Stochastic Boolean networks: an efficient approach to modeling gene regulatory networks

SPREd: a simulation-supervised neural network tool for gene regulatory network reconstruction

Summary

Reconstruction of gene regulatory networks (GRNs) from expression data is a significant open problem. Common approaches train a machine learning (ML) model to predict a gene's expression using transcription factors' (TFs') expression as features and designate important features/TFs as regulators of the gene. Here, we present an entirely different paradigm, where GRN edges are directly predicted by the ML model. The new approach, named "SPREd," is a simulation-supervised neural network for GRN inference. Its inputs comprise expression relationships (e.g. correlation, mutual information) between the target gene and each TF and between pairs of TFs. The output includes binary labels indicating whether each TF regulates the target gene. We train the neural network model using synthetic expression data generated by a biophysics-inspired simulation model that incorporates linear as well as non-linear TF-gene relationships and diverse GRN configurations. We show SPREd to outperform state-of-the-art GRN reconstruction tools GENIE3, ENNET, PORTIA, and TIGRESS on synthetic datasets with high co-expression among TFs, similar to that seen in real data. A key advantage of the new approach is its robustness to relatively small numbers of conditions (columns) in the expression matrix, which is a common problem faced by existing methods. Finally, we evaluate SPREd on real data sets in yeast that represent gold-standard benchmarks of GRN reconstruction and show it to perform significantly better than or comparably to existing methods. In addition to its high accuracy and speed, SPREd marks a first step toward incorporating biophysics principles of gene regulation into ML-based approaches to GRN reconstruction.

Availability and implementation

Data and code are available from https://github.com/iiiime/SPREd.

SPREd: A simulation-supervised neural network tool for gene regulatory network reconstruction

Reconstruction of gene regulatory networks (GRNs) from expression data is a significant open problem. Common approaches train a machine learning (ML) model to predict a gene's expression using transcription factors' (TFs') expression as features and designate important features/TFs as regulators of the gene. Here, we present an entirely different paradigm, where GRN edges are directly predicted by the ML model. The new approach, named "SPREd" is a simulation-supervised neural network for GRN inference. Its inputs comprise expression relationships (e.g., correlation, mutual information) between the target gene and each TF and between pairs of TFs. The output includes binary labels indicating whether each TF regulates the target gene. We train the neural network model using synthetic expression data generated by a biophysics-inspired simulation model that incorporates linear as well as non-linear TF-gene relationships and diverse GRN configurations. We show SPREd to outperform state-of-the-art GRN reconstruction tools GENIE3, ENNET, PORTIA and TIGRESS on synthetic datasets with high co-expression among TFs, similar to that seen in real data. A key advantage of the new approach is its robustness to relatively small numbers of conditions (columns) in the expression matrix, which is a common problem faced by existing methods. Finally, we evaluate SPREd on real data sets in yeast that represent gold standard benchmarks of GRN reconstruction and show it to perform significantly better than or comparably to existing methods. In addition to its high accuracy and speed, SPREd marks a first step towards incorporating biophysics principles of gene regulation into ML-based approaches to GRN reconstruction.

Understanding multimorbidity requires sign-disease networks and higher-order interactions, a perspective

Background

Count scores, disease clustering, and pairwise associations between diseases remain ubiquitous in multimorbidity research despite two major shortcomings: they yield no insight into plausible mechanisms underlying multimorbidity, and they ignore higher-order interactions such as effect modification.

Objectives

We argue that two components are currently missing but vital to develop novel multimorbidity metrics. Firstly, networks should be constructed which consists simultaneously of signs, symptoms, and diseases, since only then could they yield insight into plausible shared biological mechanisms underlying diseases.Secondly, learning pairwise associations is insufficient to fully characterize the correlations in a system. That is, synergistic (e.g., cooperative or antagonistic) effects are widespread in complex systems, where two or more elements combined give a larger or smaller effect than the sum of their individual effects. It can even occur that pairs of symptoms have no pairwise associations whatsoever, but in combination have a significant association. Therefore, higher-order interactions should be included in networks used to study multimorbidity, resulting in so-called hypergraphs.

Methods

We illustrate our argument using a synthetic Bayesian Network model of symptoms, signs and diseases, composed of pairwise and higher-order interactions. We simulate network interventions on both individual and population levels and compare the ground-truth outcomes with the predictions from pairwise associations.

Conclusion

We find that, when judged purely from the pairwise associations, interventions can have unexpected 'side-effects' or the most opportune intervention could be missed. The hypergraph uncovers links missed in pairwise networks, giving a more complete overview of sign and disease associations.

Mathematical model of the cell signaling pathway based on the extended Boolean network model with a stochastic process

BACKGROUND

In cell signaling pathways, proteins interact with each other to determine cell fate in response to either cell-extrinsic (micro-environmental) or intrinsic cues. One of the well-studied pathways, the mitogen-activated protein kinase (MAPK) signaling pathway, regulates cell processes such as differentiation, proliferation, apoptosis, and survival in response to various micro-environmental stimuli in eukaryotes. Upon micro-environmental stimulus, receptors on the cell membrane become activated. Activated receptors initiate a cascade of protein activation in the MAPK pathway. This activation involves protein binding, creating scaffold proteins, which are known to facilitate effective MAPK signaling transduction.

