Prion diseases, also known as Transmissible Spongiform Encephalopathies, are neurodegenerative diseases that pose a major threat to both humans and animals. They fall into a category of misfolding diseases known as amyloidoses where accumulation of fibrous protein aggregates correlates with disease symptoms. Unlike other amyloid diseases, prion diseases are infectious and not strictly linked with age. Victims of prion diseases experience dementia, hallucinations, and an inability to take care of themselves among other symptoms before inevitably succumbing to disease. While the time between presentation of symptoms and death is often less than one year, symptoms can take decades to appear. This makes the immediate cause of sporadic disease difficult to determine.

Prion diseases currently lack any form of treatment or means of prevention outside of selective breeding in sheep, which takes advantage of a disease-preventing sequence polymorphism. Infectious prions share β-sheet rich cores that produce a cross-β diffraction pattern not observed in natively folded PrPC. Knowledge of the atomic structures adopted by prions will aid not only in structure-based drug design and prion disease prevention, but also provide answers to the centuries old question of what makes a protein infectious.

The aim of this dissertation is to uncover the structural characteristics of prions that distinguish them from other amyloids. The dissertation is also aimed at uncovering molecular explanations for species barriers, whereby PrPSc from one species converts PrPC of another species to a misfolded form with an efficiency dependent on both the original and newly infected host prions. These aims will be achieved through a combination of technological advancements made in atomic-level amyloid structure determination, with a focus on micro-crystal electron diffraction (MicroED) of the building blocks that make up prion cores (chapters 1 and 2) and single particle cryo-electron microscopy (cryo-EM) of prion filaments (chapters 3 and 4).

Amyloid inclusions—typical of synucleinopathies such as Alzheimer’s and Parkinson’s disease—have been identified for the past two decades within the brains of infants and young children afflicted by lysosomal storage diseases. Lysosomal storage diseases are a family of seventy rare monogenic disorders, many of which involve nonfunctional mutations in enzymes pertaining to lysosomal degradation pathways. A sizable proportion of these cases presenting amyloid inclusions have involved lysosomal storage diseases characterized by aberrant sphingolipid metabolism, in which specific sphingolipids accumulate due to particular hydrolases being rendered nonfunctional. These findings strengthen the emerging relationship between early-onset lysosomal storage diseases and late-onset neurodegenerative diseases initially established by the identification of lysosomal storage disease-implicated genes as risk factors that lead to a more severe and earlier onset form of Parkinson’s disease. More generally, these lysosome-related genetic risk factors point to a link between metabolic dysfunction and proteopathic aggregation that has implications for not only these rare diseases but also prevalent neurodegenerative diseases as well. Here, I review what is currently understood about the role of the lysosome within alpha-synuclein pathology setting up the presentation of my thesis research: an investigation of how disease-implicated lipids may directly contribute to the pathogenesis of a-syn inclusions. With Thioflavin-T fluorescence kinetic assays and negative-stain electron microscopy, I found that psychosine, glucopsychosine, and sphingosine greatly reduce the lag phase---representative of amyloid nucleation---of recombinant alpha-synuclein aggregation in vitro when compared to other disease-implicated lipids. My experimental findings prove that the effect of these sphingolipids is specific and not solely due to molecular crowding. Together with recent literature findings, these results suggest that the primary amine group of these three lipids of interest influences the propensity of alpha-synuclein to form fibrils. The kinetic evidence put forth by this research serves as a foundation on which further studies can be built to understand the consequences of these lipids on the resulting structural and functional properties of the proteopathic aggregates within their relevant disease contexts. This will ultimately support future therapeutic intervention strategies for neurodegenerative diseases that span the age spectrum.

