Multiobjectivization for parameter estimation: a case-study on the segment polarity network of drosophila

Mathematical modeling for gene regulative networks (GRNs) provides an effective tool for hypothesis testing in biology. A necessary step in setting up such models is the estimation of model parameters, i.e., an optimization process during which the difference between model output and given experimental data is minimized. This parameter estimation step is often difficult, especially for larger systems due to often incomplete quantitative data, the large size of the parameter space, and non-linearities in system behavior. Addressing the task of parameter estimation, we investigate the influence multiobjectivization can have on the optimization process. On the example of an established model for the segment polarity GRN in Drosophila, we test different multiobjectivization scenarios compared to a singleobjective function proposed earlier for the parameter optimization of the segment polarity network model. Since, instead of a single optimal parameter setting, a set of optimal parameter settings exists for this GRN, the comparison of the different optimization scenarios focuses on the capabilities of the different scenarios to identify optimal parameter settings showing good diversity in the parameter space. By embedding the objective functions in an evolutionary algorithm (EA), we show the superiority of the multiobjective approaches in exploring the model's parameter space.