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Enriching Architectures for Biosensing and Motor-Filament Systems Through the Programmability of DNA
Get PDFSince its inception, the field of DNA nanotechnology has focused on studying the fundamental behaviors and capabilities of engineered nucleic acids. A deep understanding of this toolkit has enabled advancements in several fields, for research tools and in translational applications. Together with its programmability and nanometric resolution, the great promise of DNA nanotechnology lies in the incorporation of structure and function in a single molecule. In this work, we show how these advantages can be leveraged to expand the capabilities of two different systems: a sensor for biomarkers and a motor-filament architecture. During our exploration, we also discover and work to overcome some of the less obvious limitations of the technology, shining light on more foundational questions.
We demonstrate an electrochemical biosensor based on a DNA origami that can detect and quantify nucleic acids and proteins in a package easily adaptable to different analytes by simply replacing the binder molecules. Upon target binding, the structure undergoes a large conformational change, bringing a multitude of redox reporters to the electrode surface where an electric current can be measured. The high number of reporter molecules on a single detector results in improved signal gain per binding event, allowing for the detection of low analyte concentrations, while the conformational change yields an unprecedented gain between the off and on state. We demonstrate how the system can be readily adapted to different analyte molecules and reused over several cycles to analyze multiple samples. We then run simulations of the detector molecule to understand structural deformations intrinsic to this design, in order to optimize the number and placement of the redox reporters. We discover and investigate a phenomenon that causes significant curling of the DNA origami, possibly limiting the contribution of many of the reporter molecules. We explore experimental directions to mitigate the issue by changing the configuration of the redox molecules and by designing stiffer sensors.
We then set out to integrate DNA origami-based nanostructures with an engineered dynein protein that can bind to and kick double-stranded DNA instead of tubulin. Motor-filament architectures have been studied as the main mechanism for cellular transport and as a system that can exhibit mesoscopic active matter behaviors in biology, but the relative difficulty of engineering microtubules has hindered the exploration of their properties. The high-resolution programmability of DNA nanostructures makes them prime candidates to overcome this obstacle and this study has been enabled by the recent development of new protein motors where the tubulin binding domain is replaced by a DNA binding domain. We first look at DNA nanotubes, structures that resemble microtubules, but that retain a level of programmability that is typical of DNA nanotechnology. By exploiting the DNA strand displacement technique, we incorporate machinery that enables new behaviors, with a focus on different ways to turn gliding on and off by stopping the DNA nanotubes.
We then turn our focus to more complex gliders designed with DNA origami. We explore the space of DNA origami polymers in order to assemble superstructures that can be detected under light microscopy, encountering again issues of deformations due to the addition of overhangs. We then assess the gliding capabilities of DNA origami, designing ways to incorporate motor binding sequences on them, but we find that DNA origami sticks nonspecifically to the engineered dynein motors. After testing several different hypotheses, we gather evidence that this interaction might be caused by the large sequence variability of the scaffold strand in DNA origami, coupled with the recognition of spurious binding sequences by the motor proteins.</p
Mechanical Characterization of Irregular Architected Two-Phase Materials
Get PDFArchitected materials offer a wide range of mechanical properties through the choice of their constitutive materials and the design of their structure. Periodic architected materials are the most widely studied and used in practical applications, as their repeating unit cells are easy to design, fabricate, and analytically model, but these materials are only a small subset of the possible design space. Irregular architected materials, which are aperiodic but not necessarily stochastic, offer a way to achieve a wider design space of mechanical properties.