RESULTS

This paper presents a novel mathematical model of a cell signaling pathway coordinated by protein scaffolding. The model is based on the extended Boolean network approach with stochastic processes. Protein production or decay in a cell was modeled considering the stochastic process, whereas the protein-protein interactions were modeled based on the extended Boolean network approach. Our model fills a gap in the binary set applied to previous models. The model simultaneously considers the stochastic process directly. Using the model, we simulated a simplified mitogen-activated protein kinase (MAPK) signaling pathway upon stimulation of both a single receptor at the initial time and multiple receptors at several time points. Our simulations showed that the signal is amplified as it travels down to the pathway from the receptor, generating substantially amplified downstream ERK activity. The noise generated by the stochastic process of protein self-activity in the model was also amplified as the signaling propagated through the pathway.

CONCLUSIONS

The signaling transduction in a simplified MAPK signaling pathway could be explained by a mathematical model based on the extended Boolean network model with a stochastic process. The model simulations demonstrated signaling amplifications when it travels downstream, which was already observed in experimental settings. We also highlight the importance of stochastic activity in regulating protein inactivation.

Review and assessment of Boolean approaches for inference of gene regulatory networks

Boolean descriptions of gene regulatory networks can provide an insight into interactions between genes. Boolean networks hold predictive power, are easy to understand, and can be used to simulate the observed networks in different scenarios. We review fundamental and state-of-the-art methods for inference of Boolean networks. We introduce a methodology for a straightforward evaluation of Boolean inference approaches based on the generation of evaluation datasets, application of selected inference methods, and evaluation of performance measures to guide the selection of the best method for a given inference problem. We demonstrate this procedure on inference methods REVEAL (REVerse Engineering ALgorithm), Best-Fit Extension, MIBNI (Mutual Information-based Boolean Network Inference), GABNI (Genetic Algorithm-based Boolean Network Inference) and ATEN (AND/OR Tree ENsemble algorithm), which infers Boolean descriptions of gene regulatory networks from discretised time series data. Boolean inference approaches tend to perform better in terms of dynamic accuracy, and slightly worse in terms of structural correctness. We believe that the proposed methodology and provided guidelines will help researchers to develop Boolean inference approaches with a good predictive capability while maintaining structural correctness and biological relevance.

Fast and accurate inference of gene regulatory networks through robust precision matrix estimation

MOTIVATION

Transcriptional regulation mechanisms allow cells to adapt and respond to external stimuli by altering gene expression. The possible cell transcriptional states are determined by the underlying gene regulatory network (GRN), and reliably inferring such network would be invaluable to understand biological processes and disease progression.

RESULTS

In this article, we present a novel method for the inference of GRNs, called PORTIA, which is based on robust precision matrix estimation, and we show that it positively compares with state-of-the-art methods while being orders of magnitude faster. We extensively validated PORTIA using the DREAM and MERLIN+P datasets as benchmarks. In addition, we propose a novel scoring metric that builds on graph-theoretical concepts.

AVAILABILITY AND IMPLEMENTATION

The code and instructions for data acquisition and full reproduction of our results are available at https://github.com/AntoinePassemiers/PORTIA-Manuscript. PORTIA is available on PyPI as a Python package (portia-grn).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Simulating ATO Mechanism and EGFR Signaling with Fuzzy Logic and Petri Net

Background:

Interactions of many key proteins or genes in signalling pathway have been studied qualitatively in the literature, but only little quantitative information is available.

Objective:

Although much has been done to clarify the biochemistry of transcriptional dynamics in signalling pathway, it remains difficult to find out and predict quantitative responses. The aim of this study is to construct a computational model of epidermal growth factor receptor (EGFR) signalling pathway as one of hallmarks of cancer so as to predict quantitative responses.

Material and Methods:

In this analytical study, we presented a computational model to investigate EGFR signalling pathway. Interaction of Arsenic trioxide (ATO) with EGFR signalling pathway factors has been elicited by systematic search in data bases, as ATO is one of the mysterious chemotherapy agents that control EGFR expression in cancer. ATO has dichotomous manner in vivo, dependent on its concentration. According to fuzzy rules based upon qualitative knowledge and Petri Net, we can construct a quantitative model to describe ATO mechanism in EGFR signalling pathway.

Results:

By Fuzzy Logic models that have the potential to trade with the loss of quantitative information on how different species interact, along with Petri net quantitatively describe the dynamics of EGFR signalling pathway. By this model the dynamic of different factors in EGFR signalling pathway is achieved.

Conclusion:

The use of Fuzzy Logic and PNs in biological network modelling causes a deeper understanding and comprehensive analysis of the biological networks.

Uniform patterns based area-efficient and accurate stochastic computing finite impulse response filter

Stochastic computing has recently gained attention due to its low hardware complexity and better fault tolerance against soft errors. However, stochastic computing based circuits suffer from different errors which affect the output accuracy of these circuits. In this paper, an accurate and area-efficient stochastic computing based digital finite impulse response filter is designed. In the proposed work, constant uniform patterns are used as stochastic numbers for the select lines of different MUXes in the filter and the error performance of filter is analysed. Based on the error performance, the combinations of these patterns are proposed for reducing the output error of stochastic computing based filters. The architectures for generating these uniform patterns are also proposed. Results show that the proposed design methodology has better error performance and comparable hardware complexity as compared to the state-of-the-art implementations.

