Multivariate Models and Algorithms for Systems Biology

Rapid advances in high-throughput data acquisition technologies, such as microarraysand next-generation sequencing, have enabled the scientists to interrogate the expression levels of tens of thousands of genes simultaneously. However, challenges remain in developingeffective computational methods for analyzing data generated from such platforms. In thisdissertation, we address some of these challenges. We divide our work into two parts. Inthe first part, we present a suite of multivariate approaches for a reliable discovery of geneclusters, often interpreted as pathway components, from molecular profiling data with replicated measurements. We translate our goal into learning an optimal correlation structure from replicated complete and incomplete measurements. In the second part, we focus on thereconstruction of signal transduction mechanisms in the signaling pathway components. Wepropose gene set based approaches for inferring the structure of a signaling pathway.First, we present a constrained multivariate Gaussian model, referred to as the informed-case model, for estimating the correlation structure from replicated and complete molecular profiling data. Informed-case model generalizes previously known blind-case modelby accommodating prior knowledge of replication mechanisms. Second, we generalize theblind-case model by designing a two-component mixture model. Our idea is to strike anoptimal balance between a fully constrained correlation structure and an unconstrained one.Third, we develop an Expectation-Maximization algorithm to infer the underlying correlation structure from replicated molecular profiling data with missing (incomplete) measurements.We utilize our correlation estimators for clustering real-world replicated complete and incompletemolecular profiling data sets. The above three components constitute the first partof the dissertation. For the structural inference of signaling pathways, we hypothesize a directed signal pathway structure as an ensemble of overlapping and linear signal transduction events. We then propose two algorithms to reverse engineer the underlying signaling pathway structure using unordered gene sets corresponding to signal transduction events. Throughout we treat gene sets as variables and the associated gene orderings as random.The first algorithm has been developed under the Gibbs sampling framework and the secondalgorithm utilizes the framework of simulated annealing. Finally, we summarize our findingsand discuss possible future directions

Multivariate Models and Algorithms for Systems Biology

Rapid advances in high-throughput data acquisition technologies, such as microarraysand next-generation sequencing, have enabled the scientists to interrogate the expression levels of tens of thousands of genes simultaneously. However, challenges remain in developingeffective computational methods for analyzing data generated from such platforms. In thisdissertation, we address some of these challenges. We divide our work into two parts. Inthe first part, we present a suite of multivariate approaches for a reliable discovery of geneclusters, often interpreted as pathway components, from molecular profiling data with replicated measurements. We translate our goal into learning an optimal correlation structure from replicated complete and incomplete measurements. In the second part, we focus on thereconstruction of signal transduction mechanisms in the signaling pathway components. Wepropose gene set based approaches for inferring the structure of a signaling pathway.First, we present a constrained multivariate Gaussian model, referred to as the informed-case model, for estimating the correlation structure from replicated and complete molecular profiling data. Informed-case model generalizes previously known blind-case modelby accommodating prior knowledge of replication mechanisms. Second, we generalize theblind-case model by designing a two-component mixture model. Our idea is to strike anoptimal balance between a fully constrained correlation structure and an unconstrained one.Third, we develop an Expectation-Maximization algorithm to infer the underlying correlation structure from replicated molecular profiling data with missing (incomplete) measurements.We utilize our correlation estimators for clustering real-world replicated complete and incompletemolecular profiling data sets. The above three components constitute the first partof the dissertation. For the structural inference of signaling pathways, we hypothesize a directed signal pathway structure as an ensemble of overlapping and linear signal transduction events. We then propose two algorithms to reverse engineer the underlying signaling pathway structure using unordered gene sets corresponding to signal transduction events. Throughout we treat gene sets as variables and the associated gene orderings as random.The first algorithm has been developed under the Gibbs sampling framework and the secondalgorithm utilizes the framework of simulated annealing. Finally, we summarize our findingsand discuss possible future directions

Recursive regularization for inferring gene networks from time-course gene expression profiles

<p>Abstract</p> <p>Background</p> <p>Inferring gene networks from time-course microarray experiments with vector autoregressive (VAR) model is the process of identifying functional associations between genes through multivariate time series. This problem can be cast as a variable selection problem in Statistics. One of the promising methods for variable selection is the elastic net proposed by Zou and Hastie (2005). However, VAR modeling with the elastic net succeeds in increasing the number of true positives while it also results in increasing the number of false positives.</p> <p>Results</p> <p>By incorporating relative importance of the VAR coefficients into the elastic net, we propose a new class of regularization, called recursive elastic net, to increase the capability of the elastic net and estimate gene networks based on the VAR model. The recursive elastic net can reduce the number of false positives gradually by updating the importance. Numerical simulations and comparisons demonstrate that the proposed method succeeds in reducing the number of false positives drastically while keeping the high number of true positives in the network inference and achieves two or more times higher true discovery rate (the proportion of true positives among the selected edges) than the competing methods even when the number of time points is small. We also compared our method with various reverse-engineering algorithms on experimental data of MCF-7 breast cancer cells stimulated with two ErbB ligands, EGF and HRG.</p> <p>Conclusion</p> <p>The recursive elastic net is a powerful tool for inferring gene networks from time-course gene expression profiles.</p

