Motivation: To understand the behaviour of complex biological regulatory networks, a proper integration of molecular data into a full-fledge formal dynamical model is ultimately required. As most available data on regulatory interactions are qualitative, logical modelling offers an interesting framework to delineate the main dynamical properties of the underlying networks. Results: Transposing a generic model of the core network controlling the mammalian cell cycle into the logical framework, we compare different strategies to explore its dynamical properties. In particular, we assess the respective advantages and limits of synchronous versus asynchronous updating assumptions to delineate the asymptotical behaviour of regulatory networks. Furthermore, we propose several intermediate strategies to optimize the computation of asymptotical properties depending on available knowledge. Availability: The mammalian cell cycle model is available in a dedicated XML format (GINML) on our website, along with our logical simulation software GINsim (). Higher resolution state transitions graphs are also found on this web site (Model Repository page). Contact: thieffry@ibdm.univ-mrs.fr

Mathematical modelling is increasingly used to get insights into the functioning of complex biological networks. In this context, Petri nets (PNs) have recently emerged as a promising tool among the various methods employed for the modelling and analysis of molecular networks. PNs come with a series of extensions, which allow different abstraction levels, from purely qualitative to more complex quantitative models. Noteworthily, each of these models preserves the underlying graph, which depicts the interactions between the biological components. This article intends to present the basics of the approach and to foster the potential role PNs could play in the development of the computational systems biology.

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction‐based models and packages that extend the core with features suited to other model types including constraint‐based models, reaction‐diffusion models, logical network models, and rule‐based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single‐cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution.

In breast cancer, overexpression of the transmembrane tyrosine kinase ERBB2 is an adverse prognostic marker, and occurs in almost 30% of the patients. For therapeutic intervention, ERBB2 is targeted by monoclonal antibody trastuzumab in adjuvant settings; however, de novo resistance to this antibody is still a serious issue, requiring the identification of additional targets to overcome resistance. In this study, we have combined computational simulations, experimental testing of simulation results, and finally reverse engineering of a protein interaction network to define potential therapeutic strategies for de novo trastuzumab resistant breast cancer. First, we employed Boolean logic to model regulatory interactions and simulated single and multiple protein loss-of-functions. Then, our simulation results were tested experimentally by producing single and double knockdowns of the network components and measuring their effects on G1/S transition during cell cycle progression. Combinatorial targeting of ERBB2 and EGFR did not affect the response to trastuzumab in de novo resistant cells, which might be due to decoupling of receptor activation and cell cycle progression. Furthermore, examination of c-MYC in resistant as well as in sensitive cell lines, using a specific chemical inhibitor of c-MYC (alone or in combination with trastuzumab), demonstrated that both trastuzumab sensitive and resistant cells responded to c-MYC perturbation. In this study, we connected ERBB signaling with G1/S transition of the cell cycle via two major cell signaling pathways and two key transcription factors, to model an interaction network that allows for the identification of novel targets in the treatment of trastuzumab resistant breast cancer. Applying this new strategy, we found that, in contrast to trastuzumab sensitive breast cancer cells, combinatorial targeting of ERBB receptors or of key signaling intermediates does not have potential for treatment of de novo trastuzumab resistant cells. Instead, c-MYC was identified as a novel potential target protein in breast cancer cells.

The logical (or logic) formalism is increasingly used to model regulatory and signaling networks. Complementing these applications, several groups contributed various methods and tools to support the definition and analysis of logical models. After an introduction to the logical modeling framework and to several of its variants, we review here a number of recent methodological advances to ease the analysis of large and intricate networks. In particular, we survey approaches to determine model attractors and their reachability properties, to assess the dynamical impact of variations of external signals, and to consistently reduce large models. To illustrate these developments, we further consider several published logical models for two important biological processes, namely the differentiation of T helper cells and the control of mammalian cell cycle.