The last two decades have seen revolutionary progress in the field of cryo electron microscopy, granting views of previously unresolved biological structures utilizing both electron diffraction and electron imaging. Microcrystal electron diffraction (MicroED) has become applicable to protein, peptide, and small molecule structures while cryo-electron microscopy (cryo-EM) has allowed for high-resolution structure determination of proteins and macromolecular complexes outside the confines of crystallographic restraints. The use of MicroED to interrogate a wider variety of structures has revealed important molecular insights in the worlds of biology and chemistry but has also revealed some of the shortcomings of the method that could be limiting to novel structure determination. Namely, there remains a limited selection of phasing methodologies for electron diffraction data: molecular replacement, requiring a highly similar structural model, or direct methods, requiring an atomic resolution dataset. The experiments presented in chapters 2 and 3 of this thesis explore the implementation of fragment-based phasing methodologies to electron diffraction data to overcome these limitations and demonstrate their applicability to protein and amyloid peptide structures. Electron microscopy has been particularly important in the study of amyloid proteins. The defining characteristic of amyloid proteins is the formation long, unbranched fibrillar aggregates which can be disease-associated, as is observed in many neurodegenerative diseases, or functional within the context of cell. Short peptide segments of these proteins which recapitulate the underlying cross-β structure of the fibrils have been lucrative targets for both X-ray crystallography and MicroED due to the small size of crystals they form. Meanwhile, improvements in cryo-EM resolution and data processing have permitted the first high-resolution views of full-length amyloid fibril structures. The fourth chapter of this thesis takes advantage of these advancements to elucidate the structure of the amyloid fibril form of human leukocyte cell-derived chemotaxin-2 (LECT2) by cryo-EM. ALECT2, the systemic amyloid disease associated with LECT2 aggregation, is clinically well characterized but poorly understood molecularly. While predictions of the aggregation-prone segments which contribute to amyloid formation have been made, a lack of structural information has limited the rational design of targeting agents and therapeutics. The work presented here offers a first step in uncovering the molecular mechanisms behind LECT2 aggregation and their role in ALECT2 disease progression.

The cytoplasmic polyadenylation element-binding protein 3 (CPEB3) is a functional prion thought to modulate protein synthesis at synapses and enable consolidation of long-term memory in neurons. The biophysical characteristics of the prion state may facilitate the endurance of CPEB3 in environments with high molecular turnover and enable rapid aggregation and localization of targets to subcellular sites. Truncations to the CPEB3 prion-like domain cause loss of stimulation induced protein upregulation and impede long-term potentiation in mice, highlighting the critical role of its putative prion conformation.

The prion state often requires polypeptides to adopt beta-sheet rich conformations of amyloid to generate and propagate faithful conformations in fluctuating environments, an alluring feature if controlled properly. Because of their association with neurodegenerative diseases, functional amyloid proteins and their regulation in the refined structure of the brain are not entirely understood. CPEB3 undergoes extensive post-translational modifications that control its subcellular localization and activity. Proper shuttling of the prion-like protein from RNA storage granules to polysomes is thought to be a critical component in its ability to exist within the homeostasis of neurons.

The work presented in this dissertation aims to determine the ability of CPEB3’s prion-like domain to form amyloid conformations and the role of this conformation in translation regulation. Through in vitro experiments investigating the ordered amyloid core of CPEB3, reversibility and lack of stability are observed as key differences in CPEB3 fibrils when compared to pathogenic counterparts. The data provide insights into the reversible amyloid core and show its requirement for proper storage and translation regulation in neurons. These results bridge the studies from in vitro generated structure to supramolecular assemblies observed inside of neurons. The native environments and structured complexes begin to show potential conformations of CPEB3 that are complementary to its function.

Amyloid proteins call into question our long-standing notions of the relationship between a proteinsequence and its three-dimensional fold. These proteins exhibit distinct conformations associated with soluble and fibrillar states and potentially various fibril polymorphs. This conformational plasticity contributes to the diverse roles of amyloids, which fall into two distinct categories within biological systems. Pathogenic amyloids are observed in patients suffering from debilitating neurodegenerative and systemic disorders such as Alzheimer’s Disease and Parkinson’s Disease and can be infectious as is the case with prion-related diseases. In contrast to pathogenic amyloids, functional amyloid assemblies have a defined function in living systems. Such functional amyloids are prevalent across both eukaryotic and prokaryotic domains of life, implying the fold may be an early and conserved mechanism with value to cellular function. This dichotomy raises an important question: What dictates the fold adopted by amyloid- forming sequences and in turn, what determines the function of a particular amyloid fold? This thesis attempts to address this puzzle with computational tools and experimental validation, as a stepping stone toward a broader understanding of amyloids across the tree of life.