Extended local similarity analysis (eLSA) of microbial community and other time series data with replicates

© The Author(s), 2011. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in BMC Systems Biology 5 Suppl 2 (2011): S15, doi:10.1186/1752-0509-5-S2-S15.The increasing availability of time series microbial community data from metagenomics and other molecular biological studies has enabled the analysis of large-scale microbial co-occurrence and association networks. Among the many analytical techniques available, the Local Similarity Analysis (LSA) method is unique in that it captures local and potentially time-delayed co-occurrence and association patterns in time series data that cannot otherwise be identified by ordinary correlation analysis. However LSA, as originally developed, does not consider time series data with replicates, which hinders the full exploitation of available information. With replicates, it is possible to understand the variability of local similarity (LS) score and to obtain its confidence interval. We extended our LSA technique to time series data with replicates and termed it extended LSA, or eLSA. Simulations showed the capability of eLSA to capture subinterval and time-delayed associations. We implemented the eLSA technique into an easy-to-use analytic software package. The software pipeline integrates data normalization, statistical correlation calculation, statistical significance evaluation, and association network construction steps. We applied the eLSA technique to microbial community and gene expression datasets, where unique time-dependent associations were identified. The extended LSA analysis technique was demonstrated to reveal statistically significant local and potentially time-delayed association patterns in replicated time series data beyond that of ordinary correlation analysis. These statistically significant associations can provide insights to the real dynamics of biological systems. The newly designed eLSA software efficiently streamlines the analysis and is freely available from the eLSA homepage, which can be accessed at http://meta.usc.edu/softs/lsaThis research is partially supported by the National Science Foundation (NSF) DMS-1043075 and OCE 1136818

Statistical Integration of Heterogeneous Data with PO2PLS

The availability of multi-omics data has revolutionized the life sciences by creating avenues for integrated system-level approaches. Data integration links the information across datasets to better understand the underlying biological processes. However, high-dimensionality, correlations and heterogeneity pose statistical and computational challenges. We propose a general framework, probabilistic two-way partial least squares (PO2PLS), which addresses these challenges. PO2PLS models the relationship between two datasets using joint and data-specific latent variables. For maximum likelihood estimation of the parameters, we implement a fast EM algorithm and show that the estimator is asymptotically normally distributed. A global test for testing the relationship between two datasets is proposed, and its asymptotic distribution is derived. Notably, several existing omics integration methods are special cases of PO2PLS. Via extensive simulations, we show that PO2PLS performs better than alternatives in feature selection and prediction performance. In addition, the asymptotic distribution appears to hold when the sample size is sufficiently large. We illustrate PO2PLS with two examples from commonly used study designs: a large population cohort and a small case-control study. Besides recovering known relationships, PO2PLS also identified novel findings. The methods are implemented in our R-package PO2PLS. Supplementary materials for this article are available online.Comment: 36 pages, 4 figures, Submitted to Journal of the American Statistical Associatio

An assessment of gene regulatory network inference algorithms

A conceptual issue regarding gene regulatory network (GRN) inference algorithms is establishing their validity or correctness. In this study, we argue that for this purpose it is useful to conceive these algorithms as estimators of graph-valued parameters of explicit models for gene expression data. On this basis, we perform an assessment of a selection of influential GRN inference algorithms as estimators for two types of models: (i) causal graphs with associated structural equations models (SEMs), and (ii) differential equations models based on the thermodynamics of gene expression. Our findings corroborate that networks of marginal dependence fail in estimating GRNs, but they also suggest that the strength of statistical association as measured by mutual information may be indicative of GRN structure. Also, in simulations, we find that the GRN inference algorithms GENIE3 and TIGRESS outperform competing algorithms. However, more importantly, we also find that many observed patterns hinge on the GRN topology and the assumed data generating mechanism.Un problema conceptual con respecto a los algoritmos de inferencia de redes de regulación génica (RRG) es cómo establecer su validez. En este estudio sostenemos que para este objetivo conviene concebir estos algoritmos como estimadores de parámetros de modelos estadísticos explícitos para datos de expresión génica. Sobre esta base, realizamos una evaluación de una selección de algoritmos de inferencia de RRG como estimadores para dos tipos de modelos: (i) modelos de grafos causales asociados a modelos de ecuaciones estructurales (MEE), y (ii) modelos de ecuaciones diferenciales basados en la termodinámica de la expresion genica. Nuestros hallazgos corroboran que las redes de dependencias marginales fallan en la estimación de las RRG, pero también sugieren que la fuerza de la asociación estadística medida por la información mutua puede reflejar en cierto grado la estructura de las RRG. Además, en un estudio de simulaciones, encontramos que los algoritmos de inferencia GENIE3 y TIGRESS son los de mejor desempeño. Sin embargo, crucialmente, también encontramos que muchos patrones observados en las simulaciones dependen de la topología de la RRG y del modelo generador de datos.Maestrí