Integration of single-cell multi-omics for gene regulatory network inference

The advancement of single-cell sequencing technology in recent years has provided an opportunity to reconstruct gene regulatory networks (GRNs) with the data from thousands of single cells in one sample. This uncovers regulatory interactions in cells and speeds up the discoveries of regulatory mechanisms in diseases and biological processes. Therefore, more methods have been proposed to reconstruct GRNs using single-cell sequencing data. In this review, we introduce technologies for sequencing single-cell genome, transcriptome, and epigenome. At the same time, we present an overview of current GRN reconstruction strategies utilizing different single-cell sequencing data. Bioinformatics tools were grouped by their input data type and mathematical principles for reader's convenience, and the fundamental mathematics inherent in each group will be discussed. Furthermore, the adaptabilities and limitations of these different methods will also be summarized and compared, with the hope to facilitate researchers recognizing the most suitable tools for them.

D3GRN: a data driven dynamic network construction method to infer gene regulatory networks

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.

Algorithmic and Stochastic Representations of Gene Regulatory Networks and Protein-Protein Interactions

BACKGROUND

Latest studies reveal the importance of Protein-Protein interactions on physiologic functions and biological structures. Several stochastic and algorithmic methods have been published until now, for the modeling of the complex nature of the biological systems.

OBJECTIVE

Biological Networks computational modeling is still a challenging task. The formulation of the complex cellular interactions is a research field of great interest. In this review paper, several computational methods for the modeling of GRN and PPI are presented analytically.

METHODS

Several well-known GRN and PPI models are presented and discussed in this review study such as: Graphs representation, Boolean Networks, Generalized Logical Networks, Bayesian Networks, Relevance Networks, Graphical Gaussian models, Weight Matrices, Reverse Engineering Approach, Evolutionary Algorithms, Forward Modeling Approach, Deterministic models, Static models, Hybrid models, Stochastic models, Petri Nets, BioAmbients calculus and Differential Equations.

RESULTS

GRN and PPI methods have been already applied in various clinical processes with potential positive results, establishing promising diagnostic tools.

CONCLUSION

In literature many stochastic algorithms are focused in the simulation, analysis and visualization of the various biological networks and their dynamics interactions, which are referred and described in depth in this review paper.

Robustness of Nutrient Signaling Is Maintained by Interconnectivity Between Signal Transduction Pathways

Systems biology approaches provide means to study the interplay between biological processes leading to the mechanistic understanding of the properties of complex biological systems. Here, we developed a vector format rule-based Boolean logic model of the yeast S. cerevisiae cAMP-PKA, Snf1, and the Snf3-Rgt2 pathway to better understand the role of crosstalk on network robustness and function. We identified that phosphatases are the common unknown components of the network and that crosstalk from the cAMP-PKA pathway to other pathways plays a critical role in nutrient sensing events. The model was simulated with known crosstalk combinations and subsequent analysis led to the identification of characteristics and impact of pathway interconnections. Our results revealed that the interconnections between the Snf1 and Snf3-Rgt2 pathway led to increased robustness in these signaling pathways. Overall, our approach contributes to the understanding of the function and importance of crosstalk in nutrient signaling.

Representing dynamic biological networks with multi-scale probabilistic models

Dynamic models analyzing gene regulation and metabolism face challenges when adapted to modeling signal transduction networks. During signal transduction, molecular reactions and mechanisms occur in different spatial and temporal frames and involve feedbacks. This impedes the straight-forward use of methods based on Boolean networks, Bayesian approaches, and differential equations. We propose a new approach, ProbRules, that combines probabilities and logical rules to represent the dynamics of a system across multiple scales. We demonstrate that ProbRules models can represent various network motifs of biological systems. As an example of a comprehensive model of signal transduction, we provide a Wnt network that shows remarkable robustness under a range of phenotypical and pathological conditions. Its simulation allows the clarification of controversially discussed molecular mechanisms of Wnt signaling by predicting wet-lab measurements. ProbRules provides an avenue in current computational modeling by enabling systems biologists to integrate vast amounts of available data on different scales.

An experimental design framework for Markovian gene regulatory networks under stationary control policy

BACKGROUND

A fundamental problem for translational genomics is to find optimal therapies based on gene regulatory intervention. Dynamic intervention involves a control policy that optimally reduces a cost function based on phenotype by externally altering the state of the network over time. When a gene regulatory network (GRN) model is fully known, the problem is addressed using classical dynamic programming based on the Markov chain associated with the network. When the network is uncertain, a Bayesian framework can be applied, where policy optimality is with respect to both the dynamical objective and the uncertainty, as characterized by a prior distribution. In the presence of uncertainty, it is of great practical interest to develop an experimental design strategy and thereby select experiments that optimally reduce a measure of uncertainty.

RESULTS

In this paper, we employ mean objective cost of uncertainty (MOCU), which quantifies uncertainty based on the degree to which uncertainty degrades the operational objective, that being the cost owing to undesirable phenotypes. We assume that a number of conditional probabilities characterizing regulatory relationships among genes are unknown in the Markovian GRN. In sum, there is a prior distribution which can be updated to a posterior distribution by observing a regulatory trajectory, and an optimal control policy, known as an "intrinsically Bayesian robust" (IBR) policy. To obtain a better IBR policy, we select an experiment that minimizes the MOCU remaining after applying its output to the network. At this point, we can either stop and find the resulting IBR policy or proceed to determine more unknown conditional probabilities via regulatory observation and find the IBR policy from the resulting posterior distribution. For sequential experimental design this entire process is iterated. Owing to the computational complexity of experimental design, which requires computation of many potential IBR policies, we implement an approximate method utilizing mean first passage times (MFPTs) - but only in experimental design, the final policy being an IBR policy.