In this thesis, we explore the design space of irregular architected materials and relate structural irregularity to the mechanical properties using measures of topology and geometry. We show that these measures of irregularity can be used to spatially and temporally control the mechanical response across linear and non-linear regimes, including fracture and dynamic impact, and we show that irregularity leads to improved mechanical properties when compared with periodic equivalents. To generate the irregular architected materials, we use a virtual growth algorithm, which imitates the stochastic growth process of biological structures by assembling a finite set of building blocks according to local connectivity rules. By varying the building blocks and connectivity rules, we show how to achieve a wide range of structures with varying degrees of irregularity all the way up to fully periodic structures. This thesis primarily focuses on the fabrication and characterization of additively manufactured two-phase polymer composites, but the design methods and irregular structure characterizations are material-agnostic, opening up a wide design space for future architected materials which use irregularity to achieve excellent mechanical performances.</p
Synthesis and Spectroscopy of Open-Shell Complexes Bearing Unusual M-E (E = N, C) Bonding Motifs and Synthesis of Novel Weakly-Coordinating Anions with Applications in Coordination Chemistry and Electrochemistry
No full textThis dissertation focuses on a diverse range of topics centered around inorganic synthesis, ranging from spectroscopic studies of rare bonding motifs (Chapter 3 and Chapter 4) and applications of novel weakly-coordinating anions in applications in coordination chemistry and electrochemistry (Chapter 1 and Chapter 2). While the projects described herein are distinct in the nature of their execution, the utility and applications of synthetic inorganic chemistry are highlighted in all of the projects.
Chapter 1 describes the design principles and the synthesis a novel weakly-coordinating anion based on alkyl or aryl substituted silicates bearing fluorinated pinacolate ligands. A wide range of anions bearing distinct R groups were prepared, enabling facile tuning of anion sterics and solubility. A range of cations invoked in chemical reactivity studies supported by these novel anions was prepared, highlighting the utility of these novel anions in both coordination and catalysis. Cations relevant to electrochemical studies were also accessed, wherein the exceptionally wide stability window for the methyl-substituted variant was demonstrated. Reversible magnesium deposition and stripping supported by these anions were also shown, demonstrating the utility of these novel anions in next-generation battery chemistry applications.
Chapter 2 describes efforts towards developing reproducible and stable magnesium deposition and stripping chemistry supported by a novel silicon-based weakly-coordinating anion. Aspects that impact reproducible and stable magnesium electrochemistry described in prior literature were studied in detail. Emphasis was placed on probing the prevalent hypothesis in magnesium electrolyte literature that magnesium alkyl, aryl, and amido additives improve electrochemical performance by acting as water or impurity scavengers. A range of magnesium additives were tested, wherein the identity of the additives was shown to dictate magnesium deposition and stripping behavior. An unconventional magnesium hydrocarbyl species was identified as the active species responsible for improved Mg deposition/stripping performance, highlighting the utility of synthetic inorganic chemistry in elucidating fundamental electrochemistry.
Chapter 3 describes the synthesis and the spectroscopy of an unusual molybdenum para-terphenyl diphosphine complex bearing a terminal nitride and a parent amide motif. Detailed continuous wave- and pulse-electron paramagnetic resonance techniques were employed the interrogate the electronic structure of this unusual open-shell motif, revealing significant radical character on the amide motif. On the other hand, the terminal nitride motif showed negligible spin density. With further insight obtained from density functional theory calculations, the high spin density on the terminal amide motif was attributed to significant orbital overlap between the amide nitrogen py orbital with the Mo dxy orbital.
Chapter 4 describes the synthetic, spectroscopic, and computational studies of a pentametallic molybdenum-iron-sulfur cluster of MoS3Fe3CMo composition with μ4-carbide and μ2-CO motifs that resembles the lo-CO form of nitrogenase. The cluster was accessed via carbide transfer from a Mo carbide complex supported by a para-terphenyl diphosphine ligand. Different isotopologues of this cluster were accessed by selectively labelling the molybdenum para-terphenyl diphosphine precursor. This cluster displays an S = ½ ground spin state amenable for pulse electron paramagnetic resonance spectroscopy. Detailed spectroscopic studies reveal a significantly larger carbide hyperfine interaction than any observed for various states of nitrogenase studied thus far, thereby providing benchmarking information for metal-carbon interactions studied by electron paramagnetic resonance methods.
