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SuperCDMS HVeV Run 2 Low-Mass Dark Matter Search, Highly Multiplexed Phonon-Mediated Particle Detector with Kinetic Inductance Detector, and the Blackbody Radiation in Cryogenic Experiments
Get PDFThere is ample evidence of dark matter (DM), a phenomenon responsible for ≈ 85% of the matter content of the Universe that cannot be explained by the Standard Model (SM). One of the most compelling hypotheses is that DM consists of beyond-SM particle(s) that are nonluminous and nonbaryonic. So far, numerous efforts have been made to search for particle DM, and yet none has yielded an unambiguous observation of DM particles.
We present in Chapter 2 the SuperCDMS HVeV Run 2 experiment, where we search for DM in the mass ranges of 0.5--10⁴ MeV/c² for the electron-recoil DM and 1.2--50 eV/c² for the dark photon and the Axion-like particle (ALP). SuperCDMS utilizes cryogenic crystals as detectors to search for DM interaction with the crystal atoms. The interaction is detected in the form of recoil energy mediated by phonons. In the HVeV project, we look for electron recoil, where we enhance the signal by the Neganov-Trofimov-Luke effect under high-voltage biases. The technique enabled us to detect quantized e⁻h⁺ creation at a 3% ionization energy resolution. Our work is the first DM search analysis considering charge trapping and impact ionization effects for solid-state detectors. We report our results as upper limits for the assumed particle models as functions of DM mass. Our results exclude the DM-electron scattering cross section, the dark photon kinetic mixing parameter, and the ALP axioelectric coupling above 8.4 x 10⁻³⁴ cm², 3.3 x 10⁻¹⁴, and 1.0 x 10⁻⁹, respectively.
Currently every SuperCDMS detector is equipped with a few phonon sensors based on the transition-edge sensor (TES) technology. In order to improve phonon-mediated particle detectors' background rejection performance, we are developing highly multiplexed detectors utilizing kinetic inductance detectors (KIDs) as phonon sensors. This work is detailed in chapter 3 and chapter 4. We have improved our previous KID and readout line designs, which enabled us to produce our first ø3" detector with 80 phonon sensors. The detector yielded a frequency placement accuracy of 0.07%, indicating our capability of implementing hundreds of phonon sensors in a typical SuperCDMS-style detector. We detail our fabrication technique for simultaneously employing Al and Nb for the KID circuit. We explain our signal model that includes extracting the RF signal, calibrating the RF signal into pair-breaking energy, and then the pulse detection. We summarize our noise condition and develop models for different noise sources. We combine the signal and the noise models to be an energy resolution model for KID-based phonon-mediated detectors. From this model, we propose strategies to further improve future detectors' energy resolution and introduce our ongoing implementations.
Blackbody (BB) radiation is one of the plausible background sources responsible for the low-energy background currently preventing low-threshold DM experiments to search for lower DM mass ranges. In Chapter 5, we present our study for such background for cryogenic experiments. We have developed physical models and, based on the models, simulation tools for BB radiation propagation as photons or waves. We have also developed a theoretical model for BB photons' interaction with semiconductor impurities, which is one of the possible channels for generating the leakage current background in SuperCDMS-style detectors. We have planned for an experiment to calibrate our simulation and leakage current generation model. For the experiment, we have developed a specialized ``mesh TES'' photon detector inspired by cosmic microwave background experiments. We present its sensitivity model, the radiation source developed for the calibration, and the general plan of the experiment.</p
Incorporation of Non-Canonical Proline Residues into Proteins Expressed in Escherichia coli
Get PDFNon-canonical proline residues expand the chemical space about proline, while maintaining some conformational properties of the canonical residue. The translational machinery of Escherichia coli can accommodate close structural analogs of proline, which has enabled the production of recombinant proteins that contain non-canonical residues at proline positions. However, proline mutagenesis in E. coli is restricted to a relatively small set of proline variants, and protein science and engineering efforts utilizing non-canonical proline residues are limited.