Advances in structural biology have provided atomic-level views of amyloids, from short 'steric zipper’segments and to full amyloid fibril structures, offering researchers detailed insights into the features of amyloid proteins. Concurrently, the advent of machine learning techniques has allowed for the exploration of data that previously had been unfeasible. Importantly, despite their differences, pathogenic and functional amyloids have been found to share a common architecture: long unbranched fibrils with polypeptide chains folded nearly two-dimensionally within a layer, and with adjacent layers stacked parallel in register. The work presented in Chapter 2 of this dissertation explores the application of machine learning strategies to expand the capabilities of steric zipper prediction and investigates their utility in mining organism proteomes for high zipper propensity proteins that may harbor amyloid-forming domains. The approach offers a fast way to survey proteomes for putative amyloid-forming proteins or domains, providing insight into the prevalence and distribution of steric zippers across proteomes. Chapter 3 presents an alternative application of the methods developed in Chapter 2. Here, we employ computational approaches to design novel peptide sequences indented to bind a known fibril surface. Subsequently, we investigate the effects of these designed peptides on amyloid fibril growth and their resulting structures. By combining structural biology, machine learning, and targeted peptide design, the work presented in this thesis aims to deepen our understanding of amyloid proteins across diverse biological contexts, potentially paving the way for novel therapeutic strategies and insights into both pathogenic and functional amyloid formations.

In the last few decades there has been tremendous technological and computational advances in the field of cryo-electron microscopy which has led to a phenomena referred to as “The Resolution Revolution,” in which the number of high resolution structures solved via this technique has exploded. Despite these advances, there still remains a size limitation for your target of interest, below which high resolution microscopy remains challenging. Adding to this, a vast majority of the biologically relevant proteins and nucleic acids inside of cells lie below this size limit. Parallel advances in protein design may provide an avenue for progress on this challenging problem. By designing large protein assemblies, we are able to artificially increase the size of a given target, making it amenable to cryo-EM studies. This thesis describes recent advances in the field as well as efforts to generate imaging scaffolds for both small cancer-related protein targets, and RNA molecules. The knowledge gained through these endeavors will better guide future design efforts.

Nature self-assembles protein structures for various functions, including: storage, protection, and fortification. These self-assemblies range from filaments to full three-dimensional crystals and are pervasive across the tree of life. They include the granules present in immune system cells, the packing of hormones in the pancreas, the storage of proteins in plants, carboxysomes, viruses, and cell-grown crystals in microbes. To accomplish this, a better understanding of how certain organisms are able to naturally self-assemble macromolecules and how to recreate these in living cells must be achieved. Bacillus thuringiensis subsp. israelenesis’ (Bti) crystalline inclusions are of exceptional interest, since they naturally package a single protein into a crystalline inclusion through a life cycle process called sporulation. Compared to classical macromolecular crystallography that takes a plethora of variables to exhaustion can still yield no crystals. The laborious process could be prevented; however, by better understanding Bt and these crystalline inclusions’ cellular self-assembly process. Cry11Ba is a protein packed into these crystalline (Cry) inclusions and found to be one of the most toxic pesticidal proteins. These crystals are then ingested by their host and switch from their packaged toxin crystal to their inactive protoxin at the high pH within their gut. My interests have been in elucidating the macromolecular structure from in vivo produced crystals, further understanding the ambiguous mode of action to gain better perspective for other δ-endotoxins, and probing the self-assembly of the crystalline inclusions in vivo throughout the sporulation process. I have studied Cry11Ba with structural analysis, solubility & toxicity assays, mutational studies, and imaging capabilities developed in cryo-EM to successfully in solve a de novo structure via in vivo crystalline inclusions, charting the pH sensitivity of the crystals, identifying key residues for stability and toxicity, analyzed the monomeric and multimeric particles in alkaline environments to understand Cry11Ba’s mode of action, and visualized previously unobserved sporulation stages for Bti.

Numerical algebraic geometry provides numerical descriptions of solution sets of polynomial systems of equations in several unknown. Such sets are called algebraic varieties.

In algebraic statistics, a statistical model is associated to an algebraic variety to study its geometric structure.

