The conversion of genetic information into functional RNA and protein is of fundamental importance to all known life forms. In cellular organisms, this hinges on the interaction of double stranded DNA and the transcription factor class of proteins. Substantial progress in the fields of biochemistry and genomics have made the identification of transcription factor binding sites and the resultant change in transcriptional output relatively routine. However, fully understanding this central life process requires knowing not only where transcription factors bind DNA, but why and how. These questions are approached here using solution state NMR spectroscopy and the statistical technique of bootstrap aggregation in order to: i) glean biologically relevant insights into the dynamics of the GCN4 transcription factor from NMR relaxation experiments; ii) examine the influence of electrostatics on the structure of GCN4 in the absence of DNA; iii) analyze the conformational state of several Hox transcription factor DNA binding sites. NMR spectroscopy capitalizes on connections between electromagnetism and the quantum mechanical property of nuclear spin angular momentum to study the structure of molecules. Application of NMR relaxation experiments provides further information on molecular structure and dynamics. When performed in solution, the data generated by this technique occurs in conditions more similar to those found within a cell than other approaches used in structural biology. However, the biological relevance of any insights derived from solution state NMR relaxation experiments depends on the application of an appropriate model for nuclear spin relaxation. Typically, this involves applying a statistical test to select the best model from among several candidates in the model-free formalism. Chapter 3 uses 15N relaxation data collected on the basic leucine zipper (bZip) domain of the GCN4 transcription factor to detail the potential problems and model selection errors that arise from this approach, and presents the alternative method of bootstrap aggregation. Applying this statistical technique allowed for the generation of multimodel inferences about the internal motions and rigidity of the basic region of GCN4, enhancing the likelihood of their biological relevance. The results presented in Chapter 3 further confirmed the presence of nascent helices in the generally disordered basic region of the GCN4 bZip domain. Interestingly, when complexed with appropriate DNA substrate, this region assumes a fully α-helical conformation. A long standing hypothesis assumes the inability of the basic region to form an α-helix in the absence of DNA arises, in part, due to repulsion between its charged amino acids. This hypothesis is tested in Chapter 4 using NMR relaxation experiments performed in solutions containing either increased or decreased concentrations of salt. Surprisingly, screening the electrostatic repulsion between charged residues using higher levels of salt had no discernible effect on the structure or dynamics of the basic region. Chapter 5 examines the other side of the interaction between DNA and transcription factors. Here, previous work performed with the Hox family of transcription factors indicated the conformational state of DNA has an important role in enhancing the specificity with which Hox proteins bind certain sequences. In particular, the geometry of the DNA minor groove strongly influences the recruitment of appropriate Hox transcription factors. This relationship is examined using solution state NMR to study four Hox DNA binding sequences. The binding affinity between each of these sequences and the Hox protein AbdB was previously shown to correlate with the native unbound state of the DNA. The two sequences predicted to have native minor groove widths similar to those of the bound DNA had higher affinity for AbdB than those that deformed upon binding. Though mixed, the results of NMR experiments generally support the predicted structures, particularly for the high affinity sequences, indicating a single pronounced narrowing of the minor groove. Taken together, the results presented here illustrate the complex interactions underpinning the appropriate binding of DNA and transcription factors. It further highlights the need to study the structure and dynamics of both DNA and protein, as well as that of the bound complex, in order to fully understand how and why specific sequences are bound in response to stimuli.

