# A Model-Driven Approach for Conducting Simulation Experiments
## 5 Evaluation
### Increasing Productivity and Quality for Complex Experiments
#### 5.2.1 Sensitivity Analysis of a Wnt Signaling Model  
To understand how electrically active implants affect the differentiation and proliferation of cells (and, thus, the composition and regeneration of tissue), the impact of external electric fields on central cellular signaling pathways needs to be studied. The Wnt/\(\beta\)-catenin signaling pathway is one of the central pathways that regulate the proliferation, as well as differentiation of cells [63]. Deregulated forms of this pathway are involved in several human cancers and developmental disorders [64]. Effects on membrane-related dynamics are of particular interest for the development of electrically active implants. Lipid rafts, specialized microdomains of the membrane, have been found to sense the electric field and to direct the responses of cells [65]. Therefore, in the simulation study by [PERSON] et al., a Wnt simulation model [48] was extended to capture both raft- and non-raft-associated endocytic processes of the Wnt/\(\beta\)-catenin receptor LRP6 in detail, including stochastic effects [47].  
The model was written in ML-Rules [66] and simulated using stochastic DES (the Wnt model, the SA experiment, and the analysis results are available at [[https://github.com/SFB-ELAINE/Case-Study-Endocytosis](https://github.com/SFB-ELAINE/Case-Study-Endocytosis)]([https://github.com/SFB-ELAINE/Case-Study-Endocytosis](https://github.com/SFB-ELAINE/Case-Study-Endocytosis)), accessed on 26 July 2022). The experiment meta model for DES is available in the repository of the framework and can therefore be used to guide the modeler through the specification of the base experiment. Similarly, the meta model for global sensitivity analysis is available to guide the modeler through the definition of the global SA. In the global SA, the modeler is interested in the sensitivity of the fraction of the cell membrane receptor LRP6 (observed quantity), with regard to the model parameters \(ke_{mmpf}\) and \(ke_{mpf}\), which represent the internalization rates of bound LRP6 receptor complexes and the parameter \(kLRAss\). Furthermore, the modeler specifies uniform distributions for these three factors, as well as minimum and maximum values and enters the information via the generated GUI for this experiment type. As the sampling strategy, an OLHC design with 1750 samples was selected.  
Once all inputs for the SA have been collected, executable experiment code can be generated, i.e., a combination of an R script with an SESSL/ML-Rules script, as illustrated in Figure 4A. Without the experiment generation, the user would have had required expertise in writing both SESSL/ML-Rules scripts and R scripts, as well as expertise in the  
Figure 4: Schematic of the generated code for the three SA experiments for (**A**) the Wnt signaling model, (**B**) the battery model, and (**C**) the electric fields model. The experiments take the user-given base inputs and SA inputs and produce Sobol indices as outputs.  
types of sensitivity analyses and the respective libraries. Especially for novice modelers, correctly setting up a sensitivity analysis involving two specification languages can be challenging and error-prone, and therefore, quality and productivity can be improved by the MDE approach.  
Since we have implemented bindings to both SESSL/ML-Rules and R, the composed experiment can also be executed automatically. Note that, for now, we do not support the automatic analysis of simulation results and the generation of plots; however, this could be included as a feature of this framework in the future. Figure 5A presents the results of the experiment to be interpreted by the user. They show almost no impact of the parameter \(ke_{m\#}\) on the results. The variances of each of the other two parameters (\(ke_{mom\#}\) and \(kLRAss\)) make up about half of the variance of the result.