Sparsity as Cellular Objective to Infer Directed Metabolic Networks from Steady-State Metabolome Data: A Theoretical Analysis

Since metabolome data are derived from the underlying metabolic network, reverse engineering of such data to recover the network topology is of wide interest. Lyapunov equation puts a constraint to the link between data and network by coupling the covariance of data with the strength of interactions (Jacobian matrix). This equation, when expressed as a linear set of equations at steady state, constitutes a basis to infer the network structure given the covariance matrix of data. The sparse structure of metabolic networks points to reactions which are active based on minimal enzyme production, hinting at sparsity as a cellular objective. Therefore, for a given covariance matrix, we solved Lyapunov equation to calculate Jacobian matrix by a simultaneous use of minimization of Euclidean norm of residuals and maximization of sparsity (the number of zeros in Jacobian matrix) as objective functions to infer directed small-scale networks from three kingdoms of life (bacteria, fungi, mammalian). The inference performance of the approach was found to be promising, with zero False Positive Rate, and almost one True positive Rate. The effect of missing data on results was additionally analyzed, revealing superiority over similarity-based approaches which infer undirected networks. Our findings suggest that the covariance of metabolome data implies an underlying network with sparsest pattern. The theoretical analysis forms a framework for further investigation of sparsity-based inference of metabolic networks from real metabolome data.     

Integration of Steady-State and Temporal Gene Expression Data for the Inference of Gene Regulatory Networks

We develop a new regression algorithm, cMIKANA, for inference of gene regulatory networks from combinations of steady-state and time-series gene expression data. Using simulated gene expression datasets to assess the accuracy of reconstructing gene regulatory networks, we show that steady-state and time-series data sets can successfully be combined to identify gene regulatory interactions using the new algorithm. Inferring gene networks from combined data sets was found to be advantageous when using noisy measurements collected with either lower sampling rates or a limited number of experimental replicates. We illustrate our method by applying it to a microarray gene expression dataset from human umbilical vein endothelial cells (HUVECs) which combines time series data from treatment with growth factor TNF and steady state data from siRNA knockdown treatments. Our results suggest that the combination of steady-state and time-series datasets may provide better prediction of RNA-to-RNA interactions, and may also reveal biological features that cannot be identified from dynamic or steady state information alone. Finally, we consider the experimental design of genomics experiments for gene regulatory network inference and show that network inference can be improved by incorporating steady-state measurements with time-series data.     

Sets2Networks: network inference from repeated observations of sets

Background

The skeleton of complex systems can be represented as networks where vertices represent entities, and edges represent the relations between these entities. Often it is impossible, or expensive, to determine the network structure by experimental validation of the binary interactions between every vertex pair. It is usually more practical to infer the network from surrogate observations. Network inference is the process by which an underlying network of relations between entities is determined from indirect evidence. While many algorithms have been developed to infer networks from quantitative data, less attention has been paid to methods which infer networks from repeated co-occurrence of entities in related sets. This type of data is ubiquitous in the field of systems biology and in other areas of complex systems research. Hence, such methods would be of great utility and value.

Results

Here we present a general method for network inference from repeated observations of sets of related entities. Given experimental observations of such sets, we infer the underlying network connecting these entities by generating an ensemble of networks consistent with the data. The frequency of occurrence of a given link throughout this ensemble is interpreted as the probability that the link is present in the underlying real network conditioned on the data. Exponential random graphs are used to generate and sample the ensemble of consistent networks, and we take an algorithmic approach to numerically execute the inference method. The effectiveness of the method is demonstrated on synthetic data before employing this inference approach to problems in systems biology and systems pharmacology, as well as to construct a co-authorship collaboration network. We predict direct protein-protein interactions from high-throughput mass-spectrometry proteomics, integrate data from Chip-seq and loss-of-function/gain-of-function followed by expression data to infer a network of associations between pluripotency regulators, extract a network that connects 53 cancer drugs to each other and to 34 severe adverse events by mining the FDA’s Adverse Events Reporting Systems (AERS), and construct a co-authorship network that connects Mount Sinai School of Medicine investigators. The predicted networks and online software to create networks from entity-set libraries are provided online at http://www.maayanlab.net/S2N.

