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Fifteen years ago, the advent of modern high-throughput sequencing revolutionized computational genetics with a flood of data. Today, high-throughput biochemical assays promise to make biochemistry the next data-rich domain for machine learning. However, existing computational methods, built for small analyses of about 1,000 molecules, do not scale to emerging multi-million molecule datasets. For many algorithms, pairwise similarity comparisons between molecules are a critical bottleneck, presenting a 1,000x-1,000,000x scaling barrier. In this dissertation, I describe the design of SIML and PAPER, our GPU implementations of 2D and 3D chemical similarities, as well as SCISSORS, our metric embedding algorithm. On a model problem of interest, combining these techniques allows up to 274,000x speedup in time and up to 2.8 million-fold reduction in space while retaining excellent accuracy. I further discuss how these high-speed techniques have allowed insight into chemical shape similarity and the behavior of machine learning kernel methods in the presence of noise.

RNA plays critical roles in fundamental biological processes, including transcription, translation, post-transcriptional regulation of genetic expression, and catalysis as enzymes. These critical RNA functions are determined by the structures and dynamics of the RNA molecules. Computational methods might be used to predict the structures and dynamics of RNA. Unfortunately, the prediction accuracies of current computational methods are still inferior compared to experiments. In this dissertation, I discuss recent advances I made in improving and developing computational methods to make accurate predictions on the RNA structures and dynamics. The dissertation contains three individual research projects. In the first part, I present a protocol for Enumerative Real-space Refinement ASsisted by Electron density under Rosetta (ERRASER). ERRASER combined RNA structure prediction algorithm with experimental constraints from crystallography, to correct the pervasive ambiguities in RNA crystal structures. On 24 RNA crystallographic datasets, ERRASER corrects the majority of steric clashes and anomalous backbone geometries, improves the average Rfree by 0.014, resolves functionally important structural discrepancies, and refines low-resolution structures to better match higher resolution structures. In the second part, I present HelixMC, a package for simulating kilobase-length double-stranded DNA and RNA (dsDNA and dsRNA) under external forces and torques, which is typical in single-molecule tweezers experiments. It recovered the experimental bending persistence length of dsRNA within the error of the simulations and accurately predicted that dsRNA's "spring-like" conformation would give a two-fold decrease of stretch modulus relative to dsDNA. In the third part, I developed a framework of Reweighting of Energy-function Collection with Conformational Ensemble Sampling (RECCES), to predict the folding free energies of RNA duplexes. With efficient sampling and reweighting, RECCES allows comprehensive exploration of the prediction power of Rosetta energy function, and provides a powerful platform for testing future improvement of the energy function. In all the projects above, I leveraged rich datasets from previous experiments to develop novel algorithms that gave predictions with unprecedented accuracies, which were validated by independent blind tests. These computational methods I developed could also serve as a solid foundation for future efforts of improving prediction accuracies of RNA computational algorithms.

Proteins are frequently characterized as molecular machines, with atomic-level motions driving biological function. Past decades have witnessed a dramatic increase in the tools available to probe these dynamics, but few methods enable us to resolve these collective motions with high spatial resolution. This dissertation investigates the potential of x-ray diffuse scattering from protein crystals to meet this critical need. Specifically, I review the models of correlated disorder that have previously been suggested to account for this signal and describe algorithms for processing the diffuse scattering in experimental diffraction data. These models and algorithms are applied to dissect the physical origins of the diffuse scattering observed from three protein crystals. Though considerable progress is still required for the analysis of diffuse scattering to become a routine biophysical method for studying protein dynamics, the framework and findings described in this dissertation make concrete steps toward that end.

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.

This thesis discusses the role of analysis in the application of molecular dynamics (MD) simulations for studying phenomena at an atomic level of detail. Many interesting questions can be asked of the physical world: How do proteins fold? Are there two liquid phases of supercooled water? How does a drug inhibit an enzyme? Many of these questions, however, are not quantitatively specific, meaning that the answers depend on scientists' interpretation. Researchers tend to describe these phenomena through hand-chosen functions, or order parameters, that are based on physical intuition. However, there is an immense amount of information contained in a large-scale simulation that is typically not used. Here, we attempt to illustrate the usefulness of data-driven analysis in the study of physical phenomena with MD. In all cases, the strategy begins by reformulating the nebulous physical questions into a specific and quantitative question, which can be used to derive an appropriate unsupervised learning method for the given problem. This strategy rests on physical intuition, because the problem formulation must be done in a physically meaningful way, but the advantage is that the specific solutions are driven by the data itself, allowing for interesting phenomena to be discovered rather than required to be known a priori.

