? Experiments that examine normal and regulative development will provide direct evidence for reasoning out the answers to these fundamental questions. Recent advances in technology have led to experimental determinations of increasingly complex gene regulatory networks (GRNs) underlying embryonic development. These GRNs offer a window into systems level properties of the developmental process, but at the same time present the challenge of characterizing their behavior. A suitable modeling framework for developmental systems is needed to help gain insights into embryonic development. Such models should contain enough detail to capture features of interest to developmental biologists, while staying simple enough to be computationally tractable and amenable to conceptual analysis. Combining experiments with the complementary modeling framework, we can grasp a systems level understanding of the regulatory program not readily visible by focusing on individual genes or pathways.

This dissertation addresses both modeling and experimental challenges. First, we present the autonomous Boolean network modeling framework and show that it is a suitable approach for developmental regulatory systems. We show that important timing information associated with the regulatory interactions can be faithfully represented in autonomous Boolean models in which binary variables representing expression levels are updated in continuous time, and that such models can provide direct insight into features that are difficult to extract from ordinary differential equation (ODE) models. As an application, we model the experimentally well-studied network controlling fly body segmentation. The Boolean model successfully generates the patterns formed in normal and genetically perturbed fly embryos, permits the derivation of constraints on the time delay parameters, clarifies the logic associated with different ODE parameter sets, and provides a platform for studying connectivity and robustness in parameter space. By elucidating the role of regulatory time delays in pattern formation, the results suggest new types of experimental measurements in early embryonic development. We then use this framework to model the much more complicated sea urchin endomesoderm specification system and describe our recent progress on this long term effort.

Second, we present experimental results on developmental plasticity of the sea urchin embryo. The sea urchin embryo has the remarkable ability to replace surgically removed tissues by reprogramming the presumptive fate of remaining tissues, a process known as transfating, which in turn is a form of regulative development. We show that regulative development requires cellular competence, and that competence is lost early on but can be regained after further differentiation. We demonstrate that regulative replacement of missing tissues can induce distal germ layers to participate in reprogramming, leading to a complete re-patterning in the remainder of the embryo. To understand the molecular mechanism of cell fate reprogramming, we examined micromere depletion induced non-skeletogenic mesoderm (NSM) transfating. We found that the skeletogenic program was greatly temporally compressed in this case, and that akin to another NSM transfating case, the transfating cells went through a hybrid regulatory state where NSM and skeletogenic marker genes were co-expressed.

Asymptotic Modal Analysis (AMA) is a computationally efficient and accurate method for studying the response of dynamical systems experiencing banded, random harmonic excitation at high frequencies when the number of responding modes is large. In this work, AMA has been extended to systems of coupled continuous components as well as nonlinear systems. Several prototypical cases are considered to advance the technique from the current state-of-the-art. The nonlinear problem is considered in two steps. First, a method for solving problems involving nonlinear continuous multi-mode components, called Iterative Modal Analysis (IMA), is outlined. Secondly, the behavior of a plate carrying a nonlinear spring-mass system is studied, showing how nonlinear effects on system natural frequencies may be accounted for in AMA. The final chapters of this work consider the coupling of continuous systems. For example, two parallel plates coupled at a point are studied. The principal novel element of the two-plate investigation reduces transfer function sums of the coupled system to an analytic form in the AMA approximation. Secondly, a stack of three parallel plates where adjacent plates are coupled at a point are examined. The three-plate investigation refines the reduction of transfer function sums, studies spatial intensification in greater detail, and offers insight into the diminishing response amplitudes in networks of continuous components excited at one location. These chapters open the door for future work in networks of vibrating components responding to banded, high-frequency, random harmonic excitation in the linear and nonlinear regimes.

In the past decade, a challenge to the canonical model of cell cycle transcriptional control has been posed by a series of high-throughput gene expression studies in budding yeast. Using genetic methods to inhibit or lock the activity of the cyclin-CDK/APC oscillator, these population studies demonstrated that a significant proportion of cell cycle transcription persists in the absence of cyclin-CDK/APC oscillations. To account for these findings, a network of serially activating transcription factors with sources of negative feedback from transcriptional repressors (referred to as a \say{TF network}) was proposed to drive cyclin-CDK/APC independent gene expression.

