Successful application of ASPASIA is dependent on the Java Runtime (version 1.6 or higher) and R Statistical environments (version 2.13.1 or greater). ASPASIA utilises the R packages spartan, lhs, XML, and graphing packages gplots and plotrix.

ASPASIA requires an XML format settings file containing the information required for the applied technique, such as the location of the SBML model to use in the analysis, the location where generated SBML files should be produced, and the information of the SBML file parameters being modified. The complete list of settings file requirements is specified in S1 Table. To ease the generation of this file, we have produced an online ASPASIA settings file generator (www.york.ac.uk/ycil/software/aspasia) and exemplar settings files that can be modified as required.

ASPASIA eases the process of calibrating and exploring SBML models of biological systems where the dynamics are dependent upon an intervention. The first stage in an intervention analysis is to run an SBML model in any solver until a determined time-point. By taking the output from the SBML solver, ASPASIA automatically creates a series of new SBML models that add an intervention to the final state that the model was in, by changing or scaling the values of specified species or parameters (Fig 1). Interventions can be added after an SBML model has been run for any specified time, or if using a solver that allows for steady state identification to be performed, when a steady state has been reached. As ASPASIA automatically detects the final time point from the output file, interventions can automatically be added to a range of models where the steady state occurs at different times. For this work presented here, models were simulated using LibSBMLSim [17] that does not have the capacity for steady state detection thus all models were run for a length of time sufficient for all populations to become stable.

CD4⁺ T helper cells play a crucial role in the adaptive immune response following their activation through recognition of peptide/MHC complexes on antigen-presenting cells. In the presence of specific cytokines, activated CD4⁺ T cells differentiate into distinct subsets that are characterised by their cytokine-secretion profile and their expression of specific transcription factors. Thus, IL-12 drives the differentiation of Th1 cells that secrete IFN-γ and express T-bet, IL-4 drives the differentiation of Th2 cells that secrete IL-4 and express GATA-3, and a combination of IL-6 and TGF-β, along with IL-21 and IL-23 are responsible for the differentiation, maintenance and expansion of Th17 cells that secrete IL-17, IL-21, and express RORγt [19, 20]. Th17 cells have, under certain conditions, been shown to switch phenotype from an IL-17-producing Th17 cell to an IFN-γ-producing ex-Th17 cell that expresses T-bet and not RORγt (Fig 2A) [21, 22]. While in vitro-derived Th17 cells express a functional IL-12 receptor and turn on IFN-γ production following IL-12 stimulation [23], ex vivo-derived Th17 cells lack a functional IL-12 receptor [22, 24], suggesting that factors other than IL-12 are responsible for phenotype switching in vivo.

We have developed an SBML model to capture in silico the dynamics of Th17-cell plasticity in vivo (Fig 2B). This model can be used to infer the dynamics of a hypothetical receptor and cytokine involved in the phenotype switching of Th17 cells. The model builds on work by Yates et al [25] and Schulz et al [26] to capture the dynamics of transcription factors T-bet and RORγt in a CD4⁺ T cell undergoing polarisation and phenotype switching following exposure to exogenous cytokines. The model is freely available from the ASPASIA website, and the key equations underlying the model are listed in S2 Fig.

Previous models of T-cell polarisation have considered the Th1/Th2 axis, focussing on transcription factors T-bet (Th1) and GATA-3 (Th2) [25, 26]. We utilised ASPASIA to reparameterise these models to capture the dynamics of Th17 polarisation and phenotype switching, using RORγt and T-bet as markers of a particular phenotype (Fig 2B). A cell in the model is considered to be polarised if one of the transcription factors is stably expressed above baseline level. A cell that expresses both transcription factors at a higher level than at baseline is considered to be a double-positive cell.

As many of the parameters relating to polarisation of Th17 cells were unknown, we used ASPASIA technique 2 to generate 200 unique SBML models using latin-hypercube sampling over ranges defined in S3 Fig. The models were solved using an SBML solver implementing libSBMLSim [17], with a step size of 0.12 for sufficient time until stable baseline levels of T-bet and RORγt were reached. ASPASIA techniques 4 and 5 were then used to generate an SBML model with parameters and species concentrations set to baseline values, and interventions introduced representing stimulation with either type 17 (C₁₇) or type 1-polarising cytokine (C₁) (Fig 2B). From the 200 models generated we identified the one that best captured the behaviours observed in a CD4⁺ T cell undergoing Th17 polarisation, i.e. i) no expression of either T-bet or RORγt in the absence of polarising cytokines (Fig 3A), ii) stable expression of RORγt following stimulation with type 17 polarising cytokines (Fig 3B), and iii) stability of the Th17 phenotype when introduced to type 1 polarising cytokine after initial polarisation has taken place (Fig 3C). This same model also met the criteria for a CD4⁺ T cell adopting a Th1 polarisation (S1 Table). Therefore this model was selected for further experimentation.

