Nonlinear gene network inference: integrating sigmoid-response differential equations with sequential thresholded least squares

Gene regulatory networks (GRNs) are fundamental to cellular identity, differentiation, and disease. While many computational methods infer GRNs from transcriptomic data, most dynamical approaches rely on linear or non-parametric models, overlooking nonlinear features such as saturation, cooperativity, and feedback. We propose sigmoid-response sequential thresholded least squares (SRSTLS), a framework combining a sigmoid-response dynamical model with a sequential thresholded least squares optimizer to reconstruct nonlinear regulatory interactions from time-series or pseudotemporal gene expression data. SRSTLS is validated on six simulated ODE-based benchmarks, including toggle-switch and larger networks, and two real single-cell RNA-seq datasets from embryonic stem cells and hepatoblasts. Compared to SCODE and AR1MA1-VBEM, SRSTLS shows superior accuracy in edge identification and sign determination, and remains robust across noise levels and pseudotemporal ordering parameters. Our findings demonstrate that incorporating nonlinear dynamics markedly improves GRN inference, positioning SRSTLS as a reliable and interpretable tool for studying regulatory mechanisms in complex biological systems.