A host of sequential models in probability and statistics are characterized by time reversibility, from Markov chain Monte Carlo samplers to queueing networks. In physics, this property arises naturally from Hamiltonian mechanics. Molecular dynamics simulations are computer experiments which approximate classical mechanics in a system of interacting particles; in consequence, they are frequently reversible. Recent technical progress has made it possible to investigate the dynamics of biological macromolecules in silico using molecular dynamics simulations. An active area of research within this field is concerned with modeling the output of a simulation stochastically. This dissertation deals with the problem of incorporating knowledge of reversibility into the estimation and testing of stochastic models. We define a range of Bayesian inference algorithms, which are motivated by specific problems in the analysis of molecular dynamics simulations.

Understanding the structure and dynamics of biological macromolecules is a central focus of biological research. To be able to study and gain insights into these systems, it is first necessary to have an accurate and informative model for the system of interest. However, such a model is often difficult to build. For example, during protein folding, many proteins collapse into transient kinetic intermediates on timescales too fast for high-resolution experimental techniques to detect, preventing structural characterization of these species. Alternatively, current algorithms for RNA design (i.e. predicting a sequence that folds into a desired target structure) cannot accurately model structure-sequence relationships and rely primarily on brute force stochastic search, leading to poor performance on complex targets. Here, we show that it is possible to improve the quality of models for biological systems by applying a common Bayesian approach to building them, i.e. incorporating prior information to impose informative constraints on the model parameters. Through this approach, it is possible to build high-resolution models of protein dynamics given limited experimental data, as well as a state-of-the-art computational RNA design agent that outperforms all currently existing algorithms.

The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This thesis presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (t, P, T), where t is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N x N transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. 1. The method uses Bayesian analysis to determine the partition as well as the transition probabilities. 2. The method allows the construction of a Markov model for any chosen mesoscopic time scale t. 3. It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a 'consistent mesoscopic Markov model' (or CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P, T) for any chosen t. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time scale t was generated by the CMMM specified by (P, T). An optimization algorithm is used to find the most probable CMMM for the chosen mesoscopic time step. We applied this method of Markov model construction to several toy systems (random walks in one and two dimensions) as well as the dynamics of alanine dipeptide in water and of trpzip2 in water. The resulting Markov state models were indeed successful in capturing the dynamics of our test systems on a variety of mesoscopic time scales.

Bayesian statistics is a powerful method for inference--possibly the uniquely correct method for inference. As described herein, when applied to a few degrees of freedom from single molecule trajectories, Bayesian statistics yield useful insights into rates, states, and motions.

Single fluorescent molecules and particles can be localized in space with precision on the order of tens of nanometers (i.e. "super localized") using state-of-the-art microscopy techniques. The ability to probe complex environments at the sub-diffraction size scale has proven invaluable in revealing fundamental heterogeneity and improving overall understanding across the applied physical sciences. Super-localization microscopy is at the heart of both single-molecule super-resolution microscopy and single-particle tracking. The work presented in this dissertation concerns the application of super-localization microscopy to problems of biophysical interest, as well as theoretical and experimental advances in the methodology of this class of techniques. While the most common methods of super-localized position estimation ensure high localization precision, they might not always ensure high accuracy. In particular, the anisotropy of single-molecule dipole emission can result in mislocalizations of hundreds of nanometers, depending on the orientation of the molecule and its distance from the focal plane. In this dissertation I discuss different ways to correct this potential source of error. On the one hand, a theory based on a wobbling-in-a-cone model is presented that shows how this error is mitigated by molecular rotational mobility. On the other hand, for the worst-case scenario of a rotationally fixed emitter, an experimental approach based on Fourier optics is also discussed that allows for estimation of molecular orientation and enables active correction of mislocalization effects. The last third of this dissertation discusses applications of super-localization microscopy to three-dimensional tracking of fluorescently labeled genetic loci in budding yeast. In order to localize loci in the axial dimension, I used a Fourier optics approach to engineer the point spread function of the microscope into a Double-Helix Point Spread Function (DH-PSF). With this method, many single copies of a specific locus were analyzed, each with 3D spatial precision on the order of 10 nm at a rate of 10 Hz. A two-color implementation of the microscope allowed measurement of the correlations of 3D motion between pairs of loci under variable transcriptional pressure. I also discuss the importance of properly accounting for the inescapable effects of static and dynamic tracking errors caused by finite photon statistics and motion blur, respectively. These errors affect the statistics of the estimated motion and distort common metrics for characterizing stochastic motion such as the mean-squared displacement (MSD) and velocity autocorrelation (VAC). Analytical expressions for the MSD and VAC in the presence of these errors are given, along with applications to chromosomal locus tracking.

