Adding confidence to gene expression clustering

petal: Co-expression network modelling in R

Background

Networks provide effective models to study complex biological systems, such as gene and protein interaction networks. With the advent of new sequencing technologies, many life scientists are grasping for user-friendly methods and tools to examine biological components at the whole-systems level. Gene co-expression network analysis approaches are frequently used to successfully associate genes with biological processes and demonstrate great potential to gain further insights into the functionality of genes, thus becoming a standard approach in Systems Biology. Here the objective is to construct biologically meaningful and statistically strong co-expression networks, the identification of research dependent subnetworks, and the presentation of self-contained results.

Results

We introduce petal, a novel approach to generate gene co-expression network models based on experimental gene expression measures. petal focuses on statistical, mathematical, and biological characteristics of both, input data and output network models. Often over-looked issues of current co-expression analysis tools include the assumption of data normality, which is seldom the case for hight-throughput expression data obtained from RNA-seq technologies. petal does not assume data normality, making it a statistically appropriate method for RNA-seq data. Also, network models are rarely tested for their known typical architecture: scale-free and small-world. petal explicitly constructs networks based on both these characteristics, thereby generating biologically meaningful models. Furthermore, many network analysis tools require a number of user-defined input variables, these often require tuning and/or an understanding of the underlying algorithm; petal requires no user input other than experimental data. This allows for reproducible results, and simplifies the use of petal. Lastly, this approach is specifically designed for very large high-throughput datasets; this way, petal’s network models represent as much of the entire system as possible to provide a whole-system approach.

Conclusion

petal is a novel tool for generating co-expression network models of whole-genomics experiments. It is implemented in R and available as a library. Its application to several whole-genome experiments has generated novel meaningful results and has lead the way to new testing hypothesizes for further biological investigation.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0298-8) contains supplementary material, which is available to authorized users.

Significant distinct branches of hierarchical trees: a framework for statistical analysis and applications to biological data

Background

One of the most common goals of hierarchical clustering is finding those branches of a tree that form quantifiably distinct data subtypes. Achieving this goal in a statistically meaningful way requires (a) a measure of distinctness of a branch and (b) a test to determine the significance of the observed measure, applicable to all branches and across multiple scales of dissimilarity.

Results

We formulate a method termed Tree Branches Evaluated Statistically for Tightness (TBEST) for identifying significantly distinct tree branches in hierarchical clusters. For each branch of the tree a measure of distinctness, or tightness, is defined as a rational function of heights, both of the branch and of its parent. A statistical procedure is then developed to determine the significance of the observed values of tightness. We test TBEST as a tool for tree-based data partitioning by applying it to five benchmark datasets, one of them synthetic and the other four each from a different area of biology. For each dataset there is a well-defined partition of the data into classes. In all test cases TBEST performs on par with or better than the existing techniques.

Conclusions

Based on our benchmark analysis, TBEST is a tool of choice for detection of significantly distinct branches in hierarchical trees grown from biological data. An R language implementation of the method is available from the Comprehensive R Archive Network: http://www.cran.r-project.org/web/packages/TBEST/index.html.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-1000) contains supplementary material, which is available to authorized users.

Dynamic clustering of gene expression

It is well accepted that genes are simultaneously involved in multiple biological processes and that genes are coordinated over the duration of such events. Unfortunately, clustering methodologies that group genes for the purpose of novel gene discovery fail to acknowledge the dynamic nature of biological processes and provide static clusters, even when the expression of genes is assessed across time or developmental stages. By taking advantage of techniques and theories from time frequency analysis, periodic gene expression profiles are dynamically clustered based on the assumption that different spectral frequencies characterize different biological processes. A two-step cluster validation approach is proposed to statistically estimate both the optimal number of clusters and to distinguish significant clusters from noise. The resulting clusters reveal coordinated coexpressed genes. This novel dynamic clustering approach has broad applicability to a vast range of sequential data scenarios where the order of the series is of interest.