This thesis aims to expand the scope of proline analogs that can be accepted by E. coli, and demonstrate the utility of proline mutagenesis in modifying and studying protein behavior. In Chapter II, we describe the incorporation of three aliphatic proline residues into recombinantly-produced insulin, and find that these modest modifications at ProB28 alter the biophysical properties of the therapeutic protein. In particular, the addition of an exocyclic olefin at B28 accelerated insulin fibril formation, while 4-methyl substituents increased the rate of dissociation from the pharmaceutically-formulated insulin hexamer. We expand our proline mutagenesis approach to monomeric insulins in Chapter III. 4-fluorinated proline analogs replaced ProB29 of the fast-acting insulin lispro; 4S-fluorination of ProB29 slowed fibril formation. Chapter IV describes the incorporation of the photo-activatable proline analog "photo-proline" into proteins expressed in E. coli, and Chapter V discusses our efforts to engineer the E. coli prolyl-tRNA synthetase to accommodate more diverse proline substrates. Together, this work expands the proline analogs accessible to recombinant expression in E. coli, and demonstrates their use in probing and engineering the biophysical properties of proteins.</p
Experimental and Theoretical Frameworks for Enabling Environmental Synthetic Biology
Get PDFAlthough the field of synthetic biology has made great advances toward becoming a mature engineering discipline over its first quarter-century, the vast majority of these efforts have focused on improving the design and performance of genetic circuits intended to operate in well-controlled, laboratory settings. The goal of safely deploying engineered microbes to reliably perform their programmed functions in natural, uncontrolled environments begets its own set of foundational challenges that will require new frameworks that shift our existing mindsets about the way we engineer biological systems.
These frameworks, because they focus on enabling system properties that were not priorities for conventional synthetic biology research, can constitute a new field of research which I refer to as environmental synthetic biology. The central priorities of environmental synthetic biology include (1) developing and characterizing effective ways to introduce engineered biological systems into natural environments, (2) ensuring that the performance of these systems can remain robust and predictable in the face of environmental variability, (3) developing and characterizing ways to control and monitor the behavior of an engineered system after deployment in an inaccessible environment, and (4) developing fundamental architectures to enable autonomous system operation and adaptation within environmental contexts.
In this thesis, I present the initial steps towards the development of three frame- works that address these priorities of environmental synthetic biology. The first framework, described in Chapter 2, demonstrates the potential of using DNA as the substrate for addressable and adaptable intercellular communication in engineered populations. This enables the ability to one day create multicellular systems that can autonomously reconfigure their own architecture in the face of changing environmental conditions. The second framework, described in Chapters 3 and 4, presents a new mathematical representation of biomolecular reaction systems that enables geometric bounds on the space of possible behaviors under all possible configurations for a particular system architecture. The third, ongoing framework emphasizes the importance of explicitly incorporating the physiological state of the host cell into the assessment of a genetic circuit’s behavior by exploring the impact of cellular growth arrest on transcriptional response curves. The preliminary results of this work are presented in Chapter 5.</p
Structure and Mechanism of the Human ER Membrane Protein Complex
Get PDFThe successful synthesis, targeting, insertion, folding, and assembly of membrane proteins into designated membranes is a crucial process in cell biology. Recent research has shed valuable light on this process through the discovery of the endoplasmic reticulum (ER) membrane protein complex (EMC) and its role in membrane protein biogenesis and quality control. As part of my Ph.D. research in the Voorhees lab, I collaborated with esteemed scientists to investigate the EMC in atomic detail. Described in this thesis is the mechanistic basis of EMC function in membrane protein biogenesis, including recent insights into its broader role beyond its well-defined insertase function. First, we determined the structure of the human EMC using single-particle cryo-electron microscopy (cryo-EM). The structure revealed that it utilizes a mechanism similar to other protein-conducting channels, which involves membrane thinning and polar intramembrane residues to transport substrate transmembrane domains from the cytosol into the membrane. The EMC structure provided the foundation for the subsequent rigorous analysis of its role in membrane protein biogenesis. Through this work, we demonstrate the molecular mechanisms involved in the EMC-dependent path a membrane protein takes, from its initial cytosolic capture by methionine-rich loops of the EMC to its eventual membrane insertion via a hydrophilic vestibule. We further show that specific polar intramembrane residues on the EMC serve as an ER “selectivity filter” which uses charge-repulsion properties to reject mis-targeted mitochondrial membrane proteins and maintain organelle integrity. We also demonstrate that the EMC ensures that transmembrane-spanning substrates adopt the correct topology by promoting the “positive-inside” rule, which states that positively and negatively charged amino acids localize to the interior (cytoplasmic) and exterior (non-cytoplasmic) sides of membranes, respectively. Finally, our studies suggest that the EMC has a broader role beyond its well-defined insertase function. Specifically, we found that the EMC physically binds to other factors involved in membrane protein biogenesis, providing a shared interaction surface that acts as a hub to integrate signals from other pathways. Using a combination of structural and functional approaches, we identified the EMC’s interaction with Nodal modulator (NOMO) complex, which is part of the multipass translocon complex and facilitate membrane protein biogenesis. Together, these results define and expand the model for membrane protein biogenesis at the ER membrane by the EMC and highlight the complex interplay between different factors in this important process. Together, these results define and expand the model for membrane protein biogenesis at the ER membrane by the EMC and highlight the complex interplay between different factors in this important process
