Boolean Modelingof Genetic Regulatory Networks

Theoretical and computational tools to model multistable gene regulatory networks

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. It also includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and 'classical' systems typically studied in non-equilibrium statistical and quantum mechanics.

A computational investigation of cis-gene regulation in evolution

In biological processes involving gene networks, genes regulate other genes that determine the phenotypic traits. Gene regulation plays an important role in evolutionary dynamics. In a genetic algorithm, a trans-gene regulatory mechanism was shown to speed up adaptation and evolution. Here, we examine the effect of cis-gene regulation on an adaptive system. The model is haploid. A chromosome is partitioned into regulatory loci and structural loci. The regulatory genes regulate the expression and functioning of structural genes via the cis-elements in a probabilistic manner. In the simulation, the change in the allele frequency, the mean population fitness and the efficiency of phenotypic selection are monitored. Cis-gene regulation increases adaption and accelerates the evolutionary process in comparison with the case involving absence of gene regulation. Some special features of the simulation results are as follows. A low ratio of regulatory loci and structural loci gives higher adaptation for fixed total number of loci. Plasticity is advantageous beyond a threshold value. Adaptation is better for large number of total loci when the ratio of regulatory loci to structural loci is one. However, it reaches a saturation beyond which the increase in the total loci is not advantageous. Efficiency of the phenotypic selection is higher for larger value of the initial plasticity.

Gene regulatory networks exhibit several kinds of memory: quantification of memory in biological and random transcriptional networks

Gene regulatory networks (GRNs) process important information in developmental biology and biomedicine. A key knowledge gap concerns how their responses change over time. Hypothesizing long-term changes of dynamics induced by transient prior events, we created a computational framework for defining and identifying diverse types of memory in candidate GRNs. We show that GRNs from a wide range of model systems are predicted to possess several types of memory, including Pavlovian conditioning. Associative memory offers an alternative strategy for the biomedical use of powerful drugs with undesirable side effects, and a novel approach to understanding the variability and time-dependent changes of drug action. We find evidence of natural selection favoring GRN memory. Vertebrate GRNs overall exhibit more memory than invertebrate GRNs, and memory is most prevalent in differentiated metazoan cell networks compared with undifferentiated cells. Timed stimuli are a powerful alternative for biomedical control of complex in vivo dynamics without genomic editing or transgenes.

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Gene regulatory networks' dynamics are modified by transient stimuli

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GRNs have several different types of memory, including associative conditioning

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Evolution favored GRN memory, and differentiated cells have the most memory capacity

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Training GRNs offers a novel biomedical strategy not dependent on genetic rewiring

Parameter estimation of qualitative biological regulatory networks on high performance computing hardware

BACKGROUND

Biological Regulatory Networks (BRNs) are responsible for developmental and maintenance related functions in organisms. These functions are implemented by the dynamics of BRNs and are sensitive to regulations enforced by specific activators and inhibitors. The logical modeling formalism by René Thomas incorporates this sensitivity with a set of logical parameters modulated by available regulators, varying with time. With the increase in complexity of BRNs in terms of number of entities and their interactions, the task of parameters estimation becomes computationally expensive with existing sequential SMBioNET tool. We extend the existing sequential implementation of SMBioNET by using a data decomposition approach using a Java messaging library called MPJ Express. The approach divides the parameters space into different regions and each region is then explored in parallel on High Performance Computing (HPC) hardware.

RESULTS

The performance of the parallel approach is evaluated on BRNs of different sizes, and experimental results on multicore and cluster computers showed almost linear speed-up. This parallel code can be executed on a wide range of concurrent hardware including laptops equipped with multicore processors, and specialized distributed memory computer systems. To demonstrate the application of parallel implementation, we selected a case study of Hexosamine Biosynthetic Pathway (HBP) in cancer progression to identify potential therapeutic targets against cancer. A set of logical parameters were computed for HBP model that directs the biological system to a state of recovery. Furthermore, the parameters also suggest a potential therapeutic intervention that restores homeostasis. Additionally, the performance of parallel application was also evaluated on a network (comprising of 23 entities) of Fibroblast Growth Factor Signalling in Drosophila melanogaster.

CONCLUSIONS

Qualitative modeling framework is widely used for investigating dynamics of biological regulatory networks. However, computation of model parameters in qualitative modeling is computationally intensive. In this work, we presented results of our Java based parallel implementation that provides almost linear speed-up on both multicore and cluster platforms. The parallel implementation is available at https://psmbionet.github.io .

