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Proteins embedded in cell membranes translate a broad range of environmental cues---including the presence of nutrients, drugs, ions and photons---into molecular signals to induce appropriate cellular responses. Membrane proteins thus represent a control panel of the cell and constitute key drug targets for the treatment of a range of diseases. Designing medications to effectively modulate these proteins, however, remains exceedingly challenging and would benefit dramatically from an atomic-level understanding of how these proteins work. Here, I have used molecular dynamics (MD) simulations---which describe how every atom in a biological system evolves with high resolution in space and time---to reveal functional mechanisms for transporters and receptors, two essential classes of membrane proteins. This approach allowed us to address several long-standing questions in molecular biology. For example, we captured the complete process of substrate translocation through an alternating-access membrane transporter. These simulations, which revealed structural rearrangements in the protein that control substrate passage across the membrane as well as the driving forces underlying those transitions, suggest a structural foundation for the design of highly specific and more efficacious transporter-targeted medications. We also revealed the mechanism by which G protein--coupled receptors stimulate arrestins, intracellular regulators of cell signaling. By identifying atomic-level interactions at the GPCR--arrestin interface that drive arrestin activation, we provide a framework for designing drugs that could selectively block or stimulate arrestin signaling, thereby reducing unwanted side effects. In each study, we worked closely with our experimental collaborators to validate predictions derived from our computational results.

Light field microscopy is a high-speed computational imaging method, which enables reconstruction of a 3-dimensional volume from a light field image. Unlike standard imaging systems, the light field microscope uses a microlens array to capture both spatial and angular information about the incoming light in a single image, from which a volume can be reconstructed computationally. Among volumetric imaging methods in microscopy, light field microscopy is unique in that it allows imaging large volumes, spanning hundreds of microns in depth, at a speed limited only by the camera frame rate. Due to this unique advantage it has recently been adapted to in vivo imaging of neural activity, enabling biologists a glimpse into an organism's brain while in action. Despite its advantages, the light field microscope still suffers from a major limitation - its lateral spatial resolution is not uniform across depth. Some depths, particularly at the center of the imaged volume, where the microscope is focused at, show very low resolution which hinders its use in applications. This non-uniform resolution stems from the way the light field microscope samples the volume: at the center of the volume samples are angularly discriminative but spatially redundant, hence for isotropically absorptive or emissive volumes, they cannot support high resolution reconstructions. We present a method that, for such isotropic volumes, significantly improves the resolution profile of the light field microscope across depth and enables accurate control over it, thereby overcoming the limitations of traditional light field design. The key to our approach is using a technique called wavefront coding to control properties of the point spread function of the microscope. By including phase masks in the optical path we a create a wavefront coded light field microscope that samples the 3-dimensional volume more uniformly than the standard light field microscope, solving the low resolution problem at the center of the imaged volume and improving the resolution at its borders. We derive an extended optical model for the wavefront coded light field microscope and propose design guidelines and a performance metric which we use to choose adequate parameters for good phase masks. To validate our approach, we show simulated data and experimental resolution measurements, and demonstrate the wavefront coded light field microscope's utility for biological applications.

Machine learning has widely been applied to image, video, and speech datasets, but has not yet achieved broad penetration into chemistry, materials science, or other molecular design applications. However, over the last few years, machine learning and deep learning have achieved notable successes in predicting properties of molecular systems. In this thesis, I present a series of deep learning algorithms that demonstrate strong predictive improvements across a wide range of biochemical tasks such as assay activity modeling, toxicity prediction, protein-ligand binding affinity calculation, and chemical retrosynthesis. In addition to these algorithmic improvements, I introduce the comprehensive benchmark suite MoleculeNet for molecular machine learning algorithms (https://moleculenet.ai) and demonstrate how the technology of one-shot learning can be used for drug discovery applications. The work presented in this thesis culminated in my design and construction of DeepChem (https://deepchem.io), an open source package for molecular machine learning, which has achieved broad adoption among biotech startups, pharmaceutical companies, and research groups. DeepChem has attracted a thriving community of open source developers and looks to continue growing and expanding as a vibrant research tool.

We present a type of neural network that is locally equivariant to 3D rotations, translations, and permutations of points at every layer. Local 3D rotation equivariance removes the need for data augmentation to identify features in arbitrary orientations. These networks use convolution filters built from spherical harmonics; due to the mathematical consequences of this filter choice, each layer accepts as input (and guarantees as output) scalars, vectors, and higher-order tensors, in the geometric sense of these terms. We exhibit applications of these networks to supervised learning tasks in structural biology.

This dissertation covers work discussed in the following papers: "Spatial Graph Convolutions for Drug Discovery" describes new deep neural network architectures for modeling drug-receptor interactions. We argue that the future of predicting the interactions between a drug and its prospective target demands more than simply applying deep learning algorithms from other domains, like vision and natural language, to molecules. "Machine Learning Harnesses Molecular Dynamics to Discover New Opioid Chemotypes" describes an algorithm that leverages protein motion to enrich the search for active molecules. We then applied the method to find a new chemical scaffold that we experimentally verified is an agonist for the μ Opioid Receptor. "Kinetic Machine Learning Unravels Ligand-Directed Conformational Change of Opioid Receptor" describes differential pathways of deactivation and differential conformational states sampled by the μ Opioid Receptor in response to different opioid ligands.