CONCLUSIONS

Comprehensive performance analysis based on extensive simulations on synthetic and real GRNs demonstrate the efficacy of the proposed method, including the accuracy and computational advantage of the approximate MFPT-based design.

Kinetic models of hematopoietic differentiation

As cell and molecular biology is becoming increasingly quantitative, there is an upsurge of interest in mechanistic modeling at different levels of resolution. Such models mostly concern kinetics and include gene and protein interactions as well as cell population dynamics. The final goal of these models is to provide experimental predictions, which is now taking on. However, even without matured predictions, kinetic models serve the purpose of compressing a plurality of experimental results into something that can empower the data interpretation, and importantly, suggesting new experiments by turning "knobs" in silico. Once formulated, kinetic models can be executed in terms of molecular rate equations for concentrations or by stochastic simulations when only a limited number of copies are involved. Developmental processes, in particular those of stem and progenitor cell commitments, are not only topical but also particularly suitable for kinetic modeling due to the finite number of key genes involved in cellular decisions. Stem and progenitor cell commitment processes have been subject to intense experimental studies over the last decade with some emphasis on embryonic and hematopoietic stem cells. Gene and protein interactions governing these processes can be modeled by binary Boolean rules or by continuous-valued models with interactions set by binding strengths. Conceptual insights along with tested predictions have emerged from such kinetic models. Here we review kinetic modeling efforts applied to stem cell developmental systems with focus on hematopoiesis. We highlight the future challenges including multi-scale models integrating cell dynamical and transcriptional models. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Developmental Biology > Stem Cell Biology and Regeneration.

Inference of time-delayed gene regulatory networks based on dynamic Bayesian network hybrid learning method

Gene regulatory networks (GRNs) research reveals complex life phenomena from the perspective of gene interaction, which is an important research field in systems biology. Traditional Bayesian networks have a high computational complexity, and the network structure scoring model has a single feature. Information-based approaches cannot identify the direction of regulation. In order to make up for the shortcomings of the above methods, this paper presents a novel hybrid learning method (DBNCS) based on dynamic Bayesian network (DBN) to construct the multiple time-delayed GRNs for the first time, combining the comprehensive score (CS) with the DBN model. DBNCS algorithm first uses CMI2NI (conditional mutual inclusive information-based network inference) algorithm for network structure profiles learning, namely the construction of search space. Then the redundant regulations are removed by using the recursive optimization algorithm (RO), thereby reduce the false positive rate. Secondly, the network structure profiles are decomposed into a set of cliques without loss, which can significantly reduce the computational complexity. Finally, DBN model is used to identify the direction of gene regulation within the cliques and search for the optimal network structure. The performance of DBNCS algorithm is evaluated by the benchmark GRN datasets from DREAM challenge as well as the SOS DNA repair network in Escherichia coli, and compared with other state-of-the-art methods. The experimental results show the rationality of the algorithm design and the outstanding performance of the GRNs.

Towards targeted combinatorial therapy design for the treatment of castration-resistant prostate cancer

BACKGROUND

Prostate cancer is one of the most prevalent cancers in males in the United States and amongst the leading causes of cancer related deaths. A particularly virulent form of this disease is castration-resistant prostate cancer (CRPC), where patients no longer respond to medical or surgical castration. CRPC is a complex, multifaceted and heterogeneous malady with limited standard treatment options.

RESULTS

The growth and progression of prostate cancer is a complicated process that involves multiple pathways. The signaling network comprising the integral constituents of the signature pathways involved in the development and progression of prostate cancer is modeled as a combinatorial circuit. The failures in the gene regulatory network that lead to cancer are abstracted as faults in the equivalent circuit and the Boolean circuit model is then used to design therapies tailored to counteract the effect of each molecular abnormality and to propose potentially efficacious combinatorial therapy regimens. Furthermore, stochastic computational modeling is utilized to identify potentially vulnerable components in the network that may serve as viable candidates for drug development.

CONCLUSION

The results presented herein can aid in the design of scientifically well-grounded targeted therapies that can be employed for the treatment of prostate cancer patients.

Immuno-hybrid algorithm: a novel hybrid approach for GRN reconstruction

Bio-inspired algorithms are widely used to optimize the model parameters of GRN. In this paper, focus is given to develop improvised versions of bio-inspired algorithm for the specific problem of reconstruction of gene regulatory network. The approach is applied to the data set that was developed by the DNA microarray technology through biological experiments in the lab. This paper introduced a novel hybrid method, which combines the clonal selection algorithm and BFGS Quasi-Newton algorithm. The proposed approach implemented for real world E. coli data set and identified most of the relations. The results are also compared with the existing methods and proven to be efficient.