A Novel Data-Driven Boolean Model for Genetic Regulatory Networks

A Boolean model is a simple, discrete and dynamic model without the need to consider the effects at the intermediate levels. However, little effort has been made into constructing activation, inhibition, and protein decay networks, which could indicate the direct roles of a gene (or its synthesized protein) as an activator or inhibitor of a target gene. Therefore, we propose to focus on the general Boolean functions at the subfunction level taking into account the effectiveness of protein decay, and further split the subfunctions into the activation and inhibition domains. As a consequence, we developed a novel data-driven Boolean model; namely, the Fundamental Boolean Model (FBM), to draw insights into gene activation, inhibition, and protein decay. This novel Boolean model provides an intuitive definition of activation and inhibition pathways and includes mechanisms to handle protein decay issues. To prove the concept of the novel model, we implemented a platform using R language, called FBNNet. Our experimental results show that the proposed FBM could explicitly display the internal connections of the mammalian cell cycle between genes separated into the connection types of activation, inhibition and protein decay. Moreover, the method we proposed to infer the gene regulatory networks for the novel Boolean model can be run in parallel and; hence, the computation cost is affordable. Finally, the novel Boolean model and related Fundamental Boolean Networks (FBNs) could show significant trajectories in genes to reveal how genes regulated each other over a given period. This new feature could facilitate further research on drug interventions to detect the side effects of a newly-proposed drug.

Bistability and Asynchrony in a Boolean Model of the L-arabinose Operon in Escherichia coli

The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism for gene repression, and the lack of inducer exclusion by glucose. For 11 out of 12 choices of initial conditions, we use computational algebra and Sage to verify that the state space contains a single fixed point that correctly matches the biology. The final initial condition, medium levels of arabinose and no glucose, successfully predicts the system's bistability. Finally, we compare the state space under synchronous and asynchronous update and see that the former has several artificial cycles that go away under a general asynchronous update.

Principles of dynamical modularity in biological regulatory networks

Intractable diseases such as cancer are associated with breakdown in multiple individual functions, which conspire to create unhealthy phenotype-combinations. An important challenge is to decipher how these functions are coordinated in health and disease. We approach this by drawing on dynamical systems theory. We posit that distinct phenotype-combinations are generated by interactions among robust regulatory switches, each in control of a discrete set of phenotypic outcomes. First, we demonstrate the advantage of characterizing multi-switch regulatory systems in terms of their constituent switches by building a multiswitch cell cycle model which points to novel, testable interactions critical for early G2/M commitment to division. Second, we define quantitative measures of dynamical modularity, namely that global cell states are discrete combinations of switch-level phenotypes. Finally, we formulate three general principles that govern the way coupled switches coordinate their function.

In Silico Gene Regulatory Network of the Maurer's Cleft Pathway in Plasmodium falciparum

The Maurer's clefts (MCs) are very important for the survival of Plasmodium falciparum within an infected cell as they are induced by the parasite itself in the erythrocyte for protein trafficking. The MCs form an interesting part of the parasite's biology as they shed more light on how the parasite remodels the erythrocyte leading to host pathogenesis and death. Here, we predicted and analyzed the genetic regulatory network of genes identified to belong to the MCs using regularized graphical Gaussian model. Our network shows four major activators, their corresponding target genes, and predicted binding sites. One of these master activators is the serine repeat antigen 5 (SERA5), predominantly expressed among the SERA multigene family of P. falciparum, which is one of the blood-stage malaria vaccine candidates. Our results provide more details about functional interactions and the regulation of the genes in the MCs’ pathway of P. falciparum.

Time-Delayed Models of Gene Regulatory Networks

We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.

Complex regulation of Hsf1-Skn7 activities by the catalytic subunits of PKA in Saccharomyces cerevisiae: experimental and computational evidences

Background

The cAMP-dependent protein kinase regulatory network (PKA-RN) regulates metabolism, memory, learning, development, and response to stress. Previous models of this network considered the catalytic subunits (CS) as a single entity, overlooking their functional individualities. Furthermore, PKA-RN dynamics are often measured through cAMP levels in nutrient-depleted cells shortly after being fed with glucose, dismissing downstream physiological processes.

Results

Here we show that temperature stress, along with deletion of PKA-RN genes, significantly affected HSE-dependent gene expression and the dynamics of the PKA-RN in cells growing in exponential phase. Our genetic analysis revealed complex regulatory interactions between the CS that influenced the inhibition of Hsf1/Skn7 transcription factors. Accordingly, we found new roles in growth control and stress response for Hsf1/Skn7 when PKA activity was low (cdc25Δ cells). Experimental results were used to propose an interaction scheme for the PKA-RN and to build an extension of a classic synchronous discrete modeling framework. Our computational model reproduced the experimental data and predicted complex interactions between the CS and the existence of a repressor of Hsf1/Skn7 that is activated by the CS. Additional genetic analysis identified Ssa1 and Ssa2 chaperones as such repressors. Further modeling of the new data foresaw a third repressor of Hsf1/Skn7, active only in theabsence of Tpk2. By averaging the network state over all its attractors, a good quantitative agreement between computational and experimental results was obtained, as the averages reflected more accurately the population measurements.

