Statistical method for estimation of the predictive power of a gene circuit model

In this paper, a specific aspect of the prediction problem is considered: high predictive power is understood as a possibility to reproduce correct behavior of model solutions at predefined values of a subset of parameters. The problem is discussed in the context of a specific mathematical model, the gene circuit model for segmentation gap gene system in early Drosophila development. A shortcoming of the model is that it cannot be used for predicting the system behavior in mutants when fitted to wild type (WT) data. In order to answer a question whether experimental data contain enough information for the correct prediction we introduce two measures of predictive power. The first measure reveals the biologically substantiated low sensitivity of the model to parameters that are responsible for correct reconstruction of expression patterns in mutants, while the second one takes into account their correlation with the other parameters. It is demonstrated that the model solution, obtained by fitting to gene expression data in WT and Kr⁻ mutants simultaneously, and exhibiting the high predictive power, is characterized by much higher values of both measures than those fitted to WT data alone. This result leads us to the conclusion that information contained in WT data is insufficient to reliably estimate the large number of model parameters and provide predictions of mutants.