Estimating Propensity Parameters Using Google PageRank and Genetic Algorithms

Stochastic Boolean networks, or more generally, stochastic discrete networks, are an important class of computational models for molecular interaction networks. The stochasticity stems from the updating schedule. Standard updating schedules include the synchronous update, where all the nodes are updated at the same time, and the asynchronous update where a random node is updated at each time step. The former produces a deterministic dynamics while the latter a stochastic dynamics. A more general stochastic setting considers propensity parameters for updating each node. Stochastic Discrete Dynamical Systems (SDDS) are a modeling framework that considers two propensity parameters for updating each node and uses one when the update has a positive impact on the variable, that is, when the update causes the variable to increase its value, and uses the other when the update has a negative impact, that is, when the update causes it to decrease its value. This framework offers additional features for simulations but also adds a complexity in parameter estimation of the propensities. This paper presents a method for estimating the propensity parameters for SDDS. The method is based on adding noise to the system using the Google PageRank approach to make the system ergodic and thus guaranteeing the existence of a stationary distribution. Then with the use of a genetic algorithm, the propensity parameters are estimated. Approximation techniques that make the search algorithms efficient are also presented and Matlab/Octave code to test the algorithms are available at http://www.ms.uky.edu/~dmu228/GeneticAlg/Code.html.

Integrative approach for inference of gene regulatory networks using lasso-based random featuring and application to psychiatric disorders

Background

Inferring gene regulatory networks is one of the most interesting research areas in the systems biology. Many inference methods have been developed by using a variety of computational models and approaches. However, there are two issues to solve. First, depending on the structural or computational model of inference method, the results tend to be inconsistent due to innately different advantages and limitations of the methods. Therefore the combination of dissimilar approaches is demanded as an alternative way in order to overcome the limitations of standalone methods through complementary integration. Second, sparse linear regression that is penalized by the regularization parameter (lasso) and bootstrapping-based sparse linear regression methods were suggested in state of the art methods for network inference but they are not effective for a small sample size data and also a true regulator could be missed if the target gene is strongly affected by an indirect regulator with high correlation or another true regulator.

Results

We present two novel network inference methods based on the integration of three different criteria, (i) z-score to measure the variation of gene expression from knockout data, (ii) mutual information for the dependency between two genes, and (iii) linear regression-based feature selection.

Based on these criterion, we propose a lasso-based random feature selection algorithm (LARF) to achieve better performance overcoming the limitations of bootstrapping as mentioned above.

Conclusions

In this work, there are three main contributions. First, our z score-based method to measure gene expression variations from knockout data is more effective than similar criteria of related works. Second, we confirmed that the true regulator selection can be effectively improved by LARF. Lastly, we verified that an integrative approach can clearly outperform a single method when two different methods are effectively jointed. In the experiments, our methods were validated by outperforming the state of the art methods on DREAM challenge data, and then LARF was applied to inferences of gene regulatory network associated with psychiatric disorders.

Boolean modeling techniques for protein co-expression networks in systems medicine

INTRODUCTION

Application of systems biology/systems medicine approaches is promising for proteomics/biomedical research, but requires selection of an adequate modeling type.

AREAS COVERED

This article reviews the existing Boolean network modeling approaches, which provide in comparison with alternative modeling techniques several advantages for the processing of proteomics data. Application of methods for inference, reduction and validation of protein co-expression networks that are derived from quantitative high-throughput proteomics measurements is presented. It's also shown how Boolean models can be used to derive system-theoretic characteristics that describe both the dynamical behavior of such networks as a whole and the properties of different cell states (e.g. healthy or diseased cell states). Furthermore, application of methods derived from control theory is proposed in order to simulate the effects of therapeutic interventions on such networks, which is a promising approach for the computer-assisted discovery of biomarkers and drug targets. Finally, the clinical application of Boolean modeling analyses is discussed. Expert commentary: Boolean modeling of proteomics data is still in its infancy. Progress in this field strongly depends on provision of a repository with public access to relevant reference models. Also required are community supported standards that facilitate input of both proteomics and patient related data (e.g. age, gender, laboratory results, etc.).

Identification of Potential Drug Targets in Cancer Signaling Pathways using Stochastic Logical Models

The investigation of vulnerable components in a signaling pathway can contribute to development of drug therapy addressing aberrations in that pathway. Here, an original signaling pathway is derived from the published literature on breast cancer models. New stochastic logical models are then developed to analyze the vulnerability of the components in multiple signalling sub-pathways involved in this signaling cascade. The computational results are consistent with the experimental results, where the selected proteins were silenced using specific siRNAs and the viability of the cells were analyzed 72 hours after silencing. The genes elF4E and NFkB are found to have nearly no effect on the relative cell viability and the genes JAK2, Stat3, S6K, JUN, FOS, Myc, and Mcl1 are effective candidates to influence the relative cell growth. The vulnerabilities of some targets such as Myc and S6K are found to vary significantly depending on the weights of the sub-pathways; this will be indicative of the chosen target to require customization for therapy. When these targets are utilized, the response of breast cancers from different patients will be highly variable because of the known heterogeneities in signaling pathways among the patients. The targets whose vulnerabilities are invariably high might be more universally acceptable targets.