Appendix A describes the synthesis and preliminary reactivity studies of a heterometallic molybdenum-iron-nickel cubane supported by a bulky bisphenoxide ligand with a central anthracene linker, relevant to the active site of the nickel-iron carbon monoxide dehydrogenase. Preliminary electron paramagnetic resonance studies on this cubane were suggestive of an S = 2 ground state, wherein incorporation of a formal closed-shell nickel site into a trimetallic cluster significantly perturbs the electronic structure.
Appendix B describes efforts towards accessing molybdenum para-terphenyl disphosphine carbyne complexes with no bound carbon monoxide ligands. Preliminary studies on the molybdenum carbyne complexes showed that molybdenum complexes with a terminal carbide and a terminal chloride can be accessed.
Appendix C describes the synthesis and preliminary electrochemical studies of novel dianonic silicates supported by fluorinated pinacolate ligands, wherein magnesium deposition and stripping supported by a novel dianion was demonstrated
Optimization-Based Statistical Inference: Constrained Inverse Problems, Worst-Case Priors, and Kernel Regression
No full textOptimization provides a worst-case framework for quantifying uncertainty in statistical inference, delivering robust and transparent performance guarantees. While this approach provides rigorous bounds, it cannot easily incorporate large-scale data or produce estimates at a prescribed confidence level. To bridge this gap, this thesis develops optimization-based methods that assimilate data while retaining worst-case robustness, exploring three different contexts: Ill-posed inverse problems, Bayesian inference with unknown priors, and Gaussian process regression.
In the first, we introduce a new framework for frequentist, optimization-based intervals that provably achieves desired coverage. The framework unifies many previously proposed optimization-based intervals and disproves a conjecture dating back to 1965. In the second, we introduce data-likelihood constraints in Wald’s two-player zero-sum game, which renders the game computationally tractable and provides explicit certificates of minimax optimality. In the third, we develop new Gaussian process (GP) based methods for learning and solving partial differential equations and operator learning. In each setting, our GP algorithms achieve stronger convergence guarantees than existing machine-learning techniques without sacrificing predictive accuracy.
Across these three settings, estimates for the unknown quantity (a finite-dimensional parameter, a prior distribution, or a function, respectively) are obtained as the solution to an optimization problem that characterizes either worst-case or minimax optimality, therefore contributing towards a single optimization-centric view of uncertainty quantification.</p
Dynamic Safety Under Uncertainty: A Control Barrier Function Approach
No full textModern technological achievements in robotics, machine learning, and control promise an exciting future where autonomous robots are a useful part of everyday life, from automated manufacturing and driverless cars to robotic healthcare and autonomous delivery drones. However, as robots are deployed in increasingly complex, uncertain, and human-interactive environments, safety becomes paramount; we cannot deploy these systems at scale unless we are rigorously assured of their safety. Despite the capabilities of modern robotics, practical real-world safety is often achieved through conservative hardware designs, confining deployment regulations, or restrictive assumptions that severely limit a robot's capabilities.
The goal of this thesis is to develop methods for achieving dynamic safety: formal safety guarantees that preserve system performance and remain valid under uncertainty. To this end, this thesis advances the theory and practice of control barrier functions (CBFs), a leading framework for enforcing safety constraints on dynamical systems. While CBF-based methods offer strong theoretical guarantees, they do so by relying on several restrictive assumptions. Namely, they assume that the safety requirement and the system dynamics are compatible and that the dynamics model and state are perfectly known. These assumptions rarely hold in real-world settings and can result in false confidence and catastrophic safety failures when violated. This thesis addresses these gaps by systematically relaxing these assumptions and developing new theory to retain rigorous, deployable guarantees.
By leveraging structural properties of several relevant classes of system dynamics, I first present a myriad of constructive synthesis methods that make CBF design feasible for a wide range of robots. I then develop robust control methods that retain their safety guarantees in the presence of bounded dynamics and measurement uncertainty. However, despite the utility of these methods in guaranteeing safety, they often lead to highly conservative behavior that compromises system performance. Thus, to mitigate this conservatism, I leverage machine learning techniques to reduce uncertainty and determine desired levels of robustness. While this unification of machine learning techniques with safety-critical control may sacrifice formal guarantees, it enables safe and performant behavior in practice. Moreover, the robust CBF framework provides a valuable degree of interpretability absent from typical end-to-end approaches.
