Petri net-based method for the analysis of the dynamics of signal propagation in signaling pathways

Network Modeling and Control of Dynamic Disease Pathways, Review and Perspectives

Dynamic disease pathways are a combination of complex dynamical processes among bio-molecules in a cell that leads to diseases. Network modeling of disease pathways considers disease-related bio-molecules (e.g. DNA, RNA, transcription factors, enzymes, proteins, and metabolites) and their interaction (e.g. DNA methylation, histone modification, alternative splicing, and protein modification) to study disease progression and predict therapeutic responses. These bio-molecules and their interactions are the basic elements in the study of the misregulation in the disease-related gene expression that lead to abnormal cellular responses. Gene regulatory networks, cell signaling networks, and metabolic networks are the three major types of intracellular networks for the study of the cellular responses elicited from extracellular signals. The disease-related cellular responses can be prevented or regulated by designing control strategies to manipulate these extracellular or other intracellular signals. The paper reviews the regulatory mechanisms, the dynamic models, and the control strategies for each intracellular network. The applications, limitations and the prospective for modeling and control are also discussed.

Computational modeling of signal transduction networks without kinetic parameters: Petri net approaches

More and more computational techniques have been applied to model biological systems, especially signaling pathways in medical systems. Due to the large number of experimental data driven by high-throughput technologies, new computational concepts have been developed. Nevertheless, often the necessary kinetic data cannot be determined in sufficient number and quality because of experimental complexity or ethical reasons. At the same time, the number of qualitative data drastically increased, for example, gene expression data, protein-protein interaction data, and imaging data. Especially for large-scale models, the application of kinetic modeling techniques can fail. On the other hand, many large-scale models have been constructed applying qualitative and semiquantitative techniques, for example, logical models or Petri net models. These techniques make it possible to explore system's dynamics without knowing kinetic parameters. Here, we summarize the work of the last 10 years for modeling signal transduction pathways in medical applications applying Petri net formalism. We focus on analysis techniques based on system's invariants without any kinetic parameters and show predictions of all signaling pathways of the system. We start with an intuitive introduction into Petri nets and system's invariants. We illustrate the main concepts using the tumor necrosis factor receptor 1 (TNFR1)-induced nuclear factor κ-light-chain-enhancer of activated B cells (NF-κB) pathway as a case study. Summarizing recent models, we discuss the advantages and challenges of Petri net applications to medical signaling systems. In addition, we provide exemplarily interesting Petri net applications to model signaling in medical systems of the last years that use the well-known stochastic and kinetic concepts developed about 50 years ago.

Nucleoside transporters and immunosuppressive adenosine signaling in the tumor microenvironment: Potential therapeutic opportunities

Adenosine compartmentalization has a profound impact on immune cell function by regulating adenosine localization and, therefore, extracellular signaling capabilities, which suppresses immune cell function in the tumor microenvironment. Nucleoside transporters, responsible for the translocation and cellular compartmentalization of hydrophilic adenosine, represent an understudied yet crucial component of adenosine disposition in the tumor microenvironment. In this review article, we will summarize what is known regarding nucleoside transporter's function within the purinome in relation to currently devised points of intervention (i.e., ectonucleotidases, adenosine receptors) for cancer immunotherapy, alterations in nucleoside transporter expression reported in cancer, and potential avenues for targeting of nucleoside transporters for the desired modulation of adenosine compartmentalization and action. Further, we put forward that nucleoside transporters are an unexplored therapeutic opportunity, and modulation of nucleoside transport processes could attenuate the pathogenic buildup of immunosuppressive adenosine in solid tumors, particularly those enriched with nucleoside transport proteins.

Modeling and Simulation of Cell Signaling Networks for Subsequent Analytics Processes Using Big Data and Machine Learning

This work explores how much the traditional approach to modeling and simulation of biological systems, specifically cell signaling networks, can be increased and improved by integrating big data, data mining, and machine learning techniques. Specifically, we first model, simulate, validate, and calibrate the behavior of the PI3K/AKT/mTOR cancer-related signaling pathway. Subsequently, once the behavior of the simulated signaling network matches the expected behavior, the capacity of the computational simulation is increased to grow data (data farming). First, we use big data techniques to extract, collect, filter, and store large volumes of data describing all the interactions among the simulated cell signaling system components over time. Afterward, we apply data mining and machine learning techniques-specifically, exploratory data analysis, feature selection techniques, and supervised neural network models-to the resulting biological dataset to obtain new inferences and knowledge about this biological system. The results showed how the traditional approach to the simulation of biological systems could be enhanced and improved by incorporating big data, data mining, and machine learning techniques, which significantly contributed to increasing the predictive power of the simulation.

