Petri Nets with Fuzzy Logic (PNFL): Reverse Engineering and Parametrization

Background

The recent DREAM4 blind assessment provided a particularly realistic and challenging setting for network reverse engineering methods. The in silico part of DREAM4 solicited the inference of cycle-rich gene regulatory networks from heterogeneous, noisy expression data including time courses as well as knockout, knockdown and multifactorial perturbations.

Methodology and Principal Findings

We inferred and parametrized simulation models based on Petri Nets with Fuzzy Logic (PNFL). This completely automated approach correctly reconstructed networks with cycles as well as oscillating network motifs. PNFL was evaluated as the best performer on DREAM4 in silico networks of size 10 with an area under the precision-recall curve (AUPR) of 81%. Besides topology, we inferred a range of additional mechanistic details with good reliability, e.g. distinguishing activation from inhibition as well as dependent from independent regulation. Our models also performed well on new experimental conditions such as double knockout mutations that were not included in the provided datasets.

Conclusions

The inference of biological networks substantially benefits from methods that are expressive enough to deal with diverse datasets in a unified way. At the same time, overly complex approaches could generate multiple different models that explain the data equally well. PNFL appears to strike the balance between expressive power and complexity. This also applies to the intuitive representation of PNFL models combining a straightforward graphical notation with colloquial fuzzy parameters.     

A novel algorithm for alignment of multiple PPI networks based on simulated annealing

Background

To infer gene regulatory networks (GRNs) from gene-expression data is still a fundamental and challenging problem in systems biology. Several existing algorithms formulate GRNs inference as a regression problem and obtain the network with an ensemble strategy. Recent studies on data driven dynamic network construction provide us a new perspective to solve the regression problem.

Results

In this study, we propose a data driven dynamic network construction method to infer gene regulatory network (D3GRN), which transforms the regulatory relationship of each target gene into functional decomposition problem and solves each sub problem by using the Algorithm for Revealing Network Interactions (ARNI). To remedy the limitation of ARNI in constructing networks solely from the unit level, a bootstrapping and area based scoring method is taken to infer the final network. On DREAM4 and DREAM5 benchmark datasets, D3GRN performs competitively with the state-of-the-art algorithms in terms of AUPR.

Conclusions

We have proposed a novel data driven dynamic network construction method by combining ARNI with bootstrapping and area based scoring strategy. The proposed method performs well on the benchmark datasets, contributing as a competitive method to infer gene regulatory networks in a new perspective.

     

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.     

Ensemble Inference and Inferability of Gene Regulatory Networks

The inference of gene regulatory network (GRN) from gene expression data is an unsolved problem of great importance. This inference has been stated, though not proven, to be underdetermined implying that there could be many equivalent (indistinguishable) solutions. Motivated by this fundamental limitation, we have developed new framework and algorithm, called TRaCE, for the ensemble inference of GRNs. The ensemble corresponds to the inherent uncertainty associated with discriminating direct and indirect gene regulations from steady-state data of gene knock-out (KO) experiments. We applied TRaCE to analyze the inferability of random GRNs and the GRNs of E. coli and yeast from single- and double-gene KO experiments. The results showed that, with the exception of networks with very few edges, GRNs are typically not inferable even when the data are ideal (unbiased and noise-free). Finally, we compared the performance of TRaCE with top performing methods of DREAM4 in silico network inference challenge.     

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.     

Inferring Regulatory Networks from Expression Data Using Tree-Based Methods

One of the pressing open problems of computational systems biology is the elucidation of the topology of genetic regulatory networks (GRNs) using high throughput genomic data, in particular microarray gene expression data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) challenge aims to evaluate the success of GRN inference algorithms on benchmarks of simulated data. In this article, we present GENIE3, a new algorithm for the inference of GRNs that was best performer in the DREAM4 In Silico Multifactorial challenge. GENIE3 decomposes the prediction of a regulatory network between p genes into p different regression problems. In each of the regression problems, the expression pattern of one of the genes (target gene) is predicted from the expression patterns of all the other genes (input genes), using tree-based ensemble methods Random Forests or Extra-Trees. The importance of an input gene in the prediction of the target gene expression pattern is taken as an indication of a putative regulatory link. Putative regulatory links are then aggregated over all genes to provide a ranking of interactions from which the whole network is reconstructed. In addition to performing well on the DREAM4 In Silico Multifactorial challenge simulated data, we show that GENIE3 compares favorably with existing algorithms to decipher the genetic regulatory network of Escherichia coli. It doesn''t make any assumption about the nature of gene regulation, can deal with combinatorial and non-linear interactions, produces directed GRNs, and is fast and scalable. In conclusion, we propose a new algorithm for GRN inference that performs well on both synthetic and real gene expression data. The algorithm, based on feature selection with tree-based ensemble methods, is simple and generic, making it adaptable to other types of genomic data and interactions.     

Gene regulatory network reconstruction using Bayesian networks, the Dantzig Selector, the Lasso and their meta-analysis

Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth "Dialogue for Reverse Engineering Assessments and Methods" (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on "Systems Genetics" proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the 16 teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics.     