Modeling Gene Networks in Saccharomyces cerevisiae Based on Gene Expression Profiles

Detailed and innovative analysis of gene regulatory network structures may reveal novel insights to biological mechanisms. Here we study how gene regulatory network in Saccharomyces cerevisiae can differ under aerobic and anaerobic conditions. To achieve this, we discretized the gene expression profiles and calculated the self-entropy of down- and upregulation of gene expression as well as joint entropy. Based on these quantities the uncertainty coefficient was calculated for each gene triplet, following which, separate gene logic networks were constructed for the aerobic and anaerobic conditions. Four structural parameters such as average degree, average clustering coefficient, average shortest path, and average betweenness were used to compare the structure of the corresponding aerobic and anaerobic logic networks. Five genes were identified to be putative key components of the two energy metabolisms. Furthermore, community analysis using the Newman fast algorithm revealed two significant communities for the aerobic but only one for the anaerobic network. David Gene Functional Classification suggests that, under aerobic conditions, one such community reflects the cell cycle and cell replication, while the other one is linked to the mitochondrial respiratory chain function.

RulNet: A Web-Oriented Platform for Regulatory Network Inference, Application to Wheat -Omics Data

With the increasing amount of -omics data available, a particular effort has to be made to provide suitable analysis tools. A major challenge is that of unraveling the molecular regulatory networks from massive and heterogeneous datasets. Here we describe RulNet, a web-oriented platform dedicated to the inference and analysis of regulatory networks from qualitative and quantitative -omics data by means of rule discovery. Queries for rule discovery can be written in an extended form of the RQL query language, which has a syntax similar to SQL. RulNet also offers users interactive features that progressively adjust and refine the inferred networks. In this paper, we present a functional characterization of RulNet and compare inferred networks with correlation-based approaches. The performance of RulNet has been evaluated using the three benchmark datasets used for the transcriptional network inference challenge DREAM5. Overall, RulNet performed as well as the best methods that participated in this challenge and it was shown to behave more consistently when compared across the three datasets. Finally, we assessed the suitability of RulNet to analyze experimental -omics data and to infer regulatory networks involved in the response to nitrogen and sulfur supply in wheat (Triticum aestivum L.) grains. The results highlight putative actors governing the response to nitrogen and sulfur supply in wheat grains. We evaluate the main characteristics and features of RulNet as an all-in-one solution for RN inference, visualization and editing. Using simple yet powerful RulNet queries allowed RNs involved in the adaptation of wheat grain to N and S supply to be discovered. We demonstrate the effectiveness and suitability of RulNet as a platform for the analysis of RNs involving different types of -omics data. The results are promising since they are consistent with what was previously established by the scientific community.

Iron acquisition and oxidative stress response in aspergillus fumigatus

BACKGROUND

Aspergillus fumigatus is a ubiquitous airborne fungal pathogen that presents a life-threatening health risk to individuals with weakened immune systems. A. fumigatus pathogenicity depends on its ability to acquire iron from the host and to resist host-generated oxidative stress. Gaining a deeper understanding of the molecular mechanisms governing A. fumigatus iron acquisition and oxidative stress response may ultimately help to improve the diagnosis and treatment of invasive aspergillus infections.

RESULTS

This study follows a systems biology approach to investigate how adaptive behaviors emerge from molecular interactions underlying A. fumigatus iron regulation and oxidative stress response. We construct a Boolean network model from known interactions and simulate how changes in environmental iron and superoxide levels affect network dynamics. We propose rules for linking long term model behavior to qualitative estimates of cell growth and cell death. These rules are used to predict phenotypes of gene deletion strains. The model is validated on the basis of its ability to reproduce literature data not used in model generation.

CONCLUSIONS

The model reproduces gene expression patterns in experimental time course data when A. fumigatus is switched from a low iron to a high iron environment. In addition, the model is able to accurately represent the phenotypes of many knockout strains under varying iron and superoxide conditions. Model simulations support the hypothesis that intracellular iron regulates A. fumigatus transcription factors, SreA and HapX, by a post-translational, rather than transcriptional, mechanism. Finally, the model predicts that blocking siderophore-mediated iron uptake reduces resistance to oxidative stress. This indicates that combined targeting of siderophore-mediated iron uptake and the oxidative stress response network may act synergistically to increase fungal cell killing.

Quantitative and logic modelling of molecular and gene networks

Behaviours of complex biomolecular systems are often irreducible to the elementary properties of their individual components. Explanatory and predictive mathematical models are therefore useful for fully understanding and precisely engineering cellular functions. The development and analyses of these models require their adaptation to the problems that need to be solved and the type and amount of available genetic or molecular data. Quantitative and logic modelling are among the main methods currently used to model molecular and gene networks. Each approach comes with inherent advantages and weaknesses. Recent developments show that hybrid approaches will become essential for further progress in synthetic biology and in the development of virtual organisms.

Asynchronous stochastic Boolean networks as gene network models

Logical models have widely been used to gain insights into the biological behavior of gene regulatory networks (GRNs). Most logical models assume a synchronous update of the genes' states in a GRN. However, this may not be appropriate, because each gene may require a different period of time for changing its state. In this article, asynchronous stochastic Boolean networks (ASBNs) are proposed for investigating various asynchronous state-updating strategies in a GRN. As in stochastic computation, ASBNs use randomly permutated stochastic sequences to encode probability. Investigated by several stochasticity models, a GRN is considered to be subject to noise and external perturbation. Hence, both stochasticity and asynchronicity are considered in the state evolution of a GRN. As a case study, ASBNs are utilized to investigate the dynamic behavior of a T helper network. It is shown that ASBNs are efficient in evaluating the steady-state distributions (SSDs) of the network with random gene perturbation. The SSDs found by using ASBNs show the robustness of the attractors of the T helper network, when various stochasticity and asynchronicity models are considered to investigate its dynamic behavior.

