Maximal information component analysis: a novel non-linear network analysis method

MicroNet-MIMRF: a microbial network inference approach based on mutual information and Markov random fields

Motivation

The human microbiome, comprises complex associations and communication networks among microbial communities, which are crucial for maintaining health. The construction of microbial networks is vital for elucidating these associations. However, existing microbial networks inference methods cannot solve the issues of zero-inflation and non-linear associations. Therefore, necessitating novel methods to improve the accuracy of microbial networks inference.

Results

In this study, we introduce the Microbial Network based on Mutual Information and Markov Random Fields (MicroNet-MIMRF) as a novel approach for inferring microbial networks. Abundance data of microbes are modeled through the zero-inflated Poisson distribution, and the discrete matrix is estimated for further calculation. Markov random fields based on mutual information are used to construct accurate microbial networks. MicroNet-MIMRF excels at estimating pairwise associations between microbes, effectively addressing zero-inflation and non-linear associations in microbial abundance data. It outperforms commonly used techniques in simulation experiments, achieving area under the curve values exceeding 0.75 for all parameters. A case study on inflammatory bowel disease data further demonstrates the method's ability to identify insightful associations. Conclusively, MicroNet-MIMRF is a powerful tool for microbial network inference that handles the biases caused by zero-inflation and overestimation of associations.

Availability and implementation

The MicroNet-MIMRF is provided at https://github.com/Fionabiostats/MicroNet-MIMRF.

KISL: knowledge-injected semi-supervised learning for biological co-expression network modules

The exploration of important biomarkers associated with cancer development is crucial for diagnosing cancer, designing therapeutic interventions, and predicting prognoses. The analysis of gene co-expression provides a systemic perspective on gene networks and can be a valuable tool for mining biomarkers. The main objective of co-expression network analysis is to discover highly synergistic sets of genes, and the most widely used method is weighted gene co-expression network analysis (WGCNA). With the Pearson correlation coefficient, WGCNA measures gene correlation, and uses hierarchical clustering to identify gene modules. The Pearson correlation coefficient reflects only the linear dependence between variables, and the main drawback of hierarchical clustering is that once two objects are clustered together, the process cannot be reversed. Hence, readjusting inappropriate cluster divisions is not possible. Existing co-expression network analysis methods rely on unsupervised methods that do not utilize prior biological knowledge for module delineation. Here we present a method for identification of outstanding modules in a co-expression network using a knowledge-injected semi-supervised learning approach (KISL), which utilizes apriori biological knowledge and a semi-supervised clustering method to address the issue existing in the current GCN-based clustering methods. To measure the linear and non-linear dependence between genes, we introduce a distance correlation due to the complexity of the gene-gene relationship. Eight RNA-seq datasets of cancer samples are used to validate its effectiveness. In all eight datasets, the KISL algorithm outperformed WGCNA when comparing the silhouette coefficient, Calinski-Harabasz index and Davies-Bouldin index evaluation metrics. According to the results, KISL clusters had better cluster evaluation values and better gene module aggregation. Enrichment analysis of the recognition modules demonstrated their effectiveness in discovering modular structures in biological co-expression networks. In addition, as a general method, KISL can be applied to various co-expression network analyses based on similarity metrics. Source codes for the KISL and the related scripts are available online at https://github.com/Mowonhoo/KISL.git.

Identification of Key Modules and Genes Associated with Major Depressive Disorder in Adolescents

Major depressive disorder (MDD) is a leading cause of disability worldwide. Adolescence is a crucial period for the occurrence and development of depression. There are essential distinctions between adolescent and adult depression patients, and the etiology of depressive disorder is unclear. The interactions of multiple genes in a co-expression network are likely to be involved in the physiopathology of MDD. In the present study, RNA-Seq data of mRNA were acquired from the peripheral blood of MDD in adolescents and healthy control (HC) subjects. Co-expression modules were constructed via weighted gene co-expression network analysis (WGCNA) to investigate the relationships between the underlying modules and MDD in adolescents. In the combined MDD and HC groups, the dynamic tree cutting method was utilized to assign genes to modules through hierarchical clustering. Moreover, functional enrichment analysis was conducted on those co-expression genes from interested modules. The results showed that eight modules were constructed by WGCNA. The blue module was significantly associated with MDD after multiple comparison adjustment. Several Gene Ontology (GO) terms and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways associated with stress and inflammation were identified in this module, including histone methylation, apoptosis, NF-kappa β signaling pathway, and TNF signaling pathway. Five genes related to inflammation, immunity, and the nervous system were identified as hub genes: CNTNAP3, IL1RAP, MEGF9, UBE2W, and UBE2D1. All of these findings supported that MDD was associated with stress, inflammation, and immune responses, helping us to obtain a better understanding of the internal molecular mechanism and to explore biomarkers for the diagnosis or treatment of depression in adolescents.

