Local wavelet-vaguelette-based functional classification of gene expression data

This paper focuses on the problem of functional statistical classification of gene expression curves. A local-wavelet-vaguelette-based functional logistic regression approach is presented. This approach is specially suitable for the classification of non-stationary singular (non-differentiable) curves. The performance of the methodology proposed is illustrated by implementing it for the classification of yeast cell-cycle temporal gene expression profiles. A simulation study is also carried out for comparison with other functional classification methodologies.     

Time ordering of gene coexpression

Temporal microarray gene expression profiles allow characterization of gene function through time dynamics of gene coexpression within the same genetic pathway. In this paper, we define and estimate a global time shift characteristic for each gene via least squares, inferred from pairwise curve alignments. These time shift characteristics of individual genes reflect a time ordering that is derived from ob- served temporal gene expression profiles. Once these time shift characteristics are obtained for each gene, they can be entered into further analyses, such as clustering. We illustrate the proposed methodology using Drosophila embryonic development and yeast cell-cycle gene expression profiles, as well as simulations. Feasibility is demonstrated through the successful recovery of time ordering. Estimated time shifts for Drosophila maternal and zygotic genes provide excellent discrimination between these two categories and confirm known genetic pathways through the time order of gene expression. The application to yeast cell-cycle data establishes a natural time order of genes that is in line with cell-cycle phases. The method does not require periodicity of gene expression profiles. Asymptotic justifications are also provided.     

Clustering of gene expression data using a local shape-based similarity measure

MOTIVATION: Microarray technology enables the study of gene expression in large scale. The application of methods for data analysis then allows for grouping genes that show a similar expression profile and that are thus likely to be co-regulated. A relationship among genes at the biological level often presents itself by locally similar and potentially time-shifted patterns in their expression profiles. RESULTS: Here, we propose a new method (CLARITY; Clustering with Local shApe-based similaRITY) for the analysis of microarray time course experiments that uses a local shape-based similarity measure based on Spearman rank correlation. This measure does not require a normalization of the expression data and is comparably robust towards noise. It is also able to detect similar and even time-shifted sub-profiles. To this end, we implemented an approach motivated by the BLAST algorithm for sequence alignment.We used CLARITY to cluster the times series of gene expression data during the mitotic cell cycle of the yeast Saccharomyces cerevisiae. The obtained clusters were related to the MIPS functional classification to assess their biological significance. We found that several clusters were significantly enriched with genes that share similar or related functions.     

Nonnegative decomposition of functional count data

We present a novel decomposition of nonnegative functional count data that draws on concepts from nonnegative matrix factorization. Our decomposition, which we refer to as NARFD (nonnegative and regularized function decomposition), enables the study of patterns in variation across subjects in a highly interpretable manner. Prototypic modes of variation are estimated directly on the observed scale of the data, are local, and are transparently added together to reconstruct observed functions. This contrasts with generalized functional principal component analysis, an alternative approach that estimates functional principal components on a transformed scale, produces components that typically vary across the entire functional domain, and reconstructs observations using complex patterns of cancellation and multiplication of functional principal components. NARFD is implemented using an alternating minimization algorithm, and we evaluate our approach in simulations. We apply NARFD to an accelerometer dataset comprising observations of physical activity for healthy older Americans.     

A supervised approach for identifying discriminating genotype patterns and its application to breast cancer data

MOTIVATION: Large-scale association studies, investigating the genetic determinants of a phenotype of interest, are producing increasing amounts of genomic variation data on human cohorts. A fundamental challenge in these studies is the detection of genotypic patterns that discriminate individuals exhibiting the phenotype under study from individuals that do not possess it. The difficulty stems from the large number of single nucleotide polymorphism (SNP) combinations that have to be tested. The discrimination problem becomes even more involved when additional high-throughput data, such as gene expression data, are available for the same cohort. RESULTS: We have developed a graph theoretic approach for identifying discriminating patterns (DPs) for a given phenotype in a genotyped population. The method is based on representing the SNP data as a bipartite graph of individuals and their SNP states, and identifying fully connected subgraphs of this graph that relate individuals enriched for a given phenotypic group. The method can handle additional data types such as expression profiles of the genotyped population. It is reminiscent of biclustering approaches with the crucial difference that its search process is guided by the phenotype under consideration in a supervised manner. We tested our approach in simulations and on real data. In simulations, our method was able to retrieve planted patterns with high success rate. We then applied our approach to a dataset of 72 breast cancer patients with available gene expression profiles, genotyped over 695 SNPs. We detected several DPs that were highly significant with respect to various clinical phenotypes, and investigated the groups of patients and the groups of genes they defined. We found the patient groups to be highly enriched for other phenotypes and to display expression coherency among their profiles. The gene groups displayed functional coherency and involved genes with known role in cancer, providing additional support to their involvement. AVAILABILITY: The program is available upon request.     