However, population studies of cell cycle gene expression are limited due to loss of phase synchrony that limits the timescale of measurement of gene expression and due to expression averaging that limits assessment of heterogeneity of expression within the population. To circumvent these limitations I used a single-cell timelapse microscopy approach to assess transcriptional dynamics of cell cycle regulated genes during extended cell cycle arrests in both the Gl/S and early mitosis (metaphase) phases of the cell cycle.

During G1/S arrest, transcriptional dynamics of four cell cycle regulated genes was assessed and activation of out-of-phase cell cycle transcription was observed in two of these genes. Though budding oscillations were observed in G1/S arrested cells, robust transcriptional oscillations were not seen for any of the four genes and budding dynamics were uncoupled from transcriptional dynamics after the first bud emergence. During cell cycle arrest in early mitosis, transcriptional dynamics of ten cell cycle regulated genes was assessed and activation of out-of-phase transcription was observed for four genes. All four genes activated once with canonical ordering but robust oscillations were not observed during mitotic arrest. Together these studies demonstrate activation, but not oscillation, of cell cycle transcription in the absence of cyclin-CDK/APC oscillations.

Bulges are ubiquitous building blocks of the three-dimensional structure of RNA. They help define the global structure of helices and points of flexibility allowing for functionally important dynamics, such as binding of proteins, ligands and small molecules to occur. This thesis utilizes a battery of nuclear magnetic resonance (NMR) methods and a model system of RNA bulge motifs, the transactivation response element (TAR) RNA from the human immunodeficiency virus type 1 (HIV-1), to characterize the dynamic energy landscape of bulges. Specifically investigating how it varies with bulge length, divalent cations, and in the presence of epi-transcriptomic modifications.

Deleting a single bulge residue (C24) from trinucleotide HIV-1 TAR bulge shifts a pre-existing equilibrium from the unstacked to a stacked conformation in which the bulge residues flip out of the helix and are highly flexible at the picosecond-to-nanosecond timescale. However, the mutation minimally impacts microsecond-to-millisecond conformational exchange directed towards two low-populated and short-lived excited conformational states that form through a reshuffling of bases pairs throughout TAR. The mutant does, however, adopt a slightly different excited conformational state on the millisecond timescale. Therefore, minor changes in bulge topology preserve motional modes occurring over the picosecond-to-millisecond timescales but alter the relative populations of the sampled states or cause subtle changes in their conformational features.

The impact of more broadly varying the length of the TAR poly-pyrimidine bulge (n = 1, 2, 3, 4 and 7) on inter-helical dynamics has been studied across a range of Mg2+ concentrations. In the absence of Mg2+ (25 mM monovalent salt), n 3 bulges adopt predominantly unstacked conformations (stacked population <15%) whereas 1-bulge and 2-bulge motifs adopt predominantly stacked conformations (stacked population >85%). The 2-bulge motif is biased toward linear conformations and increasing the bulge length leads to broader inter-helical distributions and structures that are on average more kinked. In the presence of 3 mM Mg2+, the helices predominantly coaxially stack (stacked population >75%), regardless of bulge length, and the midpoint for the Mg2+-dependent stacking transition does not vary substantially (within 3-fold) with bulge length. In the absence of Mg2+, the difference between the free energy of inter-helical coaxial stacking across the bulge variants is estimated to be ~2.9 kcal/mol, based on an NMR chemical shift mapping approach, with stacking being more energetically disfavored for the longer bulges. This difference decreases to ~0.4 kcal/mol in the presence of 3 mM Mg2+. It is proposed that Mg2+ helps to neutralize the growing electrostatic repulsion in the stacked state with increasing bulge length thus increasing the number of co-axial conformations that can be sampled.

N6-Methyladenosine (m6A) and N1-Methylpurine (m1A and m1G) xx or just refer to m1G?xx are post-transcriptional RNA modifications that are proposed to influence RNA function through mechanisms that can involve modulation of RNA structure. m6A is thought to modulate RNA structure by destabilizing base pairing. Here, it is shown that m6A can stabilize A-U base pairing and overall RNA structure when placed within the context of a bulge motif. m1A has also been shown to potently destabilize RNA duplexes due to their inability to favorably accommodate Hoogsteen base pairing. It is shown that such Hoogsteen base pairs can form in RNA when placed in the context of a bulge motif.