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.

A Pathway Analysis Approach Using Petri Net

Perturbation in the normal function of the cell signaling pathways often leads to diseases. One of the factors that help understand the mechanism of diseases is the precise identification and investigation of perturbed signaling pathways. Pathway analysis methods have been developed as their purpose is to identify perturbed signaling pathways in given conditions. Among these methods, some consider the pathways topologies in their analysis, which are referred to as topology-based methods. Most of the topology-based methods used simple graph-based models to incorporate topology in their analysis, which have some limitations. We describe a new Pathway Analysis method using Petri net (PAPet) that uses the Petri net to model the signaling pathways and then propose an algorithm to measure the perturbation on a given pathway under a given condition. Modeling with Petri net has some advantages and could overcome the shortcomings of the simple graph-based models. We illustrate the capabilities of the proposed method using sensitivity, prioritization, mean reciprocal rank, and false-positive rate metrics on 36 real datasets from various diseases. The results of comparing PAPet with five pathway analysis methods FoPA, PADOG, GSEA, CePa and SPIA show that PAPet is the best one that provides a good compromise between all metrics. In addition, the results of applying methods to gene expression profiles in normal and Pancreatic Ductal Adenocarcinoma cancer (PDAC) samples show that the PAPet method achieves the best rank among others in finding the pathways that have been previously reported for PDAC. The PAPet method is available at https://github.com/fmansoori/PAPET.

isiKnock: in silico knockouts in signaling pathways

SUMMARY

isiKnock is a new software that automatically conducts in silico knockouts for mathematical models of signaling pathways. The software allows for the prediction of the behavior of biological systems after single or multiple knockout. The implemented algorithm applies transition invariants and the novel concept of Manatee invariants. A knockout matrix visualizes the results. The tool enables the analysis of dependencies, for example, in signal flows from the receptor activation to the cell response at steady state.

AVAILABILITY AND IMPLEMENTATION

isiKnock is an open-source tool, freely available at http://www.bioinformatik.uni-frankfurt.de/tools/isiKnock/. It requires at least Java 8 and runs under Microsoft Windows, Linux, and Mac OS.

Epidermal Growth Factor Signaling towards Proliferation: Modeling and Logic Inference Using Forward and Backward Search

In biological systems, pathways define complex interaction networks where multiple molecular elements are involved in a series of controlled reactions producing responses to specific biomolecular signals. These biosystems are dynamic and there is a need for mathematical and computational methods able to analyze the symbolic elements and the interactions between them and produce adequate readouts of such systems. In this work, we use rewriting logic to analyze the cellular signaling of epidermal growth factor (EGF) and its cell surface receptor (EGFR) in order to induce cellular proliferation. Signaling is initiated by binding the ligand protein EGF to the membrane-bound receptor EGFR so as to trigger a reactions path which have several linked elements through the cell from the membrane till the nucleus. We present two different types of search for analyzing the EGF/proliferation system with the help of Pathway Logic tool, which provides a knowledge-based development environment to carry out the modeling of the signaling. The first one is a standard (forward) search. The second one is a novel approach based on narrowing, which allows us to trace backwards the causes of a given final state. The analysis allows the identification of critical elements that have to be activated to provoke proliferation.

Using Petri nets for experimental design in a multi-organ elimination pathway

Genistein is a soy metabolite with estrogenic activity that may result in (un)favorable effects on human health. Elucidation of the mechanisms through which food additives such as genistein exert their beneficiary effects is a major challenge for the food industry. A better understanding of the genistein elimination pathway could shed light on such mechanisms. We developed a Petri net model that represents this multi-organ elimination pathway and which assists in the design of future experiments. Using this model we show that metabolic profiles solely measured in venous blood are not sufficient to uniquely parameterize the model. Based on simulations we suggest two solutions that provide better results: parameterize the model using gut epithelium profiles or add additional biological constrains in the model.

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.