MATLAB 7.X生物信息工具箱的应用———基因表达图谱分析（4）*

基因表达图谱原则上可了解整体细胞基因表达的信息,是基因组功能分析的重要研究手段。MATLAB 7.X生物信息工具箱为基因表达谱数据的分析和处理提供了一个综合环境,通过众多统计函数和绘图函数的结合使用,过滤不合格的基因数据和噪声数据,从而对基因表达数据进行聚类分析和主成分分析,绘制相关的基因表达图谱,完成基因芯片数据表达图谱的分析,分析结果可视化程度高,图表清晰、直观。本文主要以酿酒酵母Saccharomyces cerevisiae为例,详细描述了利用MATLAB 7.X生物信息工具箱对其基因表达图谱进行分析的过程。     

A CART-based approach to discover emerging patterns in microarray data

MOTIVATION: Cancer diagnosis using gene expression profiles requires supervised learning and gene selection methods. Of the many suggested approaches, the method of emerging patterns (EPs) has the particular advantage of explicitly modeling interactions among genes, which improves classification accuracy. However, finding useful (i.e. short and statistically significant) EP is typically very hard. METHODS: Here we introduce a CART-based approach to discover EPs in microarray data. The method is based on growing decision trees from which the EPs are extracted. This approach combines pattern search with a statistical procedure based on Fisher's exact test to assess the significance of each EP. Subsequently, sample classification based on the inferred EPs is performed using maximum-likelihood linear discriminant analysis. RESULTS: Using simulated data as well as gene expression data from colon and leukemia cancer experiments we assessed the performance of our pattern search algorithm and classification procedure. In the simulations, our method recovers a large proportion of known EPs while for real data it is comparable in classification accuracy with three top-performing alternative classification algorithms. In addition, it assigns statistical significance to the inferred EPs and allows to rank the patterns while simultaneously avoiding overfit of the data. The new approach therefore provides a versatile and computationally fast tool for elucidating local gene interactions as well as for classification. AVAILABILITY: A computer program written in the statistical language R implementing the new approach is freely available from the web page http://www.stat.uni-muenchen.de/~socher/     

Dimension reduction methods for microarrays with application to censored survival data

MOTIVATION: Recent research has shown that gene expression profiles can potentially be used for predicting various clinical phenotypes, such as tumor class, drug response and survival time. While there has been extensive studies on tumor classification, there has been less emphasis on other phenotypic features, in particular, patient survival time or time to cancer recurrence, which are subject to right censoring. We consider in this paper an analysis of censored survival time based on microarray gene expression profiles. RESULTS: We propose a dimension reduction strategy, which combines principal components analysis and sliced inverse regression, to identify linear combinations of genes, that both account for the variability in the gene expression levels and preserve the phenotypic information. The extracted gene combinations are then employed as covariates in a predictive survival model formulation. We apply the proposed method to a large diffuse large-B-cell lymphoma dataset, which consists of 240 patients and 7399 genes, and build a Cox proportional hazards model based on the derived gene expression components. The proposed method is shown to provide a good predictive performance for patient survival, as demonstrated by both the significant survival difference between the predicted risk groups and the receiver operator characteristics analysis. AVAILABILITY: R programs are available upon request from the authors. SUPPLEMENTARY INFORMATION: http://dna.ucdavis.edu/~hli/bioinfo-surv-supp.pdf.     

Cluster-based network model for time-course gene expression data

We propose a model-based approach to unify clustering and network modeling using time-course gene expression data. Specifically, our approach uses a mixture model to cluster genes. Genes within the same cluster share a similar expression profile. The network is built over cluster-specific expression profiles using state-space models. We discuss the application of our model to simulated data as well as to time-course gene expression data arising from animal models on prostate cancer progression. The latter application shows that with a combined statistical/bioinformatics analyses, we are able to extract gene-to-gene relationships supported by the literature as well as new plausible relationships.     

Clustering of diverse genomic data using information fusion

MOTIVATION: Genome sequencing projects and high-through-put technologies like DNA and Protein arrays have resulted in a very large amount of information-rich data. Microarray experimental data are a valuable, but limited source for inferring gene regulation mechanisms on a genomic scale. Additional information such as promoter sequences of genes/DNA binding motifs, gene ontologies, and location data, when combined with gene expression analysis can increase the statistical significance of the finding. This paper introduces a machine learning approach to information fusion for combining heterogeneous genomic data. The algorithm uses an unsupervised joint learning mechanism that identifies clusters of genes using the combined data. RESULTS: The correlation between gene expression time-series patterns obtained from different experimental conditions and the presence of several distinct and repeated motifs in their upstream sequences is examined here using publicly available yeast cell-cycle data. The results show that the combined learning approach taken here identifies correlated genes effectively. The algorithm provides an automated clustering method, but allows the user to specify apriori the influence of each data type on the final clustering using probabilities. AVAILABILITY: Software code is available by request from the first author. CONTACT: jkasturi@cse.psu.edu.     

