Structural analysis to determine the core of hypoxia response network

Petri nets and ODEs as complementary methods for comprehensive analysis on an example of the ATM-p53-NF-[Formula: see text]B signaling pathways

Intracellular processes are cascades of biochemical reactions, triggered in response to various types of stimuli. Mathematical models describing their dynamics have become increasingly popular in recent years, as tools supporting experimental work in analysis of pathways and regulatory networks. Not only do they provide insights into general properties of these systems, but also help in specific tasks, such as search for drug molecular targets or treatment protocols. Different tools and methods are used to model complex biological systems. In this work, we focus on ordinary differential equations (ODEs) and Petri nets. We consider specific methods of analysis of such models, i.e., sensitivity analysis (SA) and significance analysis. So far, they have been applied separately, with different goals. In this paper, we show that they can complement each other, combining the sensitivity of ODE models and the significance analysis of Petri nets. The former is used to find parameters, whose change results in the greatest quantitative and qualitative changes in the model response, while the latter is a structural analysis and allows indicating the most important subprocesses in terms of information flow in Petri net. Ultimately, both methods facilitate finding the essential processes in a given signaling pathway or regulatory network and may be used to support medical therapy development. In the paper, the use of dual modeling is illustrated with an example of ATM/p53/NF-[Formula: see text]B pathway. Each method was applied to analyze this system, resulting in finding different subsets of important processes that might be prospective targets for changing this system behavior. While some of the processes were indicated in each of the approaches, others were found by one method only and would be missed if only that method was applied. This leads to the conclusion about the complementarity of the methods under investigation. The dual modeling approach of comprehensive structural and parametric analysis yields results that would not be possible if these two modeling approaches were applied separately. The combined approach, proposed in this paper, facilitates finding not only key processes, with which significant parameters are associated, but also significant modules, corresponding to subsystems of regulatory networks. The results provide broader insight into therapy targets in diseases in which the natural control of intracellular processes is disturbed, leading to the development of more effective therapies in medicine.

A structural analysis of the hypoxia response network

Background

The hypoxia-inducible factor-1 (HIF-1) signaling pathway is an important topic in high-altitude medicine. Network analysis is a novel method for integrating information on different aspects and levels of biological networks. However, this method has not been used in research on the HIF-1 signaling pathway network. To introduce this method into HIF-1-related research fields and verify its feasibility and effectiveness, we used a network analytical method to explore the structural attributes of the HIF-1 signaling pathway network.

Methods

First, we analyzed the overall network of the HIF-1 signaling pathway using information retrieved from the Kyoto Encyclopedia of Genes and Genomes (KEGG). We performed topology analysis, centrality analysis, and subgroup analysis of the network. Then, we analyzed the core network based on the overall network analysis. We analyzed the properties of the topology, the bow-tie structure, and the structural complexity of the core network.

Results

We obtained topological structure diagrams and quantitative indicators of the overall and core networks of the HIF-1 signaling pathway. For the structure diagrams, we generated topology diagrams of the network and the bow-tie structure of the core network. As quantitative indicators, we identified topology, centrality, subgroups, the bow-tie structure, and structural complexity. The topology indicators were the number of nodes, the number of lines, the network diameter, and the network density. The centrality indicators were the degree, closeness, and betweenness. The cohesive subgroup indicator was the components of the network. The bow-tie structure indicators included the core, input, and tendril-like structures. The structural complexity indicators included a power-law fitting model and its scale parameter.

Conclusions

The core network could be extracted based on the subgroup analysis of the overall network of the HIF-1 signaling pathway. The critical elements of the network could be identified in the centrality analysis. The results of the study show the feasibility and effectiveness of the network analytical method used to explore the network properties of the HIF-1 signaling pathway and provide support for further research.

Identification and analysis of hub genes and networks related to hypoxia preconditioning in mice (No 035215)

Hypoxia preconditioning is an effective strategy of intrinsic cell protection. An acute repetitive hypoxic mice model was developed. High-throughput microarray analysis was performed to explore the integrative alterations of gene expression in repetitive hypoxic mice. Data obtained was analyzed via multiple bioinformatics approaches to identify the hub genes, pathways and biological processes related to hypoxia preconditioning. The current study, for the first time, provides insights into the gene expression profiles in repetitive hypoxic mice. It was found that a total of 1175 genes expressed differentially between the hypoxic mice and normal mice. Overall, 113 significantly up-regulated and 138 significantly down-regulated functions were identified from the differentially expressed genes in repetitive hypoxic brains. Among them, at least fourteen of these genes were very associated with hypoxia preconditioning. The change trends of these genes were validated by reverse-transcription polymerase chain reaction and were found to be consistent with the microarray data. Combined the results of pathway and gene co-expression networks, we defined Plcb1, Cacna2d1, Atp2b4, Grin2a, Grin2b and Glra1 as the main hub genes tightly related with hypoxia preconditioning. The differential functions mainly included the mitogen-activated protein kinase pathway and ion or neurotransmitter transport. The multiple reactions in cell could be initiated by activating MAPK pathway to prevent hypoxia damage. Plcb1 was an important and hub gene and node in the hypoxia preconditioning signal networks. The findings in the hub genes and integrated gene networks provide very useful information for further exploring the molecular mechanisms of hypoxia preconditioning.