A New Asynchronous Parallel Algorithm for Inferring Large-Scale Gene Regulatory Networks

The reconstruction of gene regulatory networks (GRNs) from high-throughput experimental data has been considered one of the most important issues in systems biology research. With the development of high-throughput technology and the complexity of biological problems, we need to reconstruct GRNs that contain thousands of genes. However, when many existing algorithms are used to handle these large-scale problems, they will encounter two important issues: low accuracy and high computational cost. To overcome these difficulties, the main goal of this study is to design an effective parallel algorithm to infer large-scale GRNs based on high-performance parallel computing environments. In this study, we proposed a novel asynchronous parallel framework to improve the accuracy and lower the time complexity of large-scale GRN inference by combining splitting technology and ordinary differential equation (ODE)-based optimization. The presented algorithm uses the sparsity and modularity of GRNs to split whole large-scale GRNs into many small-scale modular subnetworks. Through the ODE-based optimization of all subnetworks in parallel and their asynchronous communications, we can easily obtain the parameters of the whole network. To test the performance of the proposed approach, we used well-known benchmark datasets from Dialogue for Reverse Engineering Assessments and Methods challenge (DREAM), experimentally determined GRN of Escherichia coli and one published dataset that contains more than 10 thousand genes to compare the proposed approach with several popular algorithms on the same high-performance computing environments in terms of both accuracy and time complexity. The numerical results demonstrate that our parallel algorithm exhibits obvious superiority in inferring large-scale GRNs.     

Efficient reverse-engineering of a developmental gene regulatory network

Understanding the complex regulatory networks underlying development and evolution of multi-cellular organisms is a major problem in biology. Computational models can be used as tools to extract the regulatory structure and dynamics of such networks from gene expression data. This approach is called reverse engineering. It has been successfully applied to many gene networks in various biological systems. However, to reconstitute the structure and non-linear dynamics of a developmental gene network in its spatial context remains a considerable challenge. Here, we address this challenge using a case study: the gap gene network involved in segment determination during early development of Drosophila melanogaster. A major problem for reverse-engineering pattern-forming networks is the significant amount of time and effort required to acquire and quantify spatial gene expression data. We have developed a simplified data processing pipeline that considerably increases the throughput of the method, but results in data of reduced accuracy compared to those previously used for gap gene network inference. We demonstrate that we can infer the correct network structure using our reduced data set, and investigate minimal data requirements for successful reverse engineering. Our results show that timing and position of expression domain boundaries are the crucial features for determining regulatory network structure from data, while it is less important to precisely measure expression levels. Based on this, we define minimal data requirements for gap gene network inference. Our results demonstrate the feasibility of reverse-engineering with much reduced experimental effort. This enables more widespread use of the method in different developmental contexts and organisms. Such systematic application of data-driven models to real-world networks has enormous potential. Only the quantitative investigation of a large number of developmental gene regulatory networks will allow us to discover whether there are rules or regularities governing development and evolution of complex multi-cellular organisms.     

Gene regulatory networks from multifactorial perturbations using Graphical Lasso: application to the DREAM4 challenge

A major challenge in the field of systems biology consists of predicting gene regulatory networks based on different training data. Within the DREAM4 initiative, we took part in the multifactorial sub-challenge that aimed to predict gene regulatory networks of size 100 from training data consisting of steady-state levels obtained after applying multifactorial perturbations to the original in silico network. Due to the static character of the challenge data, we tackled the problem via a sparse Gaussian Markov Random Field, which relates network topology with the covariance inverse generated by the gene measurements. As for the computations, we used the Graphical Lasso algorithm which provided a large range of candidate network topologies. The main task was to select the optimal network topology and for that, different model selection criteria were explored. The selected networks were compared with the golden standards and the results ranked using the scoring metrics applied in the challenge, giving a better insight in our submission and the way to improve it.Our approach provides an easy statistical and computational framework to infer gene regulatory networks that is suitable for large networks, even if the number of the observations (perturbations) is greater than the number of variables (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.     

Towards a Rigorous Assessment of Systems Biology Models: The DREAM3 Challenges

Background

Systems biology has embraced computational modeling in response to the quantitative nature and increasing scale of contemporary data sets. The onslaught of data is accelerating as molecular profiling technology evolves. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) is a community effort to catalyze discussion about the design, application, and assessment of systems biology models through annual reverse-engineering challenges.

Methodology and Principal Findings

We describe our assessments of the four challenges associated with the third DREAM conference which came to be known as the DREAM3 challenges: signaling cascade identification, signaling response prediction, gene expression prediction, and the DREAM3 in silico network challenge. The challenges, based on anonymized data sets, tested participants in network inference and prediction of measurements. Forty teams submitted 413 predicted networks and measurement test sets. Overall, a handful of best-performer teams were identified, while a majority of teams made predictions that were equivalent to random. Counterintuitively, combining the predictions of multiple teams (including the weaker teams) can in some cases improve predictive power beyond that of any single method.

Conclusions

DREAM provides valuable feedback to practitioners of systems biology modeling. Lessons learned from the predictions of the community provide much-needed context for interpreting claims of efficacy of algorithms described in the scientific literature.