Protocol for biomodel engineering of unilevel to multilevel biological models using colored Petri nets

Biological systems inherently span multiple levels, which can pose challenges in spatial representation for modelers. We present a protocol that utilizes colored Petri nets to construct and analyze biological models of systems, encompassing both unilevel and multilevel scenarios. We detail a modeling workflow exploiting the PetriNuts platform comprising a set of tools linked together via common file formats. We describe steps for modeling preparation, component-level modeling and analysis, followed by system-level modeling and analysis, and model use.

Coloured Petri nets for multilevel, multiscale and multidimensional modelling of biological systems

Owing to the availability of data of one biological phenomenon at different levels/scales, modelling of biological systems is moving from single level/scale to multiple levels/scales, which introduces a number of challenges. Coloured Petri nets (ColPNs) have been successfully applied to multilevel, multiscale and multidimensional modelling of some biological systems, addressing many of these challenges. In this article, we first review the basics of ColPNs and some popular extensions, and then their applications for multilevel, multiscale and multidimensional modelling of biological systems. This understanding of how to use ColPNs for modelling biological systems will assist readers in selecting appropriate ColPN classes for specific modelling circumstances.

Response to IL-6 trans- and IL-6 classic signalling is determined by the ratio of the IL-6 receptor α to gp130 expression: fusing experimental insights and dynamic modelling

BACKGROUND

Interleukin-6 is a pleiotropic cytokine with high clinical relevance and an important mediator of cellular communication, orchestrating both pro- and anti-inflammatory processes. Interleukin-6-induced signalling is initiated by binding of IL-6 to the IL-6 receptor α and subsequent binding to the signal transducing receptor subunit gp130. This active receptor complex initiates signalling through the Janus kinase/signal transducer and activator of transcription pathway. Of note, IL-6 receptor α exists in a soluble and a transmembrane form. Binding of IL-6 to membrane-bound IL-6 receptor α induces anti-inflammatory classic signalling, whereas binding of IL-6 to soluble IL-6 receptor α induces pro-inflammatory trans-signalling. Trans-signalling has been described to be markedly stronger than classic signalling. Understanding the molecular mechanisms that drive differences between trans- and classic signalling is important for the design of trans-signalling-specific therapies. These differences will be addressed here using a combination of dynamic mathematical modelling and molecular biology.

METHODS

We apply an iterative systems biology approach using set-based modelling and validation approaches combined with quantitative biochemical and cell biological analyses.

RESULTS

The combination of experimental analyses and dynamic modelling allows to relate the observed differences between IL-6-induced trans- and classic signalling to cell-type specific differences in the expression and ratios of the individual subunits of the IL-6 receptor complex. Canonical intracellular Jak/STAT signalling is indifferent in IL-6-induced trans- and classic signalling.

CONCLUSION

This study contributes to the understanding of molecular mechanisms of IL-6 signal transduction and underlines the power of combined dynamical modelling, model-based validation and biological experiments. The opposing pro- and anti-inflammatory responses initiated by IL-6 trans- and classic signalling depend solely on the expression ratios of the subunits of the entire receptor complex. By pointing out the importance of the receptor expression ratio for the strength of IL-6 signalling this study lays a foundation for future precision medicine approaches that aim to selectively block pro-inflammatory trans-signalling. Furthermore, the derived models can be used for future therapy design.

Robustness and Information Transfer within IL-6-induced JAK/STAT Signalling

Cellular communication via intracellular signalling pathways is crucial. Expression and activation of signalling proteins is heterogenous between isogenic cells of the same cell-type. However, mechanisms evolved to enable sufficient communication and to ensure cellular functions. We use information theory to clarify mechanisms facilitating IL-6-induced JAK/STAT signalling despite cell-to-cell variability. We show that different mechanisms enabling robustness against variability complement each other. Early STAT3 activation is robust as long as cytokine concentrations are low. Robustness at high cytokine concentrations is ensured by high STAT3 expression or serine phosphorylation. Later the feedback-inhibitor SOCS3 increases robustness. Channel Capacity of JAK/STAT signalling is limited by cell-to-cell variability in STAT3 expression and is affected by the same mechanisms governing robustness. Increasing STAT3 amount increases Channel Capacity and robustness, whereas increasing STAT3 tyrosine phosphorylation reduces robustness but increases Channel Capacity. In summary, we elucidate mechanisms preventing dysregulated signalling by enabling reliable JAK/STAT signalling despite cell-to-cell heterogeneity.

BioModelKit - An Integrative Framework for Multi-Scale Biomodel-Engineering

While high-throughput technology, advanced techniques in biochemistry and molecular biology have become increasingly powerful, the coherent interpretation of experimental results in an integrative context is still a challenge. BioModelKit (BMK) approaches this challenge by offering an integrative and versatile framework for biomodel-engineering based on a modular modelling concept with the purpose: (i) to represent knowledge about molecular mechanisms by consistent executable sub-models (modules) given as Petri nets equipped with defined interfaces facilitating their reuse and recombination; (ii) to compose complex and integrative models from an ad hoc chosen set of modules including different omic and abstraction levels with the option to integrate spatial aspects; (iii) to promote the construction of alternative models by either the exchange of competing module versions or the algorithmic mutation of the composed model; and (iv) to offer concepts for (omic) data integration and integration of existing resources, and thus facilitate their reuse. BMK is accessible through a public web interface (www.biomodelkit.org), where users can interact with the modules stored in a database, and make use of the model composition features. BMK facilitates and encourages multi-scale model-driven predictions and hypotheses supporting experimental research in a multilateral exchange.

Integration of Genome Scale Metabolic Networks and Gene Regulation of Metabolic Enzymes With Physiologically Based Pharmacokinetics

The scope of physiologically based pharmacokinetic (PBPK) modeling can be expanded by assimilation of the mechanistic models of intracellular processes from systems biology field. The genome scale metabolic networks (GSMNs) represent a whole set of metabolic enzymes expressed in human tissues. Dynamic models of the gene regulation of key drug metabolism enzymes are available. Here, we introduce GSMNs and review ongoing work on integration of PBPK, GSMNs, and metabolic gene regulation. We demonstrate example models.

Fuzzy Stochastic Petri Nets for Modeling Biological Systems with Uncertain Kinetic Parameters

Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information.

Systems biology of IL-6, IL-12 family cytokines

Interleukin-6-type cytokines play important roles in the communication between cells of multicellular organisms. They are involved in the regulation of complex cellular processes such as proliferation and differentiation and act as key player during inflammation and immune response. A major challenge is to understand how these complex non-linear processes are connected and regulated. Systems biology approaches are used to tackle this challenge in an iterative process of quantitative experimental and mathematical analyses. Here we review quantitative experimental studies and systems biology approaches dealing with the function of Interleukin-6-type cytokines in physiological and pathophysiological conditions. These approaches cover the analyses of signal transduction on a cellular level up to pharmacokinetic and pharmacodynamic studies on a whole organism level.

An introduction to systems toxicology

Systems toxicology combines novel and historical experimental data to generate increasingly complex models of the biological response to chemical exposure.