Here we report that proper treatment of nonbonded interactions is essential for the accuracy of molecular dynamics (MD) simulations, especially in studies of lipid bilayers. The use of the CHARMM36 force field (C36 FF) in different MD simulation programs can result in disagreements with published simulations performed with CHARMM due to differences in the protocols used to treat the long-range and 1-4 nonbonded interactions. In this study, we systematically test the use of the C36 lipid FF in NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM. A wide range of Lennard-Jones (LJ) cutoff schemes and integrator algorithms were tested to find the optimal simulation protocol to best match bilayer properties of six lipids with varying acyl chain saturation and head groups. MD simulations of a 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) bilayer were used to obtain the optimal protocol for each program. MD simulations with all programs were found to reasonably match the DPPC bilayer properties (surface area per lipid, chain order parameters, and area compressibility modulus) obtained using the standard protocol used in CHARMM as well as from experiments. The optimal simulation protocol was then applied to the other five lipid simulations and resulted in excellent agreement between results from most simulation programs as well as with experimental data. AMBER compared least favorably with the expected membrane properties, which appears to be due to its use of the hard-truncation in the LJ potential versus a force-based switching function used to smooth the LJ potential as it approaches the cutoff distance. The optimal simulation protocol for each program has been implemented in CHARMM-GUI. This protocol is expected to be applicable to the remainder of the additive C36 FF including the proteins, nucleic acids, carbohydrates, and small molecules.

Single walled carbon nanotubes (SWNTs) are an interesting material with many possible applications including nanoelectronics, flexible electronics and sensors. One of the current challenges in the application of SWNTs is the fact that their synthesis procedures yield SWNTs with a distribution of chiralities, radii, and properties, instead of a homogenous material. It is also not currently possible to selectively fabricate specific distributions for different applications. In an effort to understand and control SWNT growth, we explored a range of growth conditions in the chemical vapor deposition (CVD) growth of SWNTs, including the use of liquid carbon sources instead of gaseous carbon sources. Some of the condition variables explored were carbon source composition, carbon source concentration, growth temperature, and carrier gas composition. Using a combination of Raman spectroscopy and SEM imaging, we demonstrate a clear dependence of changes in the distribution of SWNTs on that growth conditions varied. Of particular interest was the ratio of semiconducting SWNTs to metallic SWNTs, which was determined by correlating Raman spectroscopy data with device measurements. Distribution changes were seen using a range of carbon source molecules and can be used to tune as required for different applications. The greatest single chirality enrichment was seen at high temperatures using 2-butanol as the carbon source, while the greatest range of chiralities within a single growth was seen with ethanol as the carbon source. Correlating the SWNT distribution changes with the growth conditions varied also yielded insight into the growth mechanism of CVD grown SWNTs. This insight and a better understanding of the SWNT growth mechanism will lead to a further realization of SWNT application potentials.

Lattice models of proteins have been extensively used to study protein thermodynamics, folding dynamics and evolution. Our study considers two different hydrophobic-polar (HP) models on the two-dimensional square lattice: the purely HP model and a model where a compactness-favoring term is added. We exhaustively enumerate all the possible structures in our models and perform the study of their corresponding folds, HP arrangements in space and shapes. The two models considered differ greatly in their numbers of structures, folds, arrangements, and shapes. Despite their differences both lattice models have distinctive protein-like features: (1) Shapes are compact in both models, especially when a compactness-favoring energy term is added. (2) The residue composition is independent of the chain length and is very close to 50% hydrophobic in both models, as we observe in real proteins. (3) Comparative modeling works well in both models, particularly in the more compact one. The fact that our models show protein-like features suggests that lattice models incorporate the fundamental physical principles of proteins. Our work supports the use of lattice models to study questions about proteins that require exactness and extensive calculations, such as protein design and evolution, which are often too complex and computationally demanding to be addressed with more detailed models.