Experiments in Thermal Ignition: Influence of Natural Convection on Properties of Gaseous Explosions
Get PDFExplosion hazards exist in many industrial sectors including chemical processing, mining, nuclear power, and aviation. Thermal ignition is the name given to the particular case where the initiation energy is supplied via thermal heating of a gas. The critical conditions leading to thermal ignition are in general highly configuration dependent and require a broad set of experimentation to investigate the influence of wide ranging physical processes on ignition. To aid this effort the present work comprises three main experiments covering a range of thermal ignition hazards. First, a heated atmosphere test with fuel injection (ASTM-E659) was implemented to enable the study of heavy hydrocarbon fuels such as Jet A and multicomponent surrogates. This approach showed the existence of cool flame ignition modes near the ignition thresholds for most fuels. The autoignition temperature (AIT) of commodity Jet A was found to be reasonably reproducible by most alkane fuels including n-hexane. Multicomponent surrogates were also able to match the cool flame ignition regimes reasonably well.
Next, ignition using a vertical heated surface in a cold reactive atmosphere was studied in the laminar flow regime. The effects of dilution with nitrogen and reduced pressure were explored for n-hexane/oxygen/nitrogen mixtures. Results found a modest dependence of minimum ignition temperatures on pressure and nitrogen fraction however, with a significant reduction in explosion severity as measured by the maximum overpressure and transient duration. At sufficiently reduced oxygen concentrations, localized weakly propagating flames were found to form in the thermal layer near the surface and produce sustained puffing flame instabilities. One-dimensional flame simulations with detailed kinetics were conducted to supplement and aid in interpretation of the experimental measurements for diluted mixtures. Correlation of ignition thresholds were found to be possible using simplified flame properties and laminar natural convection boundary layer theory.
Finally, a novel experiment was designed to explore the effects of turbulent transition and confinement of large heated surfaces on ignition thresholds. Modeling of the energy balance for resistive heating showed that cylinders up to 36 in. long could be heated using modest power supplies. Six cylinder sizes of varying length were chosen based on this analysis to explore laminar, transitional, and turbulent flow regimes. A large scale flow visualization system was created to study these flow regimes and found that turbulent transition occurred for cylinders as small as 10 in. long for wall temperatures of 1000 K. A study of the transitional dependence on temperatures for large temperature difference (T = 555--1140 K), highly non-Boussinesq conditions found that the transitional Rayleigh number decreased by two orders of magnitude in this regime. The thermal layer thickness at the transition height was estimated in order to obtain a relevant length scale to the boundary layer transition problem. Using this a more consistent transition criteria was obtained (Ra using the thermal thickness length scale) and found to vary by only a factor of two in the high temperature cases studied.
The implementation of these cylinders in ignition testing revealed that there was a strong influence of heating rate due to confinement. The use of absorption spectroscopy showed that for low heating rates the fuel was mostly consumed in low temperature reactions prior to or in place of rapid ignition. This resulted in larger ignition temperatures and weak flames which propagate only in the thermal boundary layer. This effect was explained as a consequence of reduced flow recirculation times due to confinement. A strong influence of turbulence was also found for ignition thresholds when compared with other data for ignition by vertical hot surfaces in the laminar regime. Turbulence was also found to strongly influence the explosion properties due to turbulent flame acceleration. This resulted in larger explosion pressures, shorter transients, and faster flames.</p
Revocable Cryptography in a Quantum World
Get PDFQuantum cryptography leverages unique features of quantum mechanics in order to construct cryptographic primitives which are oftentimes impossible for digital computers. Cryptographic applications of quantum computers therefore have the potential for useful quantum advantage---entirely without computational speed-ups. Can we use the power of quantum states to address fundamental limitations in the world of classical cryptography, such as the intricate problem of ``revoking'' information from an untrusted party? This thesis undertakes a systematic study of how to delegate and revoke privileges in a world in which quantum computers become widely available. As part of a single framework we call revocable cryptography, we show how to revoke programs, encrypted data, and even cryptographic keys under standard assumptions.
