Narrative Modelling Language
For modelling the gp130/JAK/STAT pathway, we use the Narrative Language, a high-level textual language which has been recently designed for modelling dynamically regulated and spatially-confined biochemical pathways. Here we introduce the main features of the Narrative Language; for a detailed description of the language and of its translation into an executable language, the reader is referred to  and .
The basic entities of the language are molecules (components) and sub-cellular locations (compartments). In the language molecules can interact (e.g. bind/unbind), undergo biochemical modification (e.g. phosphorylation/de-phosphorylation) and re-locate between compartments. The time-dependent behaviour of the pathway is described in the form of a narrative of events involving these basic entities and functions, which imposes a temporal sequence and defines inter-dependencies and contingencies. In the narrative approach each of the elements can denote 'real' (i.e. experimentally defined) or abstract (e.g. hypothetical) entities. In silico exploration of the pathway model is simply enabled by modifying the narrative description and/or changing parameter values.
A feature of this narrative approach is the use of reliability values associated with numerical parameters. This is a percentage value which describes the reliability of the associated numerical value, and it can be used to distinguish between values that are highly certain because obtained from high quality biological experiment, and others which are inferred as a result of un-verified assumptions or 'guesswork' (e.g. 100% indicates high precision data, while 0% indicates a value which has no experimental evidence). Reliability values do not influence the behaviour of the programme but are annotations to inform use of the model. In particular modellers can employ reliability values to identify parameter dependencies to be explored during model refinement.
Model description and simulation
The Narrative Language model of the gp130/JAK/STAT signalling pathway is supplied as Additional files 1, 2, 3, 4, 5, 6, 7 and 8. The molecular components we consider in the model are: two ligands (LIF and OSM), three membrane-bound receptors (gp130, LIFR and OSMR), one effector (STAT3), and two inhibitors (SOCS3 and PIAS3). The receptor associated kinase JAK and TC-PTP phosphatase are implicitly modelled.
Additional file 2 shows the definition of the components involved in the pathway. For each protein, the list of interaction/modification sites, states and locations are defined and initialised. Each receptor contains at least one ligand binding site (OSMR has only one site for OSM, while LIFR and gp130 also have one site for LIF), one binding site for SOCS3 inhibitor, and some phosphorylation sites. Moreover, receptors can be in dimeric state (an additional site in gp130 allows us to distinguish between the two types of OSM receptors). STAT3 has one phosphorylation and four binding sites (for receptors and PIAS3 inhibitor), and it can be monomeric or dimeric (STAT3 can form homodimers). The initial quantities are also defined. The number of ligands is calculated based on the known extracellular concentration (500 pM).
Four compartments are involved in the system (see additional file 1): the exosol (the extracellular space, where the ligands are located), the cell membrane (location of the receptors), the cytosol (initial location of the STAT3 effector), and the nucleus (to which the effector can translocate). The compartment volumes are calculated based on the average cell radius and ratio between intra-cellular compartment volumes stated in . The number of spatial dimensions is used to distinguish between 2D compartments (i.e. membranes) and 3D ones.
Additional file 3 shows the definition of the biochemical reactions occurring in the pathway. Reaction types (e.g. binding, unbinding, phosphorylation, relocation) and rates (i.e. the kinetic constants) are defined here. The reaction volume is the volume in which the reaction occurs (generally it is the size of the compartment in which the involved species are located), and it is used in deriving the actual rate at which the reaction occurs. Some of the reaction rates have been obtained from wet experiments, while others have been estimated based on information about similar reactions, or extracted from other models [22–24]; reliability values are assigned to reaction rates and volumes.
Finally, Additional files 4, 5, 6, 7 and 8 show the definition of the narrative of events, which describes the evolution of the system; it is a sequence of basic events, each of which is a constrained textual description of a biochemical reaction involving at most two components. Moreover, events are grouped into processes for the sake of readability. The defined events describe the binding/unbinding of ligand/receptor pairs, the downstream LIF and OSM pathways (formation and activation of receptor complexes), the downstream STAT3 pathway (recruitment and activation of STAT3, and its nuclear/cytoplasmic shuttling), and the inhibition mechanisms.
Additional file 4 models the binding of ligands to receptors (reaction r1 in the graphical representation of the pathway shown in Figure 1 and events 1, 3, 5, 7 and 9 in the Narrative Language model), and the inverse unbinding reaction (r2, events 2, 4, 6, 8 and 10). For each event, the involved components and the occurring interaction are specified (e.g. event 1 states that LIF binds to receptor gp130 on a specific binding site) together with the activating conditions (e.g. for event 1, the binding site in gp130 is not already occupied, LIF itself is free, and gp130 is not already in dimeric form), and the reference to the corresponding reaction in Additional file 3.
Additional file 5 models the dimerisation of pairs of receptor subunits to form receptor complexes (gp130-LIFR or gp130-OSMR), which is triggered by the binding of a ligand to one of the receptors (r3, events 11, 13, 15, 17, 19 and 21) (e.g., in events 19 and 21, OSMR and gp130 form a heterodimeric complex if one of them has been previously activated by ligand binding); the dissociation of the receptor complexes is also modelled (r4, events 12, 14, 16, 18, 20 and 22).