Next, seeking a middle ground between conservative absolute guarantees and capable-but-heuristic methods, I adopt a probabilistic notion of safety that provides risk-based guarantees in the presence of unbounded disturbances. In particular, by illustrating the fundamental connection between DCBFs and supermartingales, I develop new theoretical guarantees and propose several algorithms to achieve safety in the presence of stochastic uncertainty. I then deploy these methods on several complex systems experiencing significant uncertainty, including a quadrotor robot with a slung payload, a humanoid robot walking in unstructured environments, and multiple robots performing dynamic collision avoidance. To achieve this, we use generative modeling techniques to capture the necessary understanding of the uncertainty distribution. Here, I also forego the traditional CBF-based safety filter paradigm and show the performance and safety improvements that can be gained through the unification of CBFs and horizon-based methods such as model predictive control (MPC).
Together, the contributions of this thesis represent an advancement towards dynamic, safe, and capable robotic autonomy under uncertainty. The risk-aware, robust safety-critical control methods proposed here help close the gap between theoretical safety guarantees and the demands of real-world deployment.</p
Aqueous Metallo-Megasupramolecules: From Stability to Extensional Flow Properties
No full textThe addition of long, flexible polymers (> 1 Mg/mol) to a fluid is known to reduce turbulent drag and control droplet behavior, which has the potential to significantly enhance the efficiency of engineering flows across various industries, from agriculture to aviation. However, hydrodynamic forces can break the polymers and diminish their effectiveness, which is presently a major roadblock to their practical utilization in both applications and research. To address this challenge, the Kornfield group developed end-associative, self-healing polymers for use in fuel and, more recently, for use in water—aqueous terpyridine-ended polyacrylamide (TPAM) supramolecules. This thesis examines the relationships between the molecular structure of TPAM, the amount of metal provided to link pairs of chain ends, and kinetic processes of the resulting supramolecules and the rheological properties and performance they provide. The most useful polymers for reducing turbulent drag, controlling mist, and tailoring droplet impact behavior combine high efficacy at low concentration (< 0.1 wt%), minimal impact on shear viscosity (< 2x), and long extensional relaxation time (> 1 ms), enabling them to stretch and resist elongational flow in turbulent eddies or fluid filaments. This thesis explores the fundamental nature of TPAM supramolecules and their potential utility as a rheological modifier, using measurements of molecular weight distributions and extensional relaxation times to illuminate the relationship between supramolecular structure and flow behavior.
First, we examine chemical degradation (desirable in the environment, but not during use), revealing that its rate can be controlled by limiting air exposure, avoiding an excess of metal ions relative to ligands, and storing samples in refrigerated conditions (4℃). Next, we assess how changes in metal-to-ligand ratios (M:L) and unimer lengths influence TPAM’s megasupramolecular size, equilibration, and decay dynamics, showing that the presence of supramolecules comprising over 10 unimers gives rise to a relaxation time around 2 ms at 0.04 wt%—long and dilute enough to cause drag reduction. In pursuit of even longer supramolecules (and thus longer relaxation times) with the same amount of TPAM, we modified the solution preparation protocol by introducing metal ions to a more concentrated TPAM solution prior to dilution. This exposed new and intriguing topologies with molecular weights extending beyond our measurable limit (10 Mg/mol), expanding the envelope of the longest accessible relaxation times (from ~2 to ~6 ms with M:L = 1:2 for Ni(II):terpyridine). We evaluated their potential as chain scission-resistant, turbulent drag-reducing agents. Initially, they reduce drag while maintaining backbone integrity; however, their supramolecular structure and extended relaxation time are not retained after multiple passes through contraction, turbulent, and expansion flows. The preservation of backbone integrity, along with the broad range of relaxation times achieved using more conventional linear topologies (up to ~3 ms), suggests that TPAM is a promising and robust rheological modifier worthy of continued investigation. Our findings enhance understanding of TPAM’s structural and rheological properties under a range of conditions and lay the groundwork for further study of aqueous megasupramolecule dynamics and applications.</p
Soft Theorems from Spontaneous Symmetry Breaking
No full textSpontaneous symmetry breaking occurs when the vacuum state is not preserved under (a subset of) symmetries in the theory. Instead, the symmetry is non-linearly realized by the associated massless degrees of freedom, the Nambu-Goldstone bosons. At the level of on-shell observables, the non-linearly realized symmetry is manifested as a universal structure of scattering amplitudes in the so-called soft limit, which means sending the momenta of a Nambu-Goldstone modes to zero.
