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The advent of atomistic molecular dynamics simulations held the promise of a complete understanding of biomolecular dynamics. However, this goal has remained elusive, as increased computational power has brought with it larger systems to simulate and an overwhelming number of observables to analyze. In this work, I describe how recent advancements in Markov state modeling have helped overcome this dimensionality problem and enabled the characterization of complex phenomena, such as the folding-upon-binding processes of intrinsically disordered peptides. But is it possible to produce even more insightful models? To this end, I present a method that exploits Markov state models to infer statistically causal drivers of protein dynamics. Finally, I discuss a neural network alternative to Markov models, which yields physically interpretable insights and has the potential to replace expensive atomistic simulations.

The rapid development of deep learning methods has transformed concepts and pipelines in the analysis of large-scale data cohorts. In parallel, datasets of unprecedented size and diversity stemming from novel biological experimental techniques have largely exceeded the capacity of conventional human-engineered tools. Driven by the versatility and expressive power of deep neural networks, the past few years have witnessed a burst in efforts to incorporate deep learning-based techniques to model the rich information from experimental data. In addition to the need for accurate predictive modeling, biological research problems place great emphasis on model interpretability, aiming to unravel the underlying mechanism by extracting model-learned knowledge. With these challenges posed by the new techniques and datasets in mind, I present three works in this thesis that developed deep learning-based tools to model, analyze and understand various types of molecular and cellular data. In the first project, we summarized methods and datasets for molecular machine learning and proposed a large-scale benchmark MoleculeNet to facilitate the comparison of model efficacy. MoleculeNet curates multiple public datasets, establishes metrics for evaluation, and offers high-quality open-source implementations of multiple molecular featurization and learning algorithms. MoleculeNet benchmarks demonstrate that learnable representations are powerful tools for molecular machine learning and broadly offer the best performance, though learnable representations still struggle to deal with complex tasks under data scarcity and highly imbalanced classification. We further recognized that for quantum mechanical and biophysical datasets, the use of physics-aware featurization can be more important than the choice of modeling algorithm. In the second project, we proposed an automated analysis tool: DynaMorph for quantitative live-cell imaging. DynaMorph is composed of multiple modules sequentially applied to perform cell segmentation, tracking, and self-supervised morphology encoding. We employed DynaMorph to learn the cellular morphodynamics of live microglia through label-free measurements of optical density and anisotropy. These cells show complex behavior and have varied responses to disease-relevant perturbations. DynaMorph generates quantitative morphodynamic representations that can be used to compare the effects of the perturbations. Furthermore, by analyzing DynaMorph representations we identify distinct morphodynamic states of microglia polarization and detect rare transition events between states. In the third project, I studied spatial cellular community structures based on multiplex immunofluorescence imaging. By parsing high-resolution immunofluorescence images as graphical representations of cellular communities, we developed SPAtial CEllular Graphical Modeling (SPACE-GM), a geometric deep learning framework that models tumor microenvironments as cellular graphs. We applied SPACE-GM to human head-and-neck and colorectal cancer samples assayed with 40-plex immunofluorescence imaging to identify spatial motifs associated with patient survival and recurrence outcomes after immunotherapy. SPACE-GM achieves substantially higher accuracy in predicting patient outcomes than previous approaches based on neighborhood cell-type compositions. Computational interpretation of the disease-relevant microenvironments identified by SPACE-GM generates insights into the effect of spatial dispersion of tumor cells and granulocytes on patient prognosis

The computer-aided study and design of RNA molecules is increasingly prevalent across a range of disciplines, yet advancing RNA design will require quantitative improvements in predicting RNA structure. The first part of this dissertation describes contributions to advancing RNA thermodynamics predictions, a highlight of which is the development of a novel multitask-learning-based model that links the training of an RNA thermodynamic model to the statistical mechanics of several prediction tasks. We trained this framework using large datasets of diverse synthetic constructs obtained from the crowdsourced RNA design project, Eterna. The resulting algorithm, EternaFold, demonstrated improved performance on diverse independent datasets, including complete viral genomes probed in virion, human mRNAs probed in vivo, and synthetic designs modeling mRNA vaccines. This work establishes an extensive benchmark for evaluating RNA secondary structure ensembles through several types of experiment, and a general statistical mechanical framework for inferring energetic parameters from equilibrium experimental observables. The second part of this dissertation describes advances in a pressing application of RNA design: creating more thermostable RNA vaccines. Vaccines based on messenger RNA (mRNA) emerged as forerunners in the current COVID-19 pandemic and show promise as a novel therapeutic platform, yet their inherent chemical instability sets a fundamental limit on the stability of mRNA vaccines. Predictions from our developed biophysical models indicated that the half-life of any mRNA could be immediately increased at least two-fold through sequence design, predictions validated in vitro and in vivo. We anticipate this work will guide future therapeutic and vaccine development in potency and stability