Distance correlation application to gene co-expression network analysis

BACKGROUND

To construct gene co-expression networks, it is necessary to evaluate the correlation between different gene expression profiles. However, commonly used correlation metrics, including both linear (such as Pearson's correlation) and monotonic (such as Spearman's correlation) dependence metrics, are not enough to observe the nature of real biological systems. Hence, introducing a more informative correlation metric when constructing gene co-expression networks is still an interesting topic.

RESULTS

In this paper, we test distance correlation, a correlation metric integrating both linear and non-linear dependence, with other three typical metrics (Pearson's correlation, Spearman's correlation, and maximal information coefficient) on four different arrays (macrophage and liver) and RNA-seq (cervical cancer and pancreatic cancer) datasets. Among all the metrics, distance correlation is distribution free and can provide better performance on complex relationships and anti-outlier. Furthermore, distance correlation is applied to Weighted Gene Co-expression Network Analysis (WGCNA) for constructing a gene co-expression network analysis method which we named Distance Correlation-based Weighted Gene Co-expression Network Analysis (DC-WGCNA). Compared with traditional WGCNA, DC-WGCNA can enhance the result of enrichment analysis and improve the module stability.

CONCLUSIONS

Distance correlation is better at revealing complex biological relationships between gene profiles compared with other correlation metrics, which contribute to more meaningful modules when analyzing gene co-expression networks. However, due to the high time complexity of distance correlation, the implementation requires more computer memory.

Construction of a Pearson- and MIC-Based Co-expression Network to Identify Potential Cancer Genes

The weighted gene co-expression network analysis (WGCNA) method constructs co-expressed gene modules based on the linear similarity between paired gene expressions. Linear correlations are the main form of similarity between genes, however, nonlinear correlations still existed and had always been ignored. We proposed a modified network analysis method, WGCNA-P + M, which combines Pearson's correlation coefficient and the maximum information coefficient (MIC) as the similarity measures to assess the linear and nonlinear correlations between genes, respectively. Taking two real datasets, GSE44861 and liver hepatocellular carcinoma (TCGA-LIHC), as examples, we compared the gene modules constructed by WGCNA-P + M and WGCNA from four perspectives: the "Usefulness" score, GO enrichment analysis on genes in the gray module, prediction performance of the top hub gene, survival analysis and literature reports on different hub genes. The results showed that the modules obtained by WGCNA-P + M are more biological meaningful, the hub genes obtained from WGCNA-P + M have more potential cancer genes.

K-Module Algorithm: An Additional Step to Improve the Clustering Results of WGCNA Co-Expression Networks

Among biological networks, co-expression networks have been widely studied. One of the most commonly used pipelines for the construction of co-expression networks is weighted gene co-expression network analysis (WGCNA), which can identify highly co-expressed clusters of genes (modules). WGCNA identifies gene modules using hierarchical clustering. The major drawback of hierarchical clustering is that once two objects are clustered together, it cannot be reversed; thus, re-adjustment of the unbefitting decision is impossible. In this paper, we calculate the similarity matrix with the distance correlation for WGCNA to construct a gene co-expression network, and present a new approach called the k-module algorithm to improve the WGCNA clustering results. This method can assign all genes to the module with the highest mean connectivity with these genes. This algorithm re-adjusts the results of hierarchical clustering while retaining the advantages of the dynamic tree cut method. The validity of the algorithm is verified using six datasets from microarray and RNA-seq data. The k-module algorithm has fewer iterations, which leads to lower complexity. We verify that the gene modules obtained by the k-module algorithm have high enrichment scores and strong stability. Our method improves upon hierarchical clustering, and can be applied to general clustering algorithms based on the similarity matrix, not limited to gene co-expression network analysis.