Conclusions

The assumption of PKA being one molecular entity has hindered the study of a wide range of behaviors. Additionally, the dynamics of HSE-dependent gene expression cannot be simulated accurately by considering the activity of single PKA-RN components (i.e., cAMP, individual CS, Bcy1, etc.). We show that the differential roles of the CS are essential to understand the dynamics of the PKA-RN and its targets. Our systems level approach, which combined experimental results with theoretical modeling, unveils the relevance of the interaction scheme for the CS and offers quantitative predictions for several scenarios (WT vs. mutants in PKA-RN genes and growth at optimal temperature vs. heat shock).

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0185-8) contains supplementary material, which is available to authorized users.

PANET: a GPU-based tool for fast parallel analysis of robustness dynamics and feed-forward/feedback loop structures in large-scale biological networks

It has been a challenge in systems biology to unravel relationships between structural properties and dynamic behaviors of biological networks. A Cytoscape plugin named NetDS was recently proposed to analyze the robustness-related dynamics and feed-forward/feedback loop structures of biological networks. Despite such a useful function, limitations on the network size that can be analyzed exist due to high computational costs. In addition, the plugin cannot verify an intrinsic property which can be induced by an observed result because it has no function to simulate the observation on a large number of random networks. To overcome these limitations, we have developed a novel software tool, PANET. First, the time-consuming parts of NetDS were redesigned to be processed in parallel using the OpenCL library. This approach utilizes the full computing power of multi-core central processing units and graphics processing units. Eventually, this made it possible to investigate a large-scale network such as a human signaling network with 1,609 nodes and 5,063 links. We also developed a new function to perform a batch-mode simulation where it generates a lot of random networks and conducts robustness calculations and feed-forward/feedback loop examinations of them. This helps us to determine if the findings in real biological networks are valid in arbitrary random networks or not. We tested our plugin in two case studies based on two large-scale signaling networks and found interesting results regarding relationships between coherently coupled feed-forward/feedback loops and robustness. In addition, we verified whether or not those findings are consistently conserved in random networks through batch-mode simulations. Taken together, our plugin is expected to effectively investigate various relationships between dynamics and structural properties in large-scale networks. Our software tool, user manual and example datasets are freely available at http://panet-csc.sourceforge.net/.

Artificial neural network inference (ANNI): a study on gene-gene interaction for biomarkers in childhood sarcomas

Objective

To model the potential interaction between previously identified biomarkers in children sarcomas using artificial neural network inference (ANNI).

Method

To concisely demonstrate the biological interactions between correlated genes in an interaction network map, only 2 types of sarcomas in the children small round blue cell tumors (SRBCTs) dataset are discussed in this paper. A backpropagation neural network was used to model the potential interaction between genes. The prediction weights and signal directions were used to model the strengths of the interaction signals and the direction of the interaction link between genes. The ANN model was validated using Monte Carlo cross-validation to minimize the risk of over-fitting and to optimize generalization ability of the model.

Results

Strong connection links on certain genes (TNNT1 and FNDC5 in rhabdomyosarcoma (RMS); FCGRT and OLFM1 in Ewing’s sarcoma (EWS)) suggested their potency as central hubs in the interconnection of genes with different functionalities. The results showed that the RMS patients in this dataset are likely to be congenital and at low risk of cardiomyopathy development. The EWS patients are likely to be complicated by EWS-FLI fusion and deficiency in various signaling pathways, including Wnt, Fas/Rho and intracellular oxygen.

Conclusions

The ANN network inference approach and the examination of identified genes in the published literature within the context of the disease highlights the substantial influence of certain genes in sarcomas.

The role of visual analytics in asthma phenotyping and biomarker discovery

The exponential growth of biomedical data related to diseases such as asthma far exceeds our cognitive abilities to comprehend it for tasks such as biomarker discovery, pathway identification, and molecular-based phenotyping. This chapter discusses the cognitive and task-based reasons for why methods from visual analytics can help in analyzing such large and complex asthma data, and demonstrates how one such approach called network visualization and analysis can be used to reveal important translational insights related to asthma. The demonstration of the method helps to identify the strengths and limitations of network analysis, in addition to areas for future research that can enhance the use of networks to analyze vast and complex biomedical datasets related to diseases such as asthma.