While huge technological and scientific advances in human genomics have been made in the recent decade, critical questions still remain. In this dissertation, we focus on two problems: Determining variants within highly homologous regions of the human genome; Sequencing and quantification of differences in human regulatory regions. Core to the first problem is the lack of a scalable sequencing technology with sufficiently long read length and accuracy to enable truly unique mapping. Here we present our novel method, RFA, to confidently align short reads in highly homologous regions and enable accurate variant discovery in a cost-effective fashion by exploiting, via a Markov Random Field, the dependency among the short reads generated by a long read in read cloud technology. We test our method through both extensive simulations and experimental validation. We demonstrate that our method accurately recovers variation in 155Mbp of the human genome, including 94% of 67Mbp of segmental duplication sequence and 96% of 11Mbp of transcribed sequence that are currently hidden from short read technologies. To shed light on the second question, we study differences in chromatin state across 19 diverse individuals using six histone modifications, cohesin, Pol2 and CTCF in lymphoblastoid lines. We find extensive regulatory region differences in both activity (strong vs. weak vs. poised) and identity (enhancers vs. promoters vs. repressed regions). Enhancer activity is particularly diverse among individuals, and is divergent across populations in regions associated with signals of positive selection. Differences in modifications are inherited in trios and correlate with gene expression differences, indicating that they have functional consequences. Finally, differences in regulatory elements often reside in the same large chromosomal topological domains. Overall, our results provide fundamental insights into genetic and epigenetic differences of humans and how regulatory elements might evolve within a species.

Despite over half a century of study, many interesting questions concerning protein folding remain. I detail the gaps in our theoretical understanding of folding, describe how new theories and experiments could fill those gaps, and discuss my own attempts to understand one of biology's most amazing phenomena. Specifically, I discuss how master equations can be used to understand folding kinetics, how we can understand the surprising simplicity of folding kinetics, and how a experiments determining the rate-length law of folding could contribute to our ability to falsify theoretical arguments. I conclude with five stimulating questions that if answered would further our understanding of folding significantly.

This thesis focuses on applying machine learning methods on the process of biomedical diagnosis and chemical optimizations. The first part describes the combinination of ambient ionization mass spectrometry and machine learning for non-invasive biomedical diagnosis. In this design, mass spectrometry is used to collect chemical information from a biological sample; while machine learning methods are employed to give predictions based on the information. Moreover, the important chemicals in the prediction process can be pin-pointed by feature selection algorithms. Those chemical structures are further identified by tandem mass spectrometry. The second part of this thesis concerns solving chemical optimization problems with reinforcement learning. The processes of optimizing the yield of a chemical reaction and the property of a molecule are formulated as Markov decision processes, and solved by different reinforcement learning algorithms.

Water is a simple molecule with many unique physical properties that are critical to life on earth. Its properties arise from its extended hydrogen-bonded network, in which water-water hydrogen bonds are constantly breaking and forming. However, in many biological systems and materials, the water network is impacted by the presence of solutes and interfaces. In this thesis, the structure and dynamics of the hydrogen bond network are examined in technologically relevant materials where water plays a key role. The systems studied include fuel cell membranes, hydrogels and concentrated salt solutions. Nonlinear infrared spectroscopy can be used to experimentally observe ultrafast motions of water as well as its structural configurations within complex chemical systems. Polarization-selective pump-probe experiments on the OD stretch of dilute HOD in water provide information on both orientational and vibrational relaxation. Orientational relaxation describes the reorientation dynamics of water molecules in the hydrogen bond network. If angular diffusion is restricted, orientational relaxation also provides insight into how water may be sterically hindered within its environment. Vibrational relaxation describes coupling of vibrational energy absorbed by the HOD molecules to its surrounding media. The vibrational lifetime provides details on the local interactions of HOD and may allow separation of distinct dynamics near different species. Two-dimensional vibrational echo experiments on HOD molecules observe the time scales for structural evolution of the surrounding environment through ultrafast vibrational frequency fluctuations. With these experimental techniques, a holistic picture of the structure and motions of the water hydrogen bond network can be acquired