Systems Genetics for Mechanistic Discovery in Heart Diseases

Cardiovascular diseases are the leading cause of death worldwide. Complex diseases with highly heterogenous disease progression among patient populations, cardiovascular diseases feature multifactorial contributions from both genetic and environmental stressors. Despite significant effort utilizing multiple approaches from molecular biology to genome-wide association studies, the genetic landscape of cardiovascular diseases, particularly for the nonfamilial forms of heart failure, is still poorly understood. In the past decade, systems-level approaches based on omics technologies have become an important approach for the study of complex traits in large populations. These advances create opportunities to integrate genetic variation with other biological layers to identify and prioritize candidate genes, understand pathogenic pathways, and elucidate gene-gene and gene-environment interactions. In this review, we will highlight some of the recent progress made using systems genetics approaches to uncover novel mechanisms and molecular bases of cardiovascular pathophysiological manifestations. The key technology and data analysis platforms necessary to implement systems genetics will be described, and the current major challenges and future directions will also be discussed. For complex cardiovascular diseases, such as heart failure, systems genetics represents a powerful strategy to obtain mechanistic insights and to develop individualized diagnostic and therapeutic regiments, paving the way for precision cardiovascular medicine.

A Novel Method to Efficiently Highlight Nonlinearly Expressed Genes

For precision medicine, there is a need to identify genes that accurately distinguish the physiological state or response to a particular therapy, but this can be challenging. Many methods of analyzing differential expression have been established and applied to this problem, such as t-test, edgeR, and DEseq2. A common feature of these methods is their focus on a linear relationship (differential expression) between gene expression and phenotype. However, they may overlook nonlinear relationships due to various factors, such as the degree of disease progression, sex, age, ethnicity, and environmental factors. Maximal information coefficient (MIC) was proposed to capture a wide range of associations of two variables in both linear and nonlinear relationships. However, with MIC it is difficult to highlight genes with nonlinear expression patterns as the genes giving the most strongly supported hits are linearly expressed, especially for noisy data. It is thus important to also efficiently identify nonlinearly expressed genes in order to unravel the molecular basis of disease and to reveal new therapeutic targets. We propose a novel nonlinearity measure called normalized differential correlation (NDC) to efficiently highlight nonlinearly expressed genes in transcriptome datasets. Validation using six real-world cancer datasets revealed that the NDC method could highlight nonlinearly expressed genes that could not be highlighted by t-test, MIC, edgeR, and DEseq2, although MIC could capture nonlinear correlations. The classification accuracy indicated that analysis of these genes could adequately distinguish cancer and paracarcinoma tissue samples. Furthermore, the results of biological interpretation of the identified genes suggested that some of them were involved in key functional pathways associated with cancer progression and metastasis. All of this evidence suggests that these nonlinearly expressed genes may play a central role in regulating cancer progression.

Systems-Wide Approaches in Induced Pluripotent Stem Cell Models

Human induced pluripotent stem cells (iPSCs) provide a renewable supply of patient-specific and tissue-specific cells for cellular and molecular studies of disease mechanisms. Combined with advances in various omics technologies, iPSC models can be used to profile the expression of genes, transcripts, proteins, and metabolites in relevant tissues. In the past 2 years, large panels of iPSC lines have been derived from hundreds of genetically heterogeneous individuals, further enabling genome-wide mapping to identify coexpression networks and elucidate gene regulatory networks. Here, we review recent developments in omics profiling of various molecular phenotypes and the emergence of human iPSCs as a systems biology model of human diseases.

A Generalized Approach for Measuring Relationships Among Genes

Several methods for identifying relationships among pairs of genes have been developed. In this article, we present a generalized approach for measuring relationships between any pairs of genes, which is based on statistical prediction. We derive two particular versions of the generalized approach, least squares estimation (LSE) and nearest neighbors prediction (NNP). According to mathematical proof, LSE is equivalent to the methods based on correlation; and NNP is approximate to one popular method called the maximal information coefficient (MIC) according to the performances in simulations and real dataset. Moreover, the approach based on statistical prediction can be extended from two-genes relationships to multi-genes relationships. This application would help to identify relationships among multi-genes.

