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<p> Protein structure is fundamental to a deep understanding of how proteins function. Since structure is highly conserved, structural comparison can provide deep information about the evolution and function of protein families. The Protein Data Bank (PDB) continues to grow rapidly, providing copious opportunities for advancing our understanding of proteins through large-scale searches and structural comparisons. In this work I present several novel structural comparison methods for specific applications, as well as apply structure comparison tools systematically to better understand global properties of protein fold space. </p><p> Circular permutation describes a relationship between two proteins where the N-terminal portion of one protein is related to the C-terminal portion of the other. Proteins that are related by a circular permutation generally share the same structure despite the rearrangement of their primary sequence. This non-sequential relationship makes them difficult for many structure alignment tools to detect. Combinatorial Extension for Circular Permutations (CE-CP) was developed to align proteins that may be related by a circular permutation. It is widely available due to its incorporation into the RCSB PDB website. </p><p> Symmetry and structural repeats are common in protein structures at many levels. The CE-Symm tool was developed in order to detect internal pseudosymmetry within individual polypeptide chains. Such internal symmetry can arise from duplication events, so aligning the individual symmetry units provides insights about conservation and evolution. In many cases, internal symmetry can be shown to be important for a number of functions, including ligand binding, allostery, folding, stability, and evolution. </p><p> Structural comparison tools were applied comprehensively across all PDB structures for systematic analysis. Pairwise structural comparisons of all proteins in the PDB have been computed using the Open Science Grid computing infrastructure, and are kept continually up-to-date with the release of new structures. These provide a network-based view of protein fold space. CE-Symm was also applied to systematically survey the PDB for internally symmetric proteins. It is able to detect symmetry in ~20% of all protein families. Such PDB-wide analyses give insights into the complex evolution of protein folds. </p>

<p> Abstract: Determination is the process in which a stem cell commits to differentiation. The process of how a cell goes through determination is not well understood. Determination is important for proper regulation of cell turn-over in tissue and maintaining the adult stem cell population. Deregulation of determination or differentiation can lead to diseases such as several forms of cancer. In this study I will be using microarrays to identify candidate genes involved in determination by pulse induction of mouse erythroleukemia (MEL) cells with DMSO and looking at gene expression changes as the cells go through the early stages of erythropoiesis. The pulsed induction method I have developed to identify candidate genes is to induce cells for a short time (30 min, 2 hours, etc.) and allow them then to grow for the duration of their differentiation time (8 days). For reference, cells were also harvested at the time when the inducer is removed from the media. Results show high numbers of genes differentially expressed including erythropoiesis specific genes such as GATA1, globin genes and many novel candidate genes that have also been indicated as playing a role in the dynamic early signaling of erythropoiesis. In addition, several genes showed a pendulum effect when allowed to recover, making these interesting candidate genes for maintaining self-renewal of the adult stem cell population.</p>

<p> The sheer complexity of evolutionary systems biology requires us to develop more sophisticated tools for analysis, as well as more probing and biologically relevant representations of the data. My research has focused on three aspects of evolutionary systems biology. I ask whether a gene&rsquo;s position in the human metabolic network affects the degree to which natural selection prunes variation in that gene. Using a novel orthology inference tool that uses both sequence similarity and gene synteny, I inferred orthologous groups of genes for the full genomes of 8 mammals. With these orthologs, I estimated the selective constraint (the ratio of non-synonymous to synonymous nucleotide substitutions) on 1190 (or 80.2%) of the genes in the metabolic network using a maximum likelihood model of codon evolution and compared this value to the betweenness centrality of each enzyme (a measure of that enzyme&rsquo;s relative global position in the network). Second, I have focused on the evolution of metabolic systems in the presence of gene and genome duplication. I show that increases in a particular gene&rsquo;s copy number are correlated with limiting metabolic flux in the reaction associated with that gene. Finally, I have investigated the proliferative cell programs present in 6 different cancers (breast, colorectal, gastrointestinal, lung, oral squamous and prostate cancers). I found an overabundance of genes that share expression between cancer and embryonic tissue and that these genes form modular units within regulatory, proteininteraction, and metabolic networks. This despite the fact that these genes, as well as the proteins they encode and reactions they catalyze show little overlap among cancers, suggesting parallel independent reversion to an embryonic pattern of gene expression.</p>

<p> One of the central motivators behind genetic research is to understand how genetic variation relates to human health and disease. Recently, there has been a large-scale effort to find common genetic variants associated with many forms of disease and disorder using single nucleotide polymorphisms (SNPs). Several genome-wide association (GWAS) studies have successfully identified SNPs associated with phenotypes. However, the effect sizes attributed to individual variants is generally small, explaining only a very small amount of the genetic risk and heritability expected based on the estimates of family and twin studies. Several explanations exist for the inability of GWAS to find the "missing heritability." </p><p> The results of recent research appear to confirm the prediction made by population genetics theory that most complex phenotypes are highly polygenic, occasionally influenced by a few alleles of relatively large effect, and usually by several of small effect. Studies have also confirmed that common variants are only part of what contributes to the total genetic variance for most traits, indicating rare-variants may play a significant role. </p><p> This research addresses some of the most glaring weaknesses of the traditional GWAS approach through the application of methods of polygenic analysis. We apply several methods, including those that investigate the net effects of large sets of SNPs, more sophisticated approaches informed by biology rather than the purely statistical approach of GWAS, as well as methods that infer the effects of recessive rare variants. </p><p> Our results indicate that traditional GWAS is well complemented and improved upon by methods of polygenic analysis. We demonstrate that polygenic approaches can be used to significantly predict individual risk for disease, provide an unbiased estimate of a substantial proportion of the heritability for multiple phenotypes, identify sets of genes grouped into biological pathways that are enriched for associations, and finally, detect the significant influence of recessive rare variants.</p>