In the first part of this thesis, we focus on the following question: can we use the no-cloning principle of quantum mechanics and encode a program in such a way that it can be evaluated, yet it cannot be pirated? Naturally, we would also like to ensure that, once the program is ``returned,'' the recipient loses its ability to evaluate it. While this quantum notion of secure software leasing (SSL) was shown to be impossible for general programs by Ananth and La Placa (Eurocrypt 2021), their work left open the possibility that it is achievable for more primitive classes of programs. We construct an SSL scheme for a large class of evasive functions known as compute-and-compare programs---a more expressive generalization of point functions. Our scheme can be instantiated with any cryptographic hash function, and we prove its security in the quantum random oracle model. As a complementary result, we also construct a quantum copy-protection scheme for multi-bit point functions, which achieves a related but stronger notion of software protection previously introduced by Aaronson (CCC 2009).
In the second part of this thesis, we ask: is it possible to provably delete information by leveraging the laws of quantum mechanics? We revisit a cryptographic notion called certified deletion, which was proposed by Broadbent and Islam (TCC 2020). While this remarkable notion allows a classical verifier to be convinced that quantum ciphertext has been deleted by an untrusted party, it offers no additional layer of functionality. We use Gaussian superpositions over lattices to construct the first fully homomorphic encryption scheme with certified deletion -- a protocol which allows an untrusted quantum server to compute on encrypted data and to also prove data deletion to a client. Our scheme has the desirable property that verification of a deletion certificate is public; meaning anyone can verify whether deletion has taken place. Assuming the quantum subexponential hardness of the learning with errors problem (Regev, STOC 2005), we can prove that our scheme achieves a particularly strong information-theoretic deletion guarantee; namely, once a valid deletion certificate is presented, the plaintext remains hidden even if the adversary is subsequently allowed to run in unbounded time.
In the final part of this thesis, we ask: is it possible to revoke a crytographic key by using the power of quantum information? We give an affirmative answer to this question and design cryptosystems with key-revocation capabilities; specifically, we consider schemes with the guarantee that, once the secret key (represented as a quantum state) is successfully revoked from a user, they no longer have the ability to perform the same functionality as before. We define and construct several fundamental cryptographic primitives with key-revocation capabilities, namely pseudorandom functions, secret-key and public-key encryption, and even fully homomorphic encryption, assuming the subexponential hardness of the learning with errors problem. Central to all our constructions is our approach for making the Dual-Regev encryption scheme (Gentry, Peikert and Vaikuntanathan, STOC 2008) revocable.</p
Measuring Fundamental Symmetry Violation in Polyatomic Molecules
Get PDFOpen questions in fundamental physics, such as the cosmological origins of the observed imbalance of matter and antimatter, motivate the search for fundamental symmetry violating physics beyond the Standard Model (BSM). Recent measurements of heavy, polar, diatomic molecules constrain the existence of new, Parity (P) and Time-reversal (T) violating physics at 10-50 TeV energy scales, exceeding the reach of particle colliders. The power of existing molecular measurements motivates us to pursue the next-generation of searches for symmetry violation. By adopting polyatomic molecules as an experimental platform, we can generically combine laser-cooling and trapping, BSM sensitivity, and exquisite quantum control over P and/or T violating energy shifts. These improvements are projected to increase the sensitivity of measurements to the PeV energy scale. In this thesis, we develop the foundations for new physics searches using cold and ultracold, linear triatomic molecules. These molecules have long-lived vibrational bending modes with closely spaced, opposite parity doublets, a key structure that aids polarizability, molecule control, state engineering, and systematic suppression. We produce a cryogenic buffer gas beam of cold YbOH molecules, using laser-enhanced chemical reactions to increase molecular yield by an order of magnitude. As a prerequisite for precision measurements, we perform high-resolution spectroscopic characterization of both the ground and excited bending modes of YbOH. Next, we present detailed tests of quantum state preparation and readout protocols in a YbOH beam, successfully demonstrating Ramsey interferometry using two-photon transitions. Finally, as part of the PolyEDM collaboration, we illustrate the power of polyatomic molecules by combining laser cooling and optical trapping with quantum state engineering to perform proof-of-principle measurements of P,T violating physics in magnetically-insensitive states of ultracold CaOH molecules at Harvard University. Our results open the door to a wide range of quantum-enhanced symmetry violation searches benefiting from the unique structural features of polyatomic molecules.</p
Vision-Based Navigation and Large-Scale Estimation for Spacecraft Swarms
Get PDFThere has been dramatic growth in the space industry over the past 20 years. Around the same time, robotics and autonomy research has advanced significantly, resulting in a plethora of new mission concepts employing autonomy, such as on-orbit inspection, mission extension, space structure assembly, and orbital debris removal becoming within the realm of possibility. Two of the key autonomous technologies that are critical to the success of these missions are (1) advanced coordination of multi-agent systems and (2) robust vision-based navigation for on-orbit servicing in close proximity. However, there are challenges to simply applying the existing technology to space systems. First, there are domain-specific challenges that are unique to space, such as orbital mechanics and harsh lighting conditions. Second, even at a theoretical level, previous works in the controls and robotics literature are limited when applied to large-scale, locally coupled systems such as spacecraft swarms. To this end, this thesis develops novel algorithms for addressing these gaps.
