Forward-backward gene expression binarization for boolean state inference over a known regulatory network.

Binarization of gene expression data is a critical prerequisite for the synthesis of Boolean gene regulatory network (GRN) models from omics datasets. In practice, thresholding methods remain the dominant approach, yet they oversimplify the underlying biology by ignoring gene-specific functional roles and failing on sparse or single-snapshot data. To overcome these limitations, we propose Bi4Back, a novel regulation-based binarization algorithm that combines thresholding with iterative forward and backward Boolean propagation guided by a known signed regulatory graph - supplied as a required input rather than inferred - and corrects inconsistencies through a dedicated detection step. Bi4Back thus infers the binary states of genes given a network, not the network itself. The algorithm operates on as few as a single steady-state measurement and infers missing or uncertain binary states in a biologically consistent manner. Validation against ODE simulations of artificial and established Boolean GRNs spanning stable equilibria, oscillatory regimes, and continuous time-series trajectories shows exact agreement with the threshold-defined ground truth on stable artificial networks, near-exact agreement (dissimilarity distance down to d=1/11, reaching exact agreement at fully converged snapshots) on established models that converge to equilibrium, and graceful, phase- and topology-dependent degradation under oscillatory dynamics. The algorithm exhibits good robustness to up to ±50% multiplicative measurement noise, with dissimilarity distances remaining close to or better than the noise-free baseline, while performance under missing data depends critically on the topological centrality of unmeasured genes-a finding that yields a clear experimental design principle: measurement completeness for hub genes outweighs precision for peripheral ones. Robustness testing over 100,000 parameter-randomized simulations confirms reliability across diverse biological conditions. Scalability analysis across networks of 10 to 100 genes confirms computation times under 2 seconds throughout. Implementations in R and Mathematica are publicly available.