An integrated pathway system modeling of Saccharomyces cerevisiae HOG pathway: a Petri net based approach

Biochemical networks comprise many diverse components and interactions between them. It has intracellular signaling, metabolic and gene regulatory pathways which are highly integrated and whose responses are elicited by extracellular actions. Previous modeling techniques mostly consider each pathway independently without focusing on the interrelation of these which actually functions as a single system. In this paper, we propose an approach of modeling an integrated pathway using an event-driven modeling tool, i.e., Petri nets (PNs). PNs have the ability to simulate the dynamics of the system with high levels of accuracy. The integrated set of signaling, regulatory and metabolic reactions involved in Saccharomyces cerevisiae's HOG pathway has been collected from the literature. The kinetic parameter values have been used for transition firings. The dynamics of the system has been simulated and the concentrations of major biological species over time have been observed. The phenotypic characteristics of the integrated system have been investigated under two conditions, viz., under the absence and presence of osmotic pressure. The results have been validated favorably with the existing experimental results. We have also compared our study with the study of idFBA (Lee et al., PLoS Comput Biol 4:e1000-e1086, 2008) and pointed out the differences between both studies. We have simulated and monitored concentrations of multiple biological entities over time and also incorporated feedback inhibition by Ptp2 which has not been included in the idFBA study. We have concluded that our study is the first to the best of our knowledge to model signaling, metabolic and regulatory events in an integrated form through PN model framework. This study is useful in computational simulation of system dynamics for integrated pathways as there are growing evidences that the malfunctioning of the interplay among these pathways is associated with disease.

Network systems biology for targeted cancer therapies

The era of targeted cancer therapies has arrived. However, due to the complexity of biological systems, the current progress is far from enough. From biological network modeling to structural/dynamic network analysis, network systems biology provides unique insight into the potential mechanisms underlying the growth and progression of cancer cells. It has also introduced great changes into the research paradigm of cancer-associated drug discovery and drug resistance.

Modeling formalisms in Systems Biology

Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future.

An enhanced Petri-net model to predict synergistic effects of pairwise drug combinations from gene microarray data

MOTIVATION

Prediction of synergistic effects of drug combinations has traditionally been relied on phenotypic response data. However, such methods cannot be used to identify molecular signaling mechanisms of synergistic drug combinations. In this article, we propose an enhanced Petri-Net (EPN) model to recognize the synergistic effects of drug combinations from the molecular response profiles, i.e. drug-treated microarray data.

METHODS

We addressed the downstream signaling network of the targets for the two individual drugs used in the pairwise combinations and applied EPN to the identified targeted signaling network. In EPN, drugs and signaling molecules are assigned to different types of places, while drug doses and molecular expressions are denoted by color tokens. The changes of molecular expressions caused by treatments of drugs are simulated by two actions of EPN: firing and blasting. Firing is to transit the drug and molecule tokens from one node or place to another, and blasting is to reduce the number of molecule tokens by drug tokens in a molecule node. The goal of EPN is to mediate the state characterized by control condition without any treatment to that of treatment and to depict the drug effects on molecules by the drug tokens.

RESULTS

We applied EPN to our generated pairwise drug combination microarray data. The synergistic predictions using EPN are consistent with those predicted using phenotypic response data. The molecules responsible for the synergistic effects with their associated feedback loops display the mechanisms of synergism.

AVAILABILITY

The software implemented in Python 2.7 programming language is available from request.

CONTACT

stwong@tmhs.org.

Time-dependent structural transformation analysis to high-level Petri net model with active state transition diagram

Background

With an accumulation of in silico data obtained by simulating large-scale biological networks, a new interest of research is emerging for elucidating how living organism functions over time in cells.

Investigating the dynamic features of current computational models promises a deeper understanding of complex cellular processes. This leads us to develop a method that utilizes structural properties of the model over all simulation time steps. Further, user-friendly overviews of dynamic behaviors can be considered to provide a great help in understanding the variations of system mechanisms.

Results

We propose a novel method for constructing and analyzing a so-called active state transition diagram (ASTD) by using time-course simulation data of a high-level Petri net. Our method includes two new algorithms. The first algorithm extracts a series of subnets (called temporal subnets) reflecting biological components contributing to the dynamics, while retaining positive mathematical qualities. The second one creates an ASTD composed of unique temporal subnets. ASTD provides users with concise information allowing them to grasp and trace how a key regulatory subnet and/or a network changes with time. The applicability of our method is demonstrated by the analysis of the underlying model for circadian rhythms in Drosophila.

Conclusions

Building ASTD is a useful means to convert a hybrid model dealing with discrete, continuous and more complicated events to finite time-dependent states. Based on ASTD, various analytical approaches can be applied to obtain new insights into not only systematic mechanisms but also dynamics.

