All living cells interact with and respond to their environment via the cellular signal-transduction network. This network encompasses all cellular components and processes that are required to receive, transmit and interpret information. Due to its key role in cellular physiology, the signalling network, and several of its subnetworks, have been intensely studied in a range of organisms. However, such networks are highly complex and difficult to analyse due to the so-called combinatorial explosion (Hlavacek et al, 2003
). This explosion refers to the fact that the specific state of each component is determined by multiple covalent modifications or interaction partners, and that these possibilities rapidly combine to a very large number of possible specific states. Experimental data do not generally distinguish between all these specific states, but instead focus mostly on reactions between pairs of components, usually giving no or limited information on other modifications or interaction partners of the reactants. Hence, there is a discrepancy between the granularity of the empirical data and the highly defined specific states used in most mathematical models. This makes the interpretation and use of empirical data in the context of such model states ambiguous and often arbitrary. These problems pose major challenges for systems biology, as they prevent us from (i) unambiguously describing a network, (ii) visualising it without simplifications or unsupported assumptions and (iii) automatically generating mathematical models from knowledge in data repositories.
Large efforts have been invested in addressing these issues. Signalling systems are commonly visualised through the informal ‘biologist's graph' that is simple and intuitive, but lacks the stringent formalism and precision required to meet the three criteria above (exemplified by Thorner et al, 2005
). The lack of standardised glyphs (defining e.g., mechanism of information transfer and how edges combines to regulate target nodes) makes the information in the ‘biologist's graph' ambiguous and difficult to reuse. To address this, the community has developed the Systems Biology Graphical Notation, SBGN (Le Novere et al, 2009
). This includes three visual formats; the activity flow diagram, the entity relationship diagram and the process description (or process diagram). The activity flow diagram shares many properties with the ‘biologist's graph', but the entity relationship diagram and process description allow precise representations. The process description corresponds to the state transition reaction format used in most models developed by the systems biology community, and which have been standardised in the Systems Biology Markup Language (SBML; Hucka et al, 2003
). The process description could meet each of the three criteria above but its utility is severely affected by the combinatorial explosion. It is based on a specific state description, which means that, for each component, each possible combination of modifications and interaction partners must be accounted for explicitly. Hence, only very simple systems can be described completely and only very few models include the entire state space (Kiselyov et al, 2009
) while the vast majority include simplifying omissions. While simplifications are often necessary, the lack of discrimination between arbitrary omissions and exclusions based on experimental evidence is a significant shortcoming. These issues are partially addressed in the entity relationship diagram, or molecular interaction map, which comes in two flavours; explicit and implicit (called heuristic and combinatorial by the author (Kohn et al, 2006
)). The explicit version requires all specific states to be displayed and hence share the limitations of the process description. In contrast, the implicit version displays only the possible reaction types (or elemental reactions, as we will call them below) and hence largely avoids the combinatorial explosion. The entity relationship diagram represents each component as a single node and reactions in a condensed format. While not as intuitive as the other SBGN formats, it has the advantage of concentrating all information on a given protein and works especially well for simple regulatory circuits, as the concentrated information makes it difficult to trace the order of events in more complex networks. The three SBGN format has complementary strengths, but there is currently no software available for conversion between the three different visualisation formats. However, the SBGN standards are under continuous development and these issues will likely be addressed in the future through the SBGN markup language, SBGN-ML.
Similar efforts on the modelling side have resulted in rule-based modelling and associated visualisation formats (Faeder et al, 2005
). Briefly, rules are defined as reactions that are valid under a particular set of contingencies, and each reaction is specified for each such contingency set. This means that when a reaction's rate is increased by phosphorylation of one component it will be defined by two rules; one where that component is phosphorylated and one where it is not. While these rules define the entire state space and the system stays subject to the full combinatorial explosion, the rule description has alleviated the combinatorial problem in two respects: (1) the system has been described more compactly and (2) the actualised state space might be significantly reduced by introducing only those states that are actually populated (Lok and Brent, 2005
), or by using agent-based stochastic modelling (Sneddon et al, 2011
). The rule definition format is also a significant step towards the granularity of empirical data, as compared with the abstract-specific states. These advantages are mirrored on the visualisation side by graphical reaction rules, which use the process description format to display individual rules (Blinov et al, 2006
). Network level visualisation has used either topological contact maps (Danos, 2007
) or entity relationship diagrams (Le Novere et al, 2009
), and these complementary visualisation formats have recently been combined in the extended contact map (Chylek et al, 2011
). Contact maps have software support, but neither entity relationship diagrams nor extended contact maps can be generated automatically from the rule-based models. Hence, the rule-based format partially addresses the automatic creation of models from data repositories (iii), as it provides the tools to generate mathematical models automatically once the knowledge has been reformulated as rules. However, the rule-based system provides a cumbersome format for (i) unambiguous network description and is not developed for (ii) comprehensive visualisations. Taken together, this raises the question whether graphical- and model-based formats are the most appropriate for stringent network definition, or whether there are more suitable network definition formats that allow both visualisation and automatic model generation.
Here, we present a new framework to describe cellular signal-transduction networks. Our network definition has the same granularity as experimental data, avoids the combinatorial complexity, can be automatically visualised in complementary graphical formats including all three SBGN formats and unambiguously defines mathematical models. The rxncon software tool complements the framework by automating visualisation and model creation. The key feature of our framework is the strict separation of elemental reactions (and their corresponding states); which defines the possible signalling events in the network, from contingencies; which describes the contextual constrains on these reactions. Importantly, each elemental reaction corresponds directly to a single empirical observation, such as a protein–protein interaction or a specific phosphorylation. The contingencies define the constraints on these elemental reactions in terms of one or more elemental states, for example, by defining the active state of a protein kinase or the composition of a functional protein complex. Hence, the format directly link model states to empirical observations at the same level of granularity, which pre-empts the need for additional assumptions or extrapolations. Moreover, the separation between reactions and contingencies largely avoids the combinatorial explosion as only combinatorial states with known functional influence are considered. The rxncon tool provides automatic export to established visual formats and to two new visualisation methods, which allow compact comprehensive representation. Finally, the framework is stringent and unambiguously defines a mathematical model, and the rxncon tool support export to SBML and rule- or agent-based models. This allows coding of models in a format that mirrors empirical data, which can be automatically visualised and which is highly suitable for iterative model building. We illustrate our new approach by conducting the most comprehensive literature survey to date of the complete MAP kinase signalling network of Saccharomyces cerevisiae. Taken together, we provide a framework that integrates the three levels of network analysis; definition, visualisation and mathematical modelling and a supporting software tool for automatic visualisation and export to mathematical models. We expect this to be highly useful for the community and envision a common framework to bridge different standards as well as experimental and theoretical systems biology efforts.