The hydrogen bond is a key intermolecular interaction in chemistry, biology, geology, and materials science, with its energy tuned for a perfect balance between structural rigidity and rapid dynamic rearrangements around ambient conditions. Ultrafast infrared spectroscopic methods are described that can interrogate the dynamics and intermolecular interactions of the hydroxyl stretch mode, a sensitive reporter of hydrogen bonding environments, of water and alcohols in complex environments far removed from the bulk liquids. New methodology for conducting noncollinear two-dimensional infrared experiments in a rotating frame to accelerate data acquisition is described. Water confined in polyacrylamide hydrogels is found to slow as one population as the size of the water pool decreases. The lack of any water with bulk-like dynamics is surprising and attributed to the continuity of hydrogen bond network between the water pool and confining polymer. Room temperature ionic liquids, a family of tunable, non-volatile, and non-flammable solvents composed entirely of cations and anions, are structured at the nanoscale by charge ordering as well as the possibility of other motifs, such as segregation of polar and apolar groups. Water and alcohols isolated in ionic liquids, as representative solutes or cosolvents, experience hydrogen bond interactions with the solvating ions. A rich hierarchy of dynamical processes in the randomization of their orientations and intermolecular interactions is observed, ranging from less than 100 femtoseconds to sometimes over 100 picoseconds. The hydrogen bond interactions are highly directional, leading to distinct forms in the polarization dependence of ultrafast IR measurements of structural dynamics (spectral diffusion), particularly in ionic liquids. Theory is developed to characterize these directional interactions and dynamics quantitatively and separate the reorientation-induced spectral diffusion (RISD) processes, arising through rotation of the tracer, from spectral diffusion that is due to the randomization of the surroundings. Related theories of RISD are presented that are appropriate for carbon dioxide, a highly symmetrical vibrational probe, as well as fluorescent probe molecules undergoing time-dependent Stokes shift with highly directional interactions that determine the absorption and emission frequencies. Measurements of the dynamics of water confined in the nanoscale pores of amorphous silica are presented. Several techniques to overcome the inherent scatter from silica particles (sand) were combined, including phase cycling, polarization control, and spatial filtering, and their individual merits are discussed. The slowdown in dynamics of water in the silica pore are compared to previous measurements of the dynamics of selenocyanate, an anion that H-bonds to the surrounding water in the pore.