In this dissertation, we further explore the link between spontaneous symmetry breaking and infrared dynamics of massless scalars. First, we derive soft theorems for theories with spontaneously broken Poincaré symmetries, corresponding to effective field theories for condensed matter systems such as solids, fluids, superfluids, and framids. We also implement a bootstrap in which the enhanced vanishing of amplitudes in the soft limit is taken as an input, thus sculpting out a subclass of exceptional solid, fluid, and framid theories.
Next, we consider spontaneous breaking of higher symmetries. We derive a new sub-leading double soft pion theorem in theories with a spontaneously-broken continuous 2-group global symmetry, which intertwines amplitudes with different numbers of pions and photons. We also provide a novel derivation of the leading soft photon theorem from the Ward identity of an emergent 1-form global symmetry in effective field theories where antiparticles are integrated out.
Finally, we turn to universal features in low-energy dynamics of generic effective field theories. We extend the scalar geometric soft theorem by allowing the massless scalar to couple to other scalars, fermions, and gauge bosons. The soft theorem keeps its geometric form, but where the field-space geometry now involves the full field content of the theory. As a bonus, we also present novel double soft theorems with fermions, which mimic the geometric structure of the double soft theorem for scalars.</p
Tuning Hybrid Optomechanics for Remote Entanglement
No full textSuperconducting microwave circuits are a leading platform for quantum computing, offering high coherence and controllability. However, their reliance on microwave photons, which are highly susceptible to thermal noise at room temperature due to their relatively low frequencies, necessitates operation at millikelvin temperatures. This requirement presents a major scalability challenge, particularly for connecting distant processors within a distributed quantum network. Microwave-optical transducers offer a promising solution by enabling coherent links between the microwave and optical domains, allowing quantum information to be shared via telecom-wavelength photons that propagate efficiently through low-loss optical fibers at room temperature. Among the various transduction platforms, hybrid piezo-optomechanical crystals (OMCs) are particularly promising due to their strong optomechanical and piezoelectric coupling and the potential for high-efficiency, low-noise transduction mediated by microwave frequency phonons. Proposed architectures for remote entanglement distribution rely on the interference of indistinguishable photons emitted from individual transducers. Although state-of-the-art fabrication techniques provide nanometer-level precision, achieving identical OMCs remains challenging, leading to device-to-device variations in optical and mechanical resonance frequencies. To enable scalable quantum networks based on optically mediated remote entanglement, a robust, selective, and precise post-fabrication tuning method is essential.
Here, we present an in situ, selective technique for tuning the optical and acoustic resonances of hybrid silicon optomechanical crystals through electric field-induced nano-oxidation using an atomic force microscope (AFM). The localized growth of a few-nanometer-thick silicon dioxide layer modifies the local permittivity, stiffness, and mass of the OMC at the oxidation region, consequently altering the optical and mechanical modes supported by the structure. Using this method, we demonstrate precise and targeted spectral alignment of both optical and mechanical modes across multiple devices within their respective mode linewidths. In addition, we extend this technique to achieve selective room-temperature pre-alignment of the optical mode of OMCs for precise wavelength alignment at millikelvin temperatures. This capability is essential for realizing indistinguishable photon emission from independently fabricated transducers toward entanglement of distant quantum processors in optically linked quantum networks.