In the first part of the thesis, we present a decentralized, scalable algorithm for swarm localization, called the Decentralized Pose Estimation (DPE) algorithm. With the DPE algorithm, each spacecraft computes relative navigation estimates with respect to others in the swarm but achieves higher performance through the benefit of multi-agent coordination. The DPE algorithm considers both communication and relative sensing graphs and defines an observable local formation. Each spacecraft jointly localizes its local subset of spacecraft using direct and communicated measurements. Since the algorithm is local, the algorithm complexity does not grow with the number of spacecraft in the swarm. As part of the DPE, we present the Swarm Reference Frame Estimation (SRFE) algorithm, a distributed consensus algorithm to co-estimate a common Local-Vertical, Local-Horizontal frame. The DPE combined with the SRFE provides a scalable, fully-decentralized navigation solution that improves the estimation accuracy compared to when without multi-agent coordination. Numerical simulations and experiments using Caltech's robotic spacecraft simulators are presented to validate the effectiveness and scalability of the DPE algorithm. We show that DPE has much higher accuracy than the best possible estimate without any coordination, while simultaneously being scalable to an arbitrarily large number of agents.
In the second part of the thesis, we propose a novel computer vision algorithm to track the pose of an unknown and uncooperative target using multiple decentralized observers. Vision-based pose determination of an unknown target is challenging due to factors such as lack of cooperative visual markers and harsh lighting conditions of space, and the problem is even harder for distributed observers. To address this challenge, we develop the algorithm called the Multi-Spacecraft Simultaneous Estimation of Pose and Shape algorithm or MSEPS. Within MSEPS, a team of chaser spacecraft, each equipped with a monocular camera, exchange information over a local network to jointly estimate the relative kinematic state of the target and its sparse shape landmarks. In this approach, each spacecraft processes its images and extracts its own set of visual keypoints in parallel. Then, the team uses the local network to jointly estimate the target pose and shape in a distributed fashion by applying the consensus algorithm over the inter-spacecraft communication links. To the best of the authors' knowledge, this is the first cooperative vision-based algorithm for estimating the pose and shape of a space object by means of an arbitrary number of spacecraft.
We validate our algorithm using simulations of relative orbits and observations captured by each chaser spacecraft and show the multiple observers successfully agree on a consistent estimate and track the target pose accurately.
In the third part of the thesis, we develop some new simulation tools that bridge the gap between robotics and space technology. When developing robotics algorithms for on-orbit systems such as DPE and MSEPS, we identified a need for new simulation tools that tightly integrate robotics algorithms with high-fidelity models of space environments such as astrodynamics effects and visual conditions. To this end, we first develop a ROS2-compatible software interface for Basilisk, the open-source astrodynamics simulation software. This tool allows running Basilisk in parallel with ROS2 in real-time and translates messages between Basilisk modules and ROS2 modules, such that control algorithms implemented in ROS2 can interact with the high-fidelity dynamics within Basilisk in a closed-loop fashion. Second, we develop a ROS2-compatible camera simulation module that uses the Neural Radiance Fields (NeRF) to rapidly generate novel images. These synthetic images are used as inputs to validate the vision-based navigation algorithm in a closed-loop fashion. To validate these simulation tools, we also developed a set of autonomous algorithms for on-orbit inspection and use the simulated measurements as inputs to the algorithm. The real-time numerical simulations demonstrate that our tools can be integrated with autonomy algorithms implemented in ROS2 in a closed-loop fashion to validate the feasibility of the mission.
