Manatee invariants reveal functional pathways in signaling networks

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.

Mathematical modeling of the molecular switch of TNFR1-mediated signaling pathways applying Petri net formalism and in silico knockout analysis

The paper describes a mathematical model of the molecular switches of cell survival, apoptosis, and necroptosis in cellular signaling pathways initiated by tumor necrosis factor 1. Based on experimental findings in the literature, we constructed a Petri net model based on detailed molecular reactions of the molecular players, protein complexes, post-translational modifications, and cross talk. The model comprises 118 biochemical entities, 130 reactions, and 299 edges. We verified the model by evaluating invariant properties of the system at steady state and by in silico knockout analysis. Applying Petri net analysis techniques, we found 279 pathways, which describe signal flows from receptor activation to cellular response, representing the combinatorial diversity of functional pathways.120 pathways steered the cell to survival, whereas 58 and 35 pathways led to apoptosis and necroptosis, respectively. For 65 pathways, the triggered response was not deterministic and led to multiple possible outcomes. We investigated the in silico knockout behavior and identified important checkpoints of the TNFR1 signaling pathway in terms of ubiquitination within complex I and the gene expression dependent on NF-κB, which controls the caspase activity in complex II and apoptosis induction. Despite not knowing enough kinetic data of sufficient quality, we estimated system’s dynamics using a discrete, semi-quantitative Petri net model.

It is still a challenge to develop mechanistic models for big molecular systems without the knowledge of enough kinetic parameters of sufficient quality. At the same time, more qualitative and semi-quantitative data have been produced in increasing numbers, e.g., by new high-throughput technologies. This has generated demands for new concepts at appropriate abstraction levels. The Petri net formalism enables the integration of qualitative as well as quantitative data and provides algorithms and methods for model verification and model simulation. Moreover, Petri nets exhibit a clear and coherent visualization. Here, we modeled the molecular switches between cell survival, apoptosis, and necroptosis induced by tumor necrosis factor 1. We were interested not only in an exhaustive exploration of all possible signaling pathways, but also in finding the system’s checkpoints. Our Petri net model comprises 118 biochemical entities, 130 reactions, and 299 edges. We found 279 pathways that describe signal flows from receptor activation to cellular response.120 pathways steered the cell to survival, whereas 58 and 35 pathways led to apoptosis and necroptosis, respectively. For 65 pathways, the triggered response was not deterministic, leading to multiple possible outcomes. We applied in silico knockout analyses to the Petri net model and could identify important checkpoints of the tumor necrosis factor 1 signaling pathway.

The canonical and non-canonical NF-κB pathways and their crosstalk: A comparative study based on Petri nets

NF-κB is a protein complex that occurs in almost all animal cell types. It regulates the cellular immune responses to stimuli in the nucleus. Dysregulation of NF-κB can cause severe diseases like chronic inflammation, autoimmune diseases or cancer. We modeled the two major pathways leading from the external cellular stimulation of the CD40 receptor to the nuclear translocation of NF-κB dimers, the canonical and non-canonical pathway. Based on literature data, we developed two Petri net models describing these pathways. In a third Petri net, we combined the two models, introducing crosstalk specific in CD40L-stimulated B cells. In terms of structural properties, we checked the Petri nets for their consistency and correctness. To explore differences and similarities, we compared structural properties and the simulation behavior of the models. The non-canonical NF-κB pathway exhibited a more diverse regulation than the canonical pathway. Applying in silico knockout analyses, we were able to quantify the relevance of individual biochemical processes. We predicted interrelationships, e.g., between the synthesis of the protein NF-κB-inducing kinase and the processing of the precursor protein p100. The activation of the transcription factors, p50-RelA and p52-RelB, was affected by most of the knockouts. The results of the in silico knockout were in accordance with experimental studies. The Petri net models provide a basis for further analyses and could be extended to include gene expression, additional pathways, molecular processes, and kinetic data.

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.