Comparative analysis of acute and chronic corticosteroid pharmacogenomic effects in rat liver: transcriptional dynamics and regulatory structures

Background

Comprehensively understanding corticosteroid pharmacogenomic effects is an essential step towards an insight into the underlying molecular mechanisms for both beneficial and detrimental clinical effects. Nevertheless, even in a single tissue different methods of corticosteroid administration can induce different patterns of expression and regulatory control structures. Therefore, rich in vivo datasets of pharmacological time-series with two dosing regimens sampled from rat liver are examined for temporal patterns of changes in gene expression and their regulatory commonalities.

Results

The study addresses two issues, including (1) identifying significant transcriptional modules coupled with dynamic expression patterns and (2) predicting relevant common transcriptional controls to better understand the underlying mechanisms of corticosteroid adverse effects. Following the orientation of meta-analysis, an extended computational approach that explores the concept of agreement matrix from consensus clustering has been proposed with the aims of identifying gene clusters that share common expression patterns across multiple dosing regimens as well as handling challenges in the analysis of microarray data from heterogeneous sources, e.g. different platforms and time-grids in this study. Six significant transcriptional modules coupled with typical patterns of expression have been identified. Functional analysis reveals that virtually all enriched functions (gene ontologies, pathways) in these modules are shown to be related to metabolic processes, implying the importance of these modules in adverse effects under the administration of corticosteroids. Relevant putative transcriptional regulators (e.g. RXRF, FKHD, SP1F) are also predicted to provide another source of information towards better understanding the complexities of expression patterns and the underlying regulatory mechanisms of those modules.

Conclusions

We have proposed a framework to identify significant coexpressed clusters of genes across multiple conditions experimented from different microarray platforms, time-grids, and also tissues if applicable. Analysis on rich in vivo datasets of corticosteroid time-series yielded significant insights into the pharmacogenomic effects of corticosteroids, especially the relevance to metabolic side-effects. This has been illustrated through enriched metabolic functions in those transcriptional modules and the presence of GRE binding motifs in those enriched pathways, providing significant modules for further analysis on pharmacogenomic corticosteroid effects.

Importance of replication in analyzing time-series gene expression data: corticosteroid dynamics and circadian patterns in rat liver

Background

Microarray technology is a powerful and widely accepted experimental technique in molecular biology that allows studying genome wide transcriptional responses. However, experimental data usually contain potential sources of uncertainty and thus many experiments are now designed with repeated measurements to better assess such inherent variability. Many computational methods have been proposed to account for the variability in replicates. As yet, there is no model to output expression profiles accounting for replicate information so that a variety of computational models that take the expression profiles as the input data can explore this information without any modification.

Results

We propose a methodology which integrates replicate variability into expression profiles, to generate so-called 'true' expression profiles. The study addresses two issues: (i) develop a statistical model that can estimate 'true' expression profiles which are more robust than the average profile, and (ii) extend our previous micro-clustering which was designed specifically for clustering time-series expression data. The model utilizes a previously proposed error model and the concept of 'relative difference'. The clustering effectiveness is demonstrated through synthetic data where several methods are compared. We subsequently analyze in vivo rat data to elucidate circadian transcriptional dynamics as well as liver-specific corticosteroid induced changes in gene expression.

Conclusions

We have proposed a model which integrates the error information from repeated measurements into the expression profiles. Through numerous synthetic and real time-series data, we demonstrated the ability of the approach to improve the clustering performance and assist in the identification and selection of informative expression motifs.

Unsupervised selection of highly coexpressed and noncoexpressed genes using a consensus clustering approach

