Research Article Exact and Heuristic Methods for Network Completion for Time-Varying Genetic Networks

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Robustness in biological networks can be regarded as an important feature of living systems. A system maintains its functions against internal and external perturbations, leading to topological changes in the network with varying delays. To understand the flexibility of biological networks, we propose a novel approach to analyze time-dependent networks, based on the framework of network completion, which aims to make the minimum amount of modifications to a given network so that the resulting network is most consistent with the observed data. We have developed a novel network completion method for time-varying networks by extending our previous method for the completion of stationary networks. In particular, we introduce a double dynamic programming technique to identify change time points and required modifications. Although this extended method allows us to guarantee the optimality of the solution, this method has relatively low computational efficiency. In order to resolve this difficulty, we developed a heuristicmethod for speeding up the calculation ofminimum least squares errors.We demonstrate the effectiveness of our proposed methods through computational experiments using synthetic data and real microarray gene expression data. The results indicate that our methods exhibit good performance in terms of completing and inferring gene association networks with time-varying structures. 1