This thesis concentrates on the development, analysis, implementation, and application of a symmetry preserving singular value decomposition (SPSVD). This new factorization enhances the singular value decomposition (SVD)---a powerful method for calculating a low rank approximation to a large data set---by producing the best symmetric low rank approximation to a matrix with respect to the Frobenius norm and matrix-2 norm. Calculating an SPSVD is a two-step process. In the first step, a matrix representation for the symmetry of a given data set must be determined. This process is presented as a novel iterative reweighting method: a scheme which is rapidly convergent in practice and seems to be extremely effective in ignoring outliers of the data. In the second step, the best approximation that maintains the symmetry calculated from the first step is computed. This approximation is designated the SPSVD of the data set. In many situations, the SPSVD needs efficient updating. For instance, if new data is given, then the symmetry of the set may change and an alternative matrix representation has to be formed. A modification in the matrix representation also alters the SPSVD. Therefore, proficient methods to address each of these issues are developed in this thesis. This thesis applies the SPSVD to molecular dynamic (MD) simulations of proteins and to face analysis. Symmetric motions of a molecule may be lost when the SVD is applied to MD trajectories of proteins. This loss is corrected by implementing the SPSVD to create major modes of motion that best describe the symmetric movements of the protein. Moreover, the SPSVD may reduce the noise that often occurs on the side chains of molecules. In face analysis, the SVD is regularly used for compression. Because faces are nearly symmetric, applying the SPSVD to faces creates a more efficient compression. This efficiency is a result of having to store only half the picture for the SPSVD. Therefore, it is apparent that the SPSVD is an effective method for calculating a symmetric low rank approximation for a set of data.

<p> This thesis focuses on methodologies and applications of module-based analysis (MBA) in omics studies to investigate the relationships of phenotypes and biomarkers, e.g., SNPs, genes, and metabolites. As an alternative to traditional single&ndash;biomarker approaches, MBA may increase the detectability and reproducibility of results because biomarkers tend to have moderate individual effects but significant aggregate effect; it may improve the interpretability of findings and facilitate the construction of follow-up biological hypotheses because MBA assesses biomarker effects in a functional context, e.g., pathways and biological processes. Finally, for exploratory &ldquo;omics&rdquo; studies, which usually begin with a full scan of a long list of candidate biomarkers, MBA provides a natural way to reduce the total number of tests, and hence relax the multiple-testing burdens and improve power.</p><p> The first MBA project focuses on genetic association analysis that assesses the main and interaction effects for sets of genetic (G) and environmental (E) factors rather than for individual factors. We develop a kernel machine regression approach to evaluate the complete effect profile (i.e., the G, E, and G-by-E interaction effects separately or in combination) and construct a kernel function for the Gene-Environmental (GE) interaction directly from the genetic kernel and the environmental kernel. We use simulation studies and real data applications to show improved performance of the Kernel Machine (KM) regression method over the commonly adapted PC regression methods across a wide range of scenarios. The largest gain in power occurs when the underlying effect structure is involved complex GE interactions, suggesting that the proposed method could be a useful and powerful tool for performing exploratory or confirmatory analyses in GxE-GWAS.</p><p> In the second MBA project, we extend the kernel machine framework developed in the first project to model biomarkers with network structure. Network summarizes the functional interplay among biological units; incorporating network information can more precisely model the biological effects, enhance the ability to detect true signals, and facilitate our understanding of the underlying biological mechanisms. In the work, we develop two kernel functions to capture different network structure information. Through simulations and metabolomics study, we show that the proposed network-based methods can have markedly improved power over the approaches ignoring network information.</p><p> Metabolites are the end products of cellular processes and reflect the ultimate responses of biology system to genetic variations or environment exposures. Because of the unique properties of metabolites, pharmcometabolomics aims to understand the underlying signatures that contribute to individual variations in drug responses and identify biomarkers that can be helpful to response predictions. To facilitate mining pharmcometabolomic data, we establish an MBA pipeline that has great practical value in detection and interpretation of signatures, which may potentially indicate a functional basis for the drug response. We illustrate the utilities of the pipeline by investigating two scientific questions in aspirin study: (1) which metabolites changes can be attributed to aspirin intake, and (2) what are the metabolic signatures that can be helpful in predicting aspirin resistance. Results show that the MBA pipeline enables us to identify metabolic signatures that are not found in preliminary single-metabolites analysis.</p>