Systems Genetics Approach Identifies Gene Pathways and Adamts2 as Drivers of Isoproterenol-Induced Cardiac Hypertrophy and Cardiomyopathy in Mice

We previously reported a genetic analysis of heart failure traits in a population of inbred mouse strains treated with isoproterenol to mimic catecholamine-driven cardiac hypertrophy. Here, we apply a co-expression network algorithm, wMICA, to perform a systems-level analysis of left ventricular transcriptomes from these mice. We describe the features of the overall network but focus on a module identified in treated hearts that is strongly related to cardiac hypertrophy and pathological remodeling. Using the causal modeling algorithm NEO, we identified the gene Adamts2 as a putative regulator of this module and validated the predictive value of NEO using small interfering RNA-mediated knockdown in neonatal rat ventricular myocytes. Adamts2 silencing regulated the expression of the genes residing within the module and impaired isoproterenol-induced cellular hypertrophy. Our results provide a view of higher order interactions in heart failure with potential for diagnostic and therapeutic insights.

Undiscovered Physiology of Transcript and Protein Networks

The past two decades have witnessed a rapid evolution in our ability to measure RNA and protein from biological systems. As a result, new principles have arisen regarding how information is processed in cells, how decisions are made, and the role of networks in biology. This essay examines this technological evolution, reviewing (and critiquing) the conceptual framework that has emerged to explain how RNA and protein networks control cellular function. We identify how future investigations into transcriptomes, proteomes, and other cellular networks will enable development of more robust, quantitative models of cellular behavior whilst also providing new avenues to use knowledge of biological networks to improve human health. © 2016 American Physiological Society. Compr Physiol 6:1851-1872, 2016.

Relationship of disease-associated gene expression to cardiac phenotype is buffered by genetic diversity and chromatin regulation

Expression of a cohort of disease-associated genes, some of which are active in fetal myocardium, is considered a hallmark of transcriptional change in cardiac hypertrophy models. How this transcriptome remodeling is affected by the common genetic variation present in populations is unknown. We examined the role of genetics, as well as contributions of chromatin proteins, to regulate cardiac gene expression and heart failure susceptibility. We examined gene expression in 84 genetically distinct inbred strains of control and isoproterenol-treated mice, which exhibited varying degrees of disease. Unexpectedly, fetal gene expression was not correlated with hypertrophic phenotypes. Unbiased modeling identified 74 predictors of heart mass after isoproterenol-induced stress, but these predictors did not enrich for any cardiac pathways. However, expanded analysis of fetal genes and chromatin remodelers as groups correlated significantly with individual systemic phenotypes. Yet, cardiac transcription factors and genes shown by gain-/loss-of-function studies to contribute to hypertrophic signaling did not correlate with cardiac mass or function in disease. Because the relationship between gene expression and phenotype was strain specific, we examined genetic contribution to expression. Strikingly, strains with similar transcriptomes in the basal heart did not cluster together in the isoproterenol state, providing comprehensive evidence that there are different genetic contributors to physiological and pathological gene expression. Furthermore, the divergence in transcriptome similarity versus genetic similarity between strains is organ specific and genome-wide, suggesting chromatin is a critical buffer between genetics and gene expression.

The Hybrid Mouse Diversity Panel: a resource for systems genetics analyses of metabolic and cardiovascular traits

The Hybrid Mouse Diversity Panel (HMDP) is a collection of approximately 100 well-characterized inbred strains of mice that can be used to analyze the genetic and environmental factors underlying complex traits. While not nearly as powerful for mapping genetic loci contributing to the traits as human genome-wide association studies, it has some important advantages. First, environmental factors can be controlled. Second, relevant tissues are accessible for global molecular phenotyping. Finally, because inbred strains are renewable, results from separate studies can be integrated. Thus far, the HMDP has been studied for traits relevant to obesity, diabetes, atherosclerosis, osteoporosis, heart failure, immune regulation, fatty liver disease, and host-gut microbiota interactions. High-throughput technologies have been used to examine the genomes, epigenomes, transcriptomes, proteomes, metabolomes, and microbiomes of the mice under various environmental conditions. All of the published data are available and can be readily used to formulate hypotheses about genes, pathways and interactions.

DTW-MIC Coexpression Networks from Time-Course Data

When modeling coexpression networks from high-throughput time course data, Pearson Correlation Coefficient (PCC) is one of the most effective and popular similarity functions. However, its reliability is limited since it cannot capture non-linear interactions and time shifts. Here we propose to overcome these two issues by employing a novel similarity function, Dynamic Time Warping Maximal Information Coefficient (DTW-MIC), combining a measure taking care of functional interactions of signals (MIC) and a measure identifying time lag (DTW). By using the Hamming-Ipsen-Mikhailov (HIM) metric to quantify network differences, the effectiveness of the DTW-MIC approach is demonstrated on a set of four synthetic and one transcriptomic datasets, also in comparison to TimeDelay ARACNE and Transfer Entropy.