Molecular dynamics (MD) simulations are becoming essential tools for many different fields, including biology, chemistry, and materials science, that provide us with a molecular picture of what is really happening at the molecular level for many biophysical phenomena. With MD simulations, we can see how the molecule forms and moves and obtain insight into its mechanisms with higher resolution than experiments. Unfortunately, MD simulations are not without limitations. They are restricted in predictive power because the molecules routinely get "stuck" in metastable states and do not change their conformations for an extended period. Hence, there is currently a huge gap between what MD simulations can model and the timescales of biological processes. Consequently, many methods have been developed for MD simulations over the past few decades to overcome this timescale barrier between MD simulations and biological processes. These are referred to as enhanced sampling methods. We need these methods to overcome the timescale barrier so that critical biophysical phenomena can be observed in a computationally tractable period. Current enhanced sampling methods have demonstrated that they can efficiently obtain thermodynamic and/or kinetic properties. However, there is still a need for an enhanced sampling method that requires little a priori knowledge about the system, is less heuristic, can obtain both thermodynamic and kinetic properties, and can be easily parallelized over the available computational resources for computational efficiency. I will go over several classes of enhanced sampling methods before diving into my new enhanced sampling methods that aim to address the issues mentioned above.

Three of the most pressing questions in human disease genetics are: 1) which genes cause disease, 2) how genes relate to each other to form biological pathways, and 3) how the environment modulates genetic disease risk. This thesis describes contributions to methods addressing each of these three questions. Regarding the problem of identifying causal genes for complex traits, this thesis explores properties of transcriptome-wide association studies (TWAS), a class of methods which intersect GWAS and expression quantitative trait locus (eQTL) datasets to find gene-trait associations, using simulations and case studies of literature-curated candidate causal genes for schizophrenia, LDL cholesterol and Crohn's disease. We explore risk loci where TWAS accurately prioritizes the likely causal gene, as well as loci where TWAS prioritizes multiple genes, some of which are unlikely to be causal, because they share the same variants as eQTLs. We illustrate that TWAS is especially prone to spurious prioritization when using expression data from tissues or cell types that are less related to the trait, due to substantial variation in both expression levels and eQTL strengths across cell types. Nonetheless, TWAS prioritizes candidate causal genes at GWAS loci more accurately than simple baselines based on proximity to lead GWAS variant and expression in trait-related tissues. We discuss current strategies and future opportunities for improving the performance of TWAS for causal gene prioritization. Our results showcase the strengths and limitations of using expression variation across individuals to determine causal genes at GWAS loci and provide guidelines and best practices when using TWAS to prioritize candidate causal genes. Regarding the problem of understanding environmental modulation of complex traits, this thesis describes an application of Mendelian Randomization (MR) to 328,459 individuals in the UK Biobank cohort to interrogate the relationship between BMI and diabetes risk across diverse strata of body mass index (BMI), diabetes family history, and genome-wide polygenic risk scores. Though lifestyle interventions to reduce BMI are critical public health strategies for type 2 diabetes prevention, and weight loss interventions have shown demonstrable benefit for high-risk individuals, it is unclear whether the same benefits apply to those at lower risk. We found that diabetes prevalence increased sharply with BMI, family history of diabetes, and genetic risk, and increased marginally with BMI-adjusted genetic risk. However, genetic risk scores were much less predictive of diabetes status than family history, particularly after correcting for BMI. Conversely, predicted risk reduction from weight loss was strikingly similar across BMI and genetic risk categories. Weight loss was predicted to substantially reduce diabetes risk even among lower-risk individuals: a 1 kg/m2 BMI reduction was associated with a 1.31-fold reduction (95% confidence interval [CI], 1.25-1.38) in diabetes odds among individuals without a family history of diabetes, a 1.26-fold reduction (95% CI, 1.18-1.35) among individuals at low genetic risk, and a 1.28-fold reduction (95% CI, 1.19-1.37) among individuals at low BMI-adjusted genetic risk, all nearly identical to the full cohort (1.29-fold reduction, 95% CI, 1.25-1.35). In fact, individuals without family history were predicted to have even greater risk reduction than individuals with family history (1.31-fold vs 1.19-fold reduction, p = 0.02). Overall, we found that lower BMI is consistently associated with reduced diabetes risk across BMI, family history and genetic risk categories, suggesting all individuals can substantially reduce their diabetes risk through weight loss. Our results support the broad deployment of weight-loss interventions to individuals at all levels of diabetes risk. Regarding the problem of how genes relate to each other, this thesis describes the development of an approach to map co-essentiality, the tendency of genes with similar functions to have correlated knockout fitness profiles across cell lines, using generalized least squares (GLS). Our approach is well-powered, flexible and statistically well-calibrated, and avoids the pervasive false positives of previous approaches by appropriately accounting for the relatedness among cell lines. Applying the method to a compendium of 485 genome-wide CRISPR/Cas9 essentiality screens substantially improves recapitulation of known protein complexes and pathway interactions relative to prior approaches. Our methodological improvements enable unbiased genome-wide clustering based on co-essentiality profiles; we recover pathways and complexes as diverse as MAPK/ERK, PI3K/ACT/mTOR, the ribosome, the peroxisome, regulators of the DNA damage response and chromatin remodeling. These clusters also nominate roles for uncharacterized and poorly characterized genes in known pathways. Our genome-wide pathway map is a valuable resource for biological hypothesis generation.

