A global sensitivity analysis approach for morphogenesis models

{\bf Background} %if any Morphogenesis is a developmental process in which cells organize into shapes and patterns. Complex, non-linear and multi-factorial models with images as output are commonly used to study morphogenesis. It is difficult to understand the relation between the uncertainty in the input and the output of such `black-box' models, giving rise to the need for sensitivity analysis tools. In this paper, we introduce a workflow for a global sensitivity analysis approach to study the impact of single parameters and the interactions between them on the output of morphogenesis models. {\bf Results} %if any To demonstrate the workflow, we used a published, well-studied model of vascular morphogenesis. The parameters of this cellular Potts model (CPM) represent cell properties and behaviors that drive the mechanisms of angiogenic sprouting. The global sensitivity analysis correctly identified the dominant parameters in the model, consistent with previous studies. Additionally, the analysis provided information on the relative impact of single parameters and of interactions between them. This is very relevant because interactions of parameters impede the experimental verification of the predicted effect of single parameters. The parameter interactions, although of low impact, provided also new insights in the mechanisms of \emph{in silico} sprouting. Finally, the analysis indicated that the model could be reduced by one parameter. {\bf Conclusions} %if any We propose global sensitivity analysis as an alternative approach to study the mechanisms of morphogenesis. Comparison of the ranking of the impact of the model parameters to knowledge derived from experimental data and from manipulation experiments can help to falsify models and to find the operand mechanisms in morphogenesis. The workflow is applicable to all `black-box' models, including high-throughput \emph{in vitro} models in which output measures are affected by a set of experimental perturbations.

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