Inference of SNP-gene regulatory networks by integrating gene expressions and genetic perturbations

In order to elucidate the overall relationships between gene expressions and genetic perturbations, we propose a network inference method to infer gene regulatory network where single nucleotide polymorphism (SNP) is involved as a regulator of genes. In the most of the network inferences named as SNP-gene regulatory network (SGRN) inference, pairs of SNP-gene are given by separately performing expression quantitative trait loci (eQTL) mappings. In this paper, we propose a SGRN inference method without predefined eQTL information assuming a gene is regulated by a single SNP at most. To evaluate the performance, the proposed method was applied to random data generated from synthetic networks and parameters. There are three main contributions. First, the proposed method provides both the gene regulatory inference and the eQTL identification. Second, the experimental results demonstrated that integration of multiple methods can produce competitive performances. Lastly, the proposed method was also applied to psychiatric disorder data in order to explore how the method works with real data.

Gene perturbation and intervention in context-sensitive stochastic Boolean networks

Background

In a gene regulatory network (GRN), gene expressions are affected by noise, and stochastic fluctuations exist in the interactions among genes. These stochastic interactions are context dependent, thus it becomes important to consider noise in a context-sensitive manner in a network model. As a logical model, context-sensitive probabilistic Boolean networks (CSPBNs) account for molecular and genetic noise in the temporal context of gene functions. In a CSPBN with n genes and k contexts, however, a computational complexity of O(nk²2²ⁿ) (or O(nk2ⁿ)) is required for an accurate (or approximate) computation of the state transition matrix (STM) of the size (2ⁿ ∙ k) × (2ⁿ ∙ k) (or 2ⁿ × 2ⁿ). The evaluation of a steady state distribution (SSD) is more challenging. Recently, stochastic Boolean networks (SBNs) have been proposed as an efficient implementation of an instantaneous PBN.

Results

The notion of stochastic Boolean networks (SBNs) is extended for the general model of PBNs, i.e., CSPBNs. This yields a novel structure of context-sensitive SBNs (CSSBNs) for modeling the stochasticity in a GRN. A CSSBN enables an efficient simulation of a CSPBN with a complexity of O(nLk2ⁿ) for computing the state transition matrix, where L is a factor related to the required sequence length in CSSBN for achieving a desired accuracy. A time-frame expanded CSSBN can further efficiently simulate the stationary behavior of a CSPBN and allow for a tunable tradeoff between accuracy and efficiency. The CSSBN approach is more efficient than an analytical method and more accurate than an approximate analysis.

Conclusions

Context-sensitive stochastic Boolean networks (CSSBNs) are proposed as an efficient approach to modeling the effects of gene perturbation and intervention in gene regulatory networks. A CSSBN analysis provides biologically meaningful insights into the oscillatory dynamics of the p53-Mdm2 network in a context-switching environment. It is shown that random gene perturbation has a greater effect on the final distribution of the steady state of a network compared to context switching activities. The CSSBN approach can further predict the steady state distribution of a glioma network under gene intervention. Ultimately, this will help drug discovery and develop effective drug intervention strategies.

Verification and optimal control of context-sensitive probabilistic Boolean networks using model checking and polynomial optimization

One of the significant topics in systems biology is to develop control theory of gene regulatory networks (GRNs). In typical control of GRNs, expression of some genes is inhibited (activated) by manipulating external stimuli and expression of other genes. It is expected to apply control theory of GRNs to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of GRNs, and gene expression is expressed by a binary value (ON or OFF). In particular, a context-sensitive probabilistic Boolean network (CS-PBN), which is one of the extended models of BNs, is used. For CS-PBNs, the verification problem and the optimal control problem are considered. For the verification problem, a solution method using the probabilistic model checker PRISM is proposed. For the optimal control problem, a solution method using polynomial optimization is proposed. Finally, a numerical example on the WNT5A network, which is related to melanoma, is presented. The proposed methods provide us useful tools in control theory of GRNs.

Hierarchical Probabilistic Interaction Modeling for Multiple Gene Expression Replicates

Microarray technology allows for the collection of multiple replicates of gene expression time course data for hundreds of genes at a handful of time points. Developing hypotheses about a gene transcriptional network, based on time course gene expression data is an important and very challenging problem. In many situations there are similarities which suggest a hierarchical structure between the replicates. This paper develops posterior probabilities for network features based on multiple hierarchical replications. Through Bayesian inference, in conjunction with the Metropolis-Hastings algorithm and model averaging, a hierarchical multiple replicate algorithm is applied to seven sets of simulated data and to a set of Arabidopsis thaliana gene expression data. The models of the simulated data suggest high posterior probabilities for pairs of genes which have at least moderate signal partial correlation. For the Arabidopsis model, many of the highest posterior probability edges agree with the literature.

