Change in the phenotype of a cell is considered as a transition of a cell from one cellular state to another. Cellular state transition can be driven by an external cue or by the noise in molecular processes. Over the years, generalized physical principles, and associated mathematical models have been developed to understand phenotypic state transition. Starting with Waddington’s epigenetic landscape, phenotypic state transition is seen as a movement of cells on a potential landscape. Though the landscape model is close to the thermodynamic principles of state change, it is difficult to envisage it from experimental observations. Therefore, phenotypic state transition is often considered as a discrete state jump process. This approach is particularly useful to estimate the paths of state transition from experimental observations. In this review, we discuss both of these approaches and the associated mathematical formulations. Furthermore, we explore the opportunities to connect these two approaches and the limitations of our current understanding and mathematical methods.

中文翻译：

---

表型状态转换的数学：路径和潜力

细胞表型的变化被认为是细胞从一种细胞状态到另一种细胞状态的转变。细胞状态转变可以由外部线索或分子过程中的噪声驱动。多年来，已经开发了广义物理原理和相关数学模型来理解表型状态转变。从 Waddington 的表观遗传景观开始，表型状态转变被视为细胞在潜在景观上的运动。虽然景观模型接近状态变化的热力学原理，但很难从实验观察中设想它。因此，表型状态转换通常被认为是一个离散的状态跳跃过程。这种方法对于从实验观察估计状态转换的路径特别有用。在这次审查中，我们讨论了这两种方法和相关的数学公式。此外，我们探索了将这两种方法联系起来的机会以及我们当前理解和数学方法的局限性。