Direct detection of dark matter remains an important outstanding problem since abundant astrophysical evidence points towards its existence, but no experiment has succeeded in detecting it. Axions and axion-like-particles are some of the most compelling candidates for dark matter given their appearance in many theories of physics beyond the Standard Model and their relatively unexplored parameter space compared to other candidates. Recently, the Cosmic Axion Spin Precession Experiment-Electric (CASPEr-e) has used nuclear magnetic resonance (NMR) to search for effective magnetic fields created by axionic dark matter. By decreasing technical noise sources, CASPEr-e is projected to reach the standard quantum limit where spin projection noise is the dominant noise source limiting sensitivity. However, some axion models predict axion couplings to normal matter that would be too small for even a quantum limited CASPEr-e experiment to detect. This creates a need for surpassing the spin projection noise limit in NMR dark matter searches. In this thesis, I explore the prospects for surpassing the quantum limit in NMR by using spin squeezed states, entangled states with variance in one projection reduced below the standard quantum limit. First, I propose an experimental scheme for generating squeezed states by coupling the spins to an off-resonant circuit to create a One-Axis-Twist Hamiltonian. Then, using exact results and numerical simulations, I determine the amount of squeezing that can be achieved given decoherence and noise. Next, I perform modeling to show that squeezing can accelerate dark matter searches despite earlier results that argued squeezing cannot improve experimental sensitivity when subject to decoherence. Finally, I apply these results to the CASPEr-e experiment and show that at axion frequencies near 100MHz, squeezing can speed up the experiment by a factor of up to 30, corresponding to a sensitivity improvement by a factor of over 5.

This thesis encompasses two studies on the application of computational techniques, including deep learning and physics-based methods, in the exploration of protein structure and dynamics. In Chapter 1, I will introduce the background knowledge. Chapter 2 describes the development of a deep learning method for protein loop modeling. We introduce a fast and accurate method for protein loop structure modeling and refinement using deep learning. This method, which is both fast and accurate, integrates a protein language model, a graph neural network, and attention-based modules to predict all-atom protein loop structures from sequences. Its accuracy was validated on benchmark datasets CASP14 and CAMEO, showing performance comparable to or better than the state-of-the-art method, AlphaFold2. The model’s robustness against loop structures outside of the training set was confirmed by testing on datasets after removing high-identity templates and train- ing set homologs. Moreover, it demonstrated significantly lower computational costs compared to existing methods. Application of this method in real-world scenarios included predicting anti- body complementarity-determining regions (CDR) loop structures and refining loop structures in inexact side-chain environments. The method achieved sub-angstrom or near-angstrom accuracy for most CDR loops and notably enhanced the quality of many suboptimal loop predictions in in- exact environments, marking an advancement in protein loop structure prediction and its practical applications. Chapter 3 presents a collaborative study that employs nuclear magnetic resonance (NMR) experiments, molecular dynamics (MD), and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations to investigate protein conformational dynamics across varying temperatures. NMR chemical shifts provide a sensitive probe of protein structure and dynamics. Prediction of shifts, and therefore interpretation of shifts, particularly for the frequently measured amidic 15N sites, remains a tall challenge. We demonstrate that protein ¹⁵N chemical shift prediction from QM/MM predictions can be improved if conformational variation is included via MD sampling, focusing on the antibiotic target, E. coli Dihydrofolate reductase (DHFR). Variations of up to 25 ppm in predicted ¹⁵N chemical shifts are observed over the trajectory. For solution shifts, the average of fluctuations on the low picosecond timescale results in a superior prediction to a single optimal conformation. For low-temperature solid-state measurements, the histogram of predicted shifts for locally minimized snapshots with specific solvent arrangements sampled from the trajectory explains the heterogeneous linewidths; in other words, the conformations and associated solvent are ‘frozen out’ at low temperatures and result in inhomogeneously broadened NMR peaks. We identified conformational degrees of freedom that contribute to chemical shift variation. Backbone torsion angles show high amplitude fluctuations during the trajectory on the low picosecond timescale. For a number of residues, including I60, 𝝍 varies by up to 60o within a conformational basin during the MD simulations, despite the fact that I60 (and other sites studied) are in a secondary structure element and remain well folded during the trajectory. Fluctuations in 𝝍 appear to be compensated by other degrees of freedom in the protein, including 𝝓 of the succeeding residue, resulting in “rocking” of the amide plane with changes in hydrogen bonding interactions. Good agreement for both room-temperature and low-temperature NMR spectra provides strong support for the specific approach to conformational averaging of computed chemical shifts.

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