Computational Methods for RNA Structure Validation and Improvement.

With increasing recognition of the roles RNA molecules and RNA/protein complexes play in an unexpected variety of biological processes, understanding of RNA structure-function relationships is of high current importance. To make clean biological interpretations from three-dimensional structures, it is imperative to have high-quality, accurate RNA crystal structures available, and the community has thoroughly embraced that goal. However, due to the many degrees of freedom inherent in RNA structure (especially for the backbone), it is a significant challenge to succeed in building accurate experimental models for RNA structures. This chapter describes the tools and techniques our research group and our collaborators have developed over the years to help RNA structural biologists both evaluate and achieve better accuracy. Expert analysis of large, high-resolution, quality-conscious RNA datasets provides the fundamental information that enables automated methods for robust and efficient error diagnosis in validating RNA structures at all resolutions. The even more crucial goal of correcting the diagnosed outliers has steadily developed toward highly effective, computationally based techniques. Automation enables solving complex issues in large RNA structures, but cannot circumvent the need for thoughtful examination of local details, and so we also provide some guidance for interpreting and acting on the results of current structure validation for RNA.

A Comparative Review of Computational Methods as Applied to Gold(I) Complexes and Mechanisms

In the last two decades, the field of homogeneous gold catalysis has been

extremely active, growing at a rapid pace. Another rapidly-growing field—that of

computational chemistry—has often been applied to the investigation of various gold-

catalyzed reaction mechanisms. Unfortunately, a number of recent mechanistic studies

have utilized computational methods that have been shown to be inappropriate and

inaccurate in their description of gold chemistry. This work presents an overview of

available computational methods with a focus on the approximations and limitations

inherent in each, and offers a review of experimentally-characterized gold(I) complexes

and proposed mechanisms as compared with their computationally-modeled

counterparts. No aim is made to identify a “recommended” computational method for

investigations of gold catalysis; rather, discrepancies between experimentally and

computationally obtained values are highlighted, and the systematic errors between

different computational methods are discussed.

Computational inference of neural information flow networks.

Determining how information flows along anatomical brain pathways is a fundamental requirement for understanding how animals perceive their environments, learn, and behave. Attempts to reveal such neural information flow have been made using linear computational methods, but neural interactions are known to be nonlinear. Here, we demonstrate that a dynamic Bayesian network (DBN) inference algorithm we originally developed to infer nonlinear transcriptional regulatory networks from gene expression data collected with microarrays is also successful at inferring nonlinear neural information flow networks from electrophysiology data collected with microelectrode arrays. The inferred networks we recover from the songbird auditory pathway are correctly restricted to a subset of known anatomical paths, are consistent with timing of the system, and reveal both the importance of reciprocal feedback in auditory processing and greater information flow to higher-order auditory areas when birds hear natural as opposed to synthetic sounds. A linear method applied to the same data incorrectly produces networks with information flow to non-neural tissue and over paths known not to exist. To our knowledge, this study represents the first biologically validated demonstration of an algorithm to successfully infer neural information flow networks.

De novo design and molecular assembly of a transmembrane diporphyrin-binding protein complex.

The de novo design of membrane proteins remains difficult despite recent advances in understanding the factors that drive membrane protein folding and association. We have designed a membrane protein PRIME (PoRphyrins In MEmbrane) that positions two non-natural iron diphenylporphyrins (Fe(III)DPP's) sufficiently close to provide a multicentered pathway for transmembrane electron transfer. Computational methods previously used for the design of multiporphyrin water-soluble helical proteins were extended to this membrane target. Four helices were arranged in a D(2)-symmetrical bundle to bind two Fe(II/III) diphenylporphyrins in a bis-His geometry further stabilized by second-shell hydrogen bonds. UV-vis absorbance, CD spectroscopy, analytical ultracentrifugation, redox potentiometry, and EPR demonstrate that PRIME binds the cofactor with high affinity and specificity in the expected geometry.

Genetic signatures in the envelope glycoproteins of HIV-1 that associate with broadly neutralizing antibodies.

A steady increase in knowledge of the molecular and antigenic structure of the gp120 and gp41 HIV-1 envelope glycoproteins (Env) is yielding important new insights for vaccine design, but it has been difficult to translate this information to an immunogen that elicits broadly neutralizing antibodies. To help bridge this gap, we used phylogenetically corrected statistical methods to identify amino acid signature patterns in Envs derived from people who have made potently neutralizing antibodies, with the hypothesis that these Envs may share common features that would be useful for incorporation in a vaccine immunogen. Before attempting this, essentially as a control, we explored the utility of our computational methods for defining signatures of complex neutralization phenotypes by analyzing Env sequences from 251 clonal viruses that were differentially sensitive to neutralization by the well-characterized gp120-specific monoclonal antibody, b12. We identified ten b12-neutralization signatures, including seven either in the b12-binding surface of gp120 or in the V2 region of gp120 that have been previously shown to impact b12 sensitivity. A simple algorithm based on the b12 signature pattern was predictive of b12 sensitivity/resistance in an additional blinded panel of 57 viruses. Upon obtaining these reassuring outcomes, we went on to apply these same computational methods to define signature patterns in Env from HIV-1 infected individuals who had potent, broadly neutralizing responses. We analyzed a checkerboard-style neutralization dataset with sera from 69 HIV-1-infected individuals tested against a panel of 25 different Envs. Distinct clusters of sera with high and low neutralization potencies were identified. Six signature positions in Env sequences obtained from the 69 samples were found to be strongly associated with either the high or low potency responses. Five sites were in the CD4-induced coreceptor binding site of gp120, suggesting an important role for this region in the elicitation of broadly neutralizing antibody responses against HIV-1.

Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

Novel Computational Protein Design Algorithms with Applications to Cystic Fibrosis and HIV

Proteins are essential components of cells and are crucial for catalyzing reactions, signaling, recognition, motility, recycling, and structural stability. This diversity of function suggests that nature is only scratching the surface of protein functional space. Protein function is determined by structure, which in turn is determined predominantly by amino acid sequence. Protein design aims to explore protein sequence and conformational space to design novel proteins with new or improved function. The vast number of possible protein sequences makes exploring the space a challenging problem.

Computational structure-based protein design (CSPD) allows for the rational design of proteins. Because of the large search space, CSPD methods must balance search accuracy and modeling simplifications. We have developed algorithms that allow for the accurate and efficient search of protein conformational space. Specifically, we focus on algorithms that maintain provability, account for protein flexibility, and use ensemble-based rankings. We present several novel algorithms for incorporating improved flexibility into CSPD with continuous rotamers. We applied these algorithms to two biomedically important design problems. We designed peptide inhibitors of the cystic fibrosis agonist CAL that were able to restore function of the vital cystic fibrosis protein CFTR. We also designed improved HIV antibodies and nanobodies to combat HIV infections.

Computational Inference of Genome-Wide Protein-DNA Interactions Using High-Throughput Genomic Data

Transcriptional regulation has been studied intensively in recent decades. One important aspect of this regulation is the interaction between regulatory proteins, such as transcription factors (TF) and nucleosomes, and the genome. Different high-throughput techniques have been invented to map these interactions genome-wide, including ChIP-based methods (ChIP-chip, ChIP-seq, etc.), nuclease digestion methods (DNase-seq, MNase-seq, etc.), and others. However, a single experimental technique often only provides partial and noisy information about the whole picture of protein-DNA interactions. Therefore, the overarching goal of this dissertation is to provide computational developments for jointly modeling different experimental datasets to achieve a holistic inference on the protein-DNA interaction landscape.

We first present a computational framework that can incorporate the protein binding information in MNase-seq data into a thermodynamic model of protein-DNA interaction. We use a correlation-based objective function to model the MNase-seq data and a Markov chain Monte Carlo method to maximize the function. Our results show that the inferred protein-DNA interaction landscape is concordant with the MNase-seq data and provides a mechanistic explanation for the experimentally collected MNase-seq fragments. Our framework is flexible and can easily incorporate other data sources. To demonstrate this flexibility, we use prior distributions to integrate experimentally measured protein concentrations.

We also study the ability of DNase-seq data to position nucleosomes. Traditionally, DNase-seq has only been widely used to identify DNase hypersensitive sites, which tend to be open chromatin regulatory regions devoid of nucleosomes. We reveal for the first time that DNase-seq datasets also contain substantial information about nucleosome translational positioning, and that existing DNase-seq data can be used to infer nucleosome positions with high accuracy. We develop a Bayes-factor-based nucleosome scoring method to position nucleosomes using DNase-seq data. Our approach utilizes several effective strategies to extract nucleosome positioning signals from the noisy DNase-seq data, including jointly modeling data points across the nucleosome body and explicitly modeling the quadratic and oscillatory DNase I digestion pattern on nucleosomes. We show that our DNase-seq-based nucleosome map is highly consistent with previous high-resolution maps. We also show that the oscillatory DNase I digestion pattern is useful in revealing the nucleosome rotational context around TF binding sites.

Finally, we present a state-space model (SSM) for jointly modeling different kinds of genomic data to provide an accurate view of the protein-DNA interaction landscape. We also provide an efficient expectation-maximization algorithm to learn model parameters from data. We first show in simulation studies that the SSM can effectively recover underlying true protein binding configurations. We then apply the SSM to model real genomic data (both DNase-seq and MNase-seq data). Through incrementally increasing the types of genomic data in the SSM, we show that different data types can contribute complementary information for the inference of protein binding landscape and that the most accurate inference comes from modeling all available datasets.

This dissertation provides a foundation for future research by taking a step toward the genome-wide inference of protein-DNA interaction landscape through data integration.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.