Nonlinear Dynamics of Nonsynonymous (dN) and Synonymous (dS) Substitution Rates Affects Inference of Selection

Selection modulates gene sequence evolution in different ways by constraining potential changes of amino acid sequences (purifying selection) or by favoring new and adaptive genetic variants (positive selection). The number of nonsynonymous differences in a pair of protein-coding sequences can be used to quantify the mode and strength of selection. To control for regional variation in substitution rates, the proportionate number of nonsynonymous differences (dN) is divided by the proportionate number of synonymous differences (dS). The resulting ratio (dN/dS) is a widely used indicator for functional divergence to identify particular genes that underwent positive selection. With the ever-growing amount of genome data, summary statistics like mean dN/dS allow gathering information on the mode of evolution for entire species. Both applications hinge on the assumption that dS and mean dS (∼branch length) are neutral and adequately control for variation in substitution rates across genes and across organisms, respectively. We here explore the validity of this assumption using empirical data based on whole-genome protein sequence alignments between human and 15 other vertebrate species and several simulation approaches. We find that dN/dS does not appropriately reflect the action of selection as it is strongly influenced by its denominator (dS). Particularly for closely related taxa, such as human and chimpanzee, dN/dS can be misleading and is not an unadulterated indicator of selection. Instead, we suggest that inconsistencies in the behavior of dN/dS are to be expected and highlight the idea that this behavior may be inherent to taking the ratio of two randomly distributed variables that are nonlinearly correlated. New null hypotheses will be needed to adequately handle these nonlinear dynamics

Sparse multivariate factor analysis regression models and its applications to integrative genomics analysis

The multivariate regression model is a useful tool to explore complex associations between two kinds of molecular markers, which enables the understanding of the biological pathways underlying disease etiology. For a set of correlated response variables, accounting for such dependency can increase statistical power. Motivated by integrative genomic data analyses, we propose a new methodologyâ sparse multivariate factor analysis regression model (smFARM), in which correlations of response variables are assumed to follow a factor analysis model with latent factors. This proposed method not only allows us to address the challenge that the number of association parameters is larger than the sample size, but also to adjust for unobserved genetic and/or nongenetic factors that potentially conceal the underlying responseâ predictor associations. The proposed smFARM is implemented by the EM algorithm and the blockwise coordinate descent algorithm. The proposed methodology is evaluated and compared to the existing methods through extensive simulation studies. Our results show that accounting for latent factors through the proposed smFARM can improve sensitivity of signal detection and accuracy of sparse association map estimation. We illustrate smFARM by two integrative genomics analysis examples, a breast cancer dataset, and an ovarian cancer dataset, to assess the relationship between DNA copy numbers and gene expression arrays to understand genetic regulatory patterns relevant to the disease. We identify two transâ hub regions: one in cytoband 17q12 whose amplification influences the RNA expression levels of important breast cancer genes, and the other in cytoband 9q21.32â 33, which is associated with chemoresistance in ovarian cancer.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135396/1/gepi22018.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135396/2/gepi22018_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135396/3/gepi22018-sup-0001-SuppMat.pd

Statistical inference from large-scale genomic data

This thesis explores the potential of statistical inference methodologies in their applications in functional genomics. In essence, it summarises algorithmic findings in this field, providing step-by-step analytical methodologies for deciphering biological knowledge from large-scale genomic data, mainly microarray gene expression time series. This thesis covers a range of topics in the investigation of complex multivariate genomic data. One focus involves using clustering as a method of inference and another is cluster validation to extract meaningful biological information from the data. Information gained from the application of these various techniques can then be used conjointly in the elucidation of gene regulatory networks, the ultimate goal of this type of analysis. First, a new tight clustering method for gene expression data is proposed to obtain tighter and potentially more informative gene clusters. Next, to fully utilise biological knowledge in clustering validation, a validity index is defined based on one of the most important ontologies within the Bioinformatics community, Gene Ontology. The method bridges a gap in current literature, in the sense that it takes into account not only the variations of Gene Ontology categories in biological specificities and their significance to the gene clusters, but also the complex structure of the Gene Ontology. Finally, Bayesian probability is applied to making inference from heterogeneous genomic data, integrated with previous efforts in this thesis, for the aim of large-scale gene network inference. The proposed system comes with a stochastic process to achieve robustness to noise, yet remains efficient enough for large-scale analysis. Ultimately, the solutions presented in this thesis serve as building blocks of an intelligent system for interpreting large-scale genomic data and understanding the functional organisation of the genome