Conclusions

The network inference method presented here can be applied to resolve different types of networks in current systems biology and systems pharmacology as well as in other fields of research.     

A Network Biology Approach Identifies Molecular Cross-Talk between Normal Prostate Epithelial and Prostate Carcinoma Cells

The advent of functional genomics has enabled the genome-wide characterization of the molecular state of cells and tissues, virtually at every level of biological organization. The difficulty in organizing and mining this unprecedented amount of information has stimulated the development of computational methods designed to infer the underlying structure of regulatory networks from observational data. These important developments had a profound impact in biological sciences since they triggered the development of a novel data-driven investigative approach. In cancer research, this strategy has been particularly successful. It has contributed to the identification of novel biomarkers, to a better characterization of disease heterogeneity and to a more in depth understanding of cancer pathophysiology. However, so far these approaches have not explicitly addressed the challenge of identifying networks representing the interaction of different cell types in a complex tissue. Since these interactions represent an essential part of the biology of both diseased and healthy tissues, it is of paramount importance that this challenge is addressed. Here we report the definition of a network reverse engineering strategy designed to infer directional signals linking adjacent cell types within a complex tissue. The application of this inference strategy to prostate cancer genome-wide expression profiling data validated the approach and revealed that normal epithelial cells exert an anti-tumour activity on prostate carcinoma cells. Moreover, by using a Bayesian hierarchical model integrating genetics and gene expression data and combining this with survival analysis, we show that the expression of putative cell communication genes related to focal adhesion and secretion is affected by epistatic gene copy number variation and it is predictive of patient survival. Ultimately, this study represents a generalizable approach to the challenge of deciphering cell communication networks in a wide spectrum of biological systems.     

Constructing a gene semantic similarity network for the inference of disease genes

MOTIVATION: The inference of genes that are truly associated with inherited human diseases from a set of candidates resulting from genetic linkage studies has been one of the most challenging tasks in human genetics. Although several computational approaches have been proposed to prioritize candidate genes relying on protein-protein interaction (PPI) networks, these methods can usually cover less than half of known human genes. RESULTS: We propose to rely on the biological process domain of the gene ontology to construct a gene semantic similarity network and then use the network to infer disease genes. We show that the constructed network covers about 50% more genes than a typical PPI network. By analyzing the gene semantic similarity network with the PPI network, we show that gene pairs tend to have higher semantic similarity scores if the corresponding proteins are closer to each other in the PPI network. By analyzing the gene semantic similarity network with a phenotype similarity network, we show that semantic similarity scores of genes associated with similar diseases are significantly different from those of genes selected at random, and that genes with higher semantic similarity scores tend to be associated with diseases with higher phenotype similarity scores. We further use the gene semantic similarity network with a random walk with restart model to infer disease genes. Through a series of large-scale leave-one-out cross-validation experiments, we show that the gene semantic similarity network can achieve not only higher coverage but also higher accuracy than the PPI network in the inference of disease genes.     

Identifying biological network structure, predicting network behavior, and classifying network state with High Dimensional Model Representation (HDMR)

This work presents an adapted Random Sampling - High Dimensional Model Representation (RS-HDMR) algorithm for synergistically addressing three key problems in network biology: (1) identifying the structure of biological networks from multivariate data, (2) predicting network response under previously unsampled conditions, and (3) inferring experimental perturbations based on the observed network state. RS-HDMR is a multivariate regression method that decomposes network interactions into a hierarchy of non-linear component functions. Sensitivity analysis based on these functions provides a clear physical and statistical interpretation of the underlying network structure. The advantages of RS-HDMR include efficient extraction of nonlinear and cooperative network relationships without resorting to discretization, prediction of network behavior without mechanistic modeling, robustness to data noise, and favorable scalability of the sampling requirement with respect to network size. As a proof-of-principle study, RS-HDMR was applied to experimental data measuring the single-cell response of a protein-protein signaling network to various experimental perturbations. A comparison to network structure identified in the literature and through other inference methods, including Bayesian and mutual-information based algorithms, suggests that RS-HDMR can successfully reveal a network structure with a low false positive rate while still capturing non-linear and cooperative interactions. RS-HDMR identified several higher-order network interactions that correspond to known feedback regulations among multiple network species and that were unidentified by other network inference methods. Furthermore, RS-HDMR has a better ability to predict network response under unsampled conditions in this application than the best statistical inference algorithm presented in the recent DREAM3 signaling-prediction competition. RS-HDMR can discern and predict differences in network state that arise from sources ranging from intrinsic cell-cell variability to altered experimental conditions, such as when drug perturbations are introduced. This ability ultimately allows RS-HDMR to accurately classify the experimental conditions of a given sample based on its observed network state.     