Additional file 6 models the activation (JAK-mediated phosphorylation) of the receptor complexes, the binding of STAT3 to a receptor complex, and the activation (phosphorylation) of STAT3. Once the receptor dimeric complex is formed, each receptor subunit (gp130, LIFR and OSMR) can phosphorylate on specific sites (r5, events 23, 25, 27 and 29). STAT3 can bind on receptors' phosphorylated sites (r7, events 31, 32 and 33), and the binding of STAT3 allows the phosphorylation of STAT3 on site Y705 (r8, events 37, 38 and 39).
Additional file 7 models the unbinding of STAT3 from receptor complexes, its homodimerisation, and nuclear/cytoplasmic shuttling (relocation into the nucleus, de-phosphorylation by TC-PTP, de-homodimerisation and relocation into the cytoplasm). Once phosphorylated, STAT3 can dissociate from the receptor complex (r10, events 41, 42 and 43); the phosphorylated site allows STAT3 to homodimerise (r11, event 44). When STAT3 is in dimeric form, it can translocate into the nucleus (r12, event 45) where it can carry out its specific functions (not modelled here): STAT3 binds to the DNA, activating the transcription of downstream gene targets. Nuclear STAT3 is inactivated through de-phosphorylation by TC-PTP (r13, event 46), which leads to its de-dimerisation (r14, event 47), and its export to the cytoplasm (r15, event 48), where STAT3 can undergo additional cycles of activation.
Additional file 8 models SOCS3 and PIAS3 inhibition mechanisms. SOCS3 is produced by active STAT3 (r16, event 49) and degraded (event 50), and it acts by competing with STAT3 in binding to receptors (r17, events 51, 52 and 53). PIAS3 acts by binding to active nuclear STAT3 (r18, event 57).
We developed a tool , N2BB, which implements an automatic translation of models described in the biologically-intuitive Narrative Language into executable computable models formulated in BlenX , a programming language inspired on the Beta-binders process calculus . Process calculi, originally developed for modelling mobile communicating systems, have recently been proposed as appropriate for simulating biological processes , and they have proved themselves as powerful tools for dynamical modelling of complex biological systems [5–8]. Differently from differential equations, process calculi also allow for analysis of models (e.g. model-checking, equivalence, reachability, causality, and locality analysis).
The BlenX model derived from the Narrative Language model is compatible with the BetaWB , a collection of tools for modelling, simulating, and analysing BlenX models. Hence, the model can be imported into the BetaWB designer, or directly simulated by means of the BetaWB simulator; the time-evolution of the simulation can be visualised by means of the BetaWB plotter or the Snazer tool . For a detailed description of the BlenX language and of the implementation of the simulator, see [25, 11].
Cells, reagents and cytokines
MCF-7 human breast cancer cells were obtained from American Type Culture Collection (Manassas, VA) and cultured as described . The human oncostatin M recombinant expression plasmid, pGEX-3C-OSM, was prepared, expressed and purified as described previously .
Western blot, immunofluorescence and data analysis
Serum starved MCF-7 cells were stimulated with 10 ng/ml oncostatin M for increasing times (up to 480 minutes) at 37°C. For Western blot analysis, cell lysates were prepared and analysed as described  and monoclonal anti-phospho STAT3 (Tyr705) and STAT3 (Cell Signalling Technology) antibodies used for immunodetection. The density of the bands representing phospho-STAT3 and STAT3 were measured using ImageJ  and expressed as the ratio of phospho-STAT3 to STAT3. For immunofluorescence studies, MCF7 cells grown on coverslips were fixed with 4% paraformaldehyde (10 min, RT), permeabilised with 0.1% saponin solution (0.02 M glycine, 0.1% saponin, 0.1 M Tris/HCl pH8.5) for 20 min and blocked for 1 hour in 0.1% saponin solution (0.1% saponin, 0.1 M Tris/HCl pH8.5) plus 2.5% foetal calf serum. Cells were immunostained with monoclonal anti-STAT3 antibody for 1 h at RT and incubated with Texas Red-conjugated secondary antibody containing Hoechst (Molecular Probes) for 45 min at RT. Coverslips were mounted with 5 μl of Mowiol solution (10% Mowiol 4–88, 25% glycerol, 0.1 M Tris/HCl pH8.5) on the slide and observed under confocal microscope. For localisation analysis, images captured were converted to greyscale and total STAT3 fluorescence calculated from the sum of pixel density values using ImageJ. Nuclear STAT3 fluorescence was calculated from selection of nuclear area (as determined by Hoechst staining) and cytoplasmic STAT3 fluorescence calculated by subtracting nuclear staining from total cellular staining. For each time-point analysis was performed on between 60 – 100 cells (from multiple coverslips) and mean values ± 2 SD were calculated for total nuclear and cytoplasmic STAT (expressed as percentage of total STAT).