Water is one of the most important substances in the world. It is used in a wide range of technologies and is an essential ingredient in all living cells we know today. The structure of water molecule is simple, yet it can form extended and versatile hydrogen bond (HB) network. This ability gives water extraordinary properties, such as high boiling and melting point. At the same time, the hydrogen bond network is not static. The constant breaking and re-forming of hydrogen bond occurs on the picosecond timescale. This dynamic network facilitates many functions of water, including ions solvation, protein folding and electricity conduction. Understanding the structure and dynamics of these processes is therefore of great importance. Ultrafast infrared (IR) spectroscopies offer a great method for accessing the sub-picosecond to picoseconds dynamics while a system in an electronic ground state. During the past two decades, hydrogen bond dynamics has been investigated extensively using ultrafast IR spectroscopies. But many questions still exist such as the effect of ions and confinement on the hydrogen bonding dynamics and the relation between the anomalous proton diffusion in dilute solution and hydrogen bonding. In Chapter 3, we examined the nature of molecular anion hydrogen bonding. The CN stretch of selenocyanate anions (SeCN-) was used as the vibrational probe in heavy water D2O. We observed the non-Condon effect on the CN stretch whose transition dipole changes with the strength of hydrogen bonding with water. In addition, HB rearrangement dynamics reported by SeCN- is almost the same as was that of the OH stretch of HOD molecules. This result shows that this anion does not perturb the surrounding HB network significantly in the low salt concentration solution. This ionic perspective is important and complements the results using OD or OH stretch of HOD molecules, which can only probe the effect of ions in a high salt concentration condition. In Chapter 4, we used SeCN- as the probe to examine water dynamics in confinement, and I focused on the nano waterpool formed in reverse micelles. The water pool is surrounded by surfactants which are further solvated by organic hydrophobic solvents. For large reverse micelle whose diameter is larger than 4 nm, the water pool is usually divided into two regions: the core region where water dynamics is like that in pure water and the interface region where water dynamics is slowed significant due to the confinement. Here we used ultrafast IR spectroscopies to measure the orientational relaxation of SeCN-, which reflects its interaction with water molecules and how "rigid" the HB network is. Based on the comparison between linear IR decomposition and ultrafast anisotropy dynamics, we proposed a three-component model of water in large reverse micelles. The interface component should be further separated into two layers. One layer corresponds to water in contact with the surfactant head group and has very slow reorientation. The other layer corresponds to water molecules whose coordinating structure still resembles that of bulk but the dynamics is slowed down due to the perturbation from confinement. In Chapter 5 and 6, hydrogen bonding dynamics in concentrated salt and acid solutions were investigated. Through electrochemical method, it was found decades ago that proton has extraordinary ion mobility, about 6 times larger than that of cations of similar sizse, such as sodium, ammonium or lithium. The great difference between them results from the cation transport mechanism. In dilute solution, the main transport mechanism of proton is through relay mechanism where the identity of proton transfers from one water molecule to another. This minimizes the physical diffusion of the atoms and greatly increases the proton mobility. The mechanism is generally called Grotthuss mechanism, which was came up with by Grotthuss in 1806 though not on the molecular level. However, the step time of a single proton transfer event between two water molecules is difficult to observe experimentally. Here we used the CN stretch of methyl thiocyanate (MeSCN) as the vibrational probe. In concentrated hydrochloric solutions, it has two frequency resolved states. One state refers to water hydrogen bonded to the nitrogen lone pair while the other state corresponds to hydronium ion hydrogen bonded to the CN. Chemical exchange phenomenon was observed between these two states. Ab initio simulation done by our collaborator shows that the proton hopping is the dominate mechanism for chemical exchange. The comparison experiment done in lithium chloride solution provides further contrast between hydronium and other metal ions. Therefore, we were able to track proton hopping in a time-resolved manner for the first time. Extrapolation to the dilute limit demonstrates that the HB rearrangement in pure water is the driving force of proton hopping in dilute solution.

