Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

BACKGROUND: Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. RESULTS: Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. CONCLUSIONS: Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

Shifting ranges and conservation challenges for lemurs in the face of climate change.

Geospatial modeling is one of the most powerful tools available to conservation biologists for estimating current species ranges of Earth's biodiversity. Now, with the advantage of predictive climate models, these methods can be deployed for understanding future impacts on threatened biota. Here, we employ predictive modeling under a conservative estimate of future climate change to examine impacts on the future abundance and geographic distributions of Malagasy lemurs. Using distribution data from the primary literature, we employed ensemble species distribution models and geospatial analyses to predict future changes in species distributions. Current species distribution models (SDMs) were created within the BIOMOD2 framework that capitalizes on ten widely used modeling techniques. Future and current SDMs were then subtracted from each other, and areas of contraction, expansion, and stability were calculated. Model overprediction is a common issue associated Malagasy taxa. Accordingly, we introduce novel methods for incorporating biological data on dispersal potential to better inform the selection of pseudo-absence points. This study predicts that 60% of the 57 species examined will experience a considerable range of reductions in the next seventy years entirely due to future climate change. Of these species, range sizes are predicted to decrease by an average of 59.6%. Nine lemur species (16%) are predicted to expand their ranges, and 13 species (22.8%) distribution sizes were predicted to be stable through time. Species ranges will experience severe shifts, typically contractions, and for the majority of lemur species, geographic distributions will be considerably altered. We identify three areas in dire need of protection, concluding that strategically managed forest corridors must be a key component of lemur and other biodiversity conservation strategies. This recommendation is all the more urgent given that the results presented here do not take into account patterns of ongoing habitat destruction relating to human activities.

Structural and Biochemical Dissection of the Trehalose Biosynthetic Complex in Pathogenic Fungi

Trehalose is a non-reducing disaccharide essential for pathogenic fungal survival and virulence. The biosynthesis of trehalose requires the trehalose-6-phosphate synthase, Tps1, and trehalose-6-phosphate phosphatase, Tps2. More importantly, the trehalose biosynthetic pathway is absent in mammals, conferring this pathway as an ideal target for antifungal drug design. However, lack of germane biochemical and structural information hinders antifungal drug design against these targets.

In this dissertation, macromolecular X-ray crystallography and biochemical assays were employed to understand the structures and functions of proteins involved in the trehalose biosynthetic pathway. I report here the first eukaryotic Tps1 structures from Candida albicans (C. albicans) and Aspergillus fumigatus (A. fumigatus) with substrates or substrate analogs. These structures reveal the key residues involved in substrate binding and catalysis. Subsequent enzymatic assays and cellular assays highlight the significance of these key Tps1 residues in enzyme function and fungal stress response. The Tps1 structure captured in its transition-state with a non-hydrolysable inhibitor demonstrates that Tps1 adopts an “internal return like” mechanism for catalysis. Furthermore, disruption of the trehalose biosynthetic complex formation through abolishing Tps1 dimerization reveals that complex formation has regulatory function in addition to trehalose production, providing additional targets for antifungal drug intervention.

I also present here the structure of the Tps2 N-terminal domain (Tps2NTD) from C. albicans, which may be involved in the proper formation of the trehalose biosynthetic complex. Deletion of the Tps2NTD results in a temperature sensitive phenotype. Further, I describe in this dissertation the structures of the Tps2 phosphatase domain (Tps2PD) from C. albicans, A. fumigatus and Cryptococcus neoformans (C. neoformans) in multiple conformational states. The structures of the C. albicans Tps2PD -BeF3-trehalose complex and C. neoformans Tps2PD(D24N)-T6P complex reveal extensive interactions between both glucose moieties of the trehalose involving all eight hydroxyl groups and multiple residues of both the cap and core domains of Tps2PD. These structures also reveal that steric hindrance is a key underlying factor for the exquisite substrate specificity of Tps2PD. In addition, the structures of Tps2PD in the open conformation provide direct visualization of the conformational changes of this domain that are effected by substrate binding and product release.

Last, I present the structure of the C. albicans trehalose synthase regulatory protein (Tps3) pseudo-phosphatase domain (Tps3PPD) structure. Tps3PPD adopts a haloacid dehydrogenase superfamily (HADSF) phosphatase fold with a core Rossmann-fold domain and a α/β fold cap domain. Despite lack of phosphatase activity, the cleft between the Tps3PPD core domain and cap domain presents a binding pocket for a yet uncharacterized ligand. Identification of this ligand could reveal the cellular function of Tps3 and any interconnection of the trehalose biosynthetic pathway with other cellular metabolic pathways.

Combined, these structures together with significant biochemical analyses advance our understanding of the proteins responsible for trehalose biosynthesis. These structures are ready to be exploited to rationally design or optimize inhibitors of the trehalose biosynthetic pathway enzymes. Hence, the work described in this thesis has laid the groundwork for the design of Tps1 and Tps2 specific inhibitors, which ultimately could lead to novel therapeutics to treat fungal infections.

Pseudo-Reimannian metrics with parallel spinor fields and vanishing Ricci tensor

I discuss geometry and normal forms for pseudo-Riemannian metrics with parallel spinor fields in some interesting dimensions. I also discuss the interaction of these conditions for parallel spinor fields with the condition that the Ricci tensor vanish (which, for pseudo-Riemannian manifolds, is not an automatic consequence of the existence of a nontrivial parallel spinor field).