Inferring Time-Varying Network Topologies from Gene Expression Data

Most current methods for gene regulatory network identification lead to the inference of steady-state networks, that is, networks prevalent over all times, a hypothesis which has been challenged. There has been a need to infer and represent networks in a dynamic, that is, time-varying fashion, in order to account for different cellular states affecting the interactions amongst genes. In this work, we present an approach, regime-SSM, to understand gene regulatory networks within such a dynamic setting. The approach uses a clustering method based on these underlying dynamics, followed by system identification using a state-space model for each learnt cluster—to infer a network adjacency matrix. We finally indicate our results on the mouse embryonic kidney dataset as well as the T-cell activation-based expression dataset and demonstrate conformity with reported experimental evidence.     

Selective integration of multiple biological data for supervised network inference

MOTIVATION: Inferring networks of proteins from biological data is a central issue of computational biology. Most network inference methods, including Bayesian networks, take unsupervised approaches in which the network is totally unknown in the beginning, and all the edges have to be predicted. A more realistic supervised framework, proposed recently, assumes that a substantial part of the network is known. We propose a new kernel-based method for supervised graph inference based on multiple types of biological datasets such as gene expression, phylogenetic profiles and amino acid sequences. Notably, our method assigns a weight to each type of dataset and thereby selects informative ones. Data selection is useful for reducing data collection costs. For example, when a similar network inference problem must be solved for other organisms, the dataset excluded by our algorithm need not be collected. RESULTS: First, we formulate supervised network inference as a kernel matrix completion problem, where the inference of edges boils down to estimation of missing entries of a kernel matrix. Then, an expectation-maximization algorithm is proposed to simultaneously infer the missing entries of the kernel matrix and the weights of multiple datasets. By introducing the weights, we can integrate multiple datasets selectively and thereby exclude irrelevant and noisy datasets. Our approach is favorably tested in two biological networks: a metabolic network and a protein interaction network. AVAILABILITY: Software is available on request.     

Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks

MOTIVATION: Bayesian networks have been applied to infer genetic regulatory interactions from microarray gene expression data. This inference problem is particularly hard in that interactions between hundreds of genes have to be learned from very small data sets, typically containing only a few dozen time points during a cell cycle. Most previous studies have assessed the inference results on real gene expression data by comparing predicted genetic regulatory interactions with those known from the biological literature. This approach is controversial due to the absence of known gold standards, which renders the estimation of the sensitivity and specificity, that is, the true and (complementary) false detection rate, unreliable and difficult. The objective of the present study is to test the viability of the Bayesian network paradigm in a realistic simulation study. First, gene expression data are simulated from a realistic biological network involving DNAs, mRNAs, inactive protein monomers and active protein dimers. Then, interaction networks are inferred from these data in a reverse engineering approach, using Bayesian networks and Bayesian learning with Markov chain Monte Carlo. RESULTS: The simulation results are presented as receiver operator characteristics curves. This allows estimating the proportion of spurious gene interactions incurred for a specified target proportion of recovered true interactions. The findings demonstrate how the network inference performance varies with the training set size, the degree of inadequacy of prior assumptions, the experimental sampling strategy and the inclusion of further, sequence-based information. AVAILABILITY: The programs and data used in the present study are available from http://www.bioss.sari.ac.uk/~dirk/Supplements     

Inferring network interactions within a cell

The continuing growth in high-throughput data acquisition has led to a proliferation of network models to represent and analyse biological systems. These networks involve distinct interaction types detected by a combination of methods, ranging from directly observed physical interactions based in biochemistry to interactions inferred from phenotype measurements, genomic expression and comparative genomics. The discovery of interactions increasingly requires a blend of experimental and computational methods. Considering yeast as a model system, recent analytical methods are reviewed here and specific aims are proposed to improve network interaction inference and facilitate predictive biological modelling.     