Room-temperature ionic liquids (RTILs), which refers to salts that are liquid at room temperature, form a class of materials that have been intensively studied in recent years. A major motivator for this explosion in research is their many special properties and proposed applications. Many of these applications rely on their properties as solvents, particularly their ability to simultaneously solvate solutes of disparate natures. These properties have been linked to the existence in certain classes of RTILs of local domains with differing properties, such as polar and apolar domains. This ordering, which occurs when one ion, usually the cation, has a large hydrophobic moiety, such as an alkyl chain, is an additional constraint imposed on both liquid ordering and the charge alternation which is observed due to the ionic nature of the material. Varying the chain length of such cations not only changes the degree of polar-apolar ordering, but also bulk properties such as viscosity. My work seeks to understand and characterize ion solvation in such ionic liquids, and especially how and to what extent the details of solvation structure and dynamics are affected by the change in bulk properties or growing influence of additional ordering. To this end, the dynamics of four 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide RTILs with carbon chain lengths 2, 4, 6, and 10 were studied by measuring the orientational and spectral diffusion dynamics of the vibrational probe SeCN‒. Vibrational absorption measurements, two-dimensional infrared (2D IR) spectroscopy, and polarization-selective pump-probe (PSPP) experiments were performed on the CN stretch of the ion. The PSPP experiments yielded triexponential anisotropy decays, which were analyzed with the wobbling-in-a-cone model. The slowest decay, the complete orientational randomization, slows with increasing chain length in a hydrodynamic trend consistent with the increasing viscosity. The shortest time scale wobbling motions are insensitive to chain length, while the intermediate time scale wobbling slows mildly as the chain length increases. Spectral diffusion from the RTIL structural fluctuations was characterized through 2D IR. The faster structural fluctuations are relatively insensitive to chain length. The slowest structural fluctuations slow substantially when going from a 2 carbon chain a 4 carbon chain and slow further, but more gradually, as the chain length is increased. The main conclusion is that there exists a complex hierarchy of motions in terms of their spatial extent and their timescale. The fastest motions, which tend to be the most local, are also the ones most insensitive to bulk properties. The largest scale motions tend to be the ones most consistent with hydrodynamics. Some intermediate scale motions can be surprisingly sensitive to details of the structure which can be related to the growth of polar-apolar ordering, where other intermediate scale motions exhibit very weak trends. A complete understanding of the structure and dynamics of these ionic liquids, especially when considering the effect of various structural modifications, must then consider the richness of motions and timescales and how they are influenced by structural differences, as well as how they relate to the specific process that is being optimized through this structural modification. In order to obtain data of sufficient quality and detail to allow such modeling to be done successfully, the way these ultrafast experiments are performed, particularly the 2D IR experiments, had to be improved in both speed and freedom from distortion. To this end, I constructed a 2D IR interferometer based on Fourier-domain pulse-shaping. The resulting phase control and stability allows the experiments to be performed free of distortions. It also allows repeating the experiment with various configurations of imparted phase, known as "phase-cycling". Phase-cycling has four immediate benefits: it permits the experiment to be performed in a semi-collinear geometry, further eliminating possible distortions; it allows many unwanted terms such as scatter to be very effectively suppressed; it allows the spectrum of the excitation pulses to be advantageously controlled; and it eliminates the need for chopping beams which alone doubles the speed of acquisition. In addition, the programmatic generation of the first two pulses via pulse-shaping eliminates moving parts from that portion of the experiment, greatly speeding acquisition. This has allowed many previously inaccessible systems to be studied using this technique and was a tremendous aid in performing the experiments described here.

The ability to reliably design molecular systems for targeted applications has the potential to revolutionize drug and material discovery. Quantum chemistry can now accurately predict useful chemical properties for a wide range of molecules and continues to enhance its predictive power as new algorithms and hardware come online. However, several major hurdles remain. In this work, I focus on two outstanding challenges: building accessible tools for the wider chemistry community to interact with quantum chemistry, and designing photochemical systems with nonadiabatic dynamics simulations. I develop ChemPix, a hand-drawn hydrocarbon structure recognition software to provide an almost barrierless molecule input method for computational chemistry software. ChemPix and other accessible molecular input tools are combined with cloud-based GPU- accelerated quantum chemistry and extended reality visualization to build a series of interactive quantum chemistry tools. These tools can compute quantum mechanical properties in real-time from hand-drawn structures or voice input. Photochemical systems can be modeled with nonadiabatic dynamics simulations. However, the complex multi-reference electronic structure calculations required for these simulations means that modelling even simple photochemical processes demands domain expertise and substantial human effort. Here, I employ cis-stilbene, a prototypical photo- switch, to explore the path towards automated photochemical design. First, nonadiabatic dynamics simulations of cis-stilbene are performed and analyzed to uncover the cis-trans photoisomerization and photocyclization mechanisms. Next, I propose the use of ensembled simulations to build stronger mechanistic predictors and link the predictions to the experimental ultrafast electron diffraction signal. Finally, a highly symmetric light- induced molecular motor is designed based on the simulations by photo-exciting cis- stilbene with circularly polarized light

