BACKGROUND The transitions between epithelial (E) and mesenchymal (M) cell phenotypes are essential in many biological processes like tissue development and cancer metastasis. Previous studies, both modeling and experimental, suggested that in addition to E and M states, the network responsible for these phenotypes exhibits intermediate phenotypes between E and M states. The number and importance of such states is subject to intense discussion in the epithelial-mesenchymal transition (EMT) community. RESULTS Previous modeling efforts used traditional bifurcation analysis to explore the number of the steady states that correspond to E, M and intermediate states by varying one or two parameters at a time. Since the system has dozens of parameters that are largely unknown, it remains a challenging problem to fully describe the potential set of states and their relationship across all parameters. We use the computational tool DSGRN (Dynamic Signatures Generated by Regulatory Networks) to explore the intermediate states of an EMT model network by computing summaries of the dynamics across all of parameter space. We find that the only attractors in the system are equilibria, that E and M states dominate across parameter space, but that bistability and multistability are common. Even at extreme levels of some of the known inducers of the transition, there is a certain proportion of the parameter space at which an E or an M state co-exists with other stable steady states. CONCLUSIONS Our results suggest that the multistability is broadly present in the EMT network across parameters and thus response of cells to signals may strongly depend on the particular cell line and genetic background.

中文翻译：

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上皮间质转化网络的多重稳定性。


背景上皮（E）和间充质（M）细胞表型之间的转变在组织发育和癌症转移等许多生物过程中至关重要。先前的建模和实验研究表明，除了 E 和 M 状态之外，负责这些表型的网络还表现出 E 和 M 状态之间的中间表型。这种状态的数量和重要性在上皮间质转化（EMT）界引起了激烈的讨论。结果以前的建模工作使用传统的分岔分析，通过一次改变一个或两个参数来探索与 E、M 和中间状态相对应的稳态数量。由于系统有数十个很大程度上未知的参数，因此充分描述潜在的状态集及其在所有参数之间的关系仍然是一个具有挑战性的问题。我们使用计算工具 DSGRN（监管网络生成的动态签名）通过计算所有参数空间的动态摘要来探索 EMT 模型网络的中间状态。我们发现系统中唯一的吸引子是平衡，E 和 M 状态在参数空间中占主导地位，但双稳态和多稳态是常见的。即使在一些已知的转变诱发因素的极端水平下，也存在一定比例的参数空间，在该比例中 E 或 M 状态与其他稳定的稳态共存。结论我们的结果表明，EMT 网络中的参数广泛存在多稳定性，因此细胞对信号的反应可能强烈依赖于特定的细胞系和遗传背景。