This thesis contains my work at UC Berkeley that uses numerical algebraic geometry for the algebraic statistics problem of maximum likelihood estimation.

In Chapter 2 we study the maximum likelihood estimation problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We determine the maximum likelihood degree for a range of determinantal varieties, and we apply numerical algebraic geometry to compute all critical points of their likelihood functions.

In Chapter 3 we prove a bijection between critical points of the likelihood function on the complex variety of matrices of rank r and critical points on the complex variety of matrices of corank r-1.

From the perspective of statistics, we show that maximum likelihood estimation for matrices of rank r is the same problem as minimum likelihood estimation for matrices of corank r-1,

and vice versa.

In Chapter 4, a description of the maximum likelihood estimation problem in terms of dual varieties and conormal varieties is given. With this description, we define the dual likelihood equations. We show how solving these dual likelihood equations give solutions to the maximum likelihood estimation problem without having the defining equations of the model itself.

In Chapter 5,

discrete algebraic statistical models are considered and solutions to the likelihood equations when the data contain zeros are studied.

Focusing on sampling and model zeros, we show that the solutions of the likelihood equations in these cases are contained in a previously studied variety, the likelihood correspondence. The number of solutions give a lower bound on the ML degree, and the problem of finding critical points to the likelihood function can be partitioned into computationally easier problems involving sampling and model zeros.

In Chapter 6

the Macaulay2 package Bertini.m2 is introduced.

Macaulay2 is a software system designed to support research in algebraic geometry, and Bertini is a popular software system for numerical algebraic geometry.

The package Bertini.m2 provides an interface to Bertini via Macaulay2.

The receptor for transferrin (Tf), otherwise known as transferrin receptor 1 (TfR1 or CD71), is a single pass type two transmembrane protein ubiquitously expressed in most vertebrate cells. TfR1 is responsible for facilitating the import of iron into cells from transferrin bound iron in circulation. In cells, release of iron from Tf occurs near pH 5.5 and requires clathrin-mediated endocytosis of the Tf-TfR1 complex to acidified endosomes, followed by its recycling to the cell surface without dissociation.

Since its discovery, high expression of TfR1 is typically associated with rapidly proliferating cells and a variety of tumor cell types. Because of its association with cancer, its cell surface accessibility, its facile entry into cells, and its critical role in the pathophysiology of cancer, TfR1 is an active target for anti-cancer therapies. Antibodies were the first vehicles designed to specifically target TfR1 with the aim of blocking Tf uptake into malignant cells and induce cytotoxicity.

Based on a panel of thirty-two mouse monoclonal antibodies developed, in the late 1980s, to recognize the extracellular domain of human TfR1, several were identified that did not appear to block binding of the receptor to Tf. One of these antibodies, otherwise referred to as 128.1, inspired the generation of a chimeric antibody-avidin fusion protein (ch128.1Av). This molecule was originally designed to act as a delivery vehicle for biotinylated agents into cancer cells. However, this molecule possesses a significant intrinsic anti-proliferative/pro-apoptotic activity against malignant B cells expressing TfR1, as did its parental chimeric antibody (ch128.1) although to a lesser extent. The detailed nature of the interactions of these antibodies (based on the murine monoclonal 128.1) with TfR1 is addressed in part by this thesis.

The experiments presented in this thesis are those from two published articles addressing the nature of the interactions between ch128.1 or ch128.1Av and TfR1, and the effects of these interactions on malignant B cells expressing the receptor. Special emphasis is placed on how these antibodies affect the recycling of TfR1 in order to reduce Tf uptake and induce lethal iron deprivation in malignant hematopoietic cells, as well as the transcriptional response of affected cells to insult by these antibodies.

While investigating the effect of a low pH (late endosome or lysosome like) environment on the stability of TfR1 in the presence of these antibodies, the unexpected observation was made of an intrinsic instability of TfR1 under these conditions. Thus, data that provide insights into the inducible proteolysis of the extracellular domain of TfR1 in a low pH environment (pH 3-5) are presented. These results show a distinct and consistent pattern of degradation of the TfR1 ectodomain selectively within this pH range, which is consistent with the enzymatic activity of a pH-dependent cysteine/serine protease.