Quasi-Steady-State Analysis based on Structural Modules and Timed Petri Net Predict System's Dynamics: The Life Cycle of the Insulin Receptor

Holistic View on the Structure of Immune Response: Petri Net Model

The simulation of immune response is a challenging task because quantitative data are scarce. Quantitative theoretical models either focus on specific cell-cell interactions or have to make assumptions about parameters. The broad variation of, e.g., the dimensions and abundance between lymph nodes as well as between individual patients hampers conclusive quantitative modeling. No theoretical model has been established representing a consensus on the set of major cellular processes involved in the immune response. In this paper, we apply the Petri net formalism to construct a semi-quantitative mathematical model of the lymph nodes. The model covers the major cellular processes of immune response and fulfills the formal requirements of Petri net models. The intention is to develop a model taking into account the viewpoints of experienced pathologists and computer scientists in the field of systems biology. In order to verify formal requirements, we discuss invariant properties and apply the asynchronous firing rule of a place/transition net. Twenty-five transition invariants cover the model, and each is assigned to a functional mode of the immune response. In simulations, the Petri net model describes the dynamic modes of the immune response, its adaption to antigens, and its loss of memory.

Nets-within-nets for modeling emergent patterns in ontogenetic processes

Ontogenesis is the development of an organism from its earliest stage to maturity, including homeostasis maintenance throughout adulthood despite environmental perturbations. Almost all cells of a multicellular organism share the same genomic information. Nevertheless, phenotypic diversity and complex supra-cellular architectures emerge at every level, starting from tissues and organs. This is possible thanks to a robust and dynamic interplay of regulative mechanisms. To study ontogenesis, it is necessary to consider different levels of regulation, both genetic and epigenetic. Each cell undergoes a specific path across a landscape of possible regulative states affecting both its structure and its functions during development. This paper proposes using the Nets-Within-Nets formalism, which combines Petri Nets' simplicity with the capability to represent and simulate the interplay between different layers of regulation connected by non-trivial and context-dependent hierarchical relations. In particular, this work introduces a modeling strategy based on Nets-Within-Nets that can model several critical processes involved in ontogenesis. Moreover, it presents a case study focusing on the first phase of Vulval Precursor Cells specification in C.Elegans. The case study shows that the proposed model can simulate the emergent morphogenetic pattern corresponding to the observed developmental outcome of that phase, in both the physiological case and different mutations. The model presented in the results section is available online at https://github.com/sysbio-polito/NWN_CElegans_VPC_model/.

A Stochastic Petri Net-Based Model of the Involvement of Interleukin 18 in Atherosclerosis

Interleukin 18 (IL-18) is a proinflammatory and proatherogenic cytokine with pleiotropic properties, which is involved in T and NK cell maturation and the synthesis of other inflammatory cytokines and cell adhesion molecules. It plays a significant role in orchestrating the cytokine cascade, accelerates atherosclerosis and influences plaque vulnerability. To investigate the influence of IL-18 cytokine on atherosclerosis development, a stochastic Petri net model was built and then analyzed. First, MCT-sets and t-clusters were generated, then knockout and simulation-based analysis was conducted. The application of systems approach that was used in this research enabled an in-depth analysis of the studied phenomenon. Our results gave us better insight into the studied phenomenon and allow revealing that activation of macrophages by the classical pathway and IL-18-MyD88 signaling axis is crucial for the modeled process.

Deciphering the expression dynamics of ANGPTL8 associated regulatory network in insulin resistance using formal modelling approaches

ANGPTL8 is a recently identified novel hormone which regulates both glucose and lipid metabolism. The increase in ANGPTL8 during compensatory insulin resistance has been recently reported to improve glucose tolerance and a part of cytoprotective metabolic circuit. However, the exact signalling entities and dynamics involved in this process have remained elusive. Therefore, the current study was conducted with a specific aim to model the regulation of ANGPTL8 with emphasis on its role in improving glucose tolerance during insulin resistance. The main contribution of this study is the construction of a discrete model (based on kinetic logic of René Thomas) and its equivalent Stochastic Petri Net model of ANGPTL8 associated Biological Regulatory Network (BRN) which can predict its dynamic behaviours. The predicted results of these models are in‐line with the previous experimental observations and provide comprehensive insights into the signalling dynamics of ANGPTL8 associated BRN. The authors’ results support the hypothesis that ANGPTL8 plays an important role in supplementing the insulin signalling pathway during insulin resistance and its loss can aggravate the pathogenic process by quickly leading towards Diabetes Mellitus. The results of this study have potential therapeutic implications for treatment of Diabetes Mellitus and are suggestive of its potential as a glucose‐lowering agent.

Manatee invariants reveal functional pathways in signaling networks

Background

Signal transduction pathways are important cellular processes to maintain the cell’s integrity. Their imbalance can cause severe pathologies. As signal transduction pathways feature complex regulations, they form intertwined networks. Mathematical models aim to capture their regulatory logic and allow an unbiased analysis of robustness and vulnerability of the signaling network. Pathway detection is yet a challenge for the analysis of signaling networks in the field of systems biology. A rigorous mathematical formalism is lacking to identify all possible signal flows in a network model.

Results

In this paper, we introduce the concept of Manatee invariants for the analysis of signal transduction networks. We present an algorithm for the characterization of the combinatorial diversity of signal flows, e.g., from signal reception to cellular response. We demonstrate the concept for a small model of the TNFR1-mediated NF- κB signaling pathway. Manatee invariants reveal all possible signal flows in the network. Further, we show the application of Manatee invariants for in silico knockout experiments. Here, we illustrate the biological relevance of the concept.

Conclusions

The proposed mathematical framework reveals the entire variety of signal flows in models of signaling systems, including cyclic regulations. Thereby, Manatee invariants allow for the analysis of robustness and vulnerability of signaling networks. The application to further analyses such as for in silico knockout was shown. The new framework of Manatee invariants contributes to an advanced examination of signaling systems.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0448-7) contains supplementary material, which is available to authorized users.

In Silico Knockout Studies of Xenophagic Capturing of Salmonella

The degradation of cytosol-invading pathogens by autophagy, a process known as xenophagy, is an important mechanism of the innate immune system. Inside the host, Salmonella Typhimurium invades epithelial cells and resides within a specialized intracellular compartment, the Salmonella-containing vacuole. A fraction of these bacteria does not persist inside the vacuole and enters the host cytosol. Salmonella Typhimurium that invades the host cytosol becomes a target of the autophagy machinery for degradation. The xenophagy pathway has recently been discovered, and the exact molecular processes are not entirely characterized. Complete kinetic data for each molecular process is not available, so far. We developed a mathematical model of the xenophagy pathway to investigate this key defense mechanism. In this paper, we present a Petri net model of Salmonella xenophagy in epithelial cells. The model is based on functional information derived from literature data. It comprises the molecular mechanism of galectin-8-dependent and ubiquitin-dependent autophagy, including regulatory processes, like nutrient-dependent regulation of autophagy and TBK1-dependent activation of the autophagy receptor, OPTN. To model the activation of TBK1, we proposed a new mechanism of TBK1 activation, suggesting a spatial and temporal regulation of this process. Using standard Petri net analysis techniques, we found basic functional modules, which describe different pathways of the autophagic capture of Salmonella and reflect the basic dynamics of the system. To verify the model, we performed in silico knockout experiments. We introduced a new concept of knockout analysis to systematically compute and visualize the results, using an in silico knockout matrix. The results of the in silico knockout analyses were consistent with published experimental results and provide a basis for future investigations of the Salmonella xenophagy pathway.