Phase-space distance between stationary states mudulates phenotypic plasticity in breast cancer

AO_SCPLOWBSTRACTC_SCPLOWTransitions between stable states are a defining feature of nonlinear dynamical systems, yet the factors controlling their probabilities and timescales remain poorly understood in non-conservative settings. In many theoretical frameworks, such control is commonly interpreted in terms of potential depth, a concept that becomes ambiguous outside equilibrium. By analyzing a gene regulatory network associated with breast cancer subtypes, we uncover a geometric framework in which the phase-space distance between stationary states, together with the bifurcation structure organizing multistability, provides a robust and well-defined determinant of transition probabilities, times, and variability. Our results show that the coexistence of stable states is only a necessary condition for transitions, while their accessibility is constrained by geometric features of the underlying state space. Within this framework, we find that the HER2+ regime exhibits dynamical robustness to intrinsic parameter variations, whereas the TNBC regime displays strong sensitivity and amplified variability. These differences emerge naturally from the geometric organization of the bistable region and offer a dynamical explanation for the pronounced heterogeneity observed in TNBC. Together, our results establish a general geometric perspective on transitions in non-conservative regulatory networks, with implications for understanding phenotypic plasticity in complex biological systems.