提出新方法破解生物网络反馈环难题，精准推断基因调控关系。

Biological networks are pivotal in deciphering the complexity and functionality of biological systems. Causal inference, which focuses on determining the directionality and strength of interactions between variables rather than merely relying on correlations, is considered a logical approach for inferring biological networks. Existing methods for causal structure inference typically assume that causal relationships between variables can be represented by directed acyclic graphs (DAGs). However, this assumption is at odds with the reality of widespread feedback loops in biological systems, making these methods unsuitable for direct use in biological network inference. In this study, we propose a new framework named SCALD (Structural CAusal model for Loop Diagram), which employs a nonlinear structure equation model and a stable feedback loop conditional constraint through continuous optimization to infer causal regulatory relationships under feedback loops. We observe that SCALD outperforms state-of-the-art methods in inferring both transcriptional regulatory networks and signaling transduction networks. SCALD has irreplaceable advantages in identifying feedback regulation. Through transcription factor (TF) perturbation data analysis, we further validate the accuracy and sensitivity of SCALD. Additionally, SCALD facilitates the discovery of previously unknown regulatory relationships, which we have subsequently confirmed through ChIP-seq data analysis. Furthermore, by utilizing SCALD, we infer the key driver genes that facilitate the transformation from colon inflammation to cancer by examining the dynamic changes within regulatory networks during the process.