# A Model-Driven Approach for Conducting Simulation Experiments
## 5 Evaluation
### Reusability  
The final Wnt model (introduced in Section 5.2.1) is the result of successively extending simpler model versions. The original Wnt model by [PERSON] et al. (2003) [69] was extended by raft- and redox-dependent signaling events in a study by [PERSON] et al. (2015) [48]. This new model was then extended further by endocytic processes in [PERSON] et al. (2020) [47]. To ensure that the basic model behavior was not changed due to the extensions, various cross-validation experiments were required that compared the trajectories of the variables of interest.  
Therefore, the original simulation experiments of the study by [PERSON] et al. shall be reused and repeated with the extended model. However, the original experiments were specified in SED-ML [9] and the corresponding model in SBML [70] (see BioModels [71] entry at [[https://www.ebi.ac.uk/biomodels/BIOMD0000000658](https://www.ebi.ac.uk/biomodels/BIOMD0000000658)]([https://www.ebi.ac.uk/biomodels/BIOMD0000000658](https://www.ebi.ac.uk/biomodels/BIOMD0000000658)), accessed on 26 July 2022). In contrast, the Wnt model by [PERSON] et al. (2015/2020) was specified using the rule-based modeling language ML-Rules [66], and the experiments were conducted using the experiment specification language SESSL [8]. Thus, in order to reproduce results from the study by [PERSON] et al., the SED-ML experiment specification needs to be adapted for the new model and translated to SESSL. This can be supported by the model-driven approach.  
First, the meta model for DES directs the automatic parsing of the original specification and provides meaning to the parts of the experiment specification. As the experiment type is a time course analysis, a base meta model suffices to capture all the inputs. Once transformed to the quasi-standardized JSON format, the experiment specification can be adapted to work with the model by [PERSON] et al., e.g., the file name and the simulation stop time (due to the use of different time scales) need to be changed. This can partly be performed automatically by exploiting additional knowledge in the form of ontologies, e.g., UniProt [72] provides a unique identifier for each protein and allows transforming the variable names in the observation expressions from one model to another. Especially, these ontology-based automatic transformations are valuable for the reuse of simulation experiments as they prevent inconsistencies that can easily happen when translating an experiment for a different model or a different specification language. As mentioned, the variable names might have a different meaning in Model A compared to Model B, but also, e.g., the units used for the rate constants might differ. Incorrect translations may lead to distorted simulation results and, therefore, seemingly different model behavior, leading to the wrong conclusion that the new model cannot be successfully cross-validated.  
The automatically parsed and transformed experiment specification is then presented to the user to ask for adaptions or additional information that could not be extracted from the old specification. Listing 3 shows the finished experiment specification in the JSON-based exchange format after being adapted for the model by [PERSON] et al. From this, the SESSL-specific experiment can be generated and executed automatically.  
The result of the cross-validation is depicted in Figure 6. It compares the trajectories of the key protein \(\beta\)-catenin, an indicator of the pathway's activity, produced by the [PERSON] et al. and the [PERSON] et al. model (with an adapted time scale) when stimulated with a transient Wnt stimulus. Both \(\beta\)-catenin curves show the same peak at the same time. From this, the user concludes that the extensions applied in the study by [PERSON] et al. do not alter the central dynamics of the pathway.  
Figure 6: Results of the cross-validation of the [PERSON] et al. model [69] and the [PERSON] et al. model [48] (after applying a scaling factor of 0.28 to the \(\beta\)-catenin trajectory).