Learning restricted Boolean network model by time-series data

Restricted Boolean networks are simplified Boolean networks that are required for either negative or positive regulations between genes. Higa et al. (BMC Proc 5:S5, 2011) proposed a three-rule algorithm to infer a restricted Boolean network from time-series data. However, the algorithm suffers from a major drawback, namely, it is very sensitive to noise. In this paper, we systematically analyze the regulatory relationships between genes based on the state switch of the target gene and propose an algorithm with which restricted Boolean networks may be inferred from time-series data. We compare the proposed algorithm with the three-rule algorithm and the best-fit algorithm based on both synthetic networks and a well-studied budding yeast cell cycle network. The performance of the algorithms is evaluated by three distance metrics: the normalized-edge Hamming distance ${\mathit{\mu }}_{\mathrm{ham}}^{\mathrm{e}}$, the normalized Hamming distance of state transition ${\mathit{\mu }}_{\mathrm{ham}}^{\mathrm{st}}$, and the steady-state distribution distance μ^ssd. Results show that the proposed algorithm outperforms the others according to both ${\mathit{\mu }}_{\mathrm{ham}}^{\mathrm{e}}$ and ${\mathit{\mu }}_{\mathrm{ham}}^{\mathrm{st}}$, whereas its performance according to μ^ssd is intermediate between best-fit and the three-rule algorithms. Thus, our new algorithm is more appropriate for inferring interactions between genes from time-series data.