A multiorganism based method for Bayesian gene network estimation

The primary goal of this article is to infer genetic interactions based on gene expression data. A new method for multiorganism Bayesian gene network estimation is presented based on multitask learning. When the input datasets are sparse, as is the case in microarray gene expression data, it becomes difficult to separate random correlations from true correlations that would lead to actual edges when modeling the gene interactions as a Bayesian network. Multitask learning takes advantage of the similarity between related tasks, in order to construct a more accurate model of the underlying relationships represented by the Bayesian networks. The proposed method is tested on synthetic data to illustrate its validity. Then it is iteratively applied on real gene expression data to learn the genetic regulatory networks of two organisms with homologous genes.     

A Multi-Method Approach for Proteomic Network Inference in 11 Human Cancers

Protein expression and post-translational modification levels are tightly regulated in neoplastic cells to maintain cellular processes known as ‘cancer hallmarks’. The first Pan-Cancer initiative of The Cancer Genome Atlas (TCGA) Research Network has aggregated protein expression profiles for 3,467 patient samples from 11 tumor types using the antibody based reverse phase protein array (RPPA) technology. The resultant proteomic data can be utilized to computationally infer protein-protein interaction (PPI) networks and to study the commonalities and differences across tumor types. In this study, we compare the performance of 13 established network inference methods in their capacity to retrieve the curated Pathway Commons interactions from RPPA data. We observe that no single method has the best performance in all tumor types, but a group of six methods, including diverse techniques such as correlation, mutual information, and regression, consistently rank highly among the tested methods. We utilize the high performing methods to obtain a consensus network; and identify four robust and densely connected modules that reveal biological processes as well as suggest antibody–related technical biases. Mapping the consensus network interactions to Reactome gene lists confirms the pan-cancer importance of signal transduction pathways, innate and adaptive immune signaling, cell cycle, metabolism, and DNA repair; and also suggests several biological processes that may be specific to a subset of tumor types. Our results illustrate the utility of the RPPA platform as a tool to study proteomic networks in cancer.     

A scalable algorithm to explore the Gibbs energy landscape of genome-scale metabolic networks

The integration of various types of genomic data into predictive models of biological networks is one of the main challenges currently faced by computational biology. Constraint-based models in particular play a key role in the attempt to obtain a quantitative understanding of cellular metabolism at genome scale. In essence, their goal is to frame the metabolic capabilities of an organism based on minimal assumptions that describe the steady states of the underlying reaction network via suitable stoichiometric constraints, specifically mass balance and energy balance (i.e. thermodynamic feasibility). The implementation of these requirements to generate viable configurations of reaction fluxes and/or to test given flux profiles for thermodynamic feasibility can however prove to be computationally intensive. We propose here a fast and scalable stoichiometry-based method to explore the Gibbs energy landscape of a biochemical network at steady state. The method is applied to the problem of reconstructing the Gibbs energy landscape underlying metabolic activity in the human red blood cell, and to that of identifying and removing thermodynamically infeasible reaction cycles in the Escherichia coli metabolic network (iAF1260). In the former case, we produce consistent predictions for chemical potentials (or log-concentrations) of intracellular metabolites; in the latter, we identify a restricted set of loops (23 in total) in the periplasmic and cytoplasmic core as the origin of thermodynamic infeasibility in a large sample (10(6)) of flux configurations generated randomly and compatibly with the prior information available on reaction reversibility.     

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.     

Gene network inference and visualization tools for biologists: application to new human transcriptome datasets

Gene regulatory networks inferred from RNA abundance data have generated significant interest, but despite this, gene network approaches are used infrequently and often require input from bioinformaticians. We have assembled a suite of tools for analysing regulatory networks, and we illustrate their use with microarray datasets generated in human endothelial cells. We infer a range of regulatory networks, and based on this analysis discuss the strengths and limitations of network inference from RNA abundance data. We welcome contact from researchers interested in using our inference and visualization tools to answer biological questions.