Quantitative assessment of gene expression network module-validation methods

Validation of pluripotent modules in diverse networks holds enormous potential for systems biology and network pharmacology. An arising challenge is how to assess the accuracy of discovering all potential modules from multi-omic networks and validating their architectural characteristics based on innovative computational methods beyond function enrichment and biological validation. To display the framework progress in this domain, we systematically divided the existing Computational Validation Approaches based on Modular Architecture (CVAMA) into topology-based approaches (TBA) and statistics-based approaches (SBA). We compared the available module validation methods based on 11 gene expression datasets, and partially consistent results in the form of homogeneous models were obtained with each individual approach, whereas discrepant contradictory results were found between TBA and SBA. The TBA of the Zsummary value had a higher Validation Success Ratio (VSR) (51%) and a higher Fluctuation Ratio (FR) (80.92%), whereas the SBA of the approximately unbiased (AU) p-value had a lower VSR (12.3%) and a lower FR (45.84%). The Gray area simulated study revealed a consistent result for these two models and indicated a lower Variation Ratio (VR) (8.10%) of TBA at 6 simulated levels. Despite facing many novel challenges and evidence limitations, CVAMA may offer novel insights into modular networks.

Two-stage genome-wide search for epistasis with implementation to Recombinant Inbred Lines (RIL) populations

OBJECTIVE AND METHODS

This paper proposes an inegrative two-stage genome-wide search for pairwise epistasis on expression quantitative trait loci (eQTL). The traits are clustered into multi-trait complexes that account for correlations between them that may result from common epistasis effects. The search is done by first screening for epistatic regions and then using dense markers within the identified regions, resulting in substantial reduction in the number of tests for epistasis. The FDR is controlled using a hierarchical procedure that accounts for the search structure. Each combination of trait and marker-pair is tested using a model that accounts for both statistical and functional interpretations of epistasis and considers orthogonal effects, such that their contributions to heritability can be estimated individually. We examine the impact of using multi-trait complexes rather than single traits, and of using a hierarchical search for epistasis rather than skipping the initial screen for epistatic regions. We apply the proposed algorithm on Arabidopsis transcription data.

PRINCIPAL FINDINGS

Both epistasis detection power and heritability contributed by epistasis increased when using multi-trait complexes rather than single traits. Epistatic effects common to the eQTLs included in the complexes have higher chance of being identified by analysis of multi-trait complexes, particularly when epistatic effects on individual traits are small. Compared to direct testing for all potential epistatic effects, the hierarchical search was substantially more powerful in detecting epistasis, while controlling the FDR at the desired level. Association in functional roles within genomic regions was observed, supporting an initial screen for epistatic QTLs.

Most associations between transcript features and gene expression are monotonic

Dozens of previous studies in the field have dealt with the relations between transcript features and their expression. Indeed, understanding the way gene expression is encoded in transcripts should not only contribute to disciplines, such as functional genomics and molecular evolution, but also to biotechnology and human health. Previous studies in the field mainly aimed at predicting protein levels of genes based on their transcript features. Most of the models employed in this context assume that the effect of each transcript feature on gene expression is monotonic. In the current study we aim to understand, for the first time, if indeed the relations between transcript features (i.e., the UTRs and ORF) and measurements related to the different stages of gene expression is monotonic. To this end, we analyze 5432 transcript features and perform gene expression measurements (mRNA levels, ribosomal densities, protein levels, etc.) of 4367 S. cerevisiae genes. We use the Maximal Information Coefficient (MIC) in order to identify potential relations that are not necessarily linear or monotonic. Our analyses demonstrate that the relation between most transcript features and the examined gene expression measurements is monotonic (only up to 1-5% of the variables, with significance levels of 0.001, are non-monotonic); in addition, in the cases of deviation from monotonicity the relation/deviation is very weak. These results should help in guiding the development of computational gene expression modeling and engineering, and improve the understanding of this process. Furthermore, the relatively simple relations between a transcript's nucleotide composition and its expression should contribute towards better understanding of transcript evolution at the molecular level.