The origin of enzymes' catalytic power is a long-standing and still largely unsolved problem in biochemistry. To compare and evaluate the role of various catalytic strategies, I have turned to a model protein ketosteroid isomerase (KSI). Low barrier hydrogen bonds (LBHB) and electrostatic stabilization are two popular theories proposed to explain KSI's catalytic proficiency. The primary difference between the two hypotheses lies in the nature of the interaction between the transition state (TS) of the reaction and the extended H-bond network in KSI's active site, which preferentially stabilizes the TS to contribute to catalysis − in a LBHB formulation, the TS would enjoy an additional energetic benefit from the presumed covalent (delocalized) nature of a strong H-bond. To enable a side-by-side comparison of the two hypotheses, I utilized amber suppression and prepared a set of 'conservative mutants' by incorporating noncanonical amino acid 3-chlorotyrosine to each of the three tyrosine residues (Y16, Y57, Y32, denoted as 'tyrosine triad') within the extended H-bond network of KSI. The site-specific incorporation enabled the incremental and simultaneous tuning of the proton affinities and the electrostatic properties of KSI's active site, as suggested by small but systematic changes in KSI's catalytic rate. Moreover, X-ray crystal structures of the mutants verified the preservation of the extended H-bond network with minimal structural perturbation. The series of conservative mutants allows me to (1) dissect the quantum delocalization of protons within the extended H-bond network of apo-KSI; (2) critically test the linear correlation between KSI's electric field and its catalytic proficiency, reinforcing the dominant contribution of electrostatics in KSI catalysis; (3) and elucidate the functional connection between the strength of the active site H-bond and the electric field it exerts, suggesting a potential unification of the two hypotheses on the origin of enzymes' catalytic power.

Biology is the ultimate emergent phenomenon, and we largely lack a full picture of its function at the smallest scales. Molecular dynamics purports to model biomolecules like proteins with all-atom resolution. Among other challenges, merely analyzing the large quantities of data that result from a simulation has become a bottleneck. In this dissertation, I present my work towards building reduced-complexity models that faithfully capture the relevant functional dynamics of biomolecular simulations. In chapter 1, I introduce a mathematical language for dealing with stochastic processes and show the connection to established modeling methods like Markov modeling and tICA. Chapter 2 develops and characterizes a method for including solvent degrees of freedom in Markov state models. In chapter 3, we apply state-of-the-art MSM modeling to understand multi-scale conformational dynamics of a potassium ion channel. Chapter 4 provides an overview of a curated selection of modeling building blocks accessible through our carefully designed software package. Chapter 5 introduces a new non-linear basis which unites the MSM and tICA approaches. Finally, in chapter 6, I introduce parameterized sets of basis functions and use the variational principle directly to optimize the basis set itself. It is my hope that these novel algorithms aided by well-engineered software implementations and validated by characterization on real biomolecular systems will lead the field closer towards truly robust dynamical models of biomolecules.

Often, the computation of molecular properties requires an accurate description of the electronic wavefunction. Unfortunately, the accuracy and computational demands of a method are typically at odds with each other. In order to reduce the computational demands of ab initio methods, we have developed the tensor hypercontraction approach. In this work, we will show how the tensor hypercontraction approximation improves the efficiency of electronic structure methods while maintaining the accuracy of the underlying ab initio approach. This work focuses on the use of tensor hypercontraction in second-order Møller-Plesset perturbation theory (MP2), second-order approximate coupled cluster singles and doubles (CC2), and the extension of CC2 for excited state computations. Recently, the high performance computing industry has incorporated the use of graphics processing units (GPUs) for general purpose computing. GPUs are massively parallel architectures that are being used to accelerate computationally intensive approaches in a variety of fields, including quantum chemistry. I will show that the tensor hypercontraction methods are highly amenable to parallelization techniques and demonstrate a performance improvement for parallel tensor hypercontraction via parallelization across compute nodes and acceleration with GPUs. I will demonstrate that the use of parallel approaches allows us to extend the applicability of tensor hypercontraction CC2 and excited state computations to chemical system sizes that are challenging for canonical CC2.

Understanding the conformational dynamics of biological macromolecules at atomic resolution remains a grand challenge at the intersection of biology, chemistry, and physics. Molecular dynamics (MD) --- which refers to computational simulations of the atomic-level interactions and equations of motions that give rise to these dynamics --- is a powerful approach that now produces immense quantities of time series data on the dynamics of these systems. Here, I describe a variety of new methodologies for analyzing the rare events in these MD data sets in an automatic, statically-sound manner, and constructing the appropriate simplified models of these processes. These techniques are rooted in the theory of reversible Markov chains. They include new classes of Markov state models, hidden Markov models, and reaction coordinate finding algorithms, with applications to protein folding and conformational change. A particular focus herein is on methods for model selection and model comparison, and computationally efficient algorithms.