Molecular dynamics (MD) simulation offers both high spatial and time resolution into biological processes at an all-atom level, but presents many unique computational challenges in terms of both system setup and compute time. To address the former, I introduce a software package, Dabble, that simplifies system building for MD simulation in a way that supports all commonly used force fields and simulation programs. To increase the accessibility of observing protein-ligand binding in simulations, I developed an adaptive sampling method that guides simulations towards interesting regions of protein-ligand conformational space while requiring no prior knowledge of binding pose or site. Together, these two computational methods improve the ability of researchers to use MD simulation for examining biological processes.

G protein coupled receptor proteins (GPCRs) couple extracellular soluble ligand binding to intracellular signaling pathway activation. GPCRs are excellent drug targets due to their positioning at the plasma membrane upstream of signaling cascades, and due to their ability to respond to ligand binding with a range of signaling outputs. Crystallography has revealed the structure of drugs bound to the inactive and active state GPCRs at high resolution; each crystal structure represents a single, low-energy GPCR conformation. Crystal structures have also defined the canonical activation mechanism for GPCRs as an opening up of the intracellular surface; for Family A GPCRs, the intracellular portion of transmembrane helix 6 (TM6) undergoes the largest conformational change upon ligand binding. Here I present the design and development of two novel fusion proteins for GPCR crystallography. Crystal structures of the M3 muscarinic receptor fused to both novel crystallization aids improved the resolution of the overall structure and extended the view of residues comprising TM6. In addition to the states seen by crystallography, recent spectroscopy studies revealed that GPCRs sample a wide variety of conformations. This raises the question of when and whether high-energy (non-crystallographic) conformations are relevant for GPCR function. In this work, I both employ and validate a high-pressure electron paramagnetic resonance (EPR) spectroscopy technique to understand the basal and ligand activation of an archetypal GPCR, the Beta-2 adrenergic receptor (β2AR). The studies demonstrate a pre-existing equilibrium between inactive and active receptor states, providing a structure-based explanation for the observed phenomenon of basal activity. Clinically, inverse agonists are used to inhibit basal activity of GPCRs, and these high-pressure studies also reveal a structural mechanism for inverse agonists: they inhibit the outward movement of TM6. Studies of β2AR endogenous and synthetic agonists under ambient and pressurized conditions reveal a distinct conformational profile for each agonist. These conformational differences may be responsible for different ligand efficacies towards two signaling pathways downstream of GPCRs: arrestin-mediated versus G-protein-mediated signaling. Overall, these studies provide further support for a general mechanism for GPCR activation, conformational selection. The ability to fine-tune drug efficacy is the next frontier in GPCR drug discovery. To this end, I contributed to a collaborative drug discovery project to find novel β2AR allosteric ligands by docking to a hypothetical allosteric binding site, at a distinct location from where endogenous ligands bind. We built upon the principles of conformational selection, searching for negative modulators by docking to the inactive crystal structure, and finding positive modulators from active-state structure docking. Some of the new allosteric ligands discovered have signal bias properties, targeting arrestin over G-protein coupling. Though the underlying mechanisms of ligand bias are difficult to assess by most physiologic and biophysical methods, EPR spectroscopy revealed subtle differences in the conformational ensemble, which may correspond to arrestin versus G protein-specific drug effects.

In recent years, single-molecule fluorescence microscopy has revolutionized the field of biological imaging. Using single-molecule localization techniques combined with control of the emitting concentration and time-sequential imaging, it is now possible to image structures with resolution an order of magnitude smaller than the classical diffraction limit, thus achieving 'super-resolution'. Such advances have established the fluorescence microscope as a powerful non-invasive imaging technology, and have been recognized with the 2014 Nobel Prize in Chemistry. This thesis aims to further extend the limits of super-resolution and single-molecule microscopy. Fluorescent molecules are versatile probes that provide a wealth of information about their nanoscale environment. However, the majority of super-resolution applications measure only the two-dimensional positions of single molecules during a typical experiment. By constructing multimodal imaging systems that sense additional physical parameters on a molecule-by-molecule basis, additional biological insight may be gleaned. Over the course of my PhD, I have developed a suite of experimental methods and computational algorithms for encoding a molecule's three-dimensional position, its orientation, and its rotational dynamics into the image that its fluorescence forms on a camera sensor. In this thesis, these techniques are combined with super-resolution microscopy, and have been demonstrated to be useful tools for cellular imaging, and for the characterization of stretched DNA strands.