Taken together, the studies show that the dynamic energy landscape of polypyridine bulges is highly robust with respect to changes in bulge length allowing for gradual variations in the population and energetics of common conformations. Mg2+ plays an important role in smoothening these variations most likely by diminishing electrostatic contributions that could vary significantly across bulges of different length. The results also show that the structural impact of epi-transcriptomic modifications can be greatly altered relative to duplex RNA when targeting bulge motifs.

As non-coding RNAs are increasingly implicated in cellular regulatory functions and disease states, there is a need to deepen our understanding of RNA structure-function relationships as well as to develop methods targeting RNA with small molecules. The transactivation response element (TAR) RNA from human immunodeficiency virus type 1 (HIV-1) is an established drug target for the development of anti-HIV therapeutics and has served as a model system for understanding RNA dynamics and RNA:ligand interactions. Like many RNAs, HIV-1 TAR is a highly flexible molecule that experiences dynamics ranging from local fluctuations in base orientation and interhelical angles to higher-order dynamics that transiently alter base pairing away from the ground state (GS) secondary structure. The work presented in this thesis is aimed at developing approaches targeting TAR with small molecules that integrate its broad range of structural dynamics.

First, nuclear magnetic resonance (NMR) chemical shift mapping is applied in concert with fluorescence binding assays and computational docking to efficiently characterize the TAR-binding modes of a focused library of amiloride derivatives. Through this work, amiloride is established as a novel RNA binding scaffold with interesting structure-activity relationships. Ultimately, this approach yielded ten novel TAR binders with demonstrated selectivity for TAR over tRNA and with up to a 100-fold increase in activity over the parent dimethyl amiloride compound.

Next, we demonstrate that ensemble-based virtual screening (EBVS) is a powerful approach to predict ligand binding for flexible RNA targets. Here, we generate a library to evaluate EBVS enrichment by subjecting HIV-1 TAR to experimental high-throughput screening against ~100,000 drug-like small molecules. EBVS against a dynamic ensemble of the TAR GS determined previously by combining NMR spectroscopy data and molecular dynamics (MD) simulations scores hits and non-hits with an area under the receiver operator characteristic curve of ~0.85-0.94 and with ~40-75% of all hits falling within the top 2% of scored molecules. Importantly, the enrichment was shown to depend on the accuracy of the ensemble.

Finally, we explore the novel strategy of specifically targeting non-native RNA excited state conformations inspired by the fact that their altered secondary structures are likely functionally inactive and highly unique. We use a mutational stabilize-and-rescue approach to demonstrate that TAR ES2 dramatically inhibits TAR activity in cells, suggesting that stabilizing the ES conformation with small molecules would similarly inhibit activity. To pursue TAR ES2 as a potential target, we have determined the first-ever dynamic ensemble of an RNA ES using a combination of MD and NMR residual dipolar couplings (RDCs) measured on a highly accurate ES2-stabilizing mutant. This dynamic ensemble was subjected to our validated EBVS approach to identify small molecules that bind and stabilize TAR ES2. Using NMR chemical shift fingerprinting, we have identified molecules that bind the TAR ES2 structure, including two that induce significant broadening in wtTAR consistent with chemical exchange and two that show a preference for TAR ES2 over the GS.

Together, this work explores multiple novel strategies for structure-specific RNA targeting.