The systems approach to the prespore-specific activation of sigma factor SigF in Bacillus subtilis

The prespore-specific activation of sigma factor SigF (sigma(F)) in Bacillus subtilis has been explained mainly by two factors, i.e., the transient genetic asymmetry and the volume difference between the mother cell and the prespore. Here, we systematically surveyed the effect of these two factors on sporulation using a quantitative modeling and simulation architecture named hybrid functional Petri net with extension (HFPNe). Considering the fact that the transient genetic asymmetry and the volume difference in sporulation of B. subtilis finally bring about the concentration difference in two proteins SpoIIAB (AB) and SpoIIAA (AA) between the mother cell and the prespore, we have surveyed the effect of AB and AA concentration on the prespore-specific activation of sigma(F) occurring in the early stage of sporulation. Our results show that the prespore-specific activation of sigma(F) could be governed by the ratio of AA to AB rather than their concentrations themselves. Our model also suggests that B. subtilis could maximize the ratio of AA to AB in the prespore and minimize it in the mother cell by employing both the transient genetic asymmetry and the volume difference simultaneously. This might give a good explanation to the co-occurrence of the transient asymmetry and the volume difference during sporulation of B. subtilis. In addition, we suggest for the first time that the sigma(F) activation in the prespore might be switched off by the decrease in the ratio of AA to AB after the transient genetic asymmetry is to an end by completion of DNA translocation into the prespore.

The crosstalk between EGF, IGF, and Insulin cell signaling pathways--computational and experimental analysis

BACKGROUND

Cellular response to external stimuli requires propagation of corresponding signals through molecular signaling pathways. However, signaling pathways are not isolated information highways, but rather interact in a number of ways forming sophisticated signaling networks. Since defects in signaling pathways are associated with many serious diseases, understanding of the crosstalk between them is fundamental for designing molecularly targeted therapy. Unfortunately, we still lack technology that would allow high throughput detailed measurement of activity of individual signaling molecules and their interactions. This necessitates developing methods to prioritize selection of the molecules such that measuring their activity would be most informative for understanding the crosstalk. Furthermore, absence of the reaction coefficients necessary for detailed modeling of signal propagation raises the question whether simple parameter-free models could provide useful information about such pathways.

RESULTS

We study the combined signaling network of three major pro-survival signaling pathways: Epidermal Growth Factor Receptor (EGFR), Insulin-like Growth Factor-1 Receptor (IGF-1R), and Insulin Receptor (IR). Our study involves static analysis and dynamic modeling of this network, as well as an experimental verification of the model by measuring the response of selected signaling molecules to differential stimulation of EGF, IGF and insulin receptors. We introduced two novel measures of the importance of a node in the context of such crosstalk. Based on these measures several molecules, namely Erk1/2, Akt1, Jnk, p70S6K, were selected for monitoring in the network simulation and for experimental studies. Our simulation method relies on the Boolean network model combined with stochastic propagation of the signal. Most (although not all) trends suggested by the simulations have been confirmed by experiments.

CONCLUSION

The simple model implemented in this paper provides a valuable first step in modeling signaling networks. However, to obtain a fully predictive model, a more detailed knowledge regarding parameters of individual interactions might be necessary.

Insights into the organization of biochemical regulatory networks using graph theory analyses

Graph theory has been a valuable mathematical modeling tool to gain insights into the topological organization of biochemical networks. There are two types of insights that may be obtained by graph theory analyses. The first provides an overview of the global organization of biochemical networks; the second uses prior knowledge to place results from multivariate experiments, such as microarray data sets, in the context of known pathways and networks to infer regulation. Using graph analyses, biochemical networks are found to be scale-free and small-world, indicating that these networks contain hubs, which are proteins that interact with many other molecules. These hubs may interact with many different types of proteins at the same time and location or at different times and locations, resulting in diverse biological responses. Groups of components in networks are organized in recurring patterns termed network motifs such as feedback and feed-forward loops. Graph analysis revealed that negative feedback loops are less common and are present mostly in proximity to the membrane, whereas positive feedback loops are highly nested in an architecture that promotes dynamical stability. Cell signaling networks have multiple pathways from some input receptors and few from others. Such topology is reminiscent of a classification system. Signaling networks display a bow-tie structure indicative of funneling information from extracellular signals and then dispatching information from a few specific central intracellular signaling nexuses. These insights show that graph theory is a valuable tool for gaining an understanding of global regulatory features of biochemical networks.