Stochastic Petri Net Modeling of Hypoxia Pathway Predicts a Novel Incoherent Feed-Forward Loop Controlling SDF-1 Expression in Acute Kidney Injury

Homing of stem cells to the sites of injury is crucial for tissue regeneration. Stromal derived factor 1 (SDF-1) is among the most important chemokines recruiting these cells. Unexpectedly, our previous experimental data on mouse models of acute kidney injury showed that SDF-1 has a declining trend following ischemic kidney insult. To describe this unforeseen observation, a stochastic Petri net model of SDF-1 regulation in the hypoxia pathway was constructed based on main related components extracted from literature. Using this strategy, predictions regarding the underlying mechanisms of SDF-1 kinetics are generated and a novel incoherent feed forward loop regulating SDF-1 expression is proposed. The computational approach suggested here can be exploited to propose novel therapies for debilitating disorders such as kidney injury.

Role of compartmentalization on HiF-1α degradation dynamics during changing oxygen conditions: a computational approach

HiF-1α is the central protein driving the cellular response to hypoxia. Its accumulation in cancer cells is linked to the appearance of chemoresistant and aggressive tumor phenotypes. As a consequence, understanding the regulation of HiF-1α dynamics is a major issue to design new anti-cancer therapies. In this paper, we propose a model of the hypoxia pathway, involving HiF-1α and its inhibitor pVHL. Based on data from the literature, we made the hypothesis that the regulation of HiF-1α involves two compartments (nucleus and cytoplasm) and a constitutive shuttle of the pVHL protein between them. We first show that this model captures correctly the main features of HiF-1α dynamics, including the bi-exponential degradation profile in normoxia, the kinetics of induction in hypoxia, and the switch-like accumulation. Second, we simulated the effects of a hypoxia/reoxygenation event, and show that it generates a strong instability of HiF-1α. The protein concentration rapidly increases 3 hours after the reoxygenation, and exhibits an oscillating pattern. This effect vanishes if we do not consider compartmentalization of HiF-1α. This result can explain various counter-intuitive observations about the specific molecular and cellular response to the reoxygenation process. Third, we simulated the HiF-1α dynamics in the tumor case. We considered different types of mutations associated with tumorigenesis, and we compared their consequences on HiF-1α dynamics. Then, we tested different therapeutics strategies. We show that a therapeutic decrease of HiF-1α nuclear level is not always correlated with an attenuation of reoxygenation-induced instabilities. Thus, it appears that the design of anti-HiF-1α therapies have to take into account these two aspects to maximize their efficiency.

Design and analysis of a Petri net model of the Von Hippel-Lindau (VHL) tumor suppressor interaction network

Von Hippel-Lindau (VHL) syndrome is a hereditary condition predisposing to the development of different cancer forms, related to germline inactivation of the homonymous tumor suppressor pVHL. The best characterized function of pVHL is the ubiquitination dependent degradation of Hypoxia Inducible Factor (HIF) via the proteasome. It is also involved in several cellular pathways acting as a molecular hub and interacting with more than 200 different proteins. Molecular details of pVHL plasticity remain in large part unknown. Here, we present a novel manually curated Petri Net (PN) model of the main pVHL functional pathways. The model was built using functional information derived from the literature. It includes all major pVHL functions and is able to credibly reproduce VHL syndrome at the molecular level. The reliability of the PN model also allowed in silico knockout experiments, driven by previous model analysis. Interestingly, PN analysis suggests that the variability of different VHL manifestations is correlated with the concomitant inactivation of different metabolic pathways.

Petri nets in Snoopy: a unifying framework for the graphical display, computational modelling, and simulation of bacterial regulatory networks

Using the example of phosphate regulation in enteric bacteria, we demonstrate the particular suitability of stochastic Petri nets to model biochemical phenomena and their simulative exploration by various features of the software tool Snoopy.

A unique transformation from ordinary differential equations to reaction networks

Many models in Systems Biology are described as a system of Ordinary Differential Equations, which allows for transient, steady-state or bifurcation analysis when kinetic information is available. Complementary structure-related qualitative analysis techniques have become increasingly popular in recent years, like qualitative model checking or pathway analysis (elementary modes, invariants, flux balance analysis, graph-based analyses, chemical organization theory, etc.). They do not rely on kinetic information but require a well-defined structure as stochastic analysis techniques equally do. In this article, we look into the structure inference problem for a model described by a system of Ordinary Differential Equations and provide conditions for the uniqueness of its solution. We describe a method to extract a structured reaction network model, represented as a bipartite multigraph, for example, a continuous Petri net (CPN), from a system of Ordinary Differential Equations (ODEs). A CPN uniquely defines an ODE, and each ODE can be transformed into a CPN. However, it is not obvious under which conditions the transformation of an ODE into a CPN is unique, that is, when a given ODE defines exactly one CPN. We provide biochemically relevant sufficient conditions under which the derived structure is unique and counterexamples showing the necessity of each condition. Our method is implemented and available; we illustrate it on some signal transduction models from the BioModels database. A prototype implementation of the method is made available to modellers at http://contraintes.inria.fr/~soliman/ode2pn.html, and the data mentioned in the “Results” section at http://contraintes.inria.fr/~soliman/ode2pn_data/. Our results yield a new recommendation for the import/export feature of tools supporting the SBML exchange format.