To date the biological factor(s) inducing Th17-cell phenotype switching in vivo is unknown. To incorporate phenotype switching of Th17 cells into the model selected in Fig 3, a hypothetical receptor that we suggest could drive phenotype switching in vivo was added to the model. The equations governing the dynamics of this receptor were based on a previous model of the upregulation of the IL-12 receptor during Th1 polarisation [26] and the reactions that were added to the model are shown in S4 Fig. To inform the estimation of unknown parameter values introduced by adding these reactions, we utilised values identified by Schulz et al. [26] and used ASPASIA technique 2 to create 200 parameter sets where the range of each parameter was specified to be 10-fold above and below the corresponding value used by Schulz et al. [26]. We postulated that the hypothetical receptor, namely receptor X, would drive phenotype switching of Th17 cells by either promoting T-bet or by inhibiting RORγt expression with a rate of + or − a₆ respectively. Thus, two versions of the model were created from each parameter set to represent both of these possibilities S4 Fig). Each of the 400 models generated were solved with step size 0.12 for 144 hours, to allow all models to reach a steady state. ASPASIA techniques 4 and 5 were then used to add a single stimulus with C_X, a hypothetical cytokine biding to receptor X and driving phenotype switching, and the models were solved again. Fig 4A shows a representative cytokine profile used to drive Th17 polarisation and phenotype switching by C₁₇ and C_X, respectively, in all models. In the scenario where receptor X acts to inhibit RORγt, there was an initial reduction in the mRNA level of RORγt, but once cytokine X had been removed by decay and absorption all models returned to a stable Th17 state (Fig 4B). This means that despite the dynamics of receptor signalling, and the strength of inhibition being different in every model, targeting RORγt was not sufficient to cause a phenotype switch. When C_X instead acted to promote T-bet, the cell switched phenotype to become T-bet expressing in 85 of the 200 models (Fig 4C). The main difference between these 85 models was the time taken for T-bet to become stable, and hence the time spent in a double positive stage (S5A Fig). In the remaining 115 models, the levels of T-bet and RORγt mRNA returned to those initially seen when the cell was in the Th17 state. These results suggest that the receptor that drives Th17 phenotype switching acts by promoting T-bet and not by inhibiting RORγt.

We next used ASPASIA technique 2 to perform a sensitivity analysis on the T-bet promotion model and parameter values described in S4 Fig to further examine the properties of receptor X during phenotype switching. From this analysis, we determined the parameters that were important in controlling the level of expression of receptor X at basal level, following a single round of stimulation with C₁₇, and after subsequent stimulation with C_X. Important parameters were defined as those that had the greatest correlation with the level of receptor X mRNA in each of these settings (Fig 5A–5C). Interestingly, different parameters were influential in controlling the level of receptor X before (Fig 5A and 5B) and after (Fig 5C) stimulation with C_X. Both of these cases are potential predictors of the dynamics that a receptor driving phenotype switching must exhibit in biology. In four of the models that undergo a phenotype switch, receptor X was expressed at high level following stimulation with C₁₇ alone (S5B Fig). This may suggest that a receptor that drives phenotype switching must have a high upregulation rate (a₅), a low decay rate (μ₇), and the level of RORγt at which formation of receptor X is at half maximum (k₉) must also be low (Fig 5B). Furthermore, following stimulation with C_X all of the models that switched phenotype had a low level of receptor X (S5C Fig). This means that the receptor X-C_X complex must decay slowly (μ₈) and C_X must also decay slowly (μ₉) (Fig 5C).

For each of the models in Fig 4C where a phenotype switch occurred, we also looked at the sensitivity of how long this switch takes using ASPASIA Technique 2. The influential parameters were the upregulation rate receptor X (a₅), the rate of promotion of T-bet (a₆), the half-maximum level of receptor X (k₉), the level of receptor X-C_X complex at which rate of T-bet promotion is half-maximum (k₁₀), and the decay rate of the receptor cytokine complex (μ₈) (Fig 5D). If data were available on how long a phenotype switch takes in biology, these could be used to determine the dynamics that the cytokine and receptor that drive the phenotype switch must exhibit and thus could play a role in identifying the potential receptors and cytokines driving switching. For the global sensitivity analyses shown here we note that the alternative global analysis method, ASPASIA technique 3, could also have been used.

We next performed an additional sensitivity analysis to determine how robust the phenotype switch was to changes in the initial concentration of C_X. The analysis was restricted to just the 85 models in Fig 4C where a cell that was Th17 polarised switched phenotypes when stimulated with C_X. When the intervention with C_X was simulated, we used ASPASIA to create 10 interventions where the initial concentration of C_X varied from 10 to 10000 for each model. We found that in all cases the model still switched phenotype regardless of the concentration of C_X applied (representative model shown in Fig 6), suggesting that the phenotype switch is extremely robust once a receptor driving switching has been introduced. This suggests that in biological systems where phenotype switching of Th17 cells does not occur, for example following infection with Candida albicans [21], either C_X and/or receptor X are not present.

We have shown how four of the techniques from the ASPASIA package have proven capable of establishing values for unknown parameters, introducing a number of biologically-inspired interventions, and conducting sensitivity analysis to understand the impact of that intervention on model response. By analysing a number of SBML models, we have been able to suggest that phenotype switching of Th17 cells is driven by the promotion of T-bet rather than the inhibition of RORγt. These conclusions have been drawn using a hypothetical model in the absence of biological data. If biological data relating to the initial and polarised levels of T-bet and RORγt in Th1 and Th17 cells had been available before model development, this would have better informed model selection prior to the addition of the hypothetical receptor to drive phenotype switching. Performing the analyses on a biologically calibrated model has the potential to assist in identifying the specific receptor driving phenotype switching of Th17 cells by highlighting the important attributes that the receptor must possess and narrowing down parameter ranges. Biological receptors that fulfil the criteria suggested via model sensitivity analysis can then be considered as potential drivers of phenotype switching, guiding further in vivo experimentation into receptor identification. The model ensembles and detailed instructions on how the analyses have been performed in this paper can be found on the ASPASIA website, permitting the reproduction of the approaches taken above.