Reconstruction of Boolean Networks Using Input–Output Data Sets

Boolean networks (BNs) are widely used to model gene regulatory networks. In practice, however, their internal states can rarely be measured directly, and the available output measurements are corrupted by noise. In this paper, we propose a data-driven framework for reconstructing the output trajectories and identifying the initial states of a BN using only input–output datasets under probabilistic bit-flip observation noise. The proposed framework consists of two steps. First, noisy output sequences obtained from repeated experiments are vectorized and partitioned into clusters by K-means clustering, and principal component analysis (PCA) is used to visualize their separability. Second, the noise within each cluster is removed by averaging and thresholding, which is justified by the law of large numbers, and the reconstructed trajectory is matched with a reference library of noise-free trajectories using the Hamming distance to identify the corresponding initial state. The effectiveness of the proposed method is demonstrated through numerical examples, including a BN model of the mammalian cell cycle. When there are three candidate initial states, all trajectories and initial states are correctly reconstructed, whereas when the number of candidates increases to seven, only two of them are identified, revealing a limitation of the K-means-based approach.