Bryostatin 1 is a marine natural product that has been of great interest to chemists and clinicians due to its highly complex structure and its remarkable biological activity. Bryostatin has been investigated for the treatment of many indications, most notably cancer, HIV, and Alzheimer's disease, collectively for which it has been entered into over 40 clinical trials. Notwithstanding the immense potential impact of bryostatin's biological activity, its current supply is nearly exhausted and future supply is uncertain. All bryostatin that has been used clinically has been sourced from one GMP isolation in 1991, and all subsequent efforts to isolate more (through isolation from source organism, aquaculture, engineered biosynthesis, or total synthesis) have been unsuccessful or not scalable. One solution to bryostatin's supply problem is the design of a shorter, supply-impacting synthesis. If accomplished, this solution would allow for a rapid replenishment of bryostatin's supply and an immediate clinical impact. A second solution to bryostatin's supply problem is the design of new bryostatin analogs. Because bryostatin was not optimized for its therapeutic use in humans, new analogs can be designed that retain or even improve upon bryostatin's biological activity while also reducing its immense complexity. Such an effort, however, is complicated by the fact that there exists little structural information about bryostatin's target, protein kinase C (PKC), in its active, membrane-associated state. Thus, a substantial portion of the work described here has used both molecular dynamics (MD) simulations and solid state NMR experiments to more fully understand the structure and function of membrane-associated PKC. Chapter 1 provides a survey of the structure, function, and membrane interactions of PKC. This chapter contains a brief overview of the different PKC isoforms, their various functions within the cell, and the biological indications that are tied to PKC regulation (such as cancer, HIV, and Alzheimer's disease). It examines the bryostatin analogs that have been synthesized in order to target these indications. Of particular emphasis is that design of new PKC activators has been complicated by the fact that while a few X-ray and NMR structures of PKC fragments exist, there are no structures of membrane-associated PKC. The importance of the membrane in PKC function is described, as are the efforts thus far to examine the role of the membrane in the activity of PKC activators. Chapter 2 details the use of molecular dynamics (MD) simulations in elucidating the membrane-associated structure of ligand-bound PKC. These simulations examine how different PKC activators differentially position the ligand-bound PKC complex in the membrane, and the role of waters and lipid headgroups at the interface of the membrane and cytosol. These simulations also provide an explanation for why bryostatin's northern region is important to its activity despite not being in contact with the binding pocket, thus providing a hypothesis for future design of new bryostatin analogs. Chapter 3 details the synthesis of a new library of greatly simplified bryostatin analogs, and the development and use of a new assay to test the PKC binding affinity of these and other compounds across all conventional and novel PKC isoforms. These greatly simplified compounds remove bryostatin's complex northern region entirely by replacing the A- and B-rings with a short diester chain, thus reducing a 20-membered macrocycle to a 14-membered one, and are synthesized in only 19 linear steps (20 total). It is also shown that while some compounds in this library bind to PKC as strongly as bryostatin 1 across all isoforms, others exhibit unprecedented selectivity between conventional and some novel PKCs. Chapter 4 addresses the lack of any existing experimental membrane-associated structure of the PKC-ligand complex. This problem is addressed through the use of solid-state REDOR NMR studies, in which interatomic distances are measured between different isotopes. These experiments used an isotopically-labeled bryostatin analog bound to the PKCδ C1b domain in the presence of phospholipid vesicles. In doing so, this represents the first experimental determination of the bound conformation of any PKC activator in a phospholipid membrane. These experiments are coupled with MD simulations to use the measured interatomic distances to construct a full picture of the ensemble of conformations that exist in this PKC-ligand-membrane complex. Chapter 5 details the total synthesis of bryostatin 1. Through the collaborative work of 8 co-workers in the Wender lab, we have accomplished the shortest reported synthesis of bryostatin 1 at 19 linear steps (29 total). My key contributions to this collaborative effort are highlighted. This short synthesis is scalable and has thus far produced more than 2 grams of bryostatin 1. This chapter also describes how such a synthesis fundamentally alters the landscape of bryostatin supply; all bryostatin that had ever been used in the clinic was from one GMP isolation in 1991 and is almost entirely exhausted. Subsequent efforts to isolate bryostatin and replenish this supply have proven either unsuccessful or not scalable. Our accomplishment in producing a short, scalable synthesis breaks through this barrier and finally provides a new, renewable source of bryostatin 1.