Constructing a holistic map of cell fate decision by hyper solution landscape

The Waddington landscape metaphor has inspired extensive quantitative studies of cell fate decisions using dynamical systems. While these approaches provide valuable insights, the intrinsic nonlinear complexity and the parameter dependence limits systematic analysis of fate transitions. Here, we introduce the Hyper Solution Landscape (HSL), a parameter-independent methodology showing a comprehensive structure of all possible landscape configurations for gene regulatory networks. Building on the concept of solution landscape that primarily captures the complete stationary points in static landscape, HSL connects different solution landscapes to reflect dynamic changes of the landscapes associated with bifurcations. Applied to the Cross-Inhibition with Self-activation motif, HSL analysis identifies key hyperparameters driving distinct directional changes in cell fate propensity. Importantly, different routes through the HSL between the same initial and final states can produce markedly different fate distributions. This enables rational design of transition strategies. We validate HSL’s utility in the seesaw model of cellular reprogramming, establishing a powerful framework for understanding and engineering cell fate decisions.