Understanding the sequential activation of Type III and Type VI Secretion Systems in Salmonella typhimurium using Boolean modeling

Background

Three pathogenicity islands, viz. SPI-1 (Salmonella pathogenicity island 1), SPI-2 (Salmonella pathogenicity island 2) and T6SS (Type VI Secretion System), present in the genome of Salmonella typhimurium have been implicated in the virulence of the pathogen. While the regulation of SPI-1 and SPI-2 (both encoding components of the Type III Secretion System - T3SS) are well understood, T6SS regulation is comparatively less studied. Interestingly, inter-connections among the regulatory elements of these three virulence determinants have also been suggested to be essential for successful infection. However, till date, an integrated view of gene regulation involving the regulators of these three secretion systems and their cross-talk is not available.

Results

In the current study, relevant regulatory information available from literature have been integrated into a single Boolean network, which portrays the dynamics of T3SS (SPI-1 and SPI-2) and T6SS mediated virulence. Some additional regulatory interactions involving a two-component system response regulator YfhA have also been predicted and included in the Boolean network. These predictions are aimed at deciphering the effects of osmolarity on T6SS regulation, an aspect that has been suggested in earlier studies, but the mechanism of which was hitherto unknown. Simulation of the regulatory network was able to recreate in silico the experimentally observed sequential activation of SPI-1, SPI-2 and T6SS.

Conclusions

The present study integrates relevant gene regulatory data (from literature and our prediction) into a single network, representing the cross-communication between T3SS (SPI-1 and SPI-2) and T6SS. This holistic view of regulatory interactions is expected to improve the current understanding of pathogenesis of S. typhimurium.

A two-scale mathematical model for DNA transcription

Unlike the earlier description of regulation of DNA transcription as a biological switch which simply turns on and off, scientists now understand that DNA transcription is a much more complex process. It can depend on several transcription factors (proteins) and DNA regulatory elements (transcription factor binding sites). The combination of these two groups of different scaled factors determines the transcription outcome. In this paper, we propose a two-scale mathematical model for the DNA transcription processes, which integrates the characteristics of both transcription factors and DNA cis-regulatory elements. The model was tested on a well designed synthetic system during early development stage of Drosophila embryo. The system involves three transcription factors (two activators and one repressor) and a reporter gene. The predicted results using the model were compared with the real experimental data using both graphical methods and statistical methods. Parameter estimation will also be discussed in the paper.

"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis

Background

In Thomas' formalism for modeling gene regulatory networks (GRNs), branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a) asynchrony, (b) incompletely specified behavior, and (c) interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulators, because infinitely many paths may appear, limiting ordinary simulators to statistical conclusions. Model checkers for branching time, by contrast, are able to prove properties in the presence of infinitely many paths.

Results

We have developed Antelope ("Analysis of Networks through TEmporal-LOgic sPEcifications", http://turing.iimas.unam.mx:8080/AntelopeWEB/), a model checker for analyzing and constructing Boolean GRNs. Currently, software systems for Boolean GRNs use branching time almost exclusively for asynchrony. Antelope, by contrast, also uses branching time for incompletely specified behavior and environment interaction. We show the usefulness of modeling these two phenomena in the development of a Boolean GRN of the Arabidopsis thaliana root stem cell niche.

There are two obstacles to a direct approach when applying model checking to Boolean GRN analysis. First, ordinary model checkers normally only verify whether or not a given set of model states has a given property. In comparison, a model checker for Boolean GRNs is preferable if it reports the set of states having a desired property. Second, for efficiency, the expressiveness of many model checkers is limited, resulting in the inability to express some interesting properties of Boolean GRNs.

Antelope tries to overcome these two drawbacks: Apart from reporting the set of all states having a given property, our model checker can express, at the expense of efficiency, some properties that ordinary model checkers (e.g., NuSMV) cannot. This additional expressiveness is achieved by employing a logic extending the standard Computation-Tree Logic (CTL) with hybrid-logic operators.

Conclusions

We illustrate the advantages of Antelope when (a) modeling incomplete networks and environment interaction, (b) exhibiting the set of all states having a given property, and (c) representing Boolean GRN properties with hybrid CTL.