In the process of addressing some lessons learned from DPE and MSEPS works, we identified that there is a gap in general frameworks for solving the optimal estimation problems for probabilistic inference of large-scale problems involving networked systems. This gap is not just applicable to spacecraft swarms, but also to a general class of large-scale, multi-agent problems in robotics and controls such as localization and mapping, wireless sensor networks, and electrical power grids. Therefore, in the fourth part of the thesis, we address this fundamental gap by developing novel algorithms for Distributed Factor Graph Optimization (DFGO) problems that arise in large-scale networked systems. We develop algorithms for both batch and real-time problems. First, for the batch DFGO problem, we derive a type of the Alternating Direction Method of Multipliers (ADMM) algorithm called the Local Consensus ADMM (LC-ADMM). LC-ADMM is fully localized; therefore, the computational effort, communication bandwidth, and memory for each agent scale like O(1) with respect to the network size. We establish two new theoretical results for LC-ADMM: (1) exponential convergence when the objective is strongly convex and has a Lipschitz continuous subdifferential, and (2) o(1/k) when the objective is convex and has a unique solution. We also show that LC-ADMM allows the use of non-quadratic loss functions, such as l1-norm and Huber loss. Second, we also develop the Incremental DFGO algorithm (iDFGO) for real-time problems by combining the ideas from LC-ADMM and the Bayes tree. To derive a time-scalable algorithm, we exploit the temporal sparsity of the real-time factor graph and the convergence of the augmented factors of LC-ADMM. The iDFGO algorithm incrementally recomputes estimates when new factors are added to the graph and is scalable with respect to both network size and time. We validate LC-ADMM and iDFGO in simulations with examples from multi-agent Simultaneous Localization and Mapping (SLAM) and power grids.</p
Long-Duration Energy Storage in Reliable Wind and Solar Electricity Systems
Get PDFSeveral U.S. states mandate zero-carbon electricity systems based primarily on renewable technologies, such as wind and solar. Reliable and affordable electricity systems based on these variable resources may depend on the ability to store large quantities of low-cost energy over long timescales. This thesis combines techno-economic analysis with materials chemistry to advance long-duration energy storage in reliable wind and solar electricity systems. Our macro-energy model incorporated multi-decadal weather datasets and revealed unique long-duration energy storage roles, such as seasonal and multi-year storage, that increase the affordability of wind- and solar-based electricity, informing technology investments and policy. We find that low-cost energy storage, such as underground hydrogen, is valuable even if the charge/discharge cost is expensive. In U.S. wind and solar systems, hydrogen energy storage and conversion capital cost improvements are more valuable than efficiency improvements. Low-cost earth-abundant catalysts may be acceptable replacements for precious metal catalysts in proton exchange membrane electrolyzers despite lower efficiency for storage applications in wind and solar systems. We synthesized earth-abundant manganese antimony oxide catalysts via a new chemical vapor deposition route and assessed their long-term electrochemical durability for oxygen evolution. Multi-day tests confirmed the activity-stability tradeoff across the Mn:Sb composition space
Crystallographic Studies of Nitrogenase
Get PDFNitrogenase is the only enzyme known to reduce atmospheric dinitrogen to ammonia, producing a biologically available form of nitrogen. The primary component of nitrogenase, the molybdenum-iron (MoFe) protein, binds and turns over substrate after reduction by multiple electron equivalents, which are supplied by the obligate reductase, the iron (Fe) protein. Previous high-resolution X-ray crystal structures have provided pictures of the nitrogenase proteins and revealed the geometry of their metalloclusters. In this thesis, we study MoFe protein crystal isoforms and their crystal pathologies to classify isomorphous candidates suitable for crystallographic merging. We then leverage this classification to determine a high-resolution structure of the MoFe protein with improved geometric accuracy and lower coordinate error than currently available models. The reduced states of the MoFe protein are challenging to capture and therefore have been minimally characterized. We explore the structural consequences of introducing reductants and oxidants into MoFe protein crystals and study the effects of X-ray induced photoreduction on the metalloclusters. Further, we determine the radiation damage-free X-ray crystal structure of MoFe protein. The Fe protein adopts various conformational states as it functions in ATP-coupled electron transfer to the MoFe protein. We examine a set of proteins that are evolutionarily related to the Fe protein and have diverse functionalities, but retain similarity in their ATP-dependent function and allostery as a result of their conserved structural features. Finally, we characterize the structural and functional aspects of the Fe protein lacking an iron-sulfur cluster. These studies expand our understanding of the structural properties of nitrogenase and shed light on previously uncharacterized states of these proteins.</p