Stochastic multiple-valued gene networks

Among various approaches to modeling gene regulatory networks (GRNs), Boolean networks (BNs) and its probabilistic extension, probabilistic Boolean networks (PBNs), have been studied to gain insights into the dynamics of GRNs. To further exploit the simplicity of logical models, a multiple-valued network employs gene states that are not limited to binary values, thus providing a finer granularity in the modeling of GRNs. In this paper, stochastic multiple-valued networks (SMNs) are proposed for modeling the effects of noise and gene perturbation in a GRN. An SMN enables an accurate and efficient simulation of a probabilistic multiple-valued network (as an extension of a PBN). In a k-level SMN of n genes, it requires a complexity of O(nLk(n)) to compute the state transition matrix, where L is a factor related to the minimum sequence length in the SMN for achieving a desired accuracy. The use of randomly permuted stochastic sequences further increases computational efficiency and allows for a tunable tradeoff between accuracy and efficiency. The analysis of a p53-Mdm2 network and a WNT5A network shows that the proposed SMN approach is efficient in evaluating the network dynamics and steady state distribution of gene networks under random gene perturbation.

Optimal control of gene regulatory networks with effectiveness of multiple drugs: a Boolean network approach

Developing control theory of gene regulatory networks is one of the significant topics in the field of systems biology, and it is expected to apply the obtained results to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of gene regulatory networks, and gene expression is expressed by a binary value (0 or 1). In the control problem, we assume that the concentration level of a part of genes is arbitrarily determined as the control input. However, there are cases that no gene satisfying this assumption exists, and it is important to consider structural control via external stimuli. Furthermore, these controls are realized by multiple drugs, and it is also important to consider multiple effects such as duration of effect and side effects. In this paper, we propose a BN model with two types of the control inputs and an optimal control method with duration of drug effectiveness. First, a BN model and duration of drug effectiveness are discussed. Next, the optimal control problem is formulated and is reduced to an integer linear programming problem. Finally, numerical simulations are shown.

An Evaluation of Methods for Inferring Boolean Networks from Time-Series Data

Regulatory networks play a central role in cellular behavior and decision making. Learning these regulatory networks is a major task in biology, and devising computational methods and mathematical models for this task is a major endeavor in bioinformatics. Boolean networks have been used extensively for modeling regulatory networks. In this model, the state of each gene can be either ‘on’ or ‘off’ and that next-state of a gene is updated, synchronously or asynchronously, according to a Boolean rule that is applied to the current-state of the entire system. Inferring a Boolean network from a set of experimental data entails two main steps: first, the experimental time-series data are discretized into Boolean trajectories, and then, a Boolean network is learned from these Boolean trajectories. In this paper, we consider three methods for data discretization, including a new one we propose, and three methods for learning Boolean networks, and study the performance of all possible nine combinations on four regulatory systems of varying dynamics complexities. We find that employing the right combination of methods for data discretization and network learning results in Boolean networks that capture the dynamics well and provide predictive power. Our findings are in contrast to a recent survey that placed Boolean networks on the low end of the “faithfulness to biological reality” and “ability to model dynamics” spectra. Further, contrary to the common argument in favor of Boolean networks, we find that a relatively large number of time points in the time-series data is required to learn good Boolean networks for certain data sets. Last but not least, while methods have been proposed for inferring Boolean networks, as discussed above, missing still are publicly available implementations thereof. Here, we make our implementation of the methods available publicly in open source at http://bioinfo.cs.rice.edu/.

Systems Modeling at Multiple Levels of Regulation: Linking Systems and Genetic Networks to Spatially Explicit Plant Populations

Selection and adaptation of individuals to their underlying environments are highly dynamical processes, encompassing interactions between the individual and its seasonally changing environment, synergistic or antagonistic interactions between individuals and interactions amongst the regulatory genes within the individual. Plants are useful organisms to study within systems modeling because their sedentary nature simplifies interactions between individuals and the environment, and many important plant processes such as germination or flowering are dependent on annual cycles which can be disrupted by climate behavior. Sedentism makes plants relevant candidates for spatially explicit modeling that is tied in with dynamical environments. We propose that in order to fully understand the complexities behind plant adaptation, a system that couples aspects from systems biology with population and landscape genetics is required. A suitable system could be represented by spatially explicit individual-based models where the virtual individuals are located within time-variable heterogeneous environments and contain mutable regulatory gene networks. These networks could directly interact with the environment, and should provide a useful approach to studying plant adaptation.

A dynamic and intricate regulatory network determines Pseudomonas aeruginosa virulence

Pseudomonas aeruginosa is a metabolically versatile bacterium that is found in a wide range of biotic and abiotic habitats. It is a major human opportunistic pathogen causing numerous acute and chronic infections. The critical traits contributing to the pathogenic potential of P. aeruginosa are the production of a myriad of virulence factors, formation of biofilms and antibiotic resistance. Expression of these traits is under stringent regulation, and it responds to largely unidentified environmental signals. This review is focused on providing a global picture of virulence gene regulation in P. aeruginosa. In addition to key regulatory pathways that control the transition from acute to chronic infection phenotypes, some regulators have been identified that modulate multiple virulence mechanisms. Despite of a propensity for chaotic behaviour, no chaotic motifs were readily observed in the P. aeruginosa virulence regulatory network. Having a ‘birds-eye’ view of the regulatory cascades provides the forum opportunities to pose questions, formulate hypotheses and evaluate theories in elucidating P. aeruginosa pathogenesis. Understanding the mechanisms involved in making P. aeruginosa a successful pathogen is essential in helping devise control strategies.