How cytokines co-occur across asthma patients: from bipartite network analysis to a molecular-based classification

Asthmatic patients are currently classified as either severe or non-severe based primarily on their response to glucocorticoids. However, because this classification is based on a post-hoc assessment of treatment response, it does not inform the rational staging of disease or therapy. Recent studies in other diseases suggest that a classification which includes molecular information could lead to more accurate diagnoses and prediction of treatment response. We therefore measured cytokine values in bronchoalveolar lavage (BAL) samples of the lower respiratory tract obtained from 83 asthma patients, and used bipartite network visualizations with associated quantitative measures to conduct an exploratory analysis of the co-occurrence of cytokines across patients. The analysis helped to identify three clusters of patients which had a complex but understandable interaction with three clusters of cytokines, leading to insights for a state-based classification of asthma patients. Furthermore, while the patient clusters were significantly different based on key pulmonary functions, they appeared to have no significant relationship to the current classification of asthma patients. These results suggest the need to define a molecular-based classification of asthma patients, which could improve the diagnosis and treatment of this disease.

Discovering hidden relationships between renal diseases and regulated genes through 3D network visualizations

Background

In a recent study, two-dimensional (2D) network layouts were used to visualize and quantitatively analyze the relationship between chronic renal diseases and regulated genes. The results revealed complex relationships between disease type, gene specificity, and gene regulation type, which led to important insights about the underlying biological pathways. Here we describe an attempt to extend our understanding of these complex relationships by reanalyzing the data using three-dimensional (3D) network layouts, displayed through 2D and 3D viewing methods.

Findings

The 3D network layout (displayed through the 3D viewing method) revealed that genes implicated in many diseases (non-specific genes) tended to be predominantly down-regulated, whereas genes regulated in a few diseases (disease-specific genes) tended to be up-regulated. This new global relationship was quantitatively validated through comparison to 1000 random permutations of networks of the same size and distribution. Our new finding appeared to be the result of using specific features of the 3D viewing method to analyze the 3D renal network.

Conclusions

The global relationship between gene regulation and gene specificity is the first clue from human studies that there exist common mechanisms across several renal diseases, which suggest hypotheses for the underlying mechanisms. Furthermore, the study suggests hypotheses for why the 3D visualization helped to make salient a new regularity that was difficult to detect in 2D. Future research that tests these hypotheses should enable a more systematic understanding of when and how to use 3D network visualizations to reveal complex regularities in biological networks.

Inference of gene regulatory networks using boolean-network inference methods

The modeling of genetic networks especially from microarray and related data has become an important aspect of the biosciences. This review takes a fresh look at a specific family of models used for constructing genetic networks, the so-called Boolean networks. The review outlines the various different types of Boolean network developed to date, from the original Random Boolean Network to the current Probabilistic Boolean Network. In addition, some of the different inference methods available to infer these genetic networks are also examined. Where possible, particular attention is paid to input requirements as well as the efficiency, advantages and drawbacks of each method. Though the Boolean network model is one of many models available for network inference today, it is well established and remains a topic of considerable interest in the field of genetic network inference. Hybrids of Boolean networks with other approaches may well be the way forward in inferring the most informative networks.

Network analysis of genes regulated in renal diseases: implications for a molecular-based classification

Background

Chronic renal diseases are currently classified based on morphological similarities such as whether they produce predominantly inflammatory or non-inflammatory responses. However, such classifications do not reliably predict the course of the disease and its response to therapy. In contrast, recent studies in diseases such as breast cancer suggest that a classification which includes molecular information could lead to more accurate diagnoses and prediction of treatment response. This article describes how we extracted gene expression profiles from biopsies of patients with chronic renal diseases, and used network visualizations and associated quantitative measures to rapidly analyze similarities and differences between the diseases.

Results

The analysis revealed three main regularities: (1) Many genes associated with a single disease, and fewer genes associated with many diseases. (2) Unexpected combinations of renal diseases that share relatively large numbers of genes. (3) Uniform concordance in the regulation of all genes in the network.

Conclusion

The overall results suggest the need to define a molecular-based classification of renal diseases, in addition to hypotheses for the unexpected patterns of shared genes and the uniformity in gene concordance. Furthermore, the results demonstrate the utility of network analyses to rapidly understand complex relationships between diseases and regulated genes.

Analysis of feedback loops and robustness in network evolution based on Boolean models

Background

Many biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention.

Results

In this paper, we focus on the robustness of a network that is acquired during its evolutionary process. Through simulations using Boolean network models, we found that preferential attachment increases the number of coupled feedback loops in the course of network evolution. Whereas, if networks evolve to have more coupled feedback loops rather than following preferential attachment, the resulting networks are more robust than those obtained through preferential attachment, although both of them have similar degree distributions.

Conclusion

The presented analysis demonstrates that coupled feedback loops may play an important role in network evolution to acquire robustness. The result also provides a hint as to why various biological networks have evolved to contain a number of coupled feedback loops.