Accounting for probe-level noise in principal component analysis of microarray data

MOTIVATION: Principal Component Analysis (PCA) is one of the most popular dimensionality reduction techniques for the analysis of high-dimensional datasets. However, in its standard form, it does not take into account any error measures associated with the data points beyond a standard spherical noise. This indiscriminate nature provides one of its main weaknesses when applied to biological data with inherently large variability, such as expression levels measured with microarrays. Methods now exist for extracting credibility intervals from the probe-level analysis of cDNA and oligonucleotide microarray experiments. These credibility intervals are gene and experiment specific, and can be propagated through an appropriate probabilistic downstream analysis. RESULTS: We propose a new model-based approach to PCA that takes into account the variances associated with each gene in each experiment. We develop an efficient EM-algorithm to estimate the parameters of our new model. The model provides significantly better results than standard PCA, while remaining computationally reasonable. We show how the model can be used to 'denoise' a microarray dataset leading to improved expression profiles and tighter clustering across profiles. The probabilistic nature of the model means that the correct number of principal components is automatically obtained.     

Bayesian hierarchical spatially correlated functional data analysis with application to colon carcinogenesis

Summary .   In this article, we present new methods to analyze data from an experiment using rodent models to investigate the role of p27, an important cell-cycle mediator, in early colon carcinogenesis. The responses modeled here are essentially functions nested within a two-stage hierarchy. Standard functional data analysis literature focuses on a single stage of hierarchy and conditionally independent functions with near white noise. However, in our experiment, there is substantial biological motivation for the existence of spatial correlation among the functions, which arise from the locations of biological structures called colonic crypts: this possible functional correlation is a phenomenon we term crypt signaling . Thus, as a point of general methodology, we require an analysis that allows for functions to be correlated at the deepest level of the hierarchy. Our approach is fully Bayesian and uses Markov chain Monte Carlo methods for inference and estimation. Analysis of this data set gives new insights into the structure of p27 expression in early colon carcinogenesis and suggests the existence of significant crypt signaling. Our methodology uses regression splines, and because of the hierarchical nature of the data, dimension reduction of the covariance matrix of the spline coefficients is important: we suggest simple methods for overcoming this problem.     

Global protein function annotation through mining genome-scale data in yeast Saccharomyces cerevisiae

As we are moving into the post genome-sequencing era, various high-throughput experimental techniques have been developed to characterize biological systems on the genomic scale. Discovering new biological knowledge from the high-throughput biological data is a major challenge to bioinformatics today. To address this challenge, we developed a Bayesian statistical method together with Boltzmann machine and simulated annealing for protein functional annotation in the yeast Saccharomyces cerevisiae through integrating various high-throughput biological data, including yeast two-hybrid data, protein complexes and microarray gene expression profiles. In our approach, we quantified the relationship between functional similarity and high-throughput data, and coded the relationship into ‘functional linkage graph’, where each node represents one protein and the weight of each edge is characterized by the Bayesian probability of function similarity between two proteins. We also integrated the evolution information and protein subcellular localization information into the prediction. Based on our method, 1802 out of 2280 unannotated proteins in yeast were assigned functions systematically.     

A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle

Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes.     

Discovering statistically significant biclusters in gene expression data

In gene expression data, a bicluster is a subset of the genes exhibiting consistent patterns over a subset of the conditions. We propose a new method to detect significant biclusters in large expression datasets. Our approach is graph theoretic coupled with statistical modelling of the data. Under plausible assumptions, our algorithm is polynomial and is guaranteed to find the most significant biclusters. We tested our method on a collection of yeast expression profiles and on a human cancer dataset. Cross validation results show high specificity in assigning function to genes based on their biclusters, and we are able to annotate in this way 196 uncharacterized yeast genes. We also demonstrate how the biclusters lead to detecting new concrete biological associations. In cancer data we are able to detect and relate finer tissue types than was previously possible. We also show that the method outperforms the biclustering algorithm of Cheng and Church (2000).     

Topology of gene expression networks as revealed by data mining and modeling

MOTIVATION: Interpretation of high-throughput gene expression profiling requires a knowledge of the design principles underlying the networks that sustain cellular machinery. Recently a novel approach based on the study of network topologies has been proposed. This methodology has proven to be useful for the analysis of a variety of biological systems, including metabolic networks, networks of protein-protein interactions, and gene networks that can be derived from gene expression data. In the present paper, we focus on several important issues related to the topology of gene expression networks that have not yet been fully studied. RESULTS: The networks derived from gene expression profiles for both time series experiments in yeast and perturbation experiments in cell lines are studied. We demonstrate that independent from the experimental organism (yeast versus cell lines) and the type of experiment (time courses versus perturbations) the extracted networks have similar topological characteristics suggesting together with the results of other common principles of the structural organization of biological networks. A novel computational model of network growth that reproduces the basic design principles of the observed networks is presented. Advantage of the model is that it provides a general mechanism to generate networks with different types of topology by a variation of a few parameters. We investigate the robustness of the network structure to random damages and to deliberate removal of the most important parts of the system and show a surprising tolerance of gene expression networks to both kinds of disturbance.