Epithelial-mesenchymal transition (EMT), a basic developmental process that might promote cancer metastasis, has been studied from various perspectives. Recently, the early warning theory has been used to anticipate critical transitions in EMT from mathematical modeling. However, the underlying mechanisms of EMT involving complex molecular networks remain to be clarified. Especially, how to quantify the global stability and stochastic transition dynamics of EMT and what the underlying mechanism for early warning theory in EMT is remain to be fully clarified. To address these issues, we constructed a comprehensive gene regulatory network model for EMT and quantified the corresponding potential landscape. The landscape for EMT displays multiple stable attractors, which correspond to E, M, and some other intermediate states. Based on the path-integral approach, we identified the most probable transition paths of EMT, which are supported by experimental data. Correspondingly, the results of transition actions demonstrated that intermediate states can accelerate EMT, consistent with recent studies. By integrating the landscape and path with early warning concept, we identified the potential barrier height from the landscape as a global and more accurate measure for early warning signals to predict critical transitions in EMT. The landscape results also provide an intuitive and quantitative explanation for the early warning theory. Overall, the landscape and path results advance our mechanistic understanding of dynamical transitions and roles of intermediate states in EMT, and the potential barrier height provides a new, to our knowledge, measure for critical transitions and quantitative explanations for the early warning theory.

上皮间质转化（EMT）是一种可能促进癌症转移的基本发育过程，人们从不同的角度进行了研究。最近，预警理论已被用于通过数学建模来预测 EMT 的关键转变。然而，涉及复杂分子网络的 EMT 的潜在机制仍有待阐明。特别是如何量化EMT的全局稳定性和随机转变动力学以及EMT预警理论的底层机制还有待充分阐明。为了解决这些问题，我们构建了一个全面的 EMT 基因调控网络模型，并量化了相应的潜在景观。 EMT 的景观显示了多个稳定吸引子，对应于 E、M 和其他一些中间状态。基于路径积分方法，我们确定了最可能的 EMT 转换路径，并得到了实验数据的支持。相应地，过渡行动的结果表明，中间状态可以加速 EMT，这与最近的研究一致。通过将景观和路径与预警概念相结合，我们将景观中的潜在屏障高度确定为预警信号的全局且更准确的衡量标准，以预测 EMT 中的关键转变。景观结果也为预警理论提供了直观、定量的解释。总体而言，景观和路径结果促进了我们对 EMT 中动态转变和中间态作用的机械理解，而势垒高度为我们所知提供了一种新的关键转变测量方法和早期预警理论的定量解释。