This thesis develops theoretical methods and simulation approaches to elucidate the dynamics of quantum mechanical processes in heterogeneous condensed phase systems. In the first part of the thesis, we consider non-equilibrium relaxation dynamics. These dynamics play a key role in many problems in chemistry, from exciton transfer in photosynthetic light harvesting to electron transfer in photocatalysis. We use the generalized quantum master equation (GQME) formalism in conjunction with quantum-classical methods to treat nonequilibrium relaxation for systems containing many quantum states, as well as fully atomistic systems. In these systems, we show that the GQME approach is highly accurate while also being more efficient than the same quantum-classical method used directly, sometimes by as much as three orders of magnitude. We present an importance sampling algorithm which efficiently generates the memory kernel of the GQME for systems with many quantum states. We then consider a series of cases where chemically tailoring a heterogeneous environment allows one to control reactivity and dynamics. In particular, we show that simulation can be used to elucidate the role of the environment in driving vibrational relaxation in functionalized self-assembled monolayers on gold. We find that vibrational dynamics measured in experiments on self-assembled monolayers arise from a variety of molecular motions including conformational rearrangement of gauche defects in the monolayer. We also show theoretically how the regioselectivity of a catalyst can be controlled by changing the solvent to enforce ion pairing. We find that mutual polarization of the ion pair and the solvent is a key source of the stabilization of ion-paired transition states that gives rise to selectivity that is observed in experiments. Overall, the theoretical methods and simulations presented allow us to accurately capture and elucidate the dynamics in a variety of heterogeneous condensed phase systems.

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.

The diverse physical principles that govern living things conform to one common precept: all biological processes operate, to some extent, out-of equilibrium. As our understanding of biological pathways advances at the nanoscale, theoretical and simulation techniques that function under non-equilibrium conditions will play an important role in elucidating the working environment of the cell. In this research, large-scale molecular dynamics simulations, discrete dynamical network models, and sophisticated non-equilibrium theories are synthesized to study glassy and dissipative processes facilitated by protein molecules. Leveraging atomistic molecular dynamics data derived from the Folding@home distributed computing project, a number of detailed biophysical systems are examined. I first describe glassy solvent structures that emerge as functional components of a protein chaperone, and I connect such observations to the theory of disordered systems. By coupling Folding@home data, Markov state models of biomolecular dynamics, and the theory of large deviations, I go on to characterize [beta] sheet-rich, amyloid-like misfolded states that appear on protein folding landscapes; I explore the relationship between these misfolded states and so-called dynamical glass transitions. Applying theory related to the Crooks fluctuation theorem, I next explicate the dissipative dynamics in detailed models of signaling proteins, and I illustrate how the input of external energy harmonizes with equilibrium fluctuations to yield functional signaling components. Lastly, I discuss methods by which protein landscapes can be sampled in an adaptive fashion and means for recovering equilibrium kinetics from biased, non-equilibrium simulation data.