In this paper we explore the concept of consensus clustering to identify, within a set of differentially expressed genes, a subset of genes that are either highly coexpressed or highly noncoexpressed based on the hypothesis that this subset would serve as a better starting point for further analyses. A number of core clustering methods form the basis for the assertion of an agreement matrix (AM) characterizing the level of coexpression between any two probesets. In order to overcome the limitations of using a single distance metric, we explore different metrics and examine the sensitivity of the AM as a function of the input number of clusters to find a suggestive number of clusters that best describes a particular dataset. The result of this level of analysis is a systematic framework for eliminating probesets that cannot be clearly characterized as either coexpressed or noncoexpressed with others, thus eliminating a number of probesets from further analysis. Subsequently, an agglomerative hierarchical clustering approach is applied to cluster the selected subset using the agreement metric information as the similarity measure. Thus, the goal of the proposed methodology is twofold: (1) we opt to identify a more "clusterable" subset of the original set; and (2) we aim at further refining the subset in order to identify a core of genes that contains genes that are either coexpressed or noncoexpressed within a certain confidence level. The approach is tested with a number of data sets, both synthetic and real, and it is demonstrated that it is successful in identifying more clusterable, also hypothesized to be more biologically relevant, subsets of genes and expression profiles.

Large-scale mRNA expression profiling in the common ice plant, Mesembryanthemum crystallinum, performing C3 photosynthesis and Crassulacean acid metabolism (CAM)

The common ice plant (Mesembryanthemum crystallinum L.) has emerged as a useful model for molecular genetic studies of Crassulacean acid metabolism (CAM) because CAM can be induced in this species by water deficit or salinity stress. Non-redundant sequence information from expressed sequence tag data was used to fabricate a custom oligonucleotide microarray to compare large-scale mRNA expression patterns in M. crystallinum plants conducting C(3) photosynthesis versus CAM. Samples were collected every 4 h over a 24 h time period at the start of the subjective second day from plants grown under constant light and temperature conditions in order to capture variation in mRNA expression due to salinity stress and circadian clock control. Of 8455 genes, a total of 2343 genes (approximately 28%) showed a significant change as judged by analysis of variance (ANOVA) in steady-state mRNA abundance at one or more time points over the 24 h period. Of these, 858 (10%) and 599 (7%) exhibited a greater than two-fold ratio (TFR) increase or decrease in mRNA abundance, respectively. Functional categorization of these TFR genes revealed that many genes encoding products that function in CAM-related C(4) acid carboxylation/decarboxylation, glycolysis/gluconeogenesis, polysaccharide, polyol, and starch biosynthesis/degradation, protein degradation, transcriptional activation, signalling, stress response, and transport facilitation, and novel, unclassified proteins exhibited stress-induced increases in mRNA abundance. In contrast, salt stress resulted in a significant decrease in transcript abundance for genes encoding photosynthetic functions, protein synthesis, and cellular biogenesis functions. Many genes with CAM-related functions exhibited phase shifts in their putative circadian expression patterns following CAM induction. This report establishes an extensive catalogue of gene expression patterns for future investigations aimed at understanding the complex, transcriptional hierarchies that govern CAM-specific expression patterns. A novel graph-theoretic approach called 'Max Clique Builder' is introduced that identifies and organizes sets of coordinately regulated genes, such as those encoding subunits of the vacuolar H(+)-ATPase complex, into tighter functionally related clusters with more similar expression patterns compared with standard hierarchical clustering methods.

The association among gene expression responses to nine abiotic stress treatments in Arabidopsis thaliana

The identification and analysis of genes exhibiting large expression responses to several different types of stress may provide insights into the functional basis of multiple stress tolerance in plant species. This study considered whole-genome transcriptional profiles from Arabidopsis thaliana root and shoot organs under nine abiotic stress conditions (cold, osmotic stress, salt, drought, genotoxic stress, ultraviolet light, oxidative stress, wounding, and high temperature) and at six different time points of stress exposure (0.5, 1, 3, 6, 12, and 24 hr). In roots, genomewide correlations between transcriptional responses to different stress treatments peaked following 1 hr of stress exposure, while in shoots, correlations tended to increase following 6 hr of stress exposure. The generality of stress responses at the transcriptional level was therefore time and organ dependent. A total of 67 genes were identified as exhibiting a statistically significant pattern of gene expression characterized by large transcriptional responses to all nine stress treatments. Most genes were identified from early to middle (1-6 hr) time points of stress exposure. Analysis of this gene set indicated that cell rescue/defense/virulence, energy, and metabolism functional classes were overrepresented, providing novel insight into the functional basis of multiple stress tolerance in Arabidopsis.