Magnetic resonance techniques are among the most powerful methods for characterization. However, they inherently suffer from an intrinsically low signal-to-noise due to the weak interaction of the nuclear spin with external magnetic fields. Hyperpolarization methods circumvent this limitation by deriving non-equilibrium spin polarization from an external source of spin order, dramatically increasing the magnetic resonance signals. Signal Amplification By Reversible Exchange, or SABRE, is a relatively new and promising method that derives spin hyperpolarization from parahydrogen, the singlet spin isomer of dihydrogen, allowing it to operate at a fraction of the cost of other hyperpolarization methods. A target molecule and parahydrogen transiently bind an organometallic complex, during which time polarization is transferred from the parahydrogen to target nuclei. The reversible nature of this interaction makes the hyperpolarization method readily scalable, giving SABRE the potential to supplant older, more expensive techniques and bring hyperpolarization technology to a broader audience. However, the current demonstrations of SABRE generate polarizations that are about an order of magnitude away from the upper theoretical limits of the technique, and variants of this experiment have been limited in target scope by the underlying physics. To address these limitations, this dissertation returns to examine the theoretical underpinnings of SABRE, and in doing so re-interrogates the unification of chemical exchange and quantum dynamics. We derive exact formulations of the chemical exchange interaction in both the magnetic resonance limits, which is used to construct a physically exhaustive computational model for SABRE. This model then facilitates in silico exploration of the system and permits us to address experimental limitations of the method. In particular, this dissertation utilizes simulations to develop and expand the capabilities of SABRE performed at arbitrarily high magnetic fields. We show that the limitations in the scope of SABRE imposed by the spin physics under these conditions may be removed, culminating in the first demonstration of simultaneous hyperpolarization of multiple components. This expansion is a key step towards translating SABRE into areas of conventional magnetic resonance such as biomolecular NMR and metabonomics. The theoretical framework presented here provides access to new routes for optimizing SABRE hyperpolarization, and we demonstrate that sequences may be developed to generate up to a five-fold increase in performance. Finally, we extend the theoretical treatment of chemical exchange within the Lindblad formalism to obtain exact master equations that are valid in any physical limit.

To accomplish the increasingly complex tasks that humans seek to achieve through technology, the advancement of the understanding and application of control systems is paramount for success. For relatively simple dynamic systems, model-based analytical control policies can be created without too much trouble (such as Proportional-Integral-Derivative (PID) or Linear-Quadratic-Regulator (LQR) controllers). However, for systems where the dynamics are very complex or even unknown, more advanced control techniques are necessary, especially when there is an interest in optimizing the control policy. This dissertation presents the application of nonlinear control methods to some challenging problems in vehicle automation and environmental testing.The first part of this dissertation presents the application of Reinforcement Learning (RL) to control a vehicle to get unstuck from a ditch. A simulation model of a vehicle moving on an arbitrary ditch surface was developed, with consideration of four different wheel-slip conditions. The transition between four state-spaces was developed as well as an integration routine to accurately integrate and switch between each of the four wheel-slip conditions. Two RL algorithms were applied to control the vehicle to escape the ditch – Probabilistic Inference for Learning COntrol (PILCO) and Deep Deterministic Policy Gradient (DDPG). PILCO was used to demonstrate the need of incorporating wheel-slip and the need for a neural network approach to capture all regions of the vehicle dynamic behavior. Reward functions were designed to incentivize the RL algorithms to achieve the desired goal. Both Rear-Wheel-Drive (RWD) and All-Wheel-Drive (AWD) simulation models were tested, and successful control policies achieved the goal of controlling the vehicle to get unstuck from the ditch while minimizing wheel-slip. Additionally, the control policies were tested over a wide range of ditch profile shapes, demonstrating a region of robustness. The second part of this dissertation presents a control solution in the area of environmental testing. In the area of environmental testing, there is an increasing demand for more challenging and aggressive environmental testing procedures. This dissertation presents a study on the convergence of the Matrix Power Control Algorithm (MPCA) for Random Vibration Control (RVC) testing, which is a particular type of environmental testing. A moving-average method was presented to reduce the control loop times and reduce the amplification of measurement noise. Additionally, Bayesian optimization was employed to optimize control parameters and the window size for the moving-average. An Euler-Bernoulli beam and the Box Assembly with Removable Component (BARC) structure were used in simulation and experiment, respectively, to demonstrate improvement in the convergence of MPCA over the baseline performance. In the experimental implementation, a LabVIEW controller was developed to implement the convergence improvements. This dissertation also presents a method for comparing Frequency Response Functions (FRFs), which is a data analysis problem in environmental testing. A Log-Frequency Shift (LFS) method was developed to shift a comparison FRF so that the dominant features (modes) of two FRFs were aligned. This then allowed the application of existing FRF comparison metrics with greater correlation with expert intuition. The Phase Similarity Metric (PSM) method was also introduced as an effective method for comparing the phases of two FRFs. These methods were demonstrated to be effective in simulation of an Euler-Bernoulli beam and validated using an experiment with random vibration applied to a thin beam.