In the second part of this thesis, we present a side-coupled two-dimensional optomechanical cavity designed for high-efficiency, low-noise phonon–photon transduction. This architecture enables near-unity conversion efficiency between optical photons and microwave frequency phonons while maintaining thermal occupancy of the phonon mode well below unity, an essential requirement for quantum-enabled operations. Finally, we describe the design, fabrication, and preliminary characterization of a microwave-to-optical transducer based on this new side-coupled 2D OMC platform.</p
Theoretical Modeling of Interactions Between Electrolytes and Surfaces
Get PDFElectrolytes are ubiquitous in science and engineering and are of active interest, owing to their applications biology, energy storage, colloidal suspensions, and even climate. Near a surface, electrolyte solutions exhibit a plethora of rich thermodynamic and structural phenomena, owing to the interplay of long-ranged electrostatics and nonelectrostatic interactions between ionic species, solvent, and the surface. In this thesis, we present a pedagogical formulation for the thermodynamics of electrolyte solutions near charged surfaces, followed by an examination of interactions and structure of different types of electrolytes near surfaces. Specifically, we investigate the difference between constant surface charge and constant surface potential boundaries in electrolyte solutions, the capacitance applications, double-layer structure, and screening behavior of a zwitterionic polymers, as well as the effect of image charge on structure, capacitance, and forces in simple electrolytes near metal, dielectric, and dielectrically-saturated metal surfaces. We conclude with a Gaussian-fluctuation model for ions with soft-core excluded volume interactions
Spin-Orbit Enhanced Superconductivity in Graphene Heterostructures
Get PDFFlat electronic bands in moire and crystalline graphene multilayers showcase emergent correlated phenomena including correlated insulators, superconductivity, topological orders, etc. This thesis focuses on the electrical transport characterization of superconductivity in moire and crystalline graphene, with the proximity of a layer of tungsten diselenide (WSe₂) that induces spin-orbit coupling (SOC). The interplay between spontaneous symmetry-breaking and explicit spin-orbit interactions emerges various unconventional superconducting pairing.
In the case of moire graphene multilayers, superconductivity in twisted bilayer graphene persists much far away from the magic angle at which electronic correlations dominate. At the lowest twist angle 0.79°, superconductivity appears despite the absence of any insulating states. By changing the moire twist angle, the ratio between Coulomb interactions and kinetic energy is reduced, and we thus established a hierarchy of various symmetry-breaking orders. Importantly, superconductivity is tightly related to the half-filling symmetry-breaking reconstructions. We further generalize the twisted moire graphene to trilayer, quadrilayer and pentalayer cases. Characterizations around their respective magic angle show that superconductivity is more prominent in filling phase space when the number of layers is increased.
We then investigated the effect of SOC on correlated phases in crystalline Bernal-stacked bilayer graphene. Surprisingly, placing monolayer WSe₂ on bilayer graphene promotes Cooper pairing to an extraordinary degree: field-induced superconductivity is stabilized at zero magnetic field, exhibits an order of magnitude enhancement in critical temperature and occurs over a density range that is wider by a factor of eight. The superconductivity descends from a broken-symmetry parent state with two out of the four spin-valley flavors being predominantly populated. Moreover, the superconductivity arises only for perpendicular electric fields that push hole wavefunctions toward WSe₂, indicating that proximity-induced Ising spin-orbit coupling plays a key role in stabilizing the pairing.
The last part of the thesis focuses on a new degree of freedom: interfacial twisting between graphene and WSe₂. We experimentally demonstrate the "moireless" tuning of superconductivity in Bernal bilayer graphene proximitized by WSe₂. The precise alignment between the two materials systematically controls the strength of the induced Ising SOC, profoundly altering the phase diagram. As Ising SOC is increased, superconductivity onsets at a higher displacement field and features a higher critical temperature, reaching up to 0.5K. Within the main superconducting dome and in the strong Ising SOC limit, we find an unusual phase transition characterized by a nematic redistribution of holes among trigonally warped Fermi pockets and enhanced resilience to in-plane magnetic fields. Moreover, we identify two additional superconducting regions, one of which descends from an inter-valley coherent normal state and exhibits a Pauli-limit violation ratio exceeding 40, among the highest for all known superconductors.</p