The embryonic stem cell (ESC) has the capacity to self-renew and maintain pluripotent, while continuously offering a source of various differentiated cell types. The fate decision process of remaining in the ground state or transiting to a differentiated state can be read out by the regulatory network of key transcription factors (TFs). However, its underlying mechanism remains to be fully elucidated. In this paper, we tackle this problem by proposing a novel cellular differentiation model for mouse embryonic stem cell (MESC) dynamics regulation: MESC-DRM. We employ nonlinear least-squares algorithm to infer model parameters by using benchmark datasets, construct a potential function by exploiting multivariate Gaussian distributions, and project the potential landscape into a 3D space to validate and replicate the stable cell states observed in experiments. The traditional cell landscape modeling techniques rely on the potential function visualization to decide the stable states of cells. But the visualization will be almost impossible when the dimensionality of the potential function is greater than 3. We handle the challenge by innovatively employing a Lyapunov method to resolve it through a more straightforward analytical approach. It also provides a more rigorous and robust way for accurate cell fate decision. The study not only validates the previous experimental results but also provides an insightful guide for cell fate decision besides inspiring future study on this topic.

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