The role of atomistic modeling of molecules and organic compounds in biology and pharmaceutical research is constantly increasing, providing insights on chemical and biological phenomena at the highest resolution. To achieve relevant results, however, computational biology has to deal with systems containing at least 1000 atoms. Such big molecules cause large computational demands and impose limitations on the level of theory used to describe molecular interactions. Classical molecular mechanics based on various empirical relationships has become a workhorse of computational biology, as a practical compromise between accuracy and computational cost. Several decades of classical force field development have seen many successes. Nevertheless, more accurate treatment of bio-molecules from first principles is highly desirable. Hartree-Fock (HF) and density functional theory (DFT) are two low-level ab initio methods that provide sufficient accuracy to interpret experimental data. They are therefore the methods of choice to study large biological systems. Recently DFT has been applied to calculate single point energy of a solvated Rubredoxin protein. The system contained 2825 atoms and required more than two hours on a supercomputer with 8196 parallel cores. This study clearly demonstrates the scale of problems one has to tackle in first principles calculations of biologically relevant systems. Dynamical simulations requiring thousands of single point energy and force evaluations therefore appear to be completely out of reach. This fact has essentially prohibited the use of first principles methods for many important biological systems. Fortunately, the computer industry is evolving quickly and novel computing architectures such as graphical processing units (GPUs) are emerging. The GPU is an indispensable part any modern desktop computer. It is special purpose hardware responsible for graphics processing. Most problems in computer graphics are embarrassingly parallel, meaning they can be split into a large number of smaller subproblems that can be solved in parallel. This fact has guided GPU development for more than a decade; and modern GPUs evolved into a massively parallel computing v architecture containing hundreds of basic computational units, which all together can perform trillions of arithmetic operations per second. The large computational performance and low price of consumer graphics cards makes it tempting to consider using them for computationally intensive general purpose computing. This fact was recognized long ago and several groups of enthusiasts attempted to use GPUs for non-graphics computing in the early 2000's. One of the few successes from these attempts is now known as Folding@Home. These early attempts were primarily stymied by three major problems: lack of adequate development frameworks, limited precision available on GPUs, and the difficulty of mapping existing algorithms onto the new architecture. The two former impediments have been recently alleviated by the introduction of efficient GPU programming toolkits such as CUDA and the latest generation of graphics cards supporting full double precision arithmetic operations in hardware. These advances led to an explosion of interest in general purpose GPU computing and led to the development of many GPU-based high performance applications in various fields such as classical molecular dynamics, magnetic resonance imaging, and computational fluid dynamics. Most of the projects, however, lie far outside of quantum chemistry which is likely caused by the complexity of quantum chemistry algorithms and the associated difficulty of mapping them onto the GPU architecture. Various specific features of the hardware require complete redesign of conventional HF and DFT algorithms in order to fully benefit from the large computational performance of GPUs. We have successfully solved this problem and implemented the new algorithms in TeraChem, a high performance general purpose quantum chemistry package designed for graphical processing units from the ground up. Using TeraChem, we performed the first ab initio molecular dynamics simulation of an entire Bovine pancreatic trypsin inhibitor (BPTI) protein for tens of picoseconds on a desktop workstation with eight GPUs operating in parallel. Coincidently, this was also the first protein ever simulated on a computer using the classical molecular mechanics approach. BPTI binds to trypsin with a binding free energy of approximately 20 kcal/mol, making BPTI one of the strongest non-covalent binders. It vi is even more remarkable that a single BPTI amino acid LYS15 contributes half of the binding free energy by forming a salt bridge with one of the trypsin's negatively charged residues inside the binding pocket. In fact, the LYS15's contribution to the overall binding energy is approximately twice as large as what would be expected based on experimental measurements of salt bridge interactions in other proteins. Our simulation of BPTI demonstrated that substantial charge transfer occurs at the proteinwater interface, where between 2.0 and 3.5 electrons are transferred from the interfacial water to the protein. This effect decreases the net protein charge from +6e as observed in gas-phase experiments to +4e or less. We demonstrate how this effect may explain the unusual binding affinity of the LYS15 amino acid.

Controlling multistep chemical reactions triggered by internal conversion via a conical intersection is a challenging task that emphasizes limitations in theoretical and experimental techniques. Hypothesis-driven methodologies (e.g. characterization of critical points and biased molecular dynamics) are commonly employed to explore the chemical space and simulate reaction events. In this dissertation, I present a discovery-based, hypothesis-free computational approach based on first principles molecular dynamics to elucidate photochemical reaction pathways in organic chemistry. Using state-of-the-art graphical processing units-enabled electronic structure calculations we performed in total ~2ns of adiabatic and nonadiabatic ab initio molecular dynamics to describe the natural evolution of both the nuclear and electronic degrees of freedom that govern the interconversion between Donor-Acceptor Stenhouse Adducts' ground state intermediates. Additionally, we present direct and unambiguous observation of the ring-opening reaction path in 1,3-cyclohexadiene (CHD) and a-phellandrene (aPH) on the femtosecond timescale and sub-Ångström length scale by megaelectronvolt ultrafast electron diffraction and ab initio Multiple Spawning. We follow the carbon-carbon bond dissociation and the structural opening of the rings in CHD and aPH by direct measurement of time-dependent changes in the distribution of interatomic distances. Our work provides unprecedented and significant elements for the future design strategies of molecular photoswitches