Validation and selection of ODE models for gene regulatory networks

• A new validation and selection method of ODE models for gene regulatory networks is proposed in this study.
• Model validation is performed by the inference of the bias of ODE models.
• Better ODE models are selected by AIC or BIC using the pure-model likelihood.

The description of network dynamics is an important and fundamental tool to understand gene regulation processes, along with the gene regulatory network. To describe the network dynamics, dynamic molecular systems consisting of ordinary differential equations (ODEs) have been often used for time-course gene expression data. However, since we cannot observe entire regulation processes through gene experiments and there might be multiple competing ODE models generating similar dynamics, validation of ODE models is essential for more accurate inference and prediction for the processes. Moreover, since ODE models are deterministic and inflexible while gene expression data typically have both measurement and instrument uncertainties with heteroscedasticity, they should be evaluated in terms of model flexibility and adequacy for observed data. This study deals with statistical validation and selection for ODE models based on a likelihood approach and the proposed method is applied to the parotid de-differentiation network data obtained from independently measured experiments.