Using GEMANOVA to explore the pattern generating properties of the Delta-Notch model

Summary

In the area of systems biology, increasingly complex models are developed to approximate biological processes. The complexity makes it difficult to derive the properties of such models analytically. An alternative to analytical considerations is to use multivariate statistical methods to reveal essential properties of the models. In this paper it is shown how the properties of a relatively complex mathematical model for describing cell-pattern development, the Delta-Notch model, can be explored by means of statistical analyses of data generated from the model. ANOVA is a well-known and one of the most commonly used methods for analyzing data from designed experiments, but it turns out that it is not always appropriate for finding and exploring higher-order interactions. For this purpose a multiplicative alternative -- GEMANOVA -- was used in the present paper for studying the Delta-Notch model, for which the properties depend on higher order interactions between the model parameters. It is shown here how a forward selection strategy combined with bootstrapping can be used to identify GEMANOVA models with reasonable fit to the data, and it is demonstrated how new